- FindStat

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Identifier

Mp00131: Permutations —descent bottoms⟶ 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]=>10
[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]=>010
[1,4,2,3]=>010
[1,4,3,2]=>011
[2,1,3,4]=>100
[2,1,4,3]=>101
[2,3,1,4]=>100
[2,3,4,1]=>100
[2,4,1,3]=>100
[2,4,3,1]=>101
[3,1,2,4]=>100
[3,1,4,2]=>110
[3,2,1,4]=>110
[3,2,4,1]=>110
[3,4,1,2]=>100
[3,4,2,1]=>110
[4,1,2,3]=>100
[4,1,3,2]=>110
[4,2,1,3]=>110
[4,2,3,1]=>110
[4,3,1,2]=>101
[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]=>0010
[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]=>0100
[1,3,4,5,2]=>0100
[1,3,5,2,4]=>0100
[1,3,5,4,2]=>0101
[1,4,2,3,5]=>0100
[1,4,2,5,3]=>0110
[1,4,3,2,5]=>0110
[1,4,3,5,2]=>0110
[1,4,5,2,3]=>0100
[1,4,5,3,2]=>0110
[1,5,2,3,4]=>0100
[1,5,2,4,3]=>0110
[1,5,3,2,4]=>0110
[1,5,3,4,2]=>0110
[1,5,4,2,3]=>0101
[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]=>1010
[2,1,5,3,4]=>1010
[2,1,5,4,3]=>1011
[2,3,1,4,5]=>1000
[2,3,1,5,4]=>1001
[2,3,4,1,5]=>1000
[2,3,4,5,1]=>1000
[2,3,5,1,4]=>1000
[2,3,5,4,1]=>1001
[2,4,1,3,5]=>1000
[2,4,1,5,3]=>1010
[2,4,3,1,5]=>1010
[2,4,3,5,1]=>1010
[2,4,5,1,3]=>1000
[2,4,5,3,1]=>1010
[2,5,1,3,4]=>1000
[2,5,1,4,3]=>1010
[2,5,3,1,4]=>1010
[2,5,3,4,1]=>1010
[2,5,4,1,3]=>1001
[2,5,4,3,1]=>1011
[3,1,2,4,5]=>1000
[3,1,2,5,4]=>1001
[3,1,4,2,5]=>1100
[3,1,4,5,2]=>1100
[3,1,5,2,4]=>1100
[3,1,5,4,2]=>1101
[3,2,1,4,5]=>1100
[3,2,1,5,4]=>1101
[3,2,4,1,5]=>1100
[3,2,4,5,1]=>1100
[3,2,5,1,4]=>1100
[3,2,5,4,1]=>1101
[3,4,1,2,5]=>1000
[3,4,1,5,2]=>1100
[3,4,2,1,5]=>1100
[3,4,2,5,1]=>1100
[3,4,5,1,2]=>1000
[3,4,5,2,1]=>1100
[3,5,1,2,4]=>1000
[3,5,1,4,2]=>1100
[3,5,2,1,4]=>1100
[3,5,2,4,1]=>1100
[3,5,4,1,2]=>1001
[3,5,4,2,1]=>1101
[4,1,2,3,5]=>1000
[4,1,2,5,3]=>1010
[4,1,3,2,5]=>1100
[4,1,3,5,2]=>1100
[4,1,5,2,3]=>1100
[4,1,5,3,2]=>1110
[4,2,1,3,5]=>1100
[4,2,1,5,3]=>1110
[4,2,3,1,5]=>1100
[4,2,3,5,1]=>1100
[4,2,5,1,3]=>1100
[4,2,5,3,1]=>1110
[4,3,1,2,5]=>1010
[4,3,1,5,2]=>1110
[4,3,2,1,5]=>1110
[4,3,2,5,1]=>1110
[4,3,5,1,2]=>1010
[4,3,5,2,1]=>1110
[4,5,1,2,3]=>1000
[4,5,1,3,2]=>1100
[4,5,2,1,3]=>1100
[4,5,2,3,1]=>1100
[4,5,3,1,2]=>1010
[4,5,3,2,1]=>1110
[5,1,2,3,4]=>1000
[5,1,2,4,3]=>1010
[5,1,3,2,4]=>1100
[5,1,3,4,2]=>1100
[5,1,4,2,3]=>1100
[5,1,4,3,2]=>1110
[5,2,1,3,4]=>1100
[5,2,1,4,3]=>1110
[5,2,3,1,4]=>1100
[5,2,3,4,1]=>1100
[5,2,4,1,3]=>1100
[5,2,4,3,1]=>1110
[5,3,1,2,4]=>1010
[5,3,1,4,2]=>1110
[5,3,2,1,4]=>1110
[5,3,2,4,1]=>1110
[5,3,4,1,2]=>1010
[5,3,4,2,1]=>1110
[5,4,1,2,3]=>1001
[5,4,1,3,2]=>1101
[5,4,2,1,3]=>1101
[5,4,2,3,1]=>1101
[5,4,3,1,2]=>1011
[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]=>00010
[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]=>00100
[1,2,4,5,6,3]=>00100
[1,2,4,6,3,5]=>00100
[1,2,4,6,5,3]=>00101
[1,2,5,3,4,6]=>00100
[1,2,5,3,6,4]=>00110
[1,2,5,4,3,6]=>00110
[1,2,5,4,6,3]=>00110
[1,2,5,6,3,4]=>00100
[1,2,5,6,4,3]=>00110
[1,2,6,3,4,5]=>00100
[1,2,6,3,5,4]=>00110
[1,2,6,4,3,5]=>00110
[1,2,6,4,5,3]=>00110
[1,2,6,5,3,4]=>00101
[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]=>01010
[1,3,2,6,4,5]=>01010
[1,3,2,6,5,4]=>01011
[1,3,4,2,5,6]=>01000
[1,3,4,2,6,5]=>01001
[1,3,4,5,2,6]=>01000
[1,3,4,5,6,2]=>01000
[1,3,4,6,2,5]=>01000
[1,3,4,6,5,2]=>01001
[1,3,5,2,4,6]=>01000
[1,3,5,2,6,4]=>01010
[1,3,5,4,2,6]=>01010
[1,3,5,4,6,2]=>01010
[1,3,5,6,2,4]=>01000
[1,3,5,6,4,2]=>01010
[1,3,6,2,4,5]=>01000
[1,3,6,2,5,4]=>01010
[1,3,6,4,2,5]=>01010
[1,3,6,4,5,2]=>01010
[1,3,6,5,2,4]=>01001
[1,3,6,5,4,2]=>01011
[1,4,2,3,5,6]=>01000
[1,4,2,3,6,5]=>01001
[1,4,2,5,3,6]=>01100
[1,4,2,5,6,3]=>01100
[1,4,2,6,3,5]=>01100
[1,4,2,6,5,3]=>01101
[1,4,3,2,5,6]=>01100
[1,4,3,2,6,5]=>01101
[1,4,3,5,2,6]=>01100
[1,4,3,5,6,2]=>01100
[1,4,3,6,2,5]=>01100
[1,4,3,6,5,2]=>01101
[1,4,5,2,3,6]=>01000
[1,4,5,2,6,3]=>01100
[1,4,5,3,2,6]=>01100
[1,4,5,3,6,2]=>01100
[1,4,5,6,2,3]=>01000
[1,4,5,6,3,2]=>01100
[1,4,6,2,3,5]=>01000
[1,4,6,2,5,3]=>01100
[1,4,6,3,2,5]=>01100
[1,4,6,3,5,2]=>01100
[1,4,6,5,2,3]=>01001
[1,4,6,5,3,2]=>01101
[1,5,2,3,4,6]=>01000
[1,5,2,3,6,4]=>01010
[1,5,2,4,3,6]=>01100
[1,5,2,4,6,3]=>01100
[1,5,2,6,3,4]=>01100
[1,5,2,6,4,3]=>01110
[1,5,3,2,4,6]=>01100
[1,5,3,2,6,4]=>01110
[1,5,3,4,2,6]=>01100
[1,5,3,4,6,2]=>01100
[1,5,3,6,2,4]=>01100
[1,5,3,6,4,2]=>01110
[1,5,4,2,3,6]=>01010
[1,5,4,2,6,3]=>01110
[1,5,4,3,2,6]=>01110
[1,5,4,3,6,2]=>01110
[1,5,4,6,2,3]=>01010
[1,5,4,6,3,2]=>01110
[1,5,6,2,3,4]=>01000
[1,5,6,2,4,3]=>01100
[1,5,6,3,2,4]=>01100
[1,5,6,3,4,2]=>01100
[1,5,6,4,2,3]=>01010
[1,5,6,4,3,2]=>01110
[1,6,2,3,4,5]=>01000
[1,6,2,3,5,4]=>01010
[1,6,2,4,3,5]=>01100
[1,6,2,4,5,3]=>01100
[1,6,2,5,3,4]=>01100
[1,6,2,5,4,3]=>01110
[1,6,3,2,4,5]=>01100
[1,6,3,2,5,4]=>01110
[1,6,3,4,2,5]=>01100
[1,6,3,4,5,2]=>01100
[1,6,3,5,2,4]=>01100
[1,6,3,5,4,2]=>01110
[1,6,4,2,3,5]=>01010
[1,6,4,2,5,3]=>01110
[1,6,4,3,2,5]=>01110
[1,6,4,3,5,2]=>01110
[1,6,4,5,2,3]=>01010
[1,6,4,5,3,2]=>01110
[1,6,5,2,3,4]=>01001
[1,6,5,2,4,3]=>01101
[1,6,5,3,2,4]=>01101
[1,6,5,3,4,2]=>01101
[1,6,5,4,2,3]=>01011
[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]=>10010
[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]=>10100
[2,1,4,5,6,3]=>10100
[2,1,4,6,3,5]=>10100
[2,1,4,6,5,3]=>10101
[2,1,5,3,4,6]=>10100
[2,1,5,3,6,4]=>10110
[2,1,5,4,3,6]=>10110
[2,1,5,4,6,3]=>10110
[2,1,5,6,3,4]=>10100
[2,1,5,6,4,3]=>10110
[2,1,6,3,4,5]=>10100
[2,1,6,3,5,4]=>10110
[2,1,6,4,3,5]=>10110
[2,1,6,4,5,3]=>10110
[2,1,6,5,3,4]=>10101
[2,1,6,5,4,3]=>10111
[2,3,1,4,5,6]=>10000
[2,3,1,4,6,5]=>10001
[2,3,1,5,4,6]=>10010
[2,3,1,5,6,4]=>10010
[2,3,1,6,4,5]=>10010
[2,3,1,6,5,4]=>10011
[2,3,4,1,5,6]=>10000
[2,3,4,1,6,5]=>10001
[2,3,4,5,1,6]=>10000
[2,3,4,5,6,1]=>10000
[2,3,4,6,1,5]=>10000
[2,3,4,6,5,1]=>10001
[2,3,5,1,4,6]=>10000
[2,3,5,1,6,4]=>10010
[2,3,5,4,1,6]=>10010
[2,3,5,4,6,1]=>10010
[2,3,5,6,1,4]=>10000
[2,3,5,6,4,1]=>10010
[2,3,6,1,4,5]=>10000
[2,3,6,1,5,4]=>10010
[2,3,6,4,1,5]=>10010
[2,3,6,4,5,1]=>10010
[2,3,6,5,1,4]=>10001
[2,3,6,5,4,1]=>10011
[2,4,1,3,5,6]=>10000
[2,4,1,3,6,5]=>10001
[2,4,1,5,3,6]=>10100
[2,4,1,5,6,3]=>10100
[2,4,1,6,3,5]=>10100
[2,4,1,6,5,3]=>10101
[2,4,3,1,5,6]=>10100
[2,4,3,1,6,5]=>10101
[2,4,3,5,1,6]=>10100
[2,4,3,5,6,1]=>10100
[2,4,3,6,1,5]=>10100
[2,4,3,6,5,1]=>10101
[2,4,5,1,3,6]=>10000
[2,4,5,1,6,3]=>10100
[2,4,5,3,1,6]=>10100
[2,4,5,3,6,1]=>10100
[2,4,5,6,1,3]=>10000
[2,4,5,6,3,1]=>10100
[2,4,6,1,3,5]=>10000
[2,4,6,1,5,3]=>10100
[2,4,6,3,1,5]=>10100
[2,4,6,3,5,1]=>10100
[2,4,6,5,1,3]=>10001
[2,4,6,5,3,1]=>10101
[2,5,1,3,4,6]=>10000
[2,5,1,3,6,4]=>10010
[2,5,1,4,3,6]=>10100
[2,5,1,4,6,3]=>10100
[2,5,1,6,3,4]=>10100
[2,5,1,6,4,3]=>10110
[2,5,3,1,4,6]=>10100
[2,5,3,1,6,4]=>10110
[2,5,3,4,1,6]=>10100
[2,5,3,4,6,1]=>10100
[2,5,3,6,1,4]=>10100
[2,5,3,6,4,1]=>10110
[2,5,4,1,3,6]=>10010
[2,5,4,1,6,3]=>10110
[2,5,4,3,1,6]=>10110
[2,5,4,3,6,1]=>10110
[2,5,4,6,1,3]=>10010
[2,5,4,6,3,1]=>10110
[2,5,6,1,3,4]=>10000
[2,5,6,1,4,3]=>10100
[2,5,6,3,1,4]=>10100
[2,5,6,3,4,1]=>10100
[2,5,6,4,1,3]=>10010
[2,5,6,4,3,1]=>10110
[2,6,1,3,4,5]=>10000
[2,6,1,3,5,4]=>10010
[2,6,1,4,3,5]=>10100
[2,6,1,4,5,3]=>10100
[2,6,1,5,3,4]=>10100
[2,6,1,5,4,3]=>10110
[2,6,3,1,4,5]=>10100
[2,6,3,1,5,4]=>10110
[2,6,3,4,1,5]=>10100
[2,6,3,4,5,1]=>10100
[2,6,3,5,1,4]=>10100
[2,6,3,5,4,1]=>10110
[2,6,4,1,3,5]=>10010
[2,6,4,1,5,3]=>10110
[2,6,4,3,1,5]=>10110
[2,6,4,3,5,1]=>10110
[2,6,4,5,1,3]=>10010
[2,6,4,5,3,1]=>10110
[2,6,5,1,3,4]=>10001
[2,6,5,1,4,3]=>10101
[2,6,5,3,1,4]=>10101
[2,6,5,3,4,1]=>10101
[2,6,5,4,1,3]=>10011
[2,6,5,4,3,1]=>10111
[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]=>10010
[3,1,2,6,4,5]=>10010
[3,1,2,6,5,4]=>10011
[3,1,4,2,5,6]=>11000
[3,1,4,2,6,5]=>11001
[3,1,4,5,2,6]=>11000
[3,1,4,5,6,2]=>11000
[3,1,4,6,2,5]=>11000
[3,1,4,6,5,2]=>11001
[3,1,5,2,4,6]=>11000
[3,1,5,2,6,4]=>11010
[3,1,5,4,2,6]=>11010
[3,1,5,4,6,2]=>11010
[3,1,5,6,2,4]=>11000
[3,1,5,6,4,2]=>11010
[3,1,6,2,4,5]=>11000
[3,1,6,2,5,4]=>11010
[3,1,6,4,2,5]=>11010
[3,1,6,4,5,2]=>11010
[3,1,6,5,2,4]=>11001
[3,1,6,5,4,2]=>11011
[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]=>11010
[3,2,1,6,4,5]=>11010
[3,2,1,6,5,4]=>11011
[3,2,4,1,5,6]=>11000
[3,2,4,1,6,5]=>11001
[3,2,4,5,1,6]=>11000
[3,2,4,5,6,1]=>11000
[3,2,4,6,1,5]=>11000
[3,2,4,6,5,1]=>11001
[3,2,5,1,4,6]=>11000
[3,2,5,1,6,4]=>11010
[3,2,5,4,1,6]=>11010
[3,2,5,4,6,1]=>11010
[3,2,5,6,1,4]=>11000
[3,2,5,6,4,1]=>11010
[3,2,6,1,4,5]=>11000
[3,2,6,1,5,4]=>11010
[3,2,6,4,1,5]=>11010
[3,2,6,4,5,1]=>11010
[3,2,6,5,1,4]=>11001
[3,2,6,5,4,1]=>11011
[3,4,1,2,5,6]=>10000
[3,4,1,2,6,5]=>10001
[3,4,1,5,2,6]=>11000
[3,4,1,5,6,2]=>11000
[3,4,1,6,2,5]=>11000
[3,4,1,6,5,2]=>11001
[3,4,2,1,5,6]=>11000
[3,4,2,1,6,5]=>11001
[3,4,2,5,1,6]=>11000
[3,4,2,5,6,1]=>11000
[3,4,2,6,1,5]=>11000
[3,4,2,6,5,1]=>11001
[3,4,5,1,2,6]=>10000
[3,4,5,1,6,2]=>11000
[3,4,5,2,1,6]=>11000
[3,4,5,2,6,1]=>11000
[3,4,5,6,1,2]=>10000
[3,4,5,6,2,1]=>11000
[3,4,6,1,2,5]=>10000
[3,4,6,1,5,2]=>11000
[3,4,6,2,1,5]=>11000
[3,4,6,2,5,1]=>11000
[3,4,6,5,1,2]=>10001
[3,4,6,5,2,1]=>11001
[3,5,1,2,4,6]=>10000
[3,5,1,2,6,4]=>10010
[3,5,1,4,2,6]=>11000
[3,5,1,4,6,2]=>11000
[3,5,1,6,2,4]=>11000
[3,5,1,6,4,2]=>11010
[3,5,2,1,4,6]=>11000
[3,5,2,1,6,4]=>11010
[3,5,2,4,1,6]=>11000
[3,5,2,4,6,1]=>11000
[3,5,2,6,1,4]=>11000
[3,5,2,6,4,1]=>11010
[3,5,4,1,2,6]=>10010
[3,5,4,1,6,2]=>11010
[3,5,4,2,1,6]=>11010
[3,5,4,2,6,1]=>11010
[3,5,4,6,1,2]=>10010
[3,5,4,6,2,1]=>11010
[3,5,6,1,2,4]=>10000
[3,5,6,1,4,2]=>11000
[3,5,6,2,1,4]=>11000
[3,5,6,2,4,1]=>11000
[3,5,6,4,1,2]=>10010
[3,5,6,4,2,1]=>11010
[3,6,1,2,4,5]=>10000
[3,6,1,2,5,4]=>10010
[3,6,1,4,2,5]=>11000
[3,6,1,4,5,2]=>11000
[3,6,1,5,2,4]=>11000
[3,6,1,5,4,2]=>11010
[3,6,2,1,4,5]=>11000
[3,6,2,1,5,4]=>11010
[3,6,2,4,1,5]=>11000
[3,6,2,4,5,1]=>11000
[3,6,2,5,1,4]=>11000
[3,6,2,5,4,1]=>11010
[3,6,4,1,2,5]=>10010
[3,6,4,1,5,2]=>11010
[3,6,4,2,1,5]=>11010
[3,6,4,2,5,1]=>11010
[3,6,4,5,1,2]=>10010
[3,6,4,5,2,1]=>11010
[3,6,5,1,2,4]=>10001
[3,6,5,1,4,2]=>11001
[3,6,5,2,1,4]=>11001
[3,6,5,2,4,1]=>11001
[3,6,5,4,1,2]=>10011
[3,6,5,4,2,1]=>11011
[4,1,2,3,5,6]=>10000
[4,1,2,3,6,5]=>10001
[4,1,2,5,3,6]=>10100
[4,1,2,5,6,3]=>10100
[4,1,2,6,3,5]=>10100
[4,1,2,6,5,3]=>10101
[4,1,3,2,5,6]=>11000
[4,1,3,2,6,5]=>11001
[4,1,3,5,2,6]=>11000
[4,1,3,5,6,2]=>11000
[4,1,3,6,2,5]=>11000
[4,1,3,6,5,2]=>11001
[4,1,5,2,3,6]=>11000
[4,1,5,2,6,3]=>11100
[4,1,5,3,2,6]=>11100
[4,1,5,3,6,2]=>11100
[4,1,5,6,2,3]=>11000
[4,1,5,6,3,2]=>11100
[4,1,6,2,3,5]=>11000
[4,1,6,2,5,3]=>11100
[4,1,6,3,2,5]=>11100
[4,1,6,3,5,2]=>11100
[4,1,6,5,2,3]=>11001
[4,1,6,5,3,2]=>11101
[4,2,1,3,5,6]=>11000
[4,2,1,3,6,5]=>11001
[4,2,1,5,3,6]=>11100
[4,2,1,5,6,3]=>11100
[4,2,1,6,3,5]=>11100
[4,2,1,6,5,3]=>11101
[4,2,3,1,5,6]=>11000
[4,2,3,1,6,5]=>11001
[4,2,3,5,1,6]=>11000
[4,2,3,5,6,1]=>11000
[4,2,3,6,1,5]=>11000
[4,2,3,6,5,1]=>11001
[4,2,5,1,3,6]=>11000
[4,2,5,1,6,3]=>11100
[4,2,5,3,1,6]=>11100
[4,2,5,3,6,1]=>11100
[4,2,5,6,1,3]=>11000
[4,2,5,6,3,1]=>11100
[4,2,6,1,3,5]=>11000
[4,2,6,1,5,3]=>11100
[4,2,6,3,1,5]=>11100
[4,2,6,3,5,1]=>11100
[4,2,6,5,1,3]=>11001
[4,2,6,5,3,1]=>11101
[4,3,1,2,5,6]=>10100
[4,3,1,2,6,5]=>10101
[4,3,1,5,2,6]=>11100
[4,3,1,5,6,2]=>11100
[4,3,1,6,2,5]=>11100
[4,3,1,6,5,2]=>11101
[4,3,2,1,5,6]=>11100
[4,3,2,1,6,5]=>11101
[4,3,2,5,1,6]=>11100
[4,3,2,5,6,1]=>11100
[4,3,2,6,1,5]=>11100
[4,3,2,6,5,1]=>11101
[4,3,5,1,2,6]=>10100
[4,3,5,1,6,2]=>11100
[4,3,5,2,1,6]=>11100
[4,3,5,2,6,1]=>11100
[4,3,5,6,1,2]=>10100
[4,3,5,6,2,1]=>11100
[4,3,6,1,2,5]=>10100
[4,3,6,1,5,2]=>11100
[4,3,6,2,1,5]=>11100
[4,3,6,2,5,1]=>11100
[4,3,6,5,1,2]=>10101
[4,3,6,5,2,1]=>11101
[4,5,1,2,3,6]=>10000
[4,5,1,2,6,3]=>10100
[4,5,1,3,2,6]=>11000
[4,5,1,3,6,2]=>11000
[4,5,1,6,2,3]=>11000
[4,5,1,6,3,2]=>11100
[4,5,2,1,3,6]=>11000
[4,5,2,1,6,3]=>11100
[4,5,2,3,1,6]=>11000
[4,5,2,3,6,1]=>11000
[4,5,2,6,1,3]=>11000
[4,5,2,6,3,1]=>11100
[4,5,3,1,2,6]=>10100
[4,5,3,1,6,2]=>11100
[4,5,3,2,1,6]=>11100
[4,5,3,2,6,1]=>11100
[4,5,3,6,1,2]=>10100
[4,5,3,6,2,1]=>11100
[4,5,6,1,2,3]=>10000
[4,5,6,1,3,2]=>11000
[4,5,6,2,1,3]=>11000
[4,5,6,2,3,1]=>11000
[4,5,6,3,1,2]=>10100
[4,5,6,3,2,1]=>11100
[4,6,1,2,3,5]=>10000
[4,6,1,2,5,3]=>10100
[4,6,1,3,2,5]=>11000
[4,6,1,3,5,2]=>11000
[4,6,1,5,2,3]=>11000
[4,6,1,5,3,2]=>11100
[4,6,2,1,3,5]=>11000
[4,6,2,1,5,3]=>11100
[4,6,2,3,1,5]=>11000
[4,6,2,3,5,1]=>11000
[4,6,2,5,1,3]=>11000
[4,6,2,5,3,1]=>11100
[4,6,3,1,2,5]=>10100
[4,6,3,1,5,2]=>11100
[4,6,3,2,1,5]=>11100
[4,6,3,2,5,1]=>11100
[4,6,3,5,1,2]=>10100
[4,6,3,5,2,1]=>11100
[4,6,5,1,2,3]=>10001
[4,6,5,1,3,2]=>11001
[4,6,5,2,1,3]=>11001
[4,6,5,2,3,1]=>11001
[4,6,5,3,1,2]=>10101
[4,6,5,3,2,1]=>11101
[5,1,2,3,4,6]=>10000
[5,1,2,3,6,4]=>10010
[5,1,2,4,3,6]=>10100
[5,1,2,4,6,3]=>10100
[5,1,2,6,3,4]=>10100
[5,1,2,6,4,3]=>10110
[5,1,3,2,4,6]=>11000
[5,1,3,2,6,4]=>11010
[5,1,3,4,2,6]=>11000
[5,1,3,4,6,2]=>11000
[5,1,3,6,2,4]=>11000
[5,1,3,6,4,2]=>11010
[5,1,4,2,3,6]=>11000
[5,1,4,2,6,3]=>11100
[5,1,4,3,2,6]=>11100
[5,1,4,3,6,2]=>11100
[5,1,4,6,2,3]=>11000
[5,1,4,6,3,2]=>11100
[5,1,6,2,3,4]=>11000
[5,1,6,2,4,3]=>11100
[5,1,6,3,2,4]=>11100
[5,1,6,3,4,2]=>11100
[5,1,6,4,2,3]=>11010
[5,1,6,4,3,2]=>11110
[5,2,1,3,4,6]=>11000
[5,2,1,3,6,4]=>11010
[5,2,1,4,3,6]=>11100
[5,2,1,4,6,3]=>11100
[5,2,1,6,3,4]=>11100
[5,2,1,6,4,3]=>11110
[5,2,3,1,4,6]=>11000
[5,2,3,1,6,4]=>11010
[5,2,3,4,1,6]=>11000
[5,2,3,4,6,1]=>11000
[5,2,3,6,1,4]=>11000
[5,2,3,6,4,1]=>11010
[5,2,4,1,3,6]=>11000
[5,2,4,1,6,3]=>11100
[5,2,4,3,1,6]=>11100
[5,2,4,3,6,1]=>11100
[5,2,4,6,1,3]=>11000
[5,2,4,6,3,1]=>11100
[5,2,6,1,3,4]=>11000
[5,2,6,1,4,3]=>11100
[5,2,6,3,1,4]=>11100
[5,2,6,3,4,1]=>11100
[5,2,6,4,1,3]=>11010
[5,2,6,4,3,1]=>11110
[5,3,1,2,4,6]=>10100
[5,3,1,2,6,4]=>10110
[5,3,1,4,2,6]=>11100
[5,3,1,4,6,2]=>11100
[5,3,1,6,2,4]=>11100
[5,3,1,6,4,2]=>11110
[5,3,2,1,4,6]=>11100
[5,3,2,1,6,4]=>11110
[5,3,2,4,1,6]=>11100
[5,3,2,4,6,1]=>11100
[5,3,2,6,1,4]=>11100
[5,3,2,6,4,1]=>11110
[5,3,4,1,2,6]=>10100
[5,3,4,1,6,2]=>11100
[5,3,4,2,1,6]=>11100
[5,3,4,2,6,1]=>11100
[5,3,4,6,1,2]=>10100
[5,3,4,6,2,1]=>11100
[5,3,6,1,2,4]=>10100
[5,3,6,1,4,2]=>11100
[5,3,6,2,1,4]=>11100
[5,3,6,2,4,1]=>11100
[5,3,6,4,1,2]=>10110
[5,3,6,4,2,1]=>11110
[5,4,1,2,3,6]=>10010
[5,4,1,2,6,3]=>10110
[5,4,1,3,2,6]=>11010
[5,4,1,3,6,2]=>11010
[5,4,1,6,2,3]=>11010
[5,4,1,6,3,2]=>11110
[5,4,2,1,3,6]=>11010
[5,4,2,1,6,3]=>11110
[5,4,2,3,1,6]=>11010
[5,4,2,3,6,1]=>11010
[5,4,2,6,1,3]=>11010
[5,4,2,6,3,1]=>11110
[5,4,3,1,2,6]=>10110
[5,4,3,1,6,2]=>11110
[5,4,3,2,1,6]=>11110
[5,4,3,2,6,1]=>11110
[5,4,3,6,1,2]=>10110
[5,4,3,6,2,1]=>11110
[5,4,6,1,2,3]=>10010
[5,4,6,1,3,2]=>11010
[5,4,6,2,1,3]=>11010
[5,4,6,2,3,1]=>11010
[5,4,6,3,1,2]=>10110
[5,4,6,3,2,1]=>11110
[5,6,1,2,3,4]=>10000
[5,6,1,2,4,3]=>10100
[5,6,1,3,2,4]=>11000
[5,6,1,3,4,2]=>11000
[5,6,1,4,2,3]=>11000
[5,6,1,4,3,2]=>11100
[5,6,2,1,3,4]=>11000
[5,6,2,1,4,3]=>11100
[5,6,2,3,1,4]=>11000
[5,6,2,3,4,1]=>11000
[5,6,2,4,1,3]=>11000
[5,6,2,4,3,1]=>11100
[5,6,3,1,2,4]=>10100
[5,6,3,1,4,2]=>11100
[5,6,3,2,1,4]=>11100
[5,6,3,2,4,1]=>11100
[5,6,3,4,1,2]=>10100
[5,6,3,4,2,1]=>11100
[5,6,4,1,2,3]=>10010
[5,6,4,1,3,2]=>11010
[5,6,4,2,1,3]=>11010
[5,6,4,2,3,1]=>11010
[5,6,4,3,1,2]=>10110
[5,6,4,3,2,1]=>11110
[6,1,2,3,4,5]=>10000
[6,1,2,3,5,4]=>10010
[6,1,2,4,3,5]=>10100
[6,1,2,4,5,3]=>10100
[6,1,2,5,3,4]=>10100
[6,1,2,5,4,3]=>10110
[6,1,3,2,4,5]=>11000
[6,1,3,2,5,4]=>11010
[6,1,3,4,2,5]=>11000
[6,1,3,4,5,2]=>11000
[6,1,3,5,2,4]=>11000
[6,1,3,5,4,2]=>11010
[6,1,4,2,3,5]=>11000
[6,1,4,2,5,3]=>11100
[6,1,4,3,2,5]=>11100
[6,1,4,3,5,2]=>11100
[6,1,4,5,2,3]=>11000
[6,1,4,5,3,2]=>11100
[6,1,5,2,3,4]=>11000
[6,1,5,2,4,3]=>11100
[6,1,5,3,2,4]=>11100
[6,1,5,3,4,2]=>11100
[6,1,5,4,2,3]=>11010
[6,1,5,4,3,2]=>11110
[6,2,1,3,4,5]=>11000
[6,2,1,3,5,4]=>11010
[6,2,1,4,3,5]=>11100
[6,2,1,4,5,3]=>11100
[6,2,1,5,3,4]=>11100
[6,2,1,5,4,3]=>11110
[6,2,3,1,4,5]=>11000
[6,2,3,1,5,4]=>11010
[6,2,3,4,1,5]=>11000
[6,2,3,4,5,1]=>11000
[6,2,3,5,1,4]=>11000
[6,2,3,5,4,1]=>11010
[6,2,4,1,3,5]=>11000
[6,2,4,1,5,3]=>11100
[6,2,4,3,1,5]=>11100
[6,2,4,3,5,1]=>11100
[6,2,4,5,1,3]=>11000
[6,2,4,5,3,1]=>11100
[6,2,5,1,3,4]=>11000
[6,2,5,1,4,3]=>11100
[6,2,5,3,1,4]=>11100
[6,2,5,3,4,1]=>11100
[6,2,5,4,1,3]=>11010
[6,2,5,4,3,1]=>11110
[6,3,1,2,4,5]=>10100
[6,3,1,2,5,4]=>10110
[6,3,1,4,2,5]=>11100
[6,3,1,4,5,2]=>11100
[6,3,1,5,2,4]=>11100
[6,3,1,5,4,2]=>11110
[6,3,2,1,4,5]=>11100
[6,3,2,1,5,4]=>11110
[6,3,2,4,1,5]=>11100
[6,3,2,4,5,1]=>11100
[6,3,2,5,1,4]=>11100
[6,3,2,5,4,1]=>11110
[6,3,4,1,2,5]=>10100
[6,3,4,1,5,2]=>11100
[6,3,4,2,1,5]=>11100
[6,3,4,2,5,1]=>11100
[6,3,4,5,1,2]=>10100
[6,3,4,5,2,1]=>11100
[6,3,5,1,2,4]=>10100
[6,3,5,1,4,2]=>11100
[6,3,5,2,1,4]=>11100
[6,3,5,2,4,1]=>11100
[6,3,5,4,1,2]=>10110
[6,3,5,4,2,1]=>11110
[6,4,1,2,3,5]=>10010
[6,4,1,2,5,3]=>10110
[6,4,1,3,2,5]=>11010
[6,4,1,3,5,2]=>11010
[6,4,1,5,2,3]=>11010
[6,4,1,5,3,2]=>11110
[6,4,2,1,3,5]=>11010
[6,4,2,1,5,3]=>11110
[6,4,2,3,1,5]=>11010
[6,4,2,3,5,1]=>11010
[6,4,2,5,1,3]=>11010
[6,4,2,5,3,1]=>11110
[6,4,3,1,2,5]=>10110
[6,4,3,1,5,2]=>11110
[6,4,3,2,1,5]=>11110
[6,4,3,2,5,1]=>11110
[6,4,3,5,1,2]=>10110
[6,4,3,5,2,1]=>11110
[6,4,5,1,2,3]=>10010
[6,4,5,1,3,2]=>11010
[6,4,5,2,1,3]=>11010
[6,4,5,2,3,1]=>11010
[6,4,5,3,1,2]=>10110
[6,4,5,3,2,1]=>11110
[6,5,1,2,3,4]=>10001
[6,5,1,2,4,3]=>10101
[6,5,1,3,2,4]=>11001
[6,5,1,3,4,2]=>11001
[6,5,1,4,2,3]=>11001
[6,5,1,4,3,2]=>11101
[6,5,2,1,3,4]=>11001
[6,5,2,1,4,3]=>11101
[6,5,2,3,1,4]=>11001
[6,5,2,3,4,1]=>11001
[6,5,2,4,1,3]=>11001
[6,5,2,4,3,1]=>11101
[6,5,3,1,2,4]=>10101
[6,5,3,1,4,2]=>11101
[6,5,3,2,1,4]=>11101
[6,5,3,2,4,1]=>11101
[6,5,3,4,1,2]=>10101
[6,5,3,4,2,1]=>11101
[6,5,4,1,2,3]=>10011
[6,5,4,1,3,2]=>11011
[6,5,4,2,1,3]=>11011
[6,5,4,2,3,1]=>11011
[6,5,4,3,1,2]=>10111
[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]=>000010
[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]=>000100
[1,2,3,5,6,7,4]=>000100
[1,2,3,5,7,4,6]=>000100
[1,2,3,5,7,6,4]=>000101
[1,2,3,6,4,5,7]=>000100
[1,2,3,6,4,7,5]=>000110
[1,2,3,6,5,4,7]=>000110
[1,2,3,6,5,7,4]=>000110
[1,2,3,6,7,4,5]=>000100
[1,2,3,6,7,5,4]=>000110
[1,2,3,7,4,5,6]=>000100
[1,2,3,7,4,6,5]=>000110
[1,2,3,7,5,4,6]=>000110
[1,2,3,7,5,6,4]=>000110
[1,2,3,7,6,4,5]=>000101
[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]=>001010
[1,2,4,3,7,5,6]=>001010
[1,2,4,3,7,6,5]=>001011
[1,2,4,5,3,6,7]=>001000
[1,2,4,5,3,7,6]=>001001
[1,2,4,5,6,3,7]=>001000
[1,2,4,5,6,7,3]=>001000
[1,2,4,5,7,3,6]=>001000
[1,2,4,5,7,6,3]=>001001
[1,2,4,6,3,5,7]=>001000
[1,2,4,6,3,7,5]=>001010
[1,2,4,6,5,3,7]=>001010
[1,2,4,6,5,7,3]=>001010
[1,2,4,6,7,3,5]=>001000
[1,2,4,6,7,5,3]=>001010
[1,2,4,7,3,5,6]=>001000
[1,2,4,7,3,6,5]=>001010
[1,2,4,7,5,3,6]=>001010
[1,2,4,7,5,6,3]=>001010
[1,2,4,7,6,3,5]=>001001
[1,2,4,7,6,5,3]=>001011
[1,2,5,3,4,6,7]=>001000
[1,2,5,3,4,7,6]=>001001
[1,2,5,3,6,4,7]=>001100
[1,2,5,3,6,7,4]=>001100
[1,2,5,3,7,4,6]=>001100
[1,2,5,3,7,6,4]=>001101
[1,2,5,4,3,6,7]=>001100
[1,2,5,4,3,7,6]=>001101
[1,2,5,4,6,3,7]=>001100
[1,2,5,4,6,7,3]=>001100
[1,2,5,4,7,3,6]=>001100
[1,2,5,4,7,6,3]=>001101
[1,2,5,6,3,4,7]=>001000
[1,2,5,6,3,7,4]=>001100
[1,2,5,6,4,3,7]=>001100
[1,2,5,6,4,7,3]=>001100
[1,2,5,6,7,3,4]=>001000
[1,2,5,6,7,4,3]=>001100
[1,2,5,7,3,4,6]=>001000
[1,2,5,7,3,6,4]=>001100
[1,2,5,7,4,3,6]=>001100
[1,2,5,7,4,6,3]=>001100
[1,2,5,7,6,3,4]=>001001
[1,2,5,7,6,4,3]=>001101
[1,2,6,3,4,5,7]=>001000
[1,2,6,3,4,7,5]=>001010
[1,2,6,3,5,4,7]=>001100
[1,2,6,3,5,7,4]=>001100
[1,2,6,3,7,4,5]=>001100
[1,2,6,3,7,5,4]=>001110
[1,2,6,4,3,5,7]=>001100
[1,2,6,4,3,7,5]=>001110
[1,2,6,4,5,3,7]=>001100
[1,2,6,4,5,7,3]=>001100
[1,2,6,4,7,3,5]=>001100
[1,2,6,4,7,5,3]=>001110
[1,2,6,5,3,4,7]=>001010
[1,2,6,5,3,7,4]=>001110
[1,2,6,5,4,3,7]=>001110
[1,2,6,5,4,7,3]=>001110
[1,2,6,5,7,3,4]=>001010
[1,2,6,5,7,4,3]=>001110
[1,2,6,7,3,4,5]=>001000
[1,2,6,7,3,5,4]=>001100
[1,2,6,7,4,3,5]=>001100
[1,2,6,7,4,5,3]=>001100
[1,2,6,7,5,3,4]=>001010
[1,2,6,7,5,4,3]=>001110
[1,2,7,3,4,5,6]=>001000
[1,2,7,3,4,6,5]=>001010
[1,2,7,3,5,4,6]=>001100
[1,2,7,3,5,6,4]=>001100
[1,2,7,3,6,4,5]=>001100
[1,2,7,3,6,5,4]=>001110
[1,2,7,4,3,5,6]=>001100
[1,2,7,4,3,6,5]=>001110
[1,2,7,4,5,3,6]=>001100
[1,2,7,4,5,6,3]=>001100
[1,2,7,4,6,3,5]=>001100
[1,2,7,4,6,5,3]=>001110
[1,2,7,5,3,4,6]=>001010
[1,2,7,5,3,6,4]=>001110
[1,2,7,5,4,3,6]=>001110
[1,2,7,5,4,6,3]=>001110
[1,2,7,5,6,3,4]=>001010
[1,2,7,5,6,4,3]=>001110
[1,2,7,6,3,4,5]=>001001
[1,2,7,6,3,5,4]=>001101
[1,2,7,6,4,3,5]=>001101
[1,2,7,6,4,5,3]=>001101
[1,2,7,6,5,3,4]=>001011
[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]=>010010
[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]=>010100
[1,3,2,5,6,7,4]=>010100
[1,3,2,5,7,4,6]=>010100
[1,3,2,5,7,6,4]=>010101
[1,3,2,6,4,5,7]=>010100
[1,3,2,6,4,7,5]=>010110
[1,3,2,6,5,4,7]=>010110
[1,3,2,6,5,7,4]=>010110
[1,3,2,6,7,4,5]=>010100
[1,3,2,6,7,5,4]=>010110
[1,3,2,7,4,5,6]=>010100
[1,3,2,7,4,6,5]=>010110
[1,3,2,7,5,4,6]=>010110
[1,3,2,7,5,6,4]=>010110
[1,3,2,7,6,4,5]=>010101
[1,3,2,7,6,5,4]=>010111
[1,3,4,2,5,6,7]=>010000
[1,3,4,2,5,7,6]=>010001
[1,3,4,2,6,5,7]=>010010
[1,3,4,2,6,7,5]=>010010
[1,3,4,2,7,5,6]=>010010
[1,3,4,2,7,6,5]=>010011
[1,3,4,5,2,6,7]=>010000
[1,3,4,5,2,7,6]=>010001
[1,3,4,5,6,2,7]=>010000
[1,3,4,5,6,7,2]=>010000
[1,3,4,5,7,2,6]=>010000
[1,3,4,5,7,6,2]=>010001
[1,3,4,6,2,5,7]=>010000
[1,3,4,6,2,7,5]=>010010
[1,3,4,6,5,2,7]=>010010
[1,3,4,6,5,7,2]=>010010
[1,3,4,6,7,2,5]=>010000
[1,3,4,6,7,5,2]=>010010
[1,3,4,7,2,5,6]=>010000
[1,3,4,7,2,6,5]=>010010
[1,3,4,7,5,2,6]=>010010
[1,3,4,7,5,6,2]=>010010
[1,3,4,7,6,2,5]=>010001
[1,3,4,7,6,5,2]=>010011
[1,3,5,2,4,6,7]=>010000
[1,3,5,2,4,7,6]=>010001
[1,3,5,2,6,4,7]=>010100
[1,3,5,2,6,7,4]=>010100
[1,3,5,2,7,4,6]=>010100
[1,3,5,2,7,6,4]=>010101
[1,3,5,4,2,6,7]=>010100
[1,3,5,4,2,7,6]=>010101
[1,3,5,4,6,2,7]=>010100
[1,3,5,4,6,7,2]=>010100
[1,3,5,4,7,2,6]=>010100
[1,3,5,4,7,6,2]=>010101
[1,3,5,6,2,4,7]=>010000
[1,3,5,6,2,7,4]=>010100
[1,3,5,6,4,2,7]=>010100
[1,3,5,6,4,7,2]=>010100
[1,3,5,6,7,2,4]=>010000
[1,3,5,6,7,4,2]=>010100
[1,3,5,7,2,4,6]=>010000
[1,3,5,7,2,6,4]=>010100
[1,3,5,7,4,2,6]=>010100
[1,3,5,7,4,6,2]=>010100
[1,3,5,7,6,2,4]=>010001
[1,3,5,7,6,4,2]=>010101
[1,3,6,2,4,5,7]=>010000
[1,3,6,2,4,7,5]=>010010
[1,3,6,2,5,4,7]=>010100
[1,3,6,2,5,7,4]=>010100
[1,3,6,2,7,4,5]=>010100
[1,3,6,2,7,5,4]=>010110
[1,3,6,4,2,5,7]=>010100
[1,3,6,4,2,7,5]=>010110
[1,3,6,4,5,2,7]=>010100
[1,3,6,4,5,7,2]=>010100
[1,3,6,4,7,2,5]=>010100
[1,3,6,4,7,5,2]=>010110
[1,3,6,5,2,4,7]=>010010
[1,3,6,5,2,7,4]=>010110
[1,3,6,5,4,2,7]=>010110
[1,3,6,5,4,7,2]=>010110
[1,3,6,5,7,2,4]=>010010
[1,3,6,5,7,4,2]=>010110
[1,3,6,7,2,4,5]=>010000
[1,3,6,7,2,5,4]=>010100
[1,3,6,7,4,2,5]=>010100
[1,3,6,7,4,5,2]=>010100
[1,3,6,7,5,2,4]=>010010
[1,3,6,7,5,4,2]=>010110
[1,3,7,2,4,5,6]=>010000
[1,3,7,2,4,6,5]=>010010
[1,3,7,2,5,4,6]=>010100
[1,3,7,2,5,6,4]=>010100
[1,3,7,2,6,4,5]=>010100
[1,3,7,2,6,5,4]=>010110
[1,3,7,4,2,5,6]=>010100
[1,3,7,4,2,6,5]=>010110
[1,3,7,4,5,2,6]=>010100
[1,3,7,4,5,6,2]=>010100
[1,3,7,4,6,2,5]=>010100
[1,3,7,4,6,5,2]=>010110
[1,3,7,5,2,4,6]=>010010
[1,3,7,5,2,6,4]=>010110
[1,3,7,5,4,2,6]=>010110
[1,3,7,5,4,6,2]=>010110
[1,3,7,5,6,2,4]=>010010
[1,3,7,5,6,4,2]=>010110
[1,3,7,6,2,4,5]=>010001
[1,3,7,6,2,5,4]=>010101
[1,3,7,6,4,2,5]=>010101
[1,3,7,6,4,5,2]=>010101
[1,3,7,6,5,2,4]=>010011
[1,3,7,6,5,4,2]=>010111
[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]=>010010
[1,4,2,3,7,5,6]=>010010
[1,4,2,3,7,6,5]=>010011
[1,4,2,5,3,6,7]=>011000
[1,4,2,5,3,7,6]=>011001
[1,4,2,5,6,3,7]=>011000
[1,4,2,5,6,7,3]=>011000
[1,4,2,5,7,3,6]=>011000
[1,4,2,5,7,6,3]=>011001
[1,4,2,6,3,5,7]=>011000
[1,4,2,6,3,7,5]=>011010
[1,4,2,6,5,3,7]=>011010
[1,4,2,6,5,7,3]=>011010
[1,4,2,6,7,3,5]=>011000
[1,4,2,6,7,5,3]=>011010
[1,4,2,7,3,5,6]=>011000
[1,4,2,7,3,6,5]=>011010
[1,4,2,7,5,3,6]=>011010
[1,4,2,7,5,6,3]=>011010
[1,4,2,7,6,3,5]=>011001
[1,4,2,7,6,5,3]=>011011
[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]=>011010
[1,4,3,2,7,5,6]=>011010
[1,4,3,2,7,6,5]=>011011
[1,4,3,5,2,6,7]=>011000
[1,4,3,5,2,7,6]=>011001
[1,4,3,5,6,2,7]=>011000
[1,4,3,5,6,7,2]=>011000
[1,4,3,5,7,2,6]=>011000
[1,4,3,5,7,6,2]=>011001
[1,4,3,6,2,5,7]=>011000
[1,4,3,6,2,7,5]=>011010
[1,4,3,6,5,2,7]=>011010
[1,4,3,6,5,7,2]=>011010
[1,4,3,6,7,2,5]=>011000
[1,4,3,6,7,5,2]=>011010
[1,4,3,7,2,5,6]=>011000
[1,4,3,7,2,6,5]=>011010
[1,4,3,7,5,2,6]=>011010
[1,4,3,7,5,6,2]=>011010
[1,4,3,7,6,2,5]=>011001
[1,4,3,7,6,5,2]=>011011
[1,4,5,2,3,6,7]=>010000
[1,4,5,2,3,7,6]=>010001
[1,4,5,2,6,3,7]=>011000
[1,4,5,2,6,7,3]=>011000
[1,4,5,2,7,3,6]=>011000
[1,4,5,2,7,6,3]=>011001
[1,4,5,3,2,6,7]=>011000
[1,4,5,3,2,7,6]=>011001
[1,4,5,3,6,2,7]=>011000
[1,4,5,3,6,7,2]=>011000
[1,4,5,3,7,2,6]=>011000
[1,4,5,3,7,6,2]=>011001
[1,4,5,6,2,3,7]=>010000
[1,4,5,6,2,7,3]=>011000
[1,4,5,6,3,2,7]=>011000
[1,4,5,6,3,7,2]=>011000
[1,4,5,6,7,2,3]=>010000
[1,4,5,6,7,3,2]=>011000
[1,4,5,7,2,3,6]=>010000
[1,4,5,7,2,6,3]=>011000
[1,4,5,7,3,2,6]=>011000
[1,4,5,7,3,6,2]=>011000
[1,4,5,7,6,2,3]=>010001
[1,4,5,7,6,3,2]=>011001
[1,4,6,2,3,5,7]=>010000
[1,4,6,2,3,7,5]=>010010
[1,4,6,2,5,3,7]=>011000
[1,4,6,2,5,7,3]=>011000
[1,4,6,2,7,3,5]=>011000
[1,4,6,2,7,5,3]=>011010
[1,4,6,3,2,5,7]=>011000
[1,4,6,3,2,7,5]=>011010
[1,4,6,3,5,2,7]=>011000
[1,4,6,3,5,7,2]=>011000
[1,4,6,3,7,2,5]=>011000
[1,4,6,3,7,5,2]=>011010
[1,4,6,5,2,3,7]=>010010
[1,4,6,5,2,7,3]=>011010
[1,4,6,5,3,2,7]=>011010
[1,4,6,5,3,7,2]=>011010
[1,4,6,5,7,2,3]=>010010
[1,4,6,5,7,3,2]=>011010
[1,4,6,7,2,3,5]=>010000
[1,4,6,7,2,5,3]=>011000
[1,4,6,7,3,2,5]=>011000
[1,4,6,7,3,5,2]=>011000
[1,4,6,7,5,2,3]=>010010
[1,4,6,7,5,3,2]=>011010
[1,4,7,2,3,5,6]=>010000
[1,4,7,2,3,6,5]=>010010
[1,4,7,2,5,3,6]=>011000
[1,4,7,2,5,6,3]=>011000
[1,4,7,2,6,3,5]=>011000
[1,4,7,2,6,5,3]=>011010
[1,4,7,3,2,5,6]=>011000
[1,4,7,3,2,6,5]=>011010
[1,4,7,3,5,2,6]=>011000
[1,4,7,3,5,6,2]=>011000
[1,4,7,3,6,2,5]=>011000
[1,4,7,3,6,5,2]=>011010
[1,4,7,5,2,3,6]=>010010
[1,4,7,5,2,6,3]=>011010
[1,4,7,5,3,2,6]=>011010
[1,4,7,5,3,6,2]=>011010
[1,4,7,5,6,2,3]=>010010
[1,4,7,5,6,3,2]=>011010
[1,4,7,6,2,3,5]=>010001
[1,4,7,6,2,5,3]=>011001
[1,4,7,6,3,2,5]=>011001
[1,4,7,6,3,5,2]=>011001
[1,4,7,6,5,2,3]=>010011
[1,4,7,6,5,3,2]=>011011
[1,5,2,3,4,6,7]=>010000
[1,5,2,3,4,7,6]=>010001
[1,5,2,3,6,4,7]=>010100
[1,5,2,3,6,7,4]=>010100
[1,5,2,3,7,4,6]=>010100
[1,5,2,3,7,6,4]=>010101
[1,5,2,4,3,6,7]=>011000
[1,5,2,4,3,7,6]=>011001
[1,5,2,4,6,3,7]=>011000
[1,5,2,4,6,7,3]=>011000
[1,5,2,4,7,3,6]=>011000
[1,5,2,4,7,6,3]=>011001
[1,5,2,6,3,4,7]=>011000
[1,5,2,6,3,7,4]=>011100
[1,5,2,6,4,3,7]=>011100
[1,5,2,6,4,7,3]=>011100
[1,5,2,6,7,3,4]=>011000
[1,5,2,6,7,4,3]=>011100
[1,5,2,7,3,4,6]=>011000
[1,5,2,7,3,6,4]=>011100
[1,5,2,7,4,3,6]=>011100
[1,5,2,7,4,6,3]=>011100
[1,5,2,7,6,3,4]=>011001
[1,5,2,7,6,4,3]=>011101
[1,5,3,2,4,6,7]=>011000
[1,5,3,2,4,7,6]=>011001
[1,5,3,2,6,4,7]=>011100
[1,5,3,2,6,7,4]=>011100
[1,5,3,2,7,4,6]=>011100
[1,5,3,2,7,6,4]=>011101
[1,5,3,4,2,6,7]=>011000
[1,5,3,4,2,7,6]=>011001
[1,5,3,4,6,2,7]=>011000
[1,5,3,4,6,7,2]=>011000
[1,5,3,4,7,2,6]=>011000
[1,5,3,4,7,6,2]=>011001
[1,5,3,6,2,4,7]=>011000
[1,5,3,6,2,7,4]=>011100
[1,5,3,6,4,2,7]=>011100
[1,5,3,6,4,7,2]=>011100
[1,5,3,6,7,2,4]=>011000
[1,5,3,6,7,4,2]=>011100
[1,5,3,7,2,4,6]=>011000
[1,5,3,7,2,6,4]=>011100
[1,5,3,7,4,2,6]=>011100
[1,5,3,7,4,6,2]=>011100
[1,5,3,7,6,2,4]=>011001
[1,5,3,7,6,4,2]=>011101
[1,5,4,2,3,6,7]=>010100
[1,5,4,2,3,7,6]=>010101
[1,5,4,2,6,3,7]=>011100
[1,5,4,2,6,7,3]=>011100
[1,5,4,2,7,3,6]=>011100
[1,5,4,2,7,6,3]=>011101
[1,5,4,3,2,6,7]=>011100
[1,5,4,3,2,7,6]=>011101
[1,5,4,3,6,2,7]=>011100
[1,5,4,3,6,7,2]=>011100
[1,5,4,3,7,2,6]=>011100
[1,5,4,3,7,6,2]=>011101
[1,5,4,6,2,3,7]=>010100
[1,5,4,6,2,7,3]=>011100
[1,5,4,6,3,2,7]=>011100
[1,5,4,6,3,7,2]=>011100
[1,5,4,6,7,2,3]=>010100
[1,5,4,6,7,3,2]=>011100
[1,5,4,7,2,3,6]=>010100
[1,5,4,7,2,6,3]=>011100
[1,5,4,7,3,2,6]=>011100
[1,5,4,7,3,6,2]=>011100
[1,5,4,7,6,2,3]=>010101
[1,5,4,7,6,3,2]=>011101
[1,5,6,2,3,4,7]=>010000
[1,5,6,2,3,7,4]=>010100
[1,5,6,2,4,3,7]=>011000
[1,5,6,2,4,7,3]=>011000
[1,5,6,2,7,3,4]=>011000
[1,5,6,2,7,4,3]=>011100
[1,5,6,3,2,4,7]=>011000
[1,5,6,3,2,7,4]=>011100
[1,5,6,3,4,2,7]=>011000
[1,5,6,3,4,7,2]=>011000
[1,5,6,3,7,2,4]=>011000
[1,5,6,3,7,4,2]=>011100
[1,5,6,4,2,3,7]=>010100
[1,5,6,4,2,7,3]=>011100
[1,5,6,4,3,2,7]=>011100
[1,5,6,4,3,7,2]=>011100
[1,5,6,4,7,2,3]=>010100
[1,5,6,4,7,3,2]=>011100
[1,5,6,7,2,3,4]=>010000
[1,5,6,7,2,4,3]=>011000
[1,5,6,7,3,2,4]=>011000
[1,5,6,7,3,4,2]=>011000
[1,5,6,7,4,2,3]=>010100
[1,5,6,7,4,3,2]=>011100
[1,5,7,2,3,4,6]=>010000
[1,5,7,2,3,6,4]=>010100
[1,5,7,2,4,3,6]=>011000
[1,5,7,2,4,6,3]=>011000
[1,5,7,2,6,3,4]=>011000
[1,5,7,2,6,4,3]=>011100
[1,5,7,3,2,4,6]=>011000
[1,5,7,3,2,6,4]=>011100
[1,5,7,3,4,2,6]=>011000
[1,5,7,3,4,6,2]=>011000
[1,5,7,3,6,2,4]=>011000
[1,5,7,3,6,4,2]=>011100
[1,5,7,4,2,3,6]=>010100
[1,5,7,4,2,6,3]=>011100
[1,5,7,4,3,2,6]=>011100
[1,5,7,4,3,6,2]=>011100
[1,5,7,4,6,2,3]=>010100
[1,5,7,4,6,3,2]=>011100
[1,5,7,6,2,3,4]=>010001
[1,5,7,6,2,4,3]=>011001
[1,5,7,6,3,2,4]=>011001
[1,5,7,6,3,4,2]=>011001
[1,5,7,6,4,2,3]=>010101
[1,5,7,6,4,3,2]=>011101
[1,6,2,3,4,5,7]=>010000
[1,6,2,3,4,7,5]=>010010
[1,6,2,3,5,4,7]=>010100
[1,6,2,3,5,7,4]=>010100
[1,6,2,3,7,4,5]=>010100
[1,6,2,3,7,5,4]=>010110
[1,6,2,4,3,5,7]=>011000
[1,6,2,4,3,7,5]=>011010
[1,6,2,4,5,3,7]=>011000
[1,6,2,4,5,7,3]=>011000
[1,6,2,4,7,3,5]=>011000
[1,6,2,4,7,5,3]=>011010
[1,6,2,5,3,4,7]=>011000
[1,6,2,5,3,7,4]=>011100
[1,6,2,5,4,3,7]=>011100
[1,6,2,5,4,7,3]=>011100
[1,6,2,5,7,3,4]=>011000
[1,6,2,5,7,4,3]=>011100
[1,6,2,7,3,4,5]=>011000
[1,6,2,7,3,5,4]=>011100
[1,6,2,7,4,3,5]=>011100
[1,6,2,7,4,5,3]=>011100
[1,6,2,7,5,3,4]=>011010
[1,6,2,7,5,4,3]=>011110
[1,6,3,2,4,5,7]=>011000
[1,6,3,2,4,7,5]=>011010
[1,6,3,2,5,4,7]=>011100
[1,6,3,2,5,7,4]=>011100
[1,6,3,2,7,4,5]=>011100
[1,6,3,2,7,5,4]=>011110
[1,6,3,4,2,5,7]=>011000
[1,6,3,4,2,7,5]=>011010
[1,6,3,4,5,2,7]=>011000
[1,6,3,4,5,7,2]=>011000
[1,6,3,4,7,2,5]=>011000
[1,6,3,4,7,5,2]=>011010
[1,6,3,5,2,4,7]=>011000
[1,6,3,5,2,7,4]=>011100
[1,6,3,5,4,2,7]=>011100
[1,6,3,5,4,7,2]=>011100
[1,6,3,5,7,2,4]=>011000
[1,6,3,5,7,4,2]=>011100
[1,6,3,7,2,4,5]=>011000
[1,6,3,7,2,5,4]=>011100
[1,6,3,7,4,2,5]=>011100
[1,6,3,7,4,5,2]=>011100
[1,6,3,7,5,2,4]=>011010
[1,6,3,7,5,4,2]=>011110
[1,6,4,2,3,5,7]=>010100
[1,6,4,2,3,7,5]=>010110
[1,6,4,2,5,3,7]=>011100
[1,6,4,2,5,7,3]=>011100
[1,6,4,2,7,3,5]=>011100
[1,6,4,2,7,5,3]=>011110
[1,6,4,3,2,5,7]=>011100
[1,6,4,3,2,7,5]=>011110
[1,6,4,3,5,2,7]=>011100
[1,6,4,3,5,7,2]=>011100
[1,6,4,3,7,2,5]=>011100
[1,6,4,3,7,5,2]=>011110
[1,6,4,5,2,3,7]=>010100
[1,6,4,5,2,7,3]=>011100
[1,6,4,5,3,2,7]=>011100
[1,6,4,5,3,7,2]=>011100
[1,6,4,5,7,2,3]=>010100
[1,6,4,5,7,3,2]=>011100
[1,6,4,7,2,3,5]=>010100
[1,6,4,7,2,5,3]=>011100
[1,6,4,7,3,2,5]=>011100
[1,6,4,7,3,5,2]=>011100
[1,6,4,7,5,2,3]=>010110
[1,6,4,7,5,3,2]=>011110
[1,6,5,2,3,4,7]=>010010
[1,6,5,2,3,7,4]=>010110
[1,6,5,2,4,3,7]=>011010
[1,6,5,2,4,7,3]=>011010
[1,6,5,2,7,3,4]=>011010
[1,6,5,2,7,4,3]=>011110
[1,6,5,3,2,4,7]=>011010
[1,6,5,3,2,7,4]=>011110
[1,6,5,3,4,2,7]=>011010
[1,6,5,3,4,7,2]=>011010
[1,6,5,3,7,2,4]=>011010
[1,6,5,3,7,4,2]=>011110
[1,6,5,4,2,3,7]=>010110
[1,6,5,4,2,7,3]=>011110
[1,6,5,4,3,2,7]=>011110
[1,6,5,4,3,7,2]=>011110
[1,6,5,4,7,2,3]=>010110
[1,6,5,4,7,3,2]=>011110
[1,6,5,7,2,3,4]=>010010
[1,6,5,7,2,4,3]=>011010
[1,6,5,7,3,2,4]=>011010
[1,6,5,7,3,4,2]=>011010
[1,6,5,7,4,2,3]=>010110
[1,6,5,7,4,3,2]=>011110
[1,6,7,2,3,4,5]=>010000
[1,6,7,2,3,5,4]=>010100
[1,6,7,2,4,3,5]=>011000
[1,6,7,2,4,5,3]=>011000
[1,6,7,2,5,3,4]=>011000
[1,6,7,2,5,4,3]=>011100
[1,6,7,3,2,4,5]=>011000
[1,6,7,3,2,5,4]=>011100
[1,6,7,3,4,2,5]=>011000
[1,6,7,3,4,5,2]=>011000
[1,6,7,3,5,2,4]=>011000
[1,6,7,3,5,4,2]=>011100
[1,6,7,4,2,3,5]=>010100
[1,6,7,4,2,5,3]=>011100
[1,6,7,4,3,2,5]=>011100
[1,6,7,4,3,5,2]=>011100
[1,6,7,4,5,2,3]=>010100
[1,6,7,4,5,3,2]=>011100
[1,6,7,5,2,3,4]=>010010
[1,6,7,5,2,4,3]=>011010
[1,6,7,5,3,2,4]=>011010
[1,6,7,5,3,4,2]=>011010
[1,6,7,5,4,2,3]=>010110
[1,6,7,5,4,3,2]=>011110
[1,7,2,3,4,5,6]=>010000
[1,7,2,3,4,6,5]=>010010
[1,7,2,3,5,4,6]=>010100
[1,7,2,3,5,6,4]=>010100
[1,7,2,3,6,4,5]=>010100
[1,7,2,3,6,5,4]=>010110
[1,7,2,4,3,5,6]=>011000
[1,7,2,4,3,6,5]=>011010
[1,7,2,4,5,3,6]=>011000
[1,7,2,4,5,6,3]=>011000
[1,7,2,4,6,3,5]=>011000
[1,7,2,4,6,5,3]=>011010
[1,7,2,5,3,4,6]=>011000
[1,7,2,5,3,6,4]=>011100
[1,7,2,5,4,3,6]=>011100
[1,7,2,5,4,6,3]=>011100
[1,7,2,5,6,3,4]=>011000
[1,7,2,5,6,4,3]=>011100
[1,7,2,6,3,4,5]=>011000
[1,7,2,6,3,5,4]=>011100
[1,7,2,6,4,3,5]=>011100
[1,7,2,6,4,5,3]=>011100
[1,7,2,6,5,3,4]=>011010
[1,7,2,6,5,4,3]=>011110
[1,7,3,2,4,5,6]=>011000
[1,7,3,2,4,6,5]=>011010
[1,7,3,2,5,4,6]=>011100
[1,7,3,2,5,6,4]=>011100
[1,7,3,2,6,4,5]=>011100
[1,7,3,2,6,5,4]=>011110
[1,7,3,4,2,5,6]=>011000
[1,7,3,4,2,6,5]=>011010
[1,7,3,4,5,2,6]=>011000
[1,7,3,4,5,6,2]=>011000
[1,7,3,4,6,2,5]=>011000
[1,7,3,4,6,5,2]=>011010
[1,7,3,5,2,4,6]=>011000
[1,7,3,5,2,6,4]=>011100
[1,7,3,5,4,2,6]=>011100
[1,7,3,5,4,6,2]=>011100
[1,7,3,5,6,2,4]=>011000
[1,7,3,5,6,4,2]=>011100
[1,7,3,6,2,4,5]=>011000
[1,7,3,6,2,5,4]=>011100
[1,7,3,6,4,2,5]=>011100
[1,7,3,6,4,5,2]=>011100
[1,7,3,6,5,2,4]=>011010
[1,7,3,6,5,4,2]=>011110
[1,7,4,2,3,5,6]=>010100
[1,7,4,2,3,6,5]=>010110
[1,7,4,2,5,3,6]=>011100
[1,7,4,2,5,6,3]=>011100
[1,7,4,2,6,3,5]=>011100
[1,7,4,2,6,5,3]=>011110
[1,7,4,3,2,5,6]=>011100
[1,7,4,3,2,6,5]=>011110
[1,7,4,3,5,2,6]=>011100
[1,7,4,3,5,6,2]=>011100
[1,7,4,3,6,2,5]=>011100
[1,7,4,3,6,5,2]=>011110
[1,7,4,5,2,3,6]=>010100
[1,7,4,5,2,6,3]=>011100
[1,7,4,5,3,2,6]=>011100
[1,7,4,5,3,6,2]=>011100
[1,7,4,5,6,2,3]=>010100
[1,7,4,5,6,3,2]=>011100
[1,7,4,6,2,3,5]=>010100
[1,7,4,6,2,5,3]=>011100
[1,7,4,6,3,2,5]=>011100
[1,7,4,6,3,5,2]=>011100
[1,7,4,6,5,2,3]=>010110
[1,7,4,6,5,3,2]=>011110
[1,7,5,2,3,4,6]=>010010
[1,7,5,2,3,6,4]=>010110
[1,7,5,2,4,3,6]=>011010
[1,7,5,2,4,6,3]=>011010
[1,7,5,2,6,3,4]=>011010
[1,7,5,2,6,4,3]=>011110
[1,7,5,3,2,4,6]=>011010
[1,7,5,3,2,6,4]=>011110
[1,7,5,3,4,2,6]=>011010
[1,7,5,3,4,6,2]=>011010
[1,7,5,3,6,2,4]=>011010
[1,7,5,3,6,4,2]=>011110
[1,7,5,4,2,3,6]=>010110
[1,7,5,4,2,6,3]=>011110
[1,7,5,4,3,2,6]=>011110
[1,7,5,4,3,6,2]=>011110
[1,7,5,4,6,2,3]=>010110
[1,7,5,4,6,3,2]=>011110
[1,7,5,6,2,3,4]=>010010
[1,7,5,6,2,4,3]=>011010
[1,7,5,6,3,2,4]=>011010
[1,7,5,6,3,4,2]=>011010
[1,7,5,6,4,2,3]=>010110
[1,7,5,6,4,3,2]=>011110
[1,7,6,2,3,4,5]=>010001
[1,7,6,2,3,5,4]=>010101
[1,7,6,2,4,3,5]=>011001
[1,7,6,2,4,5,3]=>011001
[1,7,6,2,5,3,4]=>011001
[1,7,6,2,5,4,3]=>011101
[1,7,6,3,2,4,5]=>011001
[1,7,6,3,2,5,4]=>011101
[1,7,6,3,4,2,5]=>011001
[1,7,6,3,4,5,2]=>011001
[1,7,6,3,5,2,4]=>011001
[1,7,6,3,5,4,2]=>011101
[1,7,6,4,2,3,5]=>010101
[1,7,6,4,2,5,3]=>011101
[1,7,6,4,3,2,5]=>011101
[1,7,6,4,3,5,2]=>011101
[1,7,6,4,5,2,3]=>010101
[1,7,6,4,5,3,2]=>011101
[1,7,6,5,2,3,4]=>010011
[1,7,6,5,2,4,3]=>011011
[1,7,6,5,3,2,4]=>011011
[1,7,6,5,3,4,2]=>011011
[1,7,6,5,4,2,3]=>010111
[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]=>100010
[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]=>100100
[2,1,3,5,6,7,4]=>100100
[2,1,3,5,7,4,6]=>100100
[2,1,3,5,7,6,4]=>100101
[2,1,3,6,4,5,7]=>100100
[2,1,3,6,4,7,5]=>100110
[2,1,3,6,5,4,7]=>100110
[2,1,3,6,5,7,4]=>100110
[2,1,3,6,7,4,5]=>100100
[2,1,3,6,7,5,4]=>100110
[2,1,3,7,4,5,6]=>100100
[2,1,3,7,4,6,5]=>100110
[2,1,3,7,5,4,6]=>100110
[2,1,3,7,5,6,4]=>100110
[2,1,3,7,6,4,5]=>100101
[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]=>101010
[2,1,4,3,7,5,6]=>101010
[2,1,4,3,7,6,5]=>101011
[2,1,4,5,3,6,7]=>101000
[2,1,4,5,3,7,6]=>101001
[2,1,4,5,6,3,7]=>101000
[2,1,4,5,6,7,3]=>101000
[2,1,4,5,7,3,6]=>101000
[2,1,4,5,7,6,3]=>101001
[2,1,4,6,3,5,7]=>101000
[2,1,4,6,3,7,5]=>101010
[2,1,4,6,5,3,7]=>101010
[2,1,4,6,5,7,3]=>101010
[2,1,4,6,7,3,5]=>101000
[2,1,4,6,7,5,3]=>101010
[2,1,4,7,3,5,6]=>101000
[2,1,4,7,3,6,5]=>101010
[2,1,4,7,5,3,6]=>101010
[2,1,4,7,5,6,3]=>101010
[2,1,4,7,6,3,5]=>101001
[2,1,4,7,6,5,3]=>101011
[2,1,5,3,4,6,7]=>101000
[2,1,5,3,4,7,6]=>101001
[2,1,5,3,6,4,7]=>101100
[2,1,5,3,6,7,4]=>101100
[2,1,5,3,7,4,6]=>101100
[2,1,5,3,7,6,4]=>101101
[2,1,5,4,3,6,7]=>101100
[2,1,5,4,3,7,6]=>101101
[2,1,5,4,6,3,7]=>101100
[2,1,5,4,6,7,3]=>101100
[2,1,5,4,7,3,6]=>101100
[2,1,5,4,7,6,3]=>101101
[2,1,5,6,3,4,7]=>101000
[2,1,5,6,3,7,4]=>101100
[2,1,5,6,4,3,7]=>101100
[2,1,5,6,4,7,3]=>101100
[2,1,5,6,7,3,4]=>101000
[2,1,5,6,7,4,3]=>101100
[2,1,5,7,3,4,6]=>101000
[2,1,5,7,3,6,4]=>101100
[2,1,5,7,4,3,6]=>101100
[2,1,5,7,4,6,3]=>101100
[2,1,5,7,6,3,4]=>101001
[2,1,5,7,6,4,3]=>101101
[2,1,6,3,4,5,7]=>101000
[2,1,6,3,4,7,5]=>101010
[2,1,6,3,5,4,7]=>101100
[2,1,6,3,5,7,4]=>101100
[2,1,6,3,7,4,5]=>101100
[2,1,6,3,7,5,4]=>101110
[2,1,6,4,3,5,7]=>101100
[2,1,6,4,3,7,5]=>101110
[2,1,6,4,5,3,7]=>101100
[2,1,6,4,5,7,3]=>101100
[2,1,6,4,7,3,5]=>101100
[2,1,6,4,7,5,3]=>101110
[2,1,6,5,3,4,7]=>101010
[2,1,6,5,3,7,4]=>101110
[2,1,6,5,4,3,7]=>101110
[2,1,6,5,4,7,3]=>101110
[2,1,6,5,7,3,4]=>101010
[2,1,6,5,7,4,3]=>101110
[2,1,6,7,3,4,5]=>101000
[2,1,6,7,3,5,4]=>101100
[2,1,6,7,4,3,5]=>101100
[2,1,6,7,4,5,3]=>101100
[2,1,6,7,5,3,4]=>101010
[2,1,6,7,5,4,3]=>101110
[2,1,7,3,4,5,6]=>101000
[2,1,7,3,4,6,5]=>101010
[2,1,7,3,5,4,6]=>101100
[2,1,7,3,5,6,4]=>101100
[2,1,7,3,6,4,5]=>101100
[2,1,7,3,6,5,4]=>101110
[2,1,7,4,3,5,6]=>101100
[2,1,7,4,3,6,5]=>101110
[2,1,7,4,5,3,6]=>101100
[2,1,7,4,5,6,3]=>101100
[2,1,7,4,6,3,5]=>101100
[2,1,7,4,6,5,3]=>101110
[2,1,7,5,3,4,6]=>101010
[2,1,7,5,3,6,4]=>101110
[2,1,7,5,4,3,6]=>101110
[2,1,7,5,4,6,3]=>101110
[2,1,7,5,6,3,4]=>101010
[2,1,7,5,6,4,3]=>101110
[2,1,7,6,3,4,5]=>101001
[2,1,7,6,3,5,4]=>101101
[2,1,7,6,4,3,5]=>101101
[2,1,7,6,4,5,3]=>101101
[2,1,7,6,5,3,4]=>101011
[2,1,7,6,5,4,3]=>101111
[2,3,1,4,5,6,7]=>100000
[2,3,1,4,5,7,6]=>100001
[2,3,1,4,6,5,7]=>100010
[2,3,1,4,6,7,5]=>100010
[2,3,1,4,7,5,6]=>100010
[2,3,1,4,7,6,5]=>100011
[2,3,1,5,4,6,7]=>100100
[2,3,1,5,4,7,6]=>100101
[2,3,1,5,6,4,7]=>100100
[2,3,1,5,6,7,4]=>100100
[2,3,1,5,7,4,6]=>100100
[2,3,1,5,7,6,4]=>100101
[2,3,1,6,4,5,7]=>100100
[2,3,1,6,4,7,5]=>100110
[2,3,1,6,5,4,7]=>100110
[2,3,1,6,5,7,4]=>100110
[2,3,1,6,7,4,5]=>100100
[2,3,1,6,7,5,4]=>100110
[2,3,1,7,4,5,6]=>100100
[2,3,1,7,4,6,5]=>100110
[2,3,1,7,5,4,6]=>100110
[2,3,1,7,5,6,4]=>100110
[2,3,1,7,6,4,5]=>100101
[2,3,1,7,6,5,4]=>100111
[2,3,4,1,5,6,7]=>100000
[2,3,4,1,5,7,6]=>100001
[2,3,4,1,6,5,7]=>100010
[2,3,4,1,6,7,5]=>100010
[2,3,4,1,7,5,6]=>100010
[2,3,4,1,7,6,5]=>100011
[2,3,4,5,1,6,7]=>100000
[2,3,4,5,1,7,6]=>100001
[2,3,4,5,6,1,7]=>100000
[2,3,4,5,6,7,1]=>100000
[2,3,4,5,7,1,6]=>100000
[2,3,4,5,7,6,1]=>100001
[2,3,4,6,1,5,7]=>100000
[2,3,4,6,1,7,5]=>100010
[2,3,4,6,5,1,7]=>100010
[2,3,4,6,5,7,1]=>100010
[2,3,4,6,7,1,5]=>100000
[2,3,4,6,7,5,1]=>100010
[2,3,4,7,1,5,6]=>100000
[2,3,4,7,1,6,5]=>100010
[2,3,4,7,5,1,6]=>100010
[2,3,4,7,5,6,1]=>100010
[2,3,4,7,6,1,5]=>100001
[2,3,4,7,6,5,1]=>100011
[2,3,5,1,4,6,7]=>100000
[2,3,5,1,4,7,6]=>100001
[2,3,5,1,6,4,7]=>100100
[2,3,5,1,6,7,4]=>100100
[2,3,5,1,7,4,6]=>100100
[2,3,5,1,7,6,4]=>100101
[2,3,5,4,1,6,7]=>100100
[2,3,5,4,1,7,6]=>100101
[2,3,5,4,6,1,7]=>100100
[2,3,5,4,6,7,1]=>100100
[2,3,5,4,7,1,6]=>100100
[2,3,5,4,7,6,1]=>100101
[2,3,5,6,1,4,7]=>100000
[2,3,5,6,1,7,4]=>100100
[2,3,5,6,4,1,7]=>100100
[2,3,5,6,4,7,1]=>100100
[2,3,5,6,7,1,4]=>100000
[2,3,5,6,7,4,1]=>100100
[2,3,5,7,1,4,6]=>100000
[2,3,5,7,1,6,4]=>100100
[2,3,5,7,4,1,6]=>100100
[2,3,5,7,4,6,1]=>100100
[2,3,5,7,6,1,4]=>100001
[2,3,5,7,6,4,1]=>100101
[2,3,6,1,4,5,7]=>100000
[2,3,6,1,4,7,5]=>100010
[2,3,6,1,5,4,7]=>100100
[2,3,6,1,5,7,4]=>100100
[2,3,6,1,7,4,5]=>100100
[2,3,6,1,7,5,4]=>100110
[2,3,6,4,1,5,7]=>100100
[2,3,6,4,1,7,5]=>100110
[2,3,6,4,5,1,7]=>100100
[2,3,6,4,5,7,1]=>100100
[2,3,6,4,7,1,5]=>100100
[2,3,6,4,7,5,1]=>100110
[2,3,6,5,1,4,7]=>100010
[2,3,6,5,1,7,4]=>100110
[2,3,6,5,4,1,7]=>100110
[2,3,6,5,4,7,1]=>100110
[2,3,6,5,7,1,4]=>100010
[2,3,6,5,7,4,1]=>100110
[2,3,6,7,1,4,5]=>100000
[2,3,6,7,1,5,4]=>100100
[2,3,6,7,4,1,5]=>100100
[2,3,6,7,4,5,1]=>100100
[2,3,6,7,5,1,4]=>100010
[2,3,6,7,5,4,1]=>100110
[2,3,7,1,4,5,6]=>100000
[2,3,7,1,4,6,5]=>100010
[2,3,7,1,5,4,6]=>100100
[2,3,7,1,5,6,4]=>100100
[2,3,7,1,6,4,5]=>100100
[2,3,7,1,6,5,4]=>100110
[2,3,7,4,1,5,6]=>100100
[2,3,7,4,1,6,5]=>100110
[2,3,7,4,5,1,6]=>100100
[2,3,7,4,5,6,1]=>100100
[2,3,7,4,6,1,5]=>100100
[2,3,7,4,6,5,1]=>100110
[2,3,7,5,1,4,6]=>100010
[2,3,7,5,1,6,4]=>100110
[2,3,7,5,4,1,6]=>100110
[2,3,7,5,4,6,1]=>100110
[2,3,7,5,6,1,4]=>100010
[2,3,7,5,6,4,1]=>100110
[2,3,7,6,1,4,5]=>100001
[2,3,7,6,1,5,4]=>100101
[2,3,7,6,4,1,5]=>100101
[2,3,7,6,4,5,1]=>100101
[2,3,7,6,5,1,4]=>100011
[2,3,7,6,5,4,1]=>100111
[2,4,1,3,5,6,7]=>100000
[2,4,1,3,5,7,6]=>100001
[2,4,1,3,6,5,7]=>100010
[2,4,1,3,6,7,5]=>100010
[2,4,1,3,7,5,6]=>100010
[2,4,1,3,7,6,5]=>100011
[2,4,1,5,3,6,7]=>101000
[2,4,1,5,3,7,6]=>101001
[2,4,1,5,6,3,7]=>101000
[2,4,1,5,6,7,3]=>101000
[2,4,1,5,7,3,6]=>101000
[2,4,1,5,7,6,3]=>101001
[2,4,1,6,3,5,7]=>101000
[2,4,1,6,3,7,5]=>101010
[2,4,1,6,5,3,7]=>101010
[2,4,1,6,5,7,3]=>101010
[2,4,1,6,7,3,5]=>101000
[2,4,1,6,7,5,3]=>101010
[2,4,1,7,3,5,6]=>101000
[2,4,1,7,3,6,5]=>101010
[2,4,1,7,5,3,6]=>101010
[2,4,1,7,5,6,3]=>101010
[2,4,1,7,6,3,5]=>101001
[2,4,1,7,6,5,3]=>101011
[2,4,3,1,5,6,7]=>101000
[2,4,3,1,5,7,6]=>101001
[2,4,3,1,6,5,7]=>101010
[2,4,3,1,6,7,5]=>101010
[2,4,3,1,7,5,6]=>101010
[2,4,3,1,7,6,5]=>101011
[2,4,3,5,1,6,7]=>101000
[2,4,3,5,1,7,6]=>101001
[2,4,3,5,6,1,7]=>101000
[2,4,3,5,6,7,1]=>101000
[2,4,3,5,7,1,6]=>101000
[2,4,3,5,7,6,1]=>101001
[2,4,3,6,1,5,7]=>101000
[2,4,3,6,1,7,5]=>101010
[2,4,3,6,5,1,7]=>101010
[2,4,3,6,5,7,1]=>101010
[2,4,3,6,7,1,5]=>101000
[2,4,3,6,7,5,1]=>101010
[2,4,3,7,1,5,6]=>101000
[2,4,3,7,1,6,5]=>101010
[2,4,3,7,5,1,6]=>101010
[2,4,3,7,5,6,1]=>101010
[2,4,3,7,6,1,5]=>101001
[2,4,3,7,6,5,1]=>101011
[2,4,5,1,3,6,7]=>100000
[2,4,5,1,3,7,6]=>100001
[2,4,5,1,6,3,7]=>101000
[2,4,5,1,6,7,3]=>101000
[2,4,5,1,7,3,6]=>101000
[2,4,5,1,7,6,3]=>101001
[2,4,5,3,1,6,7]=>101000
[2,4,5,3,1,7,6]=>101001
[2,4,5,3,6,1,7]=>101000
[2,4,5,3,6,7,1]=>101000
[2,4,5,3,7,1,6]=>101000
[2,4,5,3,7,6,1]=>101001
[2,4,5,6,1,3,7]=>100000
[2,4,5,6,1,7,3]=>101000
[2,4,5,6,3,1,7]=>101000
[2,4,5,6,3,7,1]=>101000
[2,4,5,6,7,1,3]=>100000
[2,4,5,6,7,3,1]=>101000
[2,4,5,7,1,3,6]=>100000
[2,4,5,7,1,6,3]=>101000
[2,4,5,7,3,1,6]=>101000
[2,4,5,7,3,6,1]=>101000
[2,4,5,7,6,1,3]=>100001
[2,4,5,7,6,3,1]=>101001
[2,4,6,1,3,5,7]=>100000
[2,4,6,1,3,7,5]=>100010
[2,4,6,1,5,3,7]=>101000
[2,4,6,1,5,7,3]=>101000
[2,4,6,1,7,3,5]=>101000
[2,4,6,1,7,5,3]=>101010
[2,4,6,3,1,5,7]=>101000
[2,4,6,3,1,7,5]=>101010
[2,4,6,3,5,1,7]=>101000
[2,4,6,3,5,7,1]=>101000
[2,4,6,3,7,1,5]=>101000
[2,4,6,3,7,5,1]=>101010
[2,4,6,5,1,3,7]=>100010
[2,4,6,5,1,7,3]=>101010
[2,4,6,5,3,1,7]=>101010
[2,4,6,5,3,7,1]=>101010
[2,4,6,5,7,1,3]=>100010
[2,4,6,5,7,3,1]=>101010
[2,4,6,7,1,3,5]=>100000
[2,4,6,7,1,5,3]=>101000
[2,4,6,7,3,1,5]=>101000
[2,4,6,7,3,5,1]=>101000
[2,4,6,7,5,1,3]=>100010
[2,4,6,7,5,3,1]=>101010
[2,4,7,1,3,5,6]=>100000
[2,4,7,1,3,6,5]=>100010
[2,4,7,1,5,3,6]=>101000
[2,4,7,1,5,6,3]=>101000
[2,4,7,1,6,3,5]=>101000
[2,4,7,1,6,5,3]=>101010
[2,4,7,3,1,5,6]=>101000
[2,4,7,3,1,6,5]=>101010
[2,4,7,3,5,1,6]=>101000
[2,4,7,3,5,6,1]=>101000
[2,4,7,3,6,1,5]=>101000
[2,4,7,3,6,5,1]=>101010
[2,4,7,5,1,3,6]=>100010
[2,4,7,5,1,6,3]=>101010
[2,4,7,5,3,1,6]=>101010
[2,4,7,5,3,6,1]=>101010
[2,4,7,5,6,1,3]=>100010
[2,4,7,5,6,3,1]=>101010
[2,4,7,6,1,3,5]=>100001
[2,4,7,6,1,5,3]=>101001
[2,4,7,6,3,1,5]=>101001
[2,4,7,6,3,5,1]=>101001
[2,4,7,6,5,1,3]=>100011
[2,4,7,6,5,3,1]=>101011
[2,5,1,3,4,6,7]=>100000
[2,5,1,3,4,7,6]=>100001
[2,5,1,3,6,4,7]=>100100
[2,5,1,3,6,7,4]=>100100
[2,5,1,3,7,4,6]=>100100
[2,5,1,3,7,6,4]=>100101
[2,5,1,4,3,6,7]=>101000
[2,5,1,4,3,7,6]=>101001
[2,5,1,4,6,3,7]=>101000
[2,5,1,4,6,7,3]=>101000
[2,5,1,4,7,3,6]=>101000
[2,5,1,4,7,6,3]=>101001
[2,5,1,6,3,4,7]=>101000
[2,5,1,6,3,7,4]=>101100
[2,5,1,6,4,3,7]=>101100
[2,5,1,6,4,7,3]=>101100
[2,5,1,6,7,3,4]=>101000
[2,5,1,6,7,4,3]=>101100
[2,5,1,7,3,4,6]=>101000
[2,5,1,7,3,6,4]=>101100
[2,5,1,7,4,3,6]=>101100
[2,5,1,7,4,6,3]=>101100
[2,5,1,7,6,3,4]=>101001
[2,5,1,7,6,4,3]=>101101
[2,5,3,1,4,6,7]=>101000
[2,5,3,1,4,7,6]=>101001
[2,5,3,1,6,4,7]=>101100
[2,5,3,1,6,7,4]=>101100
[2,5,3,1,7,4,6]=>101100
[2,5,3,1,7,6,4]=>101101
[2,5,3,4,1,6,7]=>101000
[2,5,3,4,1,7,6]=>101001
[2,5,3,4,6,1,7]=>101000
[2,5,3,4,6,7,1]=>101000
[2,5,3,4,7,1,6]=>101000
[2,5,3,4,7,6,1]=>101001
[2,5,3,6,1,4,7]=>101000
[2,5,3,6,1,7,4]=>101100
[2,5,3,6,4,1,7]=>101100
[2,5,3,6,4,7,1]=>101100
[2,5,3,6,7,1,4]=>101000
[2,5,3,6,7,4,1]=>101100
[2,5,3,7,1,4,6]=>101000
[2,5,3,7,1,6,4]=>101100
[2,5,3,7,4,1,6]=>101100
[2,5,3,7,4,6,1]=>101100
[2,5,3,7,6,1,4]=>101001
[2,5,3,7,6,4,1]=>101101
[2,5,4,1,3,6,7]=>100100
[2,5,4,1,3,7,6]=>100101
[2,5,4,1,6,3,7]=>101100
[2,5,4,1,6,7,3]=>101100
[2,5,4,1,7,3,6]=>101100
[2,5,4,1,7,6,3]=>101101
[2,5,4,3,1,6,7]=>101100
[2,5,4,3,1,7,6]=>101101
[2,5,4,3,6,1,7]=>101100
[2,5,4,3,6,7,1]=>101100
[2,5,4,3,7,1,6]=>101100
[2,5,4,3,7,6,1]=>101101
[2,5,4,6,1,3,7]=>100100
[2,5,4,6,1,7,3]=>101100
[2,5,4,6,3,1,7]=>101100
[2,5,4,6,3,7,1]=>101100
[2,5,4,6,7,1,3]=>100100
[2,5,4,6,7,3,1]=>101100
[2,5,4,7,1,3,6]=>100100
[2,5,4,7,1,6,3]=>101100
[2,5,4,7,3,1,6]=>101100
[2,5,4,7,3,6,1]=>101100
[2,5,4,7,6,1,3]=>100101
[2,5,4,7,6,3,1]=>101101
[2,5,6,1,3,4,7]=>100000
[2,5,6,1,3,7,4]=>100100
[2,5,6,1,4,3,7]=>101000
[2,5,6,1,4,7,3]=>101000
[2,5,6,1,7,3,4]=>101000
[2,5,6,1,7,4,3]=>101100
[2,5,6,3,1,4,7]=>101000
[2,5,6,3,1,7,4]=>101100
[2,5,6,3,4,1,7]=>101000
[2,5,6,3,4,7,1]=>101000
[2,5,6,3,7,1,4]=>101000
[2,5,6,3,7,4,1]=>101100
[2,5,6,4,1,3,7]=>100100
[2,5,6,4,1,7,3]=>101100
[2,5,6,4,3,1,7]=>101100
[2,5,6,4,3,7,1]=>101100
[2,5,6,4,7,1,3]=>100100
[2,5,6,4,7,3,1]=>101100
[2,5,6,7,1,3,4]=>100000
[2,5,6,7,1,4,3]=>101000
[2,5,6,7,3,1,4]=>101000
[2,5,6,7,3,4,1]=>101000
[2,5,6,7,4,1,3]=>100100
[2,5,6,7,4,3,1]=>101100
[2,5,7,1,3,4,6]=>100000
[2,5,7,1,3,6,4]=>100100
[2,5,7,1,4,3,6]=>101000
[2,5,7,1,4,6,3]=>101000
[2,5,7,1,6,3,4]=>101000
[2,5,7,1,6,4,3]=>101100
[2,5,7,3,1,4,6]=>101000
[2,5,7,3,1,6,4]=>101100
[2,5,7,3,4,1,6]=>101000
[2,5,7,3,4,6,1]=>101000
[2,5,7,3,6,1,4]=>101000
[2,5,7,3,6,4,1]=>101100
[2,5,7,4,1,3,6]=>100100
[2,5,7,4,1,6,3]=>101100
[2,5,7,4,3,1,6]=>101100
[2,5,7,4,3,6,1]=>101100
[2,5,7,4,6,1,3]=>100100
[2,5,7,4,6,3,1]=>101100
[2,5,7,6,1,3,4]=>100001
[2,5,7,6,1,4,3]=>101001
[2,5,7,6,3,1,4]=>101001
[2,5,7,6,3,4,1]=>101001
[2,5,7,6,4,1,3]=>100101
[2,5,7,6,4,3,1]=>101101
[2,6,1,3,4,5,7]=>100000
[2,6,1,3,4,7,5]=>100010
[2,6,1,3,5,4,7]=>100100
[2,6,1,3,5,7,4]=>100100
[2,6,1,3,7,4,5]=>100100
[2,6,1,3,7,5,4]=>100110
[2,6,1,4,3,5,7]=>101000
[2,6,1,4,3,7,5]=>101010
[2,6,1,4,5,3,7]=>101000
[2,6,1,4,5,7,3]=>101000
[2,6,1,4,7,3,5]=>101000
[2,6,1,4,7,5,3]=>101010
[2,6,1,5,3,4,7]=>101000
[2,6,1,5,3,7,4]=>101100
[2,6,1,5,4,3,7]=>101100
[2,6,1,5,4,7,3]=>101100
[2,6,1,5,7,3,4]=>101000
[2,6,1,5,7,4,3]=>101100
[2,6,1,7,3,4,5]=>101000
[2,6,1,7,3,5,4]=>101100
[2,6,1,7,4,3,5]=>101100
[2,6,1,7,4,5,3]=>101100
[2,6,1,7,5,3,4]=>101010
[2,6,1,7,5,4,3]=>101110
[2,6,3,1,4,5,7]=>101000
[2,6,3,1,4,7,5]=>101010
[2,6,3,1,5,4,7]=>101100
[2,6,3,1,5,7,4]=>101100
[2,6,3,1,7,4,5]=>101100
[2,6,3,1,7,5,4]=>101110
[2,6,3,4,1,5,7]=>101000
[2,6,3,4,1,7,5]=>101010
[2,6,3,4,5,1,7]=>101000
[2,6,3,4,5,7,1]=>101000
[2,6,3,4,7,1,5]=>101000
[2,6,3,4,7,5,1]=>101010
[2,6,3,5,1,4,7]=>101000
[2,6,3,5,1,7,4]=>101100
[2,6,3,5,4,1,7]=>101100
[2,6,3,5,4,7,1]=>101100
[2,6,3,5,7,1,4]=>101000
[2,6,3,5,7,4,1]=>101100
[2,6,3,7,1,4,5]=>101000
[2,6,3,7,1,5,4]=>101100
[2,6,3,7,4,1,5]=>101100
[2,6,3,7,4,5,1]=>101100
[2,6,3,7,5,1,4]=>101010
[2,6,3,7,5,4,1]=>101110
[2,6,4,1,3,5,7]=>100100
[2,6,4,1,3,7,5]=>100110
[2,6,4,1,5,3,7]=>101100
[2,6,4,1,5,7,3]=>101100
[2,6,4,1,7,3,5]=>101100
[2,6,4,1,7,5,3]=>101110
[2,6,4,3,1,5,7]=>101100
[2,6,4,3,1,7,5]=>101110
[2,6,4,3,5,1,7]=>101100
[2,6,4,3,5,7,1]=>101100
[2,6,4,3,7,1,5]=>101100
[2,6,4,3,7,5,1]=>101110
[2,6,4,5,1,3,7]=>100100
[2,6,4,5,1,7,3]=>101100
[2,6,4,5,3,1,7]=>101100
[2,6,4,5,3,7,1]=>101100
[2,6,4,5,7,1,3]=>100100
[2,6,4,5,7,3,1]=>101100
[2,6,4,7,1,3,5]=>100100
[2,6,4,7,1,5,3]=>101100
[2,6,4,7,3,1,5]=>101100
[2,6,4,7,3,5,1]=>101100
[2,6,4,7,5,1,3]=>100110
[2,6,4,7,5,3,1]=>101110
[2,6,5,1,3,4,7]=>100010
[2,6,5,1,3,7,4]=>100110
[2,6,5,1,4,3,7]=>101010
[2,6,5,1,4,7,3]=>101010
[2,6,5,1,7,3,4]=>101010
[2,6,5,1,7,4,3]=>101110
[2,6,5,3,1,4,7]=>101010
[2,6,5,3,1,7,4]=>101110
[2,6,5,3,4,1,7]=>101010
[2,6,5,3,4,7,1]=>101010
[2,6,5,3,7,1,4]=>101010
[2,6,5,3,7,4,1]=>101110
[2,6,5,4,1,3,7]=>100110
[2,6,5,4,1,7,3]=>101110
[2,6,5,4,3,1,7]=>101110
[2,6,5,4,3,7,1]=>101110
[2,6,5,4,7,1,3]=>100110
[2,6,5,4,7,3,1]=>101110
[2,6,5,7,1,3,4]=>100010
[2,6,5,7,1,4,3]=>101010
[2,6,5,7,3,1,4]=>101010
[2,6,5,7,3,4,1]=>101010
[2,6,5,7,4,1,3]=>100110
[2,6,5,7,4,3,1]=>101110
[2,6,7,1,3,4,5]=>100000
[2,6,7,1,3,5,4]=>100100
[2,6,7,1,4,3,5]=>101000
[2,6,7,1,4,5,3]=>101000
[2,6,7,1,5,3,4]=>101000
[2,6,7,1,5,4,3]=>101100
[2,6,7,3,1,4,5]=>101000
[2,6,7,3,1,5,4]=>101100
[2,6,7,3,4,1,5]=>101000
[2,6,7,3,4,5,1]=>101000
[2,6,7,3,5,1,4]=>101000
[2,6,7,3,5,4,1]=>101100
[2,6,7,4,1,3,5]=>100100
[2,6,7,4,1,5,3]=>101100
[2,6,7,4,3,1,5]=>101100
[2,6,7,4,3,5,1]=>101100
[2,6,7,4,5,1,3]=>100100
[2,6,7,4,5,3,1]=>101100
[2,6,7,5,1,3,4]=>100010
[2,6,7,5,1,4,3]=>101010
[2,6,7,5,3,1,4]=>101010
[2,6,7,5,3,4,1]=>101010
[2,6,7,5,4,1,3]=>100110
[2,6,7,5,4,3,1]=>101110
[2,7,1,3,4,5,6]=>100000
[2,7,1,3,4,6,5]=>100010
[2,7,1,3,5,4,6]=>100100
[2,7,1,3,5,6,4]=>100100
[2,7,1,3,6,4,5]=>100100
[2,7,1,3,6,5,4]=>100110
[2,7,1,4,3,5,6]=>101000
[2,7,1,4,3,6,5]=>101010
[2,7,1,4,5,3,6]=>101000
[2,7,1,4,5,6,3]=>101000
[2,7,1,4,6,3,5]=>101000
[2,7,1,4,6,5,3]=>101010
[2,7,1,5,3,4,6]=>101000
[2,7,1,5,3,6,4]=>101100
[2,7,1,5,4,3,6]=>101100
[2,7,1,5,4,6,3]=>101100
[2,7,1,5,6,3,4]=>101000
[2,7,1,5,6,4,3]=>101100
[2,7,1,6,3,4,5]=>101000
[2,7,1,6,3,5,4]=>101100
[2,7,1,6,4,3,5]=>101100
[2,7,1,6,4,5,3]=>101100
[2,7,1,6,5,3,4]=>101010
[2,7,1,6,5,4,3]=>101110
[2,7,3,1,4,5,6]=>101000
[2,7,3,1,4,6,5]=>101010
[2,7,3,1,5,4,6]=>101100
[2,7,3,1,5,6,4]=>101100
[2,7,3,1,6,4,5]=>101100
[2,7,3,1,6,5,4]=>101110
[2,7,3,4,1,5,6]=>101000
[2,7,3,4,1,6,5]=>101010
[2,7,3,4,5,1,6]=>101000
[2,7,3,4,5,6,1]=>101000
[2,7,3,4,6,1,5]=>101000
[2,7,3,4,6,5,1]=>101010
[2,7,3,5,1,4,6]=>101000
[2,7,3,5,1,6,4]=>101100
[2,7,3,5,4,1,6]=>101100
[2,7,3,5,4,6,1]=>101100
[2,7,3,5,6,1,4]=>101000
[2,7,3,5,6,4,1]=>101100
[2,7,3,6,1,4,5]=>101000
[2,7,3,6,1,5,4]=>101100
[2,7,3,6,4,1,5]=>101100
[2,7,3,6,4,5,1]=>101100
[2,7,3,6,5,1,4]=>101010
[2,7,3,6,5,4,1]=>101110
[2,7,4,1,3,5,6]=>100100
[2,7,4,1,3,6,5]=>100110
[2,7,4,1,5,3,6]=>101100
[2,7,4,1,5,6,3]=>101100
[2,7,4,1,6,3,5]=>101100
[2,7,4,1,6,5,3]=>101110
[2,7,4,3,1,5,6]=>101100
[2,7,4,3,1,6,5]=>101110
[2,7,4,3,5,1,6]=>101100
[2,7,4,3,5,6,1]=>101100
[2,7,4,3,6,1,5]=>101100
[2,7,4,3,6,5,1]=>101110
[2,7,4,5,1,3,6]=>100100
[2,7,4,5,1,6,3]=>101100
[2,7,4,5,3,1,6]=>101100
[2,7,4,5,3,6,1]=>101100
[2,7,4,5,6,1,3]=>100100
[2,7,4,5,6,3,1]=>101100
[2,7,4,6,1,3,5]=>100100
[2,7,4,6,1,5,3]=>101100
[2,7,4,6,3,1,5]=>101100
[2,7,4,6,3,5,1]=>101100
[2,7,4,6,5,1,3]=>100110
[2,7,4,6,5,3,1]=>101110
[2,7,5,1,3,4,6]=>100010
[2,7,5,1,3,6,4]=>100110
[2,7,5,1,4,3,6]=>101010
[2,7,5,1,4,6,3]=>101010
[2,7,5,1,6,3,4]=>101010
[2,7,5,1,6,4,3]=>101110
[2,7,5,3,1,4,6]=>101010
[2,7,5,3,1,6,4]=>101110
[2,7,5,3,4,1,6]=>101010
[2,7,5,3,4,6,1]=>101010
[2,7,5,3,6,1,4]=>101010
[2,7,5,3,6,4,1]=>101110
[2,7,5,4,1,3,6]=>100110
[2,7,5,4,1,6,3]=>101110
[2,7,5,4,3,1,6]=>101110
[2,7,5,4,3,6,1]=>101110
[2,7,5,4,6,1,3]=>100110
[2,7,5,4,6,3,1]=>101110
[2,7,5,6,1,3,4]=>100010
[2,7,5,6,1,4,3]=>101010
[2,7,5,6,3,1,4]=>101010
[2,7,5,6,3,4,1]=>101010
[2,7,5,6,4,1,3]=>100110
[2,7,5,6,4,3,1]=>101110
[2,7,6,1,3,4,5]=>100001
[2,7,6,1,3,5,4]=>100101
[2,7,6,1,4,3,5]=>101001
[2,7,6,1,4,5,3]=>101001
[2,7,6,1,5,3,4]=>101001
[2,7,6,1,5,4,3]=>101101
[2,7,6,3,1,4,5]=>101001
[2,7,6,3,1,5,4]=>101101
[2,7,6,3,4,1,5]=>101001
[2,7,6,3,4,5,1]=>101001
[2,7,6,3,5,1,4]=>101001
[2,7,6,3,5,4,1]=>101101
[2,7,6,4,1,3,5]=>100101
[2,7,6,4,1,5,3]=>101101
[2,7,6,4,3,1,5]=>101101
[2,7,6,4,3,5,1]=>101101
[2,7,6,4,5,1,3]=>100101
[2,7,6,4,5,3,1]=>101101
[2,7,6,5,1,3,4]=>100011
[2,7,6,5,1,4,3]=>101011
[2,7,6,5,3,1,4]=>101011
[2,7,6,5,3,4,1]=>101011
[2,7,6,5,4,1,3]=>100111
[2,7,6,5,4,3,1]=>101111
[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]=>100010
[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]=>100100
[3,1,2,5,6,7,4]=>100100
[3,1,2,5,7,4,6]=>100100
[3,1,2,5,7,6,4]=>100101
[3,1,2,6,4,5,7]=>100100
[3,1,2,6,4,7,5]=>100110
[3,1,2,6,5,4,7]=>100110
[3,1,2,6,5,7,4]=>100110
[3,1,2,6,7,4,5]=>100100
[3,1,2,6,7,5,4]=>100110
[3,1,2,7,4,5,6]=>100100
[3,1,2,7,4,6,5]=>100110
[3,1,2,7,5,4,6]=>100110
[3,1,2,7,5,6,4]=>100110
[3,1,2,7,6,4,5]=>100101
[3,1,2,7,6,5,4]=>100111
[3,1,4,2,5,6,7]=>110000
[3,1,4,2,5,7,6]=>110001
[3,1,4,2,6,5,7]=>110010
[3,1,4,2,6,7,5]=>110010
[3,1,4,2,7,5,6]=>110010
[3,1,4,2,7,6,5]=>110011
[3,1,4,5,2,6,7]=>110000
[3,1,4,5,2,7,6]=>110001
[3,1,4,5,6,2,7]=>110000
[3,1,4,5,6,7,2]=>110000
[3,1,4,5,7,2,6]=>110000
[3,1,4,5,7,6,2]=>110001
[3,1,4,6,2,5,7]=>110000
[3,1,4,6,2,7,5]=>110010
[3,1,4,6,5,2,7]=>110010
[3,1,4,6,5,7,2]=>110010
[3,1,4,6,7,2,5]=>110000
[3,1,4,6,7,5,2]=>110010
[3,1,4,7,2,5,6]=>110000
[3,1,4,7,2,6,5]=>110010
[3,1,4,7,5,2,6]=>110010
[3,1,4,7,5,6,2]=>110010
[3,1,4,7,6,2,5]=>110001
[3,1,4,7,6,5,2]=>110011
[3,1,5,2,4,6,7]=>110000
[3,1,5,2,4,7,6]=>110001
[3,1,5,2,6,4,7]=>110100
[3,1,5,2,6,7,4]=>110100
[3,1,5,2,7,4,6]=>110100
[3,1,5,2,7,6,4]=>110101
[3,1,5,4,2,6,7]=>110100
[3,1,5,4,2,7,6]=>110101
[3,1,5,4,6,2,7]=>110100
[3,1,5,4,6,7,2]=>110100
[3,1,5,4,7,2,6]=>110100
[3,1,5,4,7,6,2]=>110101
[3,1,5,6,2,4,7]=>110000
[3,1,5,6,2,7,4]=>110100
[3,1,5,6,4,2,7]=>110100
[3,1,5,6,4,7,2]=>110100
[3,1,5,6,7,2,4]=>110000
[3,1,5,6,7,4,2]=>110100
[3,1,5,7,2,4,6]=>110000
[3,1,5,7,2,6,4]=>110100
[3,1,5,7,4,2,6]=>110100
[3,1,5,7,4,6,2]=>110100
[3,1,5,7,6,2,4]=>110001
[3,1,5,7,6,4,2]=>110101
[3,1,6,2,4,5,7]=>110000
[3,1,6,2,4,7,5]=>110010
[3,1,6,2,5,4,7]=>110100
[3,1,6,2,5,7,4]=>110100
[3,1,6,2,7,4,5]=>110100
[3,1,6,2,7,5,4]=>110110
[3,1,6,4,2,5,7]=>110100
[3,1,6,4,2,7,5]=>110110
[3,1,6,4,5,2,7]=>110100
[3,1,6,4,5,7,2]=>110100
[3,1,6,4,7,2,5]=>110100
[3,1,6,4,7,5,2]=>110110
[3,1,6,5,2,4,7]=>110010
[3,1,6,5,2,7,4]=>110110
[3,1,6,5,4,2,7]=>110110
[3,1,6,5,4,7,2]=>110110
[3,1,6,5,7,2,4]=>110010
[3,1,6,5,7,4,2]=>110110
[3,1,6,7,2,4,5]=>110000
[3,1,6,7,2,5,4]=>110100
[3,1,6,7,4,2,5]=>110100
[3,1,6,7,4,5,2]=>110100
[3,1,6,7,5,2,4]=>110010
[3,1,6,7,5,4,2]=>110110
[3,1,7,2,4,5,6]=>110000
[3,1,7,2,4,6,5]=>110010
[3,1,7,2,5,4,6]=>110100
[3,1,7,2,5,6,4]=>110100
[3,1,7,2,6,4,5]=>110100
[3,1,7,2,6,5,4]=>110110
[3,1,7,4,2,5,6]=>110100
[3,1,7,4,2,6,5]=>110110
[3,1,7,4,5,2,6]=>110100
[3,1,7,4,5,6,2]=>110100
[3,1,7,4,6,2,5]=>110100
[3,1,7,4,6,5,2]=>110110
[3,1,7,5,2,4,6]=>110010
[3,1,7,5,2,6,4]=>110110
[3,1,7,5,4,2,6]=>110110
[3,1,7,5,4,6,2]=>110110
[3,1,7,5,6,2,4]=>110010
[3,1,7,5,6,4,2]=>110110
[3,1,7,6,2,4,5]=>110001
[3,1,7,6,2,5,4]=>110101
[3,1,7,6,4,2,5]=>110101
[3,1,7,6,4,5,2]=>110101
[3,1,7,6,5,2,4]=>110011
[3,1,7,6,5,4,2]=>110111
[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]=>110010
[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]=>110100
[3,2,1,5,6,7,4]=>110100
[3,2,1,5,7,4,6]=>110100
[3,2,1,5,7,6,4]=>110101
[3,2,1,6,4,5,7]=>110100
[3,2,1,6,4,7,5]=>110110
[3,2,1,6,5,4,7]=>110110
[3,2,1,6,5,7,4]=>110110
[3,2,1,6,7,4,5]=>110100
[3,2,1,6,7,5,4]=>110110
[3,2,1,7,4,5,6]=>110100
[3,2,1,7,4,6,5]=>110110
[3,2,1,7,5,4,6]=>110110
[3,2,1,7,5,6,4]=>110110
[3,2,1,7,6,4,5]=>110101
[3,2,1,7,6,5,4]=>110111
[3,2,4,1,5,6,7]=>110000
[3,2,4,1,5,7,6]=>110001
[3,2,4,1,6,5,7]=>110010
[3,2,4,1,6,7,5]=>110010
[3,2,4,1,7,5,6]=>110010
[3,2,4,1,7,6,5]=>110011
[3,2,4,5,1,6,7]=>110000
[3,2,4,5,1,7,6]=>110001
[3,2,4,5,6,1,7]=>110000
[3,2,4,5,6,7,1]=>110000
[3,2,4,5,7,1,6]=>110000
[3,2,4,5,7,6,1]=>110001
[3,2,4,6,1,5,7]=>110000
[3,2,4,6,1,7,5]=>110010
[3,2,4,6,5,1,7]=>110010
[3,2,4,6,5,7,1]=>110010
[3,2,4,6,7,1,5]=>110000
[3,2,4,6,7,5,1]=>110010
[3,2,4,7,1,5,6]=>110000
[3,2,4,7,1,6,5]=>110010
[3,2,4,7,5,1,6]=>110010
[3,2,4,7,5,6,1]=>110010
[3,2,4,7,6,1,5]=>110001
[3,2,4,7,6,5,1]=>110011
[3,2,5,1,4,6,7]=>110000
[3,2,5,1,4,7,6]=>110001
[3,2,5,1,6,4,7]=>110100
[3,2,5,1,6,7,4]=>110100
[3,2,5,1,7,4,6]=>110100
[3,2,5,1,7,6,4]=>110101
[3,2,5,4,1,6,7]=>110100
[3,2,5,4,1,7,6]=>110101
[3,2,5,4,6,1,7]=>110100
[3,2,5,4,6,7,1]=>110100
[3,2,5,4,7,1,6]=>110100
[3,2,5,4,7,6,1]=>110101
[3,2,5,6,1,4,7]=>110000
[3,2,5,6,1,7,4]=>110100
[3,2,5,6,4,1,7]=>110100
[3,2,5,6,4,7,1]=>110100
[3,2,5,6,7,1,4]=>110000
[3,2,5,6,7,4,1]=>110100
[3,2,5,7,1,4,6]=>110000
[3,2,5,7,1,6,4]=>110100
[3,2,5,7,4,1,6]=>110100
[3,2,5,7,4,6,1]=>110100
[3,2,5,7,6,1,4]=>110001
[3,2,5,7,6,4,1]=>110101
[3,2,6,1,4,5,7]=>110000
[3,2,6,1,4,7,5]=>110010
[3,2,6,1,5,4,7]=>110100
[3,2,6,1,5,7,4]=>110100
[3,2,6,1,7,4,5]=>110100
[3,2,6,1,7,5,4]=>110110
[3,2,6,4,1,5,7]=>110100
[3,2,6,4,1,7,5]=>110110
[3,2,6,4,5,1,7]=>110100
[3,2,6,4,5,7,1]=>110100
[3,2,6,4,7,1,5]=>110100
[3,2,6,4,7,5,1]=>110110
[3,2,6,5,1,4,7]=>110010
[3,2,6,5,1,7,4]=>110110
[3,2,6,5,4,1,7]=>110110
[3,2,6,5,4,7,1]=>110110
[3,2,6,5,7,1,4]=>110010
[3,2,6,5,7,4,1]=>110110
[3,2,6,7,1,4,5]=>110000
[3,2,6,7,1,5,4]=>110100
[3,2,6,7,4,1,5]=>110100
[3,2,6,7,4,5,1]=>110100
[3,2,6,7,5,1,4]=>110010
[3,2,6,7,5,4,1]=>110110
[3,2,7,1,4,5,6]=>110000
[3,2,7,1,4,6,5]=>110010
[3,2,7,1,5,4,6]=>110100
[3,2,7,1,5,6,4]=>110100
[3,2,7,1,6,4,5]=>110100
[3,2,7,1,6,5,4]=>110110
[3,2,7,4,1,5,6]=>110100
[3,2,7,4,1,6,5]=>110110
[3,2,7,4,5,1,6]=>110100
[3,2,7,4,5,6,1]=>110100
[3,2,7,4,6,1,5]=>110100
[3,2,7,4,6,5,1]=>110110
[3,2,7,5,1,4,6]=>110010
[3,2,7,5,1,6,4]=>110110
[3,2,7,5,4,1,6]=>110110
[3,2,7,5,4,6,1]=>110110
[3,2,7,5,6,1,4]=>110010
[3,2,7,5,6,4,1]=>110110
[3,2,7,6,1,4,5]=>110001
[3,2,7,6,1,5,4]=>110101
[3,2,7,6,4,1,5]=>110101
[3,2,7,6,4,5,1]=>110101
[3,2,7,6,5,1,4]=>110011
[3,2,7,6,5,4,1]=>110111
[3,4,1,2,5,6,7]=>100000
[3,4,1,2,5,7,6]=>100001
[3,4,1,2,6,5,7]=>100010
[3,4,1,2,6,7,5]=>100010
[3,4,1,2,7,5,6]=>100010
[3,4,1,2,7,6,5]=>100011
[3,4,1,5,2,6,7]=>110000
[3,4,1,5,2,7,6]=>110001
[3,4,1,5,6,2,7]=>110000
[3,4,1,5,6,7,2]=>110000
[3,4,1,5,7,2,6]=>110000
[3,4,1,5,7,6,2]=>110001
[3,4,1,6,2,5,7]=>110000
[3,4,1,6,2,7,5]=>110010
[3,4,1,6,5,2,7]=>110010
[3,4,1,6,5,7,2]=>110010
[3,4,1,6,7,2,5]=>110000
[3,4,1,6,7,5,2]=>110010
[3,4,1,7,2,5,6]=>110000
[3,4,1,7,2,6,5]=>110010
[3,4,1,7,5,2,6]=>110010
[3,4,1,7,5,6,2]=>110010
[3,4,1,7,6,2,5]=>110001
[3,4,1,7,6,5,2]=>110011
[3,4,2,1,5,6,7]=>110000
[3,4,2,1,5,7,6]=>110001
[3,4,2,1,6,5,7]=>110010
[3,4,2,1,6,7,5]=>110010
[3,4,2,1,7,5,6]=>110010
[3,4,2,1,7,6,5]=>110011
[3,4,2,5,1,6,7]=>110000
[3,4,2,5,1,7,6]=>110001
[3,4,2,5,6,1,7]=>110000
[3,4,2,5,6,7,1]=>110000
[3,4,2,5,7,1,6]=>110000
[3,4,2,5,7,6,1]=>110001
[3,4,2,6,1,5,7]=>110000
[3,4,2,6,1,7,5]=>110010
[3,4,2,6,5,1,7]=>110010
[3,4,2,6,5,7,1]=>110010
[3,4,2,6,7,1,5]=>110000
[3,4,2,6,7,5,1]=>110010
[3,4,2,7,1,5,6]=>110000
[3,4,2,7,1,6,5]=>110010
[3,4,2,7,5,1,6]=>110010
[3,4,2,7,5,6,1]=>110010
[3,4,2,7,6,1,5]=>110001
[3,4,2,7,6,5,1]=>110011
[3,4,5,1,2,6,7]=>100000
[3,4,5,1,2,7,6]=>100001
[3,4,5,1,6,2,7]=>110000
[3,4,5,1,6,7,2]=>110000
[3,4,5,1,7,2,6]=>110000
[3,4,5,1,7,6,2]=>110001
[3,4,5,2,1,6,7]=>110000
[3,4,5,2,1,7,6]=>110001
[3,4,5,2,6,1,7]=>110000
[3,4,5,2,6,7,1]=>110000
[3,4,5,2,7,1,6]=>110000
[3,4,5,2,7,6,1]=>110001
[3,4,5,6,1,2,7]=>100000
[3,4,5,6,1,7,2]=>110000
[3,4,5,6,2,1,7]=>110000
[3,4,5,6,2,7,1]=>110000
[3,4,5,6,7,1,2]=>100000
[3,4,5,6,7,2,1]=>110000
[3,4,5,7,1,2,6]=>100000
[3,4,5,7,1,6,2]=>110000
[3,4,5,7,2,1,6]=>110000
[3,4,5,7,2,6,1]=>110000
[3,4,5,7,6,1,2]=>100001
[3,4,5,7,6,2,1]=>110001
[3,4,6,1,2,5,7]=>100000
[3,4,6,1,2,7,5]=>100010
[3,4,6,1,5,2,7]=>110000
[3,4,6,1,5,7,2]=>110000
[3,4,6,1,7,2,5]=>110000
[3,4,6,1,7,5,2]=>110010
[3,4,6,2,1,5,7]=>110000
[3,4,6,2,1,7,5]=>110010
[3,4,6,2,5,1,7]=>110000
[3,4,6,2,5,7,1]=>110000
[3,4,6,2,7,1,5]=>110000
[3,4,6,2,7,5,1]=>110010
[3,4,6,5,1,2,7]=>100010
[3,4,6,5,1,7,2]=>110010
[3,4,6,5,2,1,7]=>110010
[3,4,6,5,2,7,1]=>110010
[3,4,6,5,7,1,2]=>100010
[3,4,6,5,7,2,1]=>110010
[3,4,6,7,1,2,5]=>100000
[3,4,6,7,1,5,2]=>110000
[3,4,6,7,2,1,5]=>110000
[3,4,6,7,2,5,1]=>110000
[3,4,6,7,5,1,2]=>100010
[3,4,6,7,5,2,1]=>110010
[3,4,7,1,2,5,6]=>100000
[3,4,7,1,2,6,5]=>100010
[3,4,7,1,5,2,6]=>110000
[3,4,7,1,5,6,2]=>110000
[3,4,7,1,6,2,5]=>110000
[3,4,7,1,6,5,2]=>110010
[3,4,7,2,1,5,6]=>110000
[3,4,7,2,1,6,5]=>110010
[3,4,7,2,5,1,6]=>110000
[3,4,7,2,5,6,1]=>110000
[3,4,7,2,6,1,5]=>110000
[3,4,7,2,6,5,1]=>110010
[3,4,7,5,1,2,6]=>100010
[3,4,7,5,1,6,2]=>110010
[3,4,7,5,2,1,6]=>110010
[3,4,7,5,2,6,1]=>110010
[3,4,7,5,6,1,2]=>100010
[3,4,7,5,6,2,1]=>110010
[3,4,7,6,1,2,5]=>100001
[3,4,7,6,1,5,2]=>110001
[3,4,7,6,2,1,5]=>110001
[3,4,7,6,2,5,1]=>110001
[3,4,7,6,5,1,2]=>100011
[3,4,7,6,5,2,1]=>110011
[3,5,1,2,4,6,7]=>100000
[3,5,1,2,4,7,6]=>100001
[3,5,1,2,6,4,7]=>100100
[3,5,1,2,6,7,4]=>100100
[3,5,1,2,7,4,6]=>100100
[3,5,1,2,7,6,4]=>100101
[3,5,1,4,2,6,7]=>110000
[3,5,1,4,2,7,6]=>110001
[3,5,1,4,6,2,7]=>110000
[3,5,1,4,6,7,2]=>110000
[3,5,1,4,7,2,6]=>110000
[3,5,1,4,7,6,2]=>110001
[3,5,1,6,2,4,7]=>110000
[3,5,1,6,2,7,4]=>110100
[3,5,1,6,4,2,7]=>110100
[3,5,1,6,4,7,2]=>110100
[3,5,1,6,7,2,4]=>110000
[3,5,1,6,7,4,2]=>110100
[3,5,1,7,2,4,6]=>110000
[3,5,1,7,2,6,4]=>110100
[3,5,1,7,4,2,6]=>110100
[3,5,1,7,4,6,2]=>110100
[3,5,1,7,6,2,4]=>110001
[3,5,1,7,6,4,2]=>110101
[3,5,2,1,4,6,7]=>110000
[3,5,2,1,4,7,6]=>110001
[3,5,2,1,6,4,7]=>110100
[3,5,2,1,6,7,4]=>110100
[3,5,2,1,7,4,6]=>110100
[3,5,2,1,7,6,4]=>110101
[3,5,2,4,1,6,7]=>110000
[3,5,2,4,1,7,6]=>110001
[3,5,2,4,6,1,7]=>110000
[3,5,2,4,6,7,1]=>110000
[3,5,2,4,7,1,6]=>110000
[3,5,2,4,7,6,1]=>110001
[3,5,2,6,1,4,7]=>110000
[3,5,2,6,1,7,4]=>110100
[3,5,2,6,4,1,7]=>110100
[3,5,2,6,4,7,1]=>110100
[3,5,2,6,7,1,4]=>110000
[3,5,2,6,7,4,1]=>110100
[3,5,2,7,1,4,6]=>110000
[3,5,2,7,1,6,4]=>110100
[3,5,2,7,4,1,6]=>110100
[3,5,2,7,4,6,1]=>110100
[3,5,2,7,6,1,4]=>110001
[3,5,2,7,6,4,1]=>110101
[3,5,4,1,2,6,7]=>100100
[3,5,4,1,2,7,6]=>100101
[3,5,4,1,6,2,7]=>110100
[3,5,4,1,6,7,2]=>110100
[3,5,4,1,7,2,6]=>110100
[3,5,4,1,7,6,2]=>110101
[3,5,4,2,1,6,7]=>110100
[3,5,4,2,1,7,6]=>110101
[3,5,4,2,6,1,7]=>110100
[3,5,4,2,6,7,1]=>110100
[3,5,4,2,7,1,6]=>110100
[3,5,4,2,7,6,1]=>110101
[3,5,4,6,1,2,7]=>100100
[3,5,4,6,1,7,2]=>110100
[3,5,4,6,2,1,7]=>110100
[3,5,4,6,2,7,1]=>110100
[3,5,4,6,7,1,2]=>100100
[3,5,4,6,7,2,1]=>110100
[3,5,4,7,1,2,6]=>100100
[3,5,4,7,1,6,2]=>110100
[3,5,4,7,2,1,6]=>110100
[3,5,4,7,2,6,1]=>110100
[3,5,4,7,6,1,2]=>100101
[3,5,4,7,6,2,1]=>110101
[3,5,6,1,2,4,7]=>100000
[3,5,6,1,2,7,4]=>100100
[3,5,6,1,4,2,7]=>110000
[3,5,6,1,4,7,2]=>110000
[3,5,6,1,7,2,4]=>110000
[3,5,6,1,7,4,2]=>110100
[3,5,6,2,1,4,7]=>110000
[3,5,6,2,1,7,4]=>110100
[3,5,6,2,4,1,7]=>110000
[3,5,6,2,4,7,1]=>110000
[3,5,6,2,7,1,4]=>110000
[3,5,6,2,7,4,1]=>110100
[3,5,6,4,1,2,7]=>100100
[3,5,6,4,1,7,2]=>110100
[3,5,6,4,2,1,7]=>110100
[3,5,6,4,2,7,1]=>110100
[3,5,6,4,7,1,2]=>100100
[3,5,6,4,7,2,1]=>110100
[3,5,6,7,1,2,4]=>100000
[3,5,6,7,1,4,2]=>110000
[3,5,6,7,2,1,4]=>110000
[3,5,6,7,2,4,1]=>110000
[3,5,6,7,4,1,2]=>100100
[3,5,6,7,4,2,1]=>110100
[3,5,7,1,2,4,6]=>100000
[3,5,7,1,2,6,4]=>100100
[3,5,7,1,4,2,6]=>110000
[3,5,7,1,4,6,2]=>110000
[3,5,7,1,6,2,4]=>110000
[3,5,7,1,6,4,2]=>110100
[3,5,7,2,1,4,6]=>110000
[3,5,7,2,1,6,4]=>110100
[3,5,7,2,4,1,6]=>110000
[3,5,7,2,4,6,1]=>110000
[3,5,7,2,6,1,4]=>110000
[3,5,7,2,6,4,1]=>110100
[3,5,7,4,1,2,6]=>100100
[3,5,7,4,1,6,2]=>110100
[3,5,7,4,2,1,6]=>110100
[3,5,7,4,2,6,1]=>110100
[3,5,7,4,6,1,2]=>100100
[3,5,7,4,6,2,1]=>110100
[3,5,7,6,1,2,4]=>100001
[3,5,7,6,1,4,2]=>110001
[3,5,7,6,2,1,4]=>110001
[3,5,7,6,2,4,1]=>110001
[3,5,7,6,4,1,2]=>100101
[3,5,7,6,4,2,1]=>110101
[3,6,1,2,4,5,7]=>100000
[3,6,1,2,4,7,5]=>100010
[3,6,1,2,5,4,7]=>100100
[3,6,1,2,5,7,4]=>100100
[3,6,1,2,7,4,5]=>100100
[3,6,1,2,7,5,4]=>100110
[3,6,1,4,2,5,7]=>110000
[3,6,1,4,2,7,5]=>110010
[3,6,1,4,5,2,7]=>110000
[3,6,1,4,5,7,2]=>110000
[3,6,1,4,7,2,5]=>110000
[3,6,1,4,7,5,2]=>110010
[3,6,1,5,2,4,7]=>110000
[3,6,1,5,2,7,4]=>110100
[3,6,1,5,4,2,7]=>110100
[3,6,1,5,4,7,2]=>110100
[3,6,1,5,7,2,4]=>110000
[3,6,1,5,7,4,2]=>110100
[3,6,1,7,2,4,5]=>110000
[3,6,1,7,2,5,4]=>110100
[3,6,1,7,4,2,5]=>110100
[3,6,1,7,4,5,2]=>110100
[3,6,1,7,5,2,4]=>110010
[3,6,1,7,5,4,2]=>110110
[3,6,2,1,4,5,7]=>110000
[3,6,2,1,4,7,5]=>110010
[3,6,2,1,5,4,7]=>110100
[3,6,2,1,5,7,4]=>110100
[3,6,2,1,7,4,5]=>110100
[3,6,2,1,7,5,4]=>110110
[3,6,2,4,1,5,7]=>110000
[3,6,2,4,1,7,5]=>110010
[3,6,2,4,5,1,7]=>110000
[3,6,2,4,5,7,1]=>110000
[3,6,2,4,7,1,5]=>110000
[3,6,2,4,7,5,1]=>110010
[3,6,2,5,1,4,7]=>110000
[3,6,2,5,1,7,4]=>110100
[3,6,2,5,4,1,7]=>110100
[3,6,2,5,4,7,1]=>110100
[3,6,2,5,7,1,4]=>110000
[3,6,2,5,7,4,1]=>110100
[3,6,2,7,1,4,5]=>110000
[3,6,2,7,1,5,4]=>110100
[3,6,2,7,4,1,5]=>110100
[3,6,2,7,4,5,1]=>110100
[3,6,2,7,5,1,4]=>110010
[3,6,2,7,5,4,1]=>110110
[3,6,4,1,2,5,7]=>100100
[3,6,4,1,2,7,5]=>100110
[3,6,4,1,5,2,7]=>110100
[3,6,4,1,5,7,2]=>110100
[3,6,4,1,7,2,5]=>110100
[3,6,4,1,7,5,2]=>110110
[3,6,4,2,1,5,7]=>110100
[3,6,4,2,1,7,5]=>110110
[3,6,4,2,5,1,7]=>110100
[3,6,4,2,5,7,1]=>110100
[3,6,4,2,7,1,5]=>110100
[3,6,4,2,7,5,1]=>110110
[3,6,4,5,1,2,7]=>100100
[3,6,4,5,1,7,2]=>110100
[3,6,4,5,2,1,7]=>110100
[3,6,4,5,2,7,1]=>110100
[3,6,4,5,7,1,2]=>100100
[3,6,4,5,7,2,1]=>110100
[3,6,4,7,1,2,5]=>100100
[3,6,4,7,1,5,2]=>110100
[3,6,4,7,2,1,5]=>110100
[3,6,4,7,2,5,1]=>110100
[3,6,4,7,5,1,2]=>100110
[3,6,4,7,5,2,1]=>110110
[3,6,5,1,2,4,7]=>100010
[3,6,5,1,2,7,4]=>100110
[3,6,5,1,4,2,7]=>110010
[3,6,5,1,4,7,2]=>110010
[3,6,5,1,7,2,4]=>110010
[3,6,5,1,7,4,2]=>110110
[3,6,5,2,1,4,7]=>110010
[3,6,5,2,1,7,4]=>110110
[3,6,5,2,4,1,7]=>110010
[3,6,5,2,4,7,1]=>110010
[3,6,5,2,7,1,4]=>110010
[3,6,5,2,7,4,1]=>110110
[3,6,5,4,1,2,7]=>100110
[3,6,5,4,1,7,2]=>110110
[3,6,5,4,2,1,7]=>110110
[3,6,5,4,2,7,1]=>110110
[3,6,5,4,7,1,2]=>100110
[3,6,5,4,7,2,1]=>110110
[3,6,5,7,1,2,4]=>100010
[3,6,5,7,1,4,2]=>110010
[3,6,5,7,2,1,4]=>110010
[3,6,5,7,2,4,1]=>110010
[3,6,5,7,4,1,2]=>100110
[3,6,5,7,4,2,1]=>110110
[3,6,7,1,2,4,5]=>100000
[3,6,7,1,2,5,4]=>100100
[3,6,7,1,4,2,5]=>110000
[3,6,7,1,4,5,2]=>110000
[3,6,7,1,5,2,4]=>110000
[3,6,7,1,5,4,2]=>110100
[3,6,7,2,1,4,5]=>110000
[3,6,7,2,1,5,4]=>110100
[3,6,7,2,4,1,5]=>110000
[3,6,7,2,4,5,1]=>110000
[3,6,7,2,5,1,4]=>110000
[3,6,7,2,5,4,1]=>110100
[3,6,7,4,1,2,5]=>100100
[3,6,7,4,1,5,2]=>110100
[3,6,7,4,2,1,5]=>110100
[3,6,7,4,2,5,1]=>110100
[3,6,7,4,5,1,2]=>100100
[3,6,7,4,5,2,1]=>110100
[3,6,7,5,1,2,4]=>100010
[3,6,7,5,1,4,2]=>110010
[3,6,7,5,2,1,4]=>110010
[3,6,7,5,2,4,1]=>110010
[3,6,7,5,4,1,2]=>100110
[3,6,7,5,4,2,1]=>110110
[3,7,1,2,4,5,6]=>100000
[3,7,1,2,4,6,5]=>100010
[3,7,1,2,5,4,6]=>100100
[3,7,1,2,5,6,4]=>100100
[3,7,1,2,6,4,5]=>100100
[3,7,1,2,6,5,4]=>100110
[3,7,1,4,2,5,6]=>110000
[3,7,1,4,2,6,5]=>110010
[3,7,1,4,5,2,6]=>110000
[3,7,1,4,5,6,2]=>110000
[3,7,1,4,6,2,5]=>110000
[3,7,1,4,6,5,2]=>110010
[3,7,1,5,2,4,6]=>110000
[3,7,1,5,2,6,4]=>110100
[3,7,1,5,4,2,6]=>110100
[3,7,1,5,4,6,2]=>110100
[3,7,1,5,6,2,4]=>110000
[3,7,1,5,6,4,2]=>110100
[3,7,1,6,2,4,5]=>110000
[3,7,1,6,2,5,4]=>110100
[3,7,1,6,4,2,5]=>110100
[3,7,1,6,4,5,2]=>110100
[3,7,1,6,5,2,4]=>110010
[3,7,1,6,5,4,2]=>110110
[3,7,2,1,4,5,6]=>110000
[3,7,2,1,4,6,5]=>110010
[3,7,2,1,5,4,6]=>110100
[3,7,2,1,5,6,4]=>110100
[3,7,2,1,6,4,5]=>110100
[3,7,2,1,6,5,4]=>110110
[3,7,2,4,1,5,6]=>110000
[3,7,2,4,1,6,5]=>110010
[3,7,2,4,5,1,6]=>110000
[3,7,2,4,5,6,1]=>110000
[3,7,2,4,6,1,5]=>110000
[3,7,2,4,6,5,1]=>110010
[3,7,2,5,1,4,6]=>110000
[3,7,2,5,1,6,4]=>110100
[3,7,2,5,4,1,6]=>110100
[3,7,2,5,4,6,1]=>110100
[3,7,2,5,6,1,4]=>110000
[3,7,2,5,6,4,1]=>110100
[3,7,2,6,1,4,5]=>110000
[3,7,2,6,1,5,4]=>110100
[3,7,2,6,4,1,5]=>110100
[3,7,2,6,4,5,1]=>110100
[3,7,2,6,5,1,4]=>110010
[3,7,2,6,5,4,1]=>110110
[3,7,4,1,2,5,6]=>100100
[3,7,4,1,2,6,5]=>100110
[3,7,4,1,5,2,6]=>110100
[3,7,4,1,5,6,2]=>110100
[3,7,4,1,6,2,5]=>110100
[3,7,4,1,6,5,2]=>110110
[3,7,4,2,1,5,6]=>110100
[3,7,4,2,1,6,5]=>110110
[3,7,4,2,5,1,6]=>110100
[3,7,4,2,5,6,1]=>110100
[3,7,4,2,6,1,5]=>110100
[3,7,4,2,6,5,1]=>110110
[3,7,4,5,1,2,6]=>100100
[3,7,4,5,1,6,2]=>110100
[3,7,4,5,2,1,6]=>110100
[3,7,4,5,2,6,1]=>110100
[3,7,4,5,6,1,2]=>100100
[3,7,4,5,6,2,1]=>110100
[3,7,4,6,1,2,5]=>100100
[3,7,4,6,1,5,2]=>110100
[3,7,4,6,2,1,5]=>110100
[3,7,4,6,2,5,1]=>110100
[3,7,4,6,5,1,2]=>100110
[3,7,4,6,5,2,1]=>110110
[3,7,5,1,2,4,6]=>100010
[3,7,5,1,2,6,4]=>100110
[3,7,5,1,4,2,6]=>110010
[3,7,5,1,4,6,2]=>110010
[3,7,5,1,6,2,4]=>110010
[3,7,5,1,6,4,2]=>110110
[3,7,5,2,1,4,6]=>110010
[3,7,5,2,1,6,4]=>110110
[3,7,5,2,4,1,6]=>110010
[3,7,5,2,4,6,1]=>110010
[3,7,5,2,6,1,4]=>110010
[3,7,5,2,6,4,1]=>110110
[3,7,5,4,1,2,6]=>100110
[3,7,5,4,1,6,2]=>110110
[3,7,5,4,2,1,6]=>110110
[3,7,5,4,2,6,1]=>110110
[3,7,5,4,6,1,2]=>100110
[3,7,5,4,6,2,1]=>110110
[3,7,5,6,1,2,4]=>100010
[3,7,5,6,1,4,2]=>110010
[3,7,5,6,2,1,4]=>110010
[3,7,5,6,2,4,1]=>110010
[3,7,5,6,4,1,2]=>100110
[3,7,5,6,4,2,1]=>110110
[3,7,6,1,2,4,5]=>100001
[3,7,6,1,2,5,4]=>100101
[3,7,6,1,4,2,5]=>110001
[3,7,6,1,4,5,2]=>110001
[3,7,6,1,5,2,4]=>110001
[3,7,6,1,5,4,2]=>110101
[3,7,6,2,1,4,5]=>110001
[3,7,6,2,1,5,4]=>110101
[3,7,6,2,4,1,5]=>110001
[3,7,6,2,4,5,1]=>110001
[3,7,6,2,5,1,4]=>110001
[3,7,6,2,5,4,1]=>110101
[3,7,6,4,1,2,5]=>100101
[3,7,6,4,1,5,2]=>110101
[3,7,6,4,2,1,5]=>110101
[3,7,6,4,2,5,1]=>110101
[3,7,6,4,5,1,2]=>100101
[3,7,6,4,5,2,1]=>110101
[3,7,6,5,1,2,4]=>100011
[3,7,6,5,1,4,2]=>110011
[3,7,6,5,2,1,4]=>110011
[3,7,6,5,2,4,1]=>110011
[3,7,6,5,4,1,2]=>100111
[3,7,6,5,4,2,1]=>110111
[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]=>100010
[4,1,2,3,7,5,6]=>100010
[4,1,2,3,7,6,5]=>100011
[4,1,2,5,3,6,7]=>101000
[4,1,2,5,3,7,6]=>101001
[4,1,2,5,6,3,7]=>101000
[4,1,2,5,6,7,3]=>101000
[4,1,2,5,7,3,6]=>101000
[4,1,2,5,7,6,3]=>101001
[4,1,2,6,3,5,7]=>101000
[4,1,2,6,3,7,5]=>101010
[4,1,2,6,5,3,7]=>101010
[4,1,2,6,5,7,3]=>101010
[4,1,2,6,7,3,5]=>101000
[4,1,2,6,7,5,3]=>101010
[4,1,2,7,3,5,6]=>101000
[4,1,2,7,3,6,5]=>101010
[4,1,2,7,5,3,6]=>101010
[4,1,2,7,5,6,3]=>101010
[4,1,2,7,6,3,5]=>101001
[4,1,2,7,6,5,3]=>101011
[4,1,3,2,5,6,7]=>110000
[4,1,3,2,5,7,6]=>110001
[4,1,3,2,6,5,7]=>110010
[4,1,3,2,6,7,5]=>110010
[4,1,3,2,7,5,6]=>110010
[4,1,3,2,7,6,5]=>110011
[4,1,3,5,2,6,7]=>110000
[4,1,3,5,2,7,6]=>110001
[4,1,3,5,6,2,7]=>110000
[4,1,3,5,6,7,2]=>110000
[4,1,3,5,7,2,6]=>110000
[4,1,3,5,7,6,2]=>110001
[4,1,3,6,2,5,7]=>110000
[4,1,3,6,2,7,5]=>110010
[4,1,3,6,5,2,7]=>110010
[4,1,3,6,5,7,2]=>110010
[4,1,3,6,7,2,5]=>110000
[4,1,3,6,7,5,2]=>110010
[4,1,3,7,2,5,6]=>110000
[4,1,3,7,2,6,5]=>110010
[4,1,3,7,5,2,6]=>110010
[4,1,3,7,5,6,2]=>110010
[4,1,3,7,6,2,5]=>110001
[4,1,3,7,6,5,2]=>110011
[4,1,5,2,3,6,7]=>110000
[4,1,5,2,3,7,6]=>110001
[4,1,5,2,6,3,7]=>111000
[4,1,5,2,6,7,3]=>111000
[4,1,5,2,7,3,6]=>111000
[4,1,5,2,7,6,3]=>111001
[4,1,5,3,2,6,7]=>111000
[4,1,5,3,2,7,6]=>111001
[4,1,5,3,6,2,7]=>111000
[4,1,5,3,6,7,2]=>111000
[4,1,5,3,7,2,6]=>111000
[4,1,5,3,7,6,2]=>111001
[4,1,5,6,2,3,7]=>110000
[4,1,5,6,2,7,3]=>111000
[4,1,5,6,3,2,7]=>111000
[4,1,5,6,3,7,2]=>111000
[4,1,5,6,7,2,3]=>110000
[4,1,5,6,7,3,2]=>111000
[4,1,5,7,2,3,6]=>110000
[4,1,5,7,2,6,3]=>111000
[4,1,5,7,3,2,6]=>111000
[4,1,5,7,3,6,2]=>111000
[4,1,5,7,6,2,3]=>110001
[4,1,5,7,6,3,2]=>111001
[4,1,6,2,3,5,7]=>110000
[4,1,6,2,3,7,5]=>110010
[4,1,6,2,5,3,7]=>111000
[4,1,6,2,5,7,3]=>111000
[4,1,6,2,7,3,5]=>111000
[4,1,6,2,7,5,3]=>111010
[4,1,6,3,2,5,7]=>111000
[4,1,6,3,2,7,5]=>111010
[4,1,6,3,5,2,7]=>111000
[4,1,6,3,5,7,2]=>111000
[4,1,6,3,7,2,5]=>111000
[4,1,6,3,7,5,2]=>111010
[4,1,6,5,2,3,7]=>110010
[4,1,6,5,2,7,3]=>111010
[4,1,6,5,3,2,7]=>111010
[4,1,6,5,3,7,2]=>111010
[4,1,6,5,7,2,3]=>110010
[4,1,6,5,7,3,2]=>111010
[4,1,6,7,2,3,5]=>110000
[4,1,6,7,2,5,3]=>111000
[4,1,6,7,3,2,5]=>111000
[4,1,6,7,3,5,2]=>111000
[4,1,6,7,5,2,3]=>110010
[4,1,6,7,5,3,2]=>111010
[4,1,7,2,3,5,6]=>110000
[4,1,7,2,3,6,5]=>110010
[4,1,7,2,5,3,6]=>111000
[4,1,7,2,5,6,3]=>111000
[4,1,7,2,6,3,5]=>111000
[4,1,7,2,6,5,3]=>111010
[4,1,7,3,2,5,6]=>111000
[4,1,7,3,2,6,5]=>111010
[4,1,7,3,5,2,6]=>111000
[4,1,7,3,5,6,2]=>111000
[4,1,7,3,6,2,5]=>111000
[4,1,7,3,6,5,2]=>111010
[4,1,7,5,2,3,6]=>110010
[4,1,7,5,2,6,3]=>111010
[4,1,7,5,3,2,6]=>111010
[4,1,7,5,3,6,2]=>111010
[4,1,7,5,6,2,3]=>110010
[4,1,7,5,6,3,2]=>111010
[4,1,7,6,2,3,5]=>110001
[4,1,7,6,2,5,3]=>111001
[4,1,7,6,3,2,5]=>111001
[4,1,7,6,3,5,2]=>111001
[4,1,7,6,5,2,3]=>110011
[4,1,7,6,5,3,2]=>111011
[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]=>110010
[4,2,1,3,7,5,6]=>110010
[4,2,1,3,7,6,5]=>110011
[4,2,1,5,3,6,7]=>111000
[4,2,1,5,3,7,6]=>111001
[4,2,1,5,6,3,7]=>111000
[4,2,1,5,6,7,3]=>111000
[4,2,1,5,7,3,6]=>111000
[4,2,1,5,7,6,3]=>111001
[4,2,1,6,3,5,7]=>111000
[4,2,1,6,3,7,5]=>111010
[4,2,1,6,5,3,7]=>111010
[4,2,1,6,5,7,3]=>111010
[4,2,1,6,7,3,5]=>111000
[4,2,1,6,7,5,3]=>111010
[4,2,1,7,3,5,6]=>111000
[4,2,1,7,3,6,5]=>111010
[4,2,1,7,5,3,6]=>111010
[4,2,1,7,5,6,3]=>111010
[4,2,1,7,6,3,5]=>111001
[4,2,1,7,6,5,3]=>111011
[4,2,3,1,5,6,7]=>110000
[4,2,3,1,5,7,6]=>110001
[4,2,3,1,6,5,7]=>110010
[4,2,3,1,6,7,5]=>110010
[4,2,3,1,7,5,6]=>110010
[4,2,3,1,7,6,5]=>110011
[4,2,3,5,1,6,7]=>110000
[4,2,3,5,1,7,6]=>110001
[4,2,3,5,6,1,7]=>110000
[4,2,3,5,6,7,1]=>110000
[4,2,3,5,7,1,6]=>110000
[4,2,3,5,7,6,1]=>110001
[4,2,3,6,1,5,7]=>110000
[4,2,3,6,1,7,5]=>110010
[4,2,3,6,5,1,7]=>110010
[4,2,3,6,5,7,1]=>110010
[4,2,3,6,7,1,5]=>110000
[4,2,3,6,7,5,1]=>110010
[4,2,3,7,1,5,6]=>110000
[4,2,3,7,1,6,5]=>110010
[4,2,3,7,5,1,6]=>110010
[4,2,3,7,5,6,1]=>110010
[4,2,3,7,6,1,5]=>110001
[4,2,3,7,6,5,1]=>110011
[4,2,5,1,3,6,7]=>110000
[4,2,5,1,3,7,6]=>110001
[4,2,5,1,6,3,7]=>111000
[4,2,5,1,6,7,3]=>111000
[4,2,5,1,7,3,6]=>111000
[4,2,5,1,7,6,3]=>111001
[4,2,5,3,1,6,7]=>111000
[4,2,5,3,1,7,6]=>111001
[4,2,5,3,6,1,7]=>111000
[4,2,5,3,6,7,1]=>111000
[4,2,5,3,7,1,6]=>111000
[4,2,5,3,7,6,1]=>111001
[4,2,5,6,1,3,7]=>110000
[4,2,5,6,1,7,3]=>111000
[4,2,5,6,3,1,7]=>111000
[4,2,5,6,3,7,1]=>111000
[4,2,5,6,7,1,3]=>110000
[4,2,5,6,7,3,1]=>111000
[4,2,5,7,1,3,6]=>110000
[4,2,5,7,1,6,3]=>111000
[4,2,5,7,3,1,6]=>111000
[4,2,5,7,3,6,1]=>111000
[4,2,5,7,6,1,3]=>110001
[4,2,5,7,6,3,1]=>111001
[4,2,6,1,3,5,7]=>110000
[4,2,6,1,3,7,5]=>110010
[4,2,6,1,5,3,7]=>111000
[4,2,6,1,5,7,3]=>111000
[4,2,6,1,7,3,5]=>111000
[4,2,6,1,7,5,3]=>111010
[4,2,6,3,1,5,7]=>111000
[4,2,6,3,1,7,5]=>111010
[4,2,6,3,5,1,7]=>111000
[4,2,6,3,5,7,1]=>111000
[4,2,6,3,7,1,5]=>111000
[4,2,6,3,7,5,1]=>111010
[4,2,6,5,1,3,7]=>110010
[4,2,6,5,1,7,3]=>111010
[4,2,6,5,3,1,7]=>111010
[4,2,6,5,3,7,1]=>111010
[4,2,6,5,7,1,3]=>110010
[4,2,6,5,7,3,1]=>111010
[4,2,6,7,1,3,5]=>110000
[4,2,6,7,1,5,3]=>111000
[4,2,6,7,3,1,5]=>111000
[4,2,6,7,3,5,1]=>111000
[4,2,6,7,5,1,3]=>110010
[4,2,6,7,5,3,1]=>111010
[4,2,7,1,3,5,6]=>110000
[4,2,7,1,3,6,5]=>110010
[4,2,7,1,5,3,6]=>111000
[4,2,7,1,5,6,3]=>111000
[4,2,7,1,6,3,5]=>111000
[4,2,7,1,6,5,3]=>111010
[4,2,7,3,1,5,6]=>111000
[4,2,7,3,1,6,5]=>111010
[4,2,7,3,5,1,6]=>111000
[4,2,7,3,5,6,1]=>111000
[4,2,7,3,6,1,5]=>111000
[4,2,7,3,6,5,1]=>111010
[4,2,7,5,1,3,6]=>110010
[4,2,7,5,1,6,3]=>111010
[4,2,7,5,3,1,6]=>111010
[4,2,7,5,3,6,1]=>111010
[4,2,7,5,6,1,3]=>110010
[4,2,7,5,6,3,1]=>111010
[4,2,7,6,1,3,5]=>110001
[4,2,7,6,1,5,3]=>111001
[4,2,7,6,3,1,5]=>111001
[4,2,7,6,3,5,1]=>111001
[4,2,7,6,5,1,3]=>110011
[4,2,7,6,5,3,1]=>111011
[4,3,1,2,5,6,7]=>101000
[4,3,1,2,5,7,6]=>101001
[4,3,1,2,6,5,7]=>101010
[4,3,1,2,6,7,5]=>101010
[4,3,1,2,7,5,6]=>101010
[4,3,1,2,7,6,5]=>101011
[4,3,1,5,2,6,7]=>111000
[4,3,1,5,2,7,6]=>111001
[4,3,1,5,6,2,7]=>111000
[4,3,1,5,6,7,2]=>111000
[4,3,1,5,7,2,6]=>111000
[4,3,1,5,7,6,2]=>111001
[4,3,1,6,2,5,7]=>111000
[4,3,1,6,2,7,5]=>111010
[4,3,1,6,5,2,7]=>111010
[4,3,1,6,5,7,2]=>111010
[4,3,1,6,7,2,5]=>111000
[4,3,1,6,7,5,2]=>111010
[4,3,1,7,2,5,6]=>111000
[4,3,1,7,2,6,5]=>111010
[4,3,1,7,5,2,6]=>111010
[4,3,1,7,5,6,2]=>111010
[4,3,1,7,6,2,5]=>111001
[4,3,1,7,6,5,2]=>111011
[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]=>111010
[4,3,2,1,7,5,6]=>111010
[4,3,2,1,7,6,5]=>111011
[4,3,2,5,1,6,7]=>111000
[4,3,2,5,1,7,6]=>111001
[4,3,2,5,6,1,7]=>111000
[4,3,2,5,6,7,1]=>111000
[4,3,2,5,7,1,6]=>111000
[4,3,2,5,7,6,1]=>111001
[4,3,2,6,1,5,7]=>111000
[4,3,2,6,1,7,5]=>111010
[4,3,2,6,5,1,7]=>111010
[4,3,2,6,5,7,1]=>111010
[4,3,2,6,7,1,5]=>111000
[4,3,2,6,7,5,1]=>111010
[4,3,2,7,1,5,6]=>111000
[4,3,2,7,1,6,5]=>111010
[4,3,2,7,5,1,6]=>111010
[4,3,2,7,5,6,1]=>111010
[4,3,2,7,6,1,5]=>111001
[4,3,2,7,6,5,1]=>111011
[4,3,5,1,2,6,7]=>101000
[4,3,5,1,2,7,6]=>101001
[4,3,5,1,6,2,7]=>111000
[4,3,5,1,6,7,2]=>111000
[4,3,5,1,7,2,6]=>111000
[4,3,5,1,7,6,2]=>111001
[4,3,5,2,1,6,7]=>111000
[4,3,5,2,1,7,6]=>111001
[4,3,5,2,6,1,7]=>111000
[4,3,5,2,6,7,1]=>111000
[4,3,5,2,7,1,6]=>111000
[4,3,5,2,7,6,1]=>111001
[4,3,5,6,1,2,7]=>101000
[4,3,5,6,1,7,2]=>111000
[4,3,5,6,2,1,7]=>111000
[4,3,5,6,2,7,1]=>111000
[4,3,5,6,7,1,2]=>101000
[4,3,5,6,7,2,1]=>111000
[4,3,5,7,1,2,6]=>101000
[4,3,5,7,1,6,2]=>111000
[4,3,5,7,2,1,6]=>111000
[4,3,5,7,2,6,1]=>111000
[4,3,5,7,6,1,2]=>101001
[4,3,5,7,6,2,1]=>111001
[4,3,6,1,2,5,7]=>101000
[4,3,6,1,2,7,5]=>101010
[4,3,6,1,5,2,7]=>111000
[4,3,6,1,5,7,2]=>111000
[4,3,6,1,7,2,5]=>111000
[4,3,6,1,7,5,2]=>111010
[4,3,6,2,1,5,7]=>111000
[4,3,6,2,1,7,5]=>111010
[4,3,6,2,5,1,7]=>111000
[4,3,6,2,5,7,1]=>111000
[4,3,6,2,7,1,5]=>111000
[4,3,6,2,7,5,1]=>111010
[4,3,6,5,1,2,7]=>101010
[4,3,6,5,1,7,2]=>111010
[4,3,6,5,2,1,7]=>111010
[4,3,6,5,2,7,1]=>111010
[4,3,6,5,7,1,2]=>101010
[4,3,6,5,7,2,1]=>111010
[4,3,6,7,1,2,5]=>101000
[4,3,6,7,1,5,2]=>111000
[4,3,6,7,2,1,5]=>111000
[4,3,6,7,2,5,1]=>111000
[4,3,6,7,5,1,2]=>101010
[4,3,6,7,5,2,1]=>111010
[4,3,7,1,2,5,6]=>101000
[4,3,7,1,2,6,5]=>101010
[4,3,7,1,5,2,6]=>111000
[4,3,7,1,5,6,2]=>111000
[4,3,7,1,6,2,5]=>111000
[4,3,7,1,6,5,2]=>111010
[4,3,7,2,1,5,6]=>111000
[4,3,7,2,1,6,5]=>111010
[4,3,7,2,5,1,6]=>111000
[4,3,7,2,5,6,1]=>111000
[4,3,7,2,6,1,5]=>111000
[4,3,7,2,6,5,1]=>111010
[4,3,7,5,1,2,6]=>101010
[4,3,7,5,1,6,2]=>111010
[4,3,7,5,2,1,6]=>111010
[4,3,7,5,2,6,1]=>111010
[4,3,7,5,6,1,2]=>101010
[4,3,7,5,6,2,1]=>111010
[4,3,7,6,1,2,5]=>101001
[4,3,7,6,1,5,2]=>111001
[4,3,7,6,2,1,5]=>111001
[4,3,7,6,2,5,1]=>111001
[4,3,7,6,5,1,2]=>101011
[4,3,7,6,5,2,1]=>111011
[4,5,1,2,3,6,7]=>100000
[4,5,1,2,3,7,6]=>100001
[4,5,1,2,6,3,7]=>101000
[4,5,1,2,6,7,3]=>101000
[4,5,1,2,7,3,6]=>101000
[4,5,1,2,7,6,3]=>101001
[4,5,1,3,2,6,7]=>110000
[4,5,1,3,2,7,6]=>110001
[4,5,1,3,6,2,7]=>110000
[4,5,1,3,6,7,2]=>110000
[4,5,1,3,7,2,6]=>110000
[4,5,1,3,7,6,2]=>110001
[4,5,1,6,2,3,7]=>110000
[4,5,1,6,2,7,3]=>111000
[4,5,1,6,3,2,7]=>111000
[4,5,1,6,3,7,2]=>111000
[4,5,1,6,7,2,3]=>110000
[4,5,1,6,7,3,2]=>111000
[4,5,1,7,2,3,6]=>110000
[4,5,1,7,2,6,3]=>111000
[4,5,1,7,3,2,6]=>111000
[4,5,1,7,3,6,2]=>111000
[4,5,1,7,6,2,3]=>110001
[4,5,1,7,6,3,2]=>111001
[4,5,2,1,3,6,7]=>110000
[4,5,2,1,3,7,6]=>110001
[4,5,2,1,6,3,7]=>111000
[4,5,2,1,6,7,3]=>111000
[4,5,2,1,7,3,6]=>111000
[4,5,2,1,7,6,3]=>111001
[4,5,2,3,1,6,7]=>110000
[4,5,2,3,1,7,6]=>110001
[4,5,2,3,6,1,7]=>110000
[4,5,2,3,6,7,1]=>110000
[4,5,2,3,7,1,6]=>110000
[4,5,2,3,7,6,1]=>110001
[4,5,2,6,1,3,7]=>110000
[4,5,2,6,1,7,3]=>111000
[4,5,2,6,3,1,7]=>111000
[4,5,2,6,3,7,1]=>111000
[4,5,2,6,7,1,3]=>110000
[4,5,2,6,7,3,1]=>111000
[4,5,2,7,1,3,6]=>110000
[4,5,2,7,1,6,3]=>111000
[4,5,2,7,3,1,6]=>111000
[4,5,2,7,3,6,1]=>111000
[4,5,2,7,6,1,3]=>110001
[4,5,2,7,6,3,1]=>111001
[4,5,3,1,2,6,7]=>101000
[4,5,3,1,2,7,6]=>101001
[4,5,3,1,6,2,7]=>111000
[4,5,3,1,6,7,2]=>111000
[4,5,3,1,7,2,6]=>111000
[4,5,3,1,7,6,2]=>111001
[4,5,3,2,1,6,7]=>111000
[4,5,3,2,1,7,6]=>111001
[4,5,3,2,6,1,7]=>111000
[4,5,3,2,6,7,1]=>111000
[4,5,3,2,7,1,6]=>111000
[4,5,3,2,7,6,1]=>111001
[4,5,3,6,1,2,7]=>101000
[4,5,3,6,1,7,2]=>111000
[4,5,3,6,2,1,7]=>111000
[4,5,3,6,2,7,1]=>111000
[4,5,3,6,7,1,2]=>101000
[4,5,3,6,7,2,1]=>111000
[4,5,3,7,1,2,6]=>101000
[4,5,3,7,1,6,2]=>111000
[4,5,3,7,2,1,6]=>111000
[4,5,3,7,2,6,1]=>111000
[4,5,3,7,6,1,2]=>101001
[4,5,3,7,6,2,1]=>111001
[4,5,6,1,2,3,7]=>100000
[4,5,6,1,2,7,3]=>101000
[4,5,6,1,3,2,7]=>110000
[4,5,6,1,3,7,2]=>110000
[4,5,6,1,7,2,3]=>110000
[4,5,6,1,7,3,2]=>111000
[4,5,6,2,1,3,7]=>110000
[4,5,6,2,1,7,3]=>111000
[4,5,6,2,3,1,7]=>110000
[4,5,6,2,3,7,1]=>110000
[4,5,6,2,7,1,3]=>110000
[4,5,6,2,7,3,1]=>111000
[4,5,6,3,1,2,7]=>101000
[4,5,6,3,1,7,2]=>111000
[4,5,6,3,2,1,7]=>111000
[4,5,6,3,2,7,1]=>111000
[4,5,6,3,7,1,2]=>101000
[4,5,6,3,7,2,1]=>111000
[4,5,6,7,1,2,3]=>100000
[4,5,6,7,1,3,2]=>110000
[4,5,6,7,2,1,3]=>110000
[4,5,6,7,2,3,1]=>110000
[4,5,6,7,3,1,2]=>101000
[4,5,6,7,3,2,1]=>111000
[4,5,7,1,2,3,6]=>100000
[4,5,7,1,2,6,3]=>101000
[4,5,7,1,3,2,6]=>110000
[4,5,7,1,3,6,2]=>110000
[4,5,7,1,6,2,3]=>110000
[4,5,7,1,6,3,2]=>111000
[4,5,7,2,1,3,6]=>110000
[4,5,7,2,1,6,3]=>111000
[4,5,7,2,3,1,6]=>110000
[4,5,7,2,3,6,1]=>110000
[4,5,7,2,6,1,3]=>110000
[4,5,7,2,6,3,1]=>111000
[4,5,7,3,1,2,6]=>101000
[4,5,7,3,1,6,2]=>111000
[4,5,7,3,2,1,6]=>111000
[4,5,7,3,2,6,1]=>111000
[4,5,7,3,6,1,2]=>101000
[4,5,7,3,6,2,1]=>111000
[4,5,7,6,1,2,3]=>100001
[4,5,7,6,1,3,2]=>110001
[4,5,7,6,2,1,3]=>110001
[4,5,7,6,2,3,1]=>110001
[4,5,7,6,3,1,2]=>101001
[4,5,7,6,3,2,1]=>111001
[4,6,1,2,3,5,7]=>100000
[4,6,1,2,3,7,5]=>100010
[4,6,1,2,5,3,7]=>101000
[4,6,1,2,5,7,3]=>101000
[4,6,1,2,7,3,5]=>101000
[4,6,1,2,7,5,3]=>101010
[4,6,1,3,2,5,7]=>110000
[4,6,1,3,2,7,5]=>110010
[4,6,1,3,5,2,7]=>110000
[4,6,1,3,5,7,2]=>110000
[4,6,1,3,7,2,5]=>110000
[4,6,1,3,7,5,2]=>110010
[4,6,1,5,2,3,7]=>110000
[4,6,1,5,2,7,3]=>111000
[4,6,1,5,3,2,7]=>111000
[4,6,1,5,3,7,2]=>111000
[4,6,1,5,7,2,3]=>110000
[4,6,1,5,7,3,2]=>111000
[4,6,1,7,2,3,5]=>110000
[4,6,1,7,2,5,3]=>111000
[4,6,1,7,3,2,5]=>111000
[4,6,1,7,3,5,2]=>111000
[4,6,1,7,5,2,3]=>110010
[4,6,1,7,5,3,2]=>111010
[4,6,2,1,3,5,7]=>110000
[4,6,2,1,3,7,5]=>110010
[4,6,2,1,5,3,7]=>111000
[4,6,2,1,5,7,3]=>111000
[4,6,2,1,7,3,5]=>111000
[4,6,2,1,7,5,3]=>111010
[4,6,2,3,1,5,7]=>110000
[4,6,2,3,1,7,5]=>110010
[4,6,2,3,5,1,7]=>110000
[4,6,2,3,5,7,1]=>110000
[4,6,2,3,7,1,5]=>110000
[4,6,2,3,7,5,1]=>110010
[4,6,2,5,1,3,7]=>110000
[4,6,2,5,1,7,3]=>111000
[4,6,2,5,3,1,7]=>111000
[4,6,2,5,3,7,1]=>111000
[4,6,2,5,7,1,3]=>110000
[4,6,2,5,7,3,1]=>111000
[4,6,2,7,1,3,5]=>110000
[4,6,2,7,1,5,3]=>111000
[4,6,2,7,3,1,5]=>111000
[4,6,2,7,3,5,1]=>111000
[4,6,2,7,5,1,3]=>110010
[4,6,2,7,5,3,1]=>111010
[4,6,3,1,2,5,7]=>101000
[4,6,3,1,2,7,5]=>101010
[4,6,3,1,5,2,7]=>111000
[4,6,3,1,5,7,2]=>111000
[4,6,3,1,7,2,5]=>111000
[4,6,3,1,7,5,2]=>111010
[4,6,3,2,1,5,7]=>111000
[4,6,3,2,1,7,5]=>111010
[4,6,3,2,5,1,7]=>111000
[4,6,3,2,5,7,1]=>111000
[4,6,3,2,7,1,5]=>111000
[4,6,3,2,7,5,1]=>111010
[4,6,3,5,1,2,7]=>101000
[4,6,3,5,1,7,2]=>111000
[4,6,3,5,2,1,7]=>111000
[4,6,3,5,2,7,1]=>111000
[4,6,3,5,7,1,2]=>101000
[4,6,3,5,7,2,1]=>111000
[4,6,3,7,1,2,5]=>101000
[4,6,3,7,1,5,2]=>111000
[4,6,3,7,2,1,5]=>111000
[4,6,3,7,2,5,1]=>111000
[4,6,3,7,5,1,2]=>101010
[4,6,3,7,5,2,1]=>111010
[4,6,5,1,2,3,7]=>100010
[4,6,5,1,2,7,3]=>101010
[4,6,5,1,3,2,7]=>110010
[4,6,5,1,3,7,2]=>110010
[4,6,5,1,7,2,3]=>110010
[4,6,5,1,7,3,2]=>111010
[4,6,5,2,1,3,7]=>110010
[4,6,5,2,1,7,3]=>111010
[4,6,5,2,3,1,7]=>110010
[4,6,5,2,3,7,1]=>110010
[4,6,5,2,7,1,3]=>110010
[4,6,5,2,7,3,1]=>111010
[4,6,5,3,1,2,7]=>101010
[4,6,5,3,1,7,2]=>111010
[4,6,5,3,2,1,7]=>111010
[4,6,5,3,2,7,1]=>111010
[4,6,5,3,7,1,2]=>101010
[4,6,5,3,7,2,1]=>111010
[4,6,5,7,1,2,3]=>100010
[4,6,5,7,1,3,2]=>110010
[4,6,5,7,2,1,3]=>110010
[4,6,5,7,2,3,1]=>110010
[4,6,5,7,3,1,2]=>101010
[4,6,5,7,3,2,1]=>111010
[4,6,7,1,2,3,5]=>100000
[4,6,7,1,2,5,3]=>101000
[4,6,7,1,3,2,5]=>110000
[4,6,7,1,3,5,2]=>110000
[4,6,7,1,5,2,3]=>110000
[4,6,7,1,5,3,2]=>111000
[4,6,7,2,1,3,5]=>110000
[4,6,7,2,1,5,3]=>111000
[4,6,7,2,3,1,5]=>110000
[4,6,7,2,3,5,1]=>110000
[4,6,7,2,5,1,3]=>110000
[4,6,7,2,5,3,1]=>111000
[4,6,7,3,1,2,5]=>101000
[4,6,7,3,1,5,2]=>111000
[4,6,7,3,2,1,5]=>111000
[4,6,7,3,2,5,1]=>111000
[4,6,7,3,5,1,2]=>101000
[4,6,7,3,5,2,1]=>111000
[4,6,7,5,1,2,3]=>100010
[4,6,7,5,1,3,2]=>110010
[4,6,7,5,2,1,3]=>110010
[4,6,7,5,2,3,1]=>110010
[4,6,7,5,3,1,2]=>101010
[4,6,7,5,3,2,1]=>111010
[4,7,1,2,3,5,6]=>100000
[4,7,1,2,3,6,5]=>100010
[4,7,1,2,5,3,6]=>101000
[4,7,1,2,5,6,3]=>101000
[4,7,1,2,6,3,5]=>101000
[4,7,1,2,6,5,3]=>101010
[4,7,1,3,2,5,6]=>110000
[4,7,1,3,2,6,5]=>110010
[4,7,1,3,5,2,6]=>110000
[4,7,1,3,5,6,2]=>110000
[4,7,1,3,6,2,5]=>110000
[4,7,1,3,6,5,2]=>110010
[4,7,1,5,2,3,6]=>110000
[4,7,1,5,2,6,3]=>111000
[4,7,1,5,3,2,6]=>111000
[4,7,1,5,3,6,2]=>111000
[4,7,1,5,6,2,3]=>110000
[4,7,1,5,6,3,2]=>111000
[4,7,1,6,2,3,5]=>110000
[4,7,1,6,2,5,3]=>111000
[4,7,1,6,3,2,5]=>111000
[4,7,1,6,3,5,2]=>111000
[4,7,1,6,5,2,3]=>110010
[4,7,1,6,5,3,2]=>111010
[4,7,2,1,3,5,6]=>110000
[4,7,2,1,3,6,5]=>110010
[4,7,2,1,5,3,6]=>111000
[4,7,2,1,5,6,3]=>111000
[4,7,2,1,6,3,5]=>111000
[4,7,2,1,6,5,3]=>111010
[4,7,2,3,1,5,6]=>110000
[4,7,2,3,1,6,5]=>110010
[4,7,2,3,5,1,6]=>110000
[4,7,2,3,5,6,1]=>110000
[4,7,2,3,6,1,5]=>110000
[4,7,2,3,6,5,1]=>110010
[4,7,2,5,1,3,6]=>110000
[4,7,2,5,1,6,3]=>111000
[4,7,2,5,3,1,6]=>111000
[4,7,2,5,3,6,1]=>111000
[4,7,2,5,6,1,3]=>110000
[4,7,2,5,6,3,1]=>111000
[4,7,2,6,1,3,5]=>110000
[4,7,2,6,1,5,3]=>111000
[4,7,2,6,3,1,5]=>111000
[4,7,2,6,3,5,1]=>111000
[4,7,2,6,5,1,3]=>110010
[4,7,2,6,5,3,1]=>111010
[4,7,3,1,2,5,6]=>101000
[4,7,3,1,2,6,5]=>101010
[4,7,3,1,5,2,6]=>111000
[4,7,3,1,5,6,2]=>111000
[4,7,3,1,6,2,5]=>111000
[4,7,3,1,6,5,2]=>111010
[4,7,3,2,1,5,6]=>111000
[4,7,3,2,1,6,5]=>111010
[4,7,3,2,5,1,6]=>111000
[4,7,3,2,5,6,1]=>111000
[4,7,3,2,6,1,5]=>111000
[4,7,3,2,6,5,1]=>111010
[4,7,3,5,1,2,6]=>101000
[4,7,3,5,1,6,2]=>111000
[4,7,3,5,2,1,6]=>111000
[4,7,3,5,2,6,1]=>111000
[4,7,3,5,6,1,2]=>101000
[4,7,3,5,6,2,1]=>111000
[4,7,3,6,1,2,5]=>101000
[4,7,3,6,1,5,2]=>111000
[4,7,3,6,2,1,5]=>111000
[4,7,3,6,2,5,1]=>111000
[4,7,3,6,5,1,2]=>101010
[4,7,3,6,5,2,1]=>111010
[4,7,5,1,2,3,6]=>100010
[4,7,5,1,2,6,3]=>101010
[4,7,5,1,3,2,6]=>110010
[4,7,5,1,3,6,2]=>110010
[4,7,5,1,6,2,3]=>110010
[4,7,5,1,6,3,2]=>111010
[4,7,5,2,1,3,6]=>110010
[4,7,5,2,1,6,3]=>111010
[4,7,5,2,3,1,6]=>110010
[4,7,5,2,3,6,1]=>110010
[4,7,5,2,6,1,3]=>110010
[4,7,5,2,6,3,1]=>111010
[4,7,5,3,1,2,6]=>101010
[4,7,5,3,1,6,2]=>111010
[4,7,5,3,2,1,6]=>111010
[4,7,5,3,2,6,1]=>111010
[4,7,5,3,6,1,2]=>101010
[4,7,5,3,6,2,1]=>111010
[4,7,5,6,1,2,3]=>100010
[4,7,5,6,1,3,2]=>110010
[4,7,5,6,2,1,3]=>110010
[4,7,5,6,2,3,1]=>110010
[4,7,5,6,3,1,2]=>101010
[4,7,5,6,3,2,1]=>111010
[4,7,6,1,2,3,5]=>100001
[4,7,6,1,2,5,3]=>101001
[4,7,6,1,3,2,5]=>110001
[4,7,6,1,3,5,2]=>110001
[4,7,6,1,5,2,3]=>110001
[4,7,6,1,5,3,2]=>111001
[4,7,6,2,1,3,5]=>110001
[4,7,6,2,1,5,3]=>111001
[4,7,6,2,3,1,5]=>110001
[4,7,6,2,3,5,1]=>110001
[4,7,6,2,5,1,3]=>110001
[4,7,6,2,5,3,1]=>111001
[4,7,6,3,1,2,5]=>101001
[4,7,6,3,1,5,2]=>111001
[4,7,6,3,2,1,5]=>111001
[4,7,6,3,2,5,1]=>111001
[4,7,6,3,5,1,2]=>101001
[4,7,6,3,5,2,1]=>111001
[4,7,6,5,1,2,3]=>100011
[4,7,6,5,1,3,2]=>110011
[4,7,6,5,2,1,3]=>110011
[4,7,6,5,2,3,1]=>110011
[4,7,6,5,3,1,2]=>101011
[4,7,6,5,3,2,1]=>111011
[5,1,2,3,4,6,7]=>100000
[5,1,2,3,4,7,6]=>100001
[5,1,2,3,6,4,7]=>100100
[5,1,2,3,6,7,4]=>100100
[5,1,2,3,7,4,6]=>100100
[5,1,2,3,7,6,4]=>100101
[5,1,2,4,3,6,7]=>101000
[5,1,2,4,3,7,6]=>101001
[5,1,2,4,6,3,7]=>101000
[5,1,2,4,6,7,3]=>101000
[5,1,2,4,7,3,6]=>101000
[5,1,2,4,7,6,3]=>101001
[5,1,2,6,3,4,7]=>101000
[5,1,2,6,3,7,4]=>101100
[5,1,2,6,4,3,7]=>101100
[5,1,2,6,4,7,3]=>101100
[5,1,2,6,7,3,4]=>101000
[5,1,2,6,7,4,3]=>101100
[5,1,2,7,3,4,6]=>101000
[5,1,2,7,3,6,4]=>101100
[5,1,2,7,4,3,6]=>101100
[5,1,2,7,4,6,3]=>101100
[5,1,2,7,6,3,4]=>101001
[5,1,2,7,6,4,3]=>101101
[5,1,3,2,4,6,7]=>110000
[5,1,3,2,4,7,6]=>110001
[5,1,3,2,6,4,7]=>110100
[5,1,3,2,6,7,4]=>110100
[5,1,3,2,7,4,6]=>110100
[5,1,3,2,7,6,4]=>110101
[5,1,3,4,2,6,7]=>110000
[5,1,3,4,2,7,6]=>110001
[5,1,3,4,6,2,7]=>110000
[5,1,3,4,6,7,2]=>110000
[5,1,3,4,7,2,6]=>110000
[5,1,3,4,7,6,2]=>110001
[5,1,3,6,2,4,7]=>110000
[5,1,3,6,2,7,4]=>110100
[5,1,3,6,4,2,7]=>110100
[5,1,3,6,4,7,2]=>110100
[5,1,3,6,7,2,4]=>110000
[5,1,3,6,7,4,2]=>110100
[5,1,3,7,2,4,6]=>110000
[5,1,3,7,2,6,4]=>110100
[5,1,3,7,4,2,6]=>110100
[5,1,3,7,4,6,2]=>110100
[5,1,3,7,6,2,4]=>110001
[5,1,3,7,6,4,2]=>110101
[5,1,4,2,3,6,7]=>110000
[5,1,4,2,3,7,6]=>110001
[5,1,4,2,6,3,7]=>111000
[5,1,4,2,6,7,3]=>111000
[5,1,4,2,7,3,6]=>111000
[5,1,4,2,7,6,3]=>111001
[5,1,4,3,2,6,7]=>111000
[5,1,4,3,2,7,6]=>111001
[5,1,4,3,6,2,7]=>111000
[5,1,4,3,6,7,2]=>111000
[5,1,4,3,7,2,6]=>111000
[5,1,4,3,7,6,2]=>111001
[5,1,4,6,2,3,7]=>110000
[5,1,4,6,2,7,3]=>111000
[5,1,4,6,3,2,7]=>111000
[5,1,4,6,3,7,2]=>111000
[5,1,4,6,7,2,3]=>110000
[5,1,4,6,7,3,2]=>111000
[5,1,4,7,2,3,6]=>110000
[5,1,4,7,2,6,3]=>111000
[5,1,4,7,3,2,6]=>111000
[5,1,4,7,3,6,2]=>111000
[5,1,4,7,6,2,3]=>110001
[5,1,4,7,6,3,2]=>111001
[5,1,6,2,3,4,7]=>110000
[5,1,6,2,3,7,4]=>110100
[5,1,6,2,4,3,7]=>111000
[5,1,6,2,4,7,3]=>111000
[5,1,6,2,7,3,4]=>111000
[5,1,6,2,7,4,3]=>111100
[5,1,6,3,2,4,7]=>111000
[5,1,6,3,2,7,4]=>111100
[5,1,6,3,4,2,7]=>111000
[5,1,6,3,4,7,2]=>111000
[5,1,6,3,7,2,4]=>111000
[5,1,6,3,7,4,2]=>111100
[5,1,6,4,2,3,7]=>110100
[5,1,6,4,2,7,3]=>111100
[5,1,6,4,3,2,7]=>111100
[5,1,6,4,3,7,2]=>111100
[5,1,6,4,7,2,3]=>110100
[5,1,6,4,7,3,2]=>111100
[5,1,6,7,2,3,4]=>110000
[5,1,6,7,2,4,3]=>111000
[5,1,6,7,3,2,4]=>111000
[5,1,6,7,3,4,2]=>111000
[5,1,6,7,4,2,3]=>110100
[5,1,6,7,4,3,2]=>111100
[5,1,7,2,3,4,6]=>110000
[5,1,7,2,3,6,4]=>110100
[5,1,7,2,4,3,6]=>111000
[5,1,7,2,4,6,3]=>111000
[5,1,7,2,6,3,4]=>111000
[5,1,7,2,6,4,3]=>111100
[5,1,7,3,2,4,6]=>111000
[5,1,7,3,2,6,4]=>111100
[5,1,7,3,4,2,6]=>111000
[5,1,7,3,4,6,2]=>111000
[5,1,7,3,6,2,4]=>111000
[5,1,7,3,6,4,2]=>111100
[5,1,7,4,2,3,6]=>110100
[5,1,7,4,2,6,3]=>111100
[5,1,7,4,3,2,6]=>111100
[5,1,7,4,3,6,2]=>111100
[5,1,7,4,6,2,3]=>110100
[5,1,7,4,6,3,2]=>111100
[5,1,7,6,2,3,4]=>110001
[5,1,7,6,2,4,3]=>111001
[5,1,7,6,3,2,4]=>111001
[5,1,7,6,3,4,2]=>111001
[5,1,7,6,4,2,3]=>110101
[5,1,7,6,4,3,2]=>111101
[5,2,1,3,4,6,7]=>110000
[5,2,1,3,4,7,6]=>110001
[5,2,1,3,6,4,7]=>110100
[5,2,1,3,6,7,4]=>110100
[5,2,1,3,7,4,6]=>110100
[5,2,1,3,7,6,4]=>110101
[5,2,1,4,3,6,7]=>111000
[5,2,1,4,3,7,6]=>111001
[5,2,1,4,6,3,7]=>111000
[5,2,1,4,6,7,3]=>111000
[5,2,1,4,7,3,6]=>111000
[5,2,1,4,7,6,3]=>111001
[5,2,1,6,3,4,7]=>111000
[5,2,1,6,3,7,4]=>111100
[5,2,1,6,4,3,7]=>111100
[5,2,1,6,4,7,3]=>111100
[5,2,1,6,7,3,4]=>111000
[5,2,1,6,7,4,3]=>111100
[5,2,1,7,3,4,6]=>111000
[5,2,1,7,3,6,4]=>111100
[5,2,1,7,4,3,6]=>111100
[5,2,1,7,4,6,3]=>111100
[5,2,1,7,6,3,4]=>111001
[5,2,1,7,6,4,3]=>111101
[5,2,3,1,4,6,7]=>110000
[5,2,3,1,4,7,6]=>110001
[5,2,3,1,6,4,7]=>110100
[5,2,3,1,6,7,4]=>110100
[5,2,3,1,7,4,6]=>110100
[5,2,3,1,7,6,4]=>110101
[5,2,3,4,1,6,7]=>110000
[5,2,3,4,1,7,6]=>110001
[5,2,3,4,6,1,7]=>110000
[5,2,3,4,6,7,1]=>110000
[5,2,3,4,7,1,6]=>110000
[5,2,3,4,7,6,1]=>110001
[5,2,3,6,1,4,7]=>110000
[5,2,3,6,1,7,4]=>110100
[5,2,3,6,4,1,7]=>110100
[5,2,3,6,4,7,1]=>110100
[5,2,3,6,7,1,4]=>110000
[5,2,3,6,7,4,1]=>110100
[5,2,3,7,1,4,6]=>110000
[5,2,3,7,1,6,4]=>110100
[5,2,3,7,4,1,6]=>110100
[5,2,3,7,4,6,1]=>110100
[5,2,3,7,6,1,4]=>110001
[5,2,3,7,6,4,1]=>110101
[5,2,4,1,3,6,7]=>110000
[5,2,4,1,3,7,6]=>110001
[5,2,4,1,6,3,7]=>111000
[5,2,4,1,6,7,3]=>111000
[5,2,4,1,7,3,6]=>111000
[5,2,4,1,7,6,3]=>111001
[5,2,4,3,1,6,7]=>111000
[5,2,4,3,1,7,6]=>111001
[5,2,4,3,6,1,7]=>111000
[5,2,4,3,6,7,1]=>111000
[5,2,4,3,7,1,6]=>111000
[5,2,4,3,7,6,1]=>111001
[5,2,4,6,1,3,7]=>110000
[5,2,4,6,1,7,3]=>111000
[5,2,4,6,3,1,7]=>111000
[5,2,4,6,3,7,1]=>111000
[5,2,4,6,7,1,3]=>110000
[5,2,4,6,7,3,1]=>111000
[5,2,4,7,1,3,6]=>110000
[5,2,4,7,1,6,3]=>111000
[5,2,4,7,3,1,6]=>111000
[5,2,4,7,3,6,1]=>111000
[5,2,4,7,6,1,3]=>110001
[5,2,4,7,6,3,1]=>111001
[5,2,6,1,3,4,7]=>110000
[5,2,6,1,3,7,4]=>110100
[5,2,6,1,4,3,7]=>111000
[5,2,6,1,4,7,3]=>111000
[5,2,6,1,7,3,4]=>111000
[5,2,6,1,7,4,3]=>111100
[5,2,6,3,1,4,7]=>111000
[5,2,6,3,1,7,4]=>111100
[5,2,6,3,4,1,7]=>111000
[5,2,6,3,4,7,1]=>111000
[5,2,6,3,7,1,4]=>111000
[5,2,6,3,7,4,1]=>111100
[5,2,6,4,1,3,7]=>110100
[5,2,6,4,1,7,3]=>111100
[5,2,6,4,3,1,7]=>111100
[5,2,6,4,3,7,1]=>111100
[5,2,6,4,7,1,3]=>110100
[5,2,6,4,7,3,1]=>111100
[5,2,6,7,1,3,4]=>110000
[5,2,6,7,1,4,3]=>111000
[5,2,6,7,3,1,4]=>111000
[5,2,6,7,3,4,1]=>111000
[5,2,6,7,4,1,3]=>110100
[5,2,6,7,4,3,1]=>111100
[5,2,7,1,3,4,6]=>110000
[5,2,7,1,3,6,4]=>110100
[5,2,7,1,4,3,6]=>111000
[5,2,7,1,4,6,3]=>111000
[5,2,7,1,6,3,4]=>111000
[5,2,7,1,6,4,3]=>111100
[5,2,7,3,1,4,6]=>111000
[5,2,7,3,1,6,4]=>111100
[5,2,7,3,4,1,6]=>111000
[5,2,7,3,4,6,1]=>111000
[5,2,7,3,6,1,4]=>111000
[5,2,7,3,6,4,1]=>111100
[5,2,7,4,1,3,6]=>110100
[5,2,7,4,1,6,3]=>111100
[5,2,7,4,3,1,6]=>111100
[5,2,7,4,3,6,1]=>111100
[5,2,7,4,6,1,3]=>110100
[5,2,7,4,6,3,1]=>111100
[5,2,7,6,1,3,4]=>110001
[5,2,7,6,1,4,3]=>111001
[5,2,7,6,3,1,4]=>111001
[5,2,7,6,3,4,1]=>111001
[5,2,7,6,4,1,3]=>110101
[5,2,7,6,4,3,1]=>111101
[5,3,1,2,4,6,7]=>101000
[5,3,1,2,4,7,6]=>101001
[5,3,1,2,6,4,7]=>101100
[5,3,1,2,6,7,4]=>101100
[5,3,1,2,7,4,6]=>101100
[5,3,1,2,7,6,4]=>101101
[5,3,1,4,2,6,7]=>111000
[5,3,1,4,2,7,6]=>111001
[5,3,1,4,6,2,7]=>111000
[5,3,1,4,6,7,2]=>111000
[5,3,1,4,7,2,6]=>111000
[5,3,1,4,7,6,2]=>111001
[5,3,1,6,2,4,7]=>111000
[5,3,1,6,2,7,4]=>111100
[5,3,1,6,4,2,7]=>111100
[5,3,1,6,4,7,2]=>111100
[5,3,1,6,7,2,4]=>111000
[5,3,1,6,7,4,2]=>111100
[5,3,1,7,2,4,6]=>111000
[5,3,1,7,2,6,4]=>111100
[5,3,1,7,4,2,6]=>111100
[5,3,1,7,4,6,2]=>111100
[5,3,1,7,6,2,4]=>111001
[5,3,1,7,6,4,2]=>111101
[5,3,2,1,4,6,7]=>111000
[5,3,2,1,4,7,6]=>111001
[5,3,2,1,6,4,7]=>111100
[5,3,2,1,6,7,4]=>111100
[5,3,2,1,7,4,6]=>111100
[5,3,2,1,7,6,4]=>111101
[5,3,2,4,1,6,7]=>111000
[5,3,2,4,1,7,6]=>111001
[5,3,2,4,6,1,7]=>111000
[5,3,2,4,6,7,1]=>111000
[5,3,2,4,7,1,6]=>111000
[5,3,2,4,7,6,1]=>111001
[5,3,2,6,1,4,7]=>111000
[5,3,2,6,1,7,4]=>111100
[5,3,2,6,4,1,7]=>111100
[5,3,2,6,4,7,1]=>111100
[5,3,2,6,7,1,4]=>111000
[5,3,2,6,7,4,1]=>111100
[5,3,2,7,1,4,6]=>111000
[5,3,2,7,1,6,4]=>111100
[5,3,2,7,4,1,6]=>111100
[5,3,2,7,4,6,1]=>111100
[5,3,2,7,6,1,4]=>111001
[5,3,2,7,6,4,1]=>111101
[5,3,4,1,2,6,7]=>101000
[5,3,4,1,2,7,6]=>101001
[5,3,4,1,6,2,7]=>111000
[5,3,4,1,6,7,2]=>111000
[5,3,4,1,7,2,6]=>111000
[5,3,4,1,7,6,2]=>111001
[5,3,4,2,1,6,7]=>111000
[5,3,4,2,1,7,6]=>111001
[5,3,4,2,6,1,7]=>111000
[5,3,4,2,6,7,1]=>111000
[5,3,4,2,7,1,6]=>111000
[5,3,4,2,7,6,1]=>111001
[5,3,4,6,1,2,7]=>101000
[5,3,4,6,1,7,2]=>111000
[5,3,4,6,2,1,7]=>111000
[5,3,4,6,2,7,1]=>111000
[5,3,4,6,7,1,2]=>101000
[5,3,4,6,7,2,1]=>111000
[5,3,4,7,1,2,6]=>101000
[5,3,4,7,1,6,2]=>111000
[5,3,4,7,2,1,6]=>111000
[5,3,4,7,2,6,1]=>111000
[5,3,4,7,6,1,2]=>101001
[5,3,4,7,6,2,1]=>111001
[5,3,6,1,2,4,7]=>101000
[5,3,6,1,2,7,4]=>101100
[5,3,6,1,4,2,7]=>111000
[5,3,6,1,4,7,2]=>111000
[5,3,6,1,7,2,4]=>111000
[5,3,6,1,7,4,2]=>111100
[5,3,6,2,1,4,7]=>111000
[5,3,6,2,1,7,4]=>111100
[5,3,6,2,4,1,7]=>111000
[5,3,6,2,4,7,1]=>111000
[5,3,6,2,7,1,4]=>111000
[5,3,6,2,7,4,1]=>111100
[5,3,6,4,1,2,7]=>101100
[5,3,6,4,1,7,2]=>111100
[5,3,6,4,2,1,7]=>111100
[5,3,6,4,2,7,1]=>111100
[5,3,6,4,7,1,2]=>101100
[5,3,6,4,7,2,1]=>111100
[5,3,6,7,1,2,4]=>101000
[5,3,6,7,1,4,2]=>111000
[5,3,6,7,2,1,4]=>111000
[5,3,6,7,2,4,1]=>111000
[5,3,6,7,4,1,2]=>101100
[5,3,6,7,4,2,1]=>111100
[5,3,7,1,2,4,6]=>101000
[5,3,7,1,2,6,4]=>101100
[5,3,7,1,4,2,6]=>111000
[5,3,7,1,4,6,2]=>111000
[5,3,7,1,6,2,4]=>111000
[5,3,7,1,6,4,2]=>111100
[5,3,7,2,1,4,6]=>111000
[5,3,7,2,1,6,4]=>111100
[5,3,7,2,4,1,6]=>111000
[5,3,7,2,4,6,1]=>111000
[5,3,7,2,6,1,4]=>111000
[5,3,7,2,6,4,1]=>111100
[5,3,7,4,1,2,6]=>101100
[5,3,7,4,1,6,2]=>111100
[5,3,7,4,2,1,6]=>111100
[5,3,7,4,2,6,1]=>111100
[5,3,7,4,6,1,2]=>101100
[5,3,7,4,6,2,1]=>111100
[5,3,7,6,1,2,4]=>101001
[5,3,7,6,1,4,2]=>111001
[5,3,7,6,2,1,4]=>111001
[5,3,7,6,2,4,1]=>111001
[5,3,7,6,4,1,2]=>101101
[5,3,7,6,4,2,1]=>111101
[5,4,1,2,3,6,7]=>100100
[5,4,1,2,3,7,6]=>100101
[5,4,1,2,6,3,7]=>101100
[5,4,1,2,6,7,3]=>101100
[5,4,1,2,7,3,6]=>101100
[5,4,1,2,7,6,3]=>101101
[5,4,1,3,2,6,7]=>110100
[5,4,1,3,2,7,6]=>110101
[5,4,1,3,6,2,7]=>110100
[5,4,1,3,6,7,2]=>110100
[5,4,1,3,7,2,6]=>110100
[5,4,1,3,7,6,2]=>110101
[5,4,1,6,2,3,7]=>110100
[5,4,1,6,2,7,3]=>111100
[5,4,1,6,3,2,7]=>111100
[5,4,1,6,3,7,2]=>111100
[5,4,1,6,7,2,3]=>110100
[5,4,1,6,7,3,2]=>111100
[5,4,1,7,2,3,6]=>110100
[5,4,1,7,2,6,3]=>111100
[5,4,1,7,3,2,6]=>111100
[5,4,1,7,3,6,2]=>111100
[5,4,1,7,6,2,3]=>110101
[5,4,1,7,6,3,2]=>111101
[5,4,2,1,3,6,7]=>110100
[5,4,2,1,3,7,6]=>110101
[5,4,2,1,6,3,7]=>111100
[5,4,2,1,6,7,3]=>111100
[5,4,2,1,7,3,6]=>111100
[5,4,2,1,7,6,3]=>111101
[5,4,2,3,1,6,7]=>110100
[5,4,2,3,1,7,6]=>110101
[5,4,2,3,6,1,7]=>110100
[5,4,2,3,6,7,1]=>110100
[5,4,2,3,7,1,6]=>110100
[5,4,2,3,7,6,1]=>110101
[5,4,2,6,1,3,7]=>110100
[5,4,2,6,1,7,3]=>111100
[5,4,2,6,3,1,7]=>111100
[5,4,2,6,3,7,1]=>111100
[5,4,2,6,7,1,3]=>110100
[5,4,2,6,7,3,1]=>111100
[5,4,2,7,1,3,6]=>110100
[5,4,2,7,1,6,3]=>111100
[5,4,2,7,3,1,6]=>111100
[5,4,2,7,3,6,1]=>111100
[5,4,2,7,6,1,3]=>110101
[5,4,2,7,6,3,1]=>111101
[5,4,3,1,2,6,7]=>101100
[5,4,3,1,2,7,6]=>101101
[5,4,3,1,6,2,7]=>111100
[5,4,3,1,6,7,2]=>111100
[5,4,3,1,7,2,6]=>111100
[5,4,3,1,7,6,2]=>111101
[5,4,3,2,1,6,7]=>111100
[5,4,3,2,1,7,6]=>111101
[5,4,3,2,6,1,7]=>111100
[5,4,3,2,6,7,1]=>111100
[5,4,3,2,7,1,6]=>111100
[5,4,3,2,7,6,1]=>111101
[5,4,3,6,1,2,7]=>101100
[5,4,3,6,1,7,2]=>111100
[5,4,3,6,2,1,7]=>111100
[5,4,3,6,2,7,1]=>111100
[5,4,3,6,7,1,2]=>101100
[5,4,3,6,7,2,1]=>111100
[5,4,3,7,1,2,6]=>101100
[5,4,3,7,1,6,2]=>111100
[5,4,3,7,2,1,6]=>111100
[5,4,3,7,2,6,1]=>111100
[5,4,3,7,6,1,2]=>101101
[5,4,3,7,6,2,1]=>111101
[5,4,6,1,2,3,7]=>100100
[5,4,6,1,2,7,3]=>101100
[5,4,6,1,3,2,7]=>110100
[5,4,6,1,3,7,2]=>110100
[5,4,6,1,7,2,3]=>110100
[5,4,6,1,7,3,2]=>111100
[5,4,6,2,1,3,7]=>110100
[5,4,6,2,1,7,3]=>111100
[5,4,6,2,3,1,7]=>110100
[5,4,6,2,3,7,1]=>110100
[5,4,6,2,7,1,3]=>110100
[5,4,6,2,7,3,1]=>111100
[5,4,6,3,1,2,7]=>101100
[5,4,6,3,1,7,2]=>111100
[5,4,6,3,2,1,7]=>111100
[5,4,6,3,2,7,1]=>111100
[5,4,6,3,7,1,2]=>101100
[5,4,6,3,7,2,1]=>111100
[5,4,6,7,1,2,3]=>100100
[5,4,6,7,1,3,2]=>110100
[5,4,6,7,2,1,3]=>110100
[5,4,6,7,2,3,1]=>110100
[5,4,6,7,3,1,2]=>101100
[5,4,6,7,3,2,1]=>111100
[5,4,7,1,2,3,6]=>100100
[5,4,7,1,2,6,3]=>101100
[5,4,7,1,3,2,6]=>110100
[5,4,7,1,3,6,2]=>110100
[5,4,7,1,6,2,3]=>110100
[5,4,7,1,6,3,2]=>111100
[5,4,7,2,1,3,6]=>110100
[5,4,7,2,1,6,3]=>111100
[5,4,7,2,3,1,6]=>110100
[5,4,7,2,3,6,1]=>110100
[5,4,7,2,6,1,3]=>110100
[5,4,7,2,6,3,1]=>111100
[5,4,7,3,1,2,6]=>101100
[5,4,7,3,1,6,2]=>111100
[5,4,7,3,2,1,6]=>111100
[5,4,7,3,2,6,1]=>111100
[5,4,7,3,6,1,2]=>101100
[5,4,7,3,6,2,1]=>111100
[5,4,7,6,1,2,3]=>100101
[5,4,7,6,1,3,2]=>110101
[5,4,7,6,2,1,3]=>110101
[5,4,7,6,2,3,1]=>110101
[5,4,7,6,3,1,2]=>101101
[5,4,7,6,3,2,1]=>111101
[5,6,1,2,3,4,7]=>100000
[5,6,1,2,3,7,4]=>100100
[5,6,1,2,4,3,7]=>101000
[5,6,1,2,4,7,3]=>101000
[5,6,1,2,7,3,4]=>101000
[5,6,1,2,7,4,3]=>101100
[5,6,1,3,2,4,7]=>110000
[5,6,1,3,2,7,4]=>110100
[5,6,1,3,4,2,7]=>110000
[5,6,1,3,4,7,2]=>110000
[5,6,1,3,7,2,4]=>110000
[5,6,1,3,7,4,2]=>110100
[5,6,1,4,2,3,7]=>110000
[5,6,1,4,2,7,3]=>111000
[5,6,1,4,3,2,7]=>111000
[5,6,1,4,3,7,2]=>111000
[5,6,1,4,7,2,3]=>110000
[5,6,1,4,7,3,2]=>111000
[5,6,1,7,2,3,4]=>110000
[5,6,1,7,2,4,3]=>111000
[5,6,1,7,3,2,4]=>111000
[5,6,1,7,3,4,2]=>111000
[5,6,1,7,4,2,3]=>110100
[5,6,1,7,4,3,2]=>111100
[5,6,2,1,3,4,7]=>110000
[5,6,2,1,3,7,4]=>110100
[5,6,2,1,4,3,7]=>111000
[5,6,2,1,4,7,3]=>111000
[5,6,2,1,7,3,4]=>111000
[5,6,2,1,7,4,3]=>111100
[5,6,2,3,1,4,7]=>110000
[5,6,2,3,1,7,4]=>110100
[5,6,2,3,4,1,7]=>110000
[5,6,2,3,4,7,1]=>110000
[5,6,2,3,7,1,4]=>110000
[5,6,2,3,7,4,1]=>110100
[5,6,2,4,1,3,7]=>110000
[5,6,2,4,1,7,3]=>111000
[5,6,2,4,3,1,7]=>111000
[5,6,2,4,3,7,1]=>111000
[5,6,2,4,7,1,3]=>110000
[5,6,2,4,7,3,1]=>111000
[5,6,2,7,1,3,4]=>110000
[5,6,2,7,1,4,3]=>111000
[5,6,2,7,3,1,4]=>111000
[5,6,2,7,3,4,1]=>111000
[5,6,2,7,4,1,3]=>110100
[5,6,2,7,4,3,1]=>111100
[5,6,3,1,2,4,7]=>101000
[5,6,3,1,2,7,4]=>101100
[5,6,3,1,4,2,7]=>111000
[5,6,3,1,4,7,2]=>111000
[5,6,3,1,7,2,4]=>111000
[5,6,3,1,7,4,2]=>111100
[5,6,3,2,1,4,7]=>111000
[5,6,3,2,1,7,4]=>111100
[5,6,3,2,4,1,7]=>111000
[5,6,3,2,4,7,1]=>111000
[5,6,3,2,7,1,4]=>111000
[5,6,3,2,7,4,1]=>111100
[5,6,3,4,1,2,7]=>101000
[5,6,3,4,1,7,2]=>111000
[5,6,3,4,2,1,7]=>111000
[5,6,3,4,2,7,1]=>111000
[5,6,3,4,7,1,2]=>101000
[5,6,3,4,7,2,1]=>111000
[5,6,3,7,1,2,4]=>101000
[5,6,3,7,1,4,2]=>111000
[5,6,3,7,2,1,4]=>111000
[5,6,3,7,2,4,1]=>111000
[5,6,3,7,4,1,2]=>101100
[5,6,3,7,4,2,1]=>111100
[5,6,4,1,2,3,7]=>100100
[5,6,4,1,2,7,3]=>101100
[5,6,4,1,3,2,7]=>110100
[5,6,4,1,3,7,2]=>110100
[5,6,4,1,7,2,3]=>110100
[5,6,4,1,7,3,2]=>111100
[5,6,4,2,1,3,7]=>110100
[5,6,4,2,1,7,3]=>111100
[5,6,4,2,3,1,7]=>110100
[5,6,4,2,3,7,1]=>110100
[5,6,4,2,7,1,3]=>110100
[5,6,4,2,7,3,1]=>111100
[5,6,4,3,1,2,7]=>101100
[5,6,4,3,1,7,2]=>111100
[5,6,4,3,2,1,7]=>111100
[5,6,4,3,2,7,1]=>111100
[5,6,4,3,7,1,2]=>101100
[5,6,4,3,7,2,1]=>111100
[5,6,4,7,1,2,3]=>100100
[5,6,4,7,1,3,2]=>110100
[5,6,4,7,2,1,3]=>110100
[5,6,4,7,2,3,1]=>110100
[5,6,4,7,3,1,2]=>101100
[5,6,4,7,3,2,1]=>111100
[5,6,7,1,2,3,4]=>100000
[5,6,7,1,2,4,3]=>101000
[5,6,7,1,3,2,4]=>110000
[5,6,7,1,3,4,2]=>110000
[5,6,7,1,4,2,3]=>110000
[5,6,7,1,4,3,2]=>111000
[5,6,7,2,1,3,4]=>110000
[5,6,7,2,1,4,3]=>111000
[5,6,7,2,3,1,4]=>110000
[5,6,7,2,3,4,1]=>110000
[5,6,7,2,4,1,3]=>110000
[5,6,7,2,4,3,1]=>111000
[5,6,7,3,1,2,4]=>101000
[5,6,7,3,1,4,2]=>111000
[5,6,7,3,2,1,4]=>111000
[5,6,7,3,2,4,1]=>111000
[5,6,7,3,4,1,2]=>101000
[5,6,7,3,4,2,1]=>111000
[5,6,7,4,1,2,3]=>100100
[5,6,7,4,1,3,2]=>110100
[5,6,7,4,2,1,3]=>110100
[5,6,7,4,2,3,1]=>110100
[5,6,7,4,3,1,2]=>101100
[5,6,7,4,3,2,1]=>111100
[5,7,1,2,3,4,6]=>100000
[5,7,1,2,3,6,4]=>100100
[5,7,1,2,4,3,6]=>101000
[5,7,1,2,4,6,3]=>101000
[5,7,1,2,6,3,4]=>101000
[5,7,1,2,6,4,3]=>101100
[5,7,1,3,2,4,6]=>110000
[5,7,1,3,2,6,4]=>110100
[5,7,1,3,4,2,6]=>110000
[5,7,1,3,4,6,2]=>110000
[5,7,1,3,6,2,4]=>110000
[5,7,1,3,6,4,2]=>110100
[5,7,1,4,2,3,6]=>110000
[5,7,1,4,2,6,3]=>111000
[5,7,1,4,3,2,6]=>111000
[5,7,1,4,3,6,2]=>111000
[5,7,1,4,6,2,3]=>110000
[5,7,1,4,6,3,2]=>111000
[5,7,1,6,2,3,4]=>110000
[5,7,1,6,2,4,3]=>111000
[5,7,1,6,3,2,4]=>111000
[5,7,1,6,3,4,2]=>111000
[5,7,1,6,4,2,3]=>110100
[5,7,1,6,4,3,2]=>111100
[5,7,2,1,3,4,6]=>110000
[5,7,2,1,3,6,4]=>110100
[5,7,2,1,4,3,6]=>111000
[5,7,2,1,4,6,3]=>111000
[5,7,2,1,6,3,4]=>111000
[5,7,2,1,6,4,3]=>111100
[5,7,2,3,1,4,6]=>110000
[5,7,2,3,1,6,4]=>110100
[5,7,2,3,4,1,6]=>110000
[5,7,2,3,4,6,1]=>110000
[5,7,2,3,6,1,4]=>110000
[5,7,2,3,6,4,1]=>110100
[5,7,2,4,1,3,6]=>110000
[5,7,2,4,1,6,3]=>111000
[5,7,2,4,3,1,6]=>111000
[5,7,2,4,3,6,1]=>111000
[5,7,2,4,6,1,3]=>110000
[5,7,2,4,6,3,1]=>111000
[5,7,2,6,1,3,4]=>110000
[5,7,2,6,1,4,3]=>111000
[5,7,2,6,3,1,4]=>111000
[5,7,2,6,3,4,1]=>111000
[5,7,2,6,4,1,3]=>110100
[5,7,2,6,4,3,1]=>111100
[5,7,3,1,2,4,6]=>101000
[5,7,3,1,2,6,4]=>101100
[5,7,3,1,4,2,6]=>111000
[5,7,3,1,4,6,2]=>111000
[5,7,3,1,6,2,4]=>111000
[5,7,3,1,6,4,2]=>111100
[5,7,3,2,1,4,6]=>111000
[5,7,3,2,1,6,4]=>111100
[5,7,3,2,4,1,6]=>111000
[5,7,3,2,4,6,1]=>111000
[5,7,3,2,6,1,4]=>111000
[5,7,3,2,6,4,1]=>111100
[5,7,3,4,1,2,6]=>101000
[5,7,3,4,1,6,2]=>111000
[5,7,3,4,2,1,6]=>111000
[5,7,3,4,2,6,1]=>111000
[5,7,3,4,6,1,2]=>101000
[5,7,3,4,6,2,1]=>111000
[5,7,3,6,1,2,4]=>101000
[5,7,3,6,1,4,2]=>111000
[5,7,3,6,2,1,4]=>111000
[5,7,3,6,2,4,1]=>111000
[5,7,3,6,4,1,2]=>101100
[5,7,3,6,4,2,1]=>111100
[5,7,4,1,2,3,6]=>100100
[5,7,4,1,2,6,3]=>101100
[5,7,4,1,3,2,6]=>110100
[5,7,4,1,3,6,2]=>110100
[5,7,4,1,6,2,3]=>110100
[5,7,4,1,6,3,2]=>111100
[5,7,4,2,1,3,6]=>110100
[5,7,4,2,1,6,3]=>111100
[5,7,4,2,3,1,6]=>110100
[5,7,4,2,3,6,1]=>110100
[5,7,4,2,6,1,3]=>110100
[5,7,4,2,6,3,1]=>111100
[5,7,4,3,1,2,6]=>101100
[5,7,4,3,1,6,2]=>111100
[5,7,4,3,2,1,6]=>111100
[5,7,4,3,2,6,1]=>111100
[5,7,4,3,6,1,2]=>101100
[5,7,4,3,6,2,1]=>111100
[5,7,4,6,1,2,3]=>100100
[5,7,4,6,1,3,2]=>110100
[5,7,4,6,2,1,3]=>110100
[5,7,4,6,2,3,1]=>110100
[5,7,4,6,3,1,2]=>101100
[5,7,4,6,3,2,1]=>111100
[5,7,6,1,2,3,4]=>100001
[5,7,6,1,2,4,3]=>101001
[5,7,6,1,3,2,4]=>110001
[5,7,6,1,3,4,2]=>110001
[5,7,6,1,4,2,3]=>110001
[5,7,6,1,4,3,2]=>111001
[5,7,6,2,1,3,4]=>110001
[5,7,6,2,1,4,3]=>111001
[5,7,6,2,3,1,4]=>110001
[5,7,6,2,3,4,1]=>110001
[5,7,6,2,4,1,3]=>110001
[5,7,6,2,4,3,1]=>111001
[5,7,6,3,1,2,4]=>101001
[5,7,6,3,1,4,2]=>111001
[5,7,6,3,2,1,4]=>111001
[5,7,6,3,2,4,1]=>111001
[5,7,6,3,4,1,2]=>101001
[5,7,6,3,4,2,1]=>111001
[5,7,6,4,1,2,3]=>100101
[5,7,6,4,1,3,2]=>110101
[5,7,6,4,2,1,3]=>110101
[5,7,6,4,2,3,1]=>110101
[5,7,6,4,3,1,2]=>101101
[5,7,6,4,3,2,1]=>111101
[6,1,2,3,4,5,7]=>100000
[6,1,2,3,4,7,5]=>100010
[6,1,2,3,5,4,7]=>100100
[6,1,2,3,5,7,4]=>100100
[6,1,2,3,7,4,5]=>100100
[6,1,2,3,7,5,4]=>100110
[6,1,2,4,3,5,7]=>101000
[6,1,2,4,3,7,5]=>101010
[6,1,2,4,5,3,7]=>101000
[6,1,2,4,5,7,3]=>101000
[6,1,2,4,7,3,5]=>101000
[6,1,2,4,7,5,3]=>101010
[6,1,2,5,3,4,7]=>101000
[6,1,2,5,3,7,4]=>101100
[6,1,2,5,4,3,7]=>101100
[6,1,2,5,4,7,3]=>101100
[6,1,2,5,7,3,4]=>101000
[6,1,2,5,7,4,3]=>101100
[6,1,2,7,3,4,5]=>101000
[6,1,2,7,3,5,4]=>101100
[6,1,2,7,4,3,5]=>101100
[6,1,2,7,4,5,3]=>101100
[6,1,2,7,5,3,4]=>101010
[6,1,2,7,5,4,3]=>101110
[6,1,3,2,4,5,7]=>110000
[6,1,3,2,4,7,5]=>110010
[6,1,3,2,5,4,7]=>110100
[6,1,3,2,5,7,4]=>110100
[6,1,3,2,7,4,5]=>110100
[6,1,3,2,7,5,4]=>110110
[6,1,3,4,2,5,7]=>110000
[6,1,3,4,2,7,5]=>110010
[6,1,3,4,5,2,7]=>110000
[6,1,3,4,5,7,2]=>110000
[6,1,3,4,7,2,5]=>110000
[6,1,3,4,7,5,2]=>110010
[6,1,3,5,2,4,7]=>110000
[6,1,3,5,2,7,4]=>110100
[6,1,3,5,4,2,7]=>110100
[6,1,3,5,4,7,2]=>110100
[6,1,3,5,7,2,4]=>110000
[6,1,3,5,7,4,2]=>110100
[6,1,3,7,2,4,5]=>110000
[6,1,3,7,2,5,4]=>110100
[6,1,3,7,4,2,5]=>110100
[6,1,3,7,4,5,2]=>110100
[6,1,3,7,5,2,4]=>110010
[6,1,3,7,5,4,2]=>110110
[6,1,4,2,3,5,7]=>110000
[6,1,4,2,3,7,5]=>110010
[6,1,4,2,5,3,7]=>111000
[6,1,4,2,5,7,3]=>111000
[6,1,4,2,7,3,5]=>111000
[6,1,4,2,7,5,3]=>111010
[6,1,4,3,2,5,7]=>111000
[6,1,4,3,2,7,5]=>111010
[6,1,4,3,5,2,7]=>111000
[6,1,4,3,5,7,2]=>111000
[6,1,4,3,7,2,5]=>111000
[6,1,4,3,7,5,2]=>111010
[6,1,4,5,2,3,7]=>110000
[6,1,4,5,2,7,3]=>111000
[6,1,4,5,3,2,7]=>111000
[6,1,4,5,3,7,2]=>111000
[6,1,4,5,7,2,3]=>110000
[6,1,4,5,7,3,2]=>111000
[6,1,4,7,2,3,5]=>110000
[6,1,4,7,2,5,3]=>111000
[6,1,4,7,3,2,5]=>111000
[6,1,4,7,3,5,2]=>111000
[6,1,4,7,5,2,3]=>110010
[6,1,4,7,5,3,2]=>111010
[6,1,5,2,3,4,7]=>110000
[6,1,5,2,3,7,4]=>110100
[6,1,5,2,4,3,7]=>111000
[6,1,5,2,4,7,3]=>111000
[6,1,5,2,7,3,4]=>111000
[6,1,5,2,7,4,3]=>111100
[6,1,5,3,2,4,7]=>111000
[6,1,5,3,2,7,4]=>111100
[6,1,5,3,4,2,7]=>111000
[6,1,5,3,4,7,2]=>111000
[6,1,5,3,7,2,4]=>111000
[6,1,5,3,7,4,2]=>111100
[6,1,5,4,2,3,7]=>110100
[6,1,5,4,2,7,3]=>111100
[6,1,5,4,3,2,7]=>111100
[6,1,5,4,3,7,2]=>111100
[6,1,5,4,7,2,3]=>110100
[6,1,5,4,7,3,2]=>111100
[6,1,5,7,2,3,4]=>110000
[6,1,5,7,2,4,3]=>111000
[6,1,5,7,3,2,4]=>111000
[6,1,5,7,3,4,2]=>111000
[6,1,5,7,4,2,3]=>110100
[6,1,5,7,4,3,2]=>111100
[6,1,7,2,3,4,5]=>110000
[6,1,7,2,3,5,4]=>110100
[6,1,7,2,4,3,5]=>111000
[6,1,7,2,4,5,3]=>111000
[6,1,7,2,5,3,4]=>111000
[6,1,7,2,5,4,3]=>111100
[6,1,7,3,2,4,5]=>111000
[6,1,7,3,2,5,4]=>111100
[6,1,7,3,4,2,5]=>111000
[6,1,7,3,4,5,2]=>111000
[6,1,7,3,5,2,4]=>111000
[6,1,7,3,5,4,2]=>111100
[6,1,7,4,2,3,5]=>110100
[6,1,7,4,2,5,3]=>111100
[6,1,7,4,3,2,5]=>111100
[6,1,7,4,3,5,2]=>111100
[6,1,7,4,5,2,3]=>110100
[6,1,7,4,5,3,2]=>111100
[6,1,7,5,2,3,4]=>110010
[6,1,7,5,2,4,3]=>111010
[6,1,7,5,3,2,4]=>111010
[6,1,7,5,3,4,2]=>111010
[6,1,7,5,4,2,3]=>110110
[6,1,7,5,4,3,2]=>111110
[6,2,1,3,4,5,7]=>110000
[6,2,1,3,4,7,5]=>110010
[6,2,1,3,5,4,7]=>110100
[6,2,1,3,5,7,4]=>110100
[6,2,1,3,7,4,5]=>110100
[6,2,1,3,7,5,4]=>110110
[6,2,1,4,3,5,7]=>111000
[6,2,1,4,3,7,5]=>111010
[6,2,1,4,5,3,7]=>111000
[6,2,1,4,5,7,3]=>111000
[6,2,1,4,7,3,5]=>111000
[6,2,1,4,7,5,3]=>111010
[6,2,1,5,3,4,7]=>111000
[6,2,1,5,3,7,4]=>111100
[6,2,1,5,4,3,7]=>111100
[6,2,1,5,4,7,3]=>111100
[6,2,1,5,7,3,4]=>111000
[6,2,1,5,7,4,3]=>111100
[6,2,1,7,3,4,5]=>111000
[6,2,1,7,3,5,4]=>111100
[6,2,1,7,4,3,5]=>111100
[6,2,1,7,4,5,3]=>111100
[6,2,1,7,5,3,4]=>111010
[6,2,1,7,5,4,3]=>111110
[6,2,3,1,4,5,7]=>110000
[6,2,3,1,4,7,5]=>110010
[6,2,3,1,5,4,7]=>110100
[6,2,3,1,5,7,4]=>110100
[6,2,3,1,7,4,5]=>110100
[6,2,3,1,7,5,4]=>110110
[6,2,3,4,1,5,7]=>110000
[6,2,3,4,1,7,5]=>110010
[6,2,3,4,5,1,7]=>110000
[6,2,3,4,5,7,1]=>110000
[6,2,3,4,7,1,5]=>110000
[6,2,3,4,7,5,1]=>110010
[6,2,3,5,1,4,7]=>110000
[6,2,3,5,1,7,4]=>110100
[6,2,3,5,4,1,7]=>110100
[6,2,3,5,4,7,1]=>110100
[6,2,3,5,7,1,4]=>110000
[6,2,3,5,7,4,1]=>110100
[6,2,3,7,1,4,5]=>110000
[6,2,3,7,1,5,4]=>110100
[6,2,3,7,4,1,5]=>110100
[6,2,3,7,4,5,1]=>110100
[6,2,3,7,5,1,4]=>110010
[6,2,3,7,5,4,1]=>110110
[6,2,4,1,3,5,7]=>110000
[6,2,4,1,3,7,5]=>110010
[6,2,4,1,5,3,7]=>111000
[6,2,4,1,5,7,3]=>111000
[6,2,4,1,7,3,5]=>111000
[6,2,4,1,7,5,3]=>111010
[6,2,4,3,1,5,7]=>111000
[6,2,4,3,1,7,5]=>111010
[6,2,4,3,5,1,7]=>111000
[6,2,4,3,5,7,1]=>111000
[6,2,4,3,7,1,5]=>111000
[6,2,4,3,7,5,1]=>111010
[6,2,4,5,1,3,7]=>110000
[6,2,4,5,1,7,3]=>111000
[6,2,4,5,3,1,7]=>111000
[6,2,4,5,3,7,1]=>111000
[6,2,4,5,7,1,3]=>110000
[6,2,4,5,7,3,1]=>111000
[6,2,4,7,1,3,5]=>110000
[6,2,4,7,1,5,3]=>111000
[6,2,4,7,3,1,5]=>111000
[6,2,4,7,3,5,1]=>111000
[6,2,4,7,5,1,3]=>110010
[6,2,4,7,5,3,1]=>111010
[6,2,5,1,3,4,7]=>110000
[6,2,5,1,3,7,4]=>110100
[6,2,5,1,4,3,7]=>111000
[6,2,5,1,4,7,3]=>111000
[6,2,5,1,7,3,4]=>111000
[6,2,5,1,7,4,3]=>111100
[6,2,5,3,1,4,7]=>111000
[6,2,5,3,1,7,4]=>111100
[6,2,5,3,4,1,7]=>111000
[6,2,5,3,4,7,1]=>111000
[6,2,5,3,7,1,4]=>111000
[6,2,5,3,7,4,1]=>111100
[6,2,5,4,1,3,7]=>110100
[6,2,5,4,1,7,3]=>111100
[6,2,5,4,3,1,7]=>111100
[6,2,5,4,3,7,1]=>111100
[6,2,5,4,7,1,3]=>110100
[6,2,5,4,7,3,1]=>111100
[6,2,5,7,1,3,4]=>110000
[6,2,5,7,1,4,3]=>111000
[6,2,5,7,3,1,4]=>111000
[6,2,5,7,3,4,1]=>111000
[6,2,5,7,4,1,3]=>110100
[6,2,5,7,4,3,1]=>111100
[6,2,7,1,3,4,5]=>110000
[6,2,7,1,3,5,4]=>110100
[6,2,7,1,4,3,5]=>111000
[6,2,7,1,4,5,3]=>111000
[6,2,7,1,5,3,4]=>111000
[6,2,7,1,5,4,3]=>111100
[6,2,7,3,1,4,5]=>111000
[6,2,7,3,1,5,4]=>111100
[6,2,7,3,4,1,5]=>111000
[6,2,7,3,4,5,1]=>111000
[6,2,7,3,5,1,4]=>111000
[6,2,7,3,5,4,1]=>111100
[6,2,7,4,1,3,5]=>110100
[6,2,7,4,1,5,3]=>111100
[6,2,7,4,3,1,5]=>111100
[6,2,7,4,3,5,1]=>111100
[6,2,7,4,5,1,3]=>110100
[6,2,7,4,5,3,1]=>111100
[6,2,7,5,1,3,4]=>110010
[6,2,7,5,1,4,3]=>111010
[6,2,7,5,3,1,4]=>111010
[6,2,7,5,3,4,1]=>111010
[6,2,7,5,4,1,3]=>110110
[6,2,7,5,4,3,1]=>111110
[6,3,1,2,4,5,7]=>101000
[6,3,1,2,4,7,5]=>101010
[6,3,1,2,5,4,7]=>101100
[6,3,1,2,5,7,4]=>101100
[6,3,1,2,7,4,5]=>101100
[6,3,1,2,7,5,4]=>101110
[6,3,1,4,2,5,7]=>111000
[6,3,1,4,2,7,5]=>111010
[6,3,1,4,5,2,7]=>111000
[6,3,1,4,5,7,2]=>111000
[6,3,1,4,7,2,5]=>111000
[6,3,1,4,7,5,2]=>111010
[6,3,1,5,2,4,7]=>111000
[6,3,1,5,2,7,4]=>111100
[6,3,1,5,4,2,7]=>111100
[6,3,1,5,4,7,2]=>111100
[6,3,1,5,7,2,4]=>111000
[6,3,1,5,7,4,2]=>111100
[6,3,1,7,2,4,5]=>111000
[6,3,1,7,2,5,4]=>111100
[6,3,1,7,4,2,5]=>111100
[6,3,1,7,4,5,2]=>111100
[6,3,1,7,5,2,4]=>111010
[6,3,1,7,5,4,2]=>111110
[6,3,2,1,4,5,7]=>111000
[6,3,2,1,4,7,5]=>111010
[6,3,2,1,5,4,7]=>111100
[6,3,2,1,5,7,4]=>111100
[6,3,2,1,7,4,5]=>111100
[6,3,2,1,7,5,4]=>111110
[6,3,2,4,1,5,7]=>111000
[6,3,2,4,1,7,5]=>111010
[6,3,2,4,5,1,7]=>111000
[6,3,2,4,5,7,1]=>111000
[6,3,2,4,7,1,5]=>111000
[6,3,2,4,7,5,1]=>111010
[6,3,2,5,1,4,7]=>111000
[6,3,2,5,1,7,4]=>111100
[6,3,2,5,4,1,7]=>111100
[6,3,2,5,4,7,1]=>111100
[6,3,2,5,7,1,4]=>111000
[6,3,2,5,7,4,1]=>111100
[6,3,2,7,1,4,5]=>111000
[6,3,2,7,1,5,4]=>111100
[6,3,2,7,4,1,5]=>111100
[6,3,2,7,4,5,1]=>111100
[6,3,2,7,5,1,4]=>111010
[6,3,2,7,5,4,1]=>111110
[6,3,4,1,2,5,7]=>101000
[6,3,4,1,2,7,5]=>101010
[6,3,4,1,5,2,7]=>111000
[6,3,4,1,5,7,2]=>111000
[6,3,4,1,7,2,5]=>111000
[6,3,4,1,7,5,2]=>111010
[6,3,4,2,1,5,7]=>111000
[6,3,4,2,1,7,5]=>111010
[6,3,4,2,5,1,7]=>111000
[6,3,4,2,5,7,1]=>111000
[6,3,4,2,7,1,5]=>111000
[6,3,4,2,7,5,1]=>111010
[6,3,4,5,1,2,7]=>101000
[6,3,4,5,1,7,2]=>111000
[6,3,4,5,2,1,7]=>111000
[6,3,4,5,2,7,1]=>111000
[6,3,4,5,7,1,2]=>101000
[6,3,4,5,7,2,1]=>111000
[6,3,4,7,1,2,5]=>101000
[6,3,4,7,1,5,2]=>111000
[6,3,4,7,2,1,5]=>111000
[6,3,4,7,2,5,1]=>111000
[6,3,4,7,5,1,2]=>101010
[6,3,4,7,5,2,1]=>111010
[6,3,5,1,2,4,7]=>101000
[6,3,5,1,2,7,4]=>101100
[6,3,5,1,4,2,7]=>111000
[6,3,5,1,4,7,2]=>111000
[6,3,5,1,7,2,4]=>111000
[6,3,5,1,7,4,2]=>111100
[6,3,5,2,1,4,7]=>111000
[6,3,5,2,1,7,4]=>111100
[6,3,5,2,4,1,7]=>111000
[6,3,5,2,4,7,1]=>111000
[6,3,5,2,7,1,4]=>111000
[6,3,5,2,7,4,1]=>111100
[6,3,5,4,1,2,7]=>101100
[6,3,5,4,1,7,2]=>111100
[6,3,5,4,2,1,7]=>111100
[6,3,5,4,2,7,1]=>111100
[6,3,5,4,7,1,2]=>101100
[6,3,5,4,7,2,1]=>111100
[6,3,5,7,1,2,4]=>101000
[6,3,5,7,1,4,2]=>111000
[6,3,5,7,2,1,4]=>111000
[6,3,5,7,2,4,1]=>111000
[6,3,5,7,4,1,2]=>101100
[6,3,5,7,4,2,1]=>111100
[6,3,7,1,2,4,5]=>101000
[6,3,7,1,2,5,4]=>101100
[6,3,7,1,4,2,5]=>111000
[6,3,7,1,4,5,2]=>111000
[6,3,7,1,5,2,4]=>111000
[6,3,7,1,5,4,2]=>111100
[6,3,7,2,1,4,5]=>111000
[6,3,7,2,1,5,4]=>111100
[6,3,7,2,4,1,5]=>111000
[6,3,7,2,4,5,1]=>111000
[6,3,7,2,5,1,4]=>111000
[6,3,7,2,5,4,1]=>111100
[6,3,7,4,1,2,5]=>101100
[6,3,7,4,1,5,2]=>111100
[6,3,7,4,2,1,5]=>111100
[6,3,7,4,2,5,1]=>111100
[6,3,7,4,5,1,2]=>101100
[6,3,7,4,5,2,1]=>111100
[6,3,7,5,1,2,4]=>101010
[6,3,7,5,1,4,2]=>111010
[6,3,7,5,2,1,4]=>111010
[6,3,7,5,2,4,1]=>111010
[6,3,7,5,4,1,2]=>101110
[6,3,7,5,4,2,1]=>111110
[6,4,1,2,3,5,7]=>100100
[6,4,1,2,3,7,5]=>100110
[6,4,1,2,5,3,7]=>101100
[6,4,1,2,5,7,3]=>101100
[6,4,1,2,7,3,5]=>101100
[6,4,1,2,7,5,3]=>101110
[6,4,1,3,2,5,7]=>110100
[6,4,1,3,2,7,5]=>110110
[6,4,1,3,5,2,7]=>110100
[6,4,1,3,5,7,2]=>110100
[6,4,1,3,7,2,5]=>110100
[6,4,1,3,7,5,2]=>110110
[6,4,1,5,2,3,7]=>110100
[6,4,1,5,2,7,3]=>111100
[6,4,1,5,3,2,7]=>111100
[6,4,1,5,3,7,2]=>111100
[6,4,1,5,7,2,3]=>110100
[6,4,1,5,7,3,2]=>111100
[6,4,1,7,2,3,5]=>110100
[6,4,1,7,2,5,3]=>111100
[6,4,1,7,3,2,5]=>111100
[6,4,1,7,3,5,2]=>111100
[6,4,1,7,5,2,3]=>110110
[6,4,1,7,5,3,2]=>111110
[6,4,2,1,3,5,7]=>110100
[6,4,2,1,3,7,5]=>110110
[6,4,2,1,5,3,7]=>111100
[6,4,2,1,5,7,3]=>111100
[6,4,2,1,7,3,5]=>111100
[6,4,2,1,7,5,3]=>111110
[6,4,2,3,1,5,7]=>110100
[6,4,2,3,1,7,5]=>110110
[6,4,2,3,5,1,7]=>110100
[6,4,2,3,5,7,1]=>110100
[6,4,2,3,7,1,5]=>110100
[6,4,2,3,7,5,1]=>110110
[6,4,2,5,1,3,7]=>110100
[6,4,2,5,1,7,3]=>111100
[6,4,2,5,3,1,7]=>111100
[6,4,2,5,3,7,1]=>111100
[6,4,2,5,7,1,3]=>110100
[6,4,2,5,7,3,1]=>111100
[6,4,2,7,1,3,5]=>110100
[6,4,2,7,1,5,3]=>111100
[6,4,2,7,3,1,5]=>111100
[6,4,2,7,3,5,1]=>111100
[6,4,2,7,5,1,3]=>110110
[6,4,2,7,5,3,1]=>111110
[6,4,3,1,2,5,7]=>101100
[6,4,3,1,2,7,5]=>101110
[6,4,3,1,5,2,7]=>111100
[6,4,3,1,5,7,2]=>111100
[6,4,3,1,7,2,5]=>111100
[6,4,3,1,7,5,2]=>111110
[6,4,3,2,1,5,7]=>111100
[6,4,3,2,1,7,5]=>111110
[6,4,3,2,5,1,7]=>111100
[6,4,3,2,5,7,1]=>111100
[6,4,3,2,7,1,5]=>111100
[6,4,3,2,7,5,1]=>111110
[6,4,3,5,1,2,7]=>101100
[6,4,3,5,1,7,2]=>111100
[6,4,3,5,2,1,7]=>111100
[6,4,3,5,2,7,1]=>111100
[6,4,3,5,7,1,2]=>101100
[6,4,3,5,7,2,1]=>111100
[6,4,3,7,1,2,5]=>101100
[6,4,3,7,1,5,2]=>111100
[6,4,3,7,2,1,5]=>111100
[6,4,3,7,2,5,1]=>111100
[6,4,3,7,5,1,2]=>101110
[6,4,3,7,5,2,1]=>111110
[6,4,5,1,2,3,7]=>100100
[6,4,5,1,2,7,3]=>101100
[6,4,5,1,3,2,7]=>110100
[6,4,5,1,3,7,2]=>110100
[6,4,5,1,7,2,3]=>110100
[6,4,5,1,7,3,2]=>111100
[6,4,5,2,1,3,7]=>110100
[6,4,5,2,1,7,3]=>111100
[6,4,5,2,3,1,7]=>110100
[6,4,5,2,3,7,1]=>110100
[6,4,5,2,7,1,3]=>110100
[6,4,5,2,7,3,1]=>111100
[6,4,5,3,1,2,7]=>101100
[6,4,5,3,1,7,2]=>111100
[6,4,5,3,2,1,7]=>111100
[6,4,5,3,2,7,1]=>111100
[6,4,5,3,7,1,2]=>101100
[6,4,5,3,7,2,1]=>111100
[6,4,5,7,1,2,3]=>100100
[6,4,5,7,1,3,2]=>110100
[6,4,5,7,2,1,3]=>110100
[6,4,5,7,2,3,1]=>110100
[6,4,5,7,3,1,2]=>101100
[6,4,5,7,3,2,1]=>111100
[6,4,7,1,2,3,5]=>100100
[6,4,7,1,2,5,3]=>101100
[6,4,7,1,3,2,5]=>110100
[6,4,7,1,3,5,2]=>110100
[6,4,7,1,5,2,3]=>110100
[6,4,7,1,5,3,2]=>111100
[6,4,7,2,1,3,5]=>110100
[6,4,7,2,1,5,3]=>111100
[6,4,7,2,3,1,5]=>110100
[6,4,7,2,3,5,1]=>110100
[6,4,7,2,5,1,3]=>110100
[6,4,7,2,5,3,1]=>111100
[6,4,7,3,1,2,5]=>101100
[6,4,7,3,1,5,2]=>111100
[6,4,7,3,2,1,5]=>111100
[6,4,7,3,2,5,1]=>111100
[6,4,7,3,5,1,2]=>101100
[6,4,7,3,5,2,1]=>111100
[6,4,7,5,1,2,3]=>100110
[6,4,7,5,1,3,2]=>110110
[6,4,7,5,2,1,3]=>110110
[6,4,7,5,2,3,1]=>110110
[6,4,7,5,3,1,2]=>101110
[6,4,7,5,3,2,1]=>111110
[6,5,1,2,3,4,7]=>100010
[6,5,1,2,3,7,4]=>100110
[6,5,1,2,4,3,7]=>101010
[6,5,1,2,4,7,3]=>101010
[6,5,1,2,7,3,4]=>101010
[6,5,1,2,7,4,3]=>101110
[6,5,1,3,2,4,7]=>110010
[6,5,1,3,2,7,4]=>110110
[6,5,1,3,4,2,7]=>110010
[6,5,1,3,4,7,2]=>110010
[6,5,1,3,7,2,4]=>110010
[6,5,1,3,7,4,2]=>110110
[6,5,1,4,2,3,7]=>110010
[6,5,1,4,2,7,3]=>111010
[6,5,1,4,3,2,7]=>111010
[6,5,1,4,3,7,2]=>111010
[6,5,1,4,7,2,3]=>110010
[6,5,1,4,7,3,2]=>111010
[6,5,1,7,2,3,4]=>110010
[6,5,1,7,2,4,3]=>111010
[6,5,1,7,3,2,4]=>111010
[6,5,1,7,3,4,2]=>111010
[6,5,1,7,4,2,3]=>110110
[6,5,1,7,4,3,2]=>111110
[6,5,2,1,3,4,7]=>110010
[6,5,2,1,3,7,4]=>110110
[6,5,2,1,4,3,7]=>111010
[6,5,2,1,4,7,3]=>111010
[6,5,2,1,7,3,4]=>111010
[6,5,2,1,7,4,3]=>111110
[6,5,2,3,1,4,7]=>110010
[6,5,2,3,1,7,4]=>110110
[6,5,2,3,4,1,7]=>110010
[6,5,2,3,4,7,1]=>110010
[6,5,2,3,7,1,4]=>110010
[6,5,2,3,7,4,1]=>110110
[6,5,2,4,1,3,7]=>110010
[6,5,2,4,1,7,3]=>111010
[6,5,2,4,3,1,7]=>111010
[6,5,2,4,3,7,1]=>111010
[6,5,2,4,7,1,3]=>110010
[6,5,2,4,7,3,1]=>111010
[6,5,2,7,1,3,4]=>110010
[6,5,2,7,1,4,3]=>111010
[6,5,2,7,3,1,4]=>111010
[6,5,2,7,3,4,1]=>111010
[6,5,2,7,4,1,3]=>110110
[6,5,2,7,4,3,1]=>111110
[6,5,3,1,2,4,7]=>101010
[6,5,3,1,2,7,4]=>101110
[6,5,3,1,4,2,7]=>111010
[6,5,3,1,4,7,2]=>111010
[6,5,3,1,7,2,4]=>111010
[6,5,3,1,7,4,2]=>111110
[6,5,3,2,1,4,7]=>111010
[6,5,3,2,1,7,4]=>111110
[6,5,3,2,4,1,7]=>111010
[6,5,3,2,4,7,1]=>111010
[6,5,3,2,7,1,4]=>111010
[6,5,3,2,7,4,1]=>111110
[6,5,3,4,1,2,7]=>101010
[6,5,3,4,1,7,2]=>111010
[6,5,3,4,2,1,7]=>111010
[6,5,3,4,2,7,1]=>111010
[6,5,3,4,7,1,2]=>101010
[6,5,3,4,7,2,1]=>111010
[6,5,3,7,1,2,4]=>101010
[6,5,3,7,1,4,2]=>111010
[6,5,3,7,2,1,4]=>111010
[6,5,3,7,2,4,1]=>111010
[6,5,3,7,4,1,2]=>101110
[6,5,3,7,4,2,1]=>111110
[6,5,4,1,2,3,7]=>100110
[6,5,4,1,2,7,3]=>101110
[6,5,4,1,3,2,7]=>110110
[6,5,4,1,3,7,2]=>110110
[6,5,4,1,7,2,3]=>110110
[6,5,4,1,7,3,2]=>111110
[6,5,4,2,1,3,7]=>110110
[6,5,4,2,1,7,3]=>111110
[6,5,4,2,3,1,7]=>110110
[6,5,4,2,3,7,1]=>110110
[6,5,4,2,7,1,3]=>110110
[6,5,4,2,7,3,1]=>111110
[6,5,4,3,1,2,7]=>101110
[6,5,4,3,1,7,2]=>111110
[6,5,4,3,2,1,7]=>111110
[6,5,4,3,2,7,1]=>111110
[6,5,4,3,7,1,2]=>101110
[6,5,4,3,7,2,1]=>111110
[6,5,4,7,1,2,3]=>100110
[6,5,4,7,1,3,2]=>110110
[6,5,4,7,2,1,3]=>110110
[6,5,4,7,2,3,1]=>110110
[6,5,4,7,3,1,2]=>101110
[6,5,4,7,3,2,1]=>111110
[6,5,7,1,2,3,4]=>100010
[6,5,7,1,2,4,3]=>101010
[6,5,7,1,3,2,4]=>110010
[6,5,7,1,3,4,2]=>110010
[6,5,7,1,4,2,3]=>110010
[6,5,7,1,4,3,2]=>111010
[6,5,7,2,1,3,4]=>110010
[6,5,7,2,1,4,3]=>111010
[6,5,7,2,3,1,4]=>110010
[6,5,7,2,3,4,1]=>110010
[6,5,7,2,4,1,3]=>110010
[6,5,7,2,4,3,1]=>111010
[6,5,7,3,1,2,4]=>101010
[6,5,7,3,1,4,2]=>111010
[6,5,7,3,2,1,4]=>111010
[6,5,7,3,2,4,1]=>111010
[6,5,7,3,4,1,2]=>101010
[6,5,7,3,4,2,1]=>111010
[6,5,7,4,1,2,3]=>100110
[6,5,7,4,1,3,2]=>110110
[6,5,7,4,2,1,3]=>110110
[6,5,7,4,2,3,1]=>110110
[6,5,7,4,3,1,2]=>101110
[6,5,7,4,3,2,1]=>111110
[6,7,1,2,3,4,5]=>100000
[6,7,1,2,3,5,4]=>100100
[6,7,1,2,4,3,5]=>101000
[6,7,1,2,4,5,3]=>101000
[6,7,1,2,5,3,4]=>101000
[6,7,1,2,5,4,3]=>101100
[6,7,1,3,2,4,5]=>110000
[6,7,1,3,2,5,4]=>110100
[6,7,1,3,4,2,5]=>110000
[6,7,1,3,4,5,2]=>110000
[6,7,1,3,5,2,4]=>110000
[6,7,1,3,5,4,2]=>110100
[6,7,1,4,2,3,5]=>110000
[6,7,1,4,2,5,3]=>111000
[6,7,1,4,3,2,5]=>111000
[6,7,1,4,3,5,2]=>111000
[6,7,1,4,5,2,3]=>110000
[6,7,1,4,5,3,2]=>111000
[6,7,1,5,2,3,4]=>110000
[6,7,1,5,2,4,3]=>111000
[6,7,1,5,3,2,4]=>111000
[6,7,1,5,3,4,2]=>111000
[6,7,1,5,4,2,3]=>110100
[6,7,1,5,4,3,2]=>111100
[6,7,2,1,3,4,5]=>110000
[6,7,2,1,3,5,4]=>110100
[6,7,2,1,4,3,5]=>111000
[6,7,2,1,4,5,3]=>111000
[6,7,2,1,5,3,4]=>111000
[6,7,2,1,5,4,3]=>111100
[6,7,2,3,1,4,5]=>110000
[6,7,2,3,1,5,4]=>110100
[6,7,2,3,4,1,5]=>110000
[6,7,2,3,4,5,1]=>110000
[6,7,2,3,5,1,4]=>110000
[6,7,2,3,5,4,1]=>110100
[6,7,2,4,1,3,5]=>110000
[6,7,2,4,1,5,3]=>111000
[6,7,2,4,3,1,5]=>111000
[6,7,2,4,3,5,1]=>111000
[6,7,2,4,5,1,3]=>110000
[6,7,2,4,5,3,1]=>111000
[6,7,2,5,1,3,4]=>110000
[6,7,2,5,1,4,3]=>111000
[6,7,2,5,3,1,4]=>111000
[6,7,2,5,3,4,1]=>111000
[6,7,2,5,4,1,3]=>110100
[6,7,2,5,4,3,1]=>111100
[6,7,3,1,2,4,5]=>101000
[6,7,3,1,2,5,4]=>101100
[6,7,3,1,4,2,5]=>111000
[6,7,3,1,4,5,2]=>111000
[6,7,3,1,5,2,4]=>111000
[6,7,3,1,5,4,2]=>111100
[6,7,3,2,1,4,5]=>111000
[6,7,3,2,1,5,4]=>111100
[6,7,3,2,4,1,5]=>111000
[6,7,3,2,4,5,1]=>111000
[6,7,3,2,5,1,4]=>111000
[6,7,3,2,5,4,1]=>111100
[6,7,3,4,1,2,5]=>101000
[6,7,3,4,1,5,2]=>111000
[6,7,3,4,2,1,5]=>111000
[6,7,3,4,2,5,1]=>111000
[6,7,3,4,5,1,2]=>101000
[6,7,3,4,5,2,1]=>111000
[6,7,3,5,1,2,4]=>101000
[6,7,3,5,1,4,2]=>111000
[6,7,3,5,2,1,4]=>111000
[6,7,3,5,2,4,1]=>111000
[6,7,3,5,4,1,2]=>101100
[6,7,3,5,4,2,1]=>111100
[6,7,4,1,2,3,5]=>100100
[6,7,4,1,2,5,3]=>101100
[6,7,4,1,3,2,5]=>110100
[6,7,4,1,3,5,2]=>110100
[6,7,4,1,5,2,3]=>110100
[6,7,4,1,5,3,2]=>111100
[6,7,4,2,1,3,5]=>110100
[6,7,4,2,1,5,3]=>111100
[6,7,4,2,3,1,5]=>110100
[6,7,4,2,3,5,1]=>110100
[6,7,4,2,5,1,3]=>110100
[6,7,4,2,5,3,1]=>111100
[6,7,4,3,1,2,5]=>101100
[6,7,4,3,1,5,2]=>111100
[6,7,4,3,2,1,5]=>111100
[6,7,4,3,2,5,1]=>111100
[6,7,4,3,5,1,2]=>101100
[6,7,4,3,5,2,1]=>111100
[6,7,4,5,1,2,3]=>100100
[6,7,4,5,1,3,2]=>110100
[6,7,4,5,2,1,3]=>110100
[6,7,4,5,2,3,1]=>110100
[6,7,4,5,3,1,2]=>101100
[6,7,4,5,3,2,1]=>111100
[6,7,5,1,2,3,4]=>100010
[6,7,5,1,2,4,3]=>101010
[6,7,5,1,3,2,4]=>110010
[6,7,5,1,3,4,2]=>110010
[6,7,5,1,4,2,3]=>110010
[6,7,5,1,4,3,2]=>111010
[6,7,5,2,1,3,4]=>110010
[6,7,5,2,1,4,3]=>111010
[6,7,5,2,3,1,4]=>110010
[6,7,5,2,3,4,1]=>110010
[6,7,5,2,4,1,3]=>110010
[6,7,5,2,4,3,1]=>111010
[6,7,5,3,1,2,4]=>101010
[6,7,5,3,1,4,2]=>111010
[6,7,5,3,2,1,4]=>111010
[6,7,5,3,2,4,1]=>111010
[6,7,5,3,4,1,2]=>101010
[6,7,5,3,4,2,1]=>111010
[6,7,5,4,1,2,3]=>100110
[6,7,5,4,1,3,2]=>110110
[6,7,5,4,2,1,3]=>110110
[6,7,5,4,2,3,1]=>110110
[6,7,5,4,3,1,2]=>101110
[6,7,5,4,3,2,1]=>111110
[7,1,2,3,4,5,6]=>100000
[7,1,2,3,4,6,5]=>100010
[7,1,2,3,5,4,6]=>100100
[7,1,2,3,5,6,4]=>100100
[7,1,2,3,6,4,5]=>100100
[7,1,2,3,6,5,4]=>100110
[7,1,2,4,3,5,6]=>101000
[7,1,2,4,3,6,5]=>101010
[7,1,2,4,5,3,6]=>101000
[7,1,2,4,5,6,3]=>101000
[7,1,2,4,6,3,5]=>101000
[7,1,2,4,6,5,3]=>101010
[7,1,2,5,3,4,6]=>101000
[7,1,2,5,3,6,4]=>101100
[7,1,2,5,4,3,6]=>101100
[7,1,2,5,4,6,3]=>101100
[7,1,2,5,6,3,4]=>101000
[7,1,2,5,6,4,3]=>101100
[7,1,2,6,3,4,5]=>101000
[7,1,2,6,3,5,4]=>101100
[7,1,2,6,4,3,5]=>101100
[7,1,2,6,4,5,3]=>101100
[7,1,2,6,5,3,4]=>101010
[7,1,2,6,5,4,3]=>101110
[7,1,3,2,4,5,6]=>110000
[7,1,3,2,4,6,5]=>110010
[7,1,3,2,5,4,6]=>110100
[7,1,3,2,5,6,4]=>110100
[7,1,3,2,6,4,5]=>110100
[7,1,3,2,6,5,4]=>110110
[7,1,3,4,2,5,6]=>110000
[7,1,3,4,2,6,5]=>110010
[7,1,3,4,5,2,6]=>110000
[7,1,3,4,5,6,2]=>110000
[7,1,3,4,6,2,5]=>110000
[7,1,3,4,6,5,2]=>110010
[7,1,3,5,2,4,6]=>110000
[7,1,3,5,2,6,4]=>110100
[7,1,3,5,4,2,6]=>110100
[7,1,3,5,4,6,2]=>110100
[7,1,3,5,6,2,4]=>110000
[7,1,3,5,6,4,2]=>110100
[7,1,3,6,2,4,5]=>110000
[7,1,3,6,2,5,4]=>110100
[7,1,3,6,4,2,5]=>110100
[7,1,3,6,4,5,2]=>110100
[7,1,3,6,5,2,4]=>110010
[7,1,3,6,5,4,2]=>110110
[7,1,4,2,3,5,6]=>110000
[7,1,4,2,3,6,5]=>110010
[7,1,4,2,5,3,6]=>111000
[7,1,4,2,5,6,3]=>111000
[7,1,4,2,6,3,5]=>111000
[7,1,4,2,6,5,3]=>111010
[7,1,4,3,2,5,6]=>111000
[7,1,4,3,2,6,5]=>111010
[7,1,4,3,5,2,6]=>111000
[7,1,4,3,5,6,2]=>111000
[7,1,4,3,6,2,5]=>111000
[7,1,4,3,6,5,2]=>111010
[7,1,4,5,2,3,6]=>110000
[7,1,4,5,2,6,3]=>111000
[7,1,4,5,3,2,6]=>111000
[7,1,4,5,3,6,2]=>111000
[7,1,4,5,6,2,3]=>110000
[7,1,4,5,6,3,2]=>111000
[7,1,4,6,2,3,5]=>110000
[7,1,4,6,2,5,3]=>111000
[7,1,4,6,3,2,5]=>111000
[7,1,4,6,3,5,2]=>111000
[7,1,4,6,5,2,3]=>110010
[7,1,4,6,5,3,2]=>111010
[7,1,5,2,3,4,6]=>110000
[7,1,5,2,3,6,4]=>110100
[7,1,5,2,4,3,6]=>111000
[7,1,5,2,4,6,3]=>111000
[7,1,5,2,6,3,4]=>111000
[7,1,5,2,6,4,3]=>111100
[7,1,5,3,2,4,6]=>111000
[7,1,5,3,2,6,4]=>111100
[7,1,5,3,4,2,6]=>111000
[7,1,5,3,4,6,2]=>111000
[7,1,5,3,6,2,4]=>111000
[7,1,5,3,6,4,2]=>111100
[7,1,5,4,2,3,6]=>110100
[7,1,5,4,2,6,3]=>111100
[7,1,5,4,3,2,6]=>111100
[7,1,5,4,3,6,2]=>111100
[7,1,5,4,6,2,3]=>110100
[7,1,5,4,6,3,2]=>111100
[7,1,5,6,2,3,4]=>110000
[7,1,5,6,2,4,3]=>111000
[7,1,5,6,3,2,4]=>111000
[7,1,5,6,3,4,2]=>111000
[7,1,5,6,4,2,3]=>110100
[7,1,5,6,4,3,2]=>111100
[7,1,6,2,3,4,5]=>110000
[7,1,6,2,3,5,4]=>110100
[7,1,6,2,4,3,5]=>111000
[7,1,6,2,4,5,3]=>111000
[7,1,6,2,5,3,4]=>111000
[7,1,6,2,5,4,3]=>111100
[7,1,6,3,2,4,5]=>111000
[7,1,6,3,2,5,4]=>111100
[7,1,6,3,4,2,5]=>111000
[7,1,6,3,4,5,2]=>111000
[7,1,6,3,5,2,4]=>111000
[7,1,6,3,5,4,2]=>111100
[7,1,6,4,2,3,5]=>110100
[7,1,6,4,2,5,3]=>111100
[7,1,6,4,3,2,5]=>111100
[7,1,6,4,3,5,2]=>111100
[7,1,6,4,5,2,3]=>110100
[7,1,6,4,5,3,2]=>111100
[7,1,6,5,2,3,4]=>110010
[7,1,6,5,2,4,3]=>111010
[7,1,6,5,3,2,4]=>111010
[7,1,6,5,3,4,2]=>111010
[7,1,6,5,4,2,3]=>110110
[7,1,6,5,4,3,2]=>111110
[7,2,1,3,4,5,6]=>110000
[7,2,1,3,4,6,5]=>110010
[7,2,1,3,5,4,6]=>110100
[7,2,1,3,5,6,4]=>110100
[7,2,1,3,6,4,5]=>110100
[7,2,1,3,6,5,4]=>110110
[7,2,1,4,3,5,6]=>111000
[7,2,1,4,3,6,5]=>111010
[7,2,1,4,5,3,6]=>111000
[7,2,1,4,5,6,3]=>111000
[7,2,1,4,6,3,5]=>111000
[7,2,1,4,6,5,3]=>111010
[7,2,1,5,3,4,6]=>111000
[7,2,1,5,3,6,4]=>111100
[7,2,1,5,4,3,6]=>111100
[7,2,1,5,4,6,3]=>111100
[7,2,1,5,6,3,4]=>111000
[7,2,1,5,6,4,3]=>111100
[7,2,1,6,3,4,5]=>111000
[7,2,1,6,3,5,4]=>111100
[7,2,1,6,4,3,5]=>111100
[7,2,1,6,4,5,3]=>111100
[7,2,1,6,5,3,4]=>111010
[7,2,1,6,5,4,3]=>111110
[7,2,3,1,4,5,6]=>110000
[7,2,3,1,4,6,5]=>110010
[7,2,3,1,5,4,6]=>110100
[7,2,3,1,5,6,4]=>110100
[7,2,3,1,6,4,5]=>110100
[7,2,3,1,6,5,4]=>110110
[7,2,3,4,1,5,6]=>110000
[7,2,3,4,1,6,5]=>110010
[7,2,3,4,5,1,6]=>110000
[7,2,3,4,5,6,1]=>110000
[7,2,3,4,6,1,5]=>110000
[7,2,3,4,6,5,1]=>110010
[7,2,3,5,1,4,6]=>110000
[7,2,3,5,1,6,4]=>110100
[7,2,3,5,4,1,6]=>110100
[7,2,3,5,4,6,1]=>110100
[7,2,3,5,6,1,4]=>110000
[7,2,3,5,6,4,1]=>110100
[7,2,3,6,1,4,5]=>110000
[7,2,3,6,1,5,4]=>110100
[7,2,3,6,4,1,5]=>110100
[7,2,3,6,4,5,1]=>110100
[7,2,3,6,5,1,4]=>110010
[7,2,3,6,5,4,1]=>110110
[7,2,4,1,3,5,6]=>110000
[7,2,4,1,3,6,5]=>110010
[7,2,4,1,5,3,6]=>111000
[7,2,4,1,5,6,3]=>111000
[7,2,4,1,6,3,5]=>111000
[7,2,4,1,6,5,3]=>111010
[7,2,4,3,1,5,6]=>111000
[7,2,4,3,1,6,5]=>111010
[7,2,4,3,5,1,6]=>111000
[7,2,4,3,5,6,1]=>111000
[7,2,4,3,6,1,5]=>111000
[7,2,4,3,6,5,1]=>111010
[7,2,4,5,1,3,6]=>110000
[7,2,4,5,1,6,3]=>111000
[7,2,4,5,3,1,6]=>111000
[7,2,4,5,3,6,1]=>111000
[7,2,4,5,6,1,3]=>110000
[7,2,4,5,6,3,1]=>111000
[7,2,4,6,1,3,5]=>110000
[7,2,4,6,1,5,3]=>111000
[7,2,4,6,3,1,5]=>111000
[7,2,4,6,3,5,1]=>111000
[7,2,4,6,5,1,3]=>110010
[7,2,4,6,5,3,1]=>111010
[7,2,5,1,3,4,6]=>110000
[7,2,5,1,3,6,4]=>110100
[7,2,5,1,4,3,6]=>111000
[7,2,5,1,4,6,3]=>111000
[7,2,5,1,6,3,4]=>111000
[7,2,5,1,6,4,3]=>111100
[7,2,5,3,1,4,6]=>111000
[7,2,5,3,1,6,4]=>111100
[7,2,5,3,4,1,6]=>111000
[7,2,5,3,4,6,1]=>111000
[7,2,5,3,6,1,4]=>111000
[7,2,5,3,6,4,1]=>111100
[7,2,5,4,1,3,6]=>110100
[7,2,5,4,1,6,3]=>111100
[7,2,5,4,3,1,6]=>111100
[7,2,5,4,3,6,1]=>111100
[7,2,5,4,6,1,3]=>110100
[7,2,5,4,6,3,1]=>111100
[7,2,5,6,1,3,4]=>110000
[7,2,5,6,1,4,3]=>111000
[7,2,5,6,3,1,4]=>111000
[7,2,5,6,3,4,1]=>111000
[7,2,5,6,4,1,3]=>110100
[7,2,5,6,4,3,1]=>111100
[7,2,6,1,3,4,5]=>110000
[7,2,6,1,3,5,4]=>110100
[7,2,6,1,4,3,5]=>111000
[7,2,6,1,4,5,3]=>111000
[7,2,6,1,5,3,4]=>111000
[7,2,6,1,5,4,3]=>111100
[7,2,6,3,1,4,5]=>111000
[7,2,6,3,1,5,4]=>111100
[7,2,6,3,4,1,5]=>111000
[7,2,6,3,4,5,1]=>111000
[7,2,6,3,5,1,4]=>111000
[7,2,6,3,5,4,1]=>111100
[7,2,6,4,1,3,5]=>110100
[7,2,6,4,1,5,3]=>111100
[7,2,6,4,3,1,5]=>111100
[7,2,6,4,3,5,1]=>111100
[7,2,6,4,5,1,3]=>110100
[7,2,6,4,5,3,1]=>111100
[7,2,6,5,1,3,4]=>110010
[7,2,6,5,1,4,3]=>111010
[7,2,6,5,3,1,4]=>111010
[7,2,6,5,3,4,1]=>111010
[7,2,6,5,4,1,3]=>110110
[7,2,6,5,4,3,1]=>111110
[7,3,1,2,4,5,6]=>101000
[7,3,1,2,4,6,5]=>101010
[7,3,1,2,5,4,6]=>101100
[7,3,1,2,5,6,4]=>101100
[7,3,1,2,6,4,5]=>101100
[7,3,1,2,6,5,4]=>101110
[7,3,1,4,2,5,6]=>111000
[7,3,1,4,2,6,5]=>111010
[7,3,1,4,5,2,6]=>111000
[7,3,1,4,5,6,2]=>111000
[7,3,1,4,6,2,5]=>111000
[7,3,1,4,6,5,2]=>111010
[7,3,1,5,2,4,6]=>111000
[7,3,1,5,2,6,4]=>111100
[7,3,1,5,4,2,6]=>111100
[7,3,1,5,4,6,2]=>111100
[7,3,1,5,6,2,4]=>111000
[7,3,1,5,6,4,2]=>111100
[7,3,1,6,2,4,5]=>111000
[7,3,1,6,2,5,4]=>111100
[7,3,1,6,4,2,5]=>111100
[7,3,1,6,4,5,2]=>111100
[7,3,1,6,5,2,4]=>111010
[7,3,1,6,5,4,2]=>111110
[7,3,2,1,4,5,6]=>111000
[7,3,2,1,4,6,5]=>111010
[7,3,2,1,5,4,6]=>111100
[7,3,2,1,5,6,4]=>111100
[7,3,2,1,6,4,5]=>111100
[7,3,2,1,6,5,4]=>111110
[7,3,2,4,1,5,6]=>111000
[7,3,2,4,1,6,5]=>111010
[7,3,2,4,5,1,6]=>111000
[7,3,2,4,5,6,1]=>111000
[7,3,2,4,6,1,5]=>111000
[7,3,2,4,6,5,1]=>111010
[7,3,2,5,1,4,6]=>111000
[7,3,2,5,1,6,4]=>111100
[7,3,2,5,4,1,6]=>111100
[7,3,2,5,4,6,1]=>111100
[7,3,2,5,6,1,4]=>111000
[7,3,2,5,6,4,1]=>111100
[7,3,2,6,1,4,5]=>111000
[7,3,2,6,1,5,4]=>111100
[7,3,2,6,4,1,5]=>111100
[7,3,2,6,4,5,1]=>111100
[7,3,2,6,5,1,4]=>111010
[7,3,2,6,5,4,1]=>111110
[7,3,4,1,2,5,6]=>101000
[7,3,4,1,2,6,5]=>101010
[7,3,4,1,5,2,6]=>111000
[7,3,4,1,5,6,2]=>111000
[7,3,4,1,6,2,5]=>111000
[7,3,4,1,6,5,2]=>111010
[7,3,4,2,1,5,6]=>111000
[7,3,4,2,1,6,5]=>111010
[7,3,4,2,5,1,6]=>111000
[7,3,4,2,5,6,1]=>111000
[7,3,4,2,6,1,5]=>111000
[7,3,4,2,6,5,1]=>111010
[7,3,4,5,1,2,6]=>101000
[7,3,4,5,1,6,2]=>111000
[7,3,4,5,2,1,6]=>111000
[7,3,4,5,2,6,1]=>111000
[7,3,4,5,6,1,2]=>101000
[7,3,4,5,6,2,1]=>111000
[7,3,4,6,1,2,5]=>101000
[7,3,4,6,1,5,2]=>111000
[7,3,4,6,2,1,5]=>111000
[7,3,4,6,2,5,1]=>111000
[7,3,4,6,5,1,2]=>101010
[7,3,4,6,5,2,1]=>111010
[7,3,5,1,2,4,6]=>101000
[7,3,5,1,2,6,4]=>101100
[7,3,5,1,4,2,6]=>111000
[7,3,5,1,4,6,2]=>111000
[7,3,5,1,6,2,4]=>111000
[7,3,5,1,6,4,2]=>111100
[7,3,5,2,1,4,6]=>111000
[7,3,5,2,1,6,4]=>111100
[7,3,5,2,4,1,6]=>111000
[7,3,5,2,4,6,1]=>111000
[7,3,5,2,6,1,4]=>111000
[7,3,5,2,6,4,1]=>111100
[7,3,5,4,1,2,6]=>101100
[7,3,5,4,1,6,2]=>111100
[7,3,5,4,2,1,6]=>111100
[7,3,5,4,2,6,1]=>111100
[7,3,5,4,6,1,2]=>101100
[7,3,5,4,6,2,1]=>111100
[7,3,5,6,1,2,4]=>101000
[7,3,5,6,1,4,2]=>111000
[7,3,5,6,2,1,4]=>111000
[7,3,5,6,2,4,1]=>111000
[7,3,5,6,4,1,2]=>101100
[7,3,5,6,4,2,1]=>111100
[7,3,6,1,2,4,5]=>101000
[7,3,6,1,2,5,4]=>101100
[7,3,6,1,4,2,5]=>111000
[7,3,6,1,4,5,2]=>111000
[7,3,6,1,5,2,4]=>111000
[7,3,6,1,5,4,2]=>111100
[7,3,6,2,1,4,5]=>111000
[7,3,6,2,1,5,4]=>111100
[7,3,6,2,4,1,5]=>111000
[7,3,6,2,4,5,1]=>111000
[7,3,6,2,5,1,4]=>111000
[7,3,6,2,5,4,1]=>111100
[7,3,6,4,1,2,5]=>101100
[7,3,6,4,1,5,2]=>111100
[7,3,6,4,2,1,5]=>111100
[7,3,6,4,2,5,1]=>111100
[7,3,6,4,5,1,2]=>101100
[7,3,6,4,5,2,1]=>111100
[7,3,6,5,1,2,4]=>101010
[7,3,6,5,1,4,2]=>111010
[7,3,6,5,2,1,4]=>111010
[7,3,6,5,2,4,1]=>111010
[7,3,6,5,4,1,2]=>101110
[7,3,6,5,4,2,1]=>111110
[7,4,1,2,3,5,6]=>100100
[7,4,1,2,3,6,5]=>100110
[7,4,1,2,5,3,6]=>101100
[7,4,1,2,5,6,3]=>101100
[7,4,1,2,6,3,5]=>101100
[7,4,1,2,6,5,3]=>101110
[7,4,1,3,2,5,6]=>110100
[7,4,1,3,2,6,5]=>110110
[7,4,1,3,5,2,6]=>110100
[7,4,1,3,5,6,2]=>110100
[7,4,1,3,6,2,5]=>110100
[7,4,1,3,6,5,2]=>110110
[7,4,1,5,2,3,6]=>110100
[7,4,1,5,2,6,3]=>111100
[7,4,1,5,3,2,6]=>111100
[7,4,1,5,3,6,2]=>111100
[7,4,1,5,6,2,3]=>110100
[7,4,1,5,6,3,2]=>111100
[7,4,1,6,2,3,5]=>110100
[7,4,1,6,2,5,3]=>111100
[7,4,1,6,3,2,5]=>111100
[7,4,1,6,3,5,2]=>111100
[7,4,1,6,5,2,3]=>110110
[7,4,1,6,5,3,2]=>111110
[7,4,2,1,3,5,6]=>110100
[7,4,2,1,3,6,5]=>110110
[7,4,2,1,5,3,6]=>111100
[7,4,2,1,5,6,3]=>111100
[7,4,2,1,6,3,5]=>111100
[7,4,2,1,6,5,3]=>111110
[7,4,2,3,1,5,6]=>110100
[7,4,2,3,1,6,5]=>110110
[7,4,2,3,5,1,6]=>110100
[7,4,2,3,5,6,1]=>110100
[7,4,2,3,6,1,5]=>110100
[7,4,2,3,6,5,1]=>110110
[7,4,2,5,1,3,6]=>110100
[7,4,2,5,1,6,3]=>111100
[7,4,2,5,3,1,6]=>111100
[7,4,2,5,3,6,1]=>111100
[7,4,2,5,6,1,3]=>110100
[7,4,2,5,6,3,1]=>111100
[7,4,2,6,1,3,5]=>110100
[7,4,2,6,1,5,3]=>111100
[7,4,2,6,3,1,5]=>111100
[7,4,2,6,3,5,1]=>111100
[7,4,2,6,5,1,3]=>110110
[7,4,2,6,5,3,1]=>111110
[7,4,3,1,2,5,6]=>101100
[7,4,3,1,2,6,5]=>101110
[7,4,3,1,5,2,6]=>111100
[7,4,3,1,5,6,2]=>111100
[7,4,3,1,6,2,5]=>111100
[7,4,3,1,6,5,2]=>111110
[7,4,3,2,1,5,6]=>111100
[7,4,3,2,1,6,5]=>111110
[7,4,3,2,5,1,6]=>111100
[7,4,3,2,5,6,1]=>111100
[7,4,3,2,6,1,5]=>111100
[7,4,3,2,6,5,1]=>111110
[7,4,3,5,1,2,6]=>101100
[7,4,3,5,1,6,2]=>111100
[7,4,3,5,2,1,6]=>111100
[7,4,3,5,2,6,1]=>111100
[7,4,3,5,6,1,2]=>101100
[7,4,3,5,6,2,1]=>111100
[7,4,3,6,1,2,5]=>101100
[7,4,3,6,1,5,2]=>111100
[7,4,3,6,2,1,5]=>111100
[7,4,3,6,2,5,1]=>111100
[7,4,3,6,5,1,2]=>101110
[7,4,3,6,5,2,1]=>111110
[7,4,5,1,2,3,6]=>100100
[7,4,5,1,2,6,3]=>101100
[7,4,5,1,3,2,6]=>110100
[7,4,5,1,3,6,2]=>110100
[7,4,5,1,6,2,3]=>110100
[7,4,5,1,6,3,2]=>111100
[7,4,5,2,1,3,6]=>110100
[7,4,5,2,1,6,3]=>111100
[7,4,5,2,3,1,6]=>110100
[7,4,5,2,3,6,1]=>110100
[7,4,5,2,6,1,3]=>110100
[7,4,5,2,6,3,1]=>111100
[7,4,5,3,1,2,6]=>101100
[7,4,5,3,1,6,2]=>111100
[7,4,5,3,2,1,6]=>111100
[7,4,5,3,2,6,1]=>111100
[7,4,5,3,6,1,2]=>101100
[7,4,5,3,6,2,1]=>111100
[7,4,5,6,1,2,3]=>100100
[7,4,5,6,1,3,2]=>110100
[7,4,5,6,2,1,3]=>110100
[7,4,5,6,2,3,1]=>110100
[7,4,5,6,3,1,2]=>101100
[7,4,5,6,3,2,1]=>111100
[7,4,6,1,2,3,5]=>100100
[7,4,6,1,2,5,3]=>101100
[7,4,6,1,3,2,5]=>110100
[7,4,6,1,3,5,2]=>110100
[7,4,6,1,5,2,3]=>110100
[7,4,6,1,5,3,2]=>111100
[7,4,6,2,1,3,5]=>110100
[7,4,6,2,1,5,3]=>111100
[7,4,6,2,3,1,5]=>110100
[7,4,6,2,3,5,1]=>110100
[7,4,6,2,5,1,3]=>110100
[7,4,6,2,5,3,1]=>111100
[7,4,6,3,1,2,5]=>101100
[7,4,6,3,1,5,2]=>111100
[7,4,6,3,2,1,5]=>111100
[7,4,6,3,2,5,1]=>111100
[7,4,6,3,5,1,2]=>101100
[7,4,6,3,5,2,1]=>111100
[7,4,6,5,1,2,3]=>100110
[7,4,6,5,1,3,2]=>110110
[7,4,6,5,2,1,3]=>110110
[7,4,6,5,2,3,1]=>110110
[7,4,6,5,3,1,2]=>101110
[7,4,6,5,3,2,1]=>111110
[7,5,1,2,3,4,6]=>100010
[7,5,1,2,3,6,4]=>100110
[7,5,1,2,4,3,6]=>101010
[7,5,1,2,4,6,3]=>101010
[7,5,1,2,6,3,4]=>101010
[7,5,1,2,6,4,3]=>101110
[7,5,1,3,2,4,6]=>110010
[7,5,1,3,2,6,4]=>110110
[7,5,1,3,4,2,6]=>110010
[7,5,1,3,4,6,2]=>110010
[7,5,1,3,6,2,4]=>110010
[7,5,1,3,6,4,2]=>110110
[7,5,1,4,2,3,6]=>110010
[7,5,1,4,2,6,3]=>111010
[7,5,1,4,3,2,6]=>111010
[7,5,1,4,3,6,2]=>111010
[7,5,1,4,6,2,3]=>110010
[7,5,1,4,6,3,2]=>111010
[7,5,1,6,2,3,4]=>110010
[7,5,1,6,2,4,3]=>111010
[7,5,1,6,3,2,4]=>111010
[7,5,1,6,3,4,2]=>111010
[7,5,1,6,4,2,3]=>110110
[7,5,1,6,4,3,2]=>111110
[7,5,2,1,3,4,6]=>110010
[7,5,2,1,3,6,4]=>110110
[7,5,2,1,4,3,6]=>111010
[7,5,2,1,4,6,3]=>111010
[7,5,2,1,6,3,4]=>111010
[7,5,2,1,6,4,3]=>111110
[7,5,2,3,1,4,6]=>110010
[7,5,2,3,1,6,4]=>110110
[7,5,2,3,4,1,6]=>110010
[7,5,2,3,4,6,1]=>110010
[7,5,2,3,6,1,4]=>110010
[7,5,2,3,6,4,1]=>110110
[7,5,2,4,1,3,6]=>110010
[7,5,2,4,1,6,3]=>111010
[7,5,2,4,3,1,6]=>111010
[7,5,2,4,3,6,1]=>111010
[7,5,2,4,6,1,3]=>110010
[7,5,2,4,6,3,1]=>111010
[7,5,2,6,1,3,4]=>110010
[7,5,2,6,1,4,3]=>111010
[7,5,2,6,3,1,4]=>111010
[7,5,2,6,3,4,1]=>111010
[7,5,2,6,4,1,3]=>110110
[7,5,2,6,4,3,1]=>111110
[7,5,3,1,2,4,6]=>101010
[7,5,3,1,2,6,4]=>101110
[7,5,3,1,4,2,6]=>111010
[7,5,3,1,4,6,2]=>111010
[7,5,3,1,6,2,4]=>111010
[7,5,3,1,6,4,2]=>111110
[7,5,3,2,1,4,6]=>111010
[7,5,3,2,1,6,4]=>111110
[7,5,3,2,4,1,6]=>111010
[7,5,3,2,4,6,1]=>111010
[7,5,3,2,6,1,4]=>111010
[7,5,3,2,6,4,1]=>111110
[7,5,3,4,1,2,6]=>101010
[7,5,3,4,1,6,2]=>111010
[7,5,3,4,2,1,6]=>111010
[7,5,3,4,2,6,1]=>111010
[7,5,3,4,6,1,2]=>101010
[7,5,3,4,6,2,1]=>111010
[7,5,3,6,1,2,4]=>101010
[7,5,3,6,1,4,2]=>111010
[7,5,3,6,2,1,4]=>111010
[7,5,3,6,2,4,1]=>111010
[7,5,3,6,4,1,2]=>101110
[7,5,3,6,4,2,1]=>111110
[7,5,4,1,2,3,6]=>100110
[7,5,4,1,2,6,3]=>101110
[7,5,4,1,3,2,6]=>110110
[7,5,4,1,3,6,2]=>110110
[7,5,4,1,6,2,3]=>110110
[7,5,4,1,6,3,2]=>111110
[7,5,4,2,1,3,6]=>110110
[7,5,4,2,1,6,3]=>111110
[7,5,4,2,3,1,6]=>110110
[7,5,4,2,3,6,1]=>110110
[7,5,4,2,6,1,3]=>110110
[7,5,4,2,6,3,1]=>111110
[7,5,4,3,1,2,6]=>101110
[7,5,4,3,1,6,2]=>111110
[7,5,4,3,2,1,6]=>111110
[7,5,4,3,2,6,1]=>111110
[7,5,4,3,6,1,2]=>101110
[7,5,4,3,6,2,1]=>111110
[7,5,4,6,1,2,3]=>100110
[7,5,4,6,1,3,2]=>110110
[7,5,4,6,2,1,3]=>110110
[7,5,4,6,2,3,1]=>110110
[7,5,4,6,3,1,2]=>101110
[7,5,4,6,3,2,1]=>111110
[7,5,6,1,2,3,4]=>100010
[7,5,6,1,2,4,3]=>101010
[7,5,6,1,3,2,4]=>110010
[7,5,6,1,3,4,2]=>110010
[7,5,6,1,4,2,3]=>110010
[7,5,6,1,4,3,2]=>111010
[7,5,6,2,1,3,4]=>110010
[7,5,6,2,1,4,3]=>111010
[7,5,6,2,3,1,4]=>110010
[7,5,6,2,3,4,1]=>110010
[7,5,6,2,4,1,3]=>110010
[7,5,6,2,4,3,1]=>111010
[7,5,6,3,1,2,4]=>101010
[7,5,6,3,1,4,2]=>111010
[7,5,6,3,2,1,4]=>111010
[7,5,6,3,2,4,1]=>111010
[7,5,6,3,4,1,2]=>101010
[7,5,6,3,4,2,1]=>111010
[7,5,6,4,1,2,3]=>100110
[7,5,6,4,1,3,2]=>110110
[7,5,6,4,2,1,3]=>110110
[7,5,6,4,2,3,1]=>110110
[7,5,6,4,3,1,2]=>101110
[7,5,6,4,3,2,1]=>111110
[7,6,1,2,3,4,5]=>100001
[7,6,1,2,3,5,4]=>100101
[7,6,1,2,4,3,5]=>101001
[7,6,1,2,4,5,3]=>101001
[7,6,1,2,5,3,4]=>101001
[7,6,1,2,5,4,3]=>101101
[7,6,1,3,2,4,5]=>110001
[7,6,1,3,2,5,4]=>110101
[7,6,1,3,4,2,5]=>110001
[7,6,1,3,4,5,2]=>110001
[7,6,1,3,5,2,4]=>110001
[7,6,1,3,5,4,2]=>110101
[7,6,1,4,2,3,5]=>110001
[7,6,1,4,2,5,3]=>111001
[7,6,1,4,3,2,5]=>111001
[7,6,1,4,3,5,2]=>111001
[7,6,1,4,5,2,3]=>110001
[7,6,1,4,5,3,2]=>111001
[7,6,1,5,2,3,4]=>110001
[7,6,1,5,2,4,3]=>111001
[7,6,1,5,3,2,4]=>111001
[7,6,1,5,3,4,2]=>111001
[7,6,1,5,4,2,3]=>110101
[7,6,1,5,4,3,2]=>111101
[7,6,2,1,3,4,5]=>110001
[7,6,2,1,3,5,4]=>110101
[7,6,2,1,4,3,5]=>111001
[7,6,2,1,4,5,3]=>111001
[7,6,2,1,5,3,4]=>111001
[7,6,2,1,5,4,3]=>111101
[7,6,2,3,1,4,5]=>110001
[7,6,2,3,1,5,4]=>110101
[7,6,2,3,4,1,5]=>110001
[7,6,2,3,4,5,1]=>110001
[7,6,2,3,5,1,4]=>110001
[7,6,2,3,5,4,1]=>110101
[7,6,2,4,1,3,5]=>110001
[7,6,2,4,1,5,3]=>111001
[7,6,2,4,3,1,5]=>111001
[7,6,2,4,3,5,1]=>111001
[7,6,2,4,5,1,3]=>110001
[7,6,2,4,5,3,1]=>111001
[7,6,2,5,1,3,4]=>110001
[7,6,2,5,1,4,3]=>111001
[7,6,2,5,3,1,4]=>111001
[7,6,2,5,3,4,1]=>111001
[7,6,2,5,4,1,3]=>110101
[7,6,2,5,4,3,1]=>111101
[7,6,3,1,2,4,5]=>101001
[7,6,3,1,2,5,4]=>101101
[7,6,3,1,4,2,5]=>111001
[7,6,3,1,4,5,2]=>111001
[7,6,3,1,5,2,4]=>111001
[7,6,3,1,5,4,2]=>111101
[7,6,3,2,1,4,5]=>111001
[7,6,3,2,1,5,4]=>111101
[7,6,3,2,4,1,5]=>111001
[7,6,3,2,4,5,1]=>111001
[7,6,3,2,5,1,4]=>111001
[7,6,3,2,5,4,1]=>111101
[7,6,3,4,1,2,5]=>101001
[7,6,3,4,1,5,2]=>111001
[7,6,3,4,2,1,5]=>111001
[7,6,3,4,2,5,1]=>111001
[7,6,3,4,5,1,2]=>101001
[7,6,3,4,5,2,1]=>111001
[7,6,3,5,1,2,4]=>101001
[7,6,3,5,1,4,2]=>111001
[7,6,3,5,2,1,4]=>111001
[7,6,3,5,2,4,1]=>111001
[7,6,3,5,4,1,2]=>101101
[7,6,3,5,4,2,1]=>111101
[7,6,4,1,2,3,5]=>100101
[7,6,4,1,2,5,3]=>101101
[7,6,4,1,3,2,5]=>110101
[7,6,4,1,3,5,2]=>110101
[7,6,4,1,5,2,3]=>110101
[7,6,4,1,5,3,2]=>111101
[7,6,4,2,1,3,5]=>110101
[7,6,4,2,1,5,3]=>111101
[7,6,4,2,3,1,5]=>110101
[7,6,4,2,3,5,1]=>110101
[7,6,4,2,5,1,3]=>110101
[7,6,4,2,5,3,1]=>111101
[7,6,4,3,1,2,5]=>101101
[7,6,4,3,1,5,2]=>111101
[7,6,4,3,2,1,5]=>111101
[7,6,4,3,2,5,1]=>111101
[7,6,4,3,5,1,2]=>101101
[7,6,4,3,5,2,1]=>111101
[7,6,4,5,1,2,3]=>100101
[7,6,4,5,1,3,2]=>110101
[7,6,4,5,2,1,3]=>110101
[7,6,4,5,2,3,1]=>110101
[7,6,4,5,3,1,2]=>101101
[7,6,4,5,3,2,1]=>111101
[7,6,5,1,2,3,4]=>100011
[7,6,5,1,2,4,3]=>101011
[7,6,5,1,3,2,4]=>110011
[7,6,5,1,3,4,2]=>110011
[7,6,5,1,4,2,3]=>110011
[7,6,5,1,4,3,2]=>111011
[7,6,5,2,1,3,4]=>110011
[7,6,5,2,1,4,3]=>111011
[7,6,5,2,3,1,4]=>110011
[7,6,5,2,3,4,1]=>110011
[7,6,5,2,4,1,3]=>110011
[7,6,5,2,4,3,1]=>111011
[7,6,5,3,1,2,4]=>101011
[7,6,5,3,1,4,2]=>111011
[7,6,5,3,2,1,4]=>111011
[7,6,5,3,2,4,1]=>111011
[7,6,5,3,4,1,2]=>101011
[7,6,5,3,4,2,1]=>111011
[7,6,5,4,1,2,3]=>100111
[7,6,5,4,1,3,2]=>110111
[7,6,5,4,2,1,3]=>110111
[7,6,5,4,2,3,1]=>110111
[7,6,5,4,3,1,2]=>101111
[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]=>1111110
[8,6,7,5,4,3,2,1]=>1111110
[7,6,8,5,4,3,2,1]=>1111110
[6,7,8,5,4,3,2,1]=>1111100
[8,7,5,6,4,3,2,1]=>1111101
[7,8,5,6,4,3,2,1]=>1111100
[8,6,5,7,4,3,2,1]=>1111110
[8,5,6,7,4,3,2,1]=>1111100
[7,6,5,8,4,3,2,1]=>1111110
[6,7,5,8,4,3,2,1]=>1111100
[7,5,6,8,4,3,2,1]=>1111100
[6,5,7,8,4,3,2,1]=>1111100
[5,6,7,8,4,3,2,1]=>1111000
[8,7,6,4,5,3,2,1]=>1111011
[8,6,7,4,5,3,2,1]=>1111010
[7,6,8,4,5,3,2,1]=>1111010
[8,7,5,4,6,3,2,1]=>1111101
[8,6,5,4,7,3,2,1]=>1111110
[8,5,6,4,7,3,2,1]=>1111100
[8,6,4,5,7,3,2,1]=>1111010
[7,6,5,4,8,3,2,1]=>1111110
[6,7,5,4,8,3,2,1]=>1111100
[7,5,6,4,8,3,2,1]=>1111100
[6,5,7,4,8,3,2,1]=>1111100
[5,6,7,4,8,3,2,1]=>1111000
[7,6,4,5,8,3,2,1]=>1111010
[6,7,4,5,8,3,2,1]=>1111000
[7,5,4,6,8,3,2,1]=>1111100
[7,4,5,6,8,3,2,1]=>1111000
[6,5,4,7,8,3,2,1]=>1111100
[5,6,4,7,8,3,2,1]=>1111000
[6,4,5,7,8,3,2,1]=>1111000
[5,4,6,7,8,3,2,1]=>1111000
[4,5,6,7,8,3,2,1]=>1110000
[8,7,6,5,3,4,2,1]=>1110111
[7,8,6,5,3,4,2,1]=>1110110
[7,6,8,5,3,4,2,1]=>1110110
[8,7,5,6,3,4,2,1]=>1110101
[7,8,5,6,3,4,2,1]=>1110100
[8,5,6,7,3,4,2,1]=>1110100
[7,6,5,8,3,4,2,1]=>1110110
[6,7,5,8,3,4,2,1]=>1110100
[5,6,7,8,3,4,2,1]=>1110000
[8,7,6,4,3,5,2,1]=>1111011
[7,8,6,4,3,5,2,1]=>1111010
[7,6,8,4,3,5,2,1]=>1111010
[6,7,8,4,3,5,2,1]=>1111000
[8,7,6,3,4,5,2,1]=>1110011
[7,8,6,3,4,5,2,1]=>1110010
[8,6,7,3,4,5,2,1]=>1110010
[7,6,8,3,4,5,2,1]=>1110010
[6,7,8,3,4,5,2,1]=>1110000
[8,7,5,4,3,6,2,1]=>1111101
[7,8,5,4,3,6,2,1]=>1111100
[7,8,5,3,4,6,2,1]=>1110100
[8,7,4,3,5,6,2,1]=>1111001
[8,7,3,4,5,6,2,1]=>1110001
[7,6,5,4,3,8,2,1]=>1111110
[7,5,6,4,3,8,2,1]=>1111100
[7,4,5,6,3,8,2,1]=>1111000
[6,4,5,7,3,8,2,1]=>1111000
[5,4,6,7,3,8,2,1]=>1111000
[4,5,6,7,3,8,2,1]=>1110000
[7,6,3,4,5,8,2,1]=>1110010
[7,5,4,3,6,8,2,1]=>1111100
[7,5,3,4,6,8,2,1]=>1110100
[6,5,4,3,7,8,2,1]=>1111100
[8,7,6,5,4,2,3,1]=>1101111
[8,6,7,5,4,2,3,1]=>1101110
[7,6,8,5,4,2,3,1]=>1101110
[8,5,6,7,4,2,3,1]=>1101100
[7,6,5,8,4,2,3,1]=>1101110
[6,7,5,8,4,2,3,1]=>1101100
[7,5,6,8,4,2,3,1]=>1101100
[5,6,7,8,4,2,3,1]=>1101000
[8,7,6,4,5,2,3,1]=>1101011
[8,6,7,4,5,2,3,1]=>1101010
[7,6,8,4,5,2,3,1]=>1101010
[6,7,8,4,5,2,3,1]=>1101000
[8,7,5,4,6,2,3,1]=>1101101
[8,7,4,5,6,2,3,1]=>1101001
[8,6,5,4,7,2,3,1]=>1101110
[8,5,6,4,7,2,3,1]=>1101100
[8,6,4,5,7,2,3,1]=>1101010
[6,5,7,4,8,2,3,1]=>1101100
[4,5,6,7,8,2,3,1]=>1100000
[8,7,6,5,3,2,4,1]=>1110111
[7,8,6,5,3,2,4,1]=>1110110
[8,6,7,5,3,2,4,1]=>1110110
[7,6,8,5,3,2,4,1]=>1110110
[6,7,8,5,3,2,4,1]=>1110100
[8,6,5,7,3,2,4,1]=>1110110
[8,5,6,7,3,2,4,1]=>1110100
[7,6,5,8,3,2,4,1]=>1110110
[6,7,5,8,3,2,4,1]=>1110100
[5,6,7,8,3,2,4,1]=>1110000
[8,7,6,5,2,3,4,1]=>1100111
[8,6,7,5,2,3,4,1]=>1100110
[7,6,8,5,2,3,4,1]=>1100110
[6,7,8,5,2,3,4,1]=>1100100
[8,7,5,6,2,3,4,1]=>1100101
[7,8,5,6,2,3,4,1]=>1100100
[8,6,5,7,2,3,4,1]=>1100110
[8,5,6,7,2,3,4,1]=>1100100
[7,6,5,8,2,3,4,1]=>1100110
[6,7,5,8,2,3,4,1]=>1100100
[6,5,7,8,2,3,4,1]=>1100100
[5,6,7,8,2,3,4,1]=>1100000
[8,7,6,4,3,2,5,1]=>1111011
[7,8,6,4,3,2,5,1]=>1111010
[8,6,7,4,3,2,5,1]=>1111010
[7,6,8,4,3,2,5,1]=>1111010
[6,7,8,4,3,2,5,1]=>1111000
[8,7,6,3,4,2,5,1]=>1110011
[8,6,7,3,4,2,5,1]=>1110010
[7,6,8,3,4,2,5,1]=>1110010
[7,6,8,4,2,3,5,1]=>1101010
[6,7,8,4,2,3,5,1]=>1101000
[8,6,7,3,2,4,5,1]=>1110010
[6,7,8,3,2,4,5,1]=>1110000
[8,7,6,2,3,4,5,1]=>1100011
[7,8,6,2,3,4,5,1]=>1100010
[8,6,7,2,3,4,5,1]=>1100010
[7,6,8,2,3,4,5,1]=>1100010
[6,7,8,2,3,4,5,1]=>1100000
[8,7,5,3,4,2,6,1]=>1110101
[7,8,5,3,4,2,6,1]=>1110100
[7,8,4,3,5,2,6,1]=>1111000
[8,7,5,3,2,4,6,1]=>1110101
[7,8,4,3,2,5,6,1]=>1111000
[7,8,3,4,2,5,6,1]=>1110000
[7,8,3,2,4,5,6,1]=>1110000
[8,6,5,4,3,2,7,1]=>1111110
[8,6,4,3,5,2,7,1]=>1111010
[8,6,3,4,5,2,7,1]=>1110010
[8,4,5,3,6,2,7,1]=>1111000
[8,5,6,4,2,3,7,1]=>1101100
[8,6,4,2,3,5,7,1]=>1101010
[8,5,3,4,2,6,7,1]=>1110100
[8,5,4,2,3,6,7,1]=>1101100
[7,4,5,6,3,2,8,1]=>1111000
[6,4,5,7,3,2,8,1]=>1111000
[4,5,6,7,3,2,8,1]=>1110000
[6,5,4,3,7,2,8,1]=>1111100
[6,4,5,3,7,2,8,1]=>1111000
[5,4,6,3,7,2,8,1]=>1111000
[4,5,6,3,7,2,8,1]=>1110000
[6,5,3,4,7,2,8,1]=>1110100
[5,6,3,4,7,2,8,1]=>1110000
[5,4,3,6,7,2,8,1]=>1111000
[6,7,5,4,2,3,8,1]=>1101100
[7,5,6,4,2,3,8,1]=>1101100
[6,5,7,4,2,3,8,1]=>1101100
[5,6,7,4,2,3,8,1]=>1101000
[6,7,4,5,2,3,8,1]=>1101000
[7,4,5,6,2,3,8,1]=>1101000
[6,5,4,7,2,3,8,1]=>1101100
[5,6,4,7,2,3,8,1]=>1101000
[6,4,5,7,2,3,8,1]=>1101000
[5,4,6,7,2,3,8,1]=>1101000
[4,5,6,7,2,3,8,1]=>1100000
[6,7,5,3,2,4,8,1]=>1110100
[6,5,7,3,2,4,8,1]=>1110100
[7,6,5,2,3,4,8,1]=>1100110
[5,6,7,2,3,4,8,1]=>1100000
[6,7,4,3,2,5,8,1]=>1111000
[7,6,4,2,3,5,8,1]=>1101010
[6,7,3,2,4,5,8,1]=>1110000
[6,7,2,3,4,5,8,1]=>1100000
[7,5,2,3,4,6,8,1]=>1100100
[6,5,4,3,2,7,8,1]=>1111100
[5,4,6,3,2,7,8,1]=>1111000
[5,4,3,6,2,7,8,1]=>1111000
[3,4,5,6,2,7,8,1]=>1100000
[6,5,4,2,3,7,8,1]=>1101100
[5,6,4,2,3,7,8,1]=>1101000
[6,4,5,2,3,7,8,1]=>1101000
[5,4,6,2,3,7,8,1]=>1101000
[6,5,2,3,4,7,8,1]=>1100100
[5,4,3,2,6,7,8,1]=>1111000
[4,3,5,2,6,7,8,1]=>1110000
[5,4,2,3,6,7,8,1]=>1101000
[4,5,2,3,6,7,8,1]=>1100000
[5,2,3,4,6,7,8,1]=>1100000
[4,3,2,5,6,7,8,1]=>1110000
[3,4,2,5,6,7,8,1]=>1100000
[3,2,4,5,6,7,8,1]=>1100000
[2,3,4,5,6,7,8,1]=>1000000
[8,7,6,5,4,3,1,2]=>1011111
[7,8,6,5,4,3,1,2]=>1011110
[8,7,5,6,4,3,1,2]=>1011101
[7,8,5,6,4,3,1,2]=>1011100
[7,6,5,8,4,3,1,2]=>1011110
[6,7,5,8,4,3,1,2]=>1011100
[7,5,6,8,4,3,1,2]=>1011100
[5,6,7,8,4,3,1,2]=>1011000
[7,8,6,4,5,3,1,2]=>1011010
[8,6,7,4,5,3,1,2]=>1011010
[8,7,5,4,6,3,1,2]=>1011101
[7,8,4,5,6,3,1,2]=>1011000
[8,5,6,4,7,3,1,2]=>1011100
[6,5,7,4,8,3,1,2]=>1011100
[7,6,4,5,8,3,1,2]=>1011010
[6,7,4,5,8,3,1,2]=>1011000
[5,6,4,7,8,3,1,2]=>1011000
[4,5,6,7,8,3,1,2]=>1010000
[8,7,6,5,3,4,1,2]=>1010111
[7,8,6,5,3,4,1,2]=>1010110
[6,7,8,5,3,4,1,2]=>1010100
[8,7,5,6,3,4,1,2]=>1010101
[7,8,5,6,3,4,1,2]=>1010100
[8,5,6,7,3,4,1,2]=>1010100
[7,6,5,8,3,4,1,2]=>1010110
[6,7,5,8,3,4,1,2]=>1010100
[7,5,6,8,3,4,1,2]=>1010100
[6,5,7,8,3,4,1,2]=>1010100
[5,6,7,8,3,4,1,2]=>1010000
[8,7,6,3,4,5,1,2]=>1010011
[7,8,6,3,4,5,1,2]=>1010010
[7,8,5,4,3,6,1,2]=>1011100
[8,7,4,5,3,6,1,2]=>1011001
[7,8,4,5,3,6,1,2]=>1011000
[7,8,5,3,4,6,1,2]=>1010100
[8,7,4,3,5,6,1,2]=>1011001
[7,8,4,3,5,6,1,2]=>1011000
[7,8,3,4,5,6,1,2]=>1010000
[8,5,4,6,3,7,1,2]=>1011100
[8,5,4,3,6,7,1,2]=>1011100
[8,5,3,4,6,7,1,2]=>1010100
[8,4,3,5,6,7,1,2]=>1011000
[7,6,5,4,3,8,1,2]=>1011110
[5,6,7,4,3,8,1,2]=>1011000
[6,7,4,5,3,8,1,2]=>1011000
[7,5,4,6,3,8,1,2]=>1011100
[6,5,4,7,3,8,1,2]=>1011100
[5,6,4,7,3,8,1,2]=>1011000
[5,4,6,7,3,8,1,2]=>1011000
[4,5,6,7,3,8,1,2]=>1010000
[7,5,6,3,4,8,1,2]=>1010100
[7,6,3,4,5,8,1,2]=>1010010
[7,5,4,3,6,8,1,2]=>1011100
[7,4,5,3,6,8,1,2]=>1011000
[7,5,3,4,6,8,1,2]=>1010100
[6,5,4,3,7,8,1,2]=>1011100
[5,4,6,3,7,8,1,2]=>1011000
[4,5,6,3,7,8,1,2]=>1010000
[5,6,3,4,7,8,1,2]=>1010000
[6,4,3,5,7,8,1,2]=>1011000
[6,3,4,5,7,8,1,2]=>1010000
[5,4,3,6,7,8,1,2]=>1011000
[4,5,3,6,7,8,1,2]=>1010000
[5,3,4,6,7,8,1,2]=>1010000
[4,3,5,6,7,8,1,2]=>1010000
[3,4,5,6,7,8,1,2]=>1000000
[8,7,6,5,4,2,1,3]=>1101111
[7,6,8,5,4,2,1,3]=>1101110
[6,7,8,5,4,2,1,3]=>1101100
[8,7,5,6,4,2,1,3]=>1101101
[7,8,5,6,4,2,1,3]=>1101100
[7,6,5,8,4,2,1,3]=>1101110
[6,7,5,8,4,2,1,3]=>1101100
[7,5,6,8,4,2,1,3]=>1101100
[6,5,7,8,4,2,1,3]=>1101100
[5,6,7,8,4,2,1,3]=>1101000
[7,6,8,4,5,2,1,3]=>1101010
[8,7,4,5,6,2,1,3]=>1101001
[6,7,5,4,8,2,1,3]=>1101100
[7,5,6,4,8,2,1,3]=>1101100
[7,6,4,5,8,2,1,3]=>1101010
[4,5,6,7,8,2,1,3]=>1100000
[8,7,6,5,4,1,2,3]=>1001111
[6,7,8,5,4,1,2,3]=>1001100
[7,8,5,6,4,1,2,3]=>1001100
[8,5,6,7,4,1,2,3]=>1001100
[7,6,5,8,4,1,2,3]=>1001110
[6,7,5,8,4,1,2,3]=>1001100
[6,5,7,8,4,1,2,3]=>1001100
[5,6,7,8,4,1,2,3]=>1001000
[8,6,7,4,5,1,2,3]=>1001010
[8,7,5,4,6,1,2,3]=>1001101
[8,6,5,4,7,1,2,3]=>1001110
[8,5,6,4,7,1,2,3]=>1001100
[8,6,4,5,7,1,2,3]=>1001010
[7,6,5,4,8,1,2,3]=>1001110
[6,7,5,4,8,1,2,3]=>1001100
[7,5,6,4,8,1,2,3]=>1001100
[6,5,7,4,8,1,2,3]=>1001100
[5,6,7,4,8,1,2,3]=>1001000
[7,6,4,5,8,1,2,3]=>1001010
[6,7,4,5,8,1,2,3]=>1001000
[7,5,4,6,8,1,2,3]=>1001100
[7,4,5,6,8,1,2,3]=>1001000
[6,5,4,7,8,1,2,3]=>1001100
[5,6,4,7,8,1,2,3]=>1001000
[6,4,5,7,8,1,2,3]=>1001000
[5,4,6,7,8,1,2,3]=>1001000
[4,5,6,7,8,1,2,3]=>1000000
[8,7,6,5,3,2,1,4]=>1110111
[7,8,6,5,3,2,1,4]=>1110110
[8,6,7,5,3,2,1,4]=>1110110
[7,6,8,5,3,2,1,4]=>1110110
[6,7,8,5,3,2,1,4]=>1110100
[8,7,5,6,3,2,1,4]=>1110101
[7,8,5,6,3,2,1,4]=>1110100
[8,6,5,7,3,2,1,4]=>1110110
[8,5,6,7,3,2,1,4]=>1110100
[7,6,5,8,3,2,1,4]=>1110110
[6,7,5,8,3,2,1,4]=>1110100
[7,5,6,8,3,2,1,4]=>1110100
[6,5,7,8,3,2,1,4]=>1110100
[5,6,7,8,3,2,1,4]=>1110000
[8,7,6,5,2,3,1,4]=>1100111
[7,8,6,5,2,3,1,4]=>1100110
[8,6,7,5,2,3,1,4]=>1100110
[7,6,8,5,2,3,1,4]=>1100110
[6,7,8,5,2,3,1,4]=>1100100
[8,7,5,6,2,3,1,4]=>1100101
[7,8,5,6,2,3,1,4]=>1100100
[8,6,5,7,2,3,1,4]=>1100110
[8,5,6,7,2,3,1,4]=>1100100
[7,6,5,8,2,3,1,4]=>1100110
[6,7,5,8,2,3,1,4]=>1100100
[7,5,6,8,2,3,1,4]=>1100100
[6,5,7,8,2,3,1,4]=>1100100
[5,6,7,8,2,3,1,4]=>1100000
[8,7,6,5,3,1,2,4]=>1010111
[7,8,6,5,3,1,2,4]=>1010110
[7,8,5,6,3,1,2,4]=>1010100
[7,6,5,8,3,1,2,4]=>1010110
[6,7,5,8,3,1,2,4]=>1010100
[7,5,6,8,3,1,2,4]=>1010100
[6,5,7,8,3,1,2,4]=>1010100
[5,6,7,8,3,1,2,4]=>1010000
[8,7,6,5,2,1,3,4]=>1100111
[7,6,8,5,2,1,3,4]=>1100110
[6,7,8,5,2,1,3,4]=>1100100
[7,8,5,6,2,1,3,4]=>1100100
[8,6,5,7,2,1,3,4]=>1100110
[8,5,6,7,2,1,3,4]=>1100100
[7,6,5,8,2,1,3,4]=>1100110
[6,7,5,8,2,1,3,4]=>1100100
[7,5,6,8,2,1,3,4]=>1100100
[6,5,7,8,2,1,3,4]=>1100100
[5,6,7,8,2,1,3,4]=>1100000
[8,7,6,5,1,2,3,4]=>1000111
[7,8,6,5,1,2,3,4]=>1000110
[8,6,7,5,1,2,3,4]=>1000110
[7,6,8,5,1,2,3,4]=>1000110
[6,7,8,5,1,2,3,4]=>1000100
[8,7,5,6,1,2,3,4]=>1000101
[7,8,5,6,1,2,3,4]=>1000100
[8,6,5,7,1,2,3,4]=>1000110
[8,5,6,7,1,2,3,4]=>1000100
[7,6,5,8,1,2,3,4]=>1000110
[6,7,5,8,1,2,3,4]=>1000100
[7,5,6,8,1,2,3,4]=>1000100
[6,5,7,8,1,2,3,4]=>1000100
[5,6,7,8,1,2,3,4]=>1000000
[8,7,6,4,3,2,1,5]=>1111011
[7,8,6,4,3,2,1,5]=>1111010
[8,6,7,4,3,2,1,5]=>1111010
[7,6,8,4,3,2,1,5]=>1111010
[6,7,8,4,3,2,1,5]=>1111000
[8,7,6,3,4,2,1,5]=>1110011
[7,8,6,3,4,2,1,5]=>1110010
[6,7,8,3,4,2,1,5]=>1110000
[8,7,6,4,2,3,1,5]=>1101011
[7,6,8,4,2,3,1,5]=>1101010
[6,7,8,4,2,3,1,5]=>1101000
[8,7,6,3,2,4,1,5]=>1110011
[8,6,7,3,2,4,1,5]=>1110010
[6,7,8,3,2,4,1,5]=>1110000
[8,7,6,2,3,4,1,5]=>1100011
[6,7,8,2,3,4,1,5]=>1100000
[8,7,6,4,3,1,2,5]=>1011011
[6,7,8,4,3,1,2,5]=>1011000
[8,7,6,3,4,1,2,5]=>1010011
[6,7,8,3,4,1,2,5]=>1010000
[8,7,6,4,2,1,3,5]=>1101011
[7,8,6,4,2,1,3,5]=>1101010
[8,6,7,4,2,1,3,5]=>1101010
[6,7,8,4,2,1,3,5]=>1101000
[8,7,6,4,1,2,3,5]=>1001011
[7,8,6,4,1,2,3,5]=>1001010
[7,6,8,4,1,2,3,5]=>1001010
[6,7,8,4,1,2,3,5]=>1001000
[8,7,6,3,2,1,4,5]=>1110011
[7,6,8,3,2,1,4,5]=>1110010
[6,7,8,3,2,1,4,5]=>1110000
[8,7,6,2,3,1,4,5]=>1100011
[7,6,8,2,3,1,4,5]=>1100010
[6,7,8,2,3,1,4,5]=>1100000
[8,7,6,3,1,2,4,5]=>1010011
[7,8,6,3,1,2,4,5]=>1010010
[6,7,8,3,1,2,4,5]=>1010000
[8,7,6,2,1,3,4,5]=>1100011
[7,8,6,2,1,3,4,5]=>1100010
[6,7,8,2,1,3,4,5]=>1100000
[8,7,6,1,2,3,4,5]=>1000011
[7,8,6,1,2,3,4,5]=>1000010
[8,6,7,1,2,3,4,5]=>1000010
[7,6,8,1,2,3,4,5]=>1000010
[6,7,8,1,2,3,4,5]=>1000000
[8,7,5,4,3,2,1,6]=>1111101
[7,8,5,4,3,2,1,6]=>1111100
[8,7,5,3,4,2,1,6]=>1110101
[8,7,3,4,5,2,1,6]=>1110001
[7,8,3,4,5,2,1,6]=>1110000
[8,7,4,5,2,3,1,6]=>1101001
[7,8,4,5,2,3,1,6]=>1101000
[8,7,5,3,2,4,1,6]=>1110101
[8,7,4,3,2,5,1,6]=>1111001
[7,8,4,3,2,5,1,6]=>1111000
[8,7,3,4,2,5,1,6]=>1110001
[7,8,3,4,2,5,1,6]=>1110000
[8,7,5,4,3,1,2,6]=>1011101
[7,8,5,4,3,1,2,6]=>1011100
[8,7,5,3,4,1,2,6]=>1010101
[7,8,5,3,4,1,2,6]=>1010100
[7,8,5,4,2,1,3,6]=>1101100
[7,8,5,4,1,2,3,6]=>1001100
[8,7,4,5,1,2,3,6]=>1001001
[8,7,5,3,2,1,4,6]=>1110101
[7,8,5,3,2,1,4,6]=>1110100
[8,7,5,2,3,1,4,6]=>1100101
[8,7,5,3,1,2,4,6]=>1010101
[7,8,5,3,1,2,4,6]=>1010100
[8,7,5,2,1,3,4,6]=>1100101
[7,8,5,2,1,3,4,6]=>1100100
[8,7,5,1,2,3,4,6]=>1000101
[7,8,5,1,2,3,4,6]=>1000100
[8,7,4,3,2,1,5,6]=>1111001
[7,8,4,3,2,1,5,6]=>1111000
[8,7,3,4,2,1,5,6]=>1110001
[7,8,3,4,2,1,5,6]=>1110000
[7,8,4,2,3,1,5,6]=>1101000
[8,7,3,2,4,1,5,6]=>1110001
[7,8,3,2,4,1,5,6]=>1110000
[7,8,2,3,4,1,5,6]=>1100000
[7,8,4,3,1,2,5,6]=>1011000
[8,7,3,4,1,2,5,6]=>1010001
[7,8,3,4,1,2,5,6]=>1010000
[7,8,4,2,1,3,5,6]=>1101000
[7,8,4,1,2,3,5,6]=>1001000
[8,7,3,2,1,4,5,6]=>1110001
[7,8,3,2,1,4,5,6]=>1110000
[7,8,2,3,1,4,5,6]=>1100000
[7,8,3,1,2,4,5,6]=>1010000
[8,7,2,1,3,4,5,6]=>1100001
[7,8,2,1,3,4,5,6]=>1100000
[7,8,1,2,3,4,5,6]=>1000000
[8,6,5,4,3,2,1,7]=>1111110
[8,5,6,4,3,2,1,7]=>1111100
[8,4,5,6,3,2,1,7]=>1111000
[8,6,5,3,4,2,1,7]=>1110110
[8,5,6,3,4,2,1,7]=>1110100
[8,4,5,3,6,2,1,7]=>1111000
[8,3,4,5,6,2,1,7]=>1110000
[8,6,5,4,2,3,1,7]=>1101110
[8,5,6,4,2,3,1,7]=>1101100
[8,6,5,3,2,4,1,7]=>1110110
[8,6,5,2,3,4,1,7]=>1100110
[8,5,6,2,3,4,1,7]=>1100100
[8,6,4,2,3,5,1,7]=>1101010
[8,6,3,2,4,5,1,7]=>1110010
[8,5,2,3,4,6,1,7]=>1100100
[8,6,4,5,3,1,2,7]=>1011010
[8,5,6,3,4,1,2,7]=>1010100
[8,6,3,4,5,1,2,7]=>1010010
[8,4,5,3,6,1,2,7]=>1011000
[8,4,3,5,6,1,2,7]=>1011000
[8,3,4,5,6,1,2,7]=>1010000
[8,6,5,4,2,1,3,7]=>1101110
[8,5,6,4,2,1,3,7]=>1101100
[8,5,6,4,1,2,3,7]=>1001100
[8,4,5,6,1,2,3,7]=>1001000
[8,6,5,3,2,1,4,7]=>1110110
[8,5,6,3,2,1,4,7]=>1110100
[8,6,5,2,3,1,4,7]=>1100110
[8,5,6,2,3,1,4,7]=>1100100
[8,5,6,3,1,2,4,7]=>1010100
[8,6,5,2,1,3,4,7]=>1100110
[8,5,6,2,1,3,4,7]=>1100100
[8,6,5,1,2,3,4,7]=>1000110
[8,5,6,1,2,3,4,7]=>1000100
[8,6,4,3,2,1,5,7]=>1111010
[8,6,3,4,2,1,5,7]=>1110010
[8,6,4,2,3,1,5,7]=>1101010
[8,6,3,2,4,1,5,7]=>1110010
[8,6,3,4,1,2,5,7]=>1010010
[8,6,4,2,1,3,5,7]=>1101010
[8,6,3,2,1,4,5,7]=>1110010
[8,4,5,3,2,1,6,7]=>1111000
[8,4,3,5,2,1,6,7]=>1111000
[8,3,4,5,2,1,6,7]=>1110000
[8,4,5,2,3,1,6,7]=>1101000
[8,4,2,3,5,1,6,7]=>1101000
[8,5,3,4,1,2,6,7]=>1010100
[8,5,4,2,1,3,6,7]=>1101100
[8,5,3,2,1,4,6,7]=>1110100
[8,4,3,2,1,5,6,7]=>1111000
[8,2,3,4,1,5,6,7]=>1100000
[8,3,4,1,2,5,6,7]=>1010000
[8,4,2,1,3,5,6,7]=>1101000
[8,3,2,1,4,5,6,7]=>1110000
[8,2,3,1,4,5,6,7]=>1100000
[8,3,1,2,4,5,6,7]=>1010000
[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]=>1111100
[7,5,6,4,3,2,1,8]=>1111100
[6,5,7,4,3,2,1,8]=>1111100
[5,6,7,4,3,2,1,8]=>1111000
[7,6,4,5,3,2,1,8]=>1111010
[7,4,5,6,3,2,1,8]=>1111000
[6,5,4,7,3,2,1,8]=>1111100
[5,6,4,7,3,2,1,8]=>1111000
[4,5,6,7,3,2,1,8]=>1110000
[7,6,5,3,4,2,1,8]=>1110110
[6,7,5,3,4,2,1,8]=>1110100
[7,5,6,3,4,2,1,8]=>1110100
[6,5,7,3,4,2,1,8]=>1110100
[5,6,7,3,4,2,1,8]=>1110000
[7,6,3,4,5,2,1,8]=>1110010
[7,4,5,3,6,2,1,8]=>1111000
[7,3,4,5,6,2,1,8]=>1110000
[6,5,4,3,7,2,1,8]=>1111100
[5,4,6,3,7,2,1,8]=>1111000
[5,4,3,6,7,2,1,8]=>1111000
[7,5,6,4,2,3,1,8]=>1101100
[5,6,7,4,2,3,1,8]=>1101000
[7,6,4,5,2,3,1,8]=>1101010
[6,7,4,5,2,3,1,8]=>1101000
[7,4,5,6,2,3,1,8]=>1101000
[6,5,4,7,2,3,1,8]=>1101100
[5,6,4,7,2,3,1,8]=>1101000
[5,4,6,7,2,3,1,8]=>1101000
[4,5,6,7,2,3,1,8]=>1100000
[5,6,7,3,2,4,1,8]=>1110000
[7,6,5,2,3,4,1,8]=>1100110
[6,7,5,2,3,4,1,8]=>1100100
[7,5,6,2,3,4,1,8]=>1100100
[6,5,7,2,3,4,1,8]=>1100100
[5,6,7,2,3,4,1,8]=>1100000
[6,7,4,3,2,5,1,8]=>1111000
[6,7,3,4,2,5,1,8]=>1110000
[7,6,4,2,3,5,1,8]=>1101010
[7,6,3,2,4,5,1,8]=>1110010
[6,7,3,2,4,5,1,8]=>1110000
[7,6,2,3,4,5,1,8]=>1100010
[6,7,2,3,4,5,1,8]=>1100000
[7,4,5,3,2,6,1,8]=>1111000
[7,5,3,4,2,6,1,8]=>1110100
[7,4,3,5,2,6,1,8]=>1111000
[7,4,5,2,3,6,1,8]=>1101000
[7,5,3,2,4,6,1,8]=>1110100
[5,4,6,3,2,7,1,8]=>1111000
[5,6,3,4,2,7,1,8]=>1110000
[6,3,4,5,2,7,1,8]=>1110000
[5,4,3,6,2,7,1,8]=>1111000
[4,5,3,6,2,7,1,8]=>1110000
[3,4,5,6,2,7,1,8]=>1100000
[6,5,3,2,4,7,1,8]=>1110100
[6,3,2,4,5,7,1,8]=>1110000
[6,2,3,4,5,7,1,8]=>1100000
[5,4,3,2,6,7,1,8]=>1111000
[4,5,2,3,6,7,1,8]=>1100000
[7,4,5,6,3,1,2,8]=>1011000
[5,4,6,7,3,1,2,8]=>1011000
[4,5,6,7,3,1,2,8]=>1010000
[7,5,6,3,4,1,2,8]=>1010100
[6,5,7,3,4,1,2,8]=>1010100
[6,7,3,4,5,1,2,8]=>1010000
[7,5,3,4,6,1,2,8]=>1010100
[6,5,4,3,7,1,2,8]=>1011100
[6,4,5,3,7,1,2,8]=>1011000
[3,4,5,6,7,1,2,8]=>1000000
[7,4,5,6,2,1,3,8]=>1101000
[4,5,6,7,2,1,3,8]=>1100000
[7,6,5,4,1,2,3,8]=>1001110
[7,5,6,4,1,2,3,8]=>1001100
[5,6,7,4,1,2,3,8]=>1001000
[7,6,4,5,1,2,3,8]=>1001010
[7,5,4,6,1,2,3,8]=>1001100
[7,4,5,6,1,2,3,8]=>1001000
[5,6,4,7,1,2,3,8]=>1001000
[5,4,6,7,1,2,3,8]=>1001000
[4,5,6,7,1,2,3,8]=>1000000
[7,6,5,2,3,1,4,8]=>1100110
[6,7,5,2,3,1,4,8]=>1100100
[7,5,6,2,3,1,4,8]=>1100100
[6,5,7,2,3,1,4,8]=>1100100
[5,6,7,2,3,1,4,8]=>1100000
[7,5,6,3,1,2,4,8]=>1010100
[5,6,7,3,1,2,4,8]=>1010000
[7,6,5,2,1,3,4,8]=>1100110
[5,6,7,2,1,3,4,8]=>1100000
[7,6,5,1,2,3,4,8]=>1000110
[6,7,5,1,2,3,4,8]=>1000100
[7,5,6,1,2,3,4,8]=>1000100
[6,5,7,1,2,3,4,8]=>1000100
[5,6,7,1,2,3,4,8]=>1000000
[7,6,4,3,2,1,5,8]=>1111010
[6,7,4,3,2,1,5,8]=>1111000
[6,7,3,4,2,1,5,8]=>1110000
[7,6,4,2,3,1,5,8]=>1101010
[7,6,3,2,4,1,5,8]=>1110010
[7,6,2,3,4,1,5,8]=>1100010
[6,7,2,3,4,1,5,8]=>1100000
[7,6,4,2,1,3,5,8]=>1101010
[7,6,3,2,1,4,5,8]=>1110010
[6,7,3,2,1,4,5,8]=>1110000
[7,6,2,3,1,4,5,8]=>1100010
[6,7,3,1,2,4,5,8]=>1010000
[6,7,1,2,3,4,5,8]=>1000000
[7,5,2,3,4,1,6,8]=>1100100
[7,4,2,3,5,1,6,8]=>1101000
[7,2,3,4,5,1,6,8]=>1100000
[7,5,3,4,1,2,6,8]=>1010100
[7,4,5,1,2,3,6,8]=>1001000
[7,5,3,2,1,4,6,8]=>1110100
[7,5,3,1,2,4,6,8]=>1010100
[7,5,1,2,3,4,6,8]=>1000100
[7,4,3,2,1,5,6,8]=>1111000
[7,4,3,1,2,5,6,8]=>1011000
[7,3,4,1,2,5,6,8]=>1010000
[7,3,1,2,4,5,6,8]=>1010000
[7,1,2,3,4,5,6,8]=>1000000
[5,6,4,3,2,1,7,8]=>1111000
[5,4,6,3,2,1,7,8]=>1111000
[4,5,6,3,2,1,7,8]=>1110000
[6,5,3,4,2,1,7,8]=>1110100
[5,4,3,6,2,1,7,8]=>1111000
[3,4,5,6,2,1,7,8]=>1100000
[5,4,6,2,3,1,7,8]=>1101000
[5,6,3,2,4,1,7,8]=>1110000
[6,5,2,3,4,1,7,8]=>1100100
[5,6,2,3,4,1,7,8]=>1100000
[6,4,3,2,5,1,7,8]=>1111000
[5,4,3,2,6,1,7,8]=>1111000
[4,5,3,2,6,1,7,8]=>1110000
[5,3,2,4,6,1,7,8]=>1110000
[6,5,4,3,1,2,7,8]=>1011100
[5,6,4,3,1,2,7,8]=>1011000
[5,4,6,3,1,2,7,8]=>1011000
[5,6,3,4,1,2,7,8]=>1010000
[6,4,3,5,1,2,7,8]=>1011000
[5,4,3,6,1,2,7,8]=>1011000
[5,6,4,2,1,3,7,8]=>1101000
[6,4,5,2,1,3,7,8]=>1101000
[5,4,6,2,1,3,7,8]=>1101000
[5,6,3,2,1,4,7,8]=>1110000
[6,4,3,2,1,5,7,8]=>1111000
[6,3,4,2,1,5,7,8]=>1110000
[6,4,3,1,2,5,7,8]=>1011000
[6,4,2,1,3,5,7,8]=>1101000
[5,4,3,2,1,6,7,8]=>1111000
[4,5,3,2,1,6,7,8]=>1110000
[5,3,4,2,1,6,7,8]=>1110000
[4,3,5,2,1,6,7,8]=>1110000
[3,4,5,2,1,6,7,8]=>1100000
[5,4,2,3,1,6,7,8]=>1101000
[4,5,2,3,1,6,7,8]=>1100000
[5,3,2,4,1,6,7,8]=>1110000
[5,2,3,4,1,6,7,8]=>1100000
[4,3,2,5,1,6,7,8]=>1110000
[3,4,2,5,1,6,7,8]=>1100000
[4,2,3,5,1,6,7,8]=>1100000
[3,2,4,5,1,6,7,8]=>1100000
[2,3,4,5,1,6,7,8]=>1000000
[5,4,3,1,2,6,7,8]=>1011000
[5,3,4,1,2,6,7,8]=>1010000
[5,4,2,1,3,6,7,8]=>1101000
[5,4,1,2,3,6,7,8]=>1001000
[4,5,1,2,3,6,7,8]=>1000000
[5,3,2,1,4,6,7,8]=>1110000
[5,2,3,1,4,6,7,8]=>1100000
[5,3,1,2,4,6,7,8]=>1010000
[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]=>1100000
[4,2,3,1,5,6,7,8]=>1100000
[3,2,4,1,5,6,7,8]=>1100000
[2,3,4,1,5,6,7,8]=>1000000
[4,3,1,2,5,6,7,8]=>1010000
[3,4,1,2,5,6,7,8]=>1000000
[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]=>1000000
[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]=>1111101
[5,8,7,6,4,3,2,1]=>1111011
[5,7,8,6,4,3,2,1]=>1111010
[6,5,8,7,4,3,2,1]=>1111101
[5,6,8,7,4,3,2,1]=>1111001
[5,7,6,8,4,3,2,1]=>1111010
[4,8,7,6,5,3,2,1]=>1110111
[4,7,8,6,5,3,2,1]=>1110110
[4,6,8,7,5,3,2,1]=>1110101
[4,7,6,8,5,3,2,1]=>1110110
[4,6,7,8,5,3,2,1]=>1110100
[4,5,8,7,6,3,2,1]=>1110011
[4,5,7,8,6,3,2,1]=>1110010
[4,6,5,8,7,3,2,1]=>1110101
[4,5,6,8,7,3,2,1]=>1110001
[5,7,6,4,8,3,2,1]=>1111010
[4,7,6,5,8,3,2,1]=>1110110
[4,6,7,5,8,3,2,1]=>1110100
[5,4,7,6,8,3,2,1]=>1111010
[4,5,7,6,8,3,2,1]=>1110010
[4,6,5,7,8,3,2,1]=>1110100
[3,8,7,6,5,4,2,1]=>1101111
[3,5,8,7,6,4,2,1]=>1101011
[3,5,7,8,6,4,2,1]=>1101010
[3,5,6,8,7,4,2,1]=>1101001
[3,7,6,5,8,4,2,1]=>1101110
[3,6,7,5,8,4,2,1]=>1101100
[3,5,6,7,8,4,2,1]=>1101000
[4,3,6,7,8,5,2,1]=>1110100
[3,4,8,7,6,5,2,1]=>1100111
[3,4,6,7,8,5,2,1]=>1100100
[5,4,3,7,8,6,2,1]=>1111010
[4,5,3,7,8,6,2,1]=>1110010
[4,3,5,7,8,6,2,1]=>1110010
[3,4,5,7,8,6,2,1]=>1100010
[4,5,6,3,8,7,2,1]=>1110001
[4,3,6,5,8,7,2,1]=>1110101
[5,4,3,6,8,7,2,1]=>1111001
[4,5,3,6,8,7,2,1]=>1110001
[4,3,5,6,8,7,2,1]=>1110001
[5,7,6,4,3,8,2,1]=>1111010
[4,7,6,5,3,8,2,1]=>1110110
[3,4,7,6,5,8,2,1]=>1100110
[4,5,3,7,6,8,2,1]=>1110010
[4,3,5,7,6,8,2,1]=>1110010
[3,4,6,5,7,8,2,1]=>1100100
[2,8,7,6,5,4,3,1]=>1011111
[2,7,6,8,5,4,3,1]=>1011110
[2,5,6,7,8,4,3,1]=>1011000
[2,4,8,7,6,5,3,1]=>1010111
[2,4,6,8,7,5,3,1]=>1010101
[2,4,6,7,8,5,3,1]=>1010100
[2,5,4,8,7,6,3,1]=>1011011
[2,4,5,7,8,6,3,1]=>1010010
[2,5,6,4,8,7,3,1]=>1011001
[2,4,6,5,8,7,3,1]=>1010101
[2,7,6,5,4,8,3,1]=>1011110
[2,6,7,5,4,8,3,1]=>1011100
[2,4,7,6,5,8,3,1]=>1010110
[2,6,5,4,7,8,3,1]=>1011100
[3,2,8,7,6,5,4,1]=>1101111
[3,2,6,8,7,5,4,1]=>1101101
[3,2,5,7,6,8,4,1]=>1101010
[3,2,5,6,7,8,4,1]=>1101000
[2,3,8,7,6,5,4,1]=>1001111
[2,3,6,7,8,5,4,1]=>1001100
[2,3,5,8,7,6,4,1]=>1001011
[2,3,5,7,8,6,4,1]=>1001010
[2,3,7,6,5,8,4,1]=>1001110
[2,3,5,6,7,8,4,1]=>1001000
[4,3,2,8,7,6,5,1]=>1110111
[4,3,2,7,8,6,5,1]=>1110110
[4,3,2,6,8,7,5,1]=>1110101
[3,4,2,8,7,6,5,1]=>1100111
[3,4,2,7,8,6,5,1]=>1100110
[2,4,3,8,7,6,5,1]=>1010111
[2,4,3,6,8,7,5,1]=>1010101
[3,2,4,8,7,6,5,1]=>1100111
[2,3,4,8,7,6,5,1]=>1000111
[2,3,4,6,7,8,5,1]=>1000100
[5,4,3,2,8,7,6,1]=>1111011
[5,4,3,2,7,8,6,1]=>1111010
[4,5,3,2,8,7,6,1]=>1110011
[4,3,5,2,8,7,6,1]=>1110011
[2,5,4,3,8,7,6,1]=>1011011
[2,5,4,3,7,8,6,1]=>1011010
[2,4,5,3,8,7,6,1]=>1010011
[2,3,5,4,8,7,6,1]=>1001011
[4,3,2,5,8,7,6,1]=>1110011
[2,4,3,5,8,7,6,1]=>1010011
[2,3,4,5,8,7,6,1]=>1000011
[6,5,4,3,2,8,7,1]=>1111101
[4,6,5,3,2,8,7,1]=>1110101
[5,4,6,3,2,8,7,1]=>1111001
[4,5,6,3,2,8,7,1]=>1110001
[3,6,5,4,2,8,7,1]=>1101101
[3,5,6,4,2,8,7,1]=>1101001
[4,3,6,5,2,8,7,1]=>1110101
[5,4,3,6,2,8,7,1]=>1111001
[2,6,5,4,3,8,7,1]=>1011101
[2,4,6,5,3,8,7,1]=>1010101
[4,3,2,6,5,8,7,1]=>1110101
[3,4,2,6,5,8,7,1]=>1100101
[2,4,3,6,5,8,7,1]=>1010101
[2,3,4,6,5,8,7,1]=>1000101
[5,4,3,2,6,8,7,1]=>1111001
[2,5,4,3,6,8,7,1]=>1011001
[4,3,2,5,6,8,7,1]=>1110001
[3,4,2,5,6,8,7,1]=>1100001
[2,4,3,5,6,8,7,1]=>1010001
[2,3,4,5,6,8,7,1]=>1000001
[4,7,6,5,3,2,8,1]=>1110110
[4,6,5,7,3,2,8,1]=>1110100
[3,5,7,6,4,2,8,1]=>1101010
[3,5,6,7,4,2,8,1]=>1101000
[4,3,7,6,5,2,8,1]=>1110110
[4,3,6,7,5,2,8,1]=>1110100
[3,4,7,6,5,2,8,1]=>1100110
[5,4,3,7,6,2,8,1]=>1111010
[4,6,5,3,7,2,8,1]=>1110100
[3,6,5,4,7,2,8,1]=>1101100
[3,5,6,4,7,2,8,1]=>1101000
[3,5,4,6,7,2,8,1]=>1101000
[2,5,4,7,6,3,8,1]=>1011010
[2,4,6,5,7,3,8,1]=>1010100
[2,4,5,6,7,3,8,1]=>1010000
[3,2,6,7,5,4,8,1]=>1101100
[2,3,7,6,5,4,8,1]=>1001110
[4,3,2,7,6,5,8,1]=>1110110
[4,3,2,6,7,5,8,1]=>1110100
[3,4,2,7,6,5,8,1]=>1100110
[2,4,3,7,6,5,8,1]=>1010110
[3,2,4,7,6,5,8,1]=>1100110
[2,3,4,7,6,5,8,1]=>1000110
[5,4,3,2,7,6,8,1]=>1111010
[2,5,4,3,7,6,8,1]=>1011010
[3,2,5,4,7,6,8,1]=>1101010
[2,3,5,4,7,6,8,1]=>1001010
[4,3,2,5,7,6,8,1]=>1110010
[2,4,3,5,7,6,8,1]=>1010010
[3,2,4,5,7,6,8,1]=>1100010
[2,3,4,5,7,6,8,1]=>1000010
[3,6,5,4,2,7,8,1]=>1101100
[3,5,6,4,2,7,8,1]=>1101000
[2,6,5,4,3,7,8,1]=>1011100
[2,5,4,6,3,7,8,1]=>1011000
[2,3,6,5,4,7,8,1]=>1001100
[2,3,5,6,4,7,8,1]=>1001000
[4,3,2,6,5,7,8,1]=>1110100
[3,4,2,6,5,7,8,1]=>1100100
[2,4,3,6,5,7,8,1]=>1010100
[2,3,4,6,5,7,8,1]=>1000100
[3,5,4,2,6,7,8,1]=>1101000
[2,5,4,3,6,7,8,1]=>1011000
[2,4,5,3,6,7,8,1]=>1010000
[3,2,5,4,6,7,8,1]=>1101000
[2,3,5,4,6,7,8,1]=>1001000
[2,4,3,5,6,7,8,1]=>1010000
[1,8,7,6,5,4,3,2]=>0111111
[1,7,8,6,5,4,3,2]=>0111110
[1,6,8,7,5,4,3,2]=>0111101
[1,7,6,8,5,4,3,2]=>0111110
[1,6,7,8,5,4,3,2]=>0111100
[1,7,6,5,8,4,3,2]=>0111110
[1,6,7,5,8,4,3,2]=>0111100
[1,5,7,6,8,4,3,2]=>0111010
[1,6,5,7,8,4,3,2]=>0111100
[1,5,6,7,8,4,3,2]=>0111000
[1,4,8,7,6,5,3,2]=>0110111
[1,4,7,8,6,5,3,2]=>0110110
[1,4,6,8,7,5,3,2]=>0110101
[1,4,6,7,8,5,3,2]=>0110100
[1,5,4,7,8,6,3,2]=>0111010
[1,4,5,7,8,6,3,2]=>0110010
[1,4,6,5,8,7,3,2]=>0110101
[1,5,4,6,8,7,3,2]=>0111001
[1,4,7,6,5,8,3,2]=>0110110
[1,6,5,4,7,8,3,2]=>0111100
[1,5,4,6,7,8,3,2]=>0111000
[1,3,8,7,6,5,4,2]=>0101111
[1,3,6,8,7,5,4,2]=>0101101
[1,3,6,7,8,5,4,2]=>0101100
[1,3,5,8,7,6,4,2]=>0101011
[1,3,5,7,8,6,4,2]=>0101010
[1,3,5,7,6,8,4,2]=>0101010
[1,3,6,5,7,8,4,2]=>0101100
[1,3,5,6,7,8,4,2]=>0101000
[1,4,3,8,7,6,5,2]=>0110111
[1,4,3,7,8,6,5,2]=>0110110
[1,4,3,6,8,7,5,2]=>0110101
[1,4,3,7,6,8,5,2]=>0110110
[1,3,4,8,7,6,5,2]=>0100111
[1,3,4,7,6,8,5,2]=>0100110
[1,3,4,6,7,8,5,2]=>0100100
[1,5,4,3,8,7,6,2]=>0111011
[1,3,5,4,7,8,6,2]=>0101010
[1,4,3,5,8,7,6,2]=>0110011
[1,4,3,5,7,8,6,2]=>0110010
[1,3,4,5,8,7,6,2]=>0100011
[1,6,5,4,3,8,7,2]=>0111101
[1,5,6,4,3,8,7,2]=>0111001
[1,4,6,5,3,8,7,2]=>0110101
[1,3,6,5,4,8,7,2]=>0101101
[1,4,3,6,5,8,7,2]=>0110101
[1,5,4,3,6,8,7,2]=>0111001
[1,6,7,5,4,3,8,2]=>0111100
[1,3,5,7,6,4,8,2]=>0101010
[1,3,4,7,6,5,8,2]=>0100110
[1,3,5,4,7,6,8,2]=>0101010
[1,4,3,6,5,7,8,2]=>0110100
[1,5,4,3,6,7,8,2]=>0111000
[2,1,8,7,6,5,4,3]=>1011111
[2,1,7,8,6,5,4,3]=>1011110
[2,1,6,8,7,5,4,3]=>1011101
[2,1,7,6,8,5,4,3]=>1011110
[2,1,6,7,8,5,4,3]=>1011100
[2,1,5,7,8,6,4,3]=>1011010
[2,1,6,5,8,7,4,3]=>1011101
[2,1,7,6,5,8,4,3]=>1011110
[2,1,6,7,5,8,4,3]=>1011100
[2,1,6,5,7,8,4,3]=>1011100
[2,1,5,6,7,8,4,3]=>1011000
[2,1,4,8,7,6,5,3]=>1010111
[2,1,4,7,8,6,5,3]=>1010110
[2,1,4,6,8,7,5,3]=>1010101
[2,1,4,6,7,8,5,3]=>1010100
[2,1,4,5,8,7,6,3]=>1010011
[2,1,4,5,7,8,6,3]=>1010010
[2,1,4,6,5,8,7,3]=>1010101
[2,1,4,5,6,8,7,3]=>1010001
[2,1,5,7,6,4,8,3]=>1011010
[2,1,6,5,7,4,8,3]=>1011100
[2,1,5,6,7,4,8,3]=>1011000
[2,1,4,7,6,5,8,3]=>1010110
[2,1,4,6,7,5,8,3]=>1010100
[2,1,5,4,7,6,8,3]=>1011010
[2,1,5,6,4,7,8,3]=>1011000
[2,1,4,5,6,7,8,3]=>1010000
[1,2,8,7,6,5,4,3]=>0011111
[1,2,6,7,8,5,4,3]=>0011100
[1,2,6,5,8,7,4,3]=>0011101
[1,2,7,6,5,8,4,3]=>0011110
[1,2,5,7,6,8,4,3]=>0011010
[1,2,6,5,7,8,4,3]=>0011100
[1,2,5,6,7,8,4,3]=>0011000
[1,2,4,8,7,6,5,3]=>0010111
[1,2,4,7,8,6,5,3]=>0010110
[1,2,4,6,8,7,5,3]=>0010101
[1,2,4,6,7,8,5,3]=>0010100
[1,2,5,4,8,7,6,3]=>0011011
[1,2,5,4,7,8,6,3]=>0011010
[1,2,4,5,7,8,6,3]=>0010010
[1,2,6,5,4,8,7,3]=>0011101
[1,2,4,6,5,8,7,3]=>0010101
[1,2,5,4,6,8,7,3]=>0011001
[1,2,5,7,6,4,8,3]=>0011010
[1,2,5,6,7,4,8,3]=>0011000
[1,2,4,7,6,5,8,3]=>0010110
[1,2,6,5,4,7,8,3]=>0011100
[3,2,1,8,7,6,5,4]=>1101111
[3,2,1,7,8,6,5,4]=>1101110
[3,2,1,6,8,7,5,4]=>1101101
[3,2,1,7,6,8,5,4]=>1101110
[3,2,1,6,7,8,5,4]=>1101100
[3,2,1,5,8,7,6,4]=>1101011
[3,2,1,5,7,8,6,4]=>1101010
[3,2,1,6,5,8,7,4]=>1101101
[3,2,1,5,6,8,7,4]=>1101001
[3,2,1,7,6,5,8,4]=>1101110
[3,2,1,6,7,5,8,4]=>1101100
[3,2,1,5,7,6,8,4]=>1101010
[3,2,1,6,5,7,8,4]=>1101100
[3,2,1,5,6,7,8,4]=>1101000
[2,3,1,8,7,6,5,4]=>1001111
[2,3,1,6,8,7,5,4]=>1001101
[2,3,1,7,6,8,5,4]=>1001110
[2,3,1,6,7,8,5,4]=>1001100
[2,3,1,6,5,8,7,4]=>1001101
[2,3,1,5,6,7,8,4]=>1001000
[1,3,2,8,7,6,5,4]=>0101111
[1,3,2,6,8,7,5,4]=>0101101
[1,3,2,5,7,8,6,4]=>0101010
[1,3,2,6,5,8,7,4]=>0101101
[1,3,2,7,6,5,8,4]=>0101110
[1,3,2,5,7,6,8,4]=>0101010
[1,3,2,6,5,7,8,4]=>0101100
[2,1,3,8,7,6,5,4]=>1001111
[2,1,3,7,8,6,5,4]=>1001110
[2,1,3,6,8,7,5,4]=>1001101
[1,2,3,8,7,6,5,4]=>0001111
[1,2,3,7,8,6,5,4]=>0001110
[1,2,3,6,8,7,5,4]=>0001101
[1,2,3,7,6,8,5,4]=>0001110
[1,2,3,6,7,8,5,4]=>0001100
[1,2,3,5,8,7,6,4]=>0001011
[1,2,3,5,7,8,6,4]=>0001010
[1,2,3,6,5,8,7,4]=>0001101
[1,2,3,5,6,8,7,4]=>0001001
[1,2,3,7,6,5,8,4]=>0001110
[1,2,3,6,7,5,8,4]=>0001100
[1,2,3,5,7,6,8,4]=>0001010
[1,2,3,6,5,7,8,4]=>0001100
[1,2,3,5,6,7,8,4]=>0001000
[4,3,2,1,8,7,6,5]=>1110111
[4,3,2,1,7,8,6,5]=>1110110
[4,3,2,1,6,8,7,5]=>1110101
[4,3,2,1,7,6,8,5]=>1110110
[4,3,2,1,6,7,8,5]=>1110100
[3,4,2,1,8,7,6,5]=>1100111
[3,4,2,1,7,8,6,5]=>1100110
[3,4,2,1,6,8,7,5]=>1100101
[3,4,2,1,7,6,8,5]=>1100110
[3,4,2,1,6,7,8,5]=>1100100
[2,4,3,1,8,7,6,5]=>1010111
[2,4,3,1,6,8,7,5]=>1010101
[2,4,3,1,7,6,8,5]=>1010110
[2,4,3,1,6,7,8,5]=>1010100
[3,2,4,1,8,7,6,5]=>1100111
[3,2,4,1,7,8,6,5]=>1100110
[3,2,4,1,6,8,7,5]=>1100101
[3,2,4,1,7,6,8,5]=>1100110
[3,2,4,1,6,7,8,5]=>1100100
[2,3,4,1,8,7,6,5]=>1000111
[2,3,4,1,7,8,6,5]=>1000110
[2,3,4,1,6,8,7,5]=>1000101
[2,3,4,1,7,6,8,5]=>1000110
[2,3,4,1,6,7,8,5]=>1000100
[1,4,3,2,8,7,6,5]=>0110111
[1,4,3,2,7,6,8,5]=>0110110
[1,4,3,2,6,7,8,5]=>0110100
[1,3,4,2,8,7,6,5]=>0100111
[1,3,4,2,7,8,6,5]=>0100110
[1,3,4,2,6,8,7,5]=>0100101
[1,3,4,2,7,6,8,5]=>0100110
[1,3,4,2,6,7,8,5]=>0100100
[2,1,4,3,8,7,6,5]=>1010111
[2,1,4,3,7,8,6,5]=>1010110
[2,1,4,3,6,8,7,5]=>1010101
[2,1,4,3,7,6,8,5]=>1010110
[2,1,4,3,6,7,8,5]=>1010100
[1,2,4,3,8,7,6,5]=>0010111
[1,2,4,3,7,8,6,5]=>0010110
[1,2,4,3,6,8,7,5]=>0010101
[1,2,4,3,7,6,8,5]=>0010110
[1,2,4,3,6,7,8,5]=>0010100
[3,2,1,4,8,7,6,5]=>1100111
[3,2,1,4,7,8,6,5]=>1100110
[3,2,1,4,6,8,7,5]=>1100101
[3,2,1,4,7,6,8,5]=>1100110
[3,2,1,4,6,7,8,5]=>1100100
[2,3,1,4,8,7,6,5]=>1000111
[2,3,1,4,7,8,6,5]=>1000110
[2,3,1,4,7,6,8,5]=>1000110
[2,3,1,4,6,7,8,5]=>1000100
[1,3,2,4,8,7,6,5]=>0100111
[1,3,2,4,6,8,7,5]=>0100101
[1,3,2,4,7,6,8,5]=>0100110
[1,3,2,4,6,7,8,5]=>0100100
[2,1,3,4,8,7,6,5]=>1000111
[2,1,3,4,7,6,8,5]=>1000110
[2,1,3,4,6,7,8,5]=>1000100
[1,2,3,4,8,7,6,5]=>0000111
[1,2,3,4,7,8,6,5]=>0000110
[1,2,3,4,6,8,7,5]=>0000101
[1,2,3,4,7,6,8,5]=>0000110
[1,2,3,4,6,7,8,5]=>0000100
[5,4,3,2,1,8,7,6]=>1111011
[5,4,3,2,1,7,8,6]=>1111010
[4,5,3,2,1,8,7,6]=>1110011
[3,5,4,2,1,8,7,6]=>1101011
[3,5,4,2,1,7,8,6]=>1101010
[4,3,5,2,1,8,7,6]=>1110011
[3,4,5,2,1,8,7,6]=>1100011
[3,4,5,2,1,7,8,6]=>1100010
[2,5,4,3,1,8,7,6]=>1011011
[2,5,4,3,1,7,8,6]=>1011010
[2,4,5,3,1,8,7,6]=>1010011
[3,2,5,4,1,8,7,6]=>1101011
[3,2,5,4,1,7,8,6]=>1101010
[2,3,5,4,1,8,7,6]=>1001011
[4,3,2,5,1,8,7,6]=>1110011
[3,4,2,5,1,8,7,6]=>1100011
[3,4,2,5,1,7,8,6]=>1100010
[2,4,3,5,1,8,7,6]=>1010011
[2,4,3,5,1,7,8,6]=>1010010
[3,2,4,5,1,8,7,6]=>1100011
[2,3,4,5,1,8,7,6]=>1000011
[1,3,5,4,2,7,8,6]=>0101010
[1,4,3,5,2,7,8,6]=>0110010
[1,3,4,5,2,8,7,6]=>0100011
[1,3,4,5,2,7,8,6]=>0100010
[1,2,5,4,3,7,8,6]=>0011010
[1,2,4,5,3,8,7,6]=>0010011
[1,2,4,5,3,7,8,6]=>0010010
[1,3,2,5,4,8,7,6]=>0101011
[1,3,2,5,4,7,8,6]=>0101010
[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]=>0001010
[4,3,2,1,5,8,7,6]=>1110011
[4,3,2,1,5,7,8,6]=>1110010
[3,4,2,1,5,8,7,6]=>1100011
[3,2,4,1,5,8,7,6]=>1100011
[3,2,4,1,5,7,8,6]=>1100010
[2,3,4,1,5,8,7,6]=>1000011
[2,3,4,1,5,7,8,6]=>1000010
[1,4,3,2,5,8,7,6]=>0110011
[1,4,3,2,5,7,8,6]=>0110010
[1,3,4,2,5,8,7,6]=>0100011
[1,3,4,2,5,7,8,6]=>0100010
[1,2,4,3,5,7,8,6]=>0010010
[3,2,1,4,5,8,7,6]=>1100011
[3,2,1,4,5,7,8,6]=>1100010
[2,3,1,4,5,7,8,6]=>1000010
[1,3,2,4,5,7,8,6]=>0100010
[1,2,3,4,5,8,7,6]=>0000011
[1,2,3,4,5,7,8,6]=>0000010
[6,5,4,3,2,1,8,7]=>1111101
[5,6,4,3,2,1,8,7]=>1111001
[4,6,5,3,2,1,8,7]=>1110101
[5,4,6,3,2,1,8,7]=>1111001
[4,5,6,3,2,1,8,7]=>1110001
[3,6,5,4,2,1,8,7]=>1101101
[3,5,6,4,2,1,8,7]=>1101001
[4,3,6,5,2,1,8,7]=>1110101
[5,4,3,6,2,1,8,7]=>1111001
[4,5,3,6,2,1,8,7]=>1110001
[3,4,5,6,2,1,8,7]=>1100001
[2,6,5,4,3,1,8,7]=>1011101
[2,5,6,4,3,1,8,7]=>1011001
[2,4,6,5,3,1,8,7]=>1010101
[2,3,6,5,4,1,8,7]=>1001101
[2,3,5,6,4,1,8,7]=>1001001
[2,4,3,6,5,1,8,7]=>1010101
[5,4,3,2,6,1,8,7]=>1111001
[4,5,3,2,6,1,8,7]=>1110001
[3,5,4,2,6,1,8,7]=>1101001
[4,3,5,2,6,1,8,7]=>1110001
[3,4,5,2,6,1,8,7]=>1100001
[2,5,4,3,6,1,8,7]=>1011001
[2,4,5,3,6,1,8,7]=>1010001
[3,4,2,5,6,1,8,7]=>1100001
[2,3,4,5,6,1,8,7]=>1000001
[1,5,4,6,3,2,8,7]=>0111001
[1,3,6,5,4,2,8,7]=>0101101
[2,1,6,5,4,3,8,7]=>1011101
[2,1,5,6,4,3,8,7]=>1011001
[2,1,4,6,5,3,8,7]=>1010101
[2,1,5,4,6,3,8,7]=>1011001
[2,1,4,5,6,3,8,7]=>1010001
[2,3,1,6,5,4,8,7]=>1001101
[2,1,3,6,5,4,8,7]=>1001101
[1,2,3,6,5,4,8,7]=>0001101
[1,2,3,5,6,4,8,7]=>0001001
[4,3,2,1,6,5,8,7]=>1110101
[3,4,2,1,6,5,8,7]=>1100101
[2,4,3,1,6,5,8,7]=>1010101
[3,2,4,1,6,5,8,7]=>1100101
[2,3,4,1,6,5,8,7]=>1000101
[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]=>1110001
[3,5,4,2,1,6,8,7]=>1101001
[2,5,4,3,1,6,8,7]=>1011001
[2,4,5,3,1,6,8,7]=>1010001
[3,2,5,4,1,6,8,7]=>1101001
[1,3,5,4,2,6,8,7]=>0101001
[1,3,4,5,2,6,8,7]=>0100001
[2,1,5,4,3,6,8,7]=>1011001
[2,1,4,5,3,6,8,7]=>1010001
[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]=>1100001
[2,3,4,1,5,6,8,7]=>1000001
[1,4,3,2,5,6,8,7]=>0110001
[1,3,4,2,5,6,8,7]=>0100001
[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]=>1111010
[4,7,6,5,3,2,1,8]=>1110110
[4,6,7,5,3,2,1,8]=>1110100
[4,5,7,6,3,2,1,8]=>1110010
[4,6,5,7,3,2,1,8]=>1110100
[3,5,7,6,4,2,1,8]=>1101010
[3,5,6,7,4,2,1,8]=>1101000
[3,4,7,6,5,2,1,8]=>1100110
[4,5,3,7,6,2,1,8]=>1110010
[3,5,4,7,6,2,1,8]=>1101010
[4,3,5,7,6,2,1,8]=>1110010
[2,5,6,7,4,3,1,8]=>1011000
[2,4,6,7,5,3,1,8]=>1010100
[3,2,7,6,5,4,1,8]=>1101110
[3,2,6,7,5,4,1,8]=>1101100
[3,2,5,7,6,4,1,8]=>1101010
[2,3,7,6,5,4,1,8]=>1001110
[2,3,6,7,5,4,1,8]=>1001100
[2,3,5,7,6,4,1,8]=>1001010
[2,3,6,5,7,4,1,8]=>1001100
[2,3,5,6,7,4,1,8]=>1001000
[3,2,4,6,7,5,1,8]=>1100100
[2,3,4,7,6,5,1,8]=>1000110
[5,4,3,2,7,6,1,8]=>1111010
[4,5,3,2,7,6,1,8]=>1110010
[3,5,4,2,7,6,1,8]=>1101010
[3,2,5,4,7,6,1,8]=>1101010
[4,3,2,5,7,6,1,8]=>1110010
[3,6,5,4,2,7,1,8]=>1101100
[3,4,6,5,2,7,1,8]=>1100100
[3,5,4,6,2,7,1,8]=>1101000
[2,5,4,6,3,7,1,8]=>1011000
[3,2,6,5,4,7,1,8]=>1101100
[3,4,2,6,5,7,1,8]=>1100100
[2,4,3,6,5,7,1,8]=>1010100
[3,5,4,2,6,7,1,8]=>1101000
[2,5,4,3,6,7,1,8]=>1011000
[1,5,6,7,4,3,2,8]=>0111000
[1,4,6,5,7,3,2,8]=>0110100
[1,3,5,7,6,4,2,8]=>0101010
[1,3,5,6,7,4,2,8]=>0101000
[1,3,5,4,7,6,2,8]=>0101010
[1,4,3,5,7,6,2,8]=>0110010
[1,5,4,6,3,7,2,8]=>0111000
[1,3,6,5,4,7,2,8]=>0101100
[1,4,3,6,5,7,2,8]=>0110100
[1,5,4,3,6,7,2,8]=>0111000
[1,3,4,5,6,7,2,8]=>0100000
[2,1,5,6,7,4,3,8]=>1011000
[2,1,4,6,7,5,3,8]=>1010100
[1,2,5,7,6,4,3,8]=>0011010
[1,2,5,6,7,4,3,8]=>0011000
[1,2,5,6,4,7,3,8]=>0011000
[1,2,5,4,6,7,3,8]=>0011000
[3,2,1,5,7,6,4,8]=>1101010
[3,2,1,6,5,7,4,8]=>1101100
[3,2,1,5,6,7,4,8]=>1101000
[2,3,1,6,7,5,4,8]=>1001100
[2,3,1,6,5,7,4,8]=>1001100
[2,3,1,5,6,7,4,8]=>1001000
[1,3,2,5,7,6,4,8]=>0101010
[1,3,2,6,5,7,4,8]=>0101100
[1,3,2,5,6,7,4,8]=>0101000
[2,1,3,6,7,5,4,8]=>1001100
[1,2,3,7,6,5,4,8]=>0001110
[1,2,3,6,7,5,4,8]=>0001100
[1,2,3,5,7,6,4,8]=>0001010
[1,2,3,6,5,7,4,8]=>0001100
[1,2,3,5,6,7,4,8]=>0001000
[4,3,2,1,7,6,5,8]=>1110110
[4,3,2,1,6,7,5,8]=>1110100
[3,2,4,1,7,6,5,8]=>1100110
[3,2,4,1,6,7,5,8]=>1100100
[2,3,4,1,7,6,5,8]=>1000110
[2,3,4,1,6,7,5,8]=>1000100
[1,4,3,2,7,6,5,8]=>0110110
[1,4,3,2,6,7,5,8]=>0110100
[1,3,4,2,6,7,5,8]=>0100100
[2,1,4,3,6,7,5,8]=>1010100
[1,2,4,3,6,7,5,8]=>0010100
[3,2,1,4,7,6,5,8]=>1100110
[2,3,1,4,6,7,5,8]=>1000100
[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]=>0000100
[5,4,3,2,1,7,6,8]=>1111010
[4,5,3,2,1,7,6,8]=>1110010
[3,5,4,2,1,7,6,8]=>1101010
[2,5,4,3,1,7,6,8]=>1011010
[2,4,5,3,1,7,6,8]=>1010010
[3,2,5,4,1,7,6,8]=>1101010
[3,4,2,5,1,7,6,8]=>1100010
[2,4,3,5,1,7,6,8]=>1010010
[1,3,5,4,2,7,6,8]=>0101010
[1,4,3,5,2,7,6,8]=>0110010
[1,3,4,5,2,7,6,8]=>0100010
[3,2,1,5,4,7,6,8]=>1101010
[2,3,1,5,4,7,6,8]=>1001010
[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]=>1100010
[2,3,4,1,5,7,6,8]=>1000010
[1,4,3,2,5,7,6,8]=>0110010
[1,3,4,2,5,7,6,8]=>0100010
[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]=>1101100
[4,3,6,5,2,1,7,8]=>1110100
[2,4,6,5,3,1,7,8]=>1010100
[2,4,5,6,3,1,7,8]=>1010000
[4,3,2,6,5,1,7,8]=>1110100
[3,5,4,2,6,1,7,8]=>1101000
[1,5,6,4,3,2,7,8]=>0111000
[1,4,6,5,3,2,7,8]=>0110100
[1,5,4,6,3,2,7,8]=>0111000
[1,4,5,6,3,2,7,8]=>0110000
[1,3,5,6,4,2,7,8]=>0101000
[1,4,3,6,5,2,7,8]=>0110100
[1,5,4,3,6,2,7,8]=>0111000
[2,1,5,6,4,3,7,8]=>1011000
[2,1,4,6,5,3,7,8]=>1010100
[1,2,6,5,4,3,7,8]=>0011100
[1,2,5,6,4,3,7,8]=>0011000
[1,2,4,5,6,3,7,8]=>0010000
[3,2,1,5,6,4,7,8]=>1101000
[1,3,2,5,6,4,7,8]=>0101000
[1,2,3,5,6,4,7,8]=>0001000
[4,3,2,1,6,5,7,8]=>1110100
[3,2,4,1,6,5,7,8]=>1100100
[2,3,4,1,6,5,7,8]=>1000100
[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]=>1101000
[2,5,4,3,1,6,7,8]=>1011000
[2,4,5,3,1,6,7,8]=>1010000
[3,2,5,4,1,6,7,8]=>1101000
[2,3,5,4,1,6,7,8]=>1001000
[2,4,3,5,1,6,7,8]=>1010000
[1,3,5,4,2,6,7,8]=>0101000
[1,3,4,5,2,6,7,8]=>0100000
[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]=>1010000
[1,4,3,2,5,6,7,8]=>0110000
[1,3,4,2,5,6,7,8]=>0100000
[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]=>0000110
[1,2,3,5,8,6,7,4]=>0001010
[1,2,3,7,5,6,4,8]=>0001100
[1,2,3,7,5,6,8,4]=>0001100
[1,2,3,8,5,6,7,4]=>0001100
[1,2,3,8,5,7,6,4]=>0001110
[1,2,3,8,6,5,7,4]=>0001110
[1,2,3,8,6,7,5,4]=>0001110
[1,2,4,5,8,6,7,3]=>0010010
[1,2,4,8,5,6,7,3]=>0010100
[1,2,4,8,6,5,7,3]=>0010110
[1,2,5,4,8,6,7,3]=>0011010
[1,2,6,4,5,3,7,8]=>0011000
[1,2,6,4,5,8,7,3]=>0011001
[1,2,8,4,5,6,7,3]=>0011000
[1,2,8,4,6,7,5,3]=>0011100
[1,2,8,4,7,6,5,3]=>0011110
[1,2,7,5,4,6,8,3]=>0011100
[1,2,8,5,4,6,7,3]=>0011100
[1,2,8,5,4,7,6,3]=>0011110
[1,2,8,6,5,4,7,3]=>0011110
[1,2,8,7,5,6,4,3]=>0011101
[1,3,2,7,5,6,8,4]=>0101100
[1,3,2,8,5,7,6,4]=>0101110
[1,3,4,5,8,6,7,2]=>0100010
[1,3,4,8,5,6,7,2]=>0100100
[1,3,6,4,5,2,8,7]=>0101001
[1,3,6,4,5,7,2,8]=>0101000
[1,3,6,4,5,8,7,2]=>0101001
[1,3,8,4,5,6,7,2]=>0101000
[1,3,8,4,6,5,7,2]=>0101100
[1,3,8,4,6,7,5,2]=>0101100
[1,3,8,5,4,6,7,2]=>0101100
[1,3,8,5,4,7,6,2]=>0101110
[1,3,8,5,6,7,4,2]=>0101100
[1,3,8,5,7,6,4,2]=>0101110
[1,3,8,6,5,7,4,2]=>0101110
[1,3,8,7,5,6,4,2]=>0101101
[1,4,3,8,5,6,7,2]=>0110100
[1,4,3,8,5,7,6,2]=>0110110
[1,4,3,8,6,7,5,2]=>0110110
[1,5,3,4,2,7,8,6]=>0110010
[1,5,3,4,2,8,7,6]=>0110011
[1,5,3,4,6,2,7,8]=>0110000
[1,5,3,4,6,7,2,8]=>0110000
[1,5,3,4,7,6,2,8]=>0110010
[1,5,3,4,8,6,7,2]=>0110010
[1,8,3,4,6,7,5,2]=>0110100
[1,6,3,5,4,2,7,8]=>0111000
[1,6,3,5,4,8,7,2]=>0111001
[1,8,3,5,4,7,6,2]=>0111010
[1,8,3,5,6,4,7,2]=>0111000
[1,8,3,5,7,6,4,2]=>0111010
[1,8,3,6,5,4,7,2]=>0111100
[1,8,3,7,5,6,4,2]=>0111100
[1,8,3,7,6,5,4,2]=>0111110
[1,6,4,3,5,2,7,8]=>0111000
[1,8,4,3,5,6,7,2]=>0111000
[1,8,4,3,5,7,6,2]=>0111010
[1,7,4,3,6,5,8,2]=>0111100
[1,8,4,3,6,7,5,2]=>0111100
[1,6,4,5,3,8,7,2]=>0111001
[1,8,4,5,6,3,7,2]=>0111000
[1,8,4,5,6,7,3,2]=>0111000
[1,8,4,6,5,7,3,2]=>0111100
[1,8,4,7,6,5,3,2]=>0111110
[1,7,5,4,3,6,8,2]=>0111100
[1,8,5,4,3,6,7,2]=>0111100
[1,8,5,4,3,7,6,2]=>0111110
[1,8,5,4,6,3,7,2]=>0111100
[1,8,5,4,6,7,3,2]=>0111100
[1,8,5,4,7,6,3,2]=>0111110
[1,8,6,4,5,7,3,2]=>0111010
[1,8,7,4,5,6,3,2]=>0111001
[1,8,7,4,6,5,3,2]=>0111101
[1,8,6,5,4,7,3,2]=>0111110
[1,8,7,5,4,6,3,2]=>0111101
[1,8,7,5,6,4,3,2]=>0111101
[2,1,3,4,8,6,7,5]=>1000110
[2,1,4,3,8,6,7,5]=>1010110
[2,1,4,5,8,6,7,3]=>1010010
[2,1,4,8,5,6,7,3]=>1010100
[2,1,4,8,5,7,6,3]=>1010110
[2,1,4,8,6,5,7,3]=>1010110
[2,1,4,8,6,7,5,3]=>1010110
[2,1,6,4,5,3,8,7]=>1011001
[2,1,6,4,5,7,8,3]=>1011000
[2,1,6,4,5,8,7,3]=>1011001
[2,1,8,4,5,6,7,3]=>1011000
[2,1,8,4,5,7,6,3]=>1011010
[2,1,8,4,6,5,7,3]=>1011100
[2,1,8,4,6,7,5,3]=>1011100
[2,1,8,4,7,6,5,3]=>1011110
[2,1,7,5,4,6,8,3]=>1011100
[2,1,8,5,4,6,7,3]=>1011100
[2,1,8,5,4,7,6,3]=>1011110
[2,1,7,5,6,4,8,3]=>1011100
[2,1,8,5,7,6,4,3]=>1011110
[2,1,8,7,5,6,4,3]=>1011101
[2,3,1,5,8,6,7,4]=>1001010
[2,3,1,8,5,6,7,4]=>1001100
[2,3,1,8,6,7,5,4]=>1001110
[2,3,4,1,8,6,7,5]=>1000110
[2,3,4,5,8,6,7,1]=>1000010
[2,3,4,7,5,6,1,8]=>1000100
[2,3,4,7,5,6,8,1]=>1000100
[2,3,4,8,5,6,7,1]=>1000100
[2,3,4,8,5,7,6,1]=>1000110
[2,3,4,8,6,5,7,1]=>1000110
[2,3,4,8,6,7,5,1]=>1000110
[2,3,6,4,5,1,8,7]=>1001001
[2,3,6,4,5,7,8,1]=>1001000
[2,3,7,4,5,6,8,1]=>1001000
[2,3,8,4,5,6,7,1]=>1001000
[2,3,7,4,6,5,8,1]=>1001100
[2,3,7,5,4,6,1,8]=>1001100
[2,3,7,5,4,6,8,1]=>1001100
[2,3,7,5,6,4,1,8]=>1001100
[2,3,7,5,6,4,8,1]=>1001100
[2,3,8,5,7,6,4,1]=>1001110
[2,4,3,1,8,6,7,5]=>1010110
[2,4,3,5,8,6,7,1]=>1010010
[2,4,3,8,5,6,7,1]=>1010100
[2,4,3,8,6,7,5,1]=>1010110
[2,5,3,4,1,6,7,8]=>1010000
[2,5,3,4,1,8,7,6]=>1010011
[2,5,3,4,6,7,1,8]=>1010000
[2,5,3,4,8,7,6,1]=>1010011
[2,6,3,4,5,7,8,1]=>1010000
[2,6,3,4,5,8,7,1]=>1010001
[2,6,3,5,4,1,7,8]=>1011000
[2,6,3,5,4,1,8,7]=>1011001
[2,6,3,5,4,7,8,1]=>1011000
[2,7,3,5,4,6,8,1]=>1011000
[2,7,3,5,6,4,8,1]=>1011000
[2,8,3,5,7,6,4,1]=>1011010
[2,7,3,6,5,4,1,8]=>1011100
[2,8,3,7,5,6,4,1]=>1011100
[2,5,4,3,8,6,7,1]=>1011010
[2,6,4,3,5,7,8,1]=>1011000
[2,8,4,3,5,6,7,1]=>1011000
[2,8,4,3,7,6,5,1]=>1011110
[2,6,4,5,3,1,7,8]=>1011000
[2,6,4,5,3,1,8,7]=>1011001
[2,6,4,5,3,7,8,1]=>1011000
[2,6,4,5,3,8,7,1]=>1011001
[2,7,4,5,6,3,8,1]=>1011000
[2,7,5,4,3,6,8,1]=>1011100
[2,8,5,4,3,6,7,1]=>1011100
[2,8,5,4,3,7,6,1]=>1011110
[2,7,5,4,6,3,8,1]=>1011100
[2,8,5,4,7,6,3,1]=>1011110
[2,8,7,5,4,6,3,1]=>1011101
[2,8,7,5,6,4,3,1]=>1011101
[3,2,1,4,8,6,7,5]=>1100110
[3,2,1,5,8,6,7,4]=>1101010
[3,2,1,7,5,6,4,8]=>1101100
[3,2,1,7,5,6,8,4]=>1101100
[3,2,1,8,5,6,7,4]=>1101100
[3,2,1,8,5,7,6,4]=>1101110
[3,2,1,8,6,5,7,4]=>1101110
[3,2,1,8,6,7,5,4]=>1101110
[3,2,4,1,8,6,7,5]=>1100110
[3,2,4,8,5,6,7,1]=>1100100
[3,2,6,4,5,7,1,8]=>1101000
[3,2,7,4,6,5,1,8]=>1101100
[3,2,7,4,6,5,8,1]=>1101100
[3,2,8,5,4,6,7,1]=>1101100
[3,2,7,5,6,4,1,8]=>1101100
[3,2,8,5,7,6,4,1]=>1101110
[4,2,3,1,6,5,8,7]=>1100101
[4,2,3,1,6,7,8,5]=>1100100
[4,2,3,1,6,8,7,5]=>1100101
[4,2,3,1,7,6,8,5]=>1100110
[4,2,3,1,8,6,7,5]=>1100110
[4,2,3,1,8,7,6,5]=>1100111
[4,2,3,5,1,7,8,6]=>1100010
[4,2,3,5,1,8,7,6]=>1100011
[4,2,3,5,6,1,8,7]=>1100001
[4,2,3,5,6,8,7,1]=>1100001
[4,2,3,6,5,1,7,8]=>1100100
[4,2,3,6,5,1,8,7]=>1100101
[4,2,3,6,5,8,7,1]=>1100101
[4,2,3,7,5,6,1,8]=>1100100
[4,2,3,8,5,6,7,1]=>1100100
[4,2,3,7,6,5,8,1]=>1100110
[4,2,3,8,6,7,5,1]=>1100110
[4,2,3,8,7,6,5,1]=>1100111
[5,2,3,4,1,8,7,6]=>1100011
[5,2,3,4,8,7,6,1]=>1100011
[8,2,3,4,7,6,5,1]=>1100110
[6,2,3,5,4,1,7,8]=>1101000
[6,2,3,5,4,1,8,7]=>1101001
[6,2,3,5,4,7,1,8]=>1101000
[8,2,3,5,4,7,6,1]=>1101010
[7,2,3,5,6,4,1,8]=>1101000
[8,2,3,5,6,7,4,1]=>1101000
[7,2,3,6,5,4,1,8]=>1101100
[8,2,3,7,5,6,4,1]=>1101100
[8,2,3,7,6,5,4,1]=>1101110
[5,2,4,3,1,6,7,8]=>1110000
[5,2,4,3,1,6,8,7]=>1110001
[5,2,4,3,1,7,6,8]=>1110010
[5,2,4,3,1,8,7,6]=>1110011
[5,2,4,3,6,1,7,8]=>1110000
[5,2,4,3,6,1,8,7]=>1110001
[5,2,4,3,7,6,1,8]=>1110010
[5,2,4,3,7,6,8,1]=>1110010
[6,2,4,3,5,1,8,7]=>1110001
[7,2,4,3,6,5,1,8]=>1110100
[7,2,4,3,6,5,8,1]=>1110100
[8,2,4,3,6,5,7,1]=>1110100
[8,2,4,3,7,6,5,1]=>1110110
[6,2,4,5,3,1,7,8]=>1110000
[6,2,4,5,3,1,8,7]=>1110001
[6,2,4,5,3,8,7,1]=>1110001
[7,2,4,5,3,6,1,8]=>1110000
[7,2,4,5,3,6,8,1]=>1110000
[8,2,4,7,5,6,3,1]=>1110100
[8,2,4,7,6,5,3,1]=>1110110
[6,2,5,4,3,1,8,7]=>1111001
[7,2,5,4,3,6,1,8]=>1111000
[8,2,5,4,3,7,6,1]=>1111010
[8,2,5,4,7,6,3,1]=>1111010
[8,2,6,4,5,3,7,1]=>1111000
[8,2,6,4,5,7,3,1]=>1111000
[8,2,7,4,5,6,3,1]=>1111000
[8,2,7,4,6,5,3,1]=>1111100
[7,2,6,5,4,3,1,8]=>1111100
[8,2,6,5,4,3,7,1]=>1111100
[8,2,7,5,4,6,3,1]=>1111100
[8,2,7,5,6,4,3,1]=>1111100
[8,2,7,6,5,4,3,1]=>1111110
[4,3,2,1,8,6,7,5]=>1110110
[4,3,2,7,5,6,8,1]=>1110100
[4,3,2,8,5,6,7,1]=>1110100
[4,3,2,8,6,7,5,1]=>1110110
[5,3,2,4,1,6,8,7]=>1110001
[5,3,2,4,1,8,7,6]=>1110011
[5,3,2,4,6,1,8,7]=>1110001
[6,3,2,5,4,1,7,8]=>1111000
[6,3,2,5,4,1,8,7]=>1111001
[6,3,2,5,4,7,1,8]=>1111000
[6,3,2,5,4,7,8,1]=>1111000
[8,3,2,5,4,7,6,1]=>1111010
[8,3,2,5,6,4,7,1]=>1111000
[8,3,2,5,7,6,4,1]=>1111010
[8,3,2,7,5,6,4,1]=>1111100
[8,3,2,7,6,5,4,1]=>1111110
[5,3,4,2,1,6,8,7]=>1110001
[5,3,4,2,1,7,8,6]=>1110010
[5,3,4,2,1,8,7,6]=>1110011
[5,3,4,2,7,6,1,8]=>1110010
[7,3,4,2,6,5,1,8]=>1110100
[7,3,4,2,6,5,8,1]=>1110100
[7,3,4,6,5,2,1,8]=>1110100
[6,3,5,4,2,1,8,7]=>1111001
[6,3,5,4,2,7,1,8]=>1111000
[6,3,5,4,2,7,8,1]=>1111000
[8,3,5,4,2,6,7,1]=>1111000
[7,3,5,4,6,2,1,8]=>1111000
[8,3,5,4,7,6,2,1]=>1111010
[7,3,6,4,5,2,1,8]=>1111000
[8,3,7,4,5,6,2,1]=>1111000
[7,3,6,5,4,2,1,8]=>1111100
[8,3,7,5,6,4,2,1]=>1111100
[5,4,3,2,8,6,7,1]=>1111010
[7,4,3,2,6,5,1,8]=>1111100
[7,4,3,2,6,5,8,1]=>1111100
[8,4,3,2,6,7,5,1]=>1111100
[8,4,3,2,7,6,5,1]=>1111110
[6,4,3,5,2,1,8,7]=>1111001
[8,4,3,5,7,6,2,1]=>1111010
[7,4,3,6,5,2,1,8]=>1111100
[7,4,3,6,5,2,8,1]=>1111100
[8,4,3,7,5,6,2,1]=>1111100
[6,5,3,4,2,1,8,7]=>1110101
[8,5,3,4,2,7,6,1]=>1110110
[8,5,3,4,7,6,2,1]=>1110110
[8,7,3,4,6,5,2,1]=>1110101
[7,6,3,5,4,2,1,8]=>1111010
[8,6,3,5,4,2,7,1]=>1111010
[8,7,3,5,4,6,2,1]=>1111001
[8,7,3,5,6,4,2,1]=>1111001
[8,7,3,6,5,4,2,1]=>1111101
[8,5,4,3,2,7,6,1]=>1111110
[8,5,4,3,7,6,2,1]=>1111110
[8,7,4,3,6,5,2,1]=>1111101
[2,4,1,3,6,5,8,7]=>1000101
[2,1,4,6,3,5,8,7]=>1010001
[2,4,1,6,3,5,8,7]=>1010001
[2,4,6,1,3,5,8,7]=>1000001
[2,1,4,3,6,8,5,7]=>1010100
[2,4,1,3,6,8,5,7]=>1000100
[2,1,4,6,3,8,5,7]=>1010100
[2,4,1,6,3,8,5,7]=>1010100
[2,4,6,1,3,8,5,7]=>1000100
[2,1,4,6,8,3,5,7]=>1010000
[2,4,1,6,8,3,5,7]=>1010000
[2,4,6,1,8,3,5,7]=>1010000
[2,4,6,8,1,3,5,7]=>1000000
[2,4,1,3,6,5,7,8]=>1000100
[2,4,1,6,3,7,5,8]=>1010100
[2,4,6,1,3,7,5,8]=>1000100
[2,4,6,7,1,3,5,8]=>1000000
[2,4,1,3,6,7,8,5]=>1000100
[2,1,4,6,3,7,8,5]=>1010100
[2,4,1,6,3,7,8,5]=>1010100
[2,4,6,1,3,7,8,5]=>1000100
[2,4,1,6,7,3,8,5]=>1010100
[2,4,6,1,7,3,8,5]=>1010100
[2,4,6,7,1,3,8,5]=>1000100
[2,4,1,6,7,8,3,5]=>1010000
[2,4,6,1,7,8,3,5]=>1010000
[2,4,6,7,1,8,3,5]=>1010000
[2,4,6,7,8,1,3,5]=>1000000
[2,1,4,3,7,5,8,6]=>1010110
[2,4,1,3,7,5,8,6]=>1000110
[2,4,1,7,3,5,8,6]=>1010010
[2,4,7,1,3,5,8,6]=>1000010
[2,1,4,3,7,8,5,6]=>1010100
[2,4,1,3,7,8,5,6]=>1000100
[2,4,1,7,3,8,5,6]=>1010100
[2,4,7,1,3,8,5,6]=>1000100
[2,4,1,7,8,3,5,6]=>1010000
[2,4,7,1,8,3,5,6]=>1010000
[2,4,1,5,3,7,6,8]=>1010010
[2,4,5,1,7,3,6,8]=>1010000
[2,4,1,3,5,7,8,6]=>1000010
[2,4,1,5,3,7,8,6]=>1010010
[2,4,5,1,3,7,8,6]=>1000010
[2,1,4,5,7,3,8,6]=>1010010
[2,4,1,5,7,3,8,6]=>1010010
[2,4,5,1,7,3,8,6]=>1010010
[2,4,5,7,1,3,8,6]=>1000010
[2,4,5,7,8,1,3,6]=>1000000
[2,1,4,3,8,5,6,7]=>1010100
[2,4,1,3,8,5,6,7]=>1000100
[2,1,4,8,3,5,6,7]=>1010000
[2,4,1,8,3,5,6,7]=>1010000
[2,4,1,5,3,8,6,7]=>1010010
[2,1,4,5,8,3,6,7]=>1010000
[2,4,1,5,8,3,6,7]=>1010000
[2,4,5,8,1,3,6,7]=>1000000
[2,4,1,5,6,3,8,7]=>1010001
[2,1,4,5,6,8,3,7]=>1010000
[2,4,5,1,6,8,3,7]=>1010000
[2,4,5,6,1,8,3,7]=>1010000
[2,4,5,6,8,1,3,7]=>1000000
[2,4,1,3,5,6,7,8]=>1000000
[2,4,1,5,6,3,7,8]=>1010000
[2,4,5,1,6,3,7,8]=>1010000
[2,4,5,6,1,3,7,8]=>1000000
[2,4,5,6,7,1,3,8]=>1000000
[2,4,1,5,6,7,8,3]=>1010000
[2,4,5,6,7,1,8,3]=>1010000
[2,1,5,3,6,4,8,7]=>1011001
[2,1,5,6,3,4,8,7]=>1010001
[2,1,5,3,6,8,4,7]=>1011000
[2,5,1,3,6,8,4,7]=>1001000
[2,5,1,6,3,8,4,7]=>1011000
[2,5,1,6,8,3,4,7]=>1010000
[2,1,5,6,3,4,7,8]=>1010000
[2,5,1,6,3,4,7,8]=>1010000
[2,1,5,3,6,7,4,8]=>1011000
[2,1,5,6,3,7,4,8]=>1011000
[2,5,1,6,3,7,4,8]=>1011000
[2,5,6,1,3,7,4,8]=>1001000
[2,1,5,6,7,3,4,8]=>1010000
[2,5,1,6,7,3,4,8]=>1010000
[2,1,5,3,6,7,8,4]=>1011000
[2,5,1,3,6,7,8,4]=>1001000
[2,1,5,6,3,7,8,4]=>1011000
[2,5,1,6,3,7,8,4]=>1011000
[2,5,6,1,3,7,8,4]=>1001000
[2,1,5,6,7,3,8,4]=>1011000
[2,5,1,6,7,3,8,4]=>1011000
[2,1,5,6,7,8,3,4]=>1010000
[2,5,1,6,7,8,3,4]=>1010000
[2,5,6,1,7,8,3,4]=>1010000
[2,5,6,7,8,1,3,4]=>1000000
[2,1,5,3,7,4,8,6]=>1011010
[2,5,1,3,7,4,8,6]=>1001010
[2,1,5,7,3,4,8,6]=>1010010
[2,5,1,7,3,4,8,6]=>1010010
[2,5,7,1,3,4,8,6]=>1000010
[2,1,5,3,7,8,4,6]=>1011000
[2,5,1,3,7,8,4,6]=>1001000
[2,1,5,7,3,8,4,6]=>1011000
[2,5,1,7,3,8,4,6]=>1011000
[2,5,7,1,3,8,4,6]=>1001000
[2,1,5,7,8,3,4,6]=>1010000
[2,5,1,7,8,3,4,6]=>1010000
[2,5,1,3,7,4,6,8]=>1001000
[2,1,5,7,3,4,6,8]=>1010000
[2,3,5,7,1,4,6,8]=>1000000
[2,3,5,1,7,4,8,6]=>1001010
[2,3,5,7,1,4,8,6]=>1000010
[2,3,5,7,1,8,4,6]=>1001000
[2,1,5,3,8,4,6,7]=>1011000
[2,1,5,8,3,4,6,7]=>1010000
[2,5,1,8,3,4,6,7]=>1010000
[2,3,5,1,4,8,6,7]=>1000010
[2,3,5,8,1,4,6,7]=>1000000
[2,1,5,3,4,6,8,7]=>1010001
[2,3,5,1,6,4,8,7]=>1001001
[2,3,5,6,1,4,8,7]=>1000001
[2,3,5,6,1,8,4,7]=>1001000
[2,3,5,6,8,1,4,7]=>1000000
[2,5,1,3,4,6,7,8]=>1000000
[2,3,5,6,1,4,7,8]=>1000000
[2,3,5,6,1,7,4,8]=>1001000
[2,3,5,1,6,7,8,4]=>1001000
[2,3,5,6,1,7,8,4]=>1001000
[2,3,5,6,7,1,8,4]=>1001000
[2,3,5,6,7,8,1,4]=>1000000
[2,1,6,3,7,4,8,5]=>1011100
[2,6,1,3,7,4,8,5]=>1001100
[2,6,7,1,3,4,8,5]=>1000100
[2,1,6,3,7,8,4,5]=>1011000
[2,1,6,7,3,8,4,5]=>1011000
[2,6,1,7,3,8,4,5]=>1011000
[2,1,6,7,8,3,4,5]=>1010000
[2,6,1,7,8,3,4,5]=>1010000
[2,6,7,8,1,3,4,5]=>1000000
[2,6,1,7,3,4,5,8]=>1010000
[2,6,7,1,3,4,5,8]=>1000000
[2,3,1,6,4,7,5,8]=>1001100
[2,3,6,1,4,7,5,8]=>1000100
[2,3,6,7,1,4,5,8]=>1000000
[2,1,6,3,4,7,8,5]=>1010100
[2,3,6,1,4,7,8,5]=>1000100
[2,1,3,6,7,4,8,5]=>1001100
[2,3,6,7,1,4,8,5]=>1000100
[2,3,1,6,7,8,4,5]=>1001000
[2,3,6,1,7,8,4,5]=>1001000
[2,3,6,7,1,8,4,5]=>1001000
[2,3,6,7,8,1,4,5]=>1000000
[2,6,1,8,3,4,5,7]=>1010000
[2,6,8,1,3,4,5,7]=>1000000
[2,1,6,3,4,8,5,7]=>1010100
[2,3,1,6,4,8,5,7]=>1001100
[2,3,6,1,4,8,5,7]=>1000100
[2,3,1,6,8,4,5,7]=>1001000
[2,3,6,1,8,4,5,7]=>1001000
[2,3,6,8,1,4,5,7]=>1000000
[2,1,6,3,4,5,8,7]=>1010001
[2,6,1,3,4,5,8,7]=>1000001
[2,3,6,1,4,5,8,7]=>1000001
[2,3,4,1,6,8,5,7]=>1000100
[2,3,4,6,1,8,5,7]=>1000100
[2,3,6,1,4,5,7,8]=>1000000
[2,3,4,6,7,8,1,5]=>1000000
[2,7,1,3,8,4,5,6]=>1001000
[2,1,7,8,3,4,5,6]=>1010000
[2,7,1,8,3,4,5,6]=>1010000
[2,7,8,1,3,4,5,6]=>1000000
[2,1,7,3,4,8,5,6]=>1010100
[2,1,3,7,4,8,5,6]=>1001100
[2,3,1,7,8,4,5,6]=>1001000
[2,3,7,8,1,4,5,6]=>1000000
[2,1,7,3,4,5,8,6]=>1010010
[2,3,1,7,4,5,8,6]=>1001010
[2,3,7,1,4,5,8,6]=>1000010
[2,3,4,1,7,5,8,6]=>1000110
[2,3,4,7,1,5,8,6]=>1000010
[2,1,3,4,7,8,5,6]=>1000100
[2,3,1,4,7,8,5,6]=>1000100
[2,3,4,1,7,8,5,6]=>1000100
[2,3,4,7,8,1,5,6]=>1000000
[2,3,4,1,7,5,6,8]=>1000100
[2,3,4,7,1,5,6,8]=>1000000
[2,1,8,3,4,5,6,7]=>1010000
[2,8,1,3,4,5,6,7]=>1000000
[2,1,3,8,4,5,6,7]=>1001000
[2,3,1,8,4,5,6,7]=>1001000
[2,3,8,1,4,5,6,7]=>1000000
[2,1,3,4,8,5,6,7]=>1000100
[2,3,1,4,8,5,6,7]=>1000100
[2,3,4,1,8,5,6,7]=>1000100
[2,3,4,8,1,5,6,7]=>1000000
[2,3,4,1,5,8,6,7]=>1000010
[2,3,4,5,8,1,6,7]=>1000000
[3,1,4,2,6,5,8,7]=>1100101
[3,4,1,2,6,5,8,7]=>1000101
[3,4,6,1,2,5,8,7]=>1000001
[3,1,4,2,6,8,5,7]=>1100100
[3,4,1,2,6,8,5,7]=>1000100
[3,1,4,6,2,8,5,7]=>1100100
[3,1,4,6,8,2,5,7]=>1100000
[3,4,1,6,8,2,5,7]=>1100000
[3,1,4,2,6,5,7,8]=>1100100
[3,4,1,2,6,5,7,8]=>1000100
[3,1,4,2,6,7,5,8]=>1100100
[3,4,1,2,6,7,5,8]=>1000100
[3,4,1,6,2,7,5,8]=>1100100
[3,4,6,1,2,7,5,8]=>1000100
[3,1,4,2,6,7,8,5]=>1100100
[3,4,1,2,6,7,8,5]=>1000100
[3,4,6,1,2,7,8,5]=>1000100
[3,4,6,1,7,2,8,5]=>1100100
[3,1,4,6,7,8,2,5]=>1100000
[3,4,6,1,7,8,2,5]=>1100000
[3,4,6,7,1,8,2,5]=>1100000
[3,4,6,7,8,1,2,5]=>1000000
[3,1,4,2,7,5,8,6]=>1100110
[3,4,1,2,7,5,8,6]=>1000110
[3,4,7,1,2,5,8,6]=>1000010
[3,1,4,2,7,8,5,6]=>1100100
[3,4,1,2,7,8,5,6]=>1000100
[3,4,7,1,8,2,5,6]=>1100000
[3,1,4,2,7,5,6,8]=>1100100
[3,4,1,2,7,5,6,8]=>1000100
[3,4,1,2,5,7,6,8]=>1000010
[3,1,4,5,2,7,6,8]=>1100010
[3,4,1,5,2,7,6,8]=>1100010
[3,4,1,5,7,2,6,8]=>1100000
[3,1,4,2,5,7,8,6]=>1100010
[3,4,1,2,5,7,8,6]=>1000010
[3,1,4,5,2,7,8,6]=>1100010
[3,4,1,5,7,2,8,6]=>1100010
[3,4,5,7,1,2,8,6]=>1000010
[3,1,4,5,7,8,2,6]=>1100000
[3,4,1,5,7,8,2,6]=>1100000
[3,4,5,1,7,8,2,6]=>1100000
[3,1,4,2,8,5,6,7]=>1100100
[3,4,1,2,8,5,6,7]=>1000100
[3,1,4,8,2,5,6,7]=>1100000
[3,4,1,8,2,5,6,7]=>1100000
[3,4,8,1,2,5,6,7]=>1000000
[3,1,4,2,5,8,6,7]=>1100010
[3,4,1,2,5,8,6,7]=>1000010
[3,4,1,5,2,8,6,7]=>1100010
[3,4,5,1,2,8,6,7]=>1000010
[3,4,1,5,8,2,6,7]=>1100000
[3,4,5,8,1,2,6,7]=>1000000
[3,4,1,2,5,6,8,7]=>1000001
[3,1,4,5,6,2,8,7]=>1100001
[3,4,5,1,6,2,8,7]=>1100001
[3,4,5,6,1,2,8,7]=>1000001
[3,4,1,5,6,8,2,7]=>1100000
[3,4,5,6,1,8,2,7]=>1100000
[3,4,5,6,8,1,2,7]=>1000000
[3,1,4,2,5,6,7,8]=>1100000
[3,4,1,5,6,2,7,8]=>1100000
[3,4,5,1,6,2,7,8]=>1100000
[3,4,1,5,6,7,2,8]=>1100000
[3,4,5,6,1,7,2,8]=>1100000
[3,1,4,5,6,7,8,2]=>1100000
[3,4,5,1,6,7,8,2]=>1100000
[3,4,5,6,1,7,8,2]=>1100000
[3,1,5,2,6,4,8,7]=>1101001
[3,1,5,6,2,4,8,7]=>1100001
[3,5,1,6,2,4,8,7]=>1100001
[3,5,6,1,2,4,8,7]=>1000001
[3,5,1,2,6,8,4,7]=>1001000
[3,1,5,6,2,8,4,7]=>1101000
[3,5,6,1,2,8,4,7]=>1001000
[3,1,5,6,8,2,4,7]=>1100000
[3,5,1,6,8,2,4,7]=>1100000
[3,5,6,1,8,2,4,7]=>1100000
[3,1,5,6,2,4,7,8]=>1100000
[3,5,1,6,2,4,7,8]=>1100000
[3,5,6,1,2,4,7,8]=>1000000
[3,5,1,6,2,7,4,8]=>1101000
[3,5,6,1,2,7,4,8]=>1001000
[3,5,6,1,7,2,4,8]=>1100000
[3,1,5,2,6,7,8,4]=>1101000
[3,5,1,2,6,7,8,4]=>1001000
[3,1,5,6,2,7,8,4]=>1101000
[3,5,1,6,2,7,8,4]=>1101000
[3,5,6,1,2,7,8,4]=>1001000
[3,1,5,6,7,2,8,4]=>1101000
[3,5,1,6,7,2,8,4]=>1101000
[3,5,6,1,7,2,8,4]=>1101000
[3,1,5,6,7,8,2,4]=>1100000
[3,5,1,6,7,8,2,4]=>1100000
[3,5,6,1,7,8,2,4]=>1100000
[3,5,6,7,8,1,2,4]=>1000000
[3,1,5,2,7,4,8,6]=>1101010
[3,5,1,2,7,4,8,6]=>1001010
[3,1,5,7,2,4,8,6]=>1100010
[3,5,1,7,2,4,8,6]=>1100010
[3,5,7,1,2,4,8,6]=>1000010
[3,1,5,2,7,8,4,6]=>1101000
[3,5,1,2,7,8,4,6]=>1001000
[3,1,5,7,2,8,4,6]=>1101000
[3,5,1,7,2,8,4,6]=>1101000
[3,1,5,7,8,2,4,6]=>1100000
[3,5,1,7,8,2,4,6]=>1100000
[3,5,7,8,1,2,4,6]=>1000000
[3,1,5,2,7,4,6,8]=>1101000
[3,5,1,2,7,4,6,8]=>1001000
[3,1,5,7,2,4,6,8]=>1100000
[3,5,1,7,2,4,6,8]=>1100000
[3,5,7,1,2,4,6,8]=>1000000
[3,1,5,2,4,7,6,8]=>1100010
[3,5,1,2,4,7,6,8]=>1000010
[3,1,2,5,4,7,6,8]=>1001010
[1,3,5,2,4,7,6,8]=>0100010
[3,1,2,5,7,4,6,8]=>1001000
[1,3,2,5,7,4,6,8]=>0101000
[1,3,5,2,7,4,6,8]=>0101000
[1,3,5,7,2,4,6,8]=>0100000
[3,5,1,2,4,7,8,6]=>1000010
[1,3,5,2,4,7,8,6]=>0100010
[3,1,2,5,7,4,8,6]=>1001010
[1,3,2,5,7,4,8,6]=>0101010
[1,3,5,2,7,4,8,6]=>0101010
[1,3,5,7,2,4,8,6]=>0100010
[1,3,2,5,7,8,4,6]=>0101000
[1,3,5,2,7,8,4,6]=>0101000
[1,3,5,7,2,8,4,6]=>0101000
[1,3,5,7,8,2,4,6]=>0100000
[3,1,5,2,8,4,6,7]=>1101000
[3,5,1,2,8,4,6,7]=>1001000
[3,1,5,8,2,4,6,7]=>1100000
[3,5,1,8,2,4,6,7]=>1100000
[3,1,5,2,4,8,6,7]=>1100010
[3,5,1,2,4,8,6,7]=>1000010
[1,3,2,5,4,8,6,7]=>0101010
[1,3,5,2,4,8,6,7]=>0100010
[3,1,2,5,8,4,6,7]=>1001000
[1,3,2,5,8,4,6,7]=>0101000
[1,3,5,2,8,4,6,7]=>0101000
[1,3,5,8,2,4,6,7]=>0100000
[3,5,1,2,4,6,8,7]=>1000001
[3,1,2,5,4,6,8,7]=>1001001
[1,3,5,2,4,6,8,7]=>0100001
[1,3,5,2,6,4,8,7]=>0101001
[1,3,5,6,2,4,8,7]=>0100001
[3,1,2,5,6,8,4,7]=>1001000
[1,3,5,2,6,8,4,7]=>0101000
[3,5,1,2,4,6,7,8]=>1000000
[1,3,5,2,4,6,7,8]=>0100000
[1,3,5,2,6,4,7,8]=>0101000
[1,3,5,6,2,4,7,8]=>0100000
[3,1,2,5,6,7,4,8]=>1001000
[1,3,5,2,6,7,4,8]=>0101000
[1,3,5,6,2,7,4,8]=>0101000
[1,3,5,6,7,2,4,8]=>0100000
[3,1,2,5,6,7,8,4]=>1001000
[1,3,5,6,2,7,8,4]=>0101000
[1,3,5,6,7,8,2,4]=>0100000
[3,1,6,2,7,4,8,5]=>1101100
[3,6,1,2,7,4,8,5]=>1001100
[3,6,1,7,2,4,8,5]=>1100100
[3,6,7,1,2,4,8,5]=>1000100
[3,1,6,7,2,8,4,5]=>1101000
[3,6,1,7,2,8,4,5]=>1101000
[3,6,7,1,2,8,4,5]=>1001000
[3,6,1,7,8,2,4,5]=>1100000
[3,6,7,8,1,2,4,5]=>1000000
[3,1,6,7,2,4,5,8]=>1100000
[3,6,7,1,2,4,5,8]=>1000000
[3,1,6,2,4,7,5,8]=>1100100
[3,6,1,2,4,7,5,8]=>1000100
[3,1,2,6,4,7,5,8]=>1001100
[1,3,2,6,4,7,5,8]=>0101100
[1,3,6,2,4,7,5,8]=>0100100
[1,3,2,6,7,4,5,8]=>0101000
[3,1,6,2,4,7,8,5]=>1100100
[3,6,1,2,4,7,8,5]=>1000100
[3,1,2,6,4,7,8,5]=>1001100
[1,3,2,6,4,7,8,5]=>0101100
[1,3,6,2,4,7,8,5]=>0100100
[3,1,2,6,7,4,8,5]=>1001100
[1,3,6,2,7,4,8,5]=>0101100
[1,3,6,7,2,4,8,5]=>0100100
[1,3,6,2,7,8,4,5]=>0101000
[3,1,6,2,8,4,5,7]=>1101000
[3,1,6,8,2,4,5,7]=>1100000
[3,6,1,8,2,4,5,7]=>1100000
[3,6,8,1,2,4,5,7]=>1000000
[3,1,6,2,4,8,5,7]=>1100100
[3,6,1,2,4,8,5,7]=>1000100
[1,3,2,6,4,8,5,7]=>0101100
[1,3,6,2,4,8,5,7]=>0100100
[3,1,6,2,4,5,8,7]=>1100001
[3,1,2,6,4,5,8,7]=>1001001
[1,3,4,6,2,5,8,7]=>0100001
[3,1,2,4,6,8,5,7]=>1000100
[1,3,2,4,6,8,5,7]=>0100100
[1,3,4,6,8,2,5,7]=>0100000
[3,1,6,2,4,5,7,8]=>1100000
[1,3,2,6,4,5,7,8]=>0101000
[1,3,6,2,4,5,7,8]=>0100000
[3,1,2,4,6,7,5,8]=>1000100
[3,1,2,4,6,7,8,5]=>1000100
[1,3,4,6,7,2,8,5]=>0100100
[3,7,1,2,8,4,5,6]=>1001000
[3,1,7,8,2,4,5,6]=>1100000
[3,7,1,2,4,8,5,6]=>1000100
[3,1,2,7,4,8,5,6]=>1001100
[1,3,2,7,4,8,5,6]=>0101100
[1,3,7,2,4,8,5,6]=>0100100
[3,1,2,7,8,4,5,6]=>1001000
[1,3,7,2,8,4,5,6]=>0101000
[3,7,1,2,4,5,8,6]=>1000010
[1,3,7,2,4,5,8,6]=>0100010
[3,1,2,4,7,5,8,6]=>1000110
[1,3,2,4,7,5,8,6]=>0100110
[1,3,4,7,2,5,8,6]=>0100010
[3,1,2,4,7,8,5,6]=>1000100
[1,3,2,4,7,8,5,6]=>0100100
[1,3,4,2,7,8,5,6]=>0100100
[3,7,1,2,4,5,6,8]=>1000000
[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]=>0100000
[1,3,4,5,7,2,8,6]=>0100010
[1,3,4,5,7,8,2,6]=>0100000
[3,1,8,2,4,5,6,7]=>1100000
[3,1,2,8,4,5,6,7]=>1001000
[1,3,2,8,4,5,6,7]=>0101000
[1,3,8,2,4,5,6,7]=>0100000
[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]=>0100100
[1,3,4,8,2,5,6,7]=>0100000
[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]=>0100010
[1,3,4,5,2,8,6,7]=>0100010
[1,3,4,5,8,2,6,7]=>0100000
[4,1,5,2,6,3,8,7]=>1110001
[4,5,1,2,6,3,8,7]=>1010001
[4,1,5,6,2,3,8,7]=>1100001
[4,5,1,6,2,3,8,7]=>1100001
[4,5,6,1,2,3,8,7]=>1000001
[4,1,5,2,6,8,3,7]=>1110000
[4,5,1,2,6,8,3,7]=>1010000
[4,1,5,6,2,8,3,7]=>1110000
[4,5,1,6,2,8,3,7]=>1110000
[4,1,5,6,8,2,3,7]=>1100000
[4,5,6,8,1,2,3,7]=>1000000
[4,1,5,6,2,3,7,8]=>1100000
[4,5,1,6,2,3,7,8]=>1100000
[4,5,1,6,2,7,3,8]=>1110000
[4,1,5,6,7,2,3,8]=>1100000
[4,5,1,6,7,2,3,8]=>1100000
[4,1,5,2,6,7,8,3]=>1110000
[4,5,1,2,6,7,8,3]=>1010000
[4,5,1,6,2,7,8,3]=>1110000
[4,1,5,6,7,2,8,3]=>1110000
[4,5,1,6,7,2,8,3]=>1110000
[4,5,6,1,7,2,8,3]=>1110000
[4,5,6,7,1,2,8,3]=>1010000
[4,5,1,6,7,8,2,3]=>1100000
[4,5,6,7,1,8,2,3]=>1100000
[4,1,5,2,7,3,8,6]=>1110010
[4,5,1,2,7,3,8,6]=>1010010
[4,5,1,7,2,3,8,6]=>1100010
[4,1,5,2,7,8,3,6]=>1110000
[4,5,1,2,7,8,3,6]=>1010000
[4,1,5,7,2,8,3,6]=>1110000
[4,5,1,7,2,8,3,6]=>1110000
[4,5,7,1,2,8,3,6]=>1010000
[4,5,1,7,8,2,3,6]=>1100000
[4,1,5,2,7,3,6,8]=>1110000
[4,5,1,2,7,3,6,8]=>1010000
[4,1,5,7,2,3,6,8]=>1100000
[4,5,1,7,2,3,6,8]=>1100000
[4,5,1,2,3,7,6,8]=>1000010
[1,4,2,5,3,7,6,8]=>0110010
[1,4,5,2,3,7,6,8]=>0100010
[4,1,2,5,7,3,6,8]=>1010000
[1,4,2,5,7,3,6,8]=>0110000
[1,4,5,2,7,3,6,8]=>0110000
[1,4,5,7,2,3,6,8]=>0100000
[4,1,5,2,3,7,8,6]=>1100010
[4,1,2,5,3,7,8,6]=>1010010
[1,4,2,5,3,7,8,6]=>0110010
[1,4,5,2,3,7,8,6]=>0100010
[4,1,2,5,7,3,8,6]=>1010010
[1,4,2,5,7,3,8,6]=>0110010
[1,4,5,2,7,3,8,6]=>0110010
[1,4,5,7,2,3,8,6]=>0100010
[4,1,2,5,7,8,3,6]=>1010000
[1,4,2,5,7,8,3,6]=>0110000
[1,4,5,2,7,8,3,6]=>0110000
[1,4,5,7,8,2,3,6]=>0100000
[4,1,5,2,8,3,6,7]=>1110000
[4,5,1,2,8,3,6,7]=>1010000
[4,1,5,8,2,3,6,7]=>1100000
[4,5,1,8,2,3,6,7]=>1100000
[4,5,8,1,2,3,6,7]=>1000000
[4,1,5,2,3,8,6,7]=>1100010
[4,5,1,2,3,8,6,7]=>1000010
[4,1,2,5,3,8,6,7]=>1010010
[1,4,2,5,3,8,6,7]=>0110010
[1,4,5,2,3,8,6,7]=>0100010
[4,1,2,5,8,3,6,7]=>1010000
[1,4,2,5,8,3,6,7]=>0110000
[1,4,5,2,8,3,6,7]=>0110000
[1,4,5,8,2,3,6,7]=>0100000
[1,4,2,5,3,6,8,7]=>0110001
[4,1,2,5,6,3,8,7]=>1010001
[1,4,5,2,6,3,8,7]=>0110001
[4,1,2,5,6,8,3,7]=>1010000
[1,4,5,2,6,8,3,7]=>0110000
[1,4,5,6,2,8,3,7]=>0110000
[1,4,5,6,8,2,3,7]=>0100000
[1,4,2,5,3,6,7,8]=>0110000
[1,4,5,2,3,6,7,8]=>0100000
[4,1,2,5,6,3,7,8]=>1010000
[1,4,5,2,6,3,7,8]=>0110000
[4,1,2,5,6,7,3,8]=>1010000
[1,4,2,5,6,7,3,8]=>0110000
[1,4,5,6,7,2,3,8]=>0100000
[4,1,2,5,6,7,8,3]=>1010000
[1,4,5,2,6,7,8,3]=>0110000
[1,4,5,6,7,2,8,3]=>0110000
[4,1,6,2,7,3,8,5]=>1110100
[4,1,6,7,2,3,8,5]=>1100100
[4,6,7,1,2,3,8,5]=>1000100
[4,6,1,2,7,8,3,5]=>1010000
[4,6,7,1,8,2,3,5]=>1100000
[4,6,7,8,1,2,3,5]=>1000000
[4,1,6,2,7,3,5,8]=>1110000
[4,6,1,2,7,3,5,8]=>1010000
[4,1,6,7,2,3,5,8]=>1100000
[4,6,1,7,2,3,5,8]=>1100000
[4,1,6,2,3,7,5,8]=>1100100
[4,6,1,2,3,7,5,8]=>1000100
[4,1,2,6,3,7,5,8]=>1010100
[1,4,2,6,3,7,5,8]=>0110100
[4,1,2,6,7,3,5,8]=>1010000
[1,4,2,6,7,3,5,8]=>0110000
[1,4,6,2,7,3,5,8]=>0110000
[4,1,6,2,3,7,8,5]=>1100100
[4,1,2,6,3,7,8,5]=>1010100
[1,4,6,2,3,7,8,5]=>0100100
[4,1,2,6,7,3,8,5]=>1010100
[1,4,6,2,7,3,8,5]=>0110100
[1,4,2,6,7,8,3,5]=>0110000
[1,4,6,2,7,8,3,5]=>0110000
[1,4,6,7,2,8,3,5]=>0110000
[4,1,6,2,8,3,5,7]=>1110000
[4,6,1,2,8,3,5,7]=>1010000
[4,1,6,8,2,3,5,7]=>1100000
[4,6,1,8,2,3,5,7]=>1100000
[4,6,8,1,2,3,5,7]=>1000000
[4,6,1,2,3,8,5,7]=>1000100
[4,1,2,6,3,8,5,7]=>1010100
[1,4,2,6,3,8,5,7]=>0110100
[1,4,6,2,3,8,5,7]=>0100100
[1,4,2,6,8,3,5,7]=>0110000
[1,4,6,2,8,3,5,7]=>0110000
[1,4,6,8,2,3,5,7]=>0100000
[4,1,2,6,3,5,8,7]=>1010001
[1,4,2,6,3,5,8,7]=>0110001
[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]=>1000100
[1,2,4,3,6,8,5,7]=>0010100
[1,2,4,6,3,8,5,7]=>0010100
[1,2,4,6,8,3,5,7]=>0010000
[1,4,2,6,3,5,7,8]=>0110000
[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]=>0010000
[4,1,2,3,6,7,5,8]=>1000100
[4,1,2,3,6,7,8,5]=>1000100
[1,4,2,3,6,7,8,5]=>0100100
[1,2,4,6,7,3,8,5]=>0010100
[4,1,7,2,8,3,5,6]=>1110000
[4,7,1,2,8,3,5,6]=>1010000
[4,7,1,8,2,3,5,6]=>1100000
[4,1,7,2,3,8,5,6]=>1100100
[1,4,2,7,3,8,5,6]=>0110100
[1,4,7,2,3,8,5,6]=>0100100
[4,1,2,7,8,3,5,6]=>1010000
[1,4,2,7,8,3,5,6]=>0110000
[1,4,7,2,8,3,5,6]=>0110000
[4,1,7,2,3,5,8,6]=>1100010
[4,1,2,7,3,5,8,6]=>1010010
[1,4,2,7,3,5,8,6]=>0110010
[1,4,7,2,3,5,8,6]=>0100010
[4,1,2,3,7,5,8,6]=>1000110
[1,2,4,3,7,5,8,6]=>0010110
[4,1,2,3,7,8,5,6]=>1000100
[1,4,2,3,7,8,5,6]=>0100100
[1,2,4,3,7,8,5,6]=>0010100
[1,2,4,7,3,8,5,6]=>0010100
[1,2,4,7,8,3,5,6]=>0010000
[1,4,2,7,3,5,6,8]=>0110000
[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]=>1000010
[1,4,2,3,5,7,8,6]=>0100010
[1,2,4,5,7,3,8,6]=>0010010
[4,8,1,2,3,5,6,7]=>1000000
[4,1,2,8,3,5,6,7]=>1010000
[1,4,2,8,3,5,6,7]=>0110000
[1,4,8,2,3,5,6,7]=>0100000
[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]=>0010000
[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]=>0010010
[1,2,4,5,8,3,6,7]=>0010000
[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]=>0010000
[1,4,2,3,5,6,7,8]=>0100000
[5,1,6,2,7,3,8,4]=>1111000
[5,6,1,2,7,3,8,4]=>1011000
[5,1,6,7,2,3,8,4]=>1101000
[5,6,1,7,2,3,8,4]=>1101000
[5,6,7,1,2,3,8,4]=>1001000
[5,1,6,7,2,8,3,4]=>1110000
[5,6,7,1,2,8,3,4]=>1010000
[5,1,6,7,8,2,3,4]=>1100000
[5,6,1,7,8,2,3,4]=>1100000
[5,6,7,1,8,2,3,4]=>1100000
[5,1,6,2,7,3,4,8]=>1110000
[5,1,6,2,3,7,4,8]=>1101000
[5,1,2,6,3,7,4,8]=>1011000
[1,5,2,6,3,7,4,8]=>0111000
[5,1,2,6,7,3,4,8]=>1010000
[1,5,2,6,7,3,4,8]=>0110000
[1,5,6,7,2,3,4,8]=>0100000
[5,1,6,2,3,7,8,4]=>1101000
[5,6,1,2,3,7,8,4]=>1001000
[5,1,2,6,3,7,8,4]=>1011000
[1,5,2,6,3,7,8,4]=>0111000
[1,5,6,2,3,7,8,4]=>0101000
[5,1,2,6,7,3,8,4]=>1011000
[1,5,6,7,2,3,8,4]=>0101000
[5,1,2,6,7,8,3,4]=>1010000
[1,5,6,7,8,2,3,4]=>0100000
[5,1,6,2,8,3,4,7]=>1110000
[5,6,1,2,8,3,4,7]=>1010000
[5,6,8,1,2,3,4,7]=>1000000
[5,1,6,2,3,8,4,7]=>1101000
[5,6,1,2,3,8,4,7]=>1001000
[5,1,2,6,3,8,4,7]=>1011000
[1,5,2,6,3,8,4,7]=>0111000
[1,5,6,2,3,8,4,7]=>0101000
[5,1,2,6,8,3,4,7]=>1010000
[1,5,2,6,8,3,4,7]=>0110000
[1,5,6,2,8,3,4,7]=>0110000
[1,5,6,8,2,3,4,7]=>0100000
[5,1,2,6,3,4,8,7]=>1010001
[1,5,2,6,3,4,8,7]=>0110001
[1,5,6,2,3,4,8,7]=>0100001
[1,5,2,3,6,4,8,7]=>0101001
[1,2,5,3,6,4,8,7]=>0011001
[1,2,5,6,3,4,8,7]=>0010001
[5,1,2,3,6,8,4,7]=>1001000
[1,5,2,3,6,8,4,7]=>0101000
[1,2,5,6,3,8,4,7]=>0011000
[1,2,5,6,8,3,4,7]=>0010000
[5,1,6,2,3,4,7,8]=>1100000
[5,1,2,6,3,4,7,8]=>1010000
[1,5,2,6,3,4,7,8]=>0110000
[1,2,5,6,3,4,7,8]=>0010000
[5,1,2,3,6,7,4,8]=>1001000
[1,2,5,6,3,7,4,8]=>0011000
[5,1,2,3,6,7,8,4]=>1001000
[1,5,2,3,6,7,8,4]=>0101000
[1,2,5,3,6,7,8,4]=>0011000
[1,2,5,6,3,7,8,4]=>0011000
[1,2,5,6,7,8,3,4]=>0010000
[5,1,7,2,8,3,4,6]=>1110000
[5,7,1,2,8,3,4,6]=>1010000
[5,7,8,1,2,3,4,6]=>1000000
[5,1,2,7,3,8,4,6]=>1011000
[1,5,2,7,3,8,4,6]=>0111000
[1,5,7,2,3,8,4,6]=>0101000
[5,1,2,7,8,3,4,6]=>1010000
[1,5,2,7,8,3,4,6]=>0110000
[1,5,7,2,8,3,4,6]=>0110000
[1,5,7,8,2,3,4,6]=>0100000
[5,1,7,2,3,4,8,6]=>1100010
[5,1,2,7,3,4,8,6]=>1010010
[1,5,2,7,3,4,8,6]=>0110010
[1,5,7,2,3,4,8,6]=>0100010
[5,1,2,3,7,4,8,6]=>1001010
[1,5,2,3,7,4,8,6]=>0101010
[1,2,5,3,7,4,8,6]=>0011010
[1,2,5,7,3,4,8,6]=>0010010
[5,1,2,3,7,8,4,6]=>1001000
[1,5,2,3,7,8,4,6]=>0101000
[1,2,5,3,7,8,4,6]=>0011000
[1,2,5,7,3,8,4,6]=>0011000
[1,2,5,7,8,3,4,6]=>0010000
[5,7,1,2,3,4,6,8]=>1000000
[5,1,2,7,3,4,6,8]=>1010000
[1,5,2,7,3,4,6,8]=>0110000
[1,2,5,7,3,4,6,8]=>0010000
[1,5,2,3,4,7,6,8]=>0100010
[1,2,3,5,7,4,6,8]=>0001000
[1,5,2,3,4,7,8,6]=>0100010
[1,2,5,3,4,7,8,6]=>0010010
[1,2,3,5,7,4,8,6]=>0001010
[1,2,3,5,7,8,4,6]=>0001000
[5,1,2,8,3,4,6,7]=>1010000
[1,5,2,8,3,4,6,7]=>0110000
[1,5,2,3,8,4,6,7]=>0101000
[1,2,5,3,8,4,6,7]=>0011000
[1,2,5,8,3,4,6,7]=>0010000
[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]=>0001000
[1,5,2,3,4,6,8,7]=>0100001
[1,2,3,5,6,8,4,7]=>0001000
[1,5,2,3,4,6,7,8]=>0100000
[6,1,7,2,8,3,4,5]=>1110000
[6,1,7,8,2,3,4,5]=>1100000
[6,7,1,8,2,3,4,5]=>1100000
[6,1,7,2,3,8,4,5]=>1101000
[6,7,1,2,3,8,4,5]=>1001000
[1,6,2,7,3,8,4,5]=>0111000
[1,6,7,2,3,8,4,5]=>0101000
[1,6,7,2,8,3,4,5]=>0110000
[1,6,7,8,2,3,4,5]=>0100000
[6,1,7,2,3,4,8,5]=>1100100
[6,7,1,2,3,4,8,5]=>1000100
[6,1,2,7,3,4,8,5]=>1010100
[1,6,2,7,3,4,8,5]=>0110100
[1,6,7,2,3,4,8,5]=>0100100
[1,6,2,3,7,4,8,5]=>0101100
[1,2,6,3,7,4,8,5]=>0011100
[1,2,6,7,3,4,8,5]=>0010100
[6,1,2,3,7,8,4,5]=>1001000
[1,2,6,3,7,8,4,5]=>0011000
[1,2,6,7,3,8,4,5]=>0011000
[1,2,6,7,8,3,4,5]=>0010000
[6,1,7,2,3,4,5,8]=>1100000
[1,6,2,7,3,4,5,8]=>0110000
[1,6,7,2,3,4,5,8]=>0100000
[1,6,2,3,4,7,5,8]=>0100100
[1,2,6,3,4,7,5,8]=>0010100
[1,2,3,6,4,7,5,8]=>0001100
[1,2,3,6,7,4,5,8]=>0001000
[6,1,2,3,4,7,8,5]=>1000100
[1,6,2,3,4,7,8,5]=>0100100
[1,2,6,3,4,7,8,5]=>0010100
[1,2,3,6,4,7,8,5]=>0001100
[1,2,3,6,7,4,8,5]=>0001100
[1,2,3,6,7,8,4,5]=>0001000
[6,1,8,2,3,4,5,7]=>1100000
[6,1,2,8,3,4,5,7]=>1010000
[1,6,2,8,3,4,5,7]=>0110000
[1,6,8,2,3,4,5,7]=>0100000
[1,6,2,3,8,4,5,7]=>0101000
[1,2,6,3,8,4,5,7]=>0011000
[1,2,6,8,3,4,5,7]=>0010000
[1,6,2,3,4,8,5,7]=>0100100
[1,2,6,3,4,8,5,7]=>0010100
[1,2,3,6,4,8,5,7]=>0001100
[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]=>0000100
[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]=>1010000
[1,7,2,8,3,4,5,6]=>0110000
[1,7,8,2,3,4,5,6]=>0100000
[7,1,2,3,8,4,5,6]=>1001000
[1,2,7,8,3,4,5,6]=>0010000
[1,2,7,3,4,8,5,6]=>0010100
[1,2,3,7,4,8,5,6]=>0001100
[1,2,3,7,8,4,5,6]=>0001000
[1,2,7,3,4,5,8,6]=>0010010
[1,2,3,7,4,5,8,6]=>0001010
[1,2,3,4,7,5,8,6]=>0000110
[1,2,3,4,7,8,5,6]=>0000100
[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]=>1110001
[7,3,2,5,4,8,1,6]=>1111000
[8,4,5,2,3,7,6,1]=>1101010
[7,4,5,2,3,8,1,6]=>1101000
[6,4,5,2,3,1,8,7]=>1101001
[5,4,6,2,1,3,8,7]=>1101001
[3,6,1,5,4,2,8,7]=>1101001
[4,6,5,1,3,2,8,7]=>1100101
[5,6,4,3,1,2,8,7]=>1011001
[7,5,4,3,2,8,1,6]=>1111100
[8,6,4,3,7,2,5,1]=>1111010
[7,6,4,3,8,2,1,5]=>1111010
[6,7,4,3,8,1,2,5]=>1011000
[5,7,4,3,1,8,2,6]=>1111000
[4,7,5,1,3,8,2,6]=>1100100
[3,7,1,5,4,8,2,6]=>1101000
[2,1,7,5,4,8,3,6]=>1011100
[3,8,1,5,4,7,6,2]=>1101010
[4,8,5,1,3,7,6,2]=>1100110
[5,8,4,3,1,7,6,2]=>1111010
[6,8,4,3,7,1,5,2]=>1111000
[7,8,4,3,6,5,1,2]=>1011100
[6,8,5,7,3,1,4,2]=>1110100
[5,8,6,7,1,3,4,2]=>1100010
[4,8,6,1,7,3,5,2]=>1110010
[3,8,1,6,7,4,5,2]=>1101000
[2,1,8,6,7,4,5,3]=>1011010
[2,1,7,6,8,4,3,5]=>1011010
[3,7,1,6,8,4,2,5]=>1101000
[4,7,6,1,8,3,2,5]=>1110010
[5,7,6,8,1,3,2,4]=>1100010
[5,4,7,2,1,8,3,6]=>1111000
[6,4,7,2,8,1,3,5]=>1101000
[7,4,6,2,8,3,1,5]=>1111000
[8,4,6,2,7,3,5,1]=>1111000
[8,3,2,6,7,4,5,1]=>1111000
[7,3,2,6,8,4,1,5]=>1111000
[6,3,2,7,8,1,4,5]=>1110000
[5,3,2,7,1,8,4,6]=>1111000
[4,3,2,1,7,8,5,6]=>1110100
[3,4,1,2,8,7,6,5]=>1000111
[5,3,2,8,1,7,6,4]=>1111010
[6,3,2,8,7,1,5,4]=>1111001
[7,3,2,8,6,5,1,4]=>1110110
[8,4,7,2,6,5,3,1]=>1111100
[7,4,8,2,6,5,1,3]=>1101100
[6,4,8,2,7,1,5,3]=>1111000
[5,4,8,2,1,7,6,3]=>1111010
[4,5,8,1,2,7,6,3]=>1010010
[3,5,1,8,2,7,6,4]=>1101010
[2,1,5,8,3,7,6,4]=>1011010
[2,1,6,8,7,3,5,4]=>1011001
[3,6,1,8,7,2,5,4]=>1101001
[4,6,8,1,7,2,5,3]=>1110000
[5,6,8,7,1,2,4,3]=>1010001
[6,5,8,7,2,1,4,3]=>1110101
[7,5,8,6,2,4,1,3]=>1100110
[8,5,7,6,2,4,3,1]=>1110110
[5,7,8,6,1,4,2,3]=>1100010
[4,7,8,1,6,5,2,3]=>1100100
[3,7,1,8,6,5,2,4]=>1100110
[2,1,7,8,6,5,3,4]=>1010110
[3,8,1,7,6,5,4,2]=>1101110
[4,8,7,1,6,5,3,2]=>1110101
[5,8,7,6,1,4,3,2]=>1110011
[6,8,7,5,4,1,3,2]=>1101101
[3,2,5,1,4,6,7,8]=>1100000
[5,2,4,1,3,6,7,8]=>1100000
[3,2,6,1,4,5,7,8]=>1100000
[6,3,5,1,2,4,7,8]=>1010000
[5,2,7,1,3,4,6,8]=>1100000
[5,3,7,1,2,4,6,8]=>1010000
[5,4,7,1,2,3,6,8]=>1001000
[6,2,7,1,3,4,5,8]=>1100000
[6,3,7,1,2,4,5,8]=>1010000
[6,4,7,1,2,3,5,8]=>1001000
[7,3,5,1,2,4,6,8]=>1010000
[7,4,6,1,2,3,5,8]=>1001000
[3,2,8,1,4,5,6,7]=>1100000
[5,2,8,1,3,4,6,7]=>1100000
[5,4,8,1,2,3,6,7]=>1001000
[6,2,8,1,3,4,5,7]=>1100000
[6,5,8,1,2,3,4,7]=>1000100
[7,5,8,1,2,3,4,6]=>1000100
[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]=>1001000
[8,5,7,1,2,3,4,6]=>1000100
[3,2,5,7,1,4,6,8]=>1100000
[4,2,5,7,1,3,6,8]=>1100000
[4,3,5,7,1,2,6,8]=>1010000
[5,3,4,7,1,2,6,8]=>1010000
[4,2,6,7,1,3,5,8]=>1100000
[5,2,6,7,1,3,4,8]=>1100000
[5,3,6,7,1,2,4,8]=>1010000
[7,3,5,6,1,2,4,8]=>1010000
[3,2,5,8,1,4,6,7]=>1100000
[4,2,5,8,1,3,6,7]=>1100000
[4,3,5,8,1,2,6,7]=>1010000
[5,2,4,8,1,3,6,7]=>1100000
[3,2,6,8,1,4,5,7]=>1100000
[4,2,6,8,1,3,5,7]=>1100000
[4,3,6,8,1,2,5,7]=>1010000
[5,2,6,8,1,3,4,7]=>1100000
[6,2,4,8,1,3,5,7]=>1100000
[6,2,5,8,1,3,4,7]=>1100000
[6,3,5,8,1,2,4,7]=>1010000
[3,2,7,8,1,4,5,6]=>1100000
[4,3,7,8,1,2,5,6]=>1010000
[5,4,7,8,1,2,3,6]=>1001000
[6,2,7,8,1,3,4,5]=>1100000
[6,3,7,8,1,2,4,5]=>1010000
[6,4,7,8,1,2,3,5]=>1001000
[7,2,4,8,1,3,5,6]=>1100000
[7,3,5,8,1,2,4,6]=>1010000
[7,4,5,8,1,2,3,6]=>1001000
[8,2,5,6,1,3,4,7]=>1100000
[8,2,4,7,1,3,5,6]=>1100000
[8,2,5,7,1,3,4,6]=>1100000
[8,3,5,7,1,2,4,6]=>1010000
[8,2,6,7,1,3,4,5]=>1100000
[8,4,6,7,1,2,3,5]=>1001000
[4,6,2,5,1,3,7,8]=>1100000
[4,6,3,5,1,2,7,8]=>1010000
[5,6,2,4,1,3,7,8]=>1100000
[4,7,3,5,1,2,6,8]=>1010000
[5,7,2,4,1,3,6,8]=>1100000
[5,7,3,4,1,2,6,8]=>1010000
[3,7,2,6,1,4,5,8]=>1100000
[5,7,2,6,1,3,4,8]=>1100000
[6,7,2,5,1,3,4,8]=>1100000
[4,8,2,5,1,3,6,7]=>1100000
[5,8,3,4,1,2,6,7]=>1010000
[5,8,3,6,1,2,4,7]=>1010000
[6,8,2,4,1,3,5,7]=>1100000
[6,8,3,4,1,2,5,7]=>1010000
[6,8,3,5,1,2,4,7]=>1010000
[6,8,4,5,1,2,3,7]=>1001000
[3,8,2,7,1,4,5,6]=>1100000
[4,8,2,7,1,3,5,6]=>1100000
[4,8,3,7,1,2,5,6]=>1010000
[5,8,2,7,1,3,4,6]=>1100000
[5,8,3,7,1,2,4,6]=>1010000
[5,8,4,7,1,2,3,6]=>1001000
[6,8,2,7,1,3,4,5]=>1100000
[6,8,3,7,1,2,4,5]=>1010000
[6,8,5,7,1,2,3,4]=>1000100
[7,8,2,4,1,3,5,6]=>1100000
[7,8,2,5,1,3,4,6]=>1100000
[7,8,3,5,1,2,4,6]=>1010000
[7,8,4,6,1,2,3,5]=>1001000
[4,3,2,6,1,5,7,8]=>1110000
[5,3,2,6,1,4,7,8]=>1110000
[5,4,2,6,1,3,7,8]=>1101000
[6,4,2,5,1,3,7,8]=>1101000
[6,5,2,4,1,3,7,8]=>1100100
[4,3,2,7,1,5,6,8]=>1110000
[5,3,2,7,1,4,6,8]=>1110000
[5,4,3,7,1,2,6,8]=>1011000
[6,3,2,7,1,4,5,8]=>1110000
[6,4,2,7,1,3,5,8]=>1101000
[6,4,3,7,1,2,5,8]=>1011000
[6,5,3,7,1,2,4,8]=>1010100
[7,3,2,5,1,4,6,8]=>1110000
[7,4,2,5,1,3,6,8]=>1101000
[7,3,2,6,1,4,5,8]=>1110000
[7,4,3,6,1,2,5,8]=>1011000
[7,5,2,6,1,3,4,8]=>1100100
[7,5,3,6,1,2,4,8]=>1010100
[7,6,3,5,1,2,4,8]=>1010010
[4,3,2,8,1,5,6,7]=>1110000
[5,3,2,8,1,4,6,7]=>1110000
[5,4,3,8,1,2,6,7]=>1011000
[6,3,2,8,1,4,5,7]=>1110000
[6,4,3,8,1,2,5,7]=>1011000
[6,5,2,8,1,3,4,7]=>1100100
[6,5,3,8,1,2,4,7]=>1010100
[6,5,4,8,1,2,3,7]=>1001100
[7,3,2,8,1,4,5,6]=>1110000
[7,4,2,8,1,3,5,6]=>1101000
[7,5,3,8,1,2,4,6]=>1010100
[7,6,2,8,1,3,4,5]=>1100010
[8,4,2,5,1,3,6,7]=>1101000
[8,3,2,6,1,4,5,7]=>1110000
[8,4,2,6,1,3,5,7]=>1101000
[8,5,3,6,1,2,4,7]=>1010100
[8,6,2,5,1,3,4,7]=>1100010
[8,3,2,7,1,4,5,6]=>1110000
[8,4,2,7,1,3,5,6]=>1101000
[8,4,3,7,1,2,5,6]=>1011000
[8,5,2,7,1,3,4,6]=>1100100
[8,5,3,7,1,2,4,6]=>1010100
[8,5,4,7,1,2,3,6]=>1001100
[8,6,3,7,1,2,4,5]=>1010010
[8,7,2,4,1,3,5,6]=>1100001
[8,7,2,5,1,3,4,6]=>1100001
[8,7,3,5,1,2,4,6]=>1010001
[8,7,2,6,1,3,4,5]=>1100001
[8,7,3,6,1,2,4,5]=>1010001
[8,7,4,6,1,2,3,5]=>1001001
[4,6,3,5,8,1,2,7]=>1010000
[5,6,2,4,8,1,3,7]=>1100000
[4,7,2,5,8,1,3,6]=>1100000
[4,7,3,5,8,1,2,6]=>1010000
[5,7,3,4,8,1,2,6]=>1010000
[3,7,2,6,8,1,4,5]=>1100000
[4,7,3,6,8,1,2,5]=>1010000
[5,7,4,6,8,1,2,3]=>1001000
[6,7,3,5,8,1,2,4]=>1010000
[3,8,2,5,7,1,4,6]=>1100000
[4,8,2,5,7,1,3,6]=>1100000
[4,8,3,5,7,1,2,6]=>1010000
[3,8,2,6,7,1,4,5]=>1100000
[4,8,3,6,7,1,2,5]=>1010000
[5,8,4,6,7,1,2,3]=>1001000
[6,8,2,5,7,1,3,4]=>1100000
[6,8,3,5,7,1,2,4]=>1010000
[6,8,4,5,7,1,2,3]=>1001000
[7,8,2,4,6,1,3,5]=>1100000
[7,8,3,4,6,1,2,5]=>1010000
[7,8,2,5,6,1,3,4]=>1100000
[7,8,3,5,6,1,2,4]=>1010000
[4,3,2,6,8,1,5,7]=>1110000
[5,3,2,6,8,1,4,7]=>1110000
[5,4,2,6,8,1,3,7]=>1101000
[5,4,3,6,8,1,2,7]=>1011000
[6,3,2,5,8,1,4,7]=>1110000
[6,4,3,5,8,1,2,7]=>1011000
[6,5,2,4,8,1,3,7]=>1100100
[4,3,2,7,8,1,5,6]=>1110000
[5,3,2,7,8,1,4,6]=>1110000
[5,4,2,7,8,1,3,6]=>1101000
[5,4,3,7,8,1,2,6]=>1011000
[6,4,2,7,8,1,3,5]=>1101000
[6,4,3,7,8,1,2,5]=>1011000
[6,5,2,7,8,1,3,4]=>1100100
[7,4,2,5,8,1,3,6]=>1101000
[7,3,2,6,8,1,4,5]=>1110000
[7,5,3,6,8,1,2,4]=>1010100
[7,6,3,5,8,1,2,4]=>1010010
[8,4,2,5,7,1,3,6]=>1101000
[8,5,2,6,7,1,3,4]=>1100100
[8,5,3,6,7,1,2,4]=>1010100
[8,6,2,5,7,1,3,4]=>1100010
[8,6,3,5,7,1,2,4]=>1010010
[8,7,2,4,6,1,3,5]=>1100001
[8,7,3,4,6,1,2,5]=>1010001
[8,7,2,5,6,1,3,4]=>1100001
[8,7,3,5,6,1,2,4]=>1010001
[4,3,7,2,6,1,5,8]=>1110000
[5,3,7,2,6,1,4,8]=>1110000
[5,4,7,2,6,1,3,8]=>1101000
[6,3,7,2,5,1,4,8]=>1110000
[6,4,7,2,5,1,3,8]=>1101000
[7,3,6,2,5,1,4,8]=>1110000
[4,3,8,2,6,1,5,7]=>1110000
[5,3,8,2,6,1,4,7]=>1110000
[5,4,8,2,6,1,3,7]=>1101000
[6,4,8,2,5,1,3,7]=>1101000
[6,4,8,3,5,1,2,7]=>1011000
[6,5,8,3,4,1,2,7]=>1010100
[4,3,8,2,7,1,5,6]=>1110000
[5,4,8,2,7,1,3,6]=>1101000
[6,4,8,2,7,1,3,5]=>1101000
[6,5,8,2,7,1,3,4]=>1100100
[7,3,8,2,5,1,4,6]=>1110000
[7,4,8,3,5,1,2,6]=>1011000
[7,5,8,2,4,1,3,6]=>1100100
[7,5,8,3,4,1,2,6]=>1010100
[7,3,8,2,6,1,4,5]=>1110000
[7,4,8,2,6,1,3,5]=>1101000
[7,5,8,2,6,1,3,4]=>1100100
[7,5,8,3,6,1,2,4]=>1010100
[7,5,8,4,6,1,2,3]=>1001100
[8,3,6,2,5,1,4,7]=>1110000
[8,4,6,2,5,1,3,7]=>1101000
[8,3,7,2,5,1,4,6]=>1110000
[8,4,7,3,5,1,2,6]=>1011000
[8,3,7,2,6,1,4,5]=>1110000
[8,4,7,2,6,1,3,5]=>1101000
[8,4,7,3,6,1,2,5]=>1011000
[8,5,7,2,6,1,3,4]=>1100100
[8,6,7,2,4,1,3,5]=>1100010
[8,6,7,2,5,1,3,4]=>1100010
[8,6,7,3,5,1,2,4]=>1010010
[5,4,3,2,7,1,6,8]=>1111000
[6,4,3,2,7,1,5,8]=>1111000
[6,5,3,2,7,1,4,8]=>1110100
[6,5,4,2,7,1,3,8]=>1101100
[7,5,3,2,6,1,4,8]=>1110100
[5,4,3,2,8,1,6,7]=>1111000
[6,5,3,2,8,1,4,7]=>1110100
[6,5,4,3,8,1,2,7]=>1011100
[7,5,3,2,8,1,4,6]=>1110100
[7,6,4,3,8,1,2,5]=>1011010
[7,6,5,3,8,1,2,4]=>1010110
[8,5,3,2,6,1,4,7]=>1110100
[8,5,4,2,6,1,3,7]=>1101100
[8,6,5,2,4,1,3,7]=>1100110
[8,5,3,2,7,1,4,6]=>1110100
[8,6,3,2,7,1,4,5]=>1110010
[8,6,5,3,7,1,2,4]=>1010110
[8,7,3,2,6,1,4,5]=>1110001
[8,7,4,2,6,1,3,5]=>1101001
[8,7,4,3,6,1,2,5]=>1011001
[8,7,5,2,6,1,3,4]=>1100101
[8,7,5,3,6,1,2,4]=>1010101
[8,7,6,2,4,1,3,5]=>1100011
[8,7,6,2,5,1,3,4]=>1100011
[8,7,6,3,5,1,2,4]=>1010011
[4,8,3,7,2,6,1,5]=>1110000
[5,8,3,7,2,6,1,4]=>1110000
[5,8,4,7,2,6,1,3]=>1101000
[5,8,4,7,3,6,1,2]=>1011000
[6,8,3,7,2,5,1,4]=>1110000
[6,8,4,7,2,5,1,3]=>1101000
[6,8,4,7,3,5,1,2]=>1011000
[6,8,5,7,2,4,1,3]=>1100100
[6,8,5,7,3,4,1,2]=>1010100
[7,8,3,6,2,5,1,4]=>1110000
[7,8,4,6,2,5,1,3]=>1101000
[7,8,4,6,3,5,1,2]=>1011000
[7,8,5,6,2,4,1,3]=>1100100
[6,4,3,8,2,7,1,5]=>1111000
[6,5,3,8,2,7,1,4]=>1110100
[6,5,4,8,2,7,1,3]=>1101100
[7,4,3,8,2,6,1,5]=>1111000
[7,5,3,8,2,6,1,4]=>1110100
[7,5,4,8,2,6,1,3]=>1101100
[7,6,3,8,2,5,1,4]=>1110010
[7,6,4,8,2,5,1,3]=>1101010
[7,6,5,8,2,4,1,3]=>1100110
[8,4,3,7,2,6,1,5]=>1111000
[8,5,3,7,2,6,1,4]=>1110100
[8,6,3,7,2,5,1,4]=>1110010
[8,6,4,7,2,5,1,3]=>1101010
[8,6,4,7,3,5,1,2]=>1011010
[8,6,5,7,2,4,1,3]=>1100110
[8,7,3,6,2,5,1,4]=>1110001
[8,7,4,6,3,5,1,2]=>1011001
[8,7,5,6,2,4,1,3]=>1100101
[6,5,4,3,2,8,1,7]=>1111100
[7,6,4,3,2,8,1,5]=>1111010
[8,5,4,3,2,7,1,6]=>1111100
[8,7,4,3,2,6,1,5]=>1111001
[8,7,5,3,2,6,1,4]=>1110101
[8,7,5,4,2,6,1,3]=>1101101
[8,7,6,3,2,5,1,4]=>1110011
[8,7,6,5,2,4,1,3]=>1100111
[8,1,2,3,7,4,5,6]=>1001000
[8,1,2,5,3,4,6,7]=>1010000
[6,1,2,5,3,8,4,7]=>1011000
[4,1,2,8,7,3,5,6]=>1010001
[4,1,2,7,6,3,8,5]=>1010110
[8,1,2,5,6,3,4,7]=>1010000
[8,1,2,7,6,3,4,5]=>1010010
[7,1,2,5,6,3,8,4]=>1011000
[4,1,2,5,8,7,3,6]=>1010001
[8,1,2,5,6,7,3,4]=>1010000
[3,1,7,2,6,4,8,5]=>1101100
[3,1,5,2,8,7,4,6]=>1101001
[3,1,8,2,6,7,4,5]=>1101000
[8,1,4,2,3,5,6,7]=>1100000
[7,1,4,2,3,5,8,6]=>1100010
[6,1,4,2,3,8,5,7]=>1100100
[7,1,5,2,3,4,8,6]=>1100010
[6,1,5,2,3,8,4,7]=>1101000
[6,1,5,2,3,7,8,4]=>1101000
[5,1,4,2,8,3,6,7]=>1110000
[5,1,4,2,7,3,8,6]=>1110010
[8,1,4,2,6,3,5,7]=>1110000
[7,1,4,2,6,3,8,5]=>1110100
[8,1,5,2,7,3,4,6]=>1110000
[7,1,5,2,6,3,8,4]=>1111000
[5,1,4,2,8,7,3,6]=>1110001
[8,1,4,2,6,7,3,5]=>1110000
[8,1,5,2,6,7,3,4]=>1110000
[5,1,4,2,6,7,8,3]=>1110000
[3,1,8,6,2,4,5,7]=>1100010
[3,1,6,5,2,8,4,7]=>1101100
[3,1,8,5,2,7,4,6]=>1101100
[3,1,8,6,2,7,4,5]=>1101010
[8,1,4,5,2,3,6,7]=>1100000
[7,1,8,6,2,3,4,5]=>1100010
[7,1,6,5,2,3,8,4]=>1101100
[3,1,4,8,6,2,5,7]=>1100010
[3,1,8,5,7,2,4,6]=>1100100
[3,1,7,5,6,2,8,4]=>1101100
[8,1,4,5,7,2,3,6]=>1100000
[8,1,4,7,6,2,3,5]=>1100010
[3,1,4,5,8,7,2,6]=>1100001
[3,1,8,5,6,7,2,4]=>1100100
[8,1,4,5,6,7,2,3]=>1100000
[2,8,1,3,7,4,5,6]=>1001000
[2,8,1,3,6,7,4,5]=>1001000
[2,4,1,8,3,7,5,6]=>1010100
[2,6,1,5,3,8,4,7]=>1011000
[2,6,1,5,3,7,8,4]=>1011000
[2,4,1,8,6,3,5,7]=>1010010
[2,8,1,5,7,3,4,6]=>1010000
[2,8,1,7,6,3,4,5]=>1010010
[2,4,1,5,8,7,3,6]=>1010001
[7,3,1,2,4,5,8,6]=>1010010
[6,3,1,2,4,8,5,7]=>1010100
[6,3,1,2,4,7,8,5]=>1010100
[5,3,1,2,8,4,6,7]=>1011000
[7,3,1,2,6,4,8,5]=>1011100
[5,3,1,2,8,7,4,6]=>1011001
[5,3,1,2,6,7,8,4]=>1011000
[7,6,1,2,3,4,8,5]=>1000110
[8,6,1,2,3,7,4,5]=>1001010
[5,4,1,2,8,3,6,7]=>1011000
[8,4,1,2,7,3,5,6]=>1011000
[7,4,1,2,6,3,8,5]=>1011100
[5,8,1,2,7,3,4,6]=>1010000
[8,7,1,2,6,3,4,5]=>1010001
[5,7,1,2,6,3,8,4]=>1011000
[8,4,1,2,6,7,3,5]=>1011000
[5,8,1,2,6,7,3,4]=>1010000
[5,4,1,2,6,7,8,3]=>1011000
[4,3,1,8,2,5,6,7]=>1110000
[4,3,1,7,2,5,8,6]=>1110010
[4,3,1,6,2,8,5,7]=>1110100
[4,3,1,6,2,7,8,5]=>1110100
[8,3,1,5,2,4,6,7]=>1110000
[8,3,1,6,2,4,5,7]=>1110000
[7,3,1,6,2,4,8,5]=>1110100
[8,3,1,5,2,7,4,6]=>1111000
[8,3,1,6,2,7,4,5]=>1111000
[6,3,1,5,2,7,8,4]=>1111000
[7,4,1,5,2,3,8,6]=>1101010
[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]=>1101100
[8,7,1,6,2,3,4,5]=>1100001
[6,7,1,5,2,3,8,4]=>1101000
[6,4,1,5,2,8,3,7]=>1111000
[8,4,1,6,2,7,3,5]=>1111000
[6,8,1,5,2,7,3,4]=>1110000
[6,4,1,5,2,7,8,3]=>1111000
[4,3,1,8,7,2,5,6]=>1110001
[4,3,1,7,6,2,8,5]=>1110110
[8,3,1,5,6,2,4,7]=>1110000
[8,3,1,5,7,2,4,6]=>1110000
[8,3,1,7,6,2,4,5]=>1110010
[7,3,1,5,6,2,8,4]=>1111000
[8,4,1,5,6,2,3,7]=>1101000
[7,8,1,5,6,2,3,4]=>1100000
[4,3,1,5,6,8,2,7]=>1110000
[8,4,1,5,6,7,2,3]=>1101000
[4,3,1,5,6,7,8,2]=>1110000
[2,3,7,1,6,4,8,5]=>1001100
[2,3,5,1,8,7,4,6]=>1001001
[2,3,8,1,6,7,4,5]=>1001000
[2,8,4,1,3,5,6,7]=>1001000
[2,6,4,1,3,8,5,7]=>1001100
[2,6,4,1,3,7,8,5]=>1001100
[2,7,5,1,3,4,8,6]=>1000110
[2,6,8,1,3,7,4,5]=>1001000
[2,6,5,1,3,7,8,4]=>1001100
[2,8,4,1,7,3,5,6]=>1011000
[2,7,4,1,6,3,8,5]=>1011100
[2,8,5,1,7,3,4,6]=>1010100
[2,7,5,1,6,3,8,4]=>1011100
[2,8,4,1,6,7,3,5]=>1011000
[2,5,4,1,6,7,8,3]=>1011000
[6,3,4,1,2,7,8,5]=>1010100
[7,3,5,1,2,4,8,6]=>1010010
[6,3,7,1,2,4,8,5]=>1010100
[8,3,5,1,2,7,4,6]=>1011000
[6,3,8,1,2,7,4,5]=>1011000
[7,5,4,1,2,3,8,6]=>1001110
[6,7,4,1,2,3,8,5]=>1001100
[6,8,5,1,2,3,4,7]=>1000100
[8,5,4,1,2,7,3,6]=>1011100
[6,8,4,1,2,7,3,5]=>1011000
[6,8,5,1,2,7,3,4]=>1010100
[8,3,4,1,7,2,5,6]=>1110000
[8,3,5,1,6,2,4,7]=>1110000
[7,3,8,1,6,2,4,5]=>1110000
[7,3,5,1,6,2,8,4]=>1111000
[8,5,4,1,6,2,3,7]=>1101100
[7,8,4,1,6,2,3,5]=>1101000
[7,8,5,1,6,2,3,4]=>1100100
[7,5,4,1,6,2,8,3]=>1111100
[5,3,4,1,6,7,8,2]=>1110000
[2,3,4,8,1,7,5,6]=>1000100
[2,3,7,6,1,4,8,5]=>1000110
[2,3,6,5,1,8,4,7]=>1001100
[2,3,6,5,1,7,8,4]=>1001100
[2,8,4,5,1,3,6,7]=>1001000
[2,7,4,8,1,3,5,6]=>1001000
[2,7,4,6,1,3,8,5]=>1001100
[2,8,6,5,1,3,4,7]=>1000110
[2,7,8,5,1,3,4,6]=>1000100
[2,7,6,5,1,3,8,4]=>1001110
[2,6,4,5,1,8,3,7]=>1011000
[2,8,4,6,1,7,3,5]=>1011000
[7,3,8,5,1,2,4,6]=>1010100
[8,6,4,5,1,7,2,3]=>1101010
[2,3,4,8,6,1,5,7]=>1000010
[2,3,4,8,7,1,5,6]=>1000001
[2,3,4,7,6,1,8,5]=>1000110
[2,3,8,5,7,1,4,6]=>1000100
[2,3,7,5,6,1,8,4]=>1001100
[2,8,4,7,6,1,3,5]=>1001010
[2,8,7,5,6,1,3,4]=>1000101
[8,3,4,7,6,1,2,5]=>1010010
[8,3,7,5,6,1,2,4]=>1010100
[2,3,4,5,8,7,1,6]=>1000001
[2,3,4,8,6,7,1,5]=>1000010
[2,8,4,5,6,7,1,3]=>1001000
[6,5,8,7,3,4,1,2]=>1010101
[4,6,7,3,8,5,1,2]=>1010100
[3,6,7,4,5,8,1,2]=>1001000
[2,6,7,4,5,1,8,3]=>1011000
[1,6,7,4,5,2,3,8]=>0101000
[1,5,4,7,6,2,3,8]=>0101010
[2,5,4,7,6,1,8,3]=>1011010
[3,5,4,7,6,8,1,2]=>1001010
[4,5,3,7,8,6,1,2]=>1010010
[5,4,3,8,7,6,1,2]=>1011011
[6,4,8,3,7,5,1,2]=>1011100
[6,3,8,4,5,7,1,2]=>1011000
[5,3,4,8,6,7,1,2]=>1010010
[4,3,5,6,8,7,1,2]=>1010001
[3,2,5,6,1,8,7,4]=>1101001
[4,2,5,6,8,1,7,3]=>1110000
[5,2,4,8,6,1,7,3]=>1110010
[6,2,8,4,5,1,7,3]=>1111000
[7,8,2,4,5,1,6,3]=>1110000
[7,8,1,4,5,2,3,6]=>1100000
[6,1,8,4,5,2,3,7]=>1101000
[5,1,4,8,6,2,3,7]=>1100010
[4,1,3,2,8,6,5,7]=>1100110
[5,1,3,8,2,6,4,7]=>1101000
[6,1,8,3,2,5,4,7]=>1111000
[7,8,1,3,2,5,4,6]=>1101000
[7,8,2,3,1,5,6,4]=>1101000
[6,2,8,3,1,5,7,4]=>1111000
[5,2,3,8,1,6,7,4]=>1101000
[6,3,8,2,1,7,5,4]=>1111100
[7,8,3,2,1,6,5,4]=>1111100
[7,8,4,2,6,1,5,3]=>1111000
[5,4,2,8,7,1,6,3]=>1111001
[4,5,2,7,8,1,6,3]=>1110000
[3,5,2,7,1,8,6,4]=>1101010
[2,5,3,7,1,6,8,4]=>1011000
[1,5,3,7,2,6,4,8]=>0111000
[1,6,7,3,2,5,4,8]=>0111000
[2,6,7,3,1,5,8,4]=>1011000
[3,6,7,2,1,8,5,4]=>1101100
[4,6,7,2,8,1,5,3]=>1110000
[5,6,7,8,2,1,4,3]=>1110000
[7,8,5,6,2,1,4,3]=>1110100
[6,5,8,7,1,2,3,4]=>1000101
[5,4,1,8,7,2,3,6]=>1101001
[6,4,8,1,7,2,3,5]=>1101000
[7,8,3,1,2,6,4,5]=>1011000
[5,3,1,8,2,7,4,6]=>1111000
[4,3,1,2,8,7,5,6]=>1010101
[4,2,1,3,8,5,7,6]=>1100110
[5,2,1,8,3,4,7,6]=>1110010
[6,2,8,1,3,4,7,5]=>1100100
[7,8,2,1,3,4,6,5]=>1100100
[4,5,2,3,7,6,1,8]=>1100010
[6,4,3,7,2,5,1,8]=>1111000
[8,4,3,6,5,1,2,7]=>1011100
[1,5,6,3,4,8,7,2]=>0110001
[4,6,2,7,3,5,1,8]=>1110000
[3,2,6,7,4,5,1,8]=>1101000
[8,7,5,4,1,3,2,6]=>1101101
[5,8,6,2,4,1,3,7]=>1100010
[4,8,2,6,5,1,3,7]=>1100100
[4,1,2,6,5,8,7,3]=>1010101
[5,1,6,2,4,8,7,3]=>1110001
[6,1,5,4,2,8,7,3]=>1111001
[7,1,5,4,8,2,6,3]=>1111000
[8,1,5,4,7,6,2,3]=>1101010
[1,8,6,7,4,5,3,2]=>0111010
[8,1,6,7,4,5,2,3]=>1101000
[6,1,7,8,2,4,5,3]=>1110000
[5,1,7,2,8,4,6,3]=>1111000
[4,1,2,7,8,5,6,3]=>1010100
[3,2,1,7,8,5,6,4]=>1101100
[3,2,8,7,1,5,4,6]=>1101001
[4,8,2,7,1,5,3,6]=>1110000
[5,8,7,2,1,4,3,6]=>1110001
[6,8,7,1,2,4,3,5]=>1010001
[8,7,6,1,4,3,2,5]=>1110011
[1,6,7,8,3,4,5,2]=>0110000
[8,6,7,1,3,4,2,5]=>1100010
[7,6,8,1,3,2,4,5]=>1100010
[5,7,8,2,1,3,4,6]=>1100000
[4,7,2,8,1,3,5,6]=>1100000
[3,2,6,8,4,1,5,7]=>1101000
[4,6,2,8,3,1,5,7]=>1110000
[5,6,8,2,3,1,4,7]=>1100000
[7,5,8,3,1,2,4,6]=>1010100
[8,5,7,3,1,4,2,6]=>1110100
[1,5,7,3,8,4,6,2]=>0111000
[1,4,3,7,8,5,6,2]=>0110100
[6,4,3,8,2,1,5,7]=>1111000
[4,5,2,3,8,1,6,7]=>1100000
[3,2,5,4,8,1,6,7]=>1101000
[4,5,2,3,1,8,7,6]=>1100011
[6,4,3,1,2,8,7,5]=>1011101
[7,4,3,1,8,2,6,5]=>1111100
[8,4,3,1,7,6,2,5]=>1111010
[1,5,8,3,7,6,4,2]=>0111010
[7,5,1,3,8,2,6,4]=>1101100
[5,6,1,2,3,8,7,4]=>1001001
[4,6,2,1,3,8,7,5]=>1100101
[3,2,6,1,4,8,7,5]=>1100101
[3,2,7,1,8,4,6,5]=>1101100
[5,7,1,2,8,3,6,4]=>1011000
[6,7,1,8,2,3,5,4]=>1101000
[7,6,1,8,3,2,5,4]=>1111010
[8,7,1,6,5,3,2,4]=>1110101
[7,8,1,6,5,2,3,4]=>1100100
[6,8,1,7,2,5,3,4]=>1110000
[5,8,1,2,7,6,3,4]=>1010010
[4,8,2,1,7,6,3,5]=>1110010
[3,2,8,1,7,6,4,5]=>1101010
[4,1,2,8,7,6,5,3]=>1010111
[5,1,8,2,7,6,4,3]=>1111010
[6,1,8,7,2,5,4,3]=>1111001
[8,1,7,6,5,4,2,3]=>1101110
[3,2,5,1,6,4,8,7]=>1101001
[3,2,5,4,7,1,8,6]=>1101010
[4,2,5,3,7,6,8,1]=>1110010
[4,2,5,3,6,1,8,7]=>1110001
[4,1,5,3,6,2,8,7]=>1110001
[4,3,5,2,7,1,8,6]=>1110010
[4,3,5,1,7,2,8,6]=>1110010
[4,1,5,3,7,2,8,6]=>1110010
[2,1,5,4,7,3,8,6]=>1011010
[4,3,6,5,7,1,8,2]=>1110100
[5,3,6,4,7,1,8,2]=>1111000
[4,1,6,3,7,5,8,2]=>1110100
[2,1,6,4,7,5,8,3]=>1011100
[2,1,6,4,7,3,8,5]=>1011100
[3,1,6,4,7,2,8,5]=>1101100
[4,1,6,3,7,2,8,5]=>1110100
[5,3,6,2,7,4,8,1]=>1111000
[5,2,6,3,7,4,8,1]=>1111000
[5,2,6,3,7,1,8,4]=>1111000
[5,2,6,1,7,3,8,4]=>1111000
[4,2,6,1,7,3,8,5]=>1110100
[4,2,6,3,7,1,8,5]=>1110100
[4,2,6,3,7,5,8,1]=>1110100
[3,2,6,4,7,5,8,1]=>1101100
[3,2,6,4,7,1,8,5]=>1101100
[3,2,6,1,7,4,8,5]=>1101100
[3,2,5,1,7,4,8,6]=>1101010
[3,2,4,1,7,5,8,6]=>1100110
[3,1,4,2,7,6,8,5]=>1100110
[3,2,5,1,7,6,8,4]=>1101010
[3,2,6,1,7,5,8,4]=>1101100
[4,2,6,1,7,5,8,3]=>1110100
[3,1,5,2,7,6,8,4]=>1101010
[2,1,5,3,7,6,8,4]=>1011010
[2,1,6,3,7,5,8,4]=>1011100
[3,1,6,2,7,5,8,4]=>1101100
[4,1,6,2,7,5,8,3]=>1110100
[5,1,6,2,7,4,8,3]=>1111000
[5,2,6,1,7,4,8,3]=>1111000
[5,4,6,2,7,1,8,3]=>1111000
[5,1,6,4,7,2,8,3]=>1111000
[3,1,6,5,7,2,8,4]=>1101100
[3,1,6,5,7,4,8,2]=>1101100
[4,1,6,5,7,3,8,2]=>1110100
[5,1,6,4,7,3,8,2]=>1111000
[8,6,1,3,4,2,5,7]=>1100010
[8,3,5,2,1,6,4,7]=>1111000
[8,6,3,5,2,4,1,7]=>1110010
[8,3,7,5,2,4,6,1]=>1110100
[8,2,4,5,7,3,6,1]=>1110000
[2,4,5,7,3,1,8,6]=>1010010
[8,2,4,6,5,3,1,7]=>1110100
[8,1,2,4,5,6,3,7]=>1010000
[8,2,5,1,3,6,4,7]=>1101000
[8,6,1,4,5,3,2,7]=>1110010
[8,1,5,6,4,3,2,7]=>1111000
[8,5,7,4,3,2,6,1]=>1111100
[8,5,7,4,2,1,6,3]=>1111100
[4,6,3,8,7,1,5,2]=>1110001
[1,7,4,8,6,3,5,2]=>0111010
[8,4,7,6,3,5,2,1]=>1111010
[3,1,5,8,6,7,4,2]=>1101010
[4,8,1,6,7,3,5,2]=>1110000
[3,6,4,1,8,7,5,2]=>1101101
[8,2,6,1,4,7,5,3]=>1110100
[2,7,6,8,1,4,3,5]=>1010010
[1,7,3,5,6,8,2,4]=>0110000
[3,7,6,5,8,2,1,4]=>1100110
[3,6,8,5,7,2,4,1]=>1100100
[2,3,5,7,6,8,1,4]=>1000010
[2,1,6,5,7,8,3,4]=>1010100
[5,2,7,1,3,8,4,6]=>1101000
[5,3,1,7,8,2,4,6]=>1110000
[3,7,2,6,4,8,1,5]=>1101000
[3,2,6,1,4,7,8,5]=>1100100
[5,3,7,2,1,8,4,6]=>1111000
[4,7,3,2,1,5,8,6]=>1110010
[1,7,3,4,2,5,8,6]=>0110010
[4,7,2,1,3,5,8,6]=>1100010
[8,7,6,1,3,4,2,5]=>1100011
[8,5,7,3,2,1,6,4]=>1111100
[3,7,8,6,2,1,5,4]=>1101010
[8,7,6,3,5,2,4,1]=>1110011
[2,7,4,8,1,6,5,3]=>1011100
[4,6,8,2,1,7,5,3]=>1110100
[8,5,3,7,1,6,2,4]=>1110100
[8,5,7,2,1,3,6,4]=>1101100
[4,6,1,8,7,2,5,3]=>1110001
[8,1,2,5,6,7,4,3]=>1011000
[8,2,6,5,7,4,1,3]=>1101100
[2,1,7,8,5,6,4,3]=>1011100
[2,7,6,8,5,4,1,3]=>1001110
[1,7,2,5,8,6,4,3]=>0111010
[3,7,8,1,6,5,2,4]=>1100100
[8,7,6,3,5,1,4,2]=>1110011
[8,4,7,6,5,1,3,2]=>1101110
[8,7,1,5,6,4,3,2]=>1111001
[8,1,6,7,5,4,3,2]=>1111100
[3,2,5,1,6,8,4,7]=>1101000
[3,6,2,5,4,8,1,7]=>1101000
[3,5,2,4,7,1,8,6]=>1100010
[3,5,8,2,4,7,6,1]=>1100010
[4,2,6,5,3,8,1,7]=>1110100
[5,3,1,6,8,2,4,7]=>1110000
[5,6,2,8,1,3,4,7]=>1100000
[5,4,3,2,7,1,8,6]=>1111010
[5,4,3,8,2,7,6,1]=>1111010
[4,3,6,2,8,7,5,1]=>1110101
[4,3,7,6,2,1,8,5]=>1110110
[6,4,3,1,7,2,8,5]=>1111100
[1,4,7,5,8,3,2,6]=>0110100
[7,2,5,8,4,1,3,6]=>1101000
[2,8,5,7,4,6,1,3]=>1001100
[3,5,8,7,1,4,6,2]=>1100001
[4,3,7,1,8,6,5,2]=>1110110
[4,8,3,7,6,5,2,1]=>1110110
[7,5,3,1,8,6,4,2]=>1111110
[1,5,8,6,3,7,4,2]=>0111010
[6,2,8,7,4,5,1,3]=>1101001
[6,1,7,5,3,2,8,4]=>1111100
[5,2,6,3,8,7,4,1]=>1111001
[6,5,2,1,7,3,8,4]=>1111100
[6,1,7,4,2,8,3,5]=>1111000
[6,7,2,1,8,3,4,5]=>1110000
[7,5,8,2,1,3,4,6]=>1100100
[5,7,3,1,8,2,4,6]=>1110000
[4,7,1,5,2,8,3,6]=>1110000
[2,4,8,6,3,7,5,1]=>1010110
[3,8,6,2,4,7,5,1]=>1100110
[3,5,2,7,1,8,4,6]=>1101000
[4,3,7,8,2,1,5,6]=>1110000
[8,3,7,1,4,6,2,5]=>1110000
[3,8,2,5,7,1,6,4]=>1101000
[7,8,3,6,2,1,5,4]=>1111000
[8,7,3,6,2,5,4,1]=>1111001
[4,2,6,8,1,7,5,3]=>1110100
[5,4,8,2,7,1,6,3]=>1111000
[5,8,3,7,1,6,2,4]=>1110000
[5,8,7,2,6,1,3,4]=>1100001
[8,6,2,7,5,1,3,4]=>1100110
[6,4,8,1,7,2,5,3]=>1111000
[5,1,6,8,2,7,4,3]=>1111000
[6,5,2,8,1,7,4,3]=>1111100
[5,2,7,1,8,6,4,3]=>1111010
[5,8,2,7,6,4,3,1]=>1111010
[6,2,8,7,5,4,3,1]=>1111101
[6,1,7,2,8,5,4,3]=>1111100
[4,7,1,8,6,2,5,3]=>1110010
[7,8,3,1,6,5,2,4]=>1110100
[8,7,4,6,1,5,3,2]=>1111001
[8,5,7,1,6,4,3,2]=>1111100
[6,8,1,7,5,4,3,2]=>1111100
[7,1,8,6,5,4,3,2]=>1111110
[4,1,3,2,6,5,8,7]=>1100101
[6,3,5,1,2,4,8,7]=>1010001
[4,3,5,6,1,2,8,7]=>1010001
[8,3,7,5,2,1,4,6]=>1110100
[6,3,7,5,1,8,4,2]=>1111100
[6,5,2,7,1,8,3,4]=>1110100
[3,5,2,6,4,1,8,7]=>1101001
[6,1,2,4,5,3,8,7]=>1010001
[5,6,3,2,1,4,8,7]=>1110001
[2,1,6,3,5,4,8,7]=>1011001
[6,4,3,5,1,2,8,7]=>1011001
[5,3,1,4,6,2,8,7]=>1110001
[5,7,4,6,2,8,3,1]=>1111000
[3,4,7,8,5,2,1,6]=>1100100
[2,1,8,5,7,3,4,6]=>1010100
[8,6,3,5,1,7,4,2]=>1111010
[3,4,8,6,5,7,1,2]=>1000110
[5,1,4,6,8,2,7,3]=>1110000
[2,5,4,6,7,1,8,3]=>1011000
[2,4,6,3,7,5,8,1]=>1010100
[4,1,6,3,8,5,7,2]=>1110100
[3,7,4,2,8,6,5,1]=>1101110
[8,5,3,7,4,1,6,2]=>1111100
[2,1,5,7,4,8,6,3]=>1011010
[3,1,8,2,7,6,5,4]=>1101110
[2,3,8,1,6,7,5,4]=>1001100
[4,3,7,2,6,8,5,1]=>1110100
[2,8,1,3,6,5,7,4]=>1001100
[8,1,2,3,5,6,7,4]=>1001000
[7,8,2,4,3,6,1,5]=>1110000
[6,8,3,2,4,1,7,5]=>1110100
[2,1,8,3,4,6,7,5]=>1010100
[2,1,7,8,5,4,3,6]=>1011100
[5,7,3,8,1,4,2,6]=>1110000
[7,1,8,4,5,3,2,6]=>1111000
[8,7,1,6,3,4,2,5]=>1110001
[5,3,8,7,4,2,6,1]=>1111001
[8,3,6,1,4,2,7,5]=>1110100
[7,3,5,8,2,4,1,6]=>1110000
[2,3,4,1,8,5,7,6]=>1000110
[4,1,3,2,8,5,7,6]=>1100110
[2,1,4,3,8,5,7,6]=>1010110
[4,1,3,2,6,7,8,5]=>1100100
[8,3,5,6,2,7,1,4]=>1110000
[5,3,6,1,8,7,2,4]=>1110001
[5,6,2,8,7,4,1,3]=>1101001
[7,8,5,6,1,4,2,3]=>1100100
[8,1,6,4,5,7,2,3]=>1101000
[5,8,3,6,1,7,2,4]=>1110000
[2,1,8,6,5,7,3,4]=>1010110
[2,1,7,5,3,6,8,4]=>1011100
[7,1,4,2,5,6,8,3]=>1110000
[2,7,4,1,6,5,8,3]=>1011100
[4,1,2,5,8,6,7,3]=>1010010
[7,3,5,4,6,1,8,2]=>1111000
[6,3,4,1,5,7,8,2]=>1110000
[3,1,4,5,6,8,7,2]=>1100001
[4,5,2,6,3,1,8,7]=>1110001
[6,5,2,1,4,3,8,7]=>1110101
[6,5,2,7,4,8,3,1]=>1111100
[8,5,2,7,4,1,6,3]=>1111100
[8,3,7,5,2,1,6,4]=>1111100
[6,3,7,5,2,8,4,1]=>1111100
[6,3,1,5,2,4,8,7]=>1110001
[3,1,6,5,4,2,8,7]=>1101101
[5,4,3,6,1,2,8,7]=>1011001
[5,6,3,2,4,1,8,7]=>1110001
[6,7,2,3,4,8,5,1]=>1100100
[8,7,2,3,4,1,6,5]=>1100101
[5,1,7,3,8,4,6,2]=>1111000
[2,5,7,3,8,6,4,1]=>1011010
[3,6,7,4,1,8,5,2]=>1101100
[5,6,3,7,4,8,1,2]=>1011000
[2,1,6,7,4,8,5,3]=>1011100
[2,1,8,7,4,3,6,5]=>1011101
[5,8,3,7,4,2,6,1]=>1111000
[7,8,1,3,5,2,6,4]=>1101000
[5,8,7,3,2,6,1,4]=>1110001
[2,8,6,3,1,5,7,4]=>1011010
[8,1,6,3,2,5,4,7]=>1111000
[2,8,4,1,6,3,7,5]=>1011100
[4,8,1,2,7,6,3,5]=>1010010
[6,8,3,5,2,7,4,1]=>1111000
[2,1,8,5,3,7,4,6]=>1011100
[6,5,3,2,8,7,1,4]=>1110101
[2,4,1,8,7,6,5,3]=>1010111
[4,1,2,8,7,5,6,3]=>1010101
[8,4,2,1,7,5,3,6]=>1111100
[4,3,1,8,6,7,5,2]=>1110110
[3,1,4,8,6,5,7,2]=>1100110
[7,3,5,4,8,6,1,2]=>1011010
[6,4,3,5,8,1,7,2]=>1111000
[2,1,7,6,5,8,3,4]=>1010110
[5,7,3,6,1,8,2,4]=>1110000
[2,7,6,4,5,8,1,3]=>1001010
[3,7,5,6,8,4,2,1]=>1101100
[5,7,1,6,8,2,4,3]=>1110000
[8,6,2,5,1,7,4,3]=>1111010
[7,5,2,6,3,8,1,4]=>1110100
[4,1,2,3,6,8,7,5]=>1000101
[2,4,3,1,8,5,6,7]=>1010100
[7,5,2,8,3,4,6,1]=>1110100
[4,7,2,8,1,5,3,6]=>1110000
[8,7,2,1,4,5,6,3]=>1110001
[3,6,8,7,1,5,4,2]=>1101001
[5,7,8,6,3,4,1,2]=>1010010
[5,7,3,8,1,4,6,2]=>1110000
[2,1,7,8,5,4,6,3]=>1011100
[7,5,8,4,3,6,2,1]=>1111100
[2,4,8,3,5,6,1,7]=>1010000
[4,1,8,3,6,5,2,7]=>1110100
[8,4,1,3,7,2,6,5]=>1101100
[4,3,8,2,5,1,7,6]=>1110010
[2,1,4,8,3,5,7,6]=>1010010
[6,8,2,4,3,5,1,7]=>1110000
[4,8,2,3,5,1,6,7]=>1100000
[7,8,5,6,1,4,3,2]=>1110100
[7,8,4,2,1,5,3,6]=>1111000
[7,8,2,1,6,5,3,4]=>1110100
[6,4,1,2,5,7,3,8]=>1011000
[4,3,8,1,7,2,5,6]=>1110000
[6,3,1,4,7,2,5,8]=>1110000
[7,8,1,4,6,2,5,3]=>1110000
[7,8,3,5,4,2,1,6]=>1111000
[7,8,4,1,2,3,6,5]=>1001100
[7,8,3,6,5,4,1,2]=>1011100
[7,8,2,6,4,1,3,5]=>1101000
[7,8,1,6,5,4,3,2]=>1111100
[2,1,8,7,5,4,3,6]=>1011101
[1,3,8,2,6,4,7,5]=>0101100
[5,3,7,1,6,4,8,2]=>1111000
[6,1,2,5,8,7,4,3]=>1011001
[6,3,1,8,4,2,7,5]=>1111100
[6,4,2,1,5,3,8,7]=>1111001
[6,4,3,7,5,8,1,2]=>1011100
[4,3,8,7,5,6,1,2]=>1010101
[2,4,7,1,5,3,6,8]=>1010000
[3,7,2,8,6,4,1,5]=>1101010
[3,8,1,7,6,4,5,2]=>1101010
[1,8,5,7,3,6,4,2]=>0111100
[2,7,5,8,3,6,1,4]=>1010100
[1,5,6,8,2,4,7,3]=>0110000
[2,6,1,4,7,3,5,8]=>1010000
[3,6,8,4,7,5,1,2]=>1001100
[5,6,7,3,8,4,1,2]=>1011000
[4,5,6,7,2,8,1,3]=>1100000
[4,5,7,6,1,8,3,2]=>1110010
[1,5,8,6,2,7,3,4]=>0110010
[4,7,5,6,3,1,8,2]=>1110100
[5,1,6,3,4,2,8,7]=>1110001
[5,7,1,4,2,3,8,6]=>1100010
[5,7,6,4,3,8,1,2]=>1011010
[6,3,4,5,8,7,1,2]=>1010001
[6,2,4,1,8,3,7,5]=>1110100
[6,2,3,5,4,8,1,7]=>1101000
[5,1,4,2,7,6,8,3]=>1110010
[1,6,2,4,7,8,3,5]=>0110000
[5,7,2,4,1,6,3,8]=>1110000
[6,1,4,2,8,5,3,7]=>1110100
[6,7,5,8,1,4,3,2]=>1110100
[5,8,7,6,3,4,1,2]=>1010011
[5,8,7,6,2,3,1,4]=>1100011
[4,1,7,2,6,5,3,8]=>1110100
[4,8,2,1,5,6,3,7]=>1110000
[4,2,7,8,1,6,3,5]=>1110000
[2,1,8,7,6,5,3,4]=>1010111
[4,2,7,1,6,3,8,5]=>1110100
[4,3,7,5,6,8,1,2]=>1010100
[3,8,6,5,2,4,1,7]=>1100110
[3,8,5,6,1,4,7,2]=>1100100
[5,3,7,8,2,1,6,4]=>1111000
[5,2,8,7,1,6,4,3]=>1111001
[3,6,7,8,5,1,4,2]=>1100100
[3,7,8,5,1,2,4,6]=>1000100
[4,1,8,6,2,3,5,7]=>1100010
[4,7,8,6,3,5,1,2]=>1010010
[3,8,7,6,5,4,1,2]=>1001111
[2,8,6,7,5,1,3,4]=>1000110
[5,3,7,8,2,1,4,6]=>1110000
[7,6,1,2,5,8,3,4]=>1010010
[2,1,7,8,4,3,5,6]=>1011000
[7,8,1,2,5,4,6,3]=>1011000
[2,6,8,3,1,4,7,5]=>1010100
[8,4,1,3,7,6,2,5]=>1101010
[6,5,2,1,8,7,4,3]=>1111101
[4,7,2,8,1,3,6,5]=>1100100
[7,3,8,6,1,2,5,4]=>1011010
[3,4,7,1,8,2,6,5]=>1100100
[1,8,2,4,3,5,6,7]=>0110000
[1,7,2,4,3,5,6,8]=>0110000
[1,5,2,4,3,6,7,8]=>0110000
[1,7,2,5,3,4,6,8]=>0110000
[1,8,2,5,3,4,6,7]=>0110000
[1,8,2,6,3,4,5,7]=>0110000
[1,8,2,7,3,4,5,6]=>0110000
[1,8,2,7,3,5,4,6]=>0111000
[1,7,2,8,3,5,4,6]=>0111000
[1,6,2,8,3,5,4,7]=>0111000
[1,5,2,8,3,6,4,7]=>0111000
[1,4,2,8,3,6,5,7]=>0110100
[1,3,2,8,4,6,5,7]=>0101100
[1,2,3,8,4,6,5,7]=>0001100
[1,2,3,7,4,6,5,8]=>0001100
[1,3,2,7,4,6,5,8]=>0101100
[1,4,2,7,3,6,5,8]=>0110100
[1,5,2,7,3,6,4,8]=>0111000
[1,6,2,7,3,5,4,8]=>0111000
[1,7,2,6,3,5,4,8]=>0111000
[1,8,2,6,3,5,4,7]=>0111000
[1,8,2,5,3,6,4,7]=>0111000
[1,7,2,5,3,6,4,8]=>0111000
[1,6,2,5,3,7,4,8]=>0111000
[1,5,2,4,3,7,6,8]=>0110010
[1,6,2,4,3,7,5,8]=>0110100
[1,7,2,4,3,6,5,8]=>0110100
[1,8,2,4,3,6,5,7]=>0110100
[1,8,2,4,3,7,5,6]=>0110100
[1,7,2,4,3,8,5,6]=>0110100
[1,6,2,4,3,8,5,7]=>0110100
[1,5,2,4,3,8,6,7]=>0110010
[1,6,2,5,3,8,4,7]=>0111000
[1,7,2,5,3,8,4,6]=>0111000
[1,8,2,5,3,7,4,6]=>0111000
[1,8,2,6,3,7,4,5]=>0111000
[1,7,2,6,3,8,4,5]=>0111000
[1,2,3,8,4,7,5,6]=>0001100
[1,3,2,8,4,7,5,6]=>0101100
[1,4,2,8,3,7,5,6]=>0110100
[1,5,2,8,3,7,4,6]=>0111000
[1,6,2,8,3,7,4,5]=>0111000
[1,7,2,8,3,6,4,5]=>0111000
[1,8,2,7,3,6,4,5]=>0111000
[2,8,4,1,6,5,3,7]=>1011100
[2,8,4,1,5,6,7,3]=>1011000
[2,8,7,4,1,6,3,5]=>1011001
[7,2,8,5,1,6,4,3]=>1111100
[1,3,7,5,2,6,4,8]=>0101100
[1,3,7,5,4,2,6,8]=>0101100
[7,2,8,5,4,1,6,3]=>1111100
[2,8,5,3,4,1,6,7]=>1010100
[2,8,7,6,1,4,5,3]=>1010011
[2,8,6,5,7,3,1,4]=>1010110
[7,2,8,4,5,6,1,3]=>1101000
[6,2,3,8,5,1,7,4]=>1101100
[6,3,2,8,5,1,4,7]=>1110100
[7,4,8,5,2,1,3,6]=>1101100
[6,4,8,5,1,3,7,2]=>1101100
[4,3,7,5,1,2,8,6]=>1010110
[4,3,7,1,5,6,8,2]=>1110000
[3,6,1,7,5,2,8,4]=>1101100
[3,4,1,2,7,6,8,5]=>1000110
[6,5,2,7,4,1,8,3]=>1111100
[3,5,2,6,4,8,7,1]=>1101001
[6,3,5,8,2,7,4,1]=>1111000
[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]=>1111000
[6,1,2,8,4,5,7,3]=>1011000
[5,6,8,2,3,1,7,4]=>1101000
[6,5,8,2,4,3,1,7]=>1110100
[6,5,8,4,2,3,7,1]=>1101100
[7,5,3,8,2,4,1,6]=>1110100
[1,6,5,7,3,4,2,8]=>0110100
[5,2,1,8,7,6,3,4]=>1110011
[7,1,3,8,4,6,2,5]=>1101000
[5,7,8,4,3,6,2,1]=>1111000
[4,1,8,3,5,6,7,2]=>1110000
[4,1,8,3,6,2,7,5]=>1110100
[2,3,4,8,6,1,7,5]=>1000110
[2,3,4,8,6,5,1,7]=>1000110
[2,7,3,5,8,6,1,4]=>1010010
[3,2,4,7,8,6,1,5]=>1100010
[1,5,4,6,2,7,3,8]=>0111000
[5,2,4,7,1,8,3,6]=>1110000
[5,3,6,4,1,8,7,2]=>1111001
[5,3,6,1,4,8,2,7]=>1110000
[7,3,5,6,8,4,2,1]=>1111000
[6,3,5,1,8,2,7,4]=>1111000
[5,7,1,6,3,8,4,2]=>1111000
[3,2,4,1,7,8,5,6]=>1100100
[2,5,4,6,1,7,8,3]=>1011000
[7,2,1,4,3,6,5,8]=>1110100
[7,3,4,1,2,6,5,8]=>1010100
[7,4,3,2,1,6,5,8]=>1111100
[6,7,3,2,5,4,8,1]=>1111000
[1,8,3,2,5,4,7,6]=>0111010
[1,8,4,5,2,3,7,6]=>0101010
[7,3,5,1,6,2,4,8]=>1110000
[7,2,1,5,6,3,4,8]=>1110000
[1,8,5,4,3,2,7,6]=>0111110
[6,4,7,5,1,3,8,2]=>1101100
[3,2,1,8,5,4,7,6]=>1101110
[2,3,8,1,5,4,7,6]=>1001010
[2,4,8,5,1,3,7,6]=>1000110
[2,6,8,4,3,7,1,5]=>1011000
[2,7,8,4,3,6,5,1]=>1011100
[1,8,7,5,6,3,4,2]=>0110101
[2,7,8,5,6,3,4,1]=>1010100
[2,5,8,6,7,1,3,4]=>1000010
[2,4,8,6,1,7,3,5]=>1010010
[3,2,1,8,6,7,4,5]=>1101010
[5,2,1,7,6,8,4,3]=>1111010
[5,3,7,1,6,8,4,2]=>1111000
[5,4,7,6,1,8,3,2]=>1111010
[4,5,7,6,8,1,3,2]=>1100010
[4,6,7,5,8,3,1,2]=>1010100
[1,8,5,6,7,2,3,4]=>0100100
[4,6,5,7,8,2,1,3]=>1100100
[5,4,6,7,1,8,2,3]=>1101000
[5,3,6,1,7,8,2,4]=>1110000
[5,2,1,6,7,8,3,4]=>1110000
[6,2,1,5,7,3,8,4]=>1111000
[6,3,5,1,7,2,8,4]=>1111000
[6,4,5,7,1,2,8,3]=>1011000
[5,6,4,7,2,8,1,3]=>1101000
[1,8,4,6,2,7,3,5]=>0111000
[1,8,3,2,6,7,4,5]=>0111000
[5,7,3,2,6,8,4,1]=>1111000
[6,5,3,2,7,1,8,4]=>1111100
[6,4,3,2,1,7,8,5]=>1111100
[6,2,1,4,3,7,8,5]=>1110100
[5,2,1,4,3,8,7,6]=>1110011
[5,3,4,1,2,8,7,6]=>1010011
[4,5,3,2,8,1,7,6]=>1110010
[4,6,3,2,8,7,1,5]=>1110001
[4,7,3,2,8,6,5,1]=>1110110
[1,8,3,2,7,6,5,4]=>0111110
[1,8,4,7,2,6,5,3]=>0111100
[3,6,4,8,2,7,1,5]=>1101000
[3,4,5,8,1,2,7,6]=>1000010
[4,3,5,1,8,2,7,6]=>1110010
[4,2,1,5,8,3,7,6]=>1110010
[4,2,1,6,8,7,3,5]=>1110001
[3,4,6,8,1,7,2,5]=>1100000
[3,5,6,8,7,1,2,4]=>1000001
[3,6,5,8,7,2,1,4]=>1100101
[3,6,7,8,5,4,1,2]=>1001100
[3,5,7,8,6,1,4,2]=>1100010
[4,2,1,7,8,6,5,3]=>1110110
[2,3,8,1,7,6,5,4]=>1001110
[2,4,8,7,1,6,5,3]=>1010101
[8,1,6,7,3,2,5,4]=>1111000
[8,1,6,7,2,3,4,5]=>1100000
[8,1,2,4,3,6,5,7]=>1010100
[8,1,4,3,2,7,6,5]=>1110110
[8,1,5,3,7,2,6,4]=>1111000
[8,1,3,5,6,2,7,4]=>1101000
[4,7,8,5,6,1,2,3]=>1000100
[3,7,8,5,6,2,1,4]=>1100100
[3,7,8,4,2,6,1,5]=>1101000
[3,7,8,2,4,5,1,6]=>1100000
[3,6,2,8,4,5,1,7]=>1101000
[2,3,6,7,4,5,8,1]=>1001000
[3,5,2,4,8,6,1,7]=>1100010
[3,5,4,2,8,7,1,6]=>1101001
[4,6,5,8,7,1,2,3]=>1000101
[6,4,5,1,7,8,2,3]=>1101000
[5,4,2,3,1,8,6,7]=>1101010
[6,5,3,1,8,2,7,4]=>1111100
[6,5,4,1,8,7,2,3]=>1101101
[7,5,1,4,8,6,2,3]=>1100110
[7,4,1,3,2,8,6,5]=>1101110
[7,4,1,2,3,8,5,6]=>1001100
[6,4,2,1,3,8,5,7]=>1101100
[2,6,4,8,3,7,5,1]=>1011100
[2,6,5,8,7,3,4,1]=>1010101
[6,5,2,1,8,3,4,7]=>1110100
[7,5,1,2,8,3,4,6]=>1010100
[7,6,1,8,2,3,4,5]=>1100010
[7,6,1,8,4,5,2,3]=>1101010
[6,7,8,1,4,5,2,3]=>1100000
[6,7,8,1,3,2,5,4]=>1101000
[2,5,6,7,8,3,4,1]=>1010000
[2,4,6,7,3,8,5,1]=>1010100
[4,2,6,7,3,1,5,8]=>1110000
[4,7,8,2,3,1,5,6]=>1100000
[4,7,8,3,2,1,6,5]=>1110100
[5,7,8,3,1,2,6,4]=>1011000
[5,7,8,4,1,6,2,3]=>1101000
[5,6,4,8,1,7,2,3]=>1101000
[4,6,3,8,2,1,7,5]=>1110100
[4,2,5,3,7,1,6,8]=>1110000
[5,3,6,7,1,2,8,4]=>1011000
[3,5,6,7,8,2,1,4]=>1100000
[3,4,6,7,2,8,1,5]=>1100000
[7,4,6,1,8,3,5,2]=>1111000
[7,3,5,1,8,4,6,2]=>1111000
[7,3,4,1,8,5,6,2]=>1110100
[4,5,7,3,1,8,6,2]=>1110010
[4,5,6,2,1,8,7,3]=>1110001
[1,6,5,2,7,4,3,8]=>0111100
[7,4,3,1,8,6,5,2]=>1111110
[3,6,7,5,1,8,4,2]=>1101100
[7,5,6,1,8,3,4,2]=>1110100
[7,6,5,1,8,4,3,2]=>1111110
[7,6,4,1,8,5,3,2]=>1111110
[6,4,2,1,8,7,5,3]=>1111101
[1,5,3,2,7,6,4,8]=>0111010
[2,6,5,1,7,8,4,3]=>1011100
[4,5,7,1,6,8,2,3]=>1100000
[4,5,7,1,3,8,2,6]=>1100000
[6,4,1,2,8,5,3,7]=>1011100
[5,3,1,2,8,6,4,7]=>1011010
[4,3,1,2,8,6,5,7]=>1010110
[6,1,2,5,8,3,4,7]=>1010000
[7,1,3,4,8,2,5,6]=>1100000
[2,6,1,5,7,8,3,4]=>1010000
[7,6,1,5,8,3,2,4]=>1110010
[3,6,7,1,5,8,2,4]=>1100000
[7,1,6,5,8,2,4,3]=>1110100
[7,5,1,6,8,4,2,3]=>1101100
[7,4,1,6,8,5,2,3]=>1101100
[7,3,1,5,8,6,2,4]=>1110010
[6,2,5,1,8,4,7,3]=>1111000
[7,1,6,4,8,2,5,3]=>1111000
[7,1,5,3,8,2,6,4]=>1111000
[6,1,5,2,8,3,7,4]=>1111000
[7,3,1,4,8,6,2,5]=>1110010
[6,2,1,4,8,7,3,5]=>1110001
[5,2,1,3,8,7,4,6]=>1101001
[7,4,1,3,8,5,2,6]=>1101100
[6,1,4,2,8,3,7,5]=>1110100
[7,1,4,3,8,2,6,5]=>1110100
[3,6,7,1,4,8,2,5]=>1100000
[7,6,1,4,8,3,2,5]=>1110010
[5,1,3,2,8,4,7,6]=>1101010
[4,2,1,3,8,7,5,6]=>1100101
[2,6,1,4,7,8,3,5]=>1010000
[7,1,3,5,8,2,4,6]=>1100000
[7,8,5,6,1,3,4,2]=>1100100
[7,8,1,3,6,2,5,4]=>1101000
[1,3,8,4,7,2,5,6]=>0101000
[4,6,1,2,5,7,3,8]=>1010000
[1,4,8,2,5,7,3,6]=>0110000
[7,8,4,2,5,1,3,6]=>1101000
[7,8,1,5,4,6,3,2]=>1111000
[7,8,2,1,6,3,4,5]=>1110000
[7,8,3,5,6,4,1,2]=>1011000
[7,8,4,5,3,1,6,2]=>1111000
[2,6,4,8,3,7,1,5]=>1011000
[1,4,6,8,3,7,5,2]=>0110100
[2,5,8,1,4,7,6,3]=>1010010
[2,1,8,4,7,3,6,5]=>1011100
[3,5,8,4,7,6,1,2]=>1001010
[1,6,2,4,7,3,8,5]=>0110100
[5,6,2,1,4,7,8,3]=>1110000
[4,6,2,5,3,1,8,7]=>1110001
[4,7,5,1,3,6,8,2]=>1100100
[7,5,3,6,2,4,1,8]=>1110100
[5,7,3,6,1,4,8,2]=>1110000
[5,3,6,7,2,1,8,4]=>1111000
[6,3,1,2,4,5,8,7]=>1010001
[1,4,7,2,5,3,8,6]=>0110010
[6,4,7,3,5,8,1,2]=>1011000
[3,5,6,7,8,1,4,2]=>1100000
[3,6,5,7,8,2,1,4]=>1100100
[5,2,7,6,1,4,3,8]=>1110010
[2,7,5,6,8,4,1,3]=>1001100
[2,1,6,8,4,5,3,7]=>1011000
[2,7,1,8,5,3,4,6]=>1010100
[3,7,6,8,5,4,1,2]=>1001110
[4,3,8,5,6,7,1,2]=>1010100
[4,2,8,1,6,3,7,5]=>1110100
[3,1,8,5,4,6,7,2]=>1101100
[3,4,2,8,6,1,7,5]=>1100110
[1,7,3,8,5,2,6,4]=>0111100
[4,1,8,3,6,2,5,7]=>1110000
[5,7,8,6,3,2,1,4]=>1110010
[5,7,8,6,1,3,4,2]=>1100010
[7,6,5,8,1,3,4,2]=>1100110
[1,6,4,3,8,2,5,7]=>0111000
[2,6,3,4,5,8,1,7]=>1010000
[2,6,4,1,8,3,7,5]=>1011100
[3,6,4,5,8,7,1,2]=>1001001
[7,2,1,4,8,3,5,6]=>1110000
[7,1,6,5,3,8,4,2]=>1111100
[7,2,5,6,3,8,1,4]=>1110000
[5,6,2,7,3,1,4,8]=>1110000
[5,7,6,4,1,8,3,2]=>1111010
[6,7,1,5,2,8,3,4]=>1110000
[6,1,5,2,8,3,4,7]=>1110000
[7,5,2,4,3,1,6,8]=>1110100
[6,8,1,3,7,5,4,2]=>1101100
[7,4,2,6,5,1,3,8]=>1101100
[7,4,6,3,1,5,2,8]=>1111000
[7,2,3,5,4,1,6,8]=>1101000
[6,8,1,2,3,4,7,5]=>1000100
[2,5,1,7,8,3,6,4]=>1011000
[2,5,3,6,8,4,7,1]=>1011000
[2,1,4,7,8,5,6,3]=>1010100
[2,5,7,8,1,4,6,3]=>1010000
[3,5,7,4,1,6,2,8]=>1101000
[5,2,8,4,6,1,7,3]=>1111000
[5,2,1,8,6,3,7,4]=>1111010
[4,2,8,5,7,6,3,1]=>1110110
[4,1,2,8,5,6,7,3]=>1010100
[1,4,2,7,5,8,6,3]=>0110110
[4,1,8,6,7,5,3,2]=>1110110
[5,3,8,7,6,2,4,1]=>1110011
[5,8,4,7,6,2,1,3]=>1101010
[5,8,7,4,3,6,1,2]=>1011001
[6,4,8,3,1,7,2,5]=>1111000
[6,4,2,8,7,1,3,5]=>1101001
[6,3,8,7,2,5,1,4]=>1110001
[6,3,1,8,7,2,4,5]=>1110001
[5,8,3,7,1,6,4,2]=>1111000
[5,8,7,4,1,6,2,3]=>1101001
[6,8,5,2,4,3,7,1]=>1110100
[6,8,5,3,1,2,7,4]=>1011100
[4,5,1,2,7,6,3,8]=>1010010
[4,5,1,2,6,8,7,3]=>1010001
[3,5,6,1,8,4,7,2]=>1101000
[3,5,7,1,2,8,6,4]=>1001010
[4,2,6,1,7,3,5,8]=>1110000
[4,6,3,1,2,7,5,8]=>1010100
[3,5,2,7,8,1,6,4]=>1101000
[3,1,4,7,5,6,2,8]=>1100100
[3,1,4,5,8,6,7,2]=>1100010
[3,4,6,8,5,2,7,1]=>1100100
[4,2,5,6,1,8,7,3]=>1110001
[2,1,7,5,8,6,4,3]=>1011110
[1,2,7,5,3,8,6,4]=>0011110
[4,1,2,7,3,8,6,5]=>1010110
[7,1,4,2,5,3,8,6]=>1110010
[6,1,3,7,5,2,4,8]=>1100100
[3,1,2,6,8,5,4,7]=>1001100
[3,7,1,2,5,4,8,6]=>1001010
[1,3,7,2,4,8,6,5]=>0100110
[3,2,7,8,1,6,5,4]=>1101100
[2,4,1,7,8,6,5,3]=>1010110
[2,6,8,3,1,5,7,4]=>1011000
[3,6,4,8,5,1,7,2]=>1101100
[6,3,7,4,5,1,8,2]=>1111000
[6,4,7,5,2,8,1,3]=>1101100
[2,6,3,7,5,8,1,4]=>1010100
[5,2,1,7,8,3,4,6]=>1110000
[5,7,4,6,2,8,1,3]=>1101000
[5,7,3,4,6,1,8,2]=>1110000
[4,2,8,3,6,7,1,5]=>1110000
[4,8,3,1,7,2,5,6]=>1110000
[5,2,8,4,7,1,6,3]=>1111000
[5,8,4,7,3,1,6,2]=>1111000
[4,6,8,3,1,7,5,2]=>1110100
[6,3,8,2,7,1,5,4]=>1111000
[6,3,1,8,2,4,7,5]=>1110100
[3,5,1,8,2,7,4,6]=>1101000
[7,5,1,3,6,2,4,8]=>1100100
[8,5,4,1,2,6,3,7]=>1011100
[5,1,8,4,2,7,3,6]=>1111000
[4,1,6,2,8,3,7,5]=>1110100
[1,6,2,8,5,3,7,4]=>0111100
[6,8,5,3,1,7,4,2]=>1111100
[5,6,7,3,1,8,4,2]=>1111000
[5,6,2,1,7,8,4,3]=>1111000
[8,4,5,1,2,6,3,7]=>1011000
[5,6,3,7,1,2,4,8]=>1010000
[1,6,3,7,2,8,4,5]=>0111000
[6,3,2,7,8,5,1,4]=>1110100
[6,4,7,2,8,1,5,3]=>1111000
[6,7,4,8,3,1,5,2]=>1111000
[4,5,7,8,3,1,6,2]=>1110000
[4,7,2,5,8,1,6,3]=>1110000
[5,7,3,8,2,6,1,4]=>1110000
[3,4,7,8,2,6,1,5]=>1100000
[8,1,3,4,6,2,5,7]=>1100000
[3,8,2,4,6,7,1,5]=>1100000
[2,4,5,6,8,1,7,3]=>1010000
[4,8,3,5,6,1,7,2]=>1110000
[8,4,3,6,5,1,7,2]=>1111100
[8,6,5,4,3,1,7,2]=>1111110
[1,8,6,5,2,7,3,4]=>0110110
[8,7,5,4,1,6,3,2]=>1111101
[7,8,5,4,1,3,6,2]=>1101100
[6,8,5,4,2,1,7,3]=>1111100
[5,8,6,2,4,1,7,3]=>1110010
[3,2,8,6,5,1,7,4]=>1101110
[5,1,7,3,6,2,4,8]=>1110000
[8,1,6,5,2,3,7,4]=>1101100
[1,2,8,3,7,4,5,6]=>0011000
[8,1,7,2,6,3,5,4]=>1111000
[7,1,8,2,6,4,3,5]=>1111000
[5,1,8,3,2,7,4,6]=>1111000
[3,2,1,8,4,7,5,6]=>1101100
[3,2,8,7,1,6,5,4]=>1101101
[4,8,2,7,1,6,5,3]=>1110100
[5,8,7,2,1,6,4,3]=>1111001
[8,7,6,1,5,4,3,2]=>1111011
[8,6,7,1,4,5,3,2]=>1110010
[7,6,8,1,4,3,5,2]=>1110010
[6,7,8,1,3,4,5,2]=>1100000
[5,7,8,2,1,4,6,3]=>1110000
[4,7,2,8,1,5,6,3]=>1110000
[3,2,7,8,1,5,6,4]=>1101000
[3,2,6,8,4,1,7,5]=>1101100
[4,6,2,8,3,1,7,5]=>1110100
[6,5,8,3,2,1,7,4]=>1111100
[7,5,8,3,1,4,6,2]=>1110100
[8,4,3,7,1,6,5,2]=>1111100
[6,4,3,8,2,1,7,5]=>1111100
[5,4,3,2,8,1,7,6]=>1111010
[4,5,2,3,8,1,7,6]=>1100010
[3,2,5,4,8,1,7,6]=>1101010
[6,4,3,1,5,2,7,8]=>1111000
[7,4,3,1,2,6,5,8]=>1011100
[1,5,4,2,3,6,7,8]=>0101000
[8,5,1,4,2,3,7,6]=>1100110
[7,5,1,4,2,6,3,8]=>1110100
[4,6,2,1,5,3,7,8]=>1110000
[3,2,6,1,5,4,7,8]=>1101000
[5,7,1,3,2,6,4,8]=>1101000
[6,7,1,2,4,5,3,8]=>1010000
[7,6,1,2,5,4,3,8]=>1011010
[8,6,1,2,5,3,7,4]=>1011010
[7,8,1,2,3,5,6,4]=>1001000
[6,8,1,2,4,3,7,5]=>1010100
[4,8,2,1,3,5,7,6]=>1100010
[3,2,8,1,4,5,7,6]=>1100010
[4,1,3,2,5,6,7,8]=>1100000
[5,1,2,4,3,6,7,8]=>1010000
[5,8,7,3,4,1,2,6]=>1010001
[6,7,3,8,5,1,2,4]=>1010100
[6,7,4,5,1,8,3,2]=>1111000
[5,4,7,6,2,3,8,1]=>1101010
[5,4,7,6,8,1,2,3]=>1001010
[5,3,7,8,6,1,2,4]=>1010010
[4,3,8,7,6,1,2,5]=>1010011
[4,8,3,7,5,1,2,6]=>1010100
[4,5,6,7,1,8,3,2]=>1110000
[3,5,6,2,7,4,8,1]=>1101000
[3,5,6,1,7,8,4,2]=>1101000
[2,5,6,8,1,7,3,4]=>1010000
[8,2,4,5,1,6,3,7]=>1110000
[1,4,8,6,2,3,7,5]=>0100110
[1,5,6,8,2,3,7,4]=>0101000
[1,5,6,2,8,4,7,3]=>0111000
[1,4,2,6,8,5,7,3]=>0110100
[8,1,3,2,5,4,6,7]=>1101000
[2,4,1,6,8,7,5,3]=>1010101
[4,3,1,7,6,8,5,2]=>1110110
[3,8,2,1,7,5,4,6]=>1101100
[8,3,2,1,6,5,4,7]=>1111100
[8,4,2,6,1,5,3,7]=>1111000
[4,2,8,7,1,6,3,5]=>1110001
[5,2,7,8,1,6,3,4]=>1110000
[5,3,7,2,6,4,8,1]=>1111000
[6,7,3,1,5,8,4,2]=>1111000
[6,7,2,1,8,5,4,3]=>1111100
[6,7,2,8,1,5,3,4]=>1110000
[6,7,8,2,1,4,3,5]=>1110000
[8,5,6,2,1,4,3,7]=>1110100
[5,8,7,1,2,3,4,6]=>1000001
[6,7,1,2,8,4,5,3]=>1011000
[6,7,1,3,4,8,5,2]=>1100100
[5,1,7,3,4,8,6,2]=>1110010
[5,1,7,8,2,3,6,4]=>1101000
[4,8,1,7,2,3,5,6]=>1100000
[3,8,1,2,7,4,5,6]=>1001000
[3,1,8,2,7,4,6,5]=>1101100
[3,1,2,8,7,5,6,4]=>1001101
[4,1,3,7,5,8,6,2]=>1100110
[2,1,8,3,4,7,6,5]=>1010110
[1,8,2,3,4,5,7,6]=>0100010
[1,2,8,3,4,6,7,5]=>0010100
[6,3,8,5,2,7,4,1]=>1111100
[6,5,2,8,4,7,3,1]=>1111100
[6,3,4,5,8,7,2,1]=>1110001
[5,8,1,4,7,2,3,6]=>1100000
[3,6,4,8,5,7,1,2]=>1001100
[5,1,4,8,6,3,7,2]=>1110010
[3,4,7,1,8,6,5,2]=>1100110
[6,3,8,4,2,7,1,5]=>1111000
[3,6,8,7,1,4,2,5]=>1100001
[5,3,7,1,6,8,2,4]=>1110000
[4,6,1,2,7,8,5,3]=>1010100
[3,6,4,2,8,7,5,1]=>1101101
[6,3,7,5,2,8,1,4]=>1110100
[6,5,2,7,4,8,1,3]=>1101100
[5,8,1,4,6,7,2,3]=>1100000
[6,3,7,4,2,8,5,1]=>1111100
[8,7,1,6,2,4,5,3]=>1110001
[5,6,1,8,7,3,2,4]=>1110001
[3,6,4,5,7,2,8,1]=>1101000
[5,4,2,7,3,6,8,1]=>1111000
[6,4,1,5,3,8,2,7]=>1111000
[8,2,6,3,4,7,5,1]=>1110100
[3,6,2,7,4,5,8,1]=>1101000
[4,2,5,7,3,6,8,1]=>1110000
[1,6,5,3,4,8,2,7]=>0110100
[6,8,3,1,7,2,5,4]=>1111000
[1,8,6,3,7,5,2,4]=>0110110
[8,7,5,2,6,4,3,1]=>1111101
[8,7,1,6,2,5,4,3]=>1111001
[7,8,1,6,3,2,5,4]=>1111000
[2,8,1,7,3,5,6,4]=>1011000
[4,8,1,3,7,2,6,5]=>1100100
[4,2,8,5,7,3,6,1]=>1110100
[6,7,3,1,8,4,2,5]=>1111000
[1,7,3,8,4,5,2,6]=>0111000
[1,7,2,8,5,3,4,6]=>0110100
[7,6,1,8,4,3,2,5]=>1111010
[7,1,2,8,3,5,4,6]=>1011000
[4,2,5,7,1,8,3,6]=>1110000
[3,6,2,7,1,8,4,5]=>1101000
[6,3,7,2,1,8,4,5]=>1111000
[8,2,6,1,7,3,5,4]=>1111000
[4,2,1,5,8,3,6,7]=>1110000
[5,4,2,7,1,8,3,6]=>1111000
[5,4,3,1,6,8,2,7]=>1111000
[1,5,3,4,6,8,2,7]=>0110000
[4,3,5,1,6,8,2,7]=>1110000
[4,7,5,6,8,3,2,1]=>1110100
[6,5,4,8,2,7,3,1]=>1111100
[6,5,1,8,7,4,2,3]=>1101101
[8,6,4,7,5,3,2,1]=>1111110
[5,1,8,3,7,6,2,4]=>1110010
[5,4,8,1,7,2,6,3]=>1111000
[5,7,3,8,2,6,4,1]=>1111000
[5,4,6,8,2,7,3,1]=>1111000
[3,6,8,1,7,2,5,4]=>1101000
[2,3,8,7,4,5,6,1]=>1001001
[7,2,8,6,4,3,5,1]=>1111010
[2,1,8,7,5,6,3,4]=>1010101
[7,1,8,6,5,3,2,4]=>1110110
[1,3,8,7,4,6,2,5]=>0101001
[4,7,1,8,6,5,2,3]=>1100110
[6,8,7,2,5,4,3,1]=>1111001
[6,7,4,8,3,5,1,2]=>1011000
[6,7,4,5,2,8,1,3]=>1101000
[5,7,4,6,2,3,1,8]=>1101000
[5,7,4,6,3,8,1,2]=>1011000
[5,7,4,8,3,6,1,2]=>1011000
[6,8,4,5,3,7,1,2]=>1011000
[5,8,4,6,3,7,1,2]=>1011000
[5,6,4,8,3,7,1,2]=>1011000
[5,6,3,7,2,8,1,4]=>1110000
[5,6,4,8,2,7,1,3]=>1101000
[5,8,4,6,2,7,1,3]=>1101000
[6,8,4,5,2,7,1,3]=>1101000
[7,8,4,5,2,6,1,3]=>1101000
[6,8,4,5,2,3,1,7]=>1101000
[5,8,4,6,2,3,1,7]=>1101000
[5,6,3,4,2,8,1,7]=>1110000
[4,6,3,5,2,8,1,7]=>1110000
[4,8,3,6,2,5,1,7]=>1110000
[5,8,3,6,2,4,1,7]=>1110000
[6,8,3,5,2,4,1,7]=>1110000
[7,8,3,5,2,4,1,6]=>1110000
[7,8,3,5,2,6,1,4]=>1110000
[6,8,3,5,2,7,1,4]=>1110000
[5,8,3,6,2,7,1,4]=>1110000
[4,8,3,6,2,7,1,5]=>1110000
[4,6,3,7,2,8,1,5]=>1110000
[4,6,3,7,2,5,1,8]=>1110000
[4,7,3,6,2,5,1,8]=>1110000
[4,7,3,6,2,8,1,5]=>1110000
[4,7,3,8,2,6,1,5]=>1110000
[5,7,4,8,2,6,1,3]=>1101000
[5,7,3,6,2,8,1,4]=>1110000
[5,7,3,6,2,4,1,8]=>1110000
[6,7,3,5,2,4,1,8]=>1110000
[6,7,3,5,2,8,1,4]=>1110000
[6,7,3,8,2,5,1,4]=>1110000
[6,7,4,8,2,5,1,3]=>1101000
[6,7,5,8,2,4,1,3]=>1100100
[6,8,5,7,2,3,1,4]=>1100100
[6,7,4,8,2,3,1,5]=>1101000
[6,7,3,8,2,4,1,5]=>1110000
[5,7,3,8,2,4,1,6]=>1110000
[5,7,4,8,2,3,1,6]=>1101000
[5,8,4,7,2,3,1,6]=>1101000
[6,8,4,7,2,3,1,5]=>1101000
[7,8,4,6,2,3,1,5]=>1101000
[7,8,3,6,2,4,1,5]=>1110000
[6,8,3,7,2,4,1,5]=>1110000
[5,8,3,7,2,4,1,6]=>1110000
[4,8,3,7,2,5,1,6]=>1110000
[4,7,3,8,2,5,1,6]=>1110000
[4,5,3,7,2,6,1,8]=>1110000
[5,8,3,4,2,6,1,7]=>1110000
[4,5,3,6,2,8,1,7]=>1110000
[4,7,5,2,1,8,3,6]=>1110100
[4,6,5,2,1,3,8,7]=>1100101
[5,6,4,2,3,1,8,7]=>1101001
[6,4,5,3,1,2,8,7]=>1011001
[5,4,6,1,3,2,8,7]=>1101001
[4,7,8,1,6,3,5,2]=>1110000
[7,4,8,1,6,5,3,2]=>1111100
[7,4,5,3,1,8,2,6]=>1111000
[6,4,8,1,7,5,2,3]=>1101100
[6,4,7,1,8,2,5,3]=>1111000
[8,5,7,6,4,2,1,3]=>1101110
[2,1,6,8,7,4,3,5]=>1011001
[2,1,7,8,6,4,5,3]=>1011010
[8,4,7,3,6,2,5,1]=>1111000
[7,6,8,5,2,4,3,1]=>1110110
[5,7,8,6,2,3,1,4]=>1100010
[5,8,7,6,3,2,1,4]=>1110011
[6,8,7,5,3,2,4,1]=>1110101
[7,8,4,2,6,5,3,1]=>1111100
[4,8,6,2,7,3,1,5]=>1110010
[3,6,1,8,7,4,2,5]=>1101001
[4,7,6,2,8,1,3,5]=>1100010
[6,7,4,2,8,1,5,3]=>1111000
[6,8,4,2,7,5,1,3]=>1101100
[5,7,4,2,3,8,1,6]=>1101000
[2,1,8,6,7,5,3,4]=>1010110
[8,6,4,3,7,5,1,2]=>1011110
[5,8,6,7,3,1,2,4]=>1010010
[6,7,5,8,1,3,4,2]=>1100100
[7,6,5,8,1,4,3,2]=>1110110
[8,6,5,7,4,1,3,2]=>1101110
[7,6,4,3,8,1,5,2]=>1111010
[2,1,7,6,8,3,5,4]=>1011010
[7,4,6,3,8,1,2,5]=>1011000
[7,5,6,8,1,4,2,3]=>1100100
[4,1,7,3,6,5,8,2]=>1110100
[5,1,8,4,7,6,2,3]=>1101010
[8,1,3,7,4,6,5,2]=>1101100
[6,1,5,4,3,8,7,2]=>1111001
[6,1,4,5,3,7,8,2]=>1110000
[5,1,7,8,6,2,4,3]=>1110010
[6,1,8,3,4,5,7,2]=>1110000
[6,3,2,7,5,1,8,4]=>1111100
[8,5,2,1,4,3,7,6]=>1110110
[5,6,2,1,4,8,3,7]=>1110000
[3,6,1,8,5,2,4,7]=>1100100
[3,4,1,2,8,6,5,7]=>1000110
[6,3,8,5,2,1,4,7]=>1110100
[8,5,2,7,3,1,6,4]=>1111100
[2,3,8,5,6,1,7,4]=>1001100
[7,4,5,6,3,1,8,2]=>1111000
[8,5,6,4,2,1,7,3]=>1111100
[7,5,3,6,2,8,1,4]=>1110100
[1,7,5,6,3,2,4,8]=>0110100
[8,7,5,4,1,6,2,3]=>1101101
[2,6,4,1,8,5,7,3]=>1011100
[6,1,2,3,8,5,7,4]=>1001100
[7,1,2,3,6,5,8,4]=>1001100
[7,2,1,3,8,6,4,5]=>1101010
[1,5,7,3,2,4,6,8]=>0110000
[5,2,7,3,1,8,4,6]=>1111000
[5,8,2,4,1,3,7,6]=>1100010
[8,7,2,6,3,4,1,5]=>1110001
[4,8,1,6,3,2,7,5]=>1110100
[3,1,8,6,4,2,7,5]=>1101110
[8,1,6,7,4,3,2,5]=>1111000
[3,5,8,7,2,4,1,6]=>1100001
[4,2,1,3,7,8,5,6]=>1100100
[8,6,1,3,7,2,4,5]=>1100010
[5,1,8,3,2,4,6,7]=>1110000
[5,2,7,8,6,4,1,3]=>1101010
[1,4,2,7,8,6,3,5]=>0110010
[1,6,2,4,8,5,3,7]=>0110100
[1,6,2,4,7,5,3,8]=>0110100
[1,7,3,8,5,2,4,6]=>0110100
[1,7,3,2,8,6,4,5]=>0111010
[7,8,3,6,5,2,1,4]=>1110100
[4,7,2,8,6,1,5,3]=>1110010
[4,2,5,7,8,6,1,3]=>1100010
[8,2,5,1,7,3,4,6]=>1110000
[1,3,6,4,8,5,7,2]=>0101100
[1,3,6,4,7,5,8,2]=>0101100
[6,2,4,7,5,8,1,3]=>1100100
[6,2,1,3,7,8,4,5]=>1101000
[7,2,5,1,8,3,4,6]=>1110000
[7,8,2,1,4,3,5,6]=>1110000
[7,6,4,2,3,1,8,5]=>1101110
[7,5,4,2,6,8,1,3]=>1101100
[8,2,5,4,6,7,1,3]=>1101000
[8,2,6,4,3,1,7,5]=>1111100
[8,2,7,4,1,3,5,6]=>1101000
[1,2,8,4,3,5,6,7]=>0011000
[1,8,7,4,3,2,5,6]=>0111001
[5,8,4,7,2,1,6,3]=>1111000
[1,8,7,5,4,3,6,2]=>0111101
[1,6,8,4,3,7,5,2]=>0111100
[6,8,7,3,2,5,1,4]=>1110001
[5,3,8,1,2,7,4,6]=>1011000
[5,1,8,3,2,6,4,7]=>1111000
[5,7,3,1,2,6,4,8]=>1011000
[1,4,6,2,8,3,7,5]=>0110100
[5,2,6,7,8,4,1,3]=>1101000
[5,3,6,1,2,8,4,7]=>1011000
[1,6,3,2,7,8,4,5]=>0111000
[6,7,3,8,5,2,1,4]=>1110100
[4,6,2,7,8,1,5,3]=>1110000
[1,6,4,7,8,3,5,2]=>0111000
[4,5,7,2,1,8,6,3]=>1110010
[7,8,3,4,2,1,6,5]=>1110100
[6,3,4,1,2,5,8,7]=>1010001
[6,3,1,4,2,7,5,8]=>1110100
[1,8,3,2,4,5,6,7]=>0110000
[8,6,3,2,4,1,7,5]=>1110110
[8,5,3,2,6,7,1,4]=>1110100
[7,2,3,1,4,5,8,6]=>1100010
[5,6,3,4,1,2,8,7]=>1010001
[7,8,3,5,4,6,1,2]=>1011000
[6,8,3,7,5,1,4,2]=>1110100
[2,1,7,8,5,6,3,4]=>1010100
[5,7,3,8,1,6,2,4]=>1110000
[7,5,8,4,2,6,1,3]=>1101100
[8,6,3,7,5,2,4,1]=>1110110
[8,5,3,7,2,6,4,1]=>1111100
[8,5,7,4,2,6,3,1]=>1111100
[7,8,4,6,1,5,2,3]=>1101000
[7,8,1,6,4,5,2,3]=>1101000
[6,8,1,7,4,5,2,3]=>1101000
[1,8,6,7,4,5,2,3]=>0101010
[1,8,6,7,3,5,2,4]=>0110010
[6,8,1,7,3,5,2,4]=>1110000
[7,8,1,6,3,5,2,4]=>1110000
[7,8,3,6,1,5,2,4]=>1110000
[7,8,3,6,4,5,1,2]=>1011000
[7,8,2,6,4,5,1,3]=>1101000
[7,8,2,6,3,5,1,4]=>1110000
[7,8,2,6,1,5,3,4]=>1110000
[7,8,1,6,2,5,3,4]=>1110000
[1,8,6,7,2,5,3,4]=>0110010
[1,8,5,7,2,6,3,4]=>0110100
[5,8,1,7,2,6,3,4]=>1110000
[5,8,2,7,1,6,3,4]=>1110000
[6,8,2,7,1,5,3,4]=>1110000
[6,8,2,7,3,5,1,4]=>1110000
[6,8,2,7,4,5,1,3]=>1101000
[6,8,3,7,4,5,1,2]=>1011000
[3,8,6,7,4,5,1,2]=>1001010
[2,8,6,7,4,5,1,3]=>1001010
[2,8,6,7,3,5,1,4]=>1010010
[2,8,6,7,1,5,3,4]=>1010010
[2,8,5,7,1,6,3,4]=>1010100
[2,8,1,7,5,6,3,4]=>1010100
[1,8,2,7,5,6,3,4]=>0110100
[1,8,2,7,4,6,3,5]=>0111000
[2,8,1,7,4,6,3,5]=>1011000
[2,8,4,7,1,6,3,5]=>1011000
[2,8,4,7,3,6,1,5]=>1011000
[2,8,5,7,3,6,1,4]=>1010100
[3,8,5,7,4,6,1,2]=>1001100
[5,8,3,7,4,6,1,2]=>1011000
[5,8,2,7,4,6,1,3]=>1101000
[5,8,2,7,3,6,1,4]=>1110000
[4,8,2,7,3,6,1,5]=>1110000
[4,8,2,7,1,6,3,5]=>1110000
[4,8,1,7,2,6,3,5]=>1110000
[1,8,4,7,2,6,3,5]=>0111000
[1,8,4,7,3,6,2,5]=>0111000
[4,8,1,7,3,6,2,5]=>1110000
[4,8,3,7,1,6,2,5]=>1110000
[6,8,3,7,1,5,2,4]=>1110000
[5,8,1,7,3,6,2,4]=>1110000
[1,8,5,7,3,6,2,4]=>0110100
[1,8,5,7,4,6,2,3]=>0101100
[5,8,1,7,4,6,2,3]=>1101000
[5,8,4,7,1,6,2,3]=>1101000
[6,8,4,7,1,5,2,3]=>1101000
[6,8,5,7,1,4,2,3]=>1100100
[5,8,6,7,3,4,1,2]=>1010010
[5,8,6,7,2,4,1,3]=>1100010
[5,8,6,7,1,4,2,3]=>1100010
[4,8,6,7,1,5,2,3]=>1100010
[4,8,5,7,1,6,2,3]=>1100100
[4,8,1,7,5,6,2,3]=>1100100
[1,8,4,7,5,6,2,3]=>0101100
[1,8,3,7,5,6,2,4]=>0110100
[3,8,1,7,5,6,2,4]=>1100100
[3,8,5,7,1,6,2,4]=>1100100
[3,8,6,7,1,5,2,4]=>1100010
[3,8,6,7,2,5,1,4]=>1100010
[4,8,6,7,2,5,1,3]=>1100010
[4,8,6,7,3,5,1,2]=>1010010
[4,8,5,7,3,6,1,2]=>1010100
[4,8,5,7,2,6,1,3]=>1100100
[3,8,5,7,2,6,1,4]=>1100100
[3,8,4,7,2,6,1,5]=>1101000
[3,8,4,7,1,6,2,5]=>1101000
[3,8,1,7,4,6,2,5]=>1101000
[1,8,3,7,4,6,2,5]=>0111000
[1,8,3,7,2,6,4,5]=>0111000
[3,8,1,7,2,6,4,5]=>1101000
[3,8,2,7,1,6,4,5]=>1101000
[3,8,2,7,4,6,1,5]=>1101000
[3,8,2,7,5,6,1,4]=>1100100
[4,8,2,7,5,6,1,3]=>1100100
[4,8,3,7,5,6,1,2]=>1010100
[3,8,4,7,5,6,1,2]=>1001100
[2,8,4,7,5,6,1,3]=>1001100
[2,8,3,7,5,6,1,4]=>1010100
[2,8,3,7,4,6,1,5]=>1011000
[2,8,3,7,1,6,4,5]=>1011000
[2,8,1,7,3,6,4,5]=>1011000
[7,5,2,8,6,4,1,3]=>1101110
[7,4,8,6,1,5,2,3]=>1101010
[7,1,8,4,5,2,6,3]=>1111000
[1,6,7,4,2,8,5,3]=>0111100
[1,6,7,3,8,5,2,4]=>0110100
[7,1,8,3,5,6,2,4]=>1110000
[7,3,8,6,2,5,1,4]=>1110010
[7,4,2,8,6,1,3,5]=>1101010
[6,8,1,7,2,3,4,5]=>1100000
[1,5,7,8,2,6,3,4]=>0110000
[2,6,3,7,8,5,4,1]=>1011100
[2,5,3,7,8,1,6,4]=>1011000
[2,5,4,1,3,7,8,6]=>1001010
[3,1,5,4,7,8,2,6]=>1101000
[5,3,1,4,8,2,6,7]=>1110000
[5,2,4,8,6,1,3,7]=>1100010
[4,8,1,3,6,7,2,5]=>1100000
[5,3,8,2,4,7,1,6]=>1110000
[5,4,3,8,1,2,7,6]=>1011010
[6,4,3,1,2,8,5,7]=>1011100
[6,4,2,8,1,3,7,5]=>1101100
[6,3,8,2,5,1,7,4]=>1111000
[6,3,8,1,4,7,2,5]=>1110000
[1,5,7,3,6,8,4,2]=>0111000
[1,5,7,4,2,6,8,3]=>0111000
[5,8,1,4,2,6,3,7]=>1110000
[5,8,4,1,2,7,6,3]=>1011010
[6,5,1,2,8,7,3,4]=>1010101
[6,5,3,1,4,2,8,7]=>1110101
[5,3,1,6,4,2,7,8]=>1111000
[5,2,6,4,1,7,3,8]=>1111000
[4,6,1,7,5,2,8,3]=>1110100
[3,5,6,1,2,8,7,4]=>1001001
[3,5,7,1,8,6,2,4]=>1100010
[3,6,2,7,5,1,8,4]=>1101100
[4,3,1,5,7,2,6,8]=>1110000
[3,4,7,2,8,6,1,5]=>1100010
[3,4,5,8,2,7,1,6]=>1100000
[3,4,6,2,8,1,5,7]=>1100000
[3,5,2,6,8,1,7,4]=>1101000
[5,3,6,8,4,7,2,1]=>1111000
[3,7,2,5,4,8,6,1]=>1101010
[4,2,6,5,8,3,7,1]=>1110100
[4,1,6,5,8,3,2,7]=>1110100
[5,1,6,8,4,3,2,7]=>1111000
[6,7,8,1,4,3,2,5]=>1110000
[4,7,1,5,8,3,2,6]=>1110000
[8,3,1,5,4,7,2,6]=>1111000
[8,4,1,5,7,3,2,6]=>1111000
[8,4,6,1,7,3,2,5]=>1111000
[8,3,6,1,4,7,2,5]=>1110000
[8,2,6,1,4,3,7,5]=>1110100
[3,7,6,1,4,8,2,5]=>1100010
[6,7,8,5,1,3,2,4]=>1100100
[6,7,8,2,4,3,5,1]=>1110000
[4,7,6,2,8,3,5,1]=>1110010
[3,7,6,2,4,8,5,1]=>1100110
[5,7,3,8,4,6,2,1]=>1111000
[4,7,3,5,8,6,2,1]=>1110010
[8,7,2,1,4,3,6,5]=>1110101
[8,7,3,1,4,6,2,5]=>1110001
[8,7,6,3,2,5,4,1]=>1111011
[8,7,3,5,1,6,2,4]=>1110001
[8,7,2,5,1,3,6,4]=>1101001
[8,4,6,5,7,1,2,3]=>1001100
[4,7,6,5,8,1,2,3]=>1000110
[8,7,6,5,2,1,4,3]=>1110111
[3,6,4,8,7,5,1,2]=>1001101
[5,6,4,3,8,7,1,2]=>1011001
[1,6,2,4,7,8,5,3]=>0110100
[3,6,2,4,8,1,5,7]=>1100000
[3,4,7,2,8,1,6,5]=>1100100
[1,4,7,2,5,8,6,3]=>0110010
[7,3,8,4,5,6,1,2]=>1011000
[3,8,7,5,4,6,1,2]=>1001101
[4,3,6,7,8,5,1,2]=>1010100
[3,5,6,4,8,7,1,2]=>1001001
[4,6,8,5,3,7,1,2]=>1010100
[6,5,2,1,4,7,8,3]=>1110100
[4,2,7,5,1,8,6,3]=>1110110
[2,1,6,4,8,7,5,3]=>1011101
[7,8,1,4,2,6,5,3]=>1110100
[6,5,1,3,4,2,8,7]=>1100101
[4,8,5,3,1,7,2,6]=>1110100
[7,4,5,3,2,8,1,6]=>1111000
[5,8,3,6,1,4,2,7]=>1110000
[1,4,6,2,5,8,3,7]=>0110000
[1,6,8,7,4,2,3,5]=>0101001
[7,6,1,8,3,2,4,5]=>1110010
[7,1,8,6,3,4,2,5]=>1110010
[1,8,7,6,4,3,2,5]=>0111011
[2,1,7,5,6,3,8,4]=>1011100
[3,1,6,7,5,8,2,4]=>1100100
[7,8,1,6,5,3,2,4]=>1110100
[7,8,2,1,4,5,6,3]=>1110000
[4,2,6,1,8,5,7,3]=>1110100
[2,8,1,5,4,6,7,3]=>1011000
[1,2,8,3,6,5,7,4]=>0011100
[6,1,3,2,7,5,8,4]=>1101100
[2,6,4,1,7,5,8,3]=>1011100
[7,6,5,8,1,4,2,3]=>1100110
[5,8,6,7,3,2,1,4]=>1110010
[1,6,4,3,7,2,8,5]=>0111100
[4,6,3,8,1,2,7,5]=>1010100
[4,3,7,1,2,5,8,6]=>1010010
[4,1,6,3,8,2,7,5]=>1110100
[7,8,1,3,4,2,6,5]=>1100100
[2,8,5,7,4,3,1,6]=>1011100
[7,2,5,8,3,4,1,6]=>1110000
[5,3,8,7,1,2,6,4]=>1011001
[6,5,3,8,2,1,7,4]=>1111100
[3,5,7,8,4,1,2,6]=>1001000
[5,4,7,3,6,8,1,2]=>1011000
[3,4,7,2,5,1,6,8]=>1100000
[1,4,7,2,5,8,3,6]=>0110000
[3,6,2,4,7,1,5,8]=>1100000
[7,6,3,5,4,8,1,2]=>1011010
[4,5,6,3,8,7,1,2]=>1010001
[6,3,7,5,8,4,1,2]=>1011100
[4,8,2,6,1,5,3,7]=>1110000
[4,3,6,2,5,1,8,7]=>1110001
[7,8,1,2,5,6,3,4]=>1010000
[4,1,6,2,5,7,3,8]=>1110000
[7,1,3,6,8,4,2,5]=>1101000
[1,8,3,6,7,4,5,2]=>0111000
[7,1,5,8,3,6,2,4]=>1110000
[3,1,6,4,7,2,5,8]=>1101000
[5,8,7,1,2,4,3,6]=>1010001
[1,5,7,8,2,4,6,3]=>0110000
[6,8,5,1,3,4,2,7]=>1100100
[7,6,5,1,4,3,2,8]=>1110110
[2,6,4,5,1,3,8,7]=>1001001
[3,5,6,4,1,8,2,7]=>1101000
[7,8,5,4,1,3,2,6]=>1101100
[7,8,2,3,4,1,6,5]=>1100100
[4,2,6,3,8,1,7,5]=>1110100
[7,2,3,5,4,1,8,6]=>1101010
[6,2,4,3,1,5,7,8]=>1110000
[4,2,8,3,1,7,5,6]=>1110100
[1,3,7,4,8,2,5,6]=>0101000
[5,3,7,4,1,6,2,8]=>1111000
[2,4,7,3,6,1,8,5]=>1010100
[5,8,7,6,3,1,2,4]=>1010011
[7,5,6,8,1,4,3,2]=>1110100
[2,4,7,1,6,5,3,8]=>1010100
[5,2,7,1,8,4,6,3]=>1111000
[4,2,1,3,6,5,8,7]=>1100101
[4,2,6,1,8,5,3,7]=>1110100
[7,8,2,1,4,5,3,6]=>1110000
[7,8,4,1,5,3,6,2]=>1111000
[7,5,1,6,4,3,8,2]=>1111100
[5,8,1,6,3,4,7,2]=>1110000
[6,8,1,7,5,2,3,4]=>1100100
[5,6,1,7,4,8,2,3]=>1101000
[7,8,5,1,6,4,2,3]=>1101100
[2,6,5,7,3,4,8,1]=>1010100
[1,6,4,7,5,8,2,3]=>0101100
[1,3,7,4,6,8,2,5]=>0101000
[5,2,4,7,3,6,8,1]=>1110000
[8,1,6,5,7,2,4,3]=>1110100
[7,1,6,5,8,3,2,4]=>1110100
[1,2,7,6,8,3,4,5]=>0010010
[3,8,6,4,2,7,5,1]=>1101110
[7,8,1,6,2,4,5,3]=>1110000
[2,8,1,7,4,3,6,5]=>1011100
[3,7,4,1,8,5,2,6]=>1101100
[6,7,1,4,8,3,2,5]=>1110000
[2,7,1,8,4,5,3,6]=>1011000
[6,1,2,8,4,3,5,7]=>1011000
[5,1,2,4,8,3,6,7]=>1010000
[4,1,3,2,8,5,6,7]=>1100100
[3,2,1,4,8,5,6,7]=>1100100
[4,3,6,1,5,8,2,7]=>1110000
[2,6,1,4,5,8,3,7]=>1010000
[1,6,2,5,8,3,4,7]=>0110000
[8,4,2,1,7,3,6,5]=>1111100
[7,4,2,1,8,5,3,6]=>1111100
[1,5,4,2,8,3,6,7]=>0111000
[6,4,3,1,5,8,2,7]=>1111000
[5,4,3,2,1,8,6,7]=>1111010
[2,5,3,4,1,8,6,7]=>1010010
[4,3,5,2,1,8,6,7]=>1110010
[3,7,6,8,4,5,2,1]=>1101010
[1,7,6,8,5,4,2,3]=>0101110
[2,4,8,6,7,3,5,1]=>1010010
[3,4,8,5,6,7,2,1]=>1100100
[6,3,5,8,4,7,2,1]=>1111000
[5,4,3,8,6,7,2,1]=>1111010
[3,2,8,5,7,4,6,1]=>1101100
[2,1,8,7,4,6,3,5]=>1011001
[3,1,8,5,7,6,2,4]=>1100110
[6,1,5,8,7,4,2,3]=>1101001
[5,8,6,7,4,3,2,1]=>1111010
[4,8,7,5,6,3,2,1]=>1110101
[4,2,1,6,3,5,8,7]=>1110001
[6,2,1,4,3,8,5,7]=>1110100
[8,2,1,4,3,6,5,7]=>1110100
[6,2,4,1,3,8,5,7]=>1100100
[2,1,6,4,3,5,8,7]=>1011001
[6,4,2,1,3,5,8,7]=>1101001
[8,4,2,1,3,6,5,7]=>1101100
[8,4,2,1,6,3,5,7]=>1111000
[6,4,2,1,8,3,5,7]=>1111000
[4,6,2,1,3,8,5,7]=>1100100
[2,6,1,4,3,8,5,7]=>1010100
[2,1,6,4,3,8,5,7]=>1011100
[4,8,2,1,3,6,5,7]=>1100100
[6,8,2,1,4,3,5,7]=>1110000
[8,6,2,1,4,3,5,7]=>1110010
[2,8,1,4,6,3,5,7]=>1010000
[2,6,1,4,8,3,5,7]=>1010000
[2,6,4,1,8,3,5,7]=>1011000
[2,6,4,8,1,3,5,7]=>1001000
[4,6,2,8,1,3,5,7]=>1100000
[4,2,6,1,8,3,5,7]=>1110000
[6,2,4,1,8,3,5,7]=>1110000
[4,2,1,6,8,3,5,7]=>1110000
[4,2,1,6,3,8,5,7]=>1110100
[4,2,1,3,6,8,5,7]=>1100100
[2,1,4,3,8,6,5,7]=>1010110
[2,4,1,3,8,6,5,7]=>1000110
[4,2,1,3,8,6,5,7]=>1100110
[4,2,1,8,3,6,5,7]=>1110100
[4,2,1,8,6,3,5,7]=>1110010
[8,2,1,6,4,3,5,7]=>1111000
[4,2,8,1,6,3,5,7]=>1110000
[2,4,1,8,3,6,5,7]=>1010100
[2,1,4,8,3,6,5,7]=>1010100
[2,4,8,1,6,3,5,7]=>1010000
[2,4,8,6,1,3,5,7]=>1000010
[4,2,8,6,1,3,5,7]=>1100010
[2,1,8,6,4,3,5,7]=>1011010
[2,8,6,1,4,3,5,7]=>1010010
[2,8,6,4,1,3,5,7]=>1001010
[4,8,6,2,1,3,5,7]=>1100010
[3,2,6,1,5,4,8,7]=>1101001
[6,1,5,2,4,3,8,7]=>1110001
[6,1,3,2,5,4,8,7]=>1101001
[4,3,6,1,5,2,8,7]=>1110001
[4,3,5,2,8,1,7,6]=>1110010
[4,3,7,2,6,5,8,1]=>1110100
[4,3,8,2,6,1,7,5]=>1110100
[4,3,8,1,7,2,6,5]=>1110100
[4,3,8,1,5,2,7,6]=>1110010
[2,1,5,4,8,3,7,6]=>1011010
[5,4,7,6,8,1,3,2]=>1101010
[4,3,7,6,8,1,5,2]=>1110010
[4,3,7,1,8,5,6,2]=>1110100
[4,3,6,5,8,1,7,2]=>1110100
[6,3,5,4,7,2,8,1]=>1111000
[6,3,5,4,8,1,7,2]=>1111000
[7,1,6,3,8,4,5,2]=>1111000
[7,1,6,5,8,3,4,2]=>1110100
[7,4,6,5,8,1,3,2]=>1101100
[8,4,6,1,3,2,7,5]=>1101100
[8,1,6,3,4,2,7,5]=>1110100
[8,3,5,2,6,1,7,4]=>1111000
[7,3,5,2,6,4,8,1]=>1111000
[8,2,7,1,5,3,6,4]=>1111000
[8,1,7,2,4,3,6,5]=>1110100
[8,1,3,2,7,4,6,5]=>1101100
[2,1,8,3,7,4,6,5]=>1011100
[2,1,8,3,5,4,7,6]=>1011010
[8,1,3,2,5,4,7,6]=>1101010
[8,1,5,2,4,3,7,6]=>1110010
[8,2,4,1,5,3,7,6]=>1110010
[8,2,4,1,7,3,6,5]=>1110100
[3,2,8,4,6,1,7,5]=>1101100
[3,2,8,1,7,4,6,5]=>1101100
[3,2,8,1,5,4,7,6]=>1101010
[3,2,4,1,8,5,7,6]=>1100110
[4,1,3,2,7,6,8,5]=>1100110
[3,2,7,6,8,1,5,4]=>1101010
[3,2,7,1,8,5,6,4]=>1101100
[3,2,6,5,8,1,7,4]=>1101100
[7,2,4,1,8,5,6,3]=>1110100
[7,6,8,1,5,2,4,3]=>1110010
[7,6,8,1,3,2,5,4]=>1101010
[7,1,8,5,6,2,4,3]=>1110100
[7,1,8,2,6,4,5,3]=>1111000
[7,2,8,1,5,4,6,3]=>1111000
[5,4,7,2,6,3,8,1]=>1111000
[5,4,8,2,6,1,7,3]=>1111000
[6,1,8,4,7,2,5,3]=>1111000
[6,5,8,1,3,2,7,4]=>1101100
[2,1,6,5,8,3,7,4]=>1011100
[6,5,7,4,8,1,3,2]=>1101100
[5,4,6,3,8,1,7,2]=>1111000
[3,2,1,5,8,4,6,7]=>1101000
[2,8,3,1,5,4,6,7]=>1011000
[2,4,8,3,5,7,6,1]=>1010010
[4,2,5,3,1,8,6,7]=>1110010
[1,8,4,2,5,3,6,7]=>0111000
[8,1,5,3,2,4,6,7]=>1110000
[3,8,1,5,2,4,6,7]=>1100000
[5,4,1,3,8,2,6,7]=>1101000
[1,5,7,3,8,4,2,6]=>0111000
[5,1,4,7,8,3,2,6]=>1110000
[8,1,5,3,7,4,6,2]=>1111000
[1,4,3,8,7,5,6,2]=>0110101
[1,6,8,5,3,7,4,2]=>0111100
[6,4,8,1,7,3,5,2]=>1111000
[6,4,8,7,1,5,2,3]=>1101001
[7,1,6,8,4,3,2,5]=>1111000
[1,6,7,2,8,4,3,5]=>0111000
[6,7,1,4,2,8,3,5]=>1110000
[6,3,7,1,4,8,2,5]=>1110000
[3,7,8,1,5,2,4,6]=>1100000
[7,1,2,8,5,3,4,6]=>1010100
[1,7,2,8,4,5,3,6]=>0111000
[4,2,1,7,8,5,3,6]=>1110100
[6,2,4,8,3,7,5,1]=>1110100
[7,2,6,3,4,1,8,5]=>1110100
[2,7,1,8,3,5,4,6]=>1011000
[2,1,7,3,5,8,4,6]=>1011000
[1,2,7,5,8,3,4,6]=>0010100
[8,7,1,3,6,2,4,5]=>1100001
[8,2,1,7,3,5,6,4]=>1111000
[7,8,2,6,3,1,5,4]=>1111000
[2,7,8,4,1,6,5,3]=>1011100
[2,8,4,1,6,7,5,3]=>1011100
[2,1,8,4,7,5,6,3]=>1011100
[8,3,7,1,5,6,2,4]=>1110000
[8,6,1,2,7,5,3,4]=>1010110
[8,1,6,2,7,4,5,3]=>1111000
[1,8,5,2,6,7,4,3]=>0111100
[5,2,1,8,6,7,4,3]=>1111010
[7,8,1,6,4,2,5,3]=>1111000
[8,7,6,5,1,4,2,3]=>1100111
[8,7,6,1,5,3,4,2]=>1110011
[8,1,7,5,6,4,3,2]=>1111100
[1,8,6,7,5,4,3,2]=>0111110
[6,3,5,2,1,4,8,7]=>1110001
[8,3,5,7,2,4,1,6]=>1110000
[8,5,2,7,4,3,1,6]=>1111100
[6,5,3,1,2,4,8,7]=>1010101
[4,5,3,6,1,2,8,7]=>1010001
[3,5,1,4,6,2,8,7]=>1100001
[8,1,4,7,3,6,2,5]=>1110000
[8,5,1,4,7,3,2,6]=>1110100
[8,5,3,7,1,4,2,6]=>1110100
[6,3,4,7,5,8,1,2]=>1010100
[5,1,4,6,8,3,7,2]=>1110000
[4,7,1,3,5,8,6,2]=>1100010
[4,8,3,7,1,2,6,5]=>1010100
[8,7,1,4,2,6,3,5]=>1110001
[8,6,3,1,2,4,7,5]=>1010110
[2,1,8,7,5,3,4,6]=>1010101
[8,1,7,4,5,2,3,6]=>1101000
[2,8,7,5,4,1,3,6]=>1001101
[8,7,2,6,4,1,3,5]=>1101001
[5,3,7,8,2,4,6,1]=>1110000
[5,3,7,6,2,1,8,4]=>1111010
[5,7,8,6,4,2,1,3]=>1101010
[2,6,7,5,4,8,1,3]=>1001100
[6,7,3,5,1,8,2,4]=>1110000
[2,1,6,7,5,8,3,4]=>1010100
[2,1,5,7,3,6,8,4]=>1011000
[4,1,7,2,5,6,8,3]=>1110000
[2,4,7,1,6,5,8,3]=>1010100
[3,4,6,2,7,8,5,1]=>1100100
[4,6,1,2,5,8,7,3]=>1010001
[5,6,3,1,8,7,2,4]=>1110001
[3,5,6,4,7,1,8,2]=>1101000
[3,4,6,1,5,7,8,2]=>1100000
[3,4,1,5,7,6,8,2]=>1100010
[6,3,2,1,7,4,8,5]=>1111100
[4,2,1,7,3,5,8,6]=>1110010
[7,3,1,5,4,2,8,6]=>1111010
[6,3,1,4,2,8,5,7]=>1110100
[8,4,1,5,2,7,6,3]=>1111010
[7,2,5,1,4,3,8,6]=>1110010
[3,6,2,7,1,4,8,5]=>1100100
[2,7,5,4,1,3,8,6]=>1001110
[6,4,3,2,1,8,5,7]=>1111100
[1,7,6,2,4,8,3,5]=>0110010
[2,7,3,6,4,8,1,5]=>1011000
[6,2,7,5,3,8,1,4]=>1110100
[7,1,8,5,3,6,4,2]=>1111100
[5,8,3,2,7,1,6,4]=>1111000
[8,7,2,6,1,5,4,3]=>1111001
[1,8,5,7,4,3,6,2]=>0111100
[1,8,5,7,2,4,6,3]=>0110100
[7,2,8,5,6,1,4,3]=>1110100
[3,6,5,8,1,4,2,7]=>1100100
[4,3,6,8,2,1,5,7]=>1110000
[2,5,7,4,8,1,3,6]=>1001000
[4,3,6,7,8,1,2,5]=>1010000
[5,4,6,7,2,8,1,3]=>1101000
[4,6,3,7,1,8,2,5]=>1110000
[3,5,7,1,4,8,2,6]=>1100000
[8,1,5,2,7,4,6,3]=>1111000
[8,4,1,5,7,3,6,2]=>1111000
[6,4,2,5,8,3,1,7]=>1111000
[5,4,1,6,8,2,3,7]=>1101000
[5,3,1,7,2,8,4,6]=>1111000
[6,5,2,1,7,8,3,4]=>1110100
[5,3,6,4,7,8,1,2]=>1011000
[6,3,7,4,8,5,2,1]=>1111100
[4,7,2,5,8,6,3,1]=>1110010
[6,3,1,8,4,7,5,2]=>1111100
[5,4,8,1,7,6,2,3]=>1101010
[5,2,8,1,7,3,6,4]=>1111000
[6,4,8,2,1,7,5,3]=>1111100
[5,7,3,8,1,6,4,2]=>1111000
[6,4,7,8,1,5,3,2]=>1111000
[6,3,7,8,5,2,4,1]=>1110100
[4,6,8,2,7,1,5,3]=>1110000
[2,5,8,7,1,3,6,4]=>1001001
[5,3,8,7,2,1,6,4]=>1111001
[8,3,7,6,1,5,4,2]=>1111010
[8,2,7,6,5,1,4,3]=>1110110
[4,3,8,7,6,2,1,5]=>1110011
[2,4,8,7,6,1,3,5]=>1000011
[3,5,8,7,2,6,1,4]=>1100001
[4,7,3,8,6,5,1,2]=>1010110
[7,5,8,6,4,3,2,1]=>1111110
[5,8,7,3,6,4,2,1]=>1111001
[3,8,7,6,5,1,4,2]=>1100111
[2,8,7,6,5,4,1,3]=>1001111
[7,8,5,6,3,1,4,2]=>1110100
[7,8,5,3,6,1,2,4]=>1010100
[7,5,6,3,1,4,2,8]=>1110100
[7,5,8,3,1,4,2,6]=>1110100
[7,8,5,3,1,4,2,6]=>1110100
[7,8,5,3,1,6,2,4]=>1110100
[7,8,5,3,1,6,4,2]=>1111100
[7,8,5,3,6,1,4,2]=>1110100
[7,8,5,3,6,4,1,2]=>1011100
[7,8,5,3,4,1,6,2]=>1110100
[7,8,5,3,1,4,6,2]=>1110100
[7,5,8,3,1,2,6,4]=>1011100
[7,5,8,3,4,1,6,2]=>1110100
[7,5,8,3,4,6,1,2]=>1010100
[7,5,6,3,4,1,8,2]=>1110100
[7,5,6,3,1,4,8,2]=>1110100
[7,5,3,1,6,4,8,2]=>1111100
[7,5,3,6,1,4,8,2]=>1110100
[7,5,3,6,4,1,8,2]=>1111100
[7,5,3,6,4,8,1,2]=>1011100
[7,5,3,8,4,6,1,2]=>1011100
[7,5,3,8,4,1,6,2]=>1111100
[7,5,3,8,1,4,6,2]=>1110100
[7,5,3,1,8,4,6,2]=>1111100
[7,5,3,1,8,2,6,4]=>1111100
[7,5,3,1,6,2,4,8]=>1110100
[7,5,3,1,6,4,2,8]=>1111100
[7,5,3,1,8,4,2,6]=>1111100
[7,5,3,1,8,6,2,4]=>1110110
[7,5,3,8,1,6,4,2]=>1111100
[7,5,3,8,6,1,4,2]=>1110110
[7,5,3,8,6,4,1,2]=>1011110
[7,5,8,3,6,4,1,2]=>1011100
[7,5,8,3,6,1,4,2]=>1110100
[7,5,8,3,1,6,4,2]=>1111100
[7,5,8,3,1,6,2,4]=>1110100
[7,5,3,8,1,6,2,4]=>1110100
[7,5,3,8,1,4,2,6]=>1110100
[7,5,3,6,1,4,2,8]=>1110100
[7,5,3,6,4,1,2,8]=>1011100
[7,5,3,8,4,1,2,6]=>1011100
[7,5,3,8,6,1,2,4]=>1010110
[7,5,8,6,3,1,2,4]=>1010110
[7,5,8,6,3,1,4,2]=>1110110
[7,5,8,6,3,4,1,2]=>1010110
[7,5,6,8,3,1,4,2]=>1110100
[7,5,6,3,8,1,2,4]=>1010100
[7,5,3,6,1,8,2,4]=>1110100
[7,5,6,3,1,8,2,4]=>1110100
[7,5,6,3,1,8,4,2]=>1111100
[7,5,6,3,8,1,4,2]=>1110100
[7,5,6,3,8,4,1,2]=>1011100
[7,5,3,6,8,4,1,2]=>1011100
[7,5,3,6,8,1,4,2]=>1110100
[7,5,3,6,1,8,4,2]=>1111100
[7,5,3,1,6,8,4,2]=>1111100
[7,5,3,1,6,8,2,4]=>1110100
[7,5,3,1,2,8,6,4]=>1011110
[7,5,3,4,1,6,8,2]=>1110100
[4,6,8,3,5,7,1,2]=>1010000
[6,8,1,2,4,5,7,3]=>1010000
[3,6,8,2,5,7,1,4]=>1100000
[8,3,5,2,4,1,6,7]=>1110000
[3,5,7,2,4,6,1,8]=>1100000
[4,2,5,7,3,6,1,8]=>1110000
[4,5,2,8,3,1,6,7]=>1110000
[2,1,6,8,4,7,3,5]=>1011000
[1,2,5,8,3,6,7,4]=>0011000
[5,3,6,8,4,7,1,2]=>1011000
[3,1,2,6,8,5,7,4]=>1001100
[4,3,6,2,7,5,1,8]=>1110100
[4,3,1,7,8,2,6,5]=>1110100
[5,4,7,3,8,6,1,2]=>1011010
[5,8,4,7,6,3,1,2]=>1011010
[5,8,7,1,4,2,6,3]=>1110001
[8,3,5,1,2,7,6,4]=>1011010
[4,7,3,6,5,2,1,8]=>1110100
[5,3,7,6,4,2,1,8]=>1111010
[5,3,1,6,4,2,8,7]=>1111001
[1,3,8,5,4,2,7,6]=>0101110
[1,8,3,6,2,7,5,4]=>0111100
[1,6,8,7,4,2,5,3]=>0111001
[6,4,8,7,5,3,1,2]=>1011101
[3,1,2,7,6,4,8,5]=>1001110
[5,2,6,3,7,4,1,8]=>1111000
[2,8,5,3,1,6,4,7]=>1011100
[2,1,7,3,8,5,4,6]=>1011100
[1,6,2,3,7,8,5,4]=>0101100
[1,6,7,2,8,4,5,3]=>0111000
[6,3,7,4,8,5,1,2]=>1011100
[5,7,1,8,2,4,6,3]=>1110000
[5,1,2,7,8,3,6,4]=>1011000
[2,4,1,7,8,6,3,5]=>1010010
[4,2,1,7,3,8,5,6]=>1110100
[6,2,8,4,3,1,5,7]=>1111000
[6,4,2,7,3,5,1,8]=>1111000
[7,3,2,1,8,4,5,6]=>1111000
[3,7,2,8,6,1,4,5]=>1100010
[7,8,3,2,5,6,1,4]=>1110000
[7,1,8,2,4,5,6,3]=>1110000
[8,7,6,1,2,4,5,3]=>1010011
[8,3,6,5,2,1,4,7]=>1110100
[8,2,4,1,6,5,3,7]=>1110100
[8,2,4,1,7,6,3,5]=>1110010
[8,5,1,2,7,3,6,4]=>1011100
[6,1,8,2,3,7,5,4]=>1101100
[8,1,2,6,4,3,7,5]=>1011100
[2,8,1,7,5,4,3,6]=>1011100
[1,2,7,5,4,3,8,6]=>0011110
[1,7,2,8,3,6,5,4]=>0111100
[7,3,8,6,5,4,1,2]=>1011110
[1,8,7,6,5,2,4,3]=>0110111
[8,1,7,3,2,6,5,4]=>1111100
[4,3,1,2,8,7,6,5]=>1010111
[5,1,4,3,2,8,7,6]=>1110011
[8,6,4,3,1,5,7,2]=>1111010
[8,6,4,1,5,2,7,3]=>1111010
[8,6,5,3,2,1,7,4]=>1111110
[8,7,2,4,5,3,1,6]=>1110001
[8,5,1,2,6,7,3,4]=>1010100
[8,5,1,6,4,2,7,3]=>1111100
[8,5,1,3,6,4,7,2]=>1101100
[8,6,5,1,7,3,2,4]=>1110110
[7,4,8,3,1,6,2,5]=>1111000
[7,1,5,8,3,2,6,4]=>1111000
[5,7,4,1,8,2,6,3]=>1111000
[5,7,4,3,1,8,6,2]=>1111010
[8,5,7,4,6,1,3,2]=>1101100
[1,8,7,2,5,4,6,3]=>0111001
[1,8,5,3,7,2,6,4]=>0111100
[4,3,1,8,7,5,2,6]=>1110101
[1,3,5,6,8,4,2,7]=>0101000
[3,1,4,6,8,7,2,5]=>1100001
[1,6,3,8,7,2,5,4]=>0111001
[1,6,2,4,8,7,5,3]=>0110101
[8,4,1,6,7,5,3,2]=>1111100
[7,1,6,4,8,5,2,3]=>1101100
[7,3,6,8,5,1,2,4]=>1010100
[1,3,7,2,6,8,4,5]=>0101000
[3,6,5,2,8,1,4,7]=>1100100
[6,1,2,7,8,5,3,4]=>1010100
[6,1,2,7,4,8,5,3]=>1011100
[3,1,6,4,7,8,5,2]=>1101100
[5,7,1,3,8,4,6,2]=>1101000
[5,7,1,8,4,2,6,3]=>1111000
[5,7,1,2,8,6,3,4]=>1010010
[4,2,6,3,8,1,5,7]=>1110000
[4,2,6,7,3,5,1,8]=>1110000
[3,6,2,4,7,5,1,8]=>1100100
[3,6,2,4,1,8,5,7]=>1100100
[7,1,4,5,2,8,6,3]=>1110010
[4,7,3,1,5,8,6,2]=>1110010
[8,7,6,4,1,5,2,3]=>1101011
[3,8,2,7,1,5,4,6]=>1101000
[3,6,8,2,1,5,4,7]=>1101000
[2,4,8,1,6,5,3,7]=>1010100
[4,2,8,1,5,7,3,6]=>1110000
[8,5,7,6,1,4,2,3]=>1100110
[1,8,2,4,6,7,3,5]=>0110000
[2,1,5,8,6,4,3,7]=>1011010
[1,2,5,7,8,4,3,6]=>0011000
[1,2,7,4,8,6,3,5]=>0011010
[1,2,7,8,3,6,5,4]=>0011100
[1,8,5,7,4,3,2,6]=>0111100
[1,6,8,5,4,3,2,7]=>0111100
[7,1,5,8,3,4,6,2]=>1110000
[7,1,5,8,4,3,2,6]=>1111000
[7,1,2,5,8,3,6,4]=>1011000
[7,1,6,4,2,3,5,8]=>1101000
[2,7,1,4,8,3,5,6]=>1010000
[7,1,4,6,5,8,3,2]=>1110100
[7,1,2,3,8,5,4,6]=>1001100
[7,1,5,4,3,8,2,6]=>1111000
[7,1,3,4,2,6,8,5]=>1100100
[3,6,7,1,4,8,5,2]=>1100100
[3,5,1,4,8,6,2,7]=>1100010
[3,6,2,4,7,8,1,5]=>1100000
[5,6,2,4,8,7,1,3]=>1100001
[6,5,8,7,2,3,1,4]=>1100101
[3,4,7,2,5,8,1,6]=>1100000
[4,3,8,1,2,7,5,6]=>1010100
[5,6,7,8,1,3,4,2]=>1100000
[5,7,8,6,1,2,3,4]=>1000010
[2,8,3,1,5,6,4,7]=>1011000
[3,8,7,1,5,4,2,6]=>1101001
[4,3,1,7,6,8,2,5]=>1110010
[3,4,1,7,5,6,8,2]=>1100100
[3,4,1,5,7,6,2,8]=>1100010
[2,4,6,1,7,5,8,3]=>1010100
[4,7,8,1,2,3,6,5]=>1000100
[4,2,1,5,6,3,7,8]=>1110000
[5,8,1,6,4,3,2,7]=>1111000
[5,8,1,6,3,7,2,4]=>1110000
[7,6,5,1,3,8,2,4]=>1100110
[7,6,5,1,3,4,8,2]=>1100110
[7,2,6,4,1,3,8,5]=>1101100
[8,4,5,3,7,2,6,1]=>1111000
[4,7,5,2,8,1,6,3]=>1110100
[4,6,3,8,5,1,7,2]=>1110100
[2,6,4,3,1,5,7,8]=>1011000
[3,6,4,8,1,7,2,5]=>1101000
[7,3,8,4,1,5,2,6]=>1111000
[4,2,8,3,6,1,5,7]=>1110000
[6,7,5,8,2,1,4,3]=>1110100
[6,8,5,7,2,1,3,4]=>1100100
[4,8,5,2,7,1,3,6]=>1100100
[6,3,5,2,1,7,4,8]=>1111000
[3,6,5,4,2,8,1,7]=>1101100
[7,4,5,3,8,2,1,6]=>1111000
[1,6,4,7,2,5,3,8]=>0111000
[1,4,3,7,2,6,5,8]=>0110100
[1,5,7,2,4,8,3,6]=>0110000
[1,6,5,7,2,4,3,8]=>0110100
[1,7,6,2,8,3,4,5]=>0110010
[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]=>0101101
[1,7,6,5,2,8,4,3]=>0111110
[1,6,5,2,3,8,4,7]=>0101100
[1,6,7,5,2,3,8,4]=>0101100
[1,7,5,2,8,4,3,6]=>0111100
[1,7,5,6,2,8,3,4]=>0110100
[1,5,7,6,2,4,8,3]=>0110010
[1,4,7,6,2,5,8,3]=>0110010
[1,2,6,5,3,7,4,8]=>0011100
[1,3,7,5,2,6,8,4]=>0101100
[1,7,4,6,2,8,3,5]=>0111000
[1,7,3,5,2,8,4,6]=>0111000
[1,3,7,4,2,6,8,5]=>0101100
[1,4,7,3,2,5,8,6]=>0110010
[1,5,7,3,2,4,8,6]=>0110010
[1,7,3,4,2,8,5,6]=>0110100
[1,7,4,2,8,5,3,6]=>0111100
[1,6,7,4,2,3,8,5]=>0101100
[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]=>0101100
[1,7,6,4,2,8,5,3]=>0111110
[1,7,5,3,2,8,6,4]=>0111110
[1,6,4,2,3,8,7,5]=>0101101
[1,5,3,2,4,8,7,6]=>0110011
[6,8,5,4,3,2,1,7]=>1111100
[2,8,5,4,3,7,1,6]=>1011100
[7,6,1,4,3,8,5,2]=>1110110
[7,6,5,1,3,8,4,2]=>1101110
[7,3,5,4,8,1,6,2]=>1111000
[5,6,8,4,3,1,7,2]=>1111000
[6,8,5,4,1,2,7,3]=>1011100
[6,8,2,4,3,7,1,5]=>1110000
[1,8,3,4,7,2,6,5]=>0110100
[7,5,8,4,3,2,1,6]=>1111100
[4,8,5,7,3,2,1,6]=>1110100
[7,8,1,2,4,3,5,6]=>1010000
[7,8,2,1,4,3,6,5]=>1110100
[3,4,6,5,7,8,1,2]=>1000100
[4,3,6,5,8,7,1,2]=>1010101
[4,2,6,1,8,3,7,5]=>1110100
[6,7,3,8,4,5,1,2]=>1011000
[6,7,4,5,1,8,2,3]=>1101000
[4,7,5,6,1,8,2,3]=>1100100
[4,5,3,8,6,7,1,2]=>1010010
[5,6,3,8,4,7,1,2]=>1011000
[5,6,4,7,1,8,2,3]=>1101000
[5,6,2,7,3,4,1,8]=>1110000
[4,5,1,8,6,7,2,3]=>1100010
[7,8,4,5,1,6,2,3]=>1101000
[4,5,2,3,1,8,6,7]=>1100010
[5,6,2,3,1,8,4,7]=>1101000
[5,6,3,4,1,8,2,7]=>1110000
[3,6,4,5,2,7,1,8]=>1101000
[3,6,4,5,1,8,2,7]=>1101000
[2,6,4,8,1,5,3,7]=>1011000
[2,8,3,6,1,5,4,7]=>1011000
[2,8,3,4,1,6,5,7]=>1010100
[7,8,1,5,3,6,2,4]=>1110000
[1,8,3,6,5,7,2,4]=>0110100
[1,6,4,7,3,8,2,5]=>0111000
[1,7,3,6,4,8,2,5]=>0111000
[1,7,2,8,4,6,3,5]=>0111000
[1,7,5,8,2,6,3,4]=>0110100
[6,7,1,5,3,8,2,4]=>1110000
[6,7,1,8,2,5,3,4]=>1110000
[6,7,1,8,4,5,2,3]=>1101000
[6,7,5,8,1,4,2,3]=>1100100
[5,8,6,7,2,3,1,4]=>1100010
[6,7,2,3,1,8,4,5]=>1101000
[6,7,2,8,1,4,3,5]=>1110000
[6,7,3,4,1,8,2,5]=>1110000
[3,4,2,7,5,6,1,8]=>1100100
[2,7,5,8,1,4,3,6]=>1010100
[2,3,1,8,4,7,5,6]=>1001100
[2,3,1,8,6,7,4,5]=>1001010
[7,8,2,3,1,6,4,5]=>1101000
[2,8,1,4,3,7,5,6]=>1010100
[2,8,1,7,3,5,4,6]=>1011000
[4,5,1,7,3,8,2,6]=>1110000
[3,8,1,5,2,7,4,6]=>1101000
[3,4,1,8,6,7,2,5]=>1100010
[7,8,3,4,1,6,2,5]=>1110000
[3,4,2,5,1,8,6,7]=>1100010
[3,4,2,8,1,6,5,7]=>1100100
[2,5,4,1,6,3,8,7]=>1011001
[3,6,5,1,2,4,8,7]=>1000101
[5,2,3,6,4,1,8,7]=>1101001
[6,1,4,5,3,2,8,7]=>1110001
[5,6,7,8,1,4,3,2]=>1110000
[4,2,6,8,5,7,3,1]=>1110100
[2,1,5,8,7,6,3,4]=>1010011
[2,1,4,7,6,3,8,5]=>1010110
[6,3,7,1,5,2,8,4]=>1111000
[4,2,8,6,7,3,1,5]=>1110010
[7,4,3,8,2,1,5,6]=>1111000
[2,4,1,5,8,3,7,6]=>1010010
[4,7,5,8,1,6,3,2]=>1110100
[2,1,5,8,7,3,4,6]=>1010001
[8,5,7,3,6,1,4,2]=>1110100
[4,2,5,1,6,7,8,3]=>1110000
[7,2,3,4,8,5,6,1]=>1100100
[6,1,8,5,2,7,4,3]=>1111100
[2,1,7,4,5,8,6,3]=>1011010
[2,1,8,3,6,7,5,4]=>1011100
[6,8,7,2,5,3,1,4]=>1110001
[8,2,1,6,4,7,5,3]=>1111100
[7,8,2,5,6,1,4,3]=>1110000
[7,8,4,2,5,1,6,3]=>1111000
[6,1,2,3,7,5,8,4]=>1001100
[7,6,8,4,2,5,3,1]=>1111010
[8,5,7,1,6,3,2,4]=>1110100
[4,1,2,3,7,6,8,5]=>1000110
[3,2,4,1,8,5,6,7]=>1100100
[3,4,8,6,5,2,1,7]=>1100110
[4,1,6,3,5,8,7,2]=>1110001
[8,6,7,1,5,4,3,2]=>1111010
[2,1,6,5,8,4,7,3]=>1011100
[4,1,8,5,6,2,3,7]=>1100100
[2,6,4,8,7,3,5,1]=>1011001
[3,1,8,2,7,5,4,6]=>1101100
[8,2,3,1,7,4,6,5]=>1101100
[7,4,8,6,3,2,5,1]=>1111010
[5,8,4,7,2,1,3,6]=>1101000
[2,1,8,4,3,7,5,6]=>1011100
[6,3,8,2,4,5,7,1]=>1110000
[5,8,2,4,3,1,6,7]=>1110000
[7,3,5,8,1,4,2,6]=>1110000
[3,8,7,6,1,4,2,5]=>1100011
[5,1,8,3,6,7,2,4]=>1110000
[3,6,1,4,7,8,5,2]=>1100100
[1,6,8,4,7,5,2,3]=>0101100
[6,8,1,3,5,7,2,4]=>1100000
[7,6,1,4,3,8,2,5]=>1110010
[8,4,2,6,7,5,3,1]=>1111100
[7,4,1,6,8,2,5,3]=>1111000
[1,8,6,2,5,3,4,7]=>0110010
[4,7,1,2,5,3,8,6]=>1010010
[8,7,3,6,4,5,2,1]=>1111001
[5,7,8,6,2,1,4,3]=>1110010
[1,8,6,4,5,2,3,7]=>0101010
[1,4,7,2,6,8,3,5]=>0110000
[2,5,4,3,6,8,1,7]=>1011000
[3,8,5,4,6,2,1,7]=>1101100
[4,8,2,1,3,7,5,6]=>1100100
[1,8,3,2,5,6,7,4]=>0111000
[6,4,1,2,7,5,8,3]=>1011100
[4,3,7,8,5,1,6,2]=>1110100
[1,2,7,3,6,5,8,4]=>0011100
[2,8,7,6,3,4,1,5]=>1010011
[5,8,2,6,3,4,1,7]=>1110000
[4,1,7,5,8,6,2,3]=>1100110
[1,2,4,5,8,3,7,6]=>0010010
[4,8,1,5,2,3,7,6]=>1100010
[2,4,6,3,7,1,8,5]=>1010100
[6,5,8,7,1,3,4,2]=>1100101
[3,6,7,2,4,8,1,5]=>1100000
[1,5,2,7,4,3,8,6]=>0111010
[7,6,1,2,8,3,5,4]=>1011010
[6,7,8,1,5,2,4,3]=>1110000
[5,7,8,4,1,2,6,3]=>1011000
[4,7,8,5,6,1,3,2]=>1100100
[5,6,4,8,1,2,7,3]=>1011000
[6,5,4,1,2,3,8,7]=>1001101
[7,5,1,6,2,3,8,4]=>1101100
[4,5,6,7,8,1,3,2]=>1100000
[8,1,3,6,7,4,5,2]=>1101000
[4,2,6,7,3,1,8,5]=>1110100
[7,3,1,5,4,8,2,6]=>1111000
[4,5,3,2,8,1,6,7]=>1110000
[7,4,1,5,3,2,6,8]=>1111000
[8,1,5,4,3,2,6,7]=>1111000
[8,1,6,4,2,5,3,7]=>1111000
[6,5,3,1,2,7,4,8]=>1011100
[5,6,3,8,1,4,2,7]=>1110000
[4,6,3,8,2,1,5,7]=>1110000
[4,7,8,3,2,1,5,6]=>1110000
[5,7,8,3,1,4,2,6]=>1110000
[8,1,7,2,5,4,3,6]=>1111000
[8,1,7,2,4,5,6,3]=>1110000
[7,6,1,2,4,5,8,3]=>1010010
[4,7,8,2,3,1,6,5]=>1100100
[7,5,1,3,2,6,8,4]=>1101100
[8,1,6,3,2,5,7,4]=>1111000
[8,1,5,3,4,2,7,6]=>1110010
[5,4,2,3,1,6,8,7]=>1101001
[6,3,2,1,5,7,4,8]=>1111000
[8,1,4,3,5,6,2,7]=>1110000
[3,6,5,8,2,4,1,7]=>1100100
[5,3,7,2,4,8,1,6]=>1110000
[6,2,4,5,8,3,1,7]=>1110000
[4,8,1,2,5,6,3,7]=>1010000
[8,1,3,5,2,6,4,7]=>1101000
[5,2,1,6,3,8,4,7]=>1111000
[6,1,4,5,8,3,2,7]=>1110000
[6,5,4,3,8,2,1,7]=>1111100
[4,6,8,3,7,2,5,1]=>1110000
[1,4,3,6,2,7,8,5]=>0110100
[4,7,8,5,3,1,2,6]=>1010100
[8,5,4,7,6,2,1,3]=>1101110
[5,8,7,3,1,4,6,2]=>1110001
[8,5,7,4,3,6,1,2]=>1011100
[4,7,8,3,6,1,5,2]=>1110000
[8,4,6,1,7,3,5,2]=>1111000
[1,3,8,6,4,7,5,2]=>0101110
[7,6,2,1,4,3,8,5]=>1110110
[7,6,8,1,4,3,2,5]=>1110010
[1,5,7,3,2,6,8,4]=>0111000
[3,2,6,8,5,7,4,1]=>1101100
[7,5,2,3,1,6,8,4]=>1101100
[1,6,4,7,2,3,8,5]=>0101100
[3,1,7,5,2,8,4,6]=>1101100
[1,7,4,5,2,8,3,6]=>0111000
[3,2,6,8,7,4,5,1]=>1101001
[6,3,2,1,7,8,4,5]=>1111000
[5,7,3,8,2,1,4,6]=>1110000
[3,7,1,8,4,2,5,6]=>1101000
[4,2,1,3,7,5,8,6]=>1100110
[8,4,2,1,3,7,6,5]=>1101110
[8,4,3,7,6,2,1,5]=>1111010
[3,6,2,8,7,1,5,4]=>1101001
[7,3,2,8,1,6,5,4]=>1111100
[3,8,7,2,6,5,4,1]=>1101101
[4,2,7,8,6,1,5,3]=>1110010
[5,8,4,2,7,1,6,3]=>1111000
[8,5,3,1,7,2,6,4]=>1111100
[8,2,1,6,3,7,5,4]=>1111100
[1,4,6,8,2,7,5,3]=>0110100
[2,1,7,3,8,6,5,4]=>1011110
[8,2,1,7,6,5,4,3]=>1111110
[8,6,7,5,1,4,3,2]=>1110110
[6,4,7,3,2,1,8,5]=>1111100
[4,8,7,3,2,1,6,5]=>1110101
[6,5,3,7,2,1,4,8]=>1110100
[5,8,3,6,2,1,4,7]=>1110000
[6,4,3,7,2,1,8,5]=>1111100
[4,8,3,6,2,1,7,5]=>1110100
[6,3,7,8,2,1,4,5]=>1110000
[5,3,7,6,2,1,4,8]=>1110010
[3,8,7,6,2,1,4,5]=>1100011
[5,8,4,2,6,1,3,7]=>1101000
[4,8,7,2,5,1,3,6]=>1100001
[5,8,3,2,6,1,4,7]=>1110000
[4,8,3,2,5,1,7,6]=>1110010
[4,3,7,2,5,1,8,6]=>1110010
[6,4,2,7,5,1,3,8]=>1101100
[5,4,2,6,7,1,3,8]=>1101000
[6,2,7,8,5,1,3,4]=>1100100
[2,8,7,6,5,1,3,4]=>1000111
[6,4,7,3,1,5,8,2]=>1111000
[5,4,7,3,1,8,6,2]=>1111010
[4,8,7,3,1,5,6,2]=>1110001
[6,5,3,7,1,4,8,2]=>1110100
[5,8,3,6,1,4,7,2]=>1110000
[6,4,3,7,1,5,8,2]=>1111000
[4,8,3,6,1,5,7,2]=>1110000
[5,3,7,6,1,4,8,2]=>1110010
[4,3,7,6,1,5,8,2]=>1110010
[3,8,7,6,1,4,5,2]=>1100011
[5,8,4,2,1,7,3,6]=>1111000
[6,4,7,2,1,5,3,8]=>1111000
[5,8,3,2,1,4,7,6]=>1110010
[6,3,7,2,1,4,5,8]=>1110000
[6,5,2,7,1,4,3,8]=>1110100
[5,8,2,6,1,4,3,7]=>1110000
[6,4,2,7,1,5,3,8]=>1111000
[2,8,7,6,1,4,3,5]=>1010011
[6,5,4,1,8,7,3,2]=>1111101
[5,8,4,1,6,7,3,2]=>1111000
[6,4,7,1,5,8,3,2]=>1111000
[4,8,7,1,5,6,3,2]=>1110001
[6,5,3,1,8,4,7,2]=>1111100
[5,8,3,1,6,4,7,2]=>1111000
[6,4,3,1,5,8,7,2]=>1111001
[5,8,2,1,6,4,3,7]=>1111000
[6,4,2,1,5,8,3,7]=>1111000
[3,8,2,1,5,4,6,7]=>1101000
[6,2,7,1,5,4,3,8]=>1111000
[4,2,7,1,5,6,3,8]=>1110000
[3,2,7,1,5,4,6,8]=>1101000
[2,8,7,1,5,4,3,6]=>1011001
[6,5,1,7,8,4,3,2]=>1111100
[5,4,1,6,7,8,3,2]=>1111000
[4,3,1,6,5,7,8,2]=>1110100
[5,2,1,6,7,4,3,8]=>1111000
[4,2,1,6,5,7,3,8]=>1110100
[2,8,1,6,5,4,3,7]=>1011100
[6,1,7,8,5,4,3,2]=>1111100
[5,1,7,6,8,4,3,2]=>1111010
[4,1,7,6,5,8,3,2]=>1110110
[4,5,8,1,7,2,3,6]=>1100000
[4,5,8,1,2,6,3,7]=>1010000
[8,1,3,5,7,2,4,6]=>1100000
[3,6,8,1,7,2,4,5]=>1100000
[3,4,5,6,8,1,7,2]=>1100000
[8,2,3,5,6,7,1,4]=>1100000
[8,1,2,3,5,4,6,7]=>1001000
[8,7,2,1,6,3,4,5]=>1110001
[8,7,2,1,3,5,4,6]=>1101001
[8,6,4,1,7,5,3,2]=>1111110
[2,3,6,7,8,1,5,4]=>1001000
[7,4,2,6,8,5,1,3]=>1101100
[7,3,2,5,8,6,1,4]=>1110010
[7,3,1,8,6,2,4,5]=>1110010
[3,1,7,2,5,4,8,6]=>1101010
[7,1,8,2,5,3,6,4]=>1111000
[7,3,8,4,5,1,6,2]=>1111000
[8,3,7,4,6,1,5,2]=>1111000
[8,2,7,1,6,4,5,3]=>1111000
[8,1,7,5,4,2,3,6]=>1101100
[8,1,2,6,5,4,3,7]=>1011100
[8,1,7,6,3,2,4,5]=>1110010
[8,2,7,5,6,1,4,3]=>1110100
[3,6,8,1,7,5,4,2]=>1101100
[8,2,6,7,5,4,1,3]=>1101100
[8,6,7,2,3,1,5,4]=>1101010
[2,7,8,6,3,1,5,4]=>1011010
[7,3,1,8,6,5,4,2]=>1111110
[8,1,7,6,5,4,3,2]=>1111110
[2,1,8,6,3,7,4,5]=>1011010
[8,6,1,5,2,7,4,3]=>1111010
[8,5,1,7,4,2,6,3]=>1111100
[2,1,7,8,3,6,5,4]=>1011100
[2,1,4,8,5,7,3,6]=>1010100
[7,8,1,5,2,6,3,4]=>1110000
[6,4,1,5,2,3,8,7]=>1101001
[4,3,7,8,5,2,1,6]=>1110100
[5,3,7,4,6,8,1,2]=>1011000
[5,8,3,7,6,2,1,4]=>1110010
[4,2,6,3,8,5,1,7]=>1110100
[5,8,2,1,7,6,4,3]=>1111010
[8,3,2,4,1,7,5,6]=>1110100
[6,3,4,2,1,7,8,5]=>1110100
[7,8,3,1,5,4,6,2]=>1111000
[7,2,8,1,4,6,5,3]=>1110100
[5,7,1,8,3,6,2,4]=>1110000
[6,8,1,4,5,3,2,7]=>1110000
[8,2,6,1,4,7,3,5]=>1110000
[4,2,1,3,6,7,8,5]=>1100100
[2,3,4,1,8,6,5,7]=>1000110
[6,3,5,4,1,2,8,7]=>1011001
[8,7,3,6,5,1,4,2]=>1110101
[3,4,7,2,8,1,5,6]=>1100000
[4,2,3,5,8,1,6,7]=>1100000
[3,8,4,7,1,6,5,2]=>1101100
[3,2,4,6,1,5,8,7]=>1100001
[6,8,5,4,3,7,2,1]=>1111100
[5,8,4,3,2,1,7,6]=>1111010
[6,5,4,3,1,8,7,2]=>1111101
[8,7,5,4,3,1,6,2]=>1111101
[3,4,6,2,8,5,1,7]=>1100100
[3,4,6,7,1,8,5,2]=>1100100
[3,4,6,8,1,5,2,7]=>1100000
[3,4,7,2,8,5,6,1]=>1100100
[3,5,2,6,8,4,1,7]=>1101000
[3,5,2,7,4,8,6,1]=>1101010
[3,5,2,7,8,4,6,1]=>1101000
[3,5,6,2,7,8,1,4]=>1100000
[3,5,6,2,8,4,1,7]=>1101000
[3,5,6,8,4,1,2,7]=>1001000
[3,5,7,2,4,8,6,1]=>1100010
[3,5,7,2,8,4,6,1]=>1101000
[3,5,7,8,4,1,6,2]=>1101000
[3,5,8,2,4,1,6,7]=>1100000
[3,6,2,1,7,8,5,4]=>1101100
[3,6,2,1,8,5,4,7]=>1101100
[3,6,2,7,4,8,5,1]=>1101100
[3,6,2,7,8,5,4,1]=>1101100
[3,6,8,2,4,5,1,7]=>1100000
[3,7,2,1,4,8,6,5]=>1100110
[3,7,2,8,4,5,6,1]=>1101000
[3,8,2,1,4,5,6,7]=>1100000
[4,1,5,7,3,8,6,2]=>1110010
[4,1,5,7,8,2,6,3]=>1110000
[4,1,5,8,3,2,6,7]=>1110000
[4,1,6,3,7,8,5,2]=>1110100
[4,1,6,3,8,5,2,7]=>1110100
[4,1,6,7,3,8,5,2]=>1110100
[4,1,6,8,3,5,2,7]=>1110000
[4,1,7,3,8,5,6,2]=>1110100
[4,1,8,3,2,5,6,7]=>1110000
[4,5,2,7,3,8,6,1]=>1110010
[4,5,7,3,2,8,6,1]=>1110010
[4,5,8,3,2,1,6,7]=>1110000
[4,6,2,3,7,8,5,1]=>1100100
[4,6,2,3,8,5,1,7]=>1100100
[4,6,2,8,3,5,1,7]=>1110000
[4,7,2,8,3,5,6,1]=>1110000
[4,7,8,3,2,5,6,1]=>1110000
[4,8,2,3,1,5,6,7]=>1100000
[5,1,2,6,8,4,3,7]=>1011000
[5,1,2,8,4,3,6,7]=>1011000
[5,1,6,3,7,8,2,4]=>1110000
[5,1,6,3,8,4,2,7]=>1111000
[5,1,6,7,4,8,2,3]=>1101000
[5,6,2,3,8,4,1,7]=>1101000
[5,6,2,7,4,8,1,3]=>1101000
[5,6,2,7,8,4,1,3]=>1101000
[5,6,8,3,4,2,1,7]=>1110000
[5,7,8,3,4,2,6,1]=>1110000
[6,1,2,3,7,8,5,4]=>1001100
[6,1,2,3,8,5,4,7]=>1001100
[6,1,2,7,8,5,4,3]=>1011100
[6,1,7,8,4,5,3,2]=>1111000
[6,7,2,8,4,5,3,1]=>1111000
[7,1,2,3,4,8,6,5]=>1000110
[7,1,2,3,8,5,6,4]=>1001100
[7,1,8,3,4,5,6,2]=>1110000
[2,4,6,1,8,5,7,3]=>1010100
[6,4,1,8,2,3,7,5]=>1101100
[5,8,1,2,4,3,7,6]=>1010010
[5,8,1,6,2,4,3,7]=>1110000
[1,3,5,7,2,6,4,8]=>0101000
[3,5,8,6,1,2,4,7]=>1000010
[3,5,1,8,2,4,7,6]=>1100010
[3,1,6,8,2,4,7,5]=>1100100
[2,3,5,6,8,1,7,4]=>1001000
[5,6,4,8,2,1,7,3]=>1111000
[7,1,8,6,3,4,5,2]=>1110010
[7,6,5,2,4,8,1,3]=>1100110
[6,7,4,5,2,1,8,3]=>1111000
[5,1,7,8,6,4,3,2]=>1111010
[2,5,7,8,6,3,1,4]=>1010010
[7,1,8,6,3,2,4,5]=>1110010
[7,8,1,6,4,2,3,5]=>1101000
[2,4,8,1,5,6,7,3]=>1010000
[8,4,1,2,5,6,3,7]=>1011000
[8,3,1,6,5,2,4,7]=>1110100
[2,5,3,8,7,6,1,4]=>1010011
[5,8,7,4,2,6,1,3]=>1101001
[5,1,8,4,7,6,3,2]=>1111010
[7,3,2,6,5,1,8,4]=>1111100
[8,2,3,6,5,1,7,4]=>1101100
[4,8,6,5,7,3,2,1]=>1110110
[4,8,5,6,7,3,2,1]=>1110100
[3,8,7,4,5,6,2,1]=>1101001
[2,8,7,6,3,4,5,1]=>1010011
[1,8,7,6,5,2,3,4]=>0100111
[7,2,8,6,5,4,1,3]=>1101110
[6,3,2,8,5,1,7,4]=>1111100
[8,4,7,2,5,6,3,1]=>1111000
[6,8,5,4,3,1,7,2]=>1111100
[5,8,6,4,1,3,7,2]=>1101010
[3,6,1,8,5,2,7,4]=>1101100
[3,4,1,2,8,6,7,5]=>1000110
[6,8,3,5,4,1,7,2]=>1111000
[7,6,3,8,5,2,1,4]=>1110110
[5,8,7,4,1,6,3,2]=>1111001
[4,2,3,1,7,8,5,6]=>1100100
[8,6,3,4,7,2,5,1]=>1110010
[6,8,3,4,5,1,7,2]=>1110000
[5,2,8,4,1,6,7,3]=>1111000
[4,1,3,6,8,2,5,7]=>1100000
[1,6,3,2,5,8,4,7]=>0111000
[8,3,2,1,5,4,7,6]=>1111010
[2,5,1,8,4,3,7,6]=>1011010
[5,3,6,2,4,8,1,7]=>1110000
[1,6,2,4,5,8,3,7]=>0110000
[5,3,2,1,6,8,4,7]=>1111000
[2,6,5,8,1,3,4,7]=>1000100
[4,3,1,6,5,8,2,7]=>1110100
[8,3,4,1,5,2,7,6]=>1110010
[3,4,6,5,7,1,8,2]=>1100100
[8,2,6,4,1,7,3,5]=>1111000
[5,4,6,8,1,2,7,3]=>1011000
[3,4,7,8,6,2,5,1]=>1100010
[7,5,8,2,4,6,1,3]=>1100100
[8,2,7,4,6,1,3,5]=>1101000
[4,7,3,2,8,1,6,5]=>1110100
[3,8,1,7,2,5,6,4]=>1101000
[8,3,2,5,7,6,1,4]=>1110010
[2,8,6,1,5,7,3,4]=>1010010
[1,2,8,3,5,6,7,4]=>0011000
[4,2,3,7,1,8,6,5]=>1100110
[3,2,6,4,8,1,7,5]=>1101100
[8,2,1,6,7,3,4,5]=>1110000
[2,7,8,5,4,1,3,6]=>1001100
[1,7,5,3,8,4,2,6]=>0111100
[4,7,5,3,1,2,8,6]=>1010110
[5,6,7,3,8,4,2,1]=>1111000
[5,7,3,2,4,1,8,6]=>1110010
[8,4,1,3,7,2,5,6]=>1101000
[2,8,4,7,1,3,5,6]=>1001000
[3,5,2,8,6,1,7,4]=>1101010
[1,7,6,3,2,5,8,4]=>0111010
[3,8,1,5,6,2,7,4]=>1101000
[4,3,5,6,7,1,8,2]=>1110000
[7,1,5,2,8,6,4,3]=>1111010
[6,5,4,8,7,2,1,3]=>1101101
[1,8,5,3,6,2,7,4]=>0111100
[6,5,8,7,2,1,3,4]=>1100101
[3,6,2,1,7,5,8,4]=>1101100
[4,7,2,6,5,8,1,3]=>1100100
[6,8,1,4,2,7,3,5]=>1110000
[6,3,4,7,1,8,2,5]=>1110000
[3,4,7,8,2,5,6,1]=>1100000
[1,8,2,4,5,6,7,3]=>0110000
[2,1,4,6,8,5,7,3]=>1010100
[3,2,5,7,6,1,8,4]=>1101010
[4,3,5,6,1,8,7,2]=>1110001
[3,1,4,6,5,7,8,2]=>1100100
[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]=>0001100
[1,2,3,8,6,5,4,7]=>0001110
[1,8,3,4,2,5,6,7]=>0110000
[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]=>1111110
[8,4,7,6,5,3,2,1]=>1111110
[8,4,7,5,6,3,2,1]=>1111100
[8,5,7,4,6,3,2,1]=>1111100
[8,7,6,3,5,4,2,1]=>1111011
[8,6,7,3,5,4,2,1]=>1111010
[8,5,7,3,6,4,2,1]=>1111100
[8,4,7,3,6,5,2,1]=>1111100
[8,1,7,4,6,5,3,2]=>1111100
[8,3,7,2,6,5,4,1]=>1111100
[8,5,7,2,6,4,3,1]=>1111100
[8,6,7,2,5,4,3,1]=>1111010
[8,7,6,2,5,4,3,1]=>1111011
[8,4,7,1,6,5,3,2]=>1111100
[8,3,7,1,6,5,4,2]=>1111100
[8,2,7,1,6,5,4,3]=>1111100
[8,1,7,2,6,5,4,3]=>1111100
[8,1,7,2,6,4,5,3]=>1111000
[8,3,7,1,6,4,5,2]=>1111000
[8,4,7,1,6,3,5,2]=>1111000
[8,5,7,1,6,3,4,2]=>1110100
[8,6,7,1,5,3,4,2]=>1110010
[8,7,6,2,5,3,4,1]=>1110011
[8,6,7,2,5,3,4,1]=>1110010
[8,5,7,2,6,3,4,1]=>1110100
[8,4,7,2,6,3,5,1]=>1111000
[8,3,7,2,6,4,5,1]=>1111000
[8,2,7,3,6,4,5,1]=>1111000
[8,1,7,3,6,4,5,2]=>1111000
[8,1,7,4,6,3,5,2]=>1111000
[8,2,7,4,6,3,5,1]=>1111000
[8,3,7,4,6,2,5,1]=>1111000
[8,5,7,3,6,2,4,1]=>1110100
[8,6,7,3,5,2,4,1]=>1110010
[8,5,7,4,6,2,3,1]=>1101100
[8,4,7,5,6,2,3,1]=>1101100
[8,3,7,5,6,2,4,1]=>1110100
[8,2,7,5,6,3,4,1]=>1110100
[8,1,7,5,6,3,4,2]=>1110100
[8,3,7,6,5,2,4,1]=>1110110
[8,4,7,6,5,2,3,1]=>1101110
[8,5,7,6,4,2,3,1]=>1101110
[8,7,6,5,4,1,3,2]=>1101111
[8,6,7,5,4,1,3,2]=>1101110
[8,5,7,6,4,1,3,2]=>1101110
[8,3,7,6,5,1,4,2]=>1110110
[8,1,7,5,6,2,4,3]=>1110100
[8,3,7,5,6,1,4,2]=>1110100
[8,4,7,5,6,1,3,2]=>1101100
[8,6,7,4,5,1,3,2]=>1101010
[8,7,6,4,5,1,3,2]=>1101011
[8,6,7,3,5,1,4,2]=>1110010
[8,4,7,3,6,1,5,2]=>1111000
[8,2,7,4,6,1,5,3]=>1111000
[8,1,7,4,6,2,5,3]=>1111000
[8,1,7,3,6,2,5,4]=>1111000
[8,2,7,3,6,1,5,4]=>1111000
[8,3,7,2,6,1,5,4]=>1111000
[8,4,7,2,6,1,5,3]=>1111000
[8,5,7,2,6,1,4,3]=>1110100
[8,6,7,2,5,1,4,3]=>1110010
[8,7,6,2,5,1,4,3]=>1110011
[8,7,6,1,5,2,4,3]=>1110011
[8,6,7,1,5,2,4,3]=>1110010
[8,5,7,1,6,2,4,3]=>1110100
[8,4,7,1,6,2,5,3]=>1111000
[8,3,7,1,6,2,5,4]=>1111000
[8,2,7,1,6,3,5,4]=>1111000
[4,6,7,3,8,5,2,1]=>1110100
[1,4,8,2,6,3,5,7]=>0110000
[1,6,2,4,8,3,5,7]=>0110000
[1,5,2,3,8,4,7,6]=>0101010
[1,7,2,3,5,4,8,6]=>0101010
[1,8,2,3,5,4,6,7]=>0101000
[1,7,8,2,4,5,3,6]=>0110000
[1,2,8,3,6,4,5,7]=>0011000
[1,5,8,2,3,7,4,6]=>0101000
[1,6,8,2,3,5,4,7]=>0101000
[5,7,2,6,3,8,1,4]=>1110000
[5,7,1,6,8,4,3,2]=>1111000
[4,8,1,2,5,7,3,6]=>1010000
[1,7,8,4,6,2,5,3]=>0111000
[3,7,4,8,5,1,6,2]=>1101100
[3,7,5,4,8,2,1,6]=>1101100
[4,7,1,3,2,8,6,5]=>1100110
[2,7,3,1,5,8,4,6]=>1011000
[2,7,5,8,6,4,1,3]=>1001110
[3,8,7,1,6,4,5,2]=>1101001
[3,4,2,7,8,1,6,5]=>1100100
[4,3,2,1,5,8,6,7]=>1110010
[4,1,3,7,5,6,8,2]=>1100100
[3,4,6,1,5,8,2,7]=>1100000
[6,5,8,7,1,4,2,3]=>1100101
[4,1,7,3,8,5,2,6]=>1110100
[6,1,7,3,5,4,8,2]=>1111000
[1,4,7,2,8,5,3,6]=>0110100
[5,6,8,7,2,4,1,3]=>1100001
[6,8,5,7,1,2,4,3]=>1010100
[7,1,3,4,2,8,5,6]=>1100100
[7,6,1,4,3,5,8,2]=>1110010
[3,5,4,1,6,7,8,2]=>1101000
[2,5,3,4,8,6,1,7]=>1010010
[2,4,8,3,6,1,7,5]=>1010100
[8,2,4,3,7,5,6,1]=>1110100
[6,8,2,1,5,7,3,4]=>1110000
[7,2,8,4,1,6,3,5]=>1111000
[1,2,4,8,6,5,3,7]=>0010110
[7,1,5,6,8,4,3,2]=>1111000
[7,3,5,6,1,4,8,2]=>1110000
[3,7,6,5,1,4,8,2]=>1100110
[2,7,6,5,3,8,1,4]=>1010110
[2,7,8,1,4,6,3,5]=>1010000
[4,8,2,5,7,1,6,3]=>1110000
[4,1,6,8,5,3,7,2]=>1110100
[5,2,6,4,8,3,1,7]=>1111000
[1,2,6,3,4,8,7,5]=>0010101
[5,3,6,1,4,7,8,2]=>1110000
[6,7,1,3,4,5,8,2]=>1100000
[1,7,3,2,4,8,5,6]=>0110100
[6,1,4,2,8,3,5,7]=>1110000
[5,8,6,7,2,1,4,3]=>1110010
[7,4,1,5,8,2,3,6]=>1101000
[6,3,4,2,8,7,5,1]=>1110101
[4,3,8,7,5,2,6,1]=>1110101
[6,8,7,4,2,3,5,1]=>1101001
[8,6,1,3,5,4,2,7]=>1101010
[2,7,6,3,4,5,8,1]=>1010010
[5,3,8,6,1,2,4,7]=>1010010
[2,4,8,7,3,5,6,1]=>1010001
[2,5,3,6,8,7,4,1]=>1011001
[3,8,7,2,6,4,5,1]=>1101001
[4,5,8,7,2,6,3,1]=>1110001
[8,5,2,7,1,4,3,6]=>1110100
[4,5,2,8,3,7,6,1]=>1110010
[8,2,3,7,6,4,5,1]=>1101010
[3,7,5,8,2,6,1,4]=>1100100
[1,6,7,4,8,2,3,5]=>0101000
[8,2,1,3,5,6,7,4]=>1101000
[4,1,3,8,2,6,7,5]=>1100100
[3,6,1,4,7,2,8,5]=>1100100
[6,2,7,4,5,8,1,3]=>1101000
[2,1,8,4,5,7,3,6]=>1011000
[1,8,5,7,3,2,4,6]=>0110100
[3,2,1,6,4,8,5,7]=>1101100
[2,1,8,5,4,3,6,7]=>1011100
[2,7,4,1,5,3,8,6]=>1011010
[7,4,8,6,2,3,1,5]=>1101010
[7,3,2,4,8,6,1,5]=>1110010
[7,1,3,2,8,5,4,6]=>1101100
[5,1,7,4,2,3,8,6]=>1101010
[1,3,4,8,6,5,2,7]=>0100110
[4,1,8,6,5,3,2,7]=>1110110
[4,8,5,3,6,2,7,1]=>1110100
[5,7,4,3,6,2,8,1]=>1111000
[6,7,5,1,2,8,3,4]=>1010100
[7,5,1,4,2,6,8,3]=>1110100
[5,2,6,8,3,4,7,1]=>1110000
[7,6,2,4,5,8,3,1]=>1110010
[2,6,3,8,4,7,5,1]=>1011100
[6,2,7,5,8,3,1,4]=>1110100
[2,1,5,6,8,3,7,4]=>1011000
[1,2,7,4,8,3,6,5]=>0011100
[1,6,8,3,2,7,4,5]=>0111000
[1,6,7,5,2,8,3,4]=>0110100
[7,5,1,2,8,4,6,3]=>1011100
[5,8,2,7,4,3,6,1]=>1111000
[5,7,3,8,2,4,6,1]=>1110000
[6,4,5,8,2,7,3,1]=>1111000
[5,7,3,6,4,8,2,1]=>1111000
[1,5,6,4,8,2,7,3]=>0111000
[3,6,2,4,7,1,8,5]=>1100100
[4,2,8,5,1,6,7,3]=>1110100
[2,1,6,4,8,5,3,7]=>1011100
[1,2,8,3,7,5,4,6]=>0011100
[1,6,3,8,7,4,2,5]=>0111001
[4,3,8,1,2,6,7,5]=>1010100
[6,4,5,8,1,2,7,3]=>1011000
[7,4,6,5,2,1,8,3]=>1111100
[5,1,8,6,7,4,3,2]=>1111010
[3,8,5,7,1,4,2,6]=>1100100
[4,7,2,5,1,3,8,6]=>1100010
[5,1,7,4,8,6,3,2]=>1111010
[3,6,5,2,1,8,7,4]=>1101101
[5,2,8,4,7,3,1,6]=>1111000
[5,2,7,4,1,3,6,8]=>1101000
[5,2,6,4,1,8,7,3]=>1111001
[6,3,2,1,4,8,7,5]=>1110101
[3,1,4,6,2,8,7,5]=>1100101
[6,3,5,1,7,4,2,8]=>1111000
[5,4,7,6,3,8,1,2]=>1011010
[4,6,3,7,5,8,1,2]=>1010100
[5,7,4,3,8,1,2,6]=>1011000
[1,5,7,4,8,6,3,2]=>0111010
[1,8,2,7,6,5,4,3]=>0111110
[3,8,1,6,7,5,4,2]=>1101100
[3,7,2,6,8,5,1,4]=>1100100
[8,2,4,3,6,1,5,7]=>1110000
[1,7,8,5,4,3,6,2]=>0111100
[7,3,8,1,4,2,6,5]=>1110100
[1,8,4,5,3,2,6,7]=>0111000
[3,8,7,4,2,6,1,5]=>1101001
[3,7,8,1,2,6,5,4]=>1001100
[3,5,6,2,7,1,4,8]=>1100000
[3,7,1,6,8,2,4,5]=>1100000
[8,1,7,6,2,4,3,5]=>1110010
[1,6,4,5,7,2,3,8]=>0101000
[8,3,6,1,7,2,4,5]=>1110000
[1,7,5,3,6,8,4,2]=>0111100
[7,3,5,2,1,8,4,6]=>1111000
[7,4,1,6,5,8,3,2]=>1111100
[6,4,2,8,7,5,1,3]=>1101101
[4,2,1,5,8,7,3,6]=>1110001
[1,5,3,6,8,7,4,2]=>0111001
[3,5,4,6,1,8,2,7]=>1101000
[3,1,5,7,6,8,2,4]=>1100010
[6,4,5,7,2,8,1,3]=>1101000
[5,3,6,4,2,8,1,7]=>1111000
[4,1,5,3,8,2,7,6]=>1110010
[2,6,3,5,4,8,1,7]=>1011000
[3,7,4,5,6,8,1,2]=>1001000
[2,5,7,3,6,8,1,4]=>1010000
[7,6,4,5,2,8,1,3]=>1101010
[5,4,3,1,8,2,7,6]=>1111010
[8,2,6,4,7,3,1,5]=>1111000
[1,2,8,3,5,4,6,7]=>0011000
[1,7,8,4,3,5,6,2]=>0111000
[3,1,6,8,4,5,7,2]=>1101000
[1,4,5,8,3,6,7,2]=>0110000
[2,5,7,1,8,3,6,4]=>1011000
[6,2,7,1,8,4,5,3]=>1111000
[4,7,1,3,8,5,6,2]=>1100100
[3,7,2,1,8,4,5,6]=>1101000
[2,1,5,8,3,6,7,4]=>1011000
[4,2,7,1,8,3,6,5]=>1110100
[4,3,1,6,8,2,7,5]=>1110100
[5,3,4,6,8,2,7,1]=>1110000
[3,5,1,6,8,2,7,4]=>1101000
[5,1,8,7,4,2,3,6]=>1101001
[5,8,3,2,6,4,1,7]=>1111000
[6,8,2,4,7,5,1,3]=>1100100
[7,3,8,2,6,4,1,5]=>1111000
[3,8,7,4,5,6,1,2]=>1001001
[2,7,6,3,5,4,1,8]=>1011010
[3,8,7,4,6,2,5,1]=>1101001
[5,8,3,7,6,2,4,1]=>1110010
[8,7,2,5,4,3,1,6]=>1111001
[6,8,3,2,5,4,7,1]=>1111000
[5,8,7,4,3,6,2,1]=>1111001
[5,8,6,4,3,7,1,2]=>1011010
[6,5,8,4,3,1,7,2]=>1111100
[2,6,4,7,1,5,3,8]=>1011000
[2,5,6,8,4,3,7,1]=>1011000
[5,3,8,1,7,6,4,2]=>1111010
[5,4,8,7,1,6,3,2]=>1111001
[4,8,6,7,5,3,1,2]=>1010110
[4,8,6,5,7,2,1,3]=>1100110
[4,8,5,6,7,1,2,3]=>1000100
[5,4,8,6,1,7,2,3]=>1101010
[5,3,8,1,6,7,2,4]=>1110000
[5,2,1,8,6,7,3,4]=>1110010
[6,2,1,5,8,3,7,4]=>1111000
[6,5,4,8,2,1,7,3]=>1111100
[5,8,4,7,2,6,3,1]=>1111000
[5,8,3,2,7,6,4,1]=>1111010
[5,8,3,2,6,7,1,4]=>1110000
[6,5,3,2,8,1,7,4]=>1111100
[6,4,3,2,1,8,7,5]=>1111101
[6,3,4,1,2,8,7,5]=>1010101
[6,2,1,4,3,8,7,5]=>1110101
[5,2,1,4,3,6,7,8]=>1110000
[4,6,3,2,5,1,7,8]=>1110000
[3,5,7,4,2,6,1,8]=>1101000
[4,3,6,1,5,2,7,8]=>1110000
[4,2,1,6,5,3,7,8]=>1110100
[4,2,1,5,7,6,3,8]=>1110010
[3,5,4,7,1,6,2,8]=>1101000
[3,4,7,5,6,1,2,8]=>1000100
[3,4,5,8,6,7,1,2]=>1000010
[3,4,6,5,8,1,7,2]=>1100100
[4,3,5,1,6,8,7,2]=>1110001
[2,1,5,3,8,4,7,6]=>1011010
[3,1,8,2,5,4,7,6]=>1101010
[8,1,3,2,6,4,7,5]=>1101100
[3,1,8,2,6,4,7,5]=>1101100
[2,1,8,3,6,4,7,5]=>1011100
[2,1,6,3,8,4,7,5]=>1011100
[2,1,7,3,5,4,8,6]=>1011010
[2,1,7,3,6,4,8,5]=>1011100
[2,1,7,3,8,4,6,5]=>1011100
[8,1,4,2,7,3,6,5]=>1110100
[4,1,7,2,8,3,6,5]=>1110100
[3,1,7,2,8,4,6,5]=>1101100
[3,1,6,2,5,4,8,7]=>1101001
[7,1,3,2,5,4,8,6]=>1101010
[7,1,3,2,6,4,8,5]=>1101100
[7,1,8,2,4,3,6,5]=>1110100
[7,1,5,2,8,3,6,4]=>1111000
[6,1,4,2,5,3,8,7]=>1110001
[4,1,6,2,5,3,8,7]=>1110001
[4,1,7,2,5,3,8,6]=>1110010
[4,1,7,2,6,3,8,5]=>1110100
[5,1,7,2,6,3,8,4]=>1111000
[5,1,7,2,8,3,6,4]=>1111000
[8,1,5,2,7,3,6,4]=>1111000
[8,1,5,2,6,3,7,4]=>1111000
[5,1,8,2,6,3,7,4]=>1111000
[5,1,6,2,8,3,7,4]=>1111000
[3,1,6,2,8,4,7,5]=>1101100
[4,1,8,2,6,3,7,5]=>1110100
[8,1,4,2,6,3,7,5]=>1110100
[8,1,4,2,5,3,7,6]=>1110010
[4,1,8,2,5,3,7,6]=>1110010
[4,1,5,2,8,3,7,6]=>1110010
[3,1,5,2,8,4,7,6]=>1101010
[3,1,4,2,8,5,7,6]=>1100110
[4,1,3,2,7,5,8,6]=>1100110
[5,1,4,2,8,3,7,6]=>1110010
[6,1,3,2,8,4,7,5]=>1101100
[6,1,3,2,7,4,8,5]=>1101100
[5,1,3,2,7,4,8,6]=>1101010
[5,1,3,2,6,4,8,7]=>1101001
[5,1,4,2,6,3,8,7]=>1110001
[6,1,4,2,7,3,8,5]=>1110100
[6,1,5,2,7,3,8,4]=>1111000
[6,1,7,2,8,3,5,4]=>1111000
[5,1,6,2,4,3,8,7]=>1110001
[7,8,3,1,2,5,6,4]=>1011000
[7,8,1,3,2,4,6,5]=>1100100
[2,5,3,6,1,8,7,4]=>1011001
[6,2,8,1,3,5,4,7]=>1101000
[6,2,8,3,1,7,4,5]=>1111000
[3,2,5,7,1,8,4,6]=>1101000
[3,5,2,8,1,7,4,6]=>1101000
[4,3,1,2,7,8,6,5]=>1010110
[5,3,4,7,8,6,1,2]=>1010010
[4,1,3,2,6,8,7,5]=>1100101
[5,1,3,7,2,6,8,4]=>1101000
[5,2,4,7,8,1,6,3]=>1110000
[2,5,4,6,8,1,7,3]=>1011000
[4,2,5,7,6,1,8,3]=>1110010
[6,1,8,3,2,4,7,5]=>1110100
[4,3,5,7,6,8,1,2]=>1010010
[4,2,1,3,7,6,8,5]=>1100110
[2,4,3,1,8,5,7,6]=>1010110
[5,2,1,8,3,6,4,7]=>1111000
[3,2,4,1,8,6,5,7]=>1100110
[3,4,2,1,8,7,5,6]=>1100101
[7,6,4,3,2,1,8,5]=>1111110
[7,6,5,8,2,1,4,3]=>1110110
[7,6,8,3,2,1,5,4]=>1111010
[7,8,4,3,2,1,6,5]=>1111100
[8,5,4,3,2,1,7,6]=>1111110
[7,6,3,8,2,1,5,4]=>1111010
[7,6,5,8,4,1,3,2]=>1101110
[7,4,8,3,2,1,6,5]=>1111100
[7,6,8,5,2,1,4,3]=>1110110
[4,8,6,1,7,5,2,3]=>1100110
[4,8,7,2,6,5,1,3]=>1100101
[4,7,8,2,6,1,5,3]=>1110000
[4,6,8,2,7,1,3,5]=>1100000
[8,6,4,2,7,5,3,1]=>1111110
[8,4,7,3,6,5,1,2]=>1011100
[6,4,7,1,8,3,2,5]=>1111000
[7,4,8,3,6,1,5,2]=>1111000
[7,8,4,3,6,2,5,1]=>1111000
[6,8,4,3,7,2,1,5]=>1111000
[6,7,4,2,8,3,1,5]=>1111000
[2,8,7,6,5,1,4,3]=>1010111
[7,3,2,5,4,1,6,8]=>1111000
[7,3,5,4,2,1,6,8]=>1111000
[2,7,6,3,1,5,8,4]=>1011010
[1,8,4,3,6,5,2,7]=>0111100
[1,8,4,6,5,3,2,7]=>0111100
[7,1,4,2,6,3,5,8]=>1110000
[7,3,4,1,5,6,2,8]=>1110000
[7,3,2,5,1,6,4,8]=>1111000
[7,4,1,3,5,2,6,8]=>1101000
[7,3,1,2,4,6,5,8]=>1010100
[3,6,2,1,4,8,5,7]=>1100100
[2,3,6,1,4,8,7,5]=>1000101
[3,6,7,4,1,5,8,2]=>1101000
[3,1,2,8,6,5,4,7]=>1001110
[5,4,8,6,1,2,3,7]=>1001010
[5,6,8,2,4,1,3,7]=>1100000
[5,6,8,7,4,3,1,2]=>1011001
[6,4,8,5,3,1,7,2]=>1111100
[5,7,8,6,1,3,2,4]=>1100010
[2,4,8,1,6,3,7,5]=>1010100
[1,8,4,5,2,6,7,3]=>0111000
[3,1,4,6,5,8,7,2]=>1100101
[3,7,5,4,6,8,2,1]=>1101100
[5,3,2,1,7,6,8,4]=>1111010
[5,6,1,4,7,2,8,3]=>1110000
[4,3,1,7,5,6,8,2]=>1110100
[1,8,4,3,6,2,7,5]=>0111100
[5,6,7,3,2,8,1,4]=>1110000
[5,3,2,1,4,8,6,7]=>1110010
[3,4,7,8,1,2,6,5]=>1000100
[3,6,7,8,1,4,5,2]=>1100000
[2,3,6,8,5,1,4,7]=>1000100
[3,1,6,4,8,2,5,7]=>1101000
[7,3,2,6,8,5,1,4]=>1110100
[7,3,5,8,4,6,1,2]=>1011000
[7,5,2,8,4,1,6,3]=>1111100
[1,8,4,2,3,5,7,6]=>0101010
[6,3,4,8,2,5,7,1]=>1110000
[7,5,4,8,3,6,2,1]=>1111100
[7,3,2,5,8,4,6,1]=>1111000
[5,7,8,3,1,4,6,2]=>1110000
[7,4,8,3,2,5,1,6]=>1111000
[7,3,8,2,4,5,6,1]=>1110000
[4,2,7,1,5,3,8,6]=>1110010
[2,7,1,3,5,4,8,6]=>1001010
[1,2,7,3,4,8,6,5]=>0010110
[4,7,2,1,5,8,6,3]=>1110010
[2,3,4,8,1,6,5,7]=>1000100
[3,1,4,8,2,6,7,5]=>1100100
[4,8,3,6,5,1,7,2]=>1110100
[6,4,7,3,5,1,8,2]=>1111000
[3,1,6,4,7,8,2,5]=>1101000
[7,3,1,6,8,2,4,5]=>1110000
[7,3,5,1,6,8,2,4]=>1110000
[4,7,3,5,6,1,8,2]=>1110000
[1,8,2,3,5,7,4,6]=>0101000
[2,7,3,6,1,4,5,8]=>1010000
[1,2,5,8,3,7,4,6]=>0011000
[8,2,4,1,7,5,6,3]=>1110100
[3,8,4,7,5,1,6,2]=>1101100
[8,4,3,6,1,7,5,2]=>1111100
[2,1,8,6,7,3,5,4]=>1011010
[1,2,8,6,3,4,7,5]=>0010110
[7,3,2,5,6,1,4,8]=>1110000
[8,4,1,2,7,5,3,6]=>1011100
[1,5,2,8,6,3,7,4]=>0111010
[5,8,6,3,1,7,4,2]=>1111010
[7,8,1,4,2,5,3,6]=>1110000
[5,6,2,7,1,3,4,8]=>1100000
[1,6,2,7,4,8,3,5]=>0111000
[6,2,1,7,8,5,3,4]=>1110100
[6,7,3,8,4,1,5,2]=>1111000
[2,7,1,8,5,6,3,4]=>1010100
[2,1,7,8,6,3,4,5]=>1010010
[7,8,6,2,1,3,5,4]=>1101010
[4,1,2,6,5,3,8,7]=>1010101
[2,6,5,3,1,4,8,7]=>1010101
[6,1,3,4,2,8,7,5]=>1100101
[8,2,6,4,7,3,5,1]=>1111000
[2,5,1,8,7,4,6,3]=>1011001
[6,2,3,8,4,7,5,1]=>1101100
[7,1,3,8,6,4,5,2]=>1101010
[2,3,5,8,6,7,4,1]=>1001010
[7,4,2,1,8,6,5,3]=>1111110
[2,1,6,3,4,8,7,5]=>1010101
[4,6,7,2,5,8,3,1]=>1110000
[7,6,2,5,3,8,1,4]=>1110010
[6,2,1,3,4,8,7,5]=>1100101
[8,1,4,2,5,6,7,3]=>1110000
[3,4,2,1,8,6,7,5]=>1100110
[2,7,6,8,1,5,3,4]=>1010010
[8,1,3,2,5,6,7,4]=>1101000
[3,2,8,7,4,5,1,6]=>1101001
[6,3,8,5,7,4,2,1]=>1111100
[7,4,6,8,5,1,2,3]=>1001100
[2,1,4,8,7,5,3,6]=>1010101
[7,1,5,8,2,6,3,4]=>1110000
[3,6,8,2,4,1,5,7]=>1100000
[6,2,8,1,7,5,4,3]=>1111100
[2,8,5,3,6,7,1,4]=>1010100
[7,8,5,6,4,1,3,2]=>1101100
[3,8,1,4,5,6,2,7]=>1100000
[5,8,7,3,6,1,4,2]=>1110001
[5,8,3,7,6,1,4,2]=>1110010
[7,5,8,4,6,1,3,2]=>1101100
[6,5,8,4,7,1,3,2]=>1101100
[2,4,8,1,3,7,6,5]=>1000110
[2,5,1,3,8,4,7,6]=>1001010
[2,8,1,5,4,7,3,6]=>1011000
[3,1,8,2,5,7,4,6]=>1101000
[8,3,2,6,1,4,7,5]=>1110100
[2,6,1,3,8,7,5,4]=>1001101
[2,5,7,1,3,8,6,4]=>1001010
[2,7,1,6,5,3,8,4]=>1011100
[2,8,1,7,6,5,4,3]=>1011110
[8,3,2,7,1,6,5,4]=>1111100
[7,4,2,8,1,6,5,3]=>1111100
[8,7,5,3,2,1,6,4]=>1111101
[7,5,2,6,3,1,4,8]=>1110100
[7,4,6,2,1,8,3,5]=>1111000
[7,4,5,8,6,2,1,3]=>1101010
[6,8,4,5,2,1,7,3]=>1111000
[4,6,8,5,1,7,3,2]=>1110100
[4,7,5,1,3,8,6,2]=>1100110
[5,1,7,6,4,2,8,3]=>1111010
[5,1,8,7,6,4,3,2]=>1111011
[8,5,2,1,6,3,7,4]=>1111100
[5,1,6,2,8,7,4,3]=>1111001
[4,5,6,1,8,7,2,3]=>1100001
[3,5,6,8,7,1,4,2]=>1100001
[3,6,1,7,4,8,2,5]=>1101000
[8,4,2,6,3,1,5,7]=>1111000
[4,1,5,8,7,2,3,6]=>1100001
[3,4,8,7,1,2,6,5]=>1000101
[3,4,6,8,5,7,1,2]=>1000100
[4,6,8,3,5,7,2,1]=>1110000
[4,7,3,5,8,2,6,1]=>1110000
[6,3,7,2,4,8,1,5]=>1110000
[5,6,8,3,7,2,1,4]=>1110000
[5,6,8,4,2,7,3,1]=>1111000
[6,5,2,7,1,3,8,4]=>1101100
[6,5,4,1,7,2,8,3]=>1111100
[6,4,7,3,1,8,2,5]=>1111000
[6,8,5,7,4,3,2,1]=>1111100
[7,5,8,4,6,3,2,1]=>1111100
[5,6,3,7,4,2,1,8]=>1111000
[6,1,3,8,5,2,4,7]=>1100100
[7,4,2,6,3,5,1,8]=>1111000
[3,4,7,5,6,2,1,8]=>1100100
[8,1,3,4,5,2,6,7]=>1100000
[1,6,8,4,2,5,3,7]=>0111000
[3,6,8,4,1,7,5,2]=>1101100
[8,7,2,3,6,1,4,5]=>1100001
[6,7,4,8,5,1,2,3]=>1001100
[3,2,8,1,5,4,6,7]=>1101000
[6,1,4,8,5,3,7,2]=>1110100
[1,4,8,5,2,6,7,3]=>0110100
[8,1,2,3,6,5,7,4]=>1001100
[6,1,8,4,3,7,2,5]=>1111000
[1,5,2,4,8,7,3,6]=>0110001
[3,2,6,4,1,8,7,5]=>1101101
[7,6,4,3,1,8,2,5]=>1111010
[8,4,6,5,1,7,2,3]=>1101100
[7,5,4,6,1,2,8,3]=>1011100
[3,2,5,6,1,7,8,4]=>1101000
[3,2,8,7,6,1,4,5]=>1100011
[6,8,4,7,2,1,3,5]=>1101000
[3,8,7,5,6,1,2,4]=>1000101
[8,2,7,6,5,1,3,4]=>1100110
[4,8,6,7,1,5,3,2]=>1110010
[1,8,6,7,2,3,4,5]=>0100010
[7,6,3,2,1,8,5,4]=>1111110
[3,5,4,2,7,1,8,6]=>1101010
[8,6,3,1,4,5,7,2]=>1110010
[3,2,6,1,5,7,4,8]=>1101000
[5,2,1,4,7,6,3,8]=>1110010
[4,2,1,3,5,8,7,6]=>1100011
[7,4,1,5,3,6,8,2]=>1111000
[6,8,5,3,7,1,2,4]=>1010100
[6,8,2,4,5,1,3,7]=>1100000
[6,8,3,4,1,5,2,7]=>1110000
[5,8,4,1,7,2,6,3]=>1111000
[6,8,3,1,4,5,7,2]=>1110000
[5,3,8,4,2,6,7,1]=>1111000
[4,1,8,3,5,7,2,6]=>1110000
[2,4,6,3,5,8,1,7]=>1010000
[4,5,7,2,3,6,8,1]=>1100000
[2,6,3,4,7,5,8,1]=>1010100
[4,5,2,7,1,6,8,3]=>1110000
[2,3,1,7,6,4,8,5]=>1001110
[3,4,1,6,5,8,2,7]=>1100100
[7,3,1,4,8,5,6,2]=>1110100
[7,5,1,2,8,6,3,4]=>1010110
[6,4,2,8,7,1,5,3]=>1111001
[3,1,8,2,7,6,4,5]=>1101010
[6,2,8,4,1,7,5,3]=>1111100
[3,6,4,7,2,5,1,8]=>1101000
[7,3,2,8,6,1,4,5]=>1110010
[4,3,8,7,1,2,5,6]=>1010001
[1,2,5,8,4,7,3,6]=>0011000
[1,3,6,8,5,2,7,4]=>0101100
[2,5,7,4,1,8,6,3]=>1011010
[2,4,6,1,8,3,7,5]=>1010100
[1,4,2,5,8,7,3,6]=>0110001
[3,5,1,7,2,8,6,4]=>1101010
[4,6,3,1,7,8,5,2]=>1110100
[5,3,1,6,7,8,4,2]=>1111000
[4,1,6,2,7,8,5,3]=>1110100
[2,1,3,4,8,7,5,6]=>1000101
[4,8,7,3,6,5,1,2]=>1010101
[6,3,8,7,5,4,1,2]=>1011101
[4,3,8,7,6,5,1,2]=>1010111
[2,8,7,6,1,5,4,3]=>1011011
[5,2,8,7,6,1,4,3]=>1110011
[6,2,8,7,5,1,4,3]=>1110101
[7,8,2,6,5,1,4,3]=>1110100
[6,1,8,7,5,4,3,2]=>1111101
[4,1,8,7,6,5,3,2]=>1110111
[3,1,8,7,6,5,4,2]=>1101111
[7,8,2,6,1,5,4,3]=>1111000
[4,2,8,1,7,6,5,3]=>1110110
[3,2,8,1,7,6,5,4]=>1101110
[2,8,7,1,6,5,4,3]=>1011101
[3,8,2,1,7,6,5,4]=>1101110
[4,8,2,7,6,1,5,3]=>1110010
[3,8,2,7,1,6,5,4]=>1101100
[3,8,7,2,1,6,5,4]=>1101101
[4,8,7,2,6,1,5,3]=>1110001
[5,8,7,6,2,1,4,3]=>1110011
[6,5,8,7,1,4,3,2]=>1110101
[3,8,7,1,6,5,4,2]=>1101101
[4,8,1,7,6,5,3,2]=>1110110
[5,4,1,8,7,6,3,2]=>1111011
[6,4,8,1,7,5,3,2]=>1111100
[7,8,4,1,6,5,3,2]=>1111100
[7,8,3,1,6,5,4,2]=>1111100
[5,3,1,8,7,6,4,2]=>1111011
[4,3,1,8,7,6,5,2]=>1110111
[4,2,1,8,7,6,5,3]=>1110111
[7,8,2,1,6,5,4,3]=>1111100
[6,5,3,1,8,7,4,2]=>1111101
[7,5,2,1,8,6,4,3]=>1111110
[5,4,2,1,8,7,6,3]=>1111011
[7,3,2,1,8,6,5,4]=>1111110
[6,1,4,2,3,5,8,7]=>1100001
[8,6,1,4,2,3,5,7]=>1100010
[6,8,1,4,2,3,5,7]=>1100000
[4,6,2,3,8,1,5,7]=>1100000
[6,2,3,8,4,1,5,7]=>1101000
[6,4,2,3,8,1,5,7]=>1101000
[2,8,4,3,6,1,5,7]=>1011000
[2,6,3,8,4,1,5,7]=>1011000
[6,3,8,4,2,1,5,7]=>1111000
[2,4,8,3,6,1,5,7]=>1010000
[2,4,6,3,8,1,5,7]=>1010000
[8,3,6,2,4,1,5,7]=>1110000
[8,3,6,2,1,4,5,7]=>1110000
[2,1,8,3,6,4,5,7]=>1011000
[6,3,8,2,1,4,5,7]=>1110000
[6,2,4,3,8,1,5,7]=>1110000
[3,6,4,7,8,5,1,2]=>1001100
[1,6,4,2,7,5,8,3]=>0111100
[3,4,6,8,7,5,1,2]=>1000101
[5,4,6,3,8,7,1,2]=>1011001
[6,4,8,5,3,7,1,2]=>1011100
[1,8,5,2,6,3,7,4]=>0111100
[1,4,6,2,8,5,7,3]=>0110100
[7,8,1,4,2,5,6,3]=>1110000
[3,6,5,2,4,1,8,7]=>1100101
[4,8,5,3,1,6,2,7]=>1110100
[5,2,8,6,4,1,3,7]=>1101010
[5,1,6,2,8,7,3,4]=>1110001
[6,1,8,7,4,2,3,5]=>1101001
[1,2,8,5,7,3,6,4]=>0011100
[1,3,6,8,7,5,2,4]=>0100101
[7,8,1,2,4,6,5,3]=>1010100
[1,2,6,4,8,7,5,3]=>0011101
[1,8,2,5,4,7,6,3]=>0111010
[1,2,7,3,5,8,6,4]=>0011010
[4,6,2,1,7,5,3,8]=>1110100
[4,6,2,3,7,8,1,5]=>1100000
[4,2,1,3,5,7,8,6]=>1100010
[7,3,2,4,5,1,8,6]=>1110010
[7,8,3,2,4,1,6,5]=>1110100
[7,8,4,2,6,3,1,5]=>1111000
[4,2,6,3,8,7,1,5]=>1110001
[5,8,2,7,4,3,1,6]=>1111000
[7,5,2,8,3,4,1,6]=>1110100
[4,3,6,8,1,2,7,5]=>1010100
[6,4,3,5,2,8,1,7]=>1111000
[6,5,8,4,2,3,1,7]=>1101100
[4,1,3,6,5,8,7,2]=>1100101
[2,4,1,3,8,5,7,6]=>1000110
[2,4,1,3,5,8,7,6]=>1000011
[4,6,1,3,5,8,7,2]=>1100001
[1,4,6,3,5,8,7,2]=>0110001
[4,2,1,3,6,5,7,8]=>1100100
[4,2,1,6,3,5,7,8]=>1110000
[4,2,1,8,3,5,7,6]=>1110010
[6,2,1,8,3,5,7,4]=>1111000
[6,4,1,3,8,5,7,2]=>1101100
[6,1,4,3,8,5,7,2]=>1110100
[1,6,4,3,8,5,7,2]=>0111100
[8,1,4,3,6,5,7,2]=>1110100
[8,2,1,3,6,5,7,4]=>1101100
[8,2,1,4,3,5,7,6]=>1110010
[8,1,4,6,3,5,7,2]=>1110000
[6,1,4,8,3,5,7,2]=>1110000
[6,4,8,1,3,5,7,2]=>1101000
[2,4,8,1,3,5,7,6]=>1000010
[4,6,8,1,3,5,7,2]=>1100000
[4,6,1,8,3,5,7,2]=>1110000
[4,1,6,8,3,5,7,2]=>1110000
[1,4,6,8,3,5,7,2]=>0110000
[1,4,6,3,8,5,7,2]=>0110100
[4,6,1,3,8,5,7,2]=>1100100
[2,6,1,3,8,5,7,4]=>1001100
[2,6,1,8,3,5,7,4]=>1011000
[2,1,6,3,8,5,7,4]=>1011100
[2,1,3,6,8,5,7,4]=>1001100
[4,1,3,6,8,5,7,2]=>1100100
[1,4,3,6,8,5,7,2]=>0110100
[2,1,8,3,6,5,7,4]=>1011100
[2,1,8,6,3,5,7,4]=>1011010
[2,1,8,4,3,5,7,6]=>1011010
[4,1,8,3,6,5,7,2]=>1110100
[2,8,4,1,3,5,7,6]=>1001010
[6,8,1,4,3,5,7,2]=>1110000
[1,8,6,4,3,5,7,2]=>0111010
[8,6,1,4,3,5,7,2]=>1110010
[8,6,4,1,3,5,7,2]=>1101010
[8,4,2,1,3,5,7,6]=>1101010
[8,5,7,4,3,2,1,6]=>1111100
[8,7,6,5,1,4,3,2]=>1110111
[8,7,4,3,6,2,1,5]=>1111001
[8,7,3,6,5,2,1,4]=>1110101
[6,5,8,4,3,2,1,7]=>1111100
[8,4,7,6,3,2,1,5]=>1111010
[5,8,7,4,3,2,1,6]=>1111001
[4,5,2,7,3,1,8,6]=>1110010
[4,8,2,6,3,5,7,1]=>1110000
[8,6,1,2,7,4,3,5]=>1011010
[4,3,7,8,6,5,1,2]=>1010110
[4,6,2,1,7,8,5,3]=>1110100
[2,3,8,7,4,1,6,5]=>1001101
[7,8,2,1,5,6,4,3]=>1111000
[1,6,2,5,8,4,3,7]=>0111000
[1,5,8,6,2,3,7,4]=>0101010
[5,2,7,1,8,6,3,4]=>1110010
[1,2,8,3,7,6,5,4]=>0011110
[6,5,2,8,1,7,3,4]=>1110100
[2,8,3,5,1,7,4,6]=>1011000
[2,8,5,6,1,7,3,4]=>1010100
[5,4,2,8,6,1,7,3]=>1111010
[8,5,4,3,7,2,6,1]=>1111100
[8,3,7,4,2,6,5,1]=>1111100
[3,8,7,4,1,6,5,2]=>1101101
[6,3,2,8,4,1,7,5]=>1111100
[2,8,3,4,1,7,5,6]=>1010100
[5,4,2,8,3,1,7,6]=>1111010
[2,8,6,4,1,7,5,3]=>1011110
[8,4,7,6,2,5,3,1]=>1111010
[4,8,7,6,1,5,3,2]=>1110011
[7,3,8,5,2,1,6,4]=>1111100
[7,3,8,4,2,1,6,5]=>1111100
[7,5,4,3,8,2,1,6]=>1111100
[5,4,2,3,8,1,6,7]=>1101000
[3,7,8,4,1,2,6,5]=>1001100
[8,7,4,6,3,5,2,1]=>1111001
[7,3,4,8,2,1,5,6]=>1110000
[7,5,8,6,2,1,4,3]=>1110110
[6,5,8,7,3,1,4,2]=>1110101
[2,4,8,3,1,5,7,6]=>1010010
[6,3,2,4,8,1,5,7]=>1110000
[2,4,3,8,1,6,5,7]=>1010100
[2,3,8,4,1,6,7,5]=>1001100
[8,3,4,7,2,5,6,1]=>1110000
[3,4,8,7,1,5,6,2]=>1100001
[2,5,3,8,1,6,4,7]=>1011000
[3,7,4,8,1,5,2,6]=>1101000
[8,4,6,7,2,3,5,1]=>1101000
[2,6,8,5,1,3,7,4]=>1001100
[2,6,8,4,1,3,7,5]=>1001100
[3,7,5,8,1,4,2,6]=>1100100
[2,6,5,8,1,4,3,7]=>1010100
[2,5,8,3,1,4,7,6]=>1010010
[4,7,6,8,1,3,2,5]=>1100010
[5,6,8,7,1,3,4,2]=>1100001
[8,7,4,1,6,2,5,3]=>1111001
[6,3,7,4,5,8,2,1]=>1111000
[3,5,7,4,6,8,2,1]=>1101000
[6,8,4,1,7,2,5,3]=>1111000
[3,8,5,4,6,7,2,1]=>1101100
[6,8,3,4,5,7,2,1]=>1110000
[2,5,7,4,6,3,8,1]=>1011000
[5,4,2,7,8,3,6,1]=>1111000
[8,1,6,2,4,3,5,7]=>1110000
[8,7,1,2,4,3,5,6]=>1010001
[6,8,3,1,4,7,2,5]=>1110000
[6,4,7,2,8,5,1,3]=>1101100
[5,8,1,4,7,3,2,6]=>1110000
[8,7,1,4,5,3,2,6]=>1110001
[1,7,6,2,4,3,5,8]=>0110010
[8,7,4,2,6,5,1,3]=>1101101
[8,7,3,2,4,6,5,1]=>1110101
[1,7,2,5,4,3,6,8]=>0111000
[6,8,4,3,7,5,2,1]=>1111100
[6,4,7,3,8,5,2,1]=>1111100
[6,3,7,2,4,8,5,1]=>1110100
[8,1,2,5,4,3,6,7]=>1011000
[2,7,1,5,6,3,4,8]=>1010000
[4,7,3,2,5,6,1,8]=>1110000
[3,6,4,1,2,8,7,5]=>1001101
[3,6,5,1,8,2,7,4]=>1101100
[4,6,5,1,8,7,2,3]=>1100101
[5,7,1,4,8,6,2,3]=>1100010
[5,7,1,3,8,2,6,4]=>1101000
[6,3,7,2,8,4,5,1]=>1111000
[6,7,1,8,3,2,5,4]=>1111000
[8,7,6,1,4,5,2,3]=>1100011
[8,7,6,1,3,2,5,4]=>1101011
[8,7,3,5,1,2,6,4]=>1011001
[8,7,4,5,1,6,2,3]=>1101001
[8,5,6,4,1,7,2,3]=>1101100
[8,4,6,2,3,1,7,5]=>1101100
[8,3,5,4,2,1,7,6]=>1111010
[4,7,3,5,2,1,6,8]=>1110000
[6,7,8,4,1,5,3,2]=>1111000
[7,1,6,8,4,5,3,2]=>1111000
[7,5,1,6,4,2,3,8]=>1101100
[8,1,5,7,4,6,3,2]=>1111000
[1,8,4,6,7,5,3,2]=>0111100
[6,1,8,4,7,5,3,2]=>1111100
[4,8,5,1,6,7,3,2]=>1110100
[8,4,1,5,6,7,3,2]=>1111000
[8,1,4,5,6,7,3,2]=>1110000
[8,2,5,6,1,4,7,3]=>1110000
[4,8,5,2,1,6,7,3]=>1110100
[5,1,8,4,2,6,3,7]=>1111000
[1,8,4,6,2,5,3,7]=>0111000
[8,5,6,1,2,4,3,7]=>1010100
[2,8,3,1,5,6,7,4]=>1011000
[8,2,4,3,6,7,1,5]=>1110000
[8,3,2,7,1,5,6,4]=>1111000
[3,2,8,5,7,1,6,4]=>1101100
[3,6,2,8,5,1,7,4]=>1101100
[6,2,1,8,4,7,5,3]=>1111100
[2,8,7,1,4,6,5,3]=>1010101
[8,2,7,1,5,4,6,3]=>1111000
[7,3,1,5,6,2,4,8]=>1110000
[2,7,3,6,5,8,1,4]=>1010100
[7,2,8,1,6,4,5,3]=>1111000
[7,8,2,6,4,1,5,3]=>1111000
[8,7,2,4,1,6,5,3]=>1110101
[1,2,8,6,3,7,5,4]=>0011110
[1,8,7,2,3,6,5,4]=>0101101
[1,7,8,2,6,4,3,5]=>0111000
[2,1,7,3,6,8,4,5]=>1011000
[7,2,1,5,8,3,4,6]=>1110000
[7,1,5,8,3,2,4,6]=>1110000
[7,8,1,5,2,4,3,6]=>1110000
[8,7,1,2,5,4,3,6]=>1011001
[1,6,2,8,4,3,7,5]=>0111100
[1,8,3,7,2,5,4,6]=>0111000
[8,1,4,7,3,2,5,6]=>1110000
[4,7,8,1,3,2,5,6]=>1100000
[2,1,8,3,5,7,4,6]=>1011000
[1,2,3,4,8,5,7,6]=>0000110
[8,3,5,2,4,1,7,6]=>1110010
[8,6,2,5,3,1,7,4]=>1111010
[3,7,2,5,6,4,1,8]=>1101000
[7,6,2,5,4,3,1,8]=>1111010
[4,7,5,2,6,3,1,8]=>1110100
[5,6,7,2,4,3,1,8]=>1110000
[1,8,3,4,2,7,5,6]=>0110100
[2,8,3,4,1,6,7,5]=>1010100
[7,8,2,4,3,1,6,5]=>1110100
[6,1,3,5,7,2,4,8]=>1100000
[8,1,3,6,2,4,7,5]=>1100100
[2,1,8,3,7,5,4,6]=>1011100
[7,1,8,2,5,6,3,4]=>1110000
[6,1,5,8,2,7,3,4]=>1110000
[6,2,5,8,1,4,7,3]=>1110000
[3,2,8,5,1,6,7,4]=>1101100
[2,3,8,1,5,6,7,4]=>1001000
[1,3,8,2,5,7,4,6]=>0101000
[2,8,7,1,6,4,5,3]=>1011001
[3,8,7,1,5,6,4,2]=>1101001
[4,8,7,5,1,6,3,2]=>1110101
[5,8,6,7,1,4,3,2]=>1110010
[6,7,8,5,1,4,3,2]=>1110100
[5,6,3,8,4,1,7,2]=>1111000
[7,3,8,5,4,1,6,2]=>1111100
[3,4,8,5,6,1,7,2]=>1100100
[8,3,7,4,1,6,5,2]=>1111100
[3,5,6,8,4,1,7,2]=>1101000
[5,6,4,7,8,1,3,2]=>1101000
[6,2,3,1,5,4,7,8]=>1101000
[8,5,1,3,2,4,7,6]=>1100110
[7,5,1,3,2,6,4,8]=>1101100
[3,6,4,1,5,2,7,8]=>1101000
[4,5,6,1,3,2,7,8]=>1100000
[6,7,1,4,2,5,3,8]=>1110000
[2,7,1,3,5,6,4,8]=>1001000
[8,6,1,2,4,3,7,5]=>1010110
[7,8,1,2,5,3,6,4]=>1011000
[6,8,1,4,2,3,7,5]=>1100100
[4,5,8,1,2,3,7,6]=>1000010
[1,8,2,7,5,4,6,3]=>0111100
[1,8,6,3,7,2,4,5]=>0110010
[1,8,5,3,4,7,2,6]=>0110100
[1,8,5,4,7,2,6,3]=>0111100
[1,8,2,5,4,6,7,3]=>0111000
[7,4,3,8,2,5,6,1]=>1111000
[7,2,8,4,3,5,6,1]=>1111000
[7,2,8,1,3,6,4,5]=>1101000
[1,4,7,5,2,6,8,3]=>0110100
[4,6,5,3,7,1,8,2]=>1110100
[5,6,2,7,3,1,8,4]=>1111000
[1,6,3,7,5,8,2,4]=>0110100
[5,2,4,8,1,3,7,6]=>1100010
[6,2,5,4,8,3,7,1]=>1111000
[3,5,2,4,7,1,6,8]=>1100000
[6,4,5,3,8,2,1,7]=>1111000
[6,5,3,4,8,7,1,2]=>1010101
[7,5,4,8,6,1,3,2]=>1101110
[7,6,3,8,5,4,1,2]=>1011110
[6,3,8,1,7,5,2,4]=>1110100
[6,5,8,3,1,7,4,2]=>1111100
[5,4,8,1,2,7,3,6]=>1011000
[6,2,4,8,5,1,3,7]=>1100100
[7,6,3,8,5,1,2,4]=>1010110
[6,3,8,1,7,2,4,5]=>1110000
[7,2,8,6,1,3,4,5]=>1100010
[7,2,8,6,1,5,3,4]=>1110010
[3,2,4,7,8,1,5,6]=>1100000
[4,2,6,7,3,8,1,5]=>1110000
[1,5,7,4,2,8,6,3]=>0111010
[1,3,7,2,8,6,4,5]=>0101010
[1,5,3,6,8,2,7,4]=>0111000
[4,5,2,7,1,8,6,3]=>1110010
[4,3,6,5,7,8,1,2]=>1010100
[4,2,3,5,6,8,1,7]=>1100000
[5,2,6,4,7,8,3,1]=>1111000
[4,2,6,7,3,8,5,1]=>1110100
[3,2,5,6,8,1,7,4]=>1101000
[4,2,3,6,8,1,5,7]=>1100000
[2,6,1,5,4,8,3,7]=>1011000
[3,2,1,8,7,5,6,4]=>1101101
[3,1,6,2,5,8,4,7]=>1101000
[6,5,1,3,4,8,2,7]=>1100100
[6,2,4,5,8,1,3,7]=>1100000
[2,6,1,5,8,3,4,7]=>1010000
[2,3,4,8,1,7,6,5]=>1000110
[6,3,1,7,8,4,5,2]=>1111000
[6,2,7,8,4,5,1,3]=>1101000
[3,1,4,8,7,6,2,5]=>1100011
[2,3,6,5,8,7,1,4]=>1000101
[8,4,1,2,7,6,3,5]=>1011010
[3,4,8,2,7,5,1,6]=>1100100
[6,3,2,8,5,7,4,1]=>1111100
[3,2,6,8,5,1,7,4]=>1101100
[5,2,4,1,7,8,6,3]=>1110010
[3,8,4,7,2,5,6,1]=>1101000
[1,8,7,2,4,5,6,3]=>0110001
[5,3,4,7,1,8,6,2]=>1110010
[5,3,7,1,6,2,8,4]=>1111000
[4,7,6,5,8,2,1,3]=>1100110
[7,5,1,2,6,8,4,3]=>1011100
[1,2,5,3,8,7,6,4]=>0011011
[2,8,1,5,6,3,7,4]=>1011000
[4,8,2,3,6,7,1,5]=>1100000
[8,2,4,6,7,1,3,5]=>1100000
[3,7,5,1,8,4,6,2]=>1101100
[6,5,3,1,8,4,2,7]=>1111100
[5,7,4,3,8,6,2,1]=>1111010
[4,2,3,8,5,6,1,7]=>1100100
[3,6,4,2,8,5,7,1]=>1101100
[4,7,3,2,5,1,8,6]=>1110010
[2,4,8,7,1,3,5,6]=>1000001
[2,4,3,5,1,8,6,7]=>1010010
[8,6,1,2,4,3,5,7]=>1010010
[8,6,2,5,4,1,3,7]=>1101010
[8,3,5,7,6,2,1,4]=>1110010
[6,7,5,3,8,2,4,1]=>1110100
[8,2,6,3,4,5,1,7]=>1110000
[8,1,5,4,3,6,2,7]=>1111000
[8,6,4,2,1,5,3,7]=>1111010
[8,3,2,4,6,1,5,7]=>1110000
[8,2,3,4,7,6,1,5]=>1100010
[5,7,1,8,3,4,6,2]=>1110000
[1,5,6,7,3,4,8,2]=>0110000
[8,1,3,7,6,4,2,5]=>1101010
[4,8,1,2,7,3,6,5]=>1010100
[2,5,7,8,4,1,3,6]=>1001000
[6,3,5,8,7,2,4,1]=>1110001
[5,2,8,7,1,3,4,6]=>1100001
[5,2,7,4,8,1,6,3]=>1111000
[8,3,7,4,2,5,6,1]=>1111000
[8,1,7,4,5,2,6,3]=>1111000
[1,7,8,3,5,4,6,2]=>0111000
[4,6,3,5,8,1,7,2]=>1110000
[8,2,4,1,5,6,7,3]=>1110000
[3,5,1,7,6,8,2,4]=>1100010
[2,1,7,6,4,5,8,3]=>1011010
[1,7,6,5,2,4,8,3]=>0110110
[5,1,7,6,2,8,4,3]=>1111010
[4,6,2,5,3,8,7,1]=>1110001
[8,6,4,2,3,1,7,5]=>1101110
[8,6,4,2,1,3,7,5]=>1101110
[2,5,7,3,8,4,6,1]=>1011000
[4,2,7,1,8,5,3,6]=>1110100
[8,3,6,7,1,5,4,2]=>1111000
[1,3,7,5,8,6,4,2]=>0101110
[2,7,4,5,8,3,6,1]=>1011000
[3,5,7,1,4,8,6,2]=>1100010
[3,4,1,2,8,5,7,6]=>1000110
[8,7,3,1,2,6,4,5]=>1011001
[6,2,3,1,4,8,7,5]=>1100101
[8,4,3,2,5,7,1,6]=>1111000
[5,3,6,8,2,1,4,7]=>1110000
[3,2,6,8,5,4,1,7]=>1101100
[7,3,8,2,5,4,1,6]=>1111000
[7,4,2,5,8,3,1,6]=>1111000
[3,1,2,8,5,6,4,7]=>1001100
[5,2,1,6,8,3,4,7]=>1110000
[3,1,8,6,5,4,2,7]=>1101110
[5,6,8,1,4,3,2,7]=>1110000
[6,4,8,3,7,2,5,1]=>1111000
[4,7,3,6,2,1,8,5]=>1110100
[7,8,4,1,5,3,2,6]=>1111000
[7,3,8,5,1,4,2,6]=>1110100
[1,5,4,8,3,7,6,2]=>0111010
[4,7,8,3,1,6,5,2]=>1110100
[8,7,5,3,6,4,2,1]=>1111101
[4,6,1,3,8,7,5,2]=>1100101
[3,6,1,2,7,5,8,4]=>1001100
[3,6,2,5,8,7,4,1]=>1101001
[8,5,2,3,6,7,4,1]=>1101100
[2,7,3,1,5,6,8,4]=>1011000
[6,7,1,3,2,8,4,5]=>1101000
[6,2,7,1,3,4,8,5]=>1100100
[5,2,1,7,3,8,4,6]=>1111000
[4,7,2,6,3,8,1,5]=>1110000
[4,8,2,6,3,7,5,1]=>1110100
[3,7,2,4,6,1,8,5]=>1100100
[5,3,7,2,8,1,4,6]=>1110000
[7,1,8,3,4,2,5,6]=>1110000
[7,2,4,1,8,3,5,6]=>1110000
[4,8,7,6,3,2,1,5]=>1110011
[7,3,8,2,6,5,1,4]=>1110100
[7,8,2,4,6,1,5,3]=>1110000
[3,5,1,8,7,2,6,4]=>1101001
[5,2,8,1,7,6,3,4]=>1110010
[6,2,1,3,8,7,5,4]=>1101101
[5,6,1,2,8,7,4,3]=>1011001
[6,7,8,1,2,5,4,3]=>1011000
[5,8,7,1,6,4,3,2]=>1111001
[6,8,7,5,1,4,3,2]=>1110101
[8,6,4,3,2,1,7,5]=>1111110
[6,5,4,3,8,2,7,1]=>1111100
[7,5,4,3,2,8,6,1]=>1111110
[8,5,4,3,7,2,1,6]=>1111100
[8,4,3,2,1,7,6,5]=>1111110
[3,7,5,8,1,4,6,2]=>1100100
[4,7,5,8,3,2,1,6]=>1110100
[5,7,2,3,6,1,8,4]=>1101000
[7,3,1,4,8,2,5,6]=>1110000
[7,4,1,2,5,8,3,6]=>1011000
[4,7,1,6,5,8,3,2]=>1110100
[2,7,5,4,3,8,1,6]=>1011100
[8,6,4,2,3,7,5,1]=>1101110
[7,6,4,2,3,8,1,5]=>1101010
[6,4,7,1,3,8,5,2]=>1101100
[3,1,2,4,8,7,6,5]=>1000111
[6,5,8,7,3,1,2,4]=>1010101
[5,6,7,8,1,4,2,3]=>1100000
[2,6,7,4,5,3,1,8]=>1011000
[1,3,7,4,2,8,5,6]=>0101100
[4,6,1,3,7,2,5,8]=>1100000
[6,5,7,8,3,1,4,2]=>1110100
[7,5,8,6,2,1,3,4]=>1100110
[2,8,1,3,6,5,4,7]=>1001100
[2,8,7,3,5,4,1,6]=>1011001
[3,4,2,6,8,7,1,5]=>1100001
[6,1,4,2,7,8,5,3]=>1110100
[7,3,8,4,1,2,6,5]=>1011100
[6,8,3,2,7,1,5,4]=>1111000
[5,1,4,3,6,2,7,8]=>1110000
[4,8,5,6,3,2,1,7]=>1110100
[2,8,5,6,3,7,1,4]=>1010100
[6,7,3,1,4,2,8,5]=>1110100
[3,2,6,7,4,8,1,5]=>1101000
[3,7,1,2,4,6,5,8]=>1000100
[4,1,8,2,6,3,5,7]=>1110000
[7,5,6,8,2,1,4,3]=>1110100
[5,8,6,7,1,2,3,4]=>1000010
[4,8,1,5,7,2,3,6]=>1100000
[3,5,1,4,7,6,8,2]=>1100010
[5,3,2,7,1,6,8,4]=>1111000
[8,4,3,7,5,1,6,2]=>1111100
[5,1,7,2,4,6,8,3]=>1110000
[4,5,7,1,2,6,8,3]=>1010000
[5,4,1,7,3,6,8,2]=>1111000
[3,6,4,7,5,2,8,1]=>1101100
[3,4,7,6,2,5,8,1]=>1100010
[4,8,3,6,5,2,1,7]=>1110100
[1,8,6,5,4,2,3,7]=>0101110
[8,1,7,4,2,5,6,3]=>1111000
[1,8,7,2,5,3,4,6]=>0110001
[4,8,1,5,2,6,3,7]=>1110000
[3,6,8,5,1,2,4,7]=>1000100
[1,5,2,7,8,4,6,3]=>0111000
[6,7,2,8,5,3,1,4]=>1110100
[6,7,2,8,3,1,5,4]=>1111000
[7,1,2,8,3,5,6,4]=>1011000
[6,7,5,2,8,1,4,3]=>1110100
[7,1,4,5,8,6,2,3]=>1100010
[3,1,4,6,7,8,5,2]=>1100100
[5,7,6,4,2,8,1,3]=>1101010
[7,4,6,1,8,2,3,5]=>1101000
[3,4,5,1,6,8,7,2]=>1100001
[5,1,6,8,4,2,7,3]=>1111000
[7,4,8,2,3,6,5,1]=>1101100
[7,5,8,6,3,4,2,1]=>1110110
[5,7,8,3,1,6,4,2]=>1111000
[7,5,8,3,2,4,1,6]=>1110100
[6,4,1,8,2,5,7,3]=>1111000
[5,8,2,6,3,1,4,7]=>1110000
[3,6,5,1,8,4,7,2]=>1101100
[8,2,7,5,4,1,3,6]=>1101100
[6,8,5,2,3,4,1,7]=>1100100
[2,6,8,7,1,5,3,4]=>1010001
[7,5,1,6,2,8,4,3]=>1111100
[6,2,7,3,8,4,1,5]=>1111000
[3,7,2,4,8,5,1,6]=>1100100
[1,5,2,6,3,8,7,4]=>0111001
[1,3,6,2,4,8,7,5]=>0100101
[7,3,5,2,4,1,6,8]=>1110000
[8,3,6,2,5,4,1,7]=>1111000
[3,5,8,2,4,6,1,7]=>1100000
[6,4,7,8,2,3,1,5]=>1101000
[7,4,8,5,3,2,1,6]=>1111100
[1,5,3,2,8,4,7,6]=>0111010
[2,8,7,3,5,1,4,6]=>1010001
[3,8,4,7,5,1,2,6]=>1001100
[6,1,2,7,3,8,5,4]=>1011100
[2,1,7,3,4,8,6,5]=>1010110
[8,3,1,6,7,2,5,4]=>1111000
[4,8,3,7,1,5,2,6]=>1110000
[1,3,5,8,2,4,7,6]=>0100010
[5,7,4,8,2,1,3,6]=>1101000
[4,6,8,2,5,1,3,7]=>1100000
[5,3,7,2,1,4,6,8]=>1110000
[6,4,2,8,3,1,5,7]=>1111000
[5,7,2,3,8,1,4,6]=>1100000
[6,4,7,5,8,1,2,3]=>1001100
[8,6,4,2,1,7,5,3]=>1111110
[7,4,2,1,5,8,6,3]=>1111010
[7,6,4,1,8,5,2,3]=>1101110
[1,6,4,8,7,5,3,2]=>0111101
[6,3,1,2,8,4,7,5]=>1011100
[7,4,8,1,6,3,5,2]=>1111000
[3,6,1,8,2,4,7,5]=>1100100
[6,4,1,8,3,2,7,5]=>1111100
[1,4,8,7,2,6,5,3]=>0110101
[5,4,1,8,7,3,2,6]=>1111001
[5,8,4,1,7,6,2,3]=>1101010
[8,6,1,7,5,4,3,2]=>1111110
[3,1,8,7,6,5,2,4]=>1100111
[8,1,2,4,5,3,6,7]=>1010000
[1,8,7,6,4,5,3,2]=>0111011
[2,6,8,1,3,7,5,4]=>1001100
[2,4,8,1,5,7,6,3]=>1010010
[3,2,8,6,1,7,5,4]=>1101110
[6,2,8,3,1,7,5,4]=>1111100
[7,4,3,8,5,2,1,6]=>1111100
[6,5,2,8,4,3,1,7]=>1111100
[4,3,8,7,5,1,6,2]=>1110101
[4,2,3,8,5,1,6,7]=>1100100
[4,2,8,5,1,7,6,3]=>1110110
[3,4,2,8,5,6,1,7]=>1100100
[3,2,4,8,6,1,5,7]=>1100010
[3,2,5,8,6,1,4,7]=>1100010
[8,4,3,7,5,2,6,1]=>1111100
[4,3,7,8,5,1,2,6]=>1010100
[4,2,6,8,5,1,3,7]=>1100100
[3,5,2,8,4,6,1,7]=>1101000
[5,2,6,8,4,1,3,7]=>1101000
[5,3,7,8,4,1,2,6]=>1011000
[5,6,2,8,3,4,1,7]=>1110000
[5,3,8,7,4,1,6,2]=>1111001
[6,4,2,8,5,3,1,7]=>1111100
[8,7,5,3,6,2,4,1]=>1110101
[8,7,4,3,6,2,5,1]=>1111001
[8,6,5,3,7,2,4,1]=>1110110
[7,6,4,3,8,2,5,1]=>1111010
[6,4,5,3,8,2,7,1]=>1111000
[7,4,5,3,8,2,6,1]=>1111000
[7,5,6,3,8,2,4,1]=>1110100
[8,5,6,3,7,2,4,1]=>1110100
[8,4,6,3,7,2,5,1]=>1111000
[8,4,7,3,5,2,6,1]=>1111000
[8,5,7,3,4,2,6,1]=>1110100
[7,5,8,4,3,2,6,1]=>1111100
[7,5,8,3,4,2,6,1]=>1110100
[7,6,8,3,5,2,4,1]=>1110010
[7,5,8,4,6,2,3,1]=>1101100
[7,5,8,3,6,2,4,1]=>1110100
[7,4,8,3,6,2,5,1]=>1111000
[7,4,8,3,5,2,6,1]=>1111000
[6,4,8,3,5,2,7,1]=>1111000
[5,4,7,3,6,2,8,1]=>1111000
[5,4,8,3,7,2,6,1]=>1111000
[6,5,8,3,7,2,4,1]=>1110100
[6,5,8,4,7,2,3,1]=>1101100
[6,5,8,4,7,3,2,1]=>1111100
[6,5,7,3,8,2,4,1]=>1110100
[5,4,6,3,8,2,7,1]=>1111000
[6,5,3,7,8,2,1,4]=>1110100
[6,5,4,2,8,7,1,3]=>1101101
[6,4,3,7,5,2,1,8]=>1111100
[6,3,7,8,5,2,1,4]=>1110100
[6,3,7,2,5,4,1,8]=>1111000
[6,3,2,7,5,4,1,8]=>1111100
[4,8,2,6,3,7,1,5]=>1110000
[5,8,4,1,2,7,3,6]=>1011000
[5,4,8,1,2,3,7,6]=>1001010
[1,4,7,6,3,2,5,8]=>0110010
[4,8,3,2,7,6,1,5]=>1110010
[5,8,1,7,4,2,3,6]=>1101000
[4,8,6,7,2,3,1,5]=>1100010
[4,8,7,3,6,2,1,5]=>1110001
[4,3,8,2,7,1,6,5]=>1110100
[4,1,8,7,3,2,5,6]=>1110001
[4,7,8,1,2,5,3,6]=>1010000
[4,7,5,1,2,8,3,6]=>1010100
[2,3,6,7,4,1,8,5]=>1001100
[2,6,3,4,7,8,1,5]=>1010000
[3,1,7,8,4,2,5,6]=>1101000
[4,3,1,2,8,5,7,6]=>1010110
[3,7,6,8,4,2,1,5]=>1101010
[4,7,1,8,5,2,3,6]=>1100100
[2,6,8,7,4,3,1,5]=>1011001
[3,7,8,6,2,4,1,5]=>1100010
[3,7,8,2,6,4,1,5]=>1101000
[4,2,3,8,1,6,7,5]=>1100100
[3,7,2,8,4,6,1,5]=>1101000
[4,2,8,3,6,1,7,5]=>1110100
[4,2,8,6,3,1,7,5]=>1110110
[2,6,8,4,7,3,1,5]=>1011000
[2,4,6,8,3,1,7,5]=>1010100
[3,7,2,4,8,6,1,5]=>1100010
[1,3,6,4,7,2,5,8]=>0101000
[2,4,6,3,8,1,7,5]=>1010100
[2,6,4,3,8,7,1,5]=>1011001
[2,4,3,6,1,8,7,5]=>1010101
[3,1,7,4,8,2,5,6]=>1101000
[2,6,7,3,8,4,1,5]=>1011000
[2,6,3,7,4,8,1,5]=>1011000
[1,3,5,7,6,8,2,4]=>0100010
[1,3,5,7,6,2,8,4]=>0101010
[1,3,5,7,2,6,8,4]=>0101000
[1,3,5,2,7,6,8,4]=>0101010
[1,3,5,2,7,6,4,8]=>0101010
[1,3,5,7,6,2,4,8]=>0100010
[1,3,5,7,4,6,8,2]=>0101000
[1,3,5,7,4,6,2,8]=>0101000
[1,3,5,7,4,2,6,8]=>0101000
[1,3,5,4,7,2,6,8]=>0101000
[1,3,5,4,7,8,2,6]=>0101000
[1,3,5,4,7,2,8,6]=>0101010
[1,3,5,7,4,2,8,6]=>0101010
[1,3,5,7,4,8,2,6]=>0101000
[1,3,5,7,4,8,6,2]=>0101010
[1,3,5,7,8,4,6,2]=>0101000
[1,3,5,7,8,4,2,6]=>0101000
[1,3,5,2,7,8,6,4]=>0101010
[1,3,5,7,2,8,6,4]=>0101010
[1,3,5,7,8,2,6,4]=>0101000
[1,3,5,7,8,6,2,4]=>0100010
[2,3,6,1,7,8,5,4]=>1001100
[2,3,7,1,4,8,6,5]=>1000110
[2,6,1,3,7,8,5,4]=>1001100
[2,3,6,8,4,5,1,7]=>1001000
[2,5,7,3,4,8,6,1]=>1010010
[2,6,7,3,4,8,5,1]=>1010100
[6,5,2,4,3,7,1,8]=>1110100
[2,5,4,6,7,1,3,8]=>1001000
[1,7,6,3,5,4,8,2]=>0111010
[2,4,6,3,7,5,1,8]=>1010100
[4,7,2,3,5,6,1,8]=>1100000
[5,3,2,7,4,6,1,8]=>1111000
[1,6,8,5,7,3,4,2]=>0110100
[4,1,2,5,8,3,7,6]=>1010010
[4,6,1,2,5,8,3,7]=>1010000
[4,1,7,2,6,5,8,3]=>1110100
[5,6,7,2,1,4,8,3]=>1110000
[6,4,5,7,1,3,8,2]=>1101000
[6,8,5,2,4,1,7,3]=>1110100
[5,7,6,8,1,4,2,3]=>1100010
[4,1,6,2,8,5,7,3]=>1110100
[7,1,4,2,3,6,8,5]=>1100100
[6,4,2,1,3,8,7,5]=>1101101
[1,5,8,3,4,6,7,2]=>0110000
[8,1,2,3,4,6,7,5]=>1000100
[2,8,1,3,5,4,7,6]=>1001010
[8,7,1,4,3,5,2,6]=>1110001
[8,3,2,1,4,5,7,6]=>1110010
[4,3,2,8,1,6,5,7]=>1110100
[3,8,6,4,2,1,5,7]=>1101010
[3,8,2,1,5,6,4,7]=>1101000
[8,5,2,4,3,1,6,7]=>1110100
[8,3,2,5,4,1,6,7]=>1111000
[6,1,2,7,5,3,8,4]=>1011100
[2,6,1,4,7,3,8,5]=>1010100
[7,3,2,8,6,4,1,5]=>1111010
[2,7,8,4,6,3,1,5]=>1011000
[7,8,2,5,3,6,1,4]=>1110000
[6,3,7,5,1,8,2,4]=>1110100
[8,1,6,3,5,7,2,4]=>1110000
[8,3,2,6,4,7,1,5]=>1111000
[5,8,4,6,1,7,2,3]=>1101000
[8,4,2,5,6,7,1,3]=>1101000
[2,3,8,7,6,5,1,4]=>1000111
[1,5,8,7,2,6,4,3]=>0111001
[2,5,8,7,3,6,1,4]=>1010001
[4,1,8,7,2,6,5,3]=>1110101
[1,2,8,7,3,6,5,4]=>0011101
[4,5,8,7,1,2,6,3]=>1010001
[1,5,8,7,3,2,6,4]=>0111001
[4,5,8,7,3,2,1,6]=>1110001
[2,6,8,1,7,5,4,3]=>1011100
[2,6,8,3,7,5,1,4]=>1010100
[1,6,8,4,7,2,5,3]=>0111000
[1,6,8,3,7,2,5,4]=>0111000
[2,5,8,1,7,6,4,3]=>1011010
[2,5,8,3,7,6,1,4]=>1010010
[3,2,8,4,7,6,1,5]=>1101010
[1,5,8,4,7,2,6,3]=>0111000
[1,5,8,3,7,2,6,4]=>0111000
[3,1,8,4,7,2,6,5]=>1101100
[5,6,8,1,2,7,4,3]=>1011000
[1,6,8,4,2,7,5,3]=>0111100
[1,6,8,2,3,7,5,4]=>0101100
[1,5,8,4,2,7,6,3]=>0111010
[5,6,8,4,3,2,1,7]=>1111000
[7,1,4,8,6,2,5,3]=>1110010
[7,3,1,8,6,2,5,4]=>1111010
[7,3,4,8,6,2,1,5]=>1110010
[7,1,5,8,2,6,4,3]=>1111000
[7,1,4,8,2,6,5,3]=>1110100
[7,4,5,8,1,2,6,3]=>1011000
[3,6,2,8,7,5,1,4]=>1100101
[1,6,4,8,7,2,5,3]=>0111001
[3,2,4,8,7,6,1,5]=>1100011
[1,4,5,8,7,2,6,3]=>0110001
[3,1,4,8,7,2,6,5]=>1100101
[1,6,5,8,2,7,4,3]=>0111100
[2,6,5,8,3,7,1,4]=>1010100
[1,6,4,8,2,7,5,3]=>0111100
[2,6,1,8,3,7,5,4]=>1011100
[2,4,5,8,3,7,1,6]=>1010000
[1,4,5,8,3,2,7,6]=>0110010
[4,6,5,8,3,2,1,7]=>1110100
[7,6,2,3,8,5,1,4]=>1100110
[7,6,1,4,8,2,5,3]=>1110010
[7,6,3,4,8,2,1,5]=>1110010
[7,2,5,3,8,6,1,4]=>1110010
[7,2,1,4,8,6,5,3]=>1110110
[7,2,1,3,8,6,5,4]=>1101110
[2,6,5,3,8,7,1,4]=>1010101
[2,6,1,4,8,7,5,3]=>1010101
[1,3,5,4,8,2,7,6]=>0101010
[7,6,5,1,2,8,4,3]=>1011110
[7,1,5,2,3,8,6,4]=>1101010
[7,1,2,4,3,8,6,5]=>1010110
[7,2,5,4,3,8,1,6]=>1111000
[1,6,2,4,3,8,7,5]=>0110101
[2,6,5,4,3,8,1,7]=>1011100
[7,6,5,1,3,2,8,4]=>1101110
[8,2,7,6,5,4,1,3]=>1101110
[7,2,8,6,5,4,3,1]=>1111110
[3,2,8,7,6,5,1,4]=>1100111
[4,8,7,6,5,3,1,2]=>1010111
[7,8,6,1,5,4,3,2]=>1111010
[4,8,5,7,6,3,2,1]=>1110110
[3,2,4,6,8,1,5,7]=>1100000
[3,5,7,2,4,8,1,6]=>1100000
[3,5,7,2,4,6,8,1]=>1100000
[4,5,1,3,6,8,2,7]=>1100000
[4,3,5,7,2,6,8,1]=>1110000
[4,3,5,1,7,8,2,6]=>1110000
[4,6,3,5,1,7,8,2]=>1110000
[4,6,3,5,7,2,8,1]=>1110000
[5,1,6,7,3,4,8,2]=>1110000
[1,6,7,3,4,5,8,2]=>0110000
[2,6,7,4,5,8,1,3]=>1001000
[2,6,7,4,8,1,3,5]=>1001000
[1,4,6,7,3,8,2,5]=>0110000
[3,5,2,6,7,4,8,1]=>1101000
[6,3,1,7,8,2,4,5]=>1110000
[5,7,2,8,1,3,4,6]=>1100000
[6,3,7,2,8,1,4,5]=>1110000
[6,3,7,2,5,8,1,4]=>1110000
[6,2,4,5,7,3,8,1]=>1110000
[2,4,6,7,1,5,8,3]=>1010000
[2,4,7,1,5,6,8,3]=>1010000
[3,7,1,5,6,8,2,4]=>1100000
[4,6,7,1,2,5,8,3]=>1010000
[1,5,6,7,2,4,8,3]=>0110000
[5,6,2,4,1,7,8,3]=>1110000
[1,5,4,6,2,7,8,3]=>0111000
[5,6,4,7,1,3,8,2]=>1101000
[8,4,5,2,6,1,3,7]=>1101000
[6,4,3,7,2,5,8,1]=>1111000
[6,4,3,7,2,8,1,5]=>1111000
[7,4,5,3,1,6,8,2]=>1111000
[6,4,3,7,5,1,8,2]=>1111100
[5,6,3,7,4,1,8,2]=>1111000
[6,7,4,2,1,5,8,3]=>1111000
[6,7,4,2,1,8,3,5]=>1111000
[5,6,7,3,1,8,2,4]=>1110000
[5,6,3,7,8,1,2,4]=>1010000
[5,6,3,7,2,4,8,1]=>1110000
[5,6,7,2,3,8,1,4]=>1100000
[5,6,7,2,8,1,3,4]=>1100000
[6,7,3,8,1,2,4,5]=>1010000
[6,7,3,2,8,1,4,5]=>1110000
[7,6,4,2,1,3,8,5]=>1101110
[7,6,3,4,1,2,8,5]=>1010110
[7,6,3,2,4,1,8,5]=>1110110
[7,5,3,2,6,1,8,4]=>1111100
[6,5,3,2,7,8,1,4]=>1110100
[6,4,7,2,5,1,8,3]=>1111000
[6,4,7,5,1,2,8,3]=>1011100
[5,6,4,2,7,3,8,1]=>1111000
[6,5,3,7,1,8,2,4]=>1110100
[6,5,7,2,1,4,8,3]=>1110100
[5,4,6,7,3,1,8,2]=>1111000
[5,7,8,3,6,4,1,2]=>1011000
[3,7,8,5,6,4,1,2]=>1001100
[3,7,8,5,6,1,4,2]=>1100100
[1,7,8,5,6,3,4,2]=>0110100
[1,7,5,8,6,3,4,2]=>0110110
[3,7,5,8,6,1,4,2]=>1100110
[3,7,5,8,6,4,1,2]=>1001110
[5,7,3,8,6,4,1,2]=>1011010
[7,3,8,5,6,4,1,2]=>1011100
[7,3,5,8,6,4,1,2]=>1011010
[3,5,7,8,6,4,1,2]=>1001010
[1,5,7,8,6,3,4,2]=>0110010
[1,5,7,8,3,6,4,2]=>0111000
[5,3,7,8,1,6,4,2]=>1111000
[5,3,7,8,6,1,4,2]=>1110010
[7,3,5,8,6,1,4,2]=>1110010
[7,3,8,5,6,1,4,2]=>1110100
[7,8,3,5,6,1,4,2]=>1110000
[7,8,1,5,6,3,4,2]=>1110000
[7,1,8,5,6,3,4,2]=>1110100
[7,1,5,8,6,3,4,2]=>1110010
[5,1,7,8,6,3,4,2]=>1110010
[5,1,7,8,3,6,4,2]=>1111000
[3,1,7,8,5,6,4,2]=>1101100
[1,3,7,8,5,6,4,2]=>0101100
[3,1,7,5,8,6,4,2]=>1101110
[5,1,7,3,8,6,4,2]=>1111010
[7,1,5,3,8,6,4,2]=>1111010
[7,1,5,8,3,6,4,2]=>1111000
[7,8,1,5,3,6,4,2]=>1111000
[7,8,3,5,1,6,4,2]=>1111000
[7,3,8,5,1,6,4,2]=>1111100
[7,3,5,8,1,6,4,2]=>1111000
[7,3,5,1,8,6,4,2]=>1111010
[5,3,7,1,8,6,4,2]=>1111010
[3,5,7,1,8,6,4,2]=>1101010
[1,5,7,3,8,6,4,2]=>0111010
[1,7,5,3,8,6,4,2]=>0111110
[3,7,5,1,8,6,4,2]=>1101110
[5,7,3,1,8,6,4,2]=>1111010
[5,7,3,8,6,1,4,2]=>1110010
[3,7,5,8,1,6,4,2]=>1101100
[1,7,5,8,3,6,4,2]=>0111100
[1,7,8,5,3,6,4,2]=>0111100
[3,7,8,5,1,6,4,2]=>1101100
[5,7,8,3,6,1,4,2]=>1110000
[5,7,8,6,3,1,4,2]=>1110010
[7,5,8,6,1,3,4,2]=>1100110
[5,7,8,1,6,3,4,2]=>1110000
[5,7,8,1,3,6,4,2]=>1101000
[1,7,8,3,5,6,4,2]=>0111000
[1,7,3,8,5,6,4,2]=>0111100
[3,7,1,8,5,6,4,2]=>1101100
[5,7,1,8,3,6,4,2]=>1111000
[5,7,1,8,6,3,4,2]=>1110010
[7,5,1,8,6,3,4,2]=>1110110
[7,5,8,1,6,3,4,2]=>1110100
[7,8,5,1,6,3,4,2]=>1110100
[7,8,5,1,3,6,4,2]=>1101100
[7,5,8,1,3,6,4,2]=>1101100
[7,5,1,8,3,6,4,2]=>1111100
[7,5,1,3,8,6,4,2]=>1101110
[5,7,1,3,8,6,4,2]=>1101010
[3,7,1,5,8,6,4,2]=>1101010
[1,7,3,5,8,6,4,2]=>0111010
[1,5,3,7,8,6,4,2]=>0111010
[3,5,1,7,8,6,4,2]=>1101010
[5,3,1,7,8,6,4,2]=>1111010
[7,3,1,5,8,6,4,2]=>1111010
[7,3,1,8,5,6,4,2]=>1111100
[7,8,1,3,5,6,4,2]=>1101000
[7,1,8,3,5,6,4,2]=>1111000
[7,1,3,8,5,6,4,2]=>1101100
[7,1,3,5,8,6,4,2]=>1101010
[5,1,3,7,8,6,4,2]=>1101010
[3,1,5,7,8,6,4,2]=>1101010
[4,3,1,2,6,5,8,7]=>1010101
[6,1,4,3,5,2,8,7]=>1110001
[4,6,3,5,1,2,8,7]=>1010001
[6,2,4,5,1,3,8,7]=>1100001
[2,3,6,1,5,4,8,7]=>1001001
[2,1,6,5,3,4,8,7]=>1010101
[3,5,6,2,4,1,8,7]=>1100001
[8,7,6,1,3,2,4,5]=>1100011
[2,5,3,4,8,1,7,6]=>1010010
[5,1,8,2,3,4,7,6]=>1100010
[5,4,7,6,2,8,1,3]=>1101010
[2,1,6,8,5,7,3,4]=>1010100
[2,1,8,4,6,7,3,5]=>1011000
[3,1,8,6,2,7,5,4]=>1101110
[3,8,1,5,6,7,2,4]=>1100000
[8,2,3,5,7,1,6,4]=>1101000
[5,8,4,3,7,1,6,2]=>1111000
[2,8,3,6,7,5,1,4]=>1010100
[8,1,2,7,3,5,6,4]=>1011000
[6,8,4,2,1,3,7,5]=>1101100
[4,3,8,2,7,6,1,5]=>1110010
[2,1,4,5,8,3,7,6]=>1010010
[8,4,7,1,5,2,3,6]=>1101000
[7,3,5,8,4,2,1,6]=>1111000
[2,4,8,3,5,6,7,1]=>1010000
[6,4,7,5,2,3,8,1]=>1101100
[6,4,8,1,7,3,2,5]=>1111000
[4,2,3,1,8,7,5,6]=>1100101
[2,1,4,3,8,7,5,6]=>1010101
[4,3,1,2,8,6,7,5]=>1010110
[5,1,6,7,8,4,3,2]=>1111000
[8,7,2,6,4,1,5,3]=>1111001
[2,1,5,7,8,4,6,3]=>1011000
[6,4,1,5,7,2,8,3]=>1111000
[7,4,8,1,2,5,6,3]=>1011000
[6,1,7,4,3,2,8,5]=>1111100
[6,8,3,4,2,1,7,5]=>1110100
[4,2,6,1,5,7,8,3]=>1110000
[7,1,4,8,3,5,6,2]=>1110000
[3,4,8,2,5,7,6,1]=>1100010
[3,7,1,4,5,6,8,2]=>1100000
[4,7,5,6,8,3,1,2]=>1010100
[6,5,3,8,4,7,1,2]=>1011100
[8,6,4,7,5,3,1,2]=>1011110
[1,6,3,7,5,8,4,2]=>0111100
[1,3,7,4,5,8,6,2]=>0101010
[7,3,8,5,4,6,1,2]=>1011100
[3,4,8,5,6,7,1,2]=>1000100
[4,7,3,8,5,6,1,2]=>1010100
[6,8,4,7,5,3,1,2]=>1011100
[1,7,6,5,3,8,4,2]=>0111110
[2,7,6,3,1,4,5,8]=>1010010
[2,7,6,4,5,1,3,8]=>1001010
[5,7,2,6,4,1,3,8]=>1101000
[7,6,1,5,3,8,4,2]=>1111010
[1,8,2,7,3,6,5,4]=>0111100
[2,1,3,8,4,7,5,6]=>1001100
[3,1,2,8,4,6,7,5]=>1001100
[4,1,7,2,8,5,6,3]=>1110100
[5,1,2,4,8,3,7,6]=>1010010
[2,8,4,1,5,6,3,7]=>1011000
[1,7,2,8,5,3,6,4]=>0111100
[1,2,3,8,4,5,7,6]=>0001010
[2,4,8,3,1,5,6,7]=>1010000
[3,4,2,7,1,5,6,8]=>1100000
[3,2,5,6,1,4,7,8]=>1100000
[4,7,3,8,2,1,5,6]=>1110000
[7,4,8,3,2,1,5,6]=>1111000
[1,3,7,2,8,4,6,5]=>0101100
[2,6,4,5,7,1,3,8]=>1001000
[5,4,6,2,7,1,3,8]=>1101000
[7,6,8,5,1,4,3,2]=>1110110
[6,5,1,2,8,3,7,4]=>1011100
[6,8,4,1,3,7,5,2]=>1101100
[6,3,7,1,8,4,5,2]=>1111000
[5,8,3,1,7,4,6,2]=>1111000
[4,7,1,2,8,3,6,5]=>1010100
[3,4,1,8,5,6,7,2]=>1100100
[1,2,8,7,6,3,5,4]=>0011011
[2,3,1,8,7,4,5,6]=>1001001
[2,6,1,4,8,7,3,5]=>1010001
[5,8,2,1,7,6,3,4]=>1110010
[8,7,1,6,5,4,3,2]=>1111101
[3,1,8,7,6,4,5,2]=>1101011
[1,2,3,4,8,7,5,6]=>0000101
[1,2,3,8,6,4,5,7]=>0001010
[1,2,8,5,3,4,6,7]=>0010100
[1,8,4,2,3,5,6,7]=>0101000
[2,4,7,5,6,8,3,1]=>1010100
[2,5,3,8,7,4,6,1]=>1011001
[3,1,8,5,7,4,2,6]=>1101100
[8,3,5,7,4,2,6,1]=>1111000
[8,3,6,2,4,5,7,1]=>1110000
[2,7,6,4,5,8,3,1]=>1011010
[4,8,1,7,6,3,2,5]=>1110010
[7,3,6,4,2,8,5,1]=>1111100
[4,7,8,1,3,6,2,5]=>1100000
[5,8,7,1,4,3,2,6]=>1110001
[5,6,1,2,4,3,8,7]=>1010001
[3,6,8,1,2,7,5,4]=>1001100
[8,4,6,2,1,3,7,5]=>1101100
[4,8,1,5,3,7,2,6]=>1110000
[5,4,8,7,3,1,2,6]=>1011001
[6,4,3,8,1,5,2,7]=>1111000
[6,8,3,7,2,5,4,1]=>1111000
[5,3,6,8,7,2,4,1]=>1110001
[5,7,4,2,8,3,6,1]=>1111000
[6,4,7,2,1,8,3,5]=>1111000
[6,5,3,1,4,7,2,8]=>1110100
[5,7,8,2,6,4,1,3]=>1101000
[2,6,8,4,5,7,1,3]=>1001000
[3,6,8,5,7,1,4,2]=>1100100
[1,7,4,8,6,2,3,5]=>0101010
[2,7,4,8,5,6,1,3]=>1001100
[6,3,7,2,8,5,1,4]=>1110100
[3,6,2,5,7,8,1,4]=>1100000
[5,3,6,7,1,8,4,2]=>1111000
[8,1,3,6,7,2,4,5]=>1100000
[8,1,4,2,7,5,3,6]=>1110100
[6,1,3,8,2,7,4,5]=>1101000
[4,1,5,3,2,8,6,7]=>1110010
[2,7,1,4,3,8,5,6]=>1010100
[1,7,5,2,8,6,3,4]=>0110110
[7,4,2,5,1,8,6,3]=>1111010
[5,6,3,2,1,8,7,4]=>1111001
[4,5,3,2,7,1,8,6]=>1110010
[5,3,6,2,8,1,7,4]=>1111000
[6,4,2,8,5,1,7,3]=>1111100
[1,8,4,7,2,5,3,6]=>0111000
[1,5,8,4,2,6,3,7]=>0111000
[3,5,7,4,1,6,8,2]=>1101000
[4,5,8,3,1,7,6,2]=>1110010
[3,4,7,8,2,1,6,5]=>1100100
[4,6,3,5,2,1,8,7]=>1110001
[3,5,7,1,2,6,4,8]=>1001000
[3,6,2,1,4,7,5,8]=>1100100
[7,4,1,2,8,6,3,5]=>1011010
[5,2,6,1,3,4,8,7]=>1100001
[3,8,2,6,5,4,1,7]=>1101100
[3,8,7,2,5,4,1,6]=>1101001
[7,5,1,6,8,4,3,2]=>1111100
[7,4,2,1,5,6,3,8]=>1111000
[7,3,8,1,5,4,6,2]=>1111000
[7,2,8,6,5,1,3,4]=>1100110
[6,2,7,8,5,4,1,3]=>1101100
[5,3,2,6,7,4,1,8]=>1111000
[4,8,2,6,5,7,1,3]=>1100100
[4,3,7,2,5,6,1,8]=>1110000
[3,8,7,6,2,4,1,5]=>1100011
[6,7,1,4,3,2,5,8]=>1110000
[3,5,6,2,4,7,1,8]=>1100000
[3,5,8,7,2,4,6,1]=>1100001
[1,7,8,2,5,4,3,6]=>0111000
[2,7,1,3,6,5,4,8]=>1001100
[5,7,1,4,6,3,2,8]=>1110000
[6,3,7,1,5,4,2,8]=>1111000
[4,7,1,6,3,5,2,8]=>1110000
[8,7,3,6,1,5,4,2]=>1111001
[5,7,8,3,2,1,4,6]=>1110000
[5,4,2,1,7,8,3,6]=>1111000
[4,7,8,3,5,2,1,6]=>1110000
[8,3,7,6,4,2,1,5]=>1111010
[8,3,2,1,4,7,6,5]=>1110110
[6,4,1,7,3,8,5,2]=>1111100
[1,7,5,3,8,2,6,4]=>0111100
[5,1,7,4,2,8,6,3]=>1111010
[8,6,3,2,7,5,1,4]=>1110110
[2,7,5,1,3,8,6,4]=>1001110
[8,7,4,2,6,1,5,3]=>1111001
[5,2,6,1,8,7,4,3]=>1111001
[1,7,6,4,3,8,2,5]=>0111010
[1,3,8,2,4,7,6,5]=>0100110
[3,7,5,1,8,6,2,4]=>1100110
[5,1,4,3,2,7,8,6]=>1110010
[3,7,6,2,4,1,8,5]=>1100110
[5,3,1,7,8,4,2,6]=>1111000
[4,1,7,8,5,3,2,6]=>1110100
[2,7,6,4,1,3,8,5]=>1001110
[8,4,2,7,6,3,1,5]=>1111010
[6,3,1,7,5,2,8,4]=>1111100
[6,2,7,5,3,1,8,4]=>1111100
[1,5,8,2,7,4,6,3]=>0111000
[8,4,7,3,1,6,5,2]=>1111100
[4,1,6,8,5,7,3,2]=>1110100
[1,8,6,7,3,4,2,5]=>0110010
[6,7,1,8,3,4,2,5]=>1110000
[7,8,1,6,3,4,2,5]=>1110000
[7,8,2,5,1,6,3,4]=>1110000
[1,8,5,6,2,7,3,4]=>0110100
[5,7,1,6,2,8,3,4]=>1110000
[5,6,2,7,1,8,3,4]=>1110000
[6,7,2,5,1,8,3,4]=>1110000
[6,7,2,4,3,8,1,5]=>1110000
[2,5,1,8,6,7,3,4]=>1010010
[2,6,5,8,1,7,3,4]=>1010100
[1,8,2,7,4,5,3,6]=>0111000
[2,4,3,8,5,6,1,7]=>1010100
[2,3,1,8,5,6,4,7]=>1001100
[4,6,2,7,1,5,3,8]=>1110000
[4,7,1,6,2,5,3,8]=>1110000
[4,6,3,5,1,7,2,8]=>1110000
[5,6,3,7,1,4,2,8]=>1110000
[1,8,5,6,3,4,2,7]=>0110100
[4,7,1,8,5,6,2,3]=>1100100
[3,4,2,6,5,8,1,7]=>1100100
[3,5,4,6,2,8,1,7]=>1101000
[3,7,1,6,2,8,4,5]=>1101000
[3,5,2,7,4,8,1,6]=>1101000
[4,7,2,3,1,8,5,6]=>1100100
[2,4,3,8,1,7,5,6]=>1010100
[2,5,8,3,4,1,6,7]=>1010000
[5,6,2,7,4,3,8,1]=>1111000
[5,1,7,3,4,2,8,6]=>1110010
[4,6,7,3,2,5,8,1]=>1110000
[3,7,2,1,4,5,8,6]=>1100010
[2,7,1,3,4,8,6,5]=>1000110
[2,6,7,3,8,5,4,1]=>1011100
[2,6,1,8,4,5,3,7]=>1011000
[4,2,1,6,5,3,8,7]=>1110101
[6,2,4,3,1,5,8,7]=>1110001
[4,6,2,1,5,3,8,7]=>1110001
[8,4,2,1,6,5,3,7]=>1111100
[2,6,4,5,1,8,7,3]=>1011001
[6,8,7,2,1,4,3,5]=>1110001
[6,8,2,1,7,4,3,5]=>1111000
[6,8,2,1,4,3,7,5]=>1110100
[8,6,2,4,3,1,5,7]=>1110010
[6,8,2,4,3,1,7,5]=>1110100
[2,8,4,6,7,3,1,5]=>1011000
[2,8,6,7,4,3,1,5]=>1011010
[6,8,7,2,4,3,1,5]=>1110001
[4,6,5,2,8,3,7,1]=>1110100
[2,6,4,5,8,3,7,1]=>1011000
[6,4,2,8,3,5,7,1]=>1111000
[8,4,2,6,3,5,1,7]=>1111000
[4,2,6,3,8,7,5,1]=>1110101
[8,2,4,3,6,5,1,7]=>1110100
[4,2,1,6,8,7,5,3]=>1110101
[4,2,1,6,5,8,7,3]=>1110101
[4,2,1,3,6,8,7,5]=>1100101
[2,4,3,1,8,6,5,7]=>1010110
[6,2,1,8,7,4,3,5]=>1111001
[6,2,1,8,4,3,7,5]=>1111100
[4,6,8,7,5,2,1,3]=>1100101
[4,6,5,8,7,2,1,3]=>1100101
[2,6,8,7,4,5,1,3]=>1001001
[2,4,8,6,7,5,1,3]=>1000110
[4,2,8,6,5,7,1,3]=>1100110
[6,4,8,2,1,5,7,3]=>1111000
[2,6,8,4,7,1,5,3]=>1011000
[4,6,5,8,2,1,7,3]=>1110100
[4,8,6,7,2,1,3,5]=>1100010
[6,2,3,5,1,4,8,7]=>1100001
[7,4,5,2,3,8,6,1]=>1101010
[7,3,2,5,4,8,6,1]=>1111010
[3,5,1,6,4,2,8,7]=>1101001
[3,6,2,4,5,1,8,7]=>1100001
[7,2,3,4,5,8,6,1]=>1100010
[8,2,3,4,5,7,1,6]=>1100000
[6,7,3,4,8,5,2,1]=>1110100
[5,7,1,3,8,6,2,4]=>1100010
[4,7,3,2,8,6,1,5]=>1110010
[3,8,2,6,7,4,5,1]=>1101000
[4,8,1,5,6,7,3,2]=>1110000
[6,8,2,5,1,7,3,4]=>1110000
[7,8,3,4,6,2,1,5]=>1110000
[4,8,2,5,1,6,7,3]=>1110000
[3,8,2,5,4,7,6,1]=>1101010
[3,7,6,1,8,5,2,4]=>1100110
[4,7,2,3,8,5,1,6]=>1100100
[4,6,7,1,8,5,3,2]=>1110100
[3,6,1,7,8,5,4,2]=>1101100
[2,1,5,7,3,8,6,4]=>1011010
[6,4,7,2,8,5,3,1]=>1111100
[7,6,1,4,8,5,2,3]=>1100110
[4,1,2,3,7,8,6,5]=>1000110
[3,4,2,1,8,5,6,7]=>1100100
[8,2,3,5,7,1,4,6]=>1100000
[8,1,3,6,4,7,2,5]=>1101000
[5,4,8,3,6,7,1,2]=>1011000
[4,5,8,3,6,7,2,1]=>1110000
[2,1,5,8,4,6,7,3]=>1011000
[4,6,8,3,5,2,7,1]=>1110000
[5,7,8,3,2,4,1,6]=>1110000
[3,8,2,4,5,6,7,1]=>1100000
[6,8,2,3,1,4,5,7]=>1100000
[4,3,1,6,5,8,7,2]=>1110101
[8,2,7,4,1,3,6,5]=>1101100
[3,7,8,2,1,4,6,5]=>1100100
[3,7,5,2,8,4,1,6]=>1101100
[3,1,5,2,4,8,7,6]=>1100011
[3,6,4,5,1,8,7,2]=>1101001
[4,3,6,1,2,8,7,5]=>1010101
[6,1,3,5,4,8,7,2]=>1101001
[1,7,3,8,4,6,2,5]=>0111000
[1,6,7,4,8,5,3,2]=>0111100
[8,1,2,5,4,6,3,7]=>1011000
[6,8,3,1,4,7,5,2]=>1110100
[8,4,2,5,7,1,6,3]=>1111000
[1,8,5,3,7,4,6,2]=>0111100
[5,3,2,8,7,1,4,6]=>1110001
[1,2,8,7,5,6,3,4]=>0010101
[4,2,1,7,5,3,6,8]=>1110100
[1,4,8,6,5,7,2,3]=>0100110
[3,5,4,8,6,1,2,7]=>1001010
[4,3,5,8,1,7,2,6]=>1110000
[1,4,5,8,6,7,3,2]=>0110010
[1,7,6,5,8,3,4,2]=>0110110
[7,3,6,1,8,2,4,5]=>1110000
[7,6,4,5,8,1,3,2]=>1101010
[1,6,5,4,8,2,3,7]=>0101100
[5,2,6,3,8,1,4,7]=>1110000
[4,3,1,6,8,7,5,2]=>1110101
[4,3,1,8,5,6,7,2]=>1110100
[6,2,8,4,3,1,7,5]=>1111100
[7,1,6,2,3,4,5,8]=>1100000
[3,8,6,1,2,5,4,7]=>1001010
[1,8,5,4,3,6,2,7]=>0111100
[5,3,8,4,1,2,7,6]=>1011010
[1,8,3,6,5,2,7,4]=>0111100
[4,7,1,8,2,6,5,3]=>1110100
[1,8,2,4,7,6,5,3]=>0110110
[1,4,8,3,5,7,6,2]=>0110010
[8,2,1,4,6,5,7,3]=>1110100
[6,1,5,2,4,7,8,3]=>1110000
[4,1,8,5,2,7,6,3]=>1110110
[4,3,8,5,1,2,6,7]=>1010100
[6,3,5,1,4,2,8,7]=>1110001
[4,1,8,2,3,7,5,6]=>1100100
[5,3,8,7,2,1,4,6]=>1110001
[7,6,5,4,1,3,2,8]=>1101110
[1,8,7,6,2,5,4,3]=>0111011
[4,6,3,1,5,2,7,8]=>1110000
[6,2,7,4,5,1,3,8]=>1101000
[5,2,7,4,1,6,3,8]=>1111000
[5,7,3,4,1,6,2,8]=>1110000
[4,2,8,1,5,6,7,3]=>1110000
[1,7,8,4,5,6,2,3]=>0101000
[1,6,8,4,5,2,7,3]=>0111000
[1,5,8,4,2,6,7,3]=>0111000
[1,5,3,8,2,6,7,4]=>0111000
[1,6,3,8,5,2,7,4]=>0111100
[1,7,3,8,5,6,2,4]=>0110100
[6,2,3,7,5,1,4,8]=>1100100
[4,2,6,1,5,3,7,8]=>1110000
[5,2,6,4,1,3,7,8]=>1101000
[1,2,7,8,5,6,3,4]=>0010100
[1,2,6,8,5,3,7,4]=>0011100
[1,2,6,4,8,3,7,5]=>0011100
[8,7,3,2,1,6,5,4]=>1111101
[8,7,4,1,6,2,3,5]=>1101001
[1,8,3,2,6,4,5,7]=>0111000
[7,3,8,1,5,2,4,6]=>1110000
[3,1,7,2,6,4,5,8]=>1101000
[1,8,4,2,3,6,7,5]=>0101100
[2,5,8,3,4,6,7,1]=>1010000
[4,1,7,2,3,6,8,5]=>1100100
[3,1,7,5,4,2,8,6]=>1101110
[4,6,2,1,5,7,8,3]=>1110000
[4,5,2,3,1,7,8,6]=>1100010
[3,2,6,7,4,1,8,5]=>1101100
[5,6,2,7,1,4,8,3]=>1110000
[6,4,2,8,1,5,7,3]=>1111000
[7,3,6,8,5,2,4,1]=>1110100
[2,7,8,3,6,5,1,4]=>1010100
[2,7,8,5,4,6,3,1]=>1011100
[2,6,8,3,4,7,1,5]=>1010000
[2,5,6,8,3,4,1,7]=>1010000
[2,7,8,3,6,1,4,5]=>1010000
[2,1,3,7,8,5,6,4]=>1001100
[5,1,2,4,8,7,3,6]=>1010001
[2,3,6,1,8,5,7,4]=>1001100
[5,2,6,1,7,8,4,3]=>1111000
[3,6,5,4,1,8,7,2]=>1101101
[5,4,2,3,7,8,6,1]=>1101010
[4,1,8,2,5,7,3,6]=>1110000
[3,1,8,4,7,2,5,6]=>1101000
[2,6,4,1,5,3,8,7]=>1011001
[1,5,8,2,4,7,3,6]=>0110000
[6,2,1,4,7,8,3,5]=>1110000
[3,8,1,4,2,6,5,7]=>1100100
[8,3,4,2,1,6,5,7]=>1110100
[5,3,2,8,1,6,4,7]=>1111000
[2,4,5,8,3,6,1,7]=>1010000
[3,5,8,1,2,6,4,7]=>1001000
[8,6,1,3,5,2,4,7]=>1100010
[5,7,4,3,6,1,8,2]=>1111000
[2,6,4,3,7,8,5,1]=>1011100
[7,4,1,8,3,2,5,6]=>1111000
[2,4,6,5,1,7,8,3]=>1010100
[5,6,1,7,4,2,8,3]=>1111000
[1,3,8,6,2,7,4,5]=>0101010
[4,3,7,5,6,1,8,2]=>1110100
[6,4,7,8,2,1,3,5]=>1101000
[6,7,3,8,4,1,2,5]=>1011000
[2,7,8,3,4,6,1,5]=>1010000
[3,7,8,1,5,4,2,6]=>1101000
[7,5,8,4,1,3,2,6]=>1101100
[4,7,5,8,3,1,2,6]=>1010100
[5,7,3,1,6,8,4,2]=>1111000
[4,6,7,2,8,3,1,5]=>1110000
[4,8,1,2,3,5,7,6]=>1000010
[4,5,6,7,3,1,8,2]=>1110000
[8,5,3,2,7,6,1,4]=>1110110
[7,5,4,6,2,8,1,3]=>1101100
[2,5,1,3,6,8,7,4]=>1001001
[7,5,2,8,4,1,3,6]=>1101100
[7,3,8,5,2,1,4,6]=>1110100
[5,8,3,6,4,7,1,2]=>1011000
[3,5,8,6,7,4,2,1]=>1101010
[3,7,6,8,1,2,5,4]=>1001010
[4,1,6,3,2,5,8,7]=>1110001
[8,6,1,7,2,5,4,3]=>1111010
[8,7,6,1,2,3,5,4]=>1001011
[5,4,1,6,2,3,8,7]=>1101001
[2,6,5,3,4,1,8,7]=>1010101
[5,8,7,6,1,2,3,4]=>1000011
[8,2,7,1,5,4,3,6]=>1111000
[2,1,6,3,8,5,4,7]=>1011100
[2,6,3,1,8,5,4,7]=>1011100
[4,6,2,8,5,1,3,7]=>1100100
[6,5,2,7,4,3,8,1]=>1111100
[4,6,5,2,7,3,8,1]=>1110100
[3,1,6,2,4,8,7,5]=>1100101
[8,7,5,1,2,6,4,3]=>1011101
[2,1,7,6,3,8,4,5]=>1011010
[8,2,3,4,6,7,1,5]=>1100000
[2,8,5,7,4,1,3,6]=>1001100
[7,8,5,3,6,4,2,1]=>1111100
[2,1,4,8,7,5,6,3]=>1010101
[7,4,6,8,5,1,3,2]=>1101100
[6,4,8,3,5,7,1,2]=>1011000
[8,5,7,4,6,2,1,3]=>1101100
[4,1,8,5,6,3,2,7]=>1110100
[5,8,3,2,4,6,1,7]=>1110000
[2,8,4,1,5,3,7,6]=>1011010
[4,8,7,6,5,2,3,1]=>1100111
[2,1,8,6,4,3,7,5]=>1011110
[3,6,7,1,8,5,2,4]=>1100100
[4,2,3,6,8,7,5,1]=>1100101
[6,5,7,3,1,8,4,2]=>1111100
[8,4,2,5,6,1,7,3]=>1111000
[6,1,5,7,2,4,8,3]=>1110000
[7,4,5,1,2,3,8,6]=>1001010
[8,4,7,6,2,1,5,3]=>1111010
[3,5,7,6,4,1,8,2]=>1101010
[2,4,7,5,6,3,8,1]=>1010100
[5,4,1,7,6,2,8,3]=>1111010
[3,5,6,7,1,4,8,2]=>1100000
[4,7,5,2,1,3,8,6]=>1100110
[5,7,2,3,6,4,8,1]=>1101000
[7,1,2,3,5,8,4,6]=>1001000
[6,1,8,2,7,3,4,5]=>1110000
[7,8,6,1,3,2,5,4]=>1101010
[1,8,5,7,2,3,4,6]=>0100100
[8,1,5,7,2,3,6,4]=>1101000
[1,4,5,2,8,6,7,3]=>0110010
[2,3,1,7,8,6,4,5]=>1001010
[2,1,4,6,8,3,7,5]=>1010100
[3,5,7,6,2,8,1,4]=>1100010
[5,4,1,6,3,8,7,2]=>1111001
[4,5,6,1,2,8,7,3]=>1010001
[3,5,6,2,4,8,7,1]=>1100001
[5,4,1,2,8,7,6,3]=>1011011
[5,6,3,7,8,4,2,1]=>1111000
[4,3,2,6,8,1,7,5]=>1110100
[7,1,5,6,3,8,2,4]=>1110000
[1,5,4,2,7,8,3,6]=>0111000
[6,1,2,8,7,4,3,5]=>1011001
[5,1,6,8,4,7,2,3]=>1101000
[5,1,3,8,4,2,7,6]=>1101010
[3,1,6,8,7,4,2,5]=>1101001
[3,6,5,8,4,7,1,2]=>1001100
[6,5,8,4,3,1,2,7]=>1011100
[8,5,1,3,7,4,6,2]=>1101100
[3,2,8,1,4,7,6,5]=>1100110
[6,4,3,8,2,5,7,1]=>1111000
[3,2,5,8,4,1,7,6]=>1101010
[6,8,2,3,4,7,5,1]=>1100100
[2,1,7,8,3,4,6,5]=>1010100
[7,5,1,8,4,2,6,3]=>1111100
[5,6,1,8,2,7,4,3]=>1111000
[3,6,8,5,2,7,4,1]=>1101100
[2,1,6,5,4,8,3,7]=>1011100
[2,1,7,3,5,8,6,4]=>1011010
[7,8,1,2,4,5,6,3]=>1010000
[3,8,7,4,1,2,5,6]=>1001001
[3,6,8,1,5,7,2,4]=>1100000
[3,5,7,8,4,6,1,2]=>1001000
[7,5,2,8,4,6,3,1]=>1111100
[7,8,2,4,3,1,5,6]=>1110000
[8,4,3,1,7,5,2,6]=>1111100
[7,6,2,8,5,1,4,3]=>1110110
[4,3,8,7,1,6,5,2]=>1110101
[4,7,1,8,5,2,6,3]=>1110100
[3,7,5,8,1,6,2,4]=>1100100
[3,7,6,4,5,1,8,2]=>1101010
[4,7,5,6,3,8,2,1]=>1110100
[4,2,7,5,8,3,6,1]=>1110100
[5,8,2,7,3,4,6,1]=>1110000
[5,7,2,1,8,3,6,4]=>1111000
[7,8,1,2,3,4,6,5]=>1000100
[6,8,5,2,1,7,3,4]=>1110100
[5,6,2,4,3,1,8,7]=>1110001
[4,6,2,1,7,8,3,5]=>1110000
[6,3,2,1,4,8,5,7]=>1110100
[7,1,8,3,5,4,6,2]=>1111000
[7,1,2,4,8,5,6,3]=>1010100
[8,7,6,5,1,3,2,4]=>1100111
[8,7,6,2,4,3,1,5]=>1110011
[7,6,8,1,5,4,3,2]=>1111010
[7,6,1,8,5,4,3,2]=>1111110
[6,5,8,1,7,4,3,2]=>1111100
[4,3,8,7,6,1,5,2]=>1110011
[6,5,8,7,4,1,3,2]=>1101101
[5,4,8,7,6,3,1,2]=>1011011
[1,4,8,6,3,2,5,7]=>0110010
[7,4,1,6,3,8,5,2]=>1111100
[7,6,3,1,5,8,4,2]=>1111010
[1,6,3,8,5,2,4,7]=>0110100
[4,6,3,7,5,2,1,8]=>1110100
[3,7,2,6,5,4,1,8]=>1101100
[3,2,1,6,8,4,5,7]=>1101000
[1,7,4,6,2,8,5,3]=>0111100
[6,2,5,1,7,4,8,3]=>1111000
[3,5,7,4,8,6,1,2]=>1001010
[5,2,7,4,1,6,8,3]=>1111000
[4,5,8,2,1,7,6,3]=>1110010
[1,6,4,8,5,2,7,3]=>0111100
[7,4,1,5,3,8,2,6]=>1111000
[3,4,1,2,7,8,6,5]=>1000110
[4,1,3,2,8,6,7,5]=>1100110
[3,1,2,4,7,6,8,5]=>1000110
[8,1,3,5,4,7,2,6]=>1101000
[7,1,4,3,5,2,8,6]=>1110010
[3,2,8,1,6,5,4,7]=>1101100
[6,8,4,1,2,5,3,7]=>1011000
[8,2,1,5,6,4,3,7]=>1111000
[4,7,1,8,2,5,3,6]=>1110000
[6,7,8,1,4,5,3,2]=>1110000
[3,2,5,4,7,8,1,6]=>1101000
[8,4,7,6,2,3,1,5]=>1101010
[6,1,2,8,7,3,5,4]=>1011001
[1,2,7,5,6,8,3,4]=>0010100
[5,7,2,3,8,1,6,4]=>1101000
[3,5,2,6,1,8,7,4]=>1101001
[3,2,5,6,7,8,1,4]=>1100000
[5,4,2,6,8,7,1,3]=>1101001
[6,4,1,2,8,7,3,5]=>1011001
[4,3,8,5,2,1,6,7]=>1110100
[3,6,4,5,2,1,8,7]=>1101001
[7,5,4,2,3,8,1,6]=>1101100
[5,6,3,1,8,2,7,4]=>1111000
[6,5,4,3,1,2,8,7]=>1011101
[4,5,2,1,6,8,3,7]=>1110000
[5,6,2,8,1,7,4,3]=>1111000
[1,5,6,3,4,8,2,7]=>0110000
[2,1,4,5,8,6,3,7]=>1010010
[6,7,1,3,4,8,2,5]=>1100000
[6,7,8,2,3,5,4,1]=>1101000
[5,8,6,2,3,7,4,1]=>1101010
[1,8,3,4,7,6,2,5]=>0110010
[5,8,6,1,7,2,4,3]=>1110010
[3,1,2,8,6,4,5,7]=>1001010
[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]=>1111000
[6,7,2,1,8,4,3,5]=>1111000
[6,7,3,1,5,8,2,4]=>1110000
[2,4,1,6,8,5,3,7]=>1010100
[2,5,6,1,8,4,3,7]=>1011000
[5,4,7,6,1,8,2,3]=>1101010
[3,5,6,8,4,7,2,1]=>1101000
[2,5,6,8,7,3,4,1]=>1010001
[2,4,8,5,7,3,6,1]=>1010100
[5,3,7,8,4,6,2,1]=>1111000
[6,7,3,8,4,5,2,1]=>1111000
[4,2,8,6,7,3,5,1]=>1110010
[3,2,8,7,5,4,6,1]=>1101101
[2,1,8,7,6,4,3,5]=>1011011
[6,3,8,7,5,1,2,4]=>1010101
[2,8,7,4,1,3,5,6]=>1001001
[2,5,3,7,6,8,1,4]=>1010010
[2,8,7,1,4,5,3,6]=>1010001
[4,2,1,8,7,3,5,6]=>1110001
[8,7,4,6,2,3,1,5]=>1101001
[5,1,6,3,2,8,7,4]=>1111001
[8,7,2,3,5,4,1,6]=>1101001
[3,4,2,8,6,1,5,7]=>1100010
[8,1,4,2,3,6,7,5]=>1100100
[6,8,3,5,4,7,1,2]=>1011000
[1,8,2,5,7,6,3,4]=>0110010
[4,1,6,8,2,3,7,5]=>1100100
[1,4,6,3,7,2,8,5]=>0110100
[6,2,1,8,4,5,3,7]=>1111000
[4,7,3,8,5,2,1,6]=>1110100
[3,1,7,4,8,5,2,6]=>1101100
[7,4,1,6,3,2,8,5]=>1111100
[3,8,6,2,7,4,1,5]=>1101010
[7,3,1,4,5,2,8,6]=>1110010
[8,1,3,6,7,5,4,2]=>1101100
[6,4,2,8,5,1,3,7]=>1101100
[8,6,2,4,1,3,7,5]=>1100110
[4,7,5,1,8,6,3,2]=>1110110
[6,7,5,1,4,2,8,3]=>1110100
[6,2,4,1,7,5,8,3]=>1110100
[5,2,1,8,3,6,7,4]=>1111000
[3,6,5,8,4,1,7,2]=>1101100
[7,3,8,2,5,6,4,1]=>1111000
[5,7,3,1,6,4,8,2]=>1111000
[6,1,3,7,4,8,5,2]=>1101100
[3,2,1,7,4,8,5,6]=>1101100
[3,1,5,4,2,8,6,7]=>1101010
[4,1,5,2,7,6,3,8]=>1110010
[6,2,7,1,4,8,5,3]=>1110100
[7,5,4,1,3,8,6,2]=>1101110
[4,3,2,1,8,5,7,6]=>1110110
[4,2,1,7,3,6,5,8]=>1110100
[7,4,3,2,8,1,6,5]=>1111100
[2,7,5,3,8,1,4,6]=>1010100
[1,8,5,3,6,4,2,7]=>0111100
[8,1,6,2,7,4,3,5]=>1111000
[7,3,1,6,5,4,2,8]=>1111100
[8,5,7,4,3,6,2,1]=>1111100
[2,8,5,6,1,4,3,7]=>1010100
[3,7,5,8,2,1,4,6]=>1100100
[6,5,8,4,1,3,7,2]=>1101100
[5,4,8,3,2,1,7,6]=>1111010
[2,4,7,1,3,6,5,8]=>1000100
[5,7,4,8,1,3,6,2]=>1101000
[5,1,7,8,2,4,6,3]=>1110000
[3,6,7,8,1,2,5,4]=>1001000
[4,6,7,2,8,1,3,5]=>1100000
[6,3,7,1,8,2,5,4]=>1111000
[5,7,1,4,8,2,6,3]=>1110000
[2,7,4,1,8,3,6,5]=>1011100
[6,1,2,7,8,3,5,4]=>1011000
[3,6,4,7,8,1,2,5]=>1001000
[3,7,4,8,5,2,1,6]=>1101100
[7,2,5,8,6,3,1,4]=>1110010
[4,8,1,7,6,2,3,5]=>1100010
[4,8,2,1,7,5,3,6]=>1110100
[7,3,8,1,6,4,2,5]=>1111000
[5,8,7,1,3,6,4,2]=>1101001
[2,8,7,1,6,3,5,4]=>1011001
[2,7,6,5,1,4,3,8]=>1010110
[3,8,7,6,2,1,5,4]=>1101011
[5,8,7,2,6,1,4,3]=>1110001
[7,3,8,6,5,1,2,4]=>1010110
[5,8,6,4,3,2,1,7]=>1111010
[8,7,6,2,5,3,1,4]=>1110011
[8,1,2,3,4,7,6,5]=>1000110
[3,8,2,7,6,5,4,1]=>1101110
[4,2,8,7,6,5,3,1]=>1110111
[8,3,1,7,6,5,4,2]=>1111110
[5,2,8,7,6,4,3,1]=>1111011
[8,3,2,1,7,6,5,4]=>1111110
[8,4,1,7,6,5,3,2]=>1111110
[6,4,1,3,2,8,5,7]=>1101100
[2,5,8,6,3,1,4,7]=>1010010
[4,5,6,2,3,8,1,7]=>1100000
[3,2,7,4,5,8,1,6]=>1101000
[8,1,6,2,4,5,3,7]=>1110000
[5,8,1,6,2,3,4,7]=>1100000
[5,4,6,1,3,8,2,7]=>1101000
[2,4,1,7,5,8,3,6]=>1010100
[2,4,7,6,8,3,5,1]=>1010010
[4,8,6,5,7,1,2,3]=>1000110
[8,5,7,4,3,1,6,2]=>1111100
[8,1,7,4,2,3,6,5]=>1101100
[8,2,3,1,5,7,6,4]=>1101010
[1,4,8,2,3,6,7,5]=>0100100
[3,1,2,7,8,6,4,5]=>1001010
[7,5,1,8,2,4,3,6]=>1110100
[3,5,8,1,2,4,7,6]=>1000010
[8,4,1,5,2,3,7,6]=>1101010
[3,8,4,1,2,7,6,5]=>1001110
[2,7,5,8,3,4,1,6]=>1010100
[1,4,7,3,2,8,5,6]=>0110100
[6,4,1,3,2,7,8,5]=>1101100
[2,3,7,6,8,1,5,4]=>1001010
[2,6,3,5,1,8,7,4]=>1011001
[2,7,1,6,8,3,5,4]=>1011000
[6,7,5,4,2,1,8,3]=>1111100
[4,2,1,5,8,7,6,3]=>1110011
[8,5,3,2,6,1,7,4]=>1111100
[6,2,1,5,3,8,7,4]=>1111001
[7,8,4,1,2,5,3,6]=>1011000
[7,8,1,2,6,5,3,4]=>1010100
[6,1,4,2,7,5,3,8]=>1110100
[7,8,2,1,6,3,5,4]=>1111000
[1,2,8,7,5,4,3,6]=>0011101
[1,2,8,3,6,4,7,5]=>0011100
[5,1,7,3,6,4,8,2]=>1111000
[6,2,3,7,4,1,5,8]=>1101000
[6,2,4,1,7,3,5,8]=>1110000
[3,4,8,7,5,6,1,2]=>1000101
[2,7,3,8,6,4,1,5]=>1011010
[1,8,3,7,6,4,5,2]=>0111010
[2,6,8,5,3,1,7,4]=>1011100
[5,6,2,1,7,3,8,4]=>1111000
[5,3,6,2,4,1,7,8]=>1110000
[5,7,4,2,1,3,6,8]=>1101000
[6,4,2,1,5,3,7,8]=>1111000
[5,3,1,4,6,2,7,8]=>1110000
[5,1,2,4,7,6,8,3]=>1010010
[1,6,4,2,8,7,3,5]=>0111001
[4,8,1,2,6,7,3,5]=>1010000
[3,1,2,4,6,8,7,5]=>1000101
[4,2,8,1,5,3,7,6]=>1110010
[4,3,8,5,7,6,1,2]=>1010110
[4,8,6,3,7,5,1,2]=>1010110
[3,8,6,5,2,7,1,4]=>1100110
[3,8,5,6,1,7,4,2]=>1101100
[3,7,8,5,2,1,6,4]=>1101100
[4,2,7,8,1,3,6,5]=>1100100
[2,1,8,7,6,3,5,4]=>1011011
[5,4,1,6,3,2,8,7]=>1111001
[6,8,1,5,4,7,3,2]=>1111000
[2,6,4,3,1,5,8,7]=>1011001
[5,1,7,2,8,6,4,3]=>1111010
[6,8,2,7,4,3,1,5]=>1111000
[6,8,2,5,4,7,1,3]=>1101000
[2,1,7,6,3,8,5,4]=>1011110
[7,6,2,8,4,3,1,5]=>1111010
[2,6,5,1,8,4,3,7]=>1011100
[4,2,1,6,3,8,7,5]=>1110101
[5,8,3,2,7,6,1,4]=>1110010
[2,4,8,3,1,7,5,6]=>1010100
[4,8,3,2,1,7,6,5]=>1110110
[2,6,8,3,7,1,4,5]=>1010000
[6,8,3,7,2,1,5,4]=>1111000
[5,8,3,1,6,2,7,4]=>1111000
[4,5,8,1,6,3,2,7]=>1110000
[6,8,4,7,1,5,3,2]=>1111000
[4,3,2,1,6,8,5,7]=>1110100
[2,4,1,3,8,7,6,5]=>1000111
[4,8,6,5,1,7,3,2]=>1110110
[6,5,3,1,7,2,8,4]=>1111100
[2,1,5,4,8,7,3,6]=>1011001
[3,8,5,4,2,1,7,6]=>1101110
[2,3,8,5,4,1,6,7]=>1001100
[2,1,4,8,6,5,3,7]=>1010110
[4,3,2,8,7,6,1,5]=>1110011
[3,2,8,7,5,4,1,6]=>1101101
[2,8,6,5,4,3,1,7]=>1011110
[5,4,2,6,3,1,8,7]=>1111001
[7,5,2,6,3,8,4,1]=>1111100
[7,3,6,5,2,8,4,1]=>1111100
[5,6,3,1,2,4,8,7]=>1010001
[7,1,5,3,8,4,6,2]=>1111000
[2,7,5,3,8,6,4,1]=>1011110
[3,7,6,4,2,8,5,1]=>1101110
[5,7,3,6,2,8,4,1]=>1111000
[2,1,8,7,4,3,5,6]=>1011001
[2,8,6,3,1,4,7,5]=>1010110
[3,8,4,1,5,7,2,6]=>1101000
[5,6,3,1,8,7,4,2]=>1111001
[3,5,7,4,8,6,2,1]=>1101010
[4,5,3,6,8,2,7,1]=>1110000
[5,6,3,7,4,8,2,1]=>1111000
[2,6,7,4,5,8,3,1]=>1011000
[6,3,7,5,8,4,2,1]=>1111100
[8,5,2,6,1,7,3,4]=>1110100
[5,4,2,6,8,3,7,1]=>1111000
[7,6,8,5,1,4,2,3]=>1100110
[7,1,8,5,4,2,3,6]=>1101100
[5,7,3,8,4,1,2,6]=>1011000
[2,1,7,8,5,3,4,6]=>1010100
[2,4,8,1,5,6,3,7]=>1010000
[4,1,8,2,6,5,3,7]=>1110100
[4,7,3,8,1,2,6,5]=>1010100
[4,8,1,2,5,3,6,7]=>1010000
[3,8,1,2,4,6,5,7]=>1000100
[4,8,7,6,3,5,2,1]=>1110011
[3,8,7,6,5,2,4,1]=>1100111
[4,8,7,3,6,5,2,1]=>1110101
[4,8,7,6,3,2,5,1]=>1110011
[3,8,7,6,5,2,1,4]=>1100111
[7,5,8,3,6,2,1,4]=>1110100
[7,5,8,3,2,6,1,4]=>1110100
[7,5,8,3,2,1,6,4]=>1111100
[2,3,7,8,4,1,6,5]=>1001100
[2,1,7,5,8,4,6,3]=>1011100
[2,5,6,8,1,7,4,3]=>1011000
[4,2,8,6,1,7,3,5]=>1110010
[8,6,4,1,3,2,5,7]=>1101010
[8,1,3,2,6,5,4,7]=>1101100
[8,5,3,6,2,4,1,7]=>1110100
[8,4,1,2,6,5,3,7]=>1011100
[8,3,5,6,2,1,4,7]=>1110000
[8,4,2,1,5,6,3,7]=>1111000
[5,4,7,6,8,2,3,1]=>1101010
[4,1,8,2,3,7,6,5]=>1100110
[3,7,4,5,8,2,1,6]=>1101000
[6,3,8,5,7,4,1,2]=>1011100
[7,4,1,8,3,5,6,2]=>1111000
[5,3,8,7,4,6,1,2]=>1011001
[7,5,8,2,1,4,6,3]=>1110100
[8,7,4,2,1,3,6,5]=>1101101
[7,4,8,3,2,6,1,5]=>1111000
[6,8,2,3,1,7,5,4]=>1101100
[7,4,3,2,6,8,5,1]=>1111100
[5,1,2,3,6,8,7,4]=>1001001
[2,4,7,3,8,1,6,5]=>1010100
[6,3,8,2,7,4,1,5]=>1111000
[8,2,1,3,6,4,7,5]=>1101100
[5,7,8,2,1,4,3,6]=>1110000
[3,5,1,7,8,4,2,6]=>1101000
[1,7,8,4,5,3,2,6]=>0111000
[3,2,4,8,6,7,1,5]=>1100010
[8,3,1,6,7,4,2,5]=>1111000
[3,2,5,7,4,8,1,6]=>1101000
[8,4,7,1,3,2,5,6]=>1101000
[8,4,7,2,1,3,5,6]=>1101000
[6,4,2,1,3,7,8,5]=>1101100
[7,1,6,3,5,8,2,4]=>1110000
[3,8,5,1,6,7,2,4]=>1100100
[5,3,6,7,8,4,2,1]=>1111000
[1,5,2,7,8,6,4,3]=>0111010
[1,4,2,8,6,5,7,3]=>0110110
[4,1,7,5,2,6,8,3]=>1110100
[7,6,2,4,5,1,8,3]=>1110010
[8,1,4,5,2,6,7,3]=>1110000
[8,4,6,5,2,1,7,3]=>1111100
[3,5,7,2,1,6,8,4]=>1101000
[3,7,5,4,6,8,1,2]=>1001100
[8,3,4,1,5,6,7,2]=>1110000
[3,5,2,4,7,6,1,8]=>1100010
[7,3,5,2,4,6,1,8]=>1110000
[5,3,7,2,4,6,1,8]=>1110000
[3,5,2,7,4,6,1,8]=>1101000
[3,2,5,7,4,6,1,8]=>1101000
[3,7,5,2,4,6,1,8]=>1100100
[5,7,3,2,4,6,1,8]=>1110000
[1,5,3,2,4,7,6,8]=>0110010
[1,5,3,2,7,4,6,8]=>0111000
[3,7,5,2,4,1,6,8]=>1100100
[3,7,2,5,4,1,6,8]=>1101000
[3,2,7,5,4,1,6,8]=>1101100
[5,1,3,2,4,7,6,8]=>1100010
[5,1,3,2,7,4,6,8]=>1101000
[7,1,3,2,5,4,6,8]=>1101000
[1,7,3,2,5,4,6,8]=>0111000
[1,7,3,5,2,4,6,8]=>0110000
[7,1,3,5,2,4,6,8]=>1100000
[5,1,3,7,2,4,6,8]=>1100000
[3,2,1,5,7,4,6,8]=>1101000
[3,7,5,1,2,4,6,8]=>1000100
[5,7,3,1,2,4,6,8]=>1010000
[1,5,3,7,2,4,6,8]=>0110000
[3,5,7,2,1,4,6,8]=>1100000
[3,5,2,7,1,4,6,8]=>1100000
[3,2,5,7,4,1,6,8]=>1101000
[3,5,2,7,4,1,6,8]=>1101000
[3,5,7,2,4,1,6,8]=>1100000
[5,3,7,2,4,1,6,8]=>1110000
[7,3,5,2,1,4,6,8]=>1110000
[5,3,2,4,7,1,6,8]=>1110000
[3,2,5,4,7,1,6,8]=>1101000
[3,5,2,4,1,7,6,8]=>1100010
[1,3,2,7,5,4,6,8]=>0101100
[1,3,7,2,5,4,6,8]=>0101000
[7,3,1,2,5,4,6,8]=>1011000
[5,3,1,2,7,4,6,8]=>1011000
[5,3,1,2,4,7,6,8]=>1010010
[3,5,2,1,4,7,6,8]=>1100010
[3,2,5,1,7,4,6,8]=>1101000
[3,5,2,1,7,4,6,8]=>1101000
[5,3,1,7,2,4,6,8]=>1110000
[7,3,1,5,2,4,6,8]=>1110000
[1,3,7,5,2,4,6,8]=>0100100
[7,5,1,3,2,4,6,8]=>1100100
[5,7,1,3,2,4,6,8]=>1100000
[3,7,1,5,2,4,6,8]=>1100000
[3,7,1,2,5,4,6,8]=>1001000
[3,7,2,1,5,4,6,8]=>1101000
[3,1,2,7,5,4,6,8]=>1001100
[3,1,7,2,5,4,6,8]=>1101000
[3,1,7,5,2,4,6,8]=>1100100
[5,1,7,3,2,4,6,8]=>1110000
[7,1,5,3,2,4,6,8]=>1110000
[1,7,5,3,2,4,6,8]=>0110100
[5,8,7,1,2,6,4,3]=>1011001
[6,8,2,1,7,5,4,3]=>1111100
[1,8,7,6,3,2,5,4]=>0111011
[5,8,7,4,1,2,6,3]=>1011001
[2,8,7,4,3,6,1,5]=>1011001
[1,8,5,4,2,7,6,3]=>0111110
[7,6,4,2,8,5,3,1]=>1111110
[7,6,4,8,5,1,2,3]=>1001110
[7,6,4,5,1,3,8,2]=>1101010
[1,6,7,5,3,8,4,2]=>0111100
[7,6,3,5,2,4,8,1]=>1110010
[7,6,4,2,5,1,8,3]=>1111010
[7,6,2,8,3,1,4,5]=>1110010
[1,6,7,5,8,2,3,4]=>0100100
[2,6,3,7,5,1,8,4]=>1011100
[2,6,5,7,8,3,4,1]=>1010100
[3,2,5,1,7,8,4,6]=>1101000
[5,2,3,4,8,6,1,7]=>1100010
[5,3,4,8,2,7,6,1]=>1110010
[5,3,8,2,4,1,7,6]=>1110010
[5,2,8,4,1,7,3,6]=>1111000
[6,4,2,5,1,8,7,3]=>1111001
[6,4,3,5,8,2,1,7]=>1111000
[6,3,5,4,8,2,7,1]=>1111000
[6,3,5,8,7,1,2,4]=>1010001
[1,5,7,3,4,8,6,2]=>0110010
[5,8,4,1,3,7,6,2]=>1101010
[6,4,5,3,8,1,7,2]=>1111000
[6,4,3,8,5,7,2,1]=>1111100
[5,4,2,6,3,1,7,8]=>1111000
[4,6,5,3,7,1,2,8]=>1010100
[3,5,6,1,4,8,7,2]=>1100001
[3,5,7,6,1,4,8,2]=>1100010
[3,6,5,7,4,8,1,2]=>1001100
[4,2,6,5,1,7,3,8]=>1110100
[4,3,5,7,2,1,6,8]=>1110000
[3,5,4,7,2,6,1,8]=>1101000
[3,4,7,6,8,1,2,5]=>1000010
[1,8,4,3,7,5,6,2]=>0111100
[5,2,8,6,4,7,3,1]=>1111010
[1,8,6,3,7,4,2,5]=>0111010
[1,8,6,5,7,2,3,4]=>0100110
[4,2,8,3,5,7,1,6]=>1110000
[4,3,8,6,5,7,1,2]=>1010110
[1,3,7,2,6,5,8,4]=>0101100
[1,5,7,2,4,6,8,3]=>0110000
[1,3,6,4,2,5,8,7]=>0101001
[5,6,3,4,7,1,8,2]=>1110000
[3,5,2,7,4,1,8,6]=>1101010
[5,2,3,8,4,1,7,6]=>1101010
[7,5,3,4,8,2,1,6]=>1110100
[7,6,3,8,4,2,1,5]=>1111010
[7,2,8,5,1,6,3,4]=>1110100
[7,4,3,8,5,2,6,1]=>1111100
[7,2,8,5,1,3,4,6]=>1100100
[7,6,8,1,2,5,3,4]=>1010010
[1,5,3,7,6,8,4,2]=>0111010
[1,2,6,4,5,8,3,7]=>0011000
[1,2,7,4,8,5,3,6]=>0011100
[1,6,3,7,8,2,4,5]=>0110000
[3,2,6,7,8,1,4,5]=>1100000
[1,4,7,3,5,2,6,8]=>0110000
[3,8,4,7,6,1,5,2]=>1101010
[5,7,4,2,6,3,1,8]=>1111000
[2,4,5,8,1,6,7,3]=>1010000
[6,1,3,7,4,2,5,8]=>1101000
[2,1,8,3,6,7,4,5]=>1011000
[5,1,8,6,2,7,3,4]=>1110010
[5,7,1,4,2,6,3,8]=>1110000
[3,2,6,8,1,5,7,4]=>1101000
[8,2,6,1,5,4,7,3]=>1111000
[8,6,2,7,1,5,4,3]=>1111010
[7,6,8,3,1,5,4,2]=>1111010
[7,8,5,4,1,6,3,2]=>1111100
[5,7,4,2,8,1,6,3]=>1111000
[6,3,7,2,8,1,5,4]=>1111000
[7,5,2,8,6,1,4,3]=>1110110
[3,6,2,7,8,1,5,4]=>1101000
[2,7,3,8,1,5,6,4]=>1011000
[2,6,8,4,1,5,7,3]=>1011000
[5,7,8,4,1,6,3,2]=>1111000
[8,4,6,5,3,1,7,2]=>1111100
[5,6,4,8,3,1,7,2]=>1111000
[3,4,8,1,2,5,7,6]=>1000010
[6,3,1,7,5,2,4,8]=>1110100
[6,3,1,8,2,7,4,5]=>1111000
[7,8,1,2,4,3,6,5]=>1010100
[5,2,8,1,3,4,7,6]=>1100010
[3,2,1,6,4,7,8,5]=>1101100
[4,1,3,6,5,7,8,2]=>1100100
[5,1,3,4,2,7,8,6]=>1100010
[6,1,3,4,2,8,5,7]=>1100100
[8,1,4,3,5,7,6,2]=>1110010
[5,2,4,1,3,7,8,6]=>1100010
[3,2,6,1,5,7,8,4]=>1101000
[1,4,6,3,5,7,8,2]=>0110000
[3,5,1,6,4,7,8,2]=>1101000
[3,6,4,2,1,7,8,5]=>1101100
[3,8,6,1,4,7,5,2]=>1100110
[1,8,3,2,6,7,5,4]=>0111100
[8,7,1,3,6,5,4,2]=>1101101
[1,8,5,7,4,2,6,3]=>0111100
[4,7,5,3,8,2,1,6]=>1110100
[2,7,6,5,8,3,1,4]=>1010110
[1,4,7,6,8,2,3,5]=>0100010
[3,5,7,4,8,1,2,6]=>1001000
[4,6,1,7,5,8,2,3]=>1100100
[2,3,6,7,5,8,1,4]=>1000100
[1,3,7,5,6,8,2,4]=>0100100
[3,2,7,1,6,8,4,5]=>1101000
[8,1,5,4,7,2,6,3]=>1111000
[8,2,5,3,7,1,6,4]=>1111000
[2,1,4,7,5,8,3,6]=>1010100
[1,2,6,7,4,8,3,5]=>0011000
[3,6,4,7,8,5,2,1]=>1101100
[3,2,5,8,6,7,4,1]=>1101010
[6,3,5,8,7,4,1,2]=>1011001
[8,3,5,7,6,4,2,1]=>1111010
[4,1,8,3,7,5,6,2]=>1110100
[4,7,2,8,5,6,3,1]=>1110100
[1,4,8,7,3,5,6,2]=>0110001
[3,2,8,7,1,5,6,4]=>1101001
[1,5,8,7,4,6,2,3]=>0101001
[4,7,6,8,5,3,1,2]=>1010110
[4,8,6,7,5,3,2,1]=>1110110
[3,8,7,5,6,4,2,1]=>1101101
[8,1,5,6,3,2,4,7]=>1110000
[1,7,8,3,5,2,4,6]=>0110000
[8,2,5,3,1,6,4,7]=>1111000
[8,3,2,1,5,6,4,7]=>1111000
[8,6,5,1,3,4,2,7]=>1100110
[1,7,8,5,4,3,2,6]=>0111100
[2,6,8,7,4,3,5,1]=>1011001
[2,7,6,8,4,3,1,5]=>1011010
[1,2,6,7,8,4,3,5]=>0011000
[8,5,7,1,3,4,6,2]=>1100100
[3,5,8,6,7,4,1,2]=>1001010
[3,1,6,5,8,7,4,2]=>1101101
[3,7,6,4,8,1,2,5]=>1001010
[2,3,6,5,7,1,8,4]=>1001100
[2,3,6,4,1,7,8,5]=>1001100
[4,7,2,1,5,3,8,6]=>1110010
[3,1,7,4,5,2,8,6]=>1101010
[3,7,5,4,2,1,8,6]=>1101110
[1,3,6,7,4,2,8,5]=>0101100
[4,3,7,2,6,8,1,5]=>1110000
[5,4,2,1,3,7,8,6]=>1101010
[8,7,1,5,6,3,2,4]=>1110001
[1,7,8,2,6,4,5,3]=>0111000
[8,7,2,5,4,6,1,3]=>1101001
[8,7,1,2,4,5,6,3]=>1010001
[8,7,2,5,3,1,6,4]=>1111001
[8,7,3,2,1,5,6,4]=>1111001
[8,7,6,5,1,3,4,2]=>1100111
[8,7,6,1,4,5,3,2]=>1110011
[8,7,5,6,1,4,3,2]=>1110101
[6,8,7,1,5,4,3,2]=>1111001
[8,5,7,6,1,4,3,2]=>1110110
[6,7,8,1,5,4,3,2]=>1111000
[8,7,4,6,5,1,3,2]=>1101101
[8,5,6,7,1,4,3,2]=>1110100
[8,7,6,3,5,4,1,2]=>1011011
[8,7,4,5,6,1,3,2]=>1101001
[8,7,6,5,2,4,3,1]=>1110111
[4,2,8,7,6,5,1,3]=>1100111
[7,5,8,1,6,4,3,2]=>1111100
[1,5,8,7,6,2,4,3]=>0110011
[7,5,8,4,1,6,3,2]=>1111100
[6,8,5,1,7,4,3,2]=>1111100
[1,6,8,7,2,5,4,3]=>0111001
[7,3,8,4,6,1,5,2]=>1111000
[4,8,5,7,1,6,3,2]=>1110100
[4,3,7,6,5,1,8,2]=>1110110
[5,4,3,6,7,1,8,2]=>1111000
[5,4,7,3,6,1,8,2]=>1111000
[4,8,7,6,3,1,5,2]=>1110011
[2,4,6,3,1,7,8,5]=>1010100
[6,8,5,7,3,2,1,4]=>1110100
[6,8,5,3,7,2,1,4]=>1110100
[6,8,5,7,4,2,1,3]=>1101100
[2,1,8,7,6,3,4,5]=>1010011
[5,8,7,6,2,4,1,3]=>1100011
[6,8,2,7,5,1,4,3]=>1110100
[5,8,7,2,6,4,1,3]=>1101001
[6,8,7,5,2,4,1,3]=>1100101
[5,8,7,6,4,2,3,1]=>1101011
[2,3,6,1,7,5,8,4]=>1001100
[2,3,6,1,8,5,4,7]=>1001100
[2,4,1,6,7,5,8,3]=>1010100
[2,4,1,7,3,8,6,5]=>1010110
[2,4,1,7,8,5,6,3]=>1010100
[2,4,5,3,7,1,8,6]=>1010010
[2,4,5,7,3,8,6,1]=>1010010
[2,4,6,3,1,8,5,7]=>1010100
[2,4,6,3,8,5,1,7]=>1010100
[2,4,6,8,3,5,1,7]=>1010000
[2,4,7,3,1,5,8,6]=>1010010
[2,4,7,3,1,8,6,5]=>1010110
[2,4,7,8,3,5,6,1]=>1010000
[2,5,1,6,4,8,3,7]=>1011000
[2,5,1,6,7,4,8,3]=>1011000
[2,5,1,7,4,3,8,6]=>1011010
[2,5,1,7,8,4,6,3]=>1011000
[2,5,6,3,4,8,1,7]=>1010000
[2,5,6,3,7,4,8,1]=>1011000
[2,5,6,3,8,4,1,7]=>1011000
[2,5,6,7,8,4,1,3]=>1001000
[2,5,6,8,4,3,1,7]=>1011000
[2,6,1,7,4,8,5,3]=>1011100
[6,8,4,3,2,1,7,5]=>1111100
[7,6,4,8,2,1,3,5]=>1101010
[7,6,5,2,8,4,1,3]=>1101110
[7,6,3,8,2,4,1,5]=>1110010
[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]=>1110110
[6,8,7,4,5,2,3,1]=>1101001
[6,8,4,7,5,2,3,1]=>1101100
[6,8,4,7,2,5,3,1]=>1111000
[6,4,8,7,5,2,3,1]=>1101101
[6,8,4,2,7,5,3,1]=>1111100
[6,8,4,7,2,1,5,3]=>1111000
[6,8,4,7,3,5,2,1]=>1111000
[6,4,8,2,7,5,3,1]=>1111100
[6,8,4,2,7,1,5,3]=>1111000
[6,4,2,8,7,5,3,1]=>1111101
[6,8,4,7,3,2,5,1]=>1111000
[6,8,4,2,1,7,5,3]=>1111100
[6,8,4,7,3,2,1,5]=>1111000
[6,8,5,7,1,4,3,2]=>1110100
[1,8,7,3,6,2,5,4]=>0111001
[5,8,7,2,3,6,1,4]=>1100001
[6,8,2,7,5,4,1,3]=>1101100
[6,8,3,7,5,2,1,4]=>1110100
[6,8,1,7,3,5,4,2]=>1111000
[6,8,4,7,3,1,5,2]=>1111000
[6,8,1,7,3,2,5,4]=>1111000
[3,8,5,7,6,1,4,2]=>1100110
[3,8,2,7,6,5,1,4]=>1100110
[1,8,4,7,6,2,5,3]=>0111010
[3,8,1,7,6,2,5,4]=>1101010
[1,8,4,7,3,6,5,2]=>0111100
[4,8,5,7,1,2,6,3]=>1010100
[1,8,4,7,3,2,6,5]=>0111100
[6,8,5,2,7,4,1,3]=>1101100
[6,8,3,4,7,1,5,2]=>1110000
[6,8,1,3,7,2,5,4]=>1101000
[2,8,1,3,7,6,5,4]=>1001110
[2,8,3,4,7,6,1,5]=>1010010
[6,8,5,4,2,7,1,3]=>1101100
[6,8,1,4,3,7,5,2]=>1110100
[6,8,1,4,2,7,5,3]=>1110100
[6,5,4,3,8,7,1,2]=>1011101
[3,1,7,2,8,5,6,4]=>1101100
[3,1,6,7,4,8,5,2]=>1101100
[3,1,5,7,8,4,6,2]=>1101000
[8,6,5,7,1,4,3,2]=>1110110
[8,6,4,2,7,5,1,3]=>1101110
[6,4,8,2,7,5,1,3]=>1101100
[8,4,7,6,2,5,1,3]=>1101010
[3,4,5,6,8,7,1,2]=>1000001
[3,4,5,7,8,6,1,2]=>1000010
[3,4,5,8,7,6,1,2]=>1000011
[3,4,6,7,8,5,1,2]=>1000100
[6,4,7,3,5,2,1,8]=>1111000
[5,4,7,3,6,2,1,8]=>1111000
[4,8,7,3,5,2,1,6]=>1110001
[7,5,3,6,8,2,1,4]=>1110100
[5,8,3,6,7,2,1,4]=>1110000
[6,4,7,8,2,5,1,3]=>1101000
[5,8,7,3,2,4,1,6]=>1110001
[6,4,7,3,2,5,1,8]=>1111000
[6,5,3,7,2,4,1,8]=>1110100
[7,3,8,6,2,4,1,5]=>1110010
[6,3,7,8,2,4,1,5]=>1110000
[5,3,7,6,2,4,1,8]=>1110010
[7,5,8,2,6,4,1,3]=>1101100
[7,4,8,2,5,6,1,3]=>1101000
[5,4,7,2,6,8,1,3]=>1101000
[4,8,7,2,5,6,1,3]=>1100001
[5,4,3,2,6,8,1,7]=>1111000
[4,8,3,2,5,6,1,7]=>1110000
[5,3,7,2,6,4,1,8]=>1111000
[7,5,2,6,8,4,1,3]=>1101100
[6,4,2,7,5,8,1,3]=>1101100
[7,5,8,4,1,2,6,3]=>1011100
[7,1,8,2,3,6,5,4]=>1101100
[7,3,8,4,6,2,1,5]=>1111000
[7,1,8,4,2,6,5,3]=>1111100
[7,1,8,3,6,2,5,4]=>1111000
[7,2,3,4,5,1,8,6]=>1100010
[2,8,3,4,5,1,6,7]=>1010000
[2,7,3,4,1,5,6,8]=>1010000
[5,3,6,1,2,7,4,8]=>1011000
[2,8,5,3,4,6,7,1]=>1010100
[3,8,1,4,5,6,7,2]=>1100000
[4,5,3,1,2,8,7,6]=>1010011
[5,7,3,4,1,6,8,2]=>1110000
[4,5,3,1,2,6,8,7]=>1010001
[3,4,1,2,5,8,7,6]=>1000011
[6,5,3,2,1,8,7,4]=>1111101
[4,5,2,1,8,7,6,3]=>1110011
[3,4,1,8,7,6,5,2]=>1100111
[8,1,2,4,5,6,7,3]=>1010000
[7,1,2,3,4,6,8,5]=>1000100
[6,1,2,3,5,8,7,4]=>1001001
[5,1,2,4,8,6,7,3]=>1010010
[4,1,3,8,5,6,7,2]=>1100100
[7,1,2,3,5,8,6,4]=>1001010
[6,1,2,3,5,7,8,4]=>1001000
[5,1,3,8,4,6,7,2]=>1101000
[4,1,3,5,8,6,7,2]=>1100010
[8,6,3,5,2,7,4,1]=>1111010
[7,5,2,8,6,3,4,1]=>1110110
[5,2,8,6,7,3,4,1]=>1110010
[7,5,2,3,8,6,4,1]=>1101110
[5,2,3,8,6,7,4,1]=>1101010
[8,4,1,7,3,5,6,2]=>1111000
[7,4,1,2,6,8,5,3]=>1011100
[5,3,8,4,1,2,6,7]=>1011000
[6,3,5,8,4,1,2,7]=>1011000
[7,3,5,6,8,4,1,2]=>1011000
[7,4,5,1,2,8,6,3]=>1011010
[6,3,8,4,5,1,2,7]=>1011000
[8,5,1,7,4,6,2,3]=>1101100
[7,4,5,1,8,6,2,3]=>1101010
[8,4,5,1,7,3,6,2]=>1111000
[4,2,7,5,8,6,3,1]=>1110110
[4,2,8,5,6,3,1,7]=>1110100
[8,6,3,1,5,7,4,2]=>1111010
[7,4,2,8,5,6,3,1]=>1111100
[4,2,8,5,6,7,3,1]=>1110100
[7,4,8,5,6,1,2,3]=>1001100
[7,5,8,6,1,2,3,4]=>1000110
[7,3,4,8,5,6,1,2]=>1010100
[7,3,4,5,8,6,1,2]=>1010010
[6,4,8,5,2,3,1,7]=>1101100
[8,6,3,1,7,5,2,4]=>1110110
[7,2,8,3,4,5,6,1]=>1110000
[7,4,5,2,8,6,3,1]=>1111010
[8,5,2,7,4,6,3,1]=>1111100
[5,2,4,8,6,7,3,1]=>1110010
[7,5,8,6,2,3,1,4]=>1100110
[7,4,8,5,6,2,3,1]=>1101100
[7,3,1,8,4,5,6,2]=>1111000
[7,2,4,5,6,8,3,1]=>1110000
[3,4,5,7,6,8,1,2]=>1000010
[4,8,2,5,1,3,7,6]=>1100010
[2,1,8,7,3,4,6,5]=>1010101
[2,7,4,5,6,8,1,3]=>1001000
[4,1,2,8,7,5,3,6]=>1010101
[4,1,2,6,8,3,7,5]=>1010100
[3,1,7,6,8,2,4,5]=>1100010
[8,2,6,3,1,5,4,7]=>1111000
[7,3,5,1,8,2,4,6]=>1110000
[7,8,3,1,5,2,4,6]=>1110000
[1,5,6,7,8,3,4,2]=>0110000
[1,4,6,7,8,3,5,2]=>0110000
[1,5,6,3,7,8,4,2]=>0111000
[6,1,2,3,4,8,7,5]=>1000101
[5,1,2,3,8,7,6,4]=>1001011
[5,1,2,3,8,6,7,4]=>1001010
[2,8,5,3,1,4,6,7]=>1010100
[2,4,3,5,7,8,1,6]=>1010000
[2,6,3,7,8,1,4,5]=>1010000
[3,4,6,1,7,8,5,2]=>1100100
[3,4,6,1,8,5,7,2]=>1100100
[3,4,8,1,5,6,7,2]=>1100000
[3,5,1,7,4,8,6,2]=>1101010
[3,5,6,4,8,1,7,2]=>1101000
[3,5,8,4,1,6,7,2]=>1101000
[3,6,1,8,5,4,7,2]=>1101100
[3,6,7,4,8,5,1,2]=>1001100
[3,6,8,4,5,1,7,2]=>1101000
[4,1,5,6,8,3,7,2]=>1110000
[4,1,5,7,8,6,3,2]=>1110010
[4,1,7,3,5,8,6,2]=>1110010
[4,1,7,8,5,6,3,2]=>1110100
[4,5,7,8,1,6,3,2]=>1110000
[4,5,8,3,1,6,7,2]=>1110000
[4,6,3,1,8,5,7,2]=>1110100
[4,6,7,3,5,8,1,2]=>1010000
[4,6,7,8,5,1,3,2]=>1100100
[4,6,8,3,5,1,7,2]=>1110000
[4,7,3,1,8,6,5,2]=>1110110
[4,7,8,3,5,6,1,2]=>1010000
[5,1,6,7,4,8,3,2]=>1111000
[5,1,6,7,8,3,4,2]=>1110000
[5,6,3,4,8,1,7,2]=>1110000
[5,6,7,8,4,1,3,2]=>1101000
[5,7,3,4,1,8,6,2]=>1110010
[5,7,3,4,8,6,1,2]=>1010010
[5,7,3,8,4,6,1,2]=>1011000
[5,7,8,4,3,6,1,2]=>1011000
[6,1,3,7,8,5,4,2]=>1101100
[6,1,7,4,5,8,3,2]=>1111000
[6,1,8,4,5,3,7,2]=>1111000
[6,7,3,8,5,4,1,2]=>1011100
[7,1,3,4,8,6,5,2]=>1100110
[8,4,1,3,2,5,6,7]=>1101000
[8,5,1,2,4,3,6,7]=>1010100
[8,6,1,2,3,5,4,7]=>1001010
[8,7,1,2,3,4,6,5]=>1000101
[8,5,1,4,2,3,6,7]=>1100100
[8,6,1,2,5,3,4,7]=>1010010
[8,7,1,2,3,6,4,5]=>1001001
[8,6,1,2,5,4,3,7]=>1011010
[2,5,8,6,1,7,3,4]=>1010010
[4,5,6,8,7,2,1,3]=>1100001
[5,6,8,7,2,3,1,4]=>1100001
[4,1,5,2,8,7,6,3]=>1110011
[4,8,2,5,6,1,3,7]=>1100000
[5,2,3,6,7,8,1,4]=>1100000
[4,2,8,7,5,3,1,6]=>1110101
[4,2,8,6,7,5,3,1]=>1110110
[1,3,2,4,8,5,7,6]=>0100110
[1,6,3,2,5,7,8,4]=>0111000
[2,5,6,1,8,7,3,4]=>1010001
[7,6,2,1,4,8,3,5]=>1110010
[2,6,5,1,8,7,3,4]=>1010101
[1,4,2,7,3,8,6,5]=>0110110
[1,2,7,3,8,6,5,4]=>0011110
[3,1,8,4,6,2,7,5]=>1101100
[3,4,5,1,8,2,7,6]=>1100010
[3,8,1,6,5,2,7,4]=>1101100
[1,5,2,3,8,7,4,6]=>0101001
[2,8,7,6,3,1,4,5]=>1010011
[8,7,2,5,3,1,4,6]=>1110001
[7,6,2,3,4,8,1,5]=>1100010
[8,7,6,2,1,4,3,5]=>1110011
[8,2,7,4,1,5,3,6]=>1111000
[1,7,3,2,4,5,8,6]=>0110010
[1,3,8,6,2,4,7,5]=>0100110
[8,7,3,1,4,2,6,5]=>1110101
[1,2,5,3,4,8,7,6]=>0010011
[1,2,3,8,4,7,6,5]=>0001110
[1,6,2,3,7,5,8,4]=>0101100
[4,5,1,2,8,3,7,6]=>1010010
[1,4,8,2,6,3,7,5]=>0110100
[8,4,1,7,3,2,5,6]=>1111000
[1,8,7,3,2,4,6,5]=>0110101
[8,3,1,5,6,2,7,4]=>1111000
[3,4,1,6,5,7,2,8]=>1100100
[3,5,1,6,2,8,7,4]=>1101001
[5,4,3,6,1,7,2,8]=>1111000
[4,8,7,2,1,6,5,3]=>1110101
[6,2,1,8,7,5,4,3]=>1111101
[7,5,8,6,3,2,4,1]=>1110110
[5,8,7,6,3,2,4,1]=>1110011
[5,4,7,2,8,1,6,3]=>1111000
[8,1,5,4,6,3,7,2]=>1111000
[2,1,5,8,3,7,4,6]=>1011000
[2,1,7,4,8,3,6,5]=>1011100
[1,2,3,5,8,7,4,6]=>0001001
[6,1,2,7,8,4,3,5]=>1011000
[5,1,4,8,2,7,3,6]=>1110000
[3,4,1,2,8,7,5,6]=>1000101
[1,2,5,7,8,6,3,4]=>0010010
[2,1,3,4,8,5,7,6]=>1000110
[6,2,5,1,7,3,8,4]=>1111000
[2,4,8,1,3,7,5,6]=>1000100
[1,5,4,8,6,2,7,3]=>0111010
[2,5,1,8,6,3,7,4]=>1011010
[2,1,3,7,4,8,6,5]=>1001110
[4,2,5,8,1,7,3,6]=>1110000
[2,6,8,5,1,7,3,4]=>1010100
[1,3,2,7,8,5,4,6]=>0101100
[7,1,2,3,6,8,4,5]=>1001000
[5,1,2,3,8,4,7,6]=>1001010
[3,4,5,1,8,7,2,6]=>1100001
[4,1,2,3,8,7,5,6]=>1000101
[7,4,1,6,8,2,3,5]=>1101000
[2,3,1,8,5,4,7,6]=>1001110
[2,3,8,4,1,5,7,6]=>1001010
[5,3,1,8,7,2,4,6]=>1110001
[3,6,1,8,7,2,4,5]=>1100001
[1,3,8,4,2,7,6,5]=>0101110
[1,2,3,8,5,7,4,6]=>0001100
[6,1,7,2,5,8,3,4]=>1110000
[4,5,1,8,7,2,3,6]=>1100001
[1,4,2,8,5,3,7,6]=>0110110
[4,3,8,1,6,2,7,5]=>1110100
[7,8,6,5,2,1,4,3]=>1110110
[8,6,7,5,2,1,4,3]=>1110110
[6,7,8,2,1,5,4,3]=>1111000
[8,7,5,6,2,1,4,3]=>1110101
[3,2,8,5,6,7,1,4]=>1100100
[4,2,5,1,8,7,3,6]=>1110001
[5,2,7,8,6,3,1,4]=>1110010
[4,2,6,1,5,8,3,7]=>1110000
[7,2,4,5,8,3,6,1]=>1110000
[2,4,7,8,6,1,5,3]=>1010010
[4,2,7,1,5,6,8,3]=>1110000
[3,2,5,8,1,6,7,4]=>1101000
[8,1,4,3,2,5,6,7]=>1110000
[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]=>0101000
[6,2,5,1,8,3,4,7]=>1110000
[5,1,8,2,4,3,6,7]=>1110000
[8,2,3,1,5,6,7,4]=>1101000
[1,7,2,4,5,8,6,3]=>0110010
[1,5,7,8,4,6,2,3]=>0101000
[6,5,8,3,4,2,1,7]=>1110100
[6,5,8,2,3,4,1,7]=>1100100
[4,2,1,3,5,8,6,7]=>1100010
[1,3,8,2,6,4,5,7]=>0101000
[6,1,2,7,4,3,8,5]=>1011100
[7,6,1,3,8,2,4,5]=>1100010
[5,4,1,2,3,8,6,7]=>1001010
[7,6,8,5,2,4,1,3]=>1100110
[6,7,8,5,2,4,1,3]=>1100100
[3,4,5,8,2,1,7,6]=>1100010
[3,4,6,2,7,1,5,8]=>1100000
[3,4,6,2,8,1,7,5]=>1100100
[3,4,6,8,1,5,7,2]=>1100000
[3,4,6,1,5,2,7,8]=>1100000
[3,4,7,2,1,6,5,8]=>1100100
[3,4,7,1,5,6,2,8]=>1100000
[3,5,2,6,1,4,7,8]=>1100000
[3,5,2,7,1,6,4,8]=>1101000
[3,5,2,1,4,6,7,8]=>1100000
[3,5,6,4,8,2,1,7]=>1101000
[3,5,6,4,1,2,7,8]=>1001000
[3,5,6,8,4,2,1,7]=>1101000
[3,5,6,8,1,2,7,4]=>1001000
[3,5,6,1,4,2,7,8]=>1100000
[3,5,7,4,2,8,1,6]=>1101000
[3,5,7,4,2,1,6,8]=>1101000
[3,5,7,4,8,1,6,2]=>1101000
[3,5,7,8,1,6,2,4]=>1100000
[3,5,7,1,4,6,2,8]=>1100000
[3,5,8,4,2,6,1,7]=>1101000
[3,5,8,1,4,6,7,2]=>1100000
[3,6,2,4,8,1,7,5]=>1100100
[3,6,2,7,8,5,1,4]=>1100100
[3,6,2,7,8,1,4,5]=>1100000
[3,6,2,1,5,4,7,8]=>1101000
[3,6,7,8,5,1,2,4]=>1000100
[3,6,7,8,1,5,2,4]=>1100000
[3,7,2,4,5,8,1,6]=>1100000
[3,7,2,4,8,1,6,5]=>1100100
[3,7,2,4,1,6,5,8]=>1100100
[3,7,2,8,5,6,1,4]=>1100100
[3,7,2,1,5,6,4,8]=>1101000
[3,7,8,4,5,1,6,2]=>1101000
[3,7,8,4,1,6,5,2]=>1101100
[3,8,2,4,1,6,7,5]=>1100100
[3,8,2,1,5,6,7,4]=>1101000
[8,1,5,4,3,6,7,2]=>1111000
[8,1,4,5,3,6,7,2]=>1110000
[4,1,6,3,5,7,8,2]=>1110000
[4,1,7,3,5,6,8,2]=>1110000
[6,1,7,3,8,4,5,2]=>1111000
[4,1,3,6,7,8,5,2]=>1100100
[4,6,2,3,5,1,7,8]=>1100000
[3,5,2,4,1,6,7,8]=>1100000
[5,8,2,3,4,6,1,7]=>1100000
[4,7,2,3,5,1,6,8]=>1100000
[5,7,2,3,4,6,8,1]=>1100000
[4,6,2,3,5,7,1,8]=>1100000
[2,3,7,8,1,6,5,4]=>1001100
[2,7,6,1,4,8,3,5]=>1010010
[2,6,8,1,4,5,7,3]=>1010000
[2,6,5,8,1,3,7,4]=>1001100
[6,4,7,5,8,2,3,1]=>1101100
[6,7,4,1,8,2,3,5]=>1101000
[6,7,8,1,4,2,5,3]=>1110000
[5,2,6,1,4,8,3,7]=>1110000
[7,2,3,5,8,1,4,6]=>1100000
[2,4,7,5,8,1,3,6]=>1000100
[2,3,6,5,1,8,7,4]=>1001101
[2,3,4,8,1,5,7,6]=>1000010
[2,3,4,7,8,1,6,5]=>1000100
[2,7,8,5,1,4,6,3]=>1010100
[2,3,7,5,8,1,4,6]=>1000100
[2,3,6,8,5,1,7,4]=>1001100
[7,6,4,5,1,8,2,3]=>1101010
[7,4,6,8,1,5,2,3]=>1101000
[2,7,4,6,5,8,3,1]=>1011100
[2,6,7,8,5,3,1,4]=>1010100
[2,5,6,1,4,8,3,7]=>1010000
[2,6,4,8,5,7,3,1]=>1011100
[2,5,8,1,4,6,7,3]=>1010000
[7,2,3,4,8,1,6,5]=>1100100
[3,2,5,7,8,1,6,4]=>1101000
[6,4,1,7,8,2,3,5]=>1101000
[5,7,1,6,2,8,4,3]=>1111000
[5,6,1,8,2,3,7,4]=>1101000
[7,3,5,1,6,8,4,2]=>1111000
[6,3,4,5,8,2,1,7]=>1110000
[5,7,6,1,2,8,3,4]=>1010010
[5,7,4,8,2,6,3,1]=>1111000
[5,6,8,1,2,4,7,3]=>1010000
[6,2,3,4,5,8,1,7]=>1100000
[4,7,1,3,8,2,6,5]=>1100100
[5,4,1,6,7,8,2,3]=>1101000
[7,4,1,5,8,2,6,3]=>1111000
[5,7,1,8,6,2,3,4]=>1100010
[7,3,5,1,8,2,6,4]=>1111000
[4,8,1,3,5,6,7,2]=>1100000
[8,1,2,3,7,5,6,4]=>1001100
[2,1,8,3,7,5,6,4]=>1011100
[5,6,7,3,8,2,1,4]=>1110000
[5,6,8,3,1,2,7,4]=>1011000
[5,7,3,2,8,6,1,4]=>1110010
[5,7,8,3,1,6,2,4]=>1110000
[5,8,3,2,1,6,7,4]=>1111000
[6,2,7,3,8,5,1,4]=>1110100
[6,2,3,7,8,5,1,4]=>1100100
[6,7,3,2,8,5,1,4]=>1110100
[6,7,8,3,5,1,2,4]=>1010000
[1,5,6,7,8,3,2,4]=>0110000
[6,8,3,2,5,1,7,4]=>1111000
[1,5,8,3,2,6,7,4]=>0111000
[1,6,7,8,5,2,3,4]=>0100100
[1,6,8,3,5,2,7,4]=>0111000
[1,7,3,2,8,6,5,4]=>0111110
[1,7,8,3,5,6,2,4]=>0110000
[1,6,7,8,4,2,3,5]=>0101000
[1,2,6,8,4,3,7,5]=>0011100
[1,8,3,4,2,6,7,5]=>0110100
[1,2,8,4,3,6,7,5]=>0011100
[6,2,7,8,4,1,3,5]=>1101000
[6,2,3,7,8,1,4,5]=>1100000
[4,5,7,1,8,6,2,3]=>1100010
[4,5,7,8,2,6,1,3]=>1100000
[4,6,2,8,5,1,7,3]=>1110100
[4,6,7,1,8,5,2,3]=>1100100
[4,7,2,8,5,6,1,3]=>1100100
[4,8,2,1,5,6,7,3]=>1110000
[1,2,8,4,5,3,7,6]=>0011010
[1,2,3,7,8,5,4,6]=>0001100
[1,2,3,8,5,4,7,6]=>0001110
[1,7,3,8,5,4,2,6]=>0111100
[5,2,7,4,8,6,1,3]=>1101010
[5,2,7,8,4,6,1,3]=>1101000
[7,2,3,8,5,4,1,6]=>1101100
[5,6,2,7,8,1,4,3]=>1110000
[5,8,2,4,1,6,7,3]=>1110000
[6,2,1,7,8,5,4,3]=>1111100
[6,7,2,4,8,5,1,3]=>1100100
[6,7,2,8,5,4,1,3]=>1101100
[6,8,2,4,5,1,7,3]=>1110000
[3,2,5,6,8,1,4,7]=>1100000
[7,1,3,2,8,4,5,6]=>1101000
[8,1,2,3,7,5,4,6]=>1001100
[4,1,8,2,7,5,3,6]=>1110100
[7,1,8,3,4,5,2,6]=>1110000
[7,1,6,3,8,2,4,5]=>1110000
[6,1,5,8,2,3,4,7]=>1100000
[8,1,6,7,4,2,3,5]=>1101000
[6,1,5,8,2,3,7,4]=>1101000
[4,1,7,2,5,8,3,6]=>1110000
[8,1,6,3,4,7,2,5]=>1110000
[7,1,6,8,2,5,3,4]=>1110000
[4,1,8,2,5,6,3,7]=>1110000
[8,1,7,3,2,5,6,4]=>1111000
[4,1,8,2,5,6,7,3]=>1110000
[3,8,1,2,7,5,4,6]=>1001100
[5,4,7,1,2,8,3,6]=>1011000
[8,4,7,1,3,2,6,5]=>1101100
[8,5,7,3,1,2,6,4]=>1011100
[3,8,1,2,4,5,7,6]=>1000010
[7,6,2,1,8,4,3,5]=>1111010
[8,5,2,3,6,1,4,7]=>1100100
[8,5,7,1,4,3,2,6]=>1110100
[3,6,1,4,2,8,5,7]=>1100100
[7,6,8,1,4,5,2,3]=>1100010
[3,7,1,4,2,8,6,5]=>1100110
[5,4,3,8,2,1,7,6]=>1111010
[5,8,7,3,2,1,6,4]=>1111001
[2,3,7,1,6,8,5,4]=>1001100
[2,6,1,5,7,4,8,3]=>1011000
[2,3,6,1,8,4,7,5]=>1001100
[3,5,1,4,6,7,8,2]=>1100000
[4,5,6,2,1,7,8,3]=>1110000
[5,2,4,7,6,3,8,1]=>1110010
[8,7,6,1,4,3,5,2]=>1110011
[8,7,6,1,3,4,5,2]=>1100011
[8,7,1,4,5,6,3,2]=>1110001
[8,1,5,6,7,4,3,2]=>1111000
[5,8,3,4,1,6,2,7]=>1110000
[4,2,6,1,7,8,5,3]=>1110100
[1,5,2,6,7,8,4,3]=>0111000
[4,5,2,7,8,6,1,3]=>1100010
[1,5,6,7,4,8,2,3]=>0101000
[4,2,6,8,5,1,7,3]=>1110100
[4,2,7,8,5,6,1,3]=>1100100
[3,5,2,7,4,6,8,1]=>1101000
[5,6,2,7,3,8,4,1]=>1111000
[3,5,2,8,4,6,7,1]=>1101000
[3,7,2,8,4,1,5,6]=>1101000
[3,5,2,4,7,8,6,1]=>1100010
[3,7,1,5,8,2,4,6]=>1100000
[5,1,3,8,2,4,6,7]=>1100000
[4,2,1,3,8,5,6,7]=>1100100
[1,8,7,6,3,4,5,2]=>0110011
[8,5,7,6,3,1,4,2]=>1110110
[8,5,7,6,3,2,1,4]=>1110110
[8,7,5,3,1,6,4,2]=>1111101
[4,2,8,3,1,6,7,5]=>1110100
[7,8,1,4,5,6,3,2]=>1110000
[4,2,8,3,5,1,7,6]=>1110010
[4,2,7,8,1,6,5,3]=>1110100
[6,8,1,4,5,3,7,2]=>1110000
[5,1,3,4,2,6,7,8]=>1100000
[4,2,7,3,1,6,5,8]=>1110100
[2,3,4,5,8,1,7,6]=>1000010
[4,1,5,3,6,7,8,2]=>1110000
[2,3,4,8,1,6,7,5]=>1000100
[5,1,4,6,3,7,8,2]=>1110000
[5,1,6,3,4,7,8,2]=>1110000
[2,1,7,5,3,8,6,4]=>1011110
[2,1,8,7,5,3,6,4]=>1011101
[7,5,3,2,1,8,6,4]=>1111110
[5,2,3,4,1,8,6,7]=>1100010
[3,2,1,6,4,5,7,8]=>1101000
[3,8,1,2,5,4,7,6]=>1001010
[7,4,6,8,5,3,2,1]=>1111100
[7,5,8,6,3,2,1,4]=>1110110
[7,4,8,5,6,3,2,1]=>1111100
[7,5,8,6,4,2,1,3]=>1101110
[6,4,2,1,8,5,3,7]=>1111100
[5,3,8,7,4,2,1,6]=>1111001
[7,4,2,1,6,8,5,3]=>1111100
[5,3,8,4,2,1,6,7]=>1111000
[8,6,3,5,7,4,2,1]=>1111010
[7,4,2,1,8,5,6,3]=>1111100
[6,3,5,8,4,2,1,7]=>1111000
[6,4,8,7,5,2,1,3]=>1101101
[7,5,2,1,3,8,6,4]=>1101110
[7,5,2,1,8,6,3,4]=>1110110
[6,3,8,7,4,5,2,1]=>1111001
[7,4,5,2,1,8,6,3]=>1111010
[8,5,2,1,7,4,6,3]=>1111100
[6,3,8,4,5,2,1,7]=>1111000
[7,3,6,8,4,5,2,1]=>1111000
[7,4,8,5,6,2,1,3]=>1101100
[7,3,4,5,8,6,2,1]=>1110010
[7,3,8,4,5,6,2,1]=>1111000
[1,8,7,2,6,5,4,3]=>0111101
[1,8,7,6,2,3,4,5]=>0100011
[1,8,2,5,7,6,4,3]=>0111010
[1,8,2,5,6,7,4,3]=>0111000
[1,2,8,3,4,5,7,6]=>0010010
[7,6,1,2,3,8,4,5]=>1001010
[1,6,2,3,4,8,7,5]=>0100101
[7,4,1,2,8,3,5,6]=>1011000
[6,4,1,2,8,3,5,7]=>1011000
[4,8,1,2,3,7,5,6]=>1000100
[6,4,1,7,2,3,8,5]=>1101100
[6,5,1,2,3,8,4,7]=>1001100
[1,8,5,2,3,7,4,6]=>0101100
[6,5,1,2,7,3,8,4]=>1011100
[7,6,4,1,8,2,3,5]=>1101010
[1,5,2,3,6,8,7,4]=>0101001
[7,6,3,1,8,2,4,5]=>1110010
[5,3,6,1,2,4,8,7]=>1010001
[5,8,3,1,7,2,4,6]=>1110000
[7,5,4,1,8,2,3,6]=>1101100
[7,6,1,4,8,2,3,5]=>1100010
[1,2,8,5,3,7,4,6]=>0011100
[1,2,7,3,8,6,4,5]=>0011010
[7,5,1,6,8,2,3,4]=>1100100
[4,1,2,8,6,3,7,5]=>1010110
[5,4,1,6,2,7,8,3]=>1111000
[6,3,4,1,7,2,8,5]=>1110100
[6,5,3,1,8,2,4,7]=>1110100
[3,8,1,6,7,2,4,5]=>1100000
[6,5,3,7,1,2,8,4]=>1011100
[7,1,4,2,8,5,3,6]=>1110100
[7,1,4,2,6,8,3,5]=>1110000
[1,2,6,8,3,5,4,7]=>0011000
[1,2,3,7,8,6,4,5]=>0001010
[1,6,8,5,2,7,3,4]=>0110100
[7,6,3,4,1,8,2,5]=>1110010
[1,4,8,2,3,7,6,5]=>0100110
[1,2,8,3,5,7,6,4]=>0011010
[4,5,1,7,6,8,2,3]=>1100010
[3,4,8,1,2,6,7,5]=>1000100
[3,1,8,2,5,6,7,4]=>1101000
[1,4,2,5,6,8,7,3]=>0110001
[4,5,6,3,7,1,8,2]=>1110000
[8,2,7,3,1,5,6,4]=>1111000
[7,2,1,8,4,5,6,3]=>1111000
[4,2,7,1,3,8,6,5]=>1100110
[8,2,6,3,4,7,1,5]=>1110000
[7,2,3,4,1,8,6,5]=>1100110
[6,1,8,2,7,5,3,4]=>1110100
[4,2,8,1,5,6,3,7]=>1110000
[8,2,7,3,1,4,5,6]=>1110000
[5,3,1,6,2,7,8,4]=>1111000
[5,2,1,3,6,7,8,4]=>1101000
[6,4,8,7,3,2,1,5]=>1111001
[6,5,3,8,7,2,1,4]=>1110101
[5,4,8,7,3,2,1,6]=>1111001
[6,4,3,8,7,2,1,5]=>1111001
[6,3,8,7,5,2,1,4]=>1110101
[5,6,8,1,4,2,7,3]=>1110000
[5,6,3,1,4,2,7,8]=>1110000
[5,7,3,8,4,1,6,2]=>1111000
[5,7,3,1,4,6,2,8]=>1110000
[5,7,3,4,8,1,6,2]=>1110000
[5,2,6,1,4,3,7,8]=>1110000
[5,8,3,1,4,6,7,2]=>1110000
[6,2,7,4,1,5,3,8]=>1111000
[6,7,3,8,1,5,2,4]=>1110000
[6,7,3,4,1,5,2,8]=>1110000
[6,7,8,1,5,4,2,3]=>1101000
[4,5,6,7,1,3,2,8]=>1100000
[6,7,1,4,5,3,2,8]=>1110000
[4,5,7,8,2,1,6,3]=>1110000
[7,2,3,8,1,6,5,4]=>1101100
[7,2,3,8,5,1,6,4]=>1101100
[7,2,3,1,5,6,4,8]=>1101000
[7,2,8,4,1,6,5,3]=>1111100
[7,2,8,4,5,1,6,3]=>1111000
[4,6,3,8,1,5,7,2]=>1110000
[7,8,3,4,1,6,5,2]=>1110100
[4,6,7,3,8,1,2,5]=>1010000
[4,6,7,8,1,5,3,2]=>1110000
[4,6,7,1,5,2,3,8]=>1100000
[4,6,8,3,1,5,7,2]=>1110000
[4,6,1,3,5,2,7,8]=>1100000
[4,7,3,8,5,1,6,2]=>1110100
[4,7,3,8,1,6,5,2]=>1110100
[1,7,2,3,4,6,8,5]=>0100100
[8,1,2,3,5,6,4,7]=>1001000
[4,1,8,2,7,3,5,6]=>1110000
[1,8,4,2,7,3,5,6]=>0111000
[7,4,1,2,6,8,3,5]=>1011000
[8,7,1,2,4,5,3,6]=>1010001
[4,1,8,2,3,5,7,6]=>1100010
[6,1,2,8,3,4,7,5]=>1010100
[5,4,1,2,7,8,3,6]=>1011000
[1,5,2,8,3,4,7,6]=>0110010
[7,1,2,5,3,6,8,4]=>1011000
[1,8,2,5,6,3,7,4]=>0111000
[1,5,2,4,6,7,8,3]=>0110000
[6,8,1,3,4,2,5,7]=>1100000
[3,1,8,2,5,4,6,7]=>1101000
[3,1,7,5,8,2,4,6]=>1100100
[1,7,3,2,8,4,5,6]=>0111000
[6,3,5,1,8,2,4,7]=>1110000
[1,6,4,2,3,5,8,7]=>0101001
[1,7,4,2,3,5,8,6]=>0101010
[1,7,4,2,3,6,8,5]=>0101100
[1,2,7,3,8,4,6,5]=>0011100
[7,1,3,4,5,8,2,6]=>1100000
[7,6,1,3,4,8,2,5]=>1100010
[1,8,7,6,3,2,4,5]=>0110011
[1,8,2,7,5,3,6,4]=>0111100
[1,7,4,5,2,6,8,3]=>0111000
[1,4,8,5,6,2,7,3]=>0110100
[3,2,1,8,7,6,4,5]=>1101011
[3,2,1,8,7,5,4,6]=>1101101
[3,2,1,8,7,4,6,5]=>1101101
[3,2,1,8,7,4,5,6]=>1101001
[3,2,1,8,4,7,6,5]=>1101110
[3,2,8,7,6,1,5,4]=>1101011
[5,3,8,7,6,2,1,4]=>1110011
[6,5,8,7,3,2,1,4]=>1110101
[7,4,8,5,6,3,1,2]=>1011100
[4,5,3,8,6,2,7,1]=>1110010
[4,6,2,8,5,3,7,1]=>1110100
[5,3,8,4,6,2,7,1]=>1111000
[4,6,2,7,1,8,5,3]=>1110100
[4,7,1,6,2,8,5,3]=>1110100
[6,2,5,3,8,4,7,1]=>1111000
[4,6,5,3,8,2,7,1]=>1110100
[5,7,8,4,3,2,1,6]=>1111000
[4,6,8,7,3,2,1,5]=>1110001
[2,4,8,7,6,5,1,3]=>1000111
[4,7,6,8,3,2,1,5]=>1110010
[3,6,8,5,7,2,1,4]=>1100100
[4,6,7,8,3,2,1,5]=>1110000
[3,5,6,8,7,2,1,4]=>1100001
[1,4,8,7,6,3,5,2]=>0110011
[2,4,5,8,7,6,1,3]=>1000011
[2,5,4,7,3,8,1,6]=>1011000
[2,6,4,7,8,3,1,5]=>1011000
[2,4,7,1,8,3,6,5]=>1010100
[2,4,6,1,5,8,3,7]=>1010000
[2,5,4,8,6,7,3,1]=>1011010
[3,4,1,7,6,8,5,2]=>1100110
[3,6,1,7,8,4,2,5]=>1101000
[3,5,1,7,2,6,8,4]=>1101000
[4,3,6,2,8,1,7,5]=>1110100
[5,3,4,7,2,8,1,6]=>1110000
[4,5,7,2,1,8,3,6]=>1110000
[4,6,5,2,8,7,3,1]=>1110101
[5,6,4,8,2,7,3,1]=>1111000
[4,5,8,2,1,6,7,3]=>1110000
[3,4,1,5,6,8,7,2]=>1100001
[3,6,1,7,2,5,8,4]=>1101000
[7,3,4,5,8,2,1,6]=>1110000
[6,3,7,8,2,5,1,4]=>1110000
[6,7,4,8,2,5,3,1]=>1111000
[3,5,1,4,7,2,8,6]=>1100010
[4,3,7,5,6,2,8,1]=>1110100
[7,3,4,8,6,2,5,1]=>1110010
[4,7,8,5,6,2,1,3]=>1100100
[3,5,1,4,8,7,2,6]=>1100001
[4,5,6,3,8,2,1,7]=>1110000
[4,2,6,3,7,8,1,5]=>1110000
[4,2,7,3,5,8,1,6]=>1110000
[4,5,3,7,8,1,6,2]=>1110000
[4,2,6,8,5,3,1,7]=>1110100
[5,1,2,7,8,6,4,3]=>1011010
[4,1,2,7,8,6,3,5]=>1010010
[4,1,8,7,2,6,3,5]=>1110001
[4,1,5,8,7,3,2,6]=>1110001
[5,1,8,2,7,6,3,4]=>1110010
[7,1,6,2,8,3,4,5]=>1110000
[4,7,8,3,2,5,1,6]=>1110000
[4,5,2,8,7,3,1,6]=>1110001
[4,5,7,6,8,3,1,2]=>1010010
[8,2,1,7,4,6,3,5]=>1111000
[5,2,1,6,8,4,7,3]=>1111000
[4,5,2,8,7,1,6,3]=>1110001
[4,2,5,7,3,1,8,6]=>1110010
[4,2,8,7,1,3,6,5]=>1100101
[8,2,1,7,3,5,4,6]=>1111000
[5,2,6,3,8,7,1,4]=>1110001
[5,2,8,6,4,1,7,3]=>1111010
[5,2,3,8,7,1,4,6]=>1100001
[5,1,8,3,7,4,2,6]=>1111000
[8,1,2,7,5,4,3,6]=>1011100
[6,1,2,8,3,7,4,5]=>1011000
[5,6,7,3,8,1,2,4]=>1010000
[4,1,7,6,8,3,2,5]=>1110010
[8,1,7,3,5,4,2,6]=>1111000
[7,1,6,3,4,2,8,5]=>1110100
[7,1,6,8,5,2,3,4]=>1100100
[8,1,7,3,5,2,6,4]=>1111000
[6,2,3,8,7,5,1,4]=>1100101
[3,8,5,7,2,4,1,6]=>1100100
[3,6,5,8,2,1,7,4]=>1101100
[4,7,1,8,3,5,2,6]=>1110000
[7,6,2,3,4,1,8,5]=>1100110
[4,8,6,7,1,2,3,5]=>1000010
[8,5,7,3,1,6,2,4]=>1110100
[3,4,7,2,1,5,8,6]=>1100010
[3,8,6,1,4,7,2,5]=>1100010
[3,7,6,8,2,5,1,4]=>1100010
[8,6,2,3,1,5,7,4]=>1101010
[3,8,7,1,2,5,6,4]=>1001001
[3,4,8,2,5,6,7,1]=>1100000
[4,2,1,3,7,6,5,8]=>1100110
[6,3,4,8,7,5,1,2]=>1010101
[8,3,5,7,6,1,4,2]=>1110010
[2,1,8,5,6,7,3,4]=>1010100
[6,8,4,5,7,2,3,1]=>1101000
[8,3,2,5,6,7,1,4]=>1110000
[7,3,2,6,8,5,4,1]=>1111100
[4,8,5,3,2,7,6,1]=>1110110
[7,3,5,6,8,1,4,2]=>1110000
[7,4,8,3,6,5,2,1]=>1111100
[7,5,6,3,8,4,2,1]=>1111100
[7,4,5,2,8,3,6,1]=>1111000
[4,8,6,7,3,5,2,1]=>1110010
[4,3,1,2,6,7,8,5]=>1010100
[7,4,6,5,8,3,2,1]=>1111100
[4,8,5,2,6,7,3,1]=>1110100
[2,5,8,6,7,3,1,4]=>1010010
[1,4,6,5,2,7,3,8]=>0110100
[3,7,4,8,6,2,5,1]=>1101010
[2,3,4,1,8,7,5,6]=>1000101
[4,2,6,5,1,8,7,3]=>1110101
[6,5,4,1,3,2,8,7]=>1101101
[6,5,4,2,1,3,8,7]=>1101101
[8,7,4,3,6,1,5,2]=>1111001
[7,8,4,2,1,5,6,3]=>1111000
[8,6,7,2,4,5,1,3]=>1100010
[7,8,2,3,6,1,5,4]=>1101000
[6,8,2,7,3,5,4,1]=>1111000
[2,1,7,8,4,5,6,3]=>1011000
[7,5,8,3,2,4,6,1]=>1110100
[8,6,7,3,4,1,5,2]=>1110010
[8,6,2,7,1,3,5,4]=>1101010
[8,3,2,7,6,4,1,5]=>1111010
[8,5,4,1,3,7,6,2]=>1101110
[5,8,2,3,4,7,6,1]=>1100010
[6,8,2,7,3,4,1,5]=>1110000
[5,6,1,4,7,2,3,8]=>1100000
[4,5,1,6,3,2,8,7]=>1110001
[3,6,7,4,1,2,5,8]=>1001000
[2,5,1,4,3,7,6,8]=>1010010
[1,4,5,3,7,2,8,6]=>0110010
[5,1,4,3,7,2,8,6]=>1110010
[1,6,7,4,3,2,8,5]=>0111100
[2,6,7,3,1,4,5,8]=>1010000
[5,1,4,6,7,2,3,8]=>1100000
[2,6,4,3,1,8,5,7]=>1011100
[1,6,5,2,3,4,8,7]=>0100101
[7,8,2,1,5,4,3,6]=>1111000
[7,8,1,2,3,6,4,5]=>1001000
[1,4,7,8,5,2,3,6]=>0100100
[1,3,2,6,5,8,4,7]=>0101100
[2,1,5,7,8,4,3,6]=>1011000
[3,1,7,2,6,5,8,4]=>1101100
[1,3,2,7,5,4,8,6]=>0101110
[1,4,5,8,6,2,3,7]=>0100010
[1,6,7,2,3,5,8,4]=>0101000
[2,4,1,8,6,5,3,7]=>1010110
[2,5,4,7,8,6,1,3]=>1001010
[7,1,4,5,8,3,6,2]=>1110000
[3,7,8,5,4,6,1,2]=>1001100
[5,1,7,2,6,4,8,3]=>1111000
[3,1,7,8,6,4,5,2]=>1101010
[2,3,4,6,8,5,7,1]=>1000100
[3,6,2,4,7,5,8,1]=>1100100
[3,7,2,8,4,6,5,1]=>1101100
[4,7,5,2,3,6,8,1]=>1100100
[4,3,5,8,7,2,6,1]=>1110001
[2,3,4,8,7,5,6,1]=>1000101
[5,1,6,3,7,8,4,2]=>1111000
[4,2,6,7,5,1,8,3]=>1110100
[5,7,6,3,4,8,1,2]=>1010010
[6,4,7,5,8,3,2,1]=>1111100
[3,6,7,5,8,1,4,2]=>1100100
[1,8,5,6,7,3,4,2]=>0110100
[3,2,7,4,6,1,8,5]=>1101100
[3,8,4,5,6,7,2,1]=>1101000
[8,2,4,1,6,7,5,3]=>1110100
[3,4,8,7,6,1,5,2]=>1100011
[4,3,8,7,6,2,5,1]=>1110011
[3,7,8,5,6,4,2,1]=>1101100
[4,3,7,5,8,6,2,1]=>1110110
[3,4,7,5,8,6,1,2]=>1000110
[6,3,1,5,4,2,8,7]=>1111001
[6,4,5,3,2,1,8,7]=>1111001
[2,7,5,6,8,3,4,1]=>1010100
[7,8,3,4,6,5,1,2]=>1010100
[2,1,7,6,8,4,5,3]=>1011010
[2,5,4,8,6,3,7,1]=>1011010
[3,5,4,7,6,1,8,2]=>1101010
[2,6,5,3,7,4,8,1]=>1011100
[2,1,8,5,3,7,6,4]=>1011110
[6,5,4,2,7,8,3,1]=>1111100
[2,6,8,5,7,4,3,1]=>1011100
[2,1,8,6,7,5,4,3]=>1011110
[2,5,3,1,6,4,7,8]=>1011000
[7,5,4,2,3,1,8,6]=>1101110
[6,3,2,4,5,8,1,7]=>1110000
[3,5,4,2,8,6,1,7]=>1101010
[5,6,8,7,3,2,1,4]=>1110001
[6,4,5,3,2,8,1,7]=>1111000
[4,2,5,7,3,1,6,8]=>1110000
[7,4,1,3,2,6,8,5]=>1101100
[6,1,4,3,2,7,8,5]=>1110100
[1,6,4,2,3,7,8,5]=>0101100
[1,4,5,3,8,2,6,7]=>0110000
[2,5,4,3,8,1,6,7]=>1011000
[6,2,5,1,3,7,4,8]=>1101000
[7,6,5,8,1,2,4,3]=>1010110
[5,7,4,1,3,6,2,8]=>1101000
[4,3,8,1,6,7,2,5]=>1110000
[4,3,8,1,6,5,7,2]=>1110100
[4,3,8,2,5,6,7,1]=>1110000
[5,4,8,2,3,6,7,1]=>1101000
[3,2,8,1,6,7,4,5]=>1101000
[5,2,8,1,6,7,3,4]=>1110000
[7,2,6,3,8,1,5,4]=>1111000
[7,2,8,1,6,3,5,4]=>1111000
[6,3,4,5,8,2,7,1]=>1110000
[7,4,8,2,3,5,6,1]=>1101000
[7,3,8,1,4,5,6,2]=>1110000
[7,3,4,5,8,1,6,2]=>1110000
[7,4,8,1,5,6,2,3]=>1101000
[7,2,8,1,6,5,4,3]=>1111100
[8,1,3,4,6,5,2,7]=>1100100
[8,6,5,7,2,1,4,3]=>1110110
[2,4,7,8,5,6,3,1]=>1010100
[1,8,6,3,7,4,5,2]=>0111010
[3,8,5,1,7,6,4,2]=>1101110
[2,8,1,3,5,6,7,4]=>1001000
[2,4,8,7,5,6,3,1]=>1010101
[3,8,7,5,2,6,4,1]=>1101101
[1,8,7,3,4,6,5,2]=>0110101
[2,8,1,4,5,7,6,3]=>1010010
[1,2,7,6,8,4,5,3]=>0011010
[1,2,6,7,8,3,5,4]=>0011000
[1,2,6,8,7,3,4,5]=>0010001
[1,2,5,3,7,6,8,4]=>0011010
[3,7,8,1,5,6,2,4]=>1100000
[1,2,4,8,3,6,5,7]=>0010100
[4,1,3,7,6,8,5,2]=>1100110
[6,5,7,8,1,4,3,2]=>1110100
[3,1,8,6,7,5,4,2]=>1101110
[2,8,3,1,7,5,4,6]=>1011100
[2,8,3,7,1,4,5,6]=>1010000
[4,8,2,7,5,1,3,6]=>1100100
[4,1,2,6,7,5,3,8]=>1010100
[1,2,5,3,8,6,4,7]=>0011010
[5,8,7,6,2,1,3,4]=>1100011
[6,4,8,3,7,5,2,1]=>1111100
[3,6,8,2,5,7,4,1]=>1101000
[5,4,2,6,1,8,7,3]=>1111001
[4,8,7,5,2,6,3,1]=>1110101
[3,2,8,5,6,1,7,4]=>1101100
[3,4,8,1,5,7,6,2]=>1100010
[4,5,6,2,7,3,8,1]=>1110000
[3,5,8,7,4,6,2,1]=>1101001
[4,7,5,6,2,3,8,1]=>1100100
[3,5,7,6,2,4,8,1]=>1100010
[1,6,8,7,4,5,3,2]=>0111001
[8,3,5,7,6,2,4,1]=>1110010
[6,4,5,2,8,7,3,1]=>1111001
[6,4,2,7,8,5,3,1]=>1111100
[2,4,5,8,6,7,1,3]=>1000010
[1,3,5,6,8,7,2,4]=>0100001
[5,7,4,1,6,2,8,3]=>1111000
[3,5,6,7,8,2,4,1]=>1100000
[5,2,4,1,6,7,8,3]=>1110000
[8,5,6,7,2,4,3,1]=>1110100
[7,8,4,5,1,6,3,2]=>1111000
[3,5,8,6,4,7,2,1]=>1101010
[4,5,6,8,3,7,2,1]=>1110000
[8,4,5,7,6,2,3,1]=>1101010
[4,8,6,7,5,2,3,1]=>1100110
[8,7,4,3,6,5,1,2]=>1011101
[8,1,4,3,6,5,2,7]=>1110100
[6,1,2,5,4,3,8,7]=>1011001
[2,8,6,3,4,7,1,5]=>1010010
[8,1,2,3,5,7,4,6]=>1001000
[8,1,2,3,6,5,4,7]=>1001100
[8,1,2,3,7,6,5,4]=>1001110
[2,8,1,6,7,5,3,4]=>1010100
[8,1,2,3,5,4,7,6]=>1001010
[4,8,5,2,7,1,6,3]=>1110100
[3,7,8,6,4,2,1,5]=>1101010
[3,7,8,4,6,2,1,5]=>1101000
[8,3,1,5,7,6,2,4]=>1110010
[4,5,2,8,6,7,1,3]=>1100010
[8,4,5,1,3,2,6,7]=>1101000
[8,1,2,3,6,7,5,4]=>1001100
[8,1,6,7,2,5,4,3]=>1111000
[5,4,1,3,2,8,7,6]=>1101011
[5,4,2,1,3,8,7,6]=>1101011
[3,2,7,4,1,6,5,8]=>1101100
[5,7,3,2,1,6,4,8]=>1111000
[7,6,5,1,3,4,2,8]=>1100110
[7,6,5,2,1,4,3,8]=>1110110
[8,6,2,4,3,5,1,7]=>1110010
[7,6,5,1,4,2,3,8]=>1100110
[1,7,6,3,2,4,5,8]=>0110010
[8,7,3,2,1,6,4,5]=>1111001
[1,5,7,2,4,3,6,8]=>0110000
[5,2,8,1,4,3,7,6]=>1110010
[7,1,6,8,2,4,5,3]=>1110000
[8,4,6,2,3,7,1,5]=>1101000
[8,6,1,3,7,5,2,4]=>1100110
[5,8,1,3,4,7,2,6]=>1100000
[5,8,6,2,3,1,4,7]=>1100010
[5,8,7,3,2,4,6,1]=>1110001
[7,6,2,8,3,5,4,1]=>1111010
[8,7,5,2,6,3,1,4]=>1110101
[8,4,7,3,1,5,2,6]=>1111000
[8,2,6,3,1,4,7,5]=>1110100
[8,3,2,7,6,1,4,5]=>1110010
[3,8,2,7,6,4,1,5]=>1101010
[3,6,7,5,8,2,1,4]=>1100100
[6,3,5,2,8,7,4,1]=>1111001
[5,8,4,3,2,7,6,1]=>1111010
[2,4,6,8,7,3,5,1]=>1010001
[6,3,5,7,8,2,4,1]=>1110000
[4,6,8,7,5,2,3,1]=>1100101
[3,5,6,8,7,2,4,1]=>1100001
[1,6,8,4,7,5,3,2]=>0111100
[3,8,6,5,1,7,2,4]=>1100110
[8,4,6,7,5,2,3,1]=>1101100
[6,5,8,3,7,4,2,1]=>1111100
[8,4,5,7,2,6,3,1]=>1111000
[6,7,4,3,8,5,2,1]=>1111100
[2,6,8,5,4,7,3,1]=>1011100
[2,7,4,6,8,5,3,1]=>1011100
[6,4,7,8,3,5,2,1]=>1111000
[6,3,5,2,7,4,8,1]=>1111000
[7,3,4,2,6,1,8,5]=>1110100
[2,3,7,4,6,1,8,5]=>1001100
[7,5,4,2,6,3,8,1]=>1111100
[5,4,7,2,6,1,8,3]=>1111000
[5,2,7,4,6,1,8,3]=>1111000
[5,2,4,1,7,6,8,3]=>1110010
[4,2,7,5,6,1,8,3]=>1110100
[4,2,7,5,6,3,8,1]=>1110100
[6,2,4,3,7,5,8,1]=>1110100
[2,6,4,3,7,5,8,1]=>1011100
[2,7,5,4,8,6,3,1]=>1011110
[4,3,7,5,8,6,1,2]=>1010110
[6,7,4,8,3,5,2,1]=>1111000
[2,1,5,8,7,4,6,3]=>1011001
[5,8,3,4,6,7,2,1]=>1110000
[6,4,3,8,7,2,5,1]=>1111001
[3,6,8,5,4,7,1,2]=>1001100
[7,5,3,6,8,4,2,1]=>1111100
[8,4,3,5,7,2,6,1]=>1111000
[4,7,8,6,3,5,2,1]=>1110010
[6,7,5,8,2,4,3,1]=>1110100
[2,5,4,1,7,8,6,3]=>1011010
[4,3,1,5,6,8,7,2]=>1110001
[1,6,3,2,5,8,7,4]=>0111001
[8,1,5,3,2,6,7,4]=>1111000
[1,6,8,3,2,4,7,5]=>0110100
[1,8,7,6,4,2,3,5]=>0101011
[8,1,7,3,5,4,6,2]=>1111000
[7,1,3,8,4,6,5,2]=>1101100
[3,2,8,1,5,6,7,4]=>1101000
[8,6,1,2,4,5,7,3]=>1010010
[1,8,6,7,3,4,5,2]=>0110010
[1,7,3,8,2,4,6,5]=>0110100
[8,4,3,1,5,6,7,2]=>1111000
[1,7,3,8,2,6,5,4]=>0111100
[1,8,7,6,3,4,2,5]=>0110011
[7,1,3,8,4,5,2,6]=>1101000
[1,8,5,3,7,6,2,4]=>0110110
[3,5,2,6,1,4,8,7]=>1100001
[4,5,7,2,3,8,6,1]=>1100010
[4,5,7,2,3,8,1,6]=>1100000
[4,5,6,2,3,1,8,7]=>1100001
[4,5,6,2,1,3,8,7]=>1100001
[4,5,6,1,3,2,8,7]=>1100001
[4,5,6,3,1,2,8,7]=>1010001
[4,5,7,3,2,8,1,6]=>1110000
[4,6,7,3,8,2,5,1]=>1110000
[4,6,7,3,8,2,1,5]=>1110000
[4,5,7,3,1,8,2,6]=>1110000
[3,5,1,7,4,8,2,6]=>1101000
[2,1,5,7,4,8,3,6]=>1011000
[4,5,7,1,3,8,6,2]=>1100010
[4,6,7,3,8,1,5,2]=>1110000
[5,6,7,8,3,1,4,2]=>1110000
[4,6,7,1,8,3,5,2]=>1110000
[3,6,1,7,8,4,5,2]=>1101000
[2,1,6,7,8,4,5,3]=>1011000
[2,1,6,7,8,4,3,5]=>1011000
[4,6,7,1,8,3,2,5]=>1110000
[5,6,7,8,1,3,2,4]=>1100000
[4,6,7,2,8,3,5,1]=>1110000
[3,6,2,7,8,4,5,1]=>1101000
[3,6,2,7,8,4,1,5]=>1101000
[3,4,2,1,7,8,5,6]=>1100100
[4,6,7,2,8,5,3,1]=>1110100
[4,6,7,2,8,5,1,3]=>1100100
[4,5,7,1,2,8,6,3]=>1010010
[2,1,6,7,8,3,5,4]=>1011000
[3,6,1,7,8,2,5,4]=>1101000
[4,6,7,1,8,2,5,3]=>1110000
[5,6,7,8,1,2,4,3]=>1010000
[5,6,7,8,2,4,1,3]=>1100000
[5,6,7,8,2,4,3,1]=>1110000
[3,6,1,7,8,5,2,4]=>1100100
[2,1,6,7,8,5,3,4]=>1010100
[5,3,1,6,2,4,8,7]=>1110001
[7,3,1,5,2,8,4,6]=>1111000
[8,4,5,1,2,7,3,6]=>1011000
[7,4,5,1,2,8,3,6]=>1011000
[6,4,5,1,2,3,8,7]=>1001001
[5,4,6,1,2,3,8,7]=>1001001
[3,6,1,5,2,4,8,7]=>1100001
[4,6,5,1,2,3,8,7]=>1000101
[5,6,4,1,2,3,8,7]=>1001001
[7,5,4,1,2,8,3,6]=>1011100
[8,6,4,1,7,2,3,5]=>1101010
[5,7,4,1,2,8,3,6]=>1011000
[3,7,1,5,2,8,4,6]=>1101000
[2,1,7,5,3,8,4,6]=>1011100
[4,8,5,1,2,7,3,6]=>1010100
[6,8,4,1,7,2,3,5]=>1101000
[4,8,6,1,7,2,3,5]=>1100010
[2,1,8,6,7,3,4,5]=>1010010
[2,1,7,6,8,3,4,5]=>1010010
[4,7,6,1,8,2,3,5]=>1100010
[5,7,6,8,1,2,3,4]=>1000010
[6,4,7,1,8,2,3,5]=>1101000
[8,4,6,1,7,2,3,5]=>1101000
[8,3,1,6,7,2,4,5]=>1110000
[4,3,1,2,7,8,5,6]=>1010100
[8,4,7,1,6,2,3,5]=>1101000
[7,4,8,1,6,2,3,5]=>1101000
[4,5,8,1,2,7,3,6]=>1010000
[2,1,6,8,7,3,4,5]=>1010001
[4,6,8,1,7,2,3,5]=>1100000
[5,6,8,7,1,2,3,4]=>1000001
[8,5,7,6,1,2,3,4]=>1000110
[4,7,8,1,6,2,3,5]=>1100000
[3,7,1,8,6,2,4,5]=>1100010
[3,8,1,7,6,2,4,5]=>1100010
[4,8,7,1,6,2,3,5]=>1100001
[6,8,7,5,1,2,3,4]=>1000101
[6,4,7,3,8,5,1,2]=>1011100
[5,4,2,7,6,1,3,8]=>1101010
[5,4,2,7,6,1,8,3]=>1111010
[5,4,3,7,6,8,1,2]=>1011010
[5,4,3,7,8,6,1,2]=>1011010
[5,4,3,8,6,7,1,2]=>1011010
[5,4,3,6,8,7,1,2]=>1011001
[5,4,2,6,7,1,8,3]=>1111000
[5,3,2,6,1,7,4,8]=>1111000
[5,3,2,6,1,7,8,4]=>1111000
[5,3,2,6,1,8,7,4]=>1111001
[5,4,2,6,8,1,7,3]=>1111000
[6,4,8,2,5,1,7,3]=>1111000
[5,4,2,8,6,1,3,7]=>1101010
[5,3,2,6,1,8,4,7]=>1111000
[6,3,8,2,1,5,4,7]=>1111000
[7,8,3,2,1,5,4,6]=>1111000
[7,8,3,2,1,5,6,4]=>1111000
[6,3,8,2,1,5,7,4]=>1111000
[5,3,2,8,1,6,7,4]=>1111000
[5,4,2,7,8,1,6,3]=>1111000
[5,3,2,7,1,8,6,4]=>1111010
[5,3,2,7,1,6,4,8]=>1111000
[6,3,7,2,1,5,4,8]=>1111000
[6,3,7,2,1,5,8,4]=>1111000
[6,3,7,2,1,8,5,4]=>1111100
[6,5,7,8,2,1,4,3]=>1110100
[6,3,7,2,1,4,8,5]=>1110100
[5,3,2,7,1,4,8,6]=>1110010
[5,4,2,8,7,1,3,6]=>1101001
[7,8,4,2,6,1,3,5]=>1101000
[7,8,3,2,1,6,4,5]=>1111000
[6,3,8,2,1,7,4,5]=>1111000
[5,3,2,8,1,7,4,6]=>1111000
[4,3,2,1,8,7,5,6]=>1110101
[4,3,2,1,7,5,8,6]=>1110110
[4,3,2,1,7,5,6,8]=>1110100
[5,3,2,8,1,4,7,6]=>1110010
[6,3,8,2,1,4,7,5]=>1110100
[7,8,3,2,1,4,6,5]=>1110100
[4,3,2,1,8,5,6,7]=>1110100
[7,8,5,6,1,2,4,3]=>1010100
[7,8,4,1,6,2,5,3]=>1111000
[1,6,8,3,2,7,5,4]=>0111100
[6,1,8,3,2,7,5,4]=>1111100
[7,8,1,3,2,6,5,4]=>1101100
[7,8,3,1,2,6,5,4]=>1011100
[7,8,2,3,1,6,5,4]=>1101100
[7,8,2,1,3,6,5,4]=>1101100
[7,8,1,2,3,6,5,4]=>1001100
[1,5,2,8,3,7,6,4]=>0111010
[5,1,2,8,3,7,6,4]=>1011010
[5,2,1,8,3,7,6,4]=>1111010
[6,2,8,1,3,7,5,4]=>1101100
[6,2,8,4,7,1,5,3]=>1111000
[6,3,8,4,7,5,1,2]=>1011100
[2,6,8,3,1,7,5,4]=>1011100
[2,5,1,8,3,7,6,4]=>1011010
[1,2,5,8,3,7,6,4]=>0011010
[2,5,3,8,1,7,6,4]=>1011010
[2,5,4,8,7,1,6,3]=>1011001
[3,5,4,8,7,6,1,2]=>1001011
[5,3,4,8,7,6,1,2]=>1010011
[5,2,4,8,7,1,6,3]=>1110001
[5,2,3,8,1,7,6,4]=>1101010
[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]=>1100111
[6,3,8,1,2,7,5,4]=>1011100
[5,3,1,8,2,7,6,4]=>1111010
[5,1,3,8,2,7,6,4]=>1101010
[1,5,3,8,2,7,6,4]=>0111010
[1,5,4,8,7,2,6,3]=>0111001
[5,1,4,8,7,2,6,3]=>1110001
[5,4,1,8,7,2,6,3]=>1111001
[6,5,8,7,1,2,4,3]=>1010101
[5,6,8,7,3,4,1,2]=>1010001
[5,6,8,7,2,1,4,3]=>1110001
[4,5,1,8,7,2,6,3]=>1110001
[4,1,5,8,7,2,6,3]=>1110001
[1,3,5,8,2,7,6,4]=>0101010
[3,1,5,8,2,7,6,4]=>1101010
[3,6,8,2,1,7,5,4]=>1101100
[4,6,8,3,7,5,1,2]=>1010100
[4,5,3,8,7,6,1,2]=>1010011
[3,5,2,8,1,7,6,4]=>1101010
[3,1,4,2,8,7,6,5]=>1100111
[3,2,5,8,1,7,6,4]=>1101010
[4,2,5,8,7,1,6,3]=>1110001
[4,3,5,8,7,6,1,2]=>1010011
[2,4,5,8,7,1,6,3]=>1010001
[2,3,5,8,1,7,6,4]=>1001010
[6,2,5,1,4,3,8,7]=>1110001
[5,2,6,1,4,3,8,7]=>1110001
[5,2,7,1,4,3,8,6]=>1110010
[6,2,8,1,4,3,7,5]=>1110100
[6,2,7,1,4,3,8,5]=>1110100
[7,2,6,1,4,3,8,5]=>1110100
[8,2,5,1,4,3,7,6]=>1110010
[8,1,4,3,7,2,6,5]=>1110100
[8,2,6,1,5,3,7,4]=>1111000
[7,2,6,1,5,3,8,4]=>1111000
[6,2,7,1,5,3,8,4]=>1111000
[6,2,8,1,5,3,7,4]=>1111000
[7,4,8,1,3,2,6,5]=>1101100
[8,3,7,1,4,2,6,5]=>1110100
[8,3,7,1,5,2,6,4]=>1111000
[7,3,8,1,5,2,6,4]=>1111000
[6,2,7,3,8,1,5,4]=>1111000
[6,2,8,3,7,1,5,4]=>1111000
[5,1,8,3,7,2,6,4]=>1111000
[4,1,8,3,7,2,6,5]=>1110100
[3,1,7,4,8,2,6,5]=>1101100
[4,1,7,3,8,2,6,5]=>1110100
[5,1,7,3,8,2,6,4]=>1111000
[7,3,8,2,6,1,5,4]=>1111000
[8,2,6,3,7,1,5,4]=>1111000
[3,4,2,6,8,1,5,7]=>1100000
[5,3,6,2,8,1,4,7]=>1110000
[7,4,2,5,8,3,6,1]=>1111000
[4,5,2,6,3,8,1,7]=>1110000
[3,5,6,1,4,8,2,7]=>1100000
[4,1,5,6,3,8,2,7]=>1110000
[4,5,1,6,3,8,2,7]=>1110000
[4,5,6,3,2,8,1,7]=>1110000
[6,7,4,8,3,2,5,1]=>1111000
[6,7,4,8,3,2,1,5]=>1111000
[6,7,4,1,8,3,2,5]=>1111000
[5,3,7,8,1,4,2,6]=>1110000
[7,3,5,8,1,4,6,2]=>1110000
[4,5,1,7,8,3,6,2]=>1110000
[7,4,1,5,8,3,6,2]=>1111000
[6,7,4,3,8,1,5,2]=>1111000
[5,6,1,7,3,8,4,2]=>1111000
[5,1,6,7,3,8,4,2]=>1111000
[6,4,7,1,8,3,5,2]=>1111000
[6,7,8,3,1,4,5,2]=>1110000
[6,7,2,8,4,5,1,3]=>1101000
[6,7,2,8,4,1,3,5]=>1101000
[6,1,7,4,8,3,2,5]=>1111000
[5,1,6,7,3,2,8,4]=>1111000
[5,6,1,7,3,2,8,4]=>1111000
[5,6,7,3,2,1,8,4]=>1111000
[5,6,7,3,2,8,4,1]=>1111000
[7,4,2,5,1,8,3,6]=>1111000
[6,7,4,2,8,3,5,1]=>1111000
[3,6,7,2,8,4,5,1]=>1101000
[3,6,7,2,8,4,1,5]=>1101000
[3,6,7,2,1,8,4,5]=>1101000
[3,4,7,8,2,1,5,6]=>1100000
[3,7,8,1,4,6,2,5]=>1100000
[3,6,7,2,8,5,1,4]=>1100100
[3,6,7,8,5,2,1,4]=>1100100
[3,6,7,8,5,2,4,1]=>1100100
[6,4,7,8,2,5,3,1]=>1111000
[6,4,7,8,2,1,5,3]=>1111000
[5,3,7,8,1,6,2,4]=>1110000
[6,7,2,8,5,1,3,4]=>1100100
[6,4,1,7,8,2,5,3]=>1111000
[5,1,6,2,7,8,4,3]=>1111000
[5,6,2,7,1,8,4,3]=>1111000
[5,6,2,7,8,4,3,1]=>1111000
[5,6,7,2,8,4,3,1]=>1111000
[5,6,7,2,1,8,4,3]=>1111000
[5,6,1,7,2,8,4,3]=>1111000
[5,1,6,7,2,8,4,3]=>1111000
[6,7,8,3,5,1,4,2]=>1110000
[5,6,1,7,8,4,3,2]=>1111000
[5,6,7,1,8,4,3,2]=>1111000
[8,3,2,5,1,6,4,7]=>1111000
[5,3,2,7,4,1,8,6]=>1111010
[7,5,3,8,2,4,6,1]=>1110100
[8,2,4,5,6,3,1,7]=>1110000
[8,2,4,5,6,1,3,7]=>1100000
[8,5,3,6,4,1,2,7]=>1011100
[8,4,1,5,6,3,2,7]=>1111000
[8,1,4,5,6,3,2,7]=>1110000
[4,5,3,7,2,1,8,6]=>1110010
[7,4,5,8,3,2,6,1]=>1111000
[4,3,6,7,2,8,5,1]=>1110100
[4,3,6,7,2,8,1,5]=>1110000
[1,4,3,6,7,2,8,5]=>0110100
[4,5,3,7,1,8,2,6]=>1110000
[5,3,4,7,1,2,8,6]=>1010010
[7,4,5,8,3,6,1,2]=>1011000
[4,3,6,7,8,1,5,2]=>1110000
[3,5,6,7,8,4,1,2]=>1001000
[3,1,5,6,7,8,4,2]=>1101000
[4,6,1,7,8,3,5,2]=>1110000
[6,2,4,1,7,8,5,3]=>1110100
[2,6,7,1,4,8,3,5]=>1010000
[1,5,3,6,7,8,2,4]=>0110000
[4,5,2,7,8,1,3,6]=>1100000
[4,2,6,7,8,3,1,5]=>1110000
[4,2,6,7,8,3,5,1]=>1110000
[3,6,2,7,4,8,1,5]=>1101000
[3,7,4,2,1,5,8,6]=>1101010
[7,8,4,2,1,3,6,5]=>1101100
[6,3,2,7,1,8,5,4]=>1111100
[3,6,2,7,1,8,5,4]=>1101100
[6,7,3,8,2,5,4,1]=>1111000
[6,4,7,8,5,2,3,1]=>1101100
[2,6,4,7,8,1,5,3]=>1011000
[7,4,1,5,8,6,2,3]=>1101010
[7,5,8,2,1,6,3,4]=>1110100
[6,2,7,1,3,8,5,4]=>1101100
[6,3,1,7,8,2,5,4]=>1111000
[4,6,1,7,8,5,2,3]=>1100100
[5,1,2,6,7,8,4,3]=>1011000
[5,2,6,7,8,4,3,1]=>1111000
[1,6,4,7,8,5,2,3]=>0101100
[2,6,7,1,3,8,5,4]=>1001100
[6,7,3,8,5,1,4,2]=>1110100
[6,4,7,8,5,3,1,2]=>1011100
[3,1,2,6,5,8,7,4]=>1001101
[4,5,1,2,3,8,7,6]=>1000011
[4,6,1,2,3,8,7,5]=>1000101
[1,6,5,3,4,8,7,2]=>0110101
[6,1,5,2,4,8,7,3]=>1110001
[6,5,1,2,3,8,7,4]=>1001101
[6,4,1,2,3,8,7,5]=>1001101
[5,4,1,2,3,8,7,6]=>1001011
[5,4,1,2,7,3,6,8]=>1011000
[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]=>1011100
[7,5,1,2,8,3,6,4]=>1011100
[7,1,5,2,8,4,6,3]=>1111000
[1,7,5,3,8,4,6,2]=>0111100
[8,4,1,2,7,3,6,5]=>1011100
[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]=>1101010
[8,1,6,7,2,4,5,3]=>1110000
[1,7,6,8,3,4,5,2]=>0110010
[7,6,1,8,2,3,5,4]=>1101010
[3,1,2,7,8,5,6,4]=>1001100
[3,1,8,7,2,4,5,6]=>1100001
[3,1,7,6,2,4,5,8]=>1100010
[4,7,1,6,2,3,5,8]=>1100000
[4,8,1,6,2,3,5,7]=>1100000
[5,8,1,2,7,3,6,4]=>1011000
[5,1,8,2,7,4,6,3]=>1111000
[1,5,8,3,7,4,6,2]=>0111000
[1,6,8,7,3,4,5,2]=>0110001
[6,1,8,7,2,4,5,3]=>1110001
[6,8,1,7,2,3,5,4]=>1101000
[6,8,7,1,2,3,4,5]=>1000001
[5,8,6,1,2,3,4,7]=>1000010
[5,7,6,1,2,3,4,8]=>1000010
[7,8,1,6,2,3,5,4]=>1101000
[7,1,8,6,2,4,5,3]=>1110010
[1,7,8,6,3,4,5,2]=>0110010
[8,1,7,6,2,4,5,3]=>1110010
[8,7,1,6,2,3,5,4]=>1101001
[8,5,3,7,2,1,4,6]=>1110100
[6,8,1,4,5,7,3,2]=>1110000
[8,7,2,4,5,1,3,6]=>1100001
[2,6,1,4,5,3,8,7]=>1010001
[6,3,1,4,5,2,8,7]=>1110001
[3,1,6,4,5,2,8,7]=>1101001
[8,3,7,4,5,1,2,6]=>1011000
[5,8,7,4,2,6,3,1]=>1111001
[8,1,7,4,2,6,3,5]=>1111000
[3,7,8,4,5,1,2,6]=>1001000
[5,6,3,8,1,7,2,4]=>1110000
[7,6,1,4,5,8,3,2]=>1110010
[3,7,6,4,5,8,2,1]=>1101010
[8,5,7,4,1,6,3,2]=>1111100
[2,5,8,4,7,6,1,3]=>1001010
[3,8,4,2,5,6,7,1]=>1101000
[8,4,1,3,5,6,7,2]=>1101000
[7,5,8,4,3,6,1,2]=>1011100
[6,5,3,8,4,1,7,2]=>1111100
[2,1,4,8,3,6,7,5]=>1010100
[7,3,8,4,2,6,1,5]=>1111000
[8,3,1,2,5,6,7,4]=>1011000
[4,8,2,3,5,6,7,1]=>1100000
[2,7,8,4,5,3,1,6]=>1011000
[8,7,1,4,3,6,2,5]=>1110001
[5,6,3,8,4,2,7,1]=>1111000
[8,6,3,1,4,2,7,5]=>1110110
[8,6,3,5,1,2,7,4]=>1011010
[5,8,3,2,6,1,7,4]=>1111000
[3,5,8,4,7,6,2,1]=>1101010
[5,8,2,4,7,6,1,3]=>1100010
[7,1,6,4,5,8,2,3]=>1101000
[2,1,8,5,3,6,7,4]=>1011100
[6,8,3,5,2,1,7,4]=>1111000
[7,8,5,4,2,6,1,3]=>1101100
[4,8,1,2,5,6,7,3]=>1010000
[3,4,2,8,5,6,7,1]=>1100100
[2,4,1,8,5,6,7,3]=>1010100
[8,4,2,1,5,6,7,3]=>1111000
[7,5,2,4,8,6,1,3]=>1100110
[2,1,5,3,8,6,7,4]=>1011010
[3,1,4,8,5,6,7,2]=>1100100
[6,5,3,7,2,8,4,1]=>1111100
[6,7,2,4,5,8,3,1]=>1110000
[2,5,7,4,8,6,3,1]=>1011010
[5,6,3,7,1,8,4,2]=>1111000
[3,8,7,4,5,2,1,6]=>1101001
[3,7,5,4,8,6,2,1]=>1101110
[4,6,3,5,8,2,7,1]=>1110000
[3,7,8,4,1,6,2,5]=>1101000
[5,4,2,3,7,6,1,8]=>1101010
[3,2,7,6,4,5,1,8]=>1101010
[4,7,2,6,3,5,1,8]=>1110000
[5,7,6,2,3,4,1,8]=>1100010
[1,7,5,2,8,3,4,6]=>0110100
[6,8,5,2,3,1,4,7]=>1100100
[4,8,2,6,3,1,5,7]=>1110000
[3,2,8,6,4,1,5,7]=>1101010
[7,1,5,2,8,3,4,6]=>1110000
[1,8,5,2,7,3,4,6]=>0110100
[7,1,6,8,2,3,4,5]=>1100000
[3,2,1,7,8,4,5,6]=>1101000
[3,2,8,7,1,4,5,6]=>1100001
[5,8,7,2,1,3,4,6]=>1100001
[1,7,6,8,2,3,4,5]=>0100010
[6,5,8,2,3,1,4,7]=>1100100
[8,5,7,2,1,3,4,6]=>1100100
[3,2,5,4,1,8,6,7]=>1101010
[7,4,2,1,8,3,5,6]=>1111000
[8,4,2,1,7,3,5,6]=>1111000
[1,4,2,8,7,3,5,6]=>0110001
[1,5,8,2,7,3,4,6]=>0110000
[8,5,1,2,7,3,4,6]=>1010100
[3,2,6,1,4,8,5,7]=>1100100
[3,2,7,1,8,4,5,6]=>1101000
[4,7,2,1,8,3,5,6]=>1110000
[8,6,1,7,2,3,4,5]=>1100010
[1,6,8,7,2,3,4,5]=>0100001
[1,7,8,6,2,3,4,5]=>0100010
[7,8,1,6,2,3,4,5]=>1100000
[4,8,2,1,7,3,5,6]=>1110000
[3,2,8,1,7,4,5,6]=>1101000
[5,1,8,2,7,3,4,6]=>1110000
[6,1,8,7,2,3,4,5]=>1100001
[8,1,7,6,2,3,4,5]=>1100010
[2,8,4,1,6,5,7,3]=>1011100
[2,8,5,6,7,4,3,1]=>1011100
[7,5,8,6,1,4,2,3]=>1100110
[3,5,7,6,1,4,2,8]=>1100010
[7,5,8,2,4,1,6,3]=>1110100
[2,8,5,3,4,7,6,1]=>1010110
[2,8,5,3,4,1,7,6]=>1010110
[2,8,5,3,6,1,7,4]=>1011100
[2,8,5,6,7,4,1,3]=>1001100
[2,8,5,3,4,7,1,6]=>1010100
[2,8,5,3,4,6,1,7]=>1010100
[6,5,2,7,3,1,4,8]=>1110100
[6,5,2,8,3,1,7,4]=>1111100
[6,5,2,8,3,1,4,7]=>1110100
[7,5,8,2,4,6,3,1]=>1110100
[7,5,8,6,1,4,3,2]=>1110110
[6,5,8,2,1,3,7,4]=>1101100
[3,5,6,2,1,8,7,4]=>1101001
[3,5,7,2,4,1,8,6]=>1100010
[6,5,2,7,3,1,8,4]=>1111100
[4,5,2,6,3,1,7,8]=>1110000
[6,5,2,7,3,4,8,1]=>1110100
[5,1,6,7,4,3,8,2]=>1111000
[5,1,2,6,4,8,7,3]=>1011001
[5,1,2,8,6,4,7,3]=>1011010
[5,1,6,8,7,3,4,2]=>1110001
[6,5,2,8,3,7,4,1]=>1111100
[4,1,2,3,8,6,5,7]=>1000110
[4,1,2,3,8,6,7,5]=>1000110
[4,1,2,3,8,5,7,6]=>1000110
[6,5,8,2,4,3,7,1]=>1110100
[6,5,2,8,3,7,1,4]=>1110100
[6,5,2,7,3,4,1,8]=>1110100
[5,1,6,7,4,3,2,8]=>1111000
[5,1,6,8,7,3,2,4]=>1110001
[5,7,8,6,3,4,2,1]=>1110010
[3,1,4,8,6,2,7,5]=>1100110
[3,1,4,8,6,5,2,7]=>1100110
[4,1,6,7,8,3,2,5]=>1110000
[4,1,6,5,7,3,2,8]=>1110100
[4,5,2,6,3,7,1,8]=>1110000
[4,5,2,7,3,8,1,6]=>1110000
[3,5,6,2,4,8,1,7]=>1100000
[3,7,5,6,8,4,1,2]=>1001100
[3,6,5,2,8,1,7,4]=>1101100
[6,1,2,5,8,4,7,3]=>1011000
[4,1,2,3,5,8,7,6]=>1000011
[4,1,6,7,8,3,5,2]=>1110000
[4,1,2,6,8,5,7,3]=>1010100
[4,1,2,5,6,8,7,3]=>1010001
[4,5,2,6,3,7,8,1]=>1110000
[6,3,1,2,7,4,8,5]=>1011100
[6,4,2,7,1,3,8,5]=>1101100
[7,4,2,5,1,3,8,6]=>1101010
[8,5,3,6,1,7,2,4]=>1110100
[8,3,6,2,4,7,1,5]=>1110000
[7,3,6,2,4,8,1,5]=>1110000
[6,3,7,4,1,2,8,5]=>1011100
[4,7,1,5,2,3,8,6]=>1100010
[3,7,5,1,2,4,8,6]=>1000110
[8,6,4,2,3,7,1,5]=>1101010
[4,7,6,3,8,1,2,5]=>1010010
[5,7,2,6,1,8,3,4]=>1110000
[7,4,8,5,2,6,1,3]=>1101100
[5,8,2,6,3,7,1,4]=>1110000
[3,8,6,1,2,7,4,5]=>1001010
[3,8,6,2,4,7,1,5]=>1100010
[6,8,4,3,7,1,2,5]=>1011000
[3,8,5,7,1,2,4,6]=>1000100
[2,8,5,7,1,3,4,6]=>1000100
[4,8,6,2,7,1,3,5]=>1100010
[7,3,8,5,6,1,2,4]=>1010100
[6,3,7,5,8,1,2,4]=>1010100
[2,7,6,4,8,1,3,5]=>1001010
[3,6,5,8,1,2,4,7]=>1000100
[5,4,7,3,8,1,2,6]=>1011000
[8,4,6,3,7,1,2,5]=>1011000
[8,4,1,6,7,2,3,5]=>1101000
[5,4,1,7,8,2,3,6]=>1101000
[6,5,1,2,7,8,3,4]=>1010100
[4,7,1,5,8,6,2,3]=>1100010
[7,4,1,8,6,2,3,5]=>1101010
[7,6,1,8,5,2,3,4]=>1100110
[8,6,1,7,5,2,3,4]=>1100110
[5,7,2,8,1,6,3,4]=>1110000
[6,3,7,8,5,1,2,4]=>1010100
[3,6,8,2,7,1,4,5]=>1100000
[5,3,8,7,1,2,4,6]=>1010001
[8,3,7,6,1,2,4,5]=>1010010
[8,4,7,6,1,2,3,5]=>1001010
[5,4,8,7,1,2,3,6]=>1001001
[3,5,8,7,1,2,4,6]=>1000001
[2,5,8,7,1,3,4,6]=>1000001
[4,7,1,8,6,2,3,5]=>1100010
[7,5,8,6,4,1,2,3]=>1001110
[6,8,4,7,5,1,2,3]=>1001100
[5,8,7,1,6,2,3,4]=>1100001
[2,8,7,6,1,3,4,5]=>1000011
[3,8,7,6,1,2,4,5]=>1000011
[4,8,7,6,1,2,3,5]=>1000011
[5,6,3,1,4,2,8,7]=>1110001
[7,5,3,8,2,1,6,4]=>1111100
[3,8,7,4,5,1,6,2]=>1101001
[6,7,1,4,5,8,2,3]=>1100000
[2,1,7,8,5,3,6,4]=>1011100
[5,7,3,8,1,2,6,4]=>1011000
[7,5,1,4,8,6,3,2]=>1110110
[6,4,3,8,1,5,7,2]=>1111000
[8,6,3,1,2,5,7,4]=>1011010
[8,7,1,4,2,6,5,3]=>1110101
[7,3,8,4,1,6,5,2]=>1111100
[5,3,2,7,4,6,8,1]=>1111000
[7,5,3,6,2,4,8,1]=>1110100
[6,3,2,5,1,8,4,7]=>1111000
[8,5,3,6,2,7,1,4]=>1110100
[7,2,6,3,4,5,8,1]=>1110000
[6,2,7,3,4,5,8,1]=>1110000
[6,7,3,5,2,4,8,1]=>1110000
[3,7,6,2,4,5,8,1]=>1100010
[6,5,3,1,2,8,4,7]=>1011100
[8,6,5,2,3,7,1,4]=>1100110
[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]=>0111000
[5,7,3,1,2,8,4,6]=>1011000
[4,2,6,5,1,8,3,7]=>1110100
[5,4,8,6,2,7,1,3]=>1101010
[7,8,5,2,3,6,1,4]=>1100100
[6,8,2,1,7,3,4,5]=>1110000
[2,8,1,7,3,4,5,6]=>1010000
[3,8,6,1,7,2,4,5]=>1100010
[4,2,8,3,7,1,5,6]=>1110000
[4,1,7,5,8,2,3,6]=>1100100
[1,7,3,8,2,4,5,6]=>0110000
[8,1,2,7,3,4,5,6]=>1010000
[6,3,7,1,2,8,4,5]=>1011000
[7,2,6,1,8,3,4,5]=>1110000
[8,2,6,1,7,3,4,5]=>1110000
[7,3,1,5,8,2,4,6]=>1110000
[5,4,1,3,6,8,2,7]=>1101000
[8,5,3,7,6,1,2,4]=>1010110
[6,1,8,3,7,2,4,5]=>1110000
[7,6,8,2,3,5,1,4]=>1100010
[3,7,8,2,4,6,1,5]=>1100000
[5,4,7,8,2,6,1,3]=>1101000
[4,2,5,8,7,1,3,6]=>1100001
[3,6,2,8,7,1,4,5]=>1100001
[3,7,8,1,6,2,4,5]=>1100000
[2,3,8,7,1,4,5,6]=>1000001
[2,1,8,7,3,4,5,6]=>1010001
[8,2,7,6,1,3,4,5]=>1100010
[1,2,8,7,3,4,5,6]=>0010001
[1,3,8,7,2,4,5,6]=>0100001
[1,7,8,3,6,2,4,5]=>0110000
[5,4,8,7,6,1,2,3]=>1001011
[6,8,3,7,5,1,2,4]=>1010100
[7,8,6,2,5,1,3,4]=>1100010
[8,1,6,7,3,2,4,5]=>1110000
[8,1,5,3,7,2,4,6]=>1110000
[8,1,5,3,6,2,4,7]=>1110000
[7,4,8,3,2,6,5,1]=>1111100
[7,4,1,3,2,6,5,8]=>1101100
[8,1,4,3,2,6,5,7]=>1110100
[8,1,4,3,2,7,5,6]=>1110100
[8,1,5,4,6,7,2,3]=>1101000
[8,1,5,3,6,2,7,4]=>1111000
[8,1,4,3,2,6,7,5]=>1110100
[8,1,4,3,2,5,7,6]=>1110010
[7,4,1,3,2,5,6,8]=>1101000
[7,4,8,3,2,5,6,1]=>1111000
[6,4,3,1,2,5,8,7]=>1011001
[7,4,1,3,2,5,8,6]=>1101010
[7,5,1,3,6,2,8,4]=>1101100
[7,5,1,4,6,8,2,3]=>1100100
[6,4,3,8,2,5,1,7]=>1111000
[5,4,3,2,8,6,1,7]=>1111010
[5,4,3,2,8,7,1,6]=>1111001
[6,5,4,8,7,1,2,3]=>1001101
[6,5,4,1,7,8,2,3]=>1101100
[6,4,3,1,2,7,8,5]=>1011100
[7,4,1,3,2,8,5,6]=>1101100
[6,4,3,1,2,7,5,8]=>1011100
[6,4,3,8,2,7,5,1]=>1111100
[6,5,3,8,7,2,4,1]=>1110101
[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]=>1110100
[6,4,3,7,2,8,5,1]=>1111100
[6,4,3,7,2,1,5,8]=>1111000
[7,5,8,4,1,6,2,3]=>1101100
[6,5,4,8,1,7,2,3]=>1101100
[6,5,3,8,1,2,7,4]=>1011100
[6,5,4,7,1,8,2,3]=>1101100
[5,4,3,2,7,8,1,6]=>1111000
[4,6,3,8,5,1,2,7]=>1010100
[5,6,8,3,4,1,2,7]=>1010000
[5,6,8,3,4,1,7,2]=>1110000
[4,6,2,7,5,3,1,8]=>1110100
[5,6,8,4,3,1,2,7]=>1011000
[5,7,8,4,1,3,6,2]=>1101000
[5,6,8,4,2,1,7,3]=>1111000
[5,6,8,2,4,1,7,3]=>1110000
[3,2,6,8,5,1,4,7]=>1100100
[5,6,8,4,2,1,3,7]=>1101000
[5,7,8,4,1,3,2,6]=>1101000
[5,7,8,4,1,2,3,6]=>1001000
[6,7,8,1,5,2,3,4]=>1100000
[6,7,8,1,5,3,2,4]=>1110000
[6,7,8,1,3,5,2,4]=>1100000
[5,7,8,2,1,6,3,4]=>1110000
[4,7,2,8,1,6,3,5]=>1110000
[3,2,7,8,1,6,4,5]=>1101000
[4,7,2,8,1,6,5,3]=>1110100
[5,7,8,2,1,6,4,3]=>1111000
[6,7,8,1,3,5,4,2]=>1101000
[6,7,8,1,5,3,4,2]=>1110000
[6,7,8,1,4,3,5,2]=>1110000
[5,6,8,3,2,1,7,4]=>1111000
[4,7,3,8,1,6,2,5]=>1110000
[4,7,3,8,1,5,6,2]=>1110000
[4,7,3,8,1,5,2,6]=>1110000
[4,7,3,8,1,2,5,6]=>1010000
[5,7,8,3,1,2,4,6]=>1010000
[5,6,8,3,2,1,4,7]=>1110000
[3,2,7,8,1,5,4,6]=>1101000
[6,7,8,1,3,4,2,5]=>1100000
[6,7,8,1,4,2,3,5]=>1100000
[6,7,8,1,2,5,3,4]=>1010000
[6,7,8,1,2,4,5,3]=>1010000
[5,7,8,2,1,3,6,4]=>1101000
[3,2,7,8,1,4,6,5]=>1100100
[6,7,8,1,3,2,4,5]=>1100000
[6,7,8,1,2,4,3,5]=>1010000
[6,7,8,1,2,3,5,4]=>1001000
[8,3,5,1,7,4,6,2]=>1111000
[8,3,4,1,7,5,6,2]=>1110100
[4,8,3,1,7,5,6,2]=>1110100
[4,6,2,1,7,5,8,3]=>1110100
[1,4,6,2,7,5,8,3]=>0110100
[1,7,5,2,6,8,4,3]=>0111100
[7,5,2,1,6,8,4,3]=>1111100
[6,8,4,3,1,7,5,2]=>1111100
[4,7,5,6,1,8,3,2]=>1110100
[6,7,5,1,8,4,3,2]=>1111100
[6,8,4,1,7,5,3,2]=>1111100
[6,7,5,3,1,8,4,2]=>1111100
[8,4,2,1,6,7,5,3]=>1111100
[1,8,4,2,6,7,5,3]=>0111100
[1,5,3,2,7,6,8,4]=>0111010
[2,5,3,1,7,6,8,4]=>1011010
[2,7,5,1,6,8,4,3]=>1011100
[4,7,1,6,5,8,2,3]=>1100100
[4,6,1,2,7,5,8,3]=>1010100
[8,4,1,2,6,7,5,3]=>1011100
[5,3,1,2,7,6,8,4]=>1011010
[4,3,1,2,7,6,8,5]=>1010110
[3,5,1,2,7,6,8,4]=>1001010
[6,7,1,5,8,2,3,4]=>1100000
[2,7,6,1,5,8,3,4]=>1010010
[2,3,5,1,7,6,8,4]=>1001010
[8,4,1,6,7,5,2,3]=>1101100
[5,2,3,1,7,6,8,4]=>1101010
[3,5,2,1,7,6,8,4]=>1101010
[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]=>1111000
[6,1,5,2,7,4,8,3]=>1111000
[7,6,2,5,8,3,1,4]=>1110010
[1,8,3,5,7,6,2,4]=>0110010
[1,5,2,3,7,6,8,4]=>0101010
[5,2,1,3,7,6,8,4]=>1101010
[8,4,2,6,7,5,1,3]=>1101100
[6,1,4,2,7,5,8,3]=>1110100
[8,2,6,5,7,1,4,3]=>1110100
[5,1,3,2,7,6,8,4]=>1101010
[1,4,2,3,7,6,8,5]=>0100110
[2,4,1,3,7,6,8,5]=>1000110
[2,5,1,3,7,6,8,4]=>1001010
[2,8,3,5,7,6,1,4]=>1010010
[6,8,2,3,5,7,1,4]=>1100000
[6,7,1,3,5,8,2,4]=>1100000
[8,3,5,7,6,1,2,4]=>1010010
[5,1,2,3,7,6,8,4]=>1001010
[4,7,1,2,8,6,5,3]=>1010110
[4,6,8,1,2,7,5,3]=>1010100
[6,8,7,1,5,3,2,4]=>1110001
[6,8,7,3,5,1,2,4]=>1010001
[7,8,1,3,6,5,2,4]=>1100100
[1,7,3,4,8,6,5,2]=>0110110
[4,2,7,1,8,6,5,3]=>1110110
[7,8,2,3,6,5,1,4]=>1100100
[8,5,7,1,6,2,3,4]=>1100100
[8,5,7,1,2,6,3,4]=>1010100
[6,8,2,7,1,3,5,4]=>1101000
[6,2,4,8,7,1,5,3]=>1110001
[1,6,8,3,7,4,5,2]=>0111000
[1,6,8,3,4,7,5,2]=>0110100
[6,2,4,8,1,7,5,3]=>1110100
[6,8,7,2,3,5,1,4]=>1100001
[6,8,2,1,7,3,5,4]=>1111000
[8,5,7,2,1,6,3,4]=>1110100
[8,5,7,1,2,3,6,4]=>1001100
[8,5,7,2,3,1,6,4]=>1101100
[1,8,7,5,3,4,6,2]=>0110101
[1,8,7,3,5,4,6,2]=>0111001
[8,2,5,4,7,1,6,3]=>1111000
[8,7,6,1,2,4,3,5]=>1010011
[8,7,6,1,4,2,3,5]=>1100011
[8,7,6,4,1,3,2,5]=>1101011
[8,5,7,1,3,2,6,4]=>1101100
[5,8,4,7,1,2,6,3]=>1011000
[8,1,2,6,5,7,4,3]=>1011100
[8,2,5,6,7,4,1,3]=>1101000
[4,8,5,1,7,2,6,3]=>1110100
[8,5,3,7,1,2,6,4]=>1011100
[4,6,2,8,1,7,5,3]=>1110100
[1,6,4,8,3,7,5,2]=>0111100
[1,8,7,4,5,3,6,2]=>0111001
[4,8,5,7,2,1,6,3]=>1110100
[8,5,3,7,2,1,6,4]=>1111100
[8,7,6,3,1,4,2,5]=>1110011
[8,5,3,2,7,1,6,4]=>1111100
[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]=>1110000
[8,5,2,3,7,1,6,4]=>1101100
[8,3,1,5,2,7,6,4]=>1111010
[8,5,4,2,1,7,3,6]=>1111100
[8,5,4,2,1,7,6,3]=>1111110
[6,5,4,2,3,1,8,7]=>1101101
[6,3,2,5,1,4,8,7]=>1110001
[8,5,4,1,2,7,6,3]=>1011110
[8,7,4,1,6,3,2,5]=>1111001
[8,7,4,1,6,3,5,2]=>1111001
[8,7,4,1,6,5,3,2]=>1111101
[8,5,4,3,1,7,6,2]=>1111110
[8,3,2,5,1,7,6,4]=>1111010
[8,3,2,5,1,7,4,6]=>1111000
[8,5,4,3,1,7,2,6]=>1111100
[8,5,4,1,3,7,2,6]=>1101100
[8,7,4,1,6,5,2,3]=>1101101
[2,1,8,7,6,4,5,3]=>1011011
[8,3,2,7,6,4,5,1]=>1111010
[8,5,4,2,3,7,6,1]=>1101110
[8,7,4,2,6,5,3,1]=>1111101
[8,7,4,2,6,3,5,1]=>1111001
[8,7,4,2,6,3,1,5]=>1111001
[8,3,1,7,6,4,2,5]=>1111010
[8,3,1,7,6,4,5,2]=>1111010
[8,3,1,5,4,7,6,2]=>1111010
[8,3,1,7,6,5,2,4]=>1110110
[8,3,1,7,6,2,5,4]=>1111010
[8,5,4,2,3,7,1,6]=>1101100
[8,3,2,5,4,7,1,6]=>1111000
[2,1,8,5,4,7,3,6]=>1011100
[8,3,2,7,6,5,1,4]=>1110110
[8,7,6,5,3,1,4,2]=>1110111
[8,3,2,7,6,1,5,4]=>1111010
[8,7,6,5,1,2,4,3]=>1010111
[7,4,5,2,3,1,8,6]=>1101010
[6,3,5,2,4,1,8,7]=>1110001
[4,1,6,3,5,2,8,7]=>1110001
[5,2,7,3,4,1,8,6]=>1110010
[6,2,8,5,7,3,4,1]=>1110100
[6,2,7,3,4,1,8,5]=>1110100
[4,1,7,3,5,2,8,6]=>1110010
[3,1,8,6,7,4,5,2]=>1101010
[4,1,8,6,7,3,5,2]=>1110010
[8,5,7,3,4,1,6,2]=>1110100
[8,5,6,2,7,3,4,1]=>1110100
[8,4,7,3,5,1,6,2]=>1111000
[5,1,8,4,7,3,6,2]=>1111000
[2,1,8,5,7,4,6,3]=>1011100
[4,1,7,3,6,2,8,5]=>1110100
[6,2,8,4,7,3,5,1]=>1111000
[7,3,6,2,5,1,8,4]=>1111000
[6,2,4,1,7,3,8,5]=>1110100
[8,5,6,2,3,1,7,4]=>1101100
[7,3,8,5,6,2,4,1]=>1110100
[8,5,6,2,4,1,7,3]=>1110100
[3,1,6,2,8,5,7,4]=>1101100
[5,1,6,2,8,4,7,3]=>1111000
[8,4,6,2,5,1,7,3]=>1111000
[7,3,8,4,6,2,5,1]=>1111000
[6,2,7,3,8,4,5,1]=>1111000
[8,4,5,1,6,2,7,3]=>1111000
[4,1,8,5,6,2,7,3]=>1110100
[3,1,8,5,6,2,7,4]=>1101100
[7,3,6,2,8,4,5,1]=>1111000
[6,8,7,3,4,1,2,5]=>1010001
[5,4,8,7,2,6,3,1]=>1111001
[5,3,8,7,6,1,2,4]=>1010011
[8,3,4,6,5,1,2,7]=>1010100
[3,4,8,7,6,1,2,5]=>1000011
[3,5,8,7,6,1,2,4]=>1000011
[4,5,8,7,6,1,2,3]=>1000011
[4,5,8,7,1,6,3,2]=>1110001
[3,5,8,2,7,6,4,1]=>1101010
[3,5,8,1,7,6,4,2]=>1101010
[2,5,8,7,1,6,3,4]=>1010001
[2,4,8,7,1,6,3,5]=>1010001
[2,8,4,7,1,5,3,6]=>1011000
[8,2,4,6,1,5,3,7]=>1110000
[8,1,4,6,2,5,3,7]=>1110000
[1,4,8,7,2,6,3,5]=>0110001
[1,5,8,7,2,6,3,4]=>0110001
[1,5,8,2,7,6,4,3]=>0111010
[2,5,8,3,7,6,4,1]=>1011010
[1,4,2,8,7,6,5,3]=>0110111
[1,3,8,2,7,6,4,5]=>0101010
[1,8,3,2,7,5,4,6]=>0111100
[8,2,3,1,6,5,4,7]=>1101100
[2,3,8,1,7,6,4,5]=>1001010
[5,2,8,7,1,6,3,4]=>1110001
[5,2,8,1,7,6,4,3]=>1111010
[5,3,8,2,7,6,4,1]=>1111010
[6,8,3,2,7,5,4,1]=>1111100
[6,8,3,1,7,5,4,2]=>1111100
[6,8,1,2,7,5,4,3]=>1011100
[6,8,2,3,7,5,4,1]=>1101100
[5,2,8,3,7,6,4,1]=>1111010
[5,1,8,3,7,6,4,2]=>1111010
[5,1,8,7,2,6,3,4]=>1110001
[4,8,1,7,2,5,3,6]=>1110000
[8,4,1,6,2,5,3,7]=>1111000
[8,3,1,2,6,5,4,7]=>1011100
[3,1,2,8,7,6,5,4]=>1001111
[4,1,3,8,7,6,5,2]=>1100111
[3,1,4,8,7,6,5,2]=>1100111
[2,1,8,3,7,6,4,5]=>1011010
[2,8,1,3,7,5,4,6]=>1001100
[8,2,1,3,6,5,4,7]=>1101100
[1,8,2,3,7,5,4,6]=>0101100
[1,2,8,3,7,6,4,5]=>0011010
[1,4,3,6,8,2,5,7]=>0110000
[1,4,5,2,8,3,7,6]=>0110010
[1,4,2,6,5,8,3,7]=>0110100
[1,5,4,2,6,8,3,7]=>0111000
[3,1,6,5,8,2,4,7]=>1100100
[1,6,4,2,5,8,3,7]=>0111000
[1,5,2,6,4,8,3,7]=>0111000
[1,2,6,5,4,8,3,7]=>0011100
[1,2,5,4,7,3,8,6]=>0011010
[4,1,2,6,3,8,7,5]=>1010101
[7,1,5,4,2,8,3,6]=>1111000
[1,4,7,5,2,8,3,6]=>0110100
[7,1,3,5,2,8,4,6]=>1101000
[1,4,5,2,8,7,3,6]=>0110001
[1,6,4,2,8,3,7,5]=>0111100
[1,4,2,8,3,7,6,5]=>0110110
[1,2,8,6,5,3,7,4]=>0011110
[6,2,1,8,7,3,4,5]=>1110001
[7,6,2,1,8,3,4,5]=>1110010
[7,3,1,6,2,8,4,5]=>1111000
[1,7,6,4,2,8,3,5]=>0111010
[1,7,5,2,6,3,8,4]=>0111100
[1,6,2,7,5,3,8,4]=>0111100
[1,2,7,6,5,3,8,4]=>0011110
[1,2,6,5,3,8,7,4]=>0011101
[1,5,2,7,6,3,8,4]=>0111010
[1,6,5,2,7,3,8,4]=>0111100
[1,5,7,4,2,8,3,6]=>0111000
[3,1,8,6,2,4,7,5]=>1100110
[4,3,7,1,8,2,5,6]=>1110000
[8,3,1,6,2,4,7,5]=>1110100
[7,1,8,3,2,4,6,5]=>1110100
[1,4,2,8,7,3,6,5]=>0110101
[1,7,4,2,8,3,6,5]=>0111100
[8,1,5,4,2,7,3,6]=>1111000
[1,4,8,5,2,7,3,6]=>0110100
[8,5,3,1,7,2,4,6]=>1110100
[8,6,2,1,7,3,4,5]=>1110010
[1,8,6,4,2,7,3,5]=>0111010
[1,5,2,7,3,8,6,4]=>0111010
[1,2,8,5,3,7,6,4]=>0011110
[1,2,6,3,8,7,5,4]=>0011101
[1,2,7,6,3,8,5,4]=>0011110
[1,6,2,7,3,8,5,4]=>0111100
[1,7,4,2,8,6,3,5]=>0111010
[7,1,8,3,2,6,4,5]=>1111000
[7,2,1,8,6,3,4,5]=>1110010
[1,8,7,3,2,6,4,5]=>0111001
[1,4,2,8,7,6,3,5]=>0110011
[1,2,8,7,5,3,6,4]=>0011101
[5,1,8,7,6,2,4,3]=>1110011
[8,1,7,6,3,4,5,2]=>1110010
[5,7,8,6,2,4,1,3]=>1100010
[5,7,1,6,2,4,3,8]=>1110000
[6,4,1,5,2,7,3,8]=>1111000
[8,1,4,5,3,7,6,2]=>1110010
[6,1,4,5,3,8,7,2]=>1110001
[7,1,4,5,3,8,6,2]=>1110010
[7,1,4,5,3,6,8,2]=>1110000
[7,4,1,5,2,6,3,8]=>1111000
[6,3,5,7,2,1,4,8]=>1110000
[6,3,5,8,2,1,7,4]=>1111000
[6,3,5,7,2,1,8,4]=>1111000
[8,4,5,7,3,6,1,2]=>1011000
[6,4,5,8,3,7,2,1]=>1111000
[5,4,8,6,3,1,7,2]=>1111010
[5,4,1,8,2,3,7,6]=>1101010
[8,4,1,5,2,6,3,7]=>1111000
[6,3,5,8,2,1,4,7]=>1110000
[2,3,8,5,1,4,7,6]=>1000110
[2,3,8,6,1,5,7,4]=>1001010
[2,8,6,7,1,3,5,4]=>1001010
[8,3,5,7,2,1,6,4]=>1111000
[8,4,5,6,3,1,7,2]=>1111000
[7,3,5,6,2,8,1,4]=>1110000
[7,3,5,8,2,1,6,4]=>1111000
[7,3,5,6,2,1,4,8]=>1110000
[2,7,6,5,1,3,4,8]=>1000110
[2,7,6,8,1,3,5,4]=>1001010
[8,7,5,6,1,4,2,3]=>1100101
[2,7,1,3,6,5,8,4]=>1001100
[2,7,6,1,8,3,4,5]=>1010010
[2,7,6,1,4,3,5,8]=>1010010
[7,3,5,1,2,8,4,6]=>1011000
[2,3,8,6,4,1,7,5]=>1001110
[2,8,6,1,7,3,4,5]=>1010010
[2,3,8,1,6,4,7,5]=>1001100
[2,3,8,1,4,5,7,6]=>1000010
[5,2,6,1,4,8,7,3]=>1110001
[5,7,2,3,8,6,1,4]=>1100010
[5,6,2,3,1,8,7,4]=>1101001
[5,6,2,1,3,8,7,4]=>1101001
[5,1,6,4,2,8,7,3]=>1111001
[5,6,1,3,2,8,7,4]=>1101001
[5,6,3,1,2,8,7,4]=>1011001
[5,7,3,2,8,1,6,4]=>1111000
[6,7,3,8,2,1,5,4]=>1111000
[6,7,3,8,1,2,5,4]=>1011000
[5,7,3,1,8,2,6,4]=>1111000
[5,1,7,4,8,2,6,3]=>1111000
[1,5,7,4,8,3,6,2]=>0111000
[5,1,7,4,8,6,2,3]=>1101010
[5,7,3,1,8,6,2,4]=>1110010
[6,7,8,3,1,4,2,5]=>1110000
[6,7,1,8,3,5,2,4]=>1110000
[6,1,7,8,4,5,2,3]=>1101000
[1,6,7,8,4,5,3,2]=>0111000
[1,6,7,8,4,3,5,2]=>0111000
[6,1,7,8,4,2,5,3]=>1111000
[6,7,2,8,1,3,5,4]=>1101000
[6,7,2,8,3,5,1,4]=>1110000
[6,2,7,8,4,1,5,3]=>1111000
[6,2,7,8,1,4,5,3]=>1110000
[4,2,1,7,8,5,6,3]=>1110100
[4,1,2,7,8,6,5,3]=>1010110
[6,2,7,8,1,5,4,3]=>1111000
[6,2,7,8,5,1,4,3]=>1110100
[5,7,2,1,8,6,3,4]=>1110010
[1,6,7,8,3,5,4,2]=>0111000
[6,1,7,8,2,5,4,3]=>1111000
[6,7,8,2,4,1,3,5]=>1100000
[6,7,8,2,4,3,1,5]=>1110000
[6,7,1,8,5,2,3,4]=>1100100
[6,1,7,8,5,2,4,3]=>1110100
[1,6,7,8,5,3,4,2]=>0110100
[6,1,7,8,5,4,2,3]=>1101100
[6,7,1,8,5,3,2,4]=>1110100
[6,7,8,4,1,3,2,5]=>1101000
[3,7,4,8,5,6,1,2]=>1001100
[3,7,1,8,5,6,2,4]=>1100100
[2,7,3,8,5,6,1,4]=>1010100
[1,7,4,8,5,6,2,3]=>0101100
[2,7,3,8,4,6,1,5]=>1011000
[3,7,1,8,4,6,2,5]=>1101000
[1,5,2,8,6,7,3,4]=>0110010
[2,6,1,8,5,7,3,4]=>1010100
[1,6,2,8,5,7,3,4]=>0110100
[1,6,2,8,4,7,3,5]=>0111000
[2,6,1,8,4,7,3,5]=>1011000
[3,7,2,6,1,8,4,5]=>1101000
[4,8,1,6,2,7,3,5]=>1110000
[5,8,1,6,2,7,3,4]=>1110000
[5,8,2,6,1,7,3,4]=>1110000
[4,8,2,6,1,7,3,5]=>1110000
[1,7,3,6,2,8,4,5]=>0111000
[2,7,3,6,1,8,4,5]=>1011000
[8,6,1,4,3,2,5,7]=>1110010
[3,7,5,1,8,2,4,6]=>1100100
[4,1,5,2,8,7,3,6]=>1110001
[8,1,2,4,6,5,3,7]=>1010100
[8,2,6,5,1,3,4,7]=>1100100
[8,3,1,6,2,5,4,7]=>1111000
[8,1,2,6,4,5,3,7]=>1011000
[8,1,2,5,6,4,3,7]=>1011000
[1,7,5,4,2,8,3,6]=>0111100
[1,4,6,8,2,7,3,5]=>0110000
[1,4,7,6,2,8,3,5]=>0110010
[5,1,4,7,2,8,3,6]=>1110000
[3,7,5,1,2,8,4,6]=>1001100
[4,1,5,8,2,7,3,6]=>1110000
[1,4,6,2,8,7,3,5]=>0110001
[1,4,2,8,6,7,3,5]=>0110010
[3,1,2,6,4,8,7,5]=>1001101
[2,1,7,6,3,4,8,5]=>1010110
[3,1,2,7,4,6,8,5]=>1001100
[1,2,3,6,8,5,7,4]=>0001100
[5,1,4,2,7,8,3,6]=>1110000
[1,4,2,7,6,8,3,5]=>0110010
[1,4,2,6,8,7,3,5]=>0110001
[5,3,7,1,8,2,4,6]=>1110000
[1,7,4,3,2,5,8,6]=>0111010
[4,8,7,2,1,3,5,6]=>1100001
[1,8,7,3,4,2,5,6]=>0110001
[3,1,7,8,2,6,4,5]=>1101000
[1,4,2,7,8,3,6,5]=>0110100
[2,1,8,6,3,4,7,5]=>1010110
[1,4,2,6,8,3,7,5]=>0110100
[1,2,3,7,8,5,6,4]=>0001100
[1,2,3,7,5,8,6,4]=>0001110
[3,1,7,2,8,6,4,5]=>1101010
[1,2,3,8,7,5,6,4]=>0001101
[5,7,8,4,2,6,1,3]=>1101000
[6,7,8,4,2,5,1,3]=>1101000
[8,6,3,7,2,1,5,4]=>1111010
[6,7,8,3,2,1,5,4]=>1111000
[5,7,8,3,2,1,6,4]=>1111000
[2,7,8,4,3,5,6,1]=>1011000
[3,7,8,4,2,5,1,6]=>1101000
[7,6,3,8,2,1,4,5]=>1110010
[8,6,3,7,2,1,4,5]=>1110010
[5,6,3,8,2,1,4,7]=>1110000
[3,6,4,8,2,5,1,7]=>1101000
[2,6,4,8,3,5,7,1]=>1011000
[2,6,4,7,3,5,8,1]=>1011000
[4,6,3,7,2,1,5,8]=>1110000
[5,6,3,7,2,1,4,8]=>1110000
[8,4,3,2,1,6,5,7]=>1111100
[6,4,3,2,1,7,5,8]=>1111100
[4,5,3,2,7,1,6,8]=>1110000
[7,4,3,2,1,8,5,6]=>1111100
[8,4,3,2,1,7,5,6]=>1111100
[7,4,3,2,1,8,6,5]=>1111110
[5,6,3,8,2,1,7,4]=>1111000
[7,5,3,2,8,1,6,4]=>1111100
[8,5,4,2,7,6,1,3]=>1101110
[7,5,4,2,8,6,1,3]=>1101110
[6,5,4,2,7,8,1,3]=>1101100
[8,5,4,2,6,7,1,3]=>1101100
[5,6,3,7,2,1,8,4]=>1111000
[4,6,3,7,2,1,8,5]=>1110100
[3,6,4,7,2,8,1,5]=>1101000
[2,6,4,7,3,8,5,1]=>1011100
[3,5,4,2,7,8,1,6]=>1101000
[7,4,3,2,1,6,8,5]=>1111100
[8,4,3,2,1,6,7,5]=>1111100
[8,4,3,2,1,5,7,6]=>1111010
[7,4,3,2,1,5,8,6]=>1111010
[6,4,3,2,1,5,8,7]=>1111001
[3,5,4,2,6,8,1,7]=>1101000
[3,2,6,4,8,5,1,7]=>1101100
[3,2,5,8,4,6,1,7]=>1101000
[4,2,1,5,7,3,6,8]=>1110000
[4,5,2,3,7,1,6,8]=>1100000
[4,2,5,3,8,1,6,7]=>1110000
[4,2,5,8,3,1,6,7]=>1110000
[4,1,5,3,8,2,6,7]=>1110000
[4,3,2,7,5,1,6,8]=>1110100
[4,3,6,2,5,1,7,8]=>1110000
[4,6,7,1,3,2,5,8]=>1100000
[4,5,1,7,3,2,6,8]=>1110000
[4,5,1,3,7,2,6,8]=>1100000
[3,5,1,4,2,7,6,8]=>1100010
[2,5,1,4,3,7,8,6]=>1010010
[5,2,1,4,3,7,8,6]=>1110010
[5,3,1,4,2,7,6,8]=>1110010
[4,3,1,7,5,2,6,8]=>1110100
[5,3,6,4,1,2,7,8]=>1011000
[4,3,6,1,7,2,5,8]=>1110000
[6,3,4,1,2,7,5,8]=>1010100
[6,2,4,1,3,7,8,5]=>1100100
[3,6,4,1,2,7,5,8]=>1001100
[4,6,3,1,7,2,5,8]=>1110000
[5,3,6,2,1,4,7,8]=>1110000
[4,5,2,7,3,1,6,8]=>1110000
[4,6,7,2,3,1,5,8]=>1100000
[4,6,2,1,7,3,5,8]=>1110000
[3,2,6,1,4,7,5,8]=>1100100
[3,6,7,2,4,5,1,8]=>1100000
[7,2,1,4,6,3,8,5]=>1110100
[7,3,1,4,6,8,2,5]=>1110000
[3,6,2,1,5,7,4,8]=>1101000
[7,4,1,5,6,2,3,8]=>1101000
[7,3,1,5,2,6,4,8]=>1111000
[7,2,1,5,3,6,8,4]=>1111000
[6,2,5,1,3,7,8,4]=>1101000
[6,3,5,1,2,7,4,8]=>1011000
[6,4,5,1,7,2,3,8]=>1101000
[4,6,5,1,7,2,3,8]=>1100100
[3,6,5,1,2,7,4,8]=>1001100
[2,4,1,5,3,8,7,6]=>1010011
[3,4,5,1,2,8,7,6]=>1000011
[1,8,4,5,3,2,7,6]=>0111010
[2,4,8,5,3,1,7,6]=>1010110
[3,4,5,2,8,1,7,6]=>1100010
[3,4,6,2,1,7,8,5]=>1100100
[3,4,6,2,1,7,5,8]=>1100100
[3,5,6,2,7,1,8,4]=>1101000
[3,4,6,2,8,7,1,5]=>1100001
[3,4,6,8,2,7,1,5]=>1100000
[2,4,8,6,3,7,1,5]=>1010010
[1,8,4,6,3,7,2,5]=>0111000
[1,8,4,6,3,7,5,2]=>0111100
[3,4,6,8,2,7,5,1]=>1100100
[3,4,6,2,8,7,5,1]=>1100101
[3,5,6,2,7,8,4,1]=>1101000
[3,5,6,2,7,4,1,8]=>1101000
[4,5,6,7,2,8,3,1]=>1110000
[2,5,8,6,7,3,4,1]=>1010010
[1,8,5,6,7,3,2,4]=>0110100
[4,5,6,7,2,1,8,3]=>1110000
[3,4,6,1,8,7,2,5]=>1100001
[2,4,1,6,8,7,3,5]=>1010001
[2,5,1,6,7,8,4,3]=>1011000
[2,5,1,6,7,4,3,8]=>1011000
[3,5,6,1,7,4,2,8]=>1101000
[3,5,6,1,7,4,8,2]=>1101000
[3,4,6,1,8,7,5,2]=>1100101
[3,4,6,8,1,7,5,2]=>1100100
[2,4,8,6,1,7,5,3]=>1010110
[1,8,4,6,2,7,5,3]=>0111100
[1,8,5,6,7,2,4,3]=>0110100
[2,5,8,6,7,1,4,3]=>1010010
[4,5,6,7,1,3,8,2]=>1100000
[3,5,6,8,7,4,1,2]=>1001001
[2,5,8,6,7,4,1,3]=>1001010
[1,8,5,6,7,4,2,3]=>0101100
[1,8,5,6,7,4,3,2]=>0111100
[2,5,8,6,7,4,3,1]=>1011010
[8,2,4,3,7,1,6,5]=>1110100
[5,8,2,4,3,7,1,6]=>1110000
[4,2,5,6,1,8,3,7]=>1110000
[4,2,5,6,1,7,3,8]=>1110000
[6,1,5,7,3,2,4,8]=>1110000
[6,1,5,8,3,2,4,7]=>1110000
[3,8,2,4,7,1,5,6]=>1100000
[3,6,8,2,4,7,1,5]=>1100000
[7,3,2,4,6,1,5,8]=>1110000
[3,2,5,1,8,4,6,7]=>1101000
[7,8,3,2,4,6,1,5]=>1110000
[6,1,5,7,8,3,2,4]=>1110000
[4,2,5,6,1,7,8,3]=>1110000
[5,7,6,1,8,3,4,2]=>1110010
[5,8,6,1,7,3,4,2]=>1110010
[6,1,5,8,7,3,2,4]=>1110001
[8,7,3,2,4,6,1,5]=>1110001
[3,2,5,1,8,7,4,6]=>1101001
[3,2,5,1,6,4,7,8]=>1101000
[3,2,4,1,8,7,5,6]=>1100101
[3,2,5,1,6,8,7,4]=>1101001
[3,8,6,5,1,7,4,2]=>1101110
[3,7,6,5,1,8,4,2]=>1101110
[6,5,1,7,8,4,2,3]=>1101100
[3,2,5,1,6,7,8,4]=>1101000
[3,2,4,1,7,5,6,8]=>1100100
[3,2,4,1,6,8,5,7]=>1100100
[8,3,2,4,7,6,1,5]=>1110010
[3,2,5,1,8,4,7,6]=>1101010
[3,2,5,1,6,7,4,8]=>1101000
[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]=>1101100
[5,2,6,1,8,3,7,4]=>1111000
[5,2,6,1,8,4,7,3]=>1111000
[7,4,2,3,8,5,1,6]=>1101100
[8,5,1,6,4,2,3,7]=>1101100
[3,2,5,1,7,6,4,8]=>1101010
[3,2,5,1,8,6,4,7]=>1101010
[8,6,1,5,7,3,2,4]=>1110010
[8,5,6,1,7,3,4,2]=>1110100
[3,6,8,5,1,7,4,2]=>1101100
[8,5,1,6,7,4,2,3]=>1101100
[3,2,5,1,8,6,7,4]=>1101010
[3,2,4,1,5,8,6,7]=>1100010
[3,2,5,1,7,8,6,4]=>1101010
[8,7,5,1,6,4,2,3]=>1101101
[3,2,5,1,8,7,6,4]=>1101011
[4,6,3,7,1,8,5,2]=>1110100
[4,6,3,7,5,1,8,2]=>1110100
[4,2,6,1,7,5,3,8]=>1110100
[2,5,7,4,1,6,3,8]=>1011000
[2,5,7,4,1,6,8,3]=>1011000
[5,4,7,8,3,1,6,2]=>1111000
[4,3,7,5,1,8,6,2]=>1110110
[6,4,3,8,5,1,7,2]=>1111100
[5,8,4,3,6,1,7,2]=>1111000
[5,4,8,3,6,1,7,2]=>1111000
[2,5,4,6,1,7,3,8]=>1011000
[4,6,2,1,8,5,7,3]=>1110100
[2,4,1,7,5,8,6,3]=>1010110
[2,4,1,7,5,3,8,6]=>1010110
[2,6,4,1,8,5,3,7]=>1011100
[5,4,8,2,1,6,3,7]=>1111000
[2,5,8,4,1,6,3,7]=>1011000
[3,2,5,6,1,8,4,7]=>1101000
[4,8,3,2,6,1,5,7]=>1110000
[3,5,2,8,1,6,4,7]=>1101000
[3,2,1,6,8,5,4,7]=>1101100
[3,2,7,1,5,4,8,6]=>1101010
[3,2,7,1,5,8,6,4]=>1101010
[3,8,2,5,1,6,7,4]=>1101000
[4,8,3,2,6,7,1,5]=>1110000
[4,3,8,2,6,7,1,5]=>1110000
[4,3,2,6,7,8,1,5]=>1110000
[4,3,2,6,7,1,5,8]=>1110000
[4,3,7,8,2,6,1,5]=>1110000
[2,5,7,4,8,1,6,3]=>1011000
[3,2,5,7,1,6,8,4]=>1101000
[3,2,5,7,1,6,4,8]=>1101000
[6,3,2,7,1,5,4,8]=>1111000
[6,3,2,7,1,5,8,4]=>1111000
[6,3,2,7,8,1,5,4]=>1111000
[6,5,2,1,7,8,4,3]=>1111100
[6,2,1,8,5,3,7,4]=>1111100
[6,3,2,7,1,4,8,5]=>1110100
[6,3,2,1,4,7,8,5]=>1110100
[6,3,2,1,4,7,5,8]=>1110100
[3,5,2,1,7,8,4,6]=>1101000
[4,6,2,1,8,3,7,5]=>1110100
[3,2,7,1,4,8,6,5]=>1100110
[3,5,8,2,1,7,4,6]=>1101000
[4,8,3,7,2,1,5,6]=>1110000
[4,3,7,2,8,1,5,6]=>1110000
[4,3,7,2,1,5,6,8]=>1110000
[4,8,3,2,7,1,5,6]=>1110000
[6,3,2,8,1,4,7,5]=>1110100
[3,2,1,4,7,5,8,6]=>1100110
[5,3,2,1,8,4,6,7]=>1111000
[4,8,3,2,1,5,6,7]=>1110000
[4,3,8,2,1,5,6,7]=>1110000
[6,2,3,1,5,4,8,7]=>1101001
[8,4,5,2,3,1,7,6]=>1101010
[8,2,5,3,4,1,7,6]=>1110010
[6,2,5,3,4,1,8,7]=>1110001
[6,4,5,1,3,2,8,7]=>1101001
[6,1,5,3,4,2,8,7]=>1110001
[8,3,7,2,4,1,6,5]=>1110100
[8,3,5,1,4,2,7,6]=>1110010
[8,4,5,1,3,2,7,6]=>1101010
[2,1,8,4,5,3,7,6]=>1011010
[8,1,7,3,4,2,6,5]=>1110100
[8,2,7,1,4,3,6,5]=>1110100
[8,2,7,3,4,1,6,5]=>1110100
[8,4,7,2,3,1,6,5]=>1101100
[8,2,3,1,5,4,7,6]=>1101010
[4,2,3,1,8,5,7,6]=>1100110
[8,2,3,1,7,5,6,4]=>1101100
[8,6,7,1,3,2,5,4]=>1101010
[8,1,3,2,7,5,6,4]=>1101100
[2,1,8,5,7,3,6,4]=>1011100
[4,5,8,6,3,2,7,1]=>1110010
[1,5,8,7,3,6,2,4]=>0110001
[1,7,2,8,4,6,5,3]=>0111100
[6,7,2,8,4,1,5,3]=>1111000
[3,6,2,8,4,5,7,1]=>1101000
[2,6,1,8,4,5,7,3]=>1011000
[2,8,4,6,1,5,7,3]=>1011000
[6,3,1,8,4,5,7,2]=>1111000
[2,3,6,8,4,5,7,1]=>1001000
[6,3,7,8,4,1,5,2]=>1111000
[1,3,7,8,4,6,5,2]=>0101100
[3,6,7,8,4,2,5,1]=>1101000
[7,6,1,8,4,2,5,3]=>1111010
[2,8,3,7,1,6,5,4]=>1011100
[5,2,8,7,3,6,1,4]=>1110001
[7,2,1,8,4,6,5,3]=>1111100
[3,2,7,8,4,6,5,1]=>1101100
[5,2,7,8,1,4,6,3]=>1110000
[1,2,7,8,5,4,6,3]=>0011100
[7,2,5,8,3,4,6,1]=>1110000
[6,2,8,5,4,3,1,7]=>1111100
[2,8,3,5,4,1,6,7]=>1011000
[2,8,4,5,3,1,6,7]=>1011000
[7,3,5,8,2,4,6,1]=>1110000
[4,3,1,2,8,5,6,7]=>1010100
[2,7,6,8,4,3,5,1]=>1011010
[1,7,5,8,3,4,6,2]=>0110100
[4,6,8,5,1,3,2,7]=>1100100
[2,4,8,3,6,5,1,7]=>1010100
[4,1,8,3,5,6,2,7]=>1110000
[5,6,8,4,1,3,2,7]=>1101000
[4,6,8,1,5,3,2,7]=>1110000
[1,6,8,4,5,3,2,7]=>0111000
[1,7,3,8,5,4,6,2]=>0111100
[3,7,1,8,5,4,6,2]=>1101100
[2,7,3,8,4,6,5,1]=>1011100
[2,8,7,4,1,6,5,3]=>1011101
[2,8,5,4,3,1,6,7]=>1011100
[1,4,3,2,8,5,6,7]=>0110100
[7,3,2,8,5,4,6,1]=>1111100
[6,4,8,2,5,3,1,7]=>1111000
[2,8,4,3,5,1,6,7]=>1011000
[6,2,8,4,5,3,1,7]=>1111000
[7,2,3,8,5,4,6,1]=>1101100
[4,2,3,1,8,5,6,7]=>1100100
[5,1,3,2,4,8,6,7]=>1100010
[2,8,1,5,3,4,7,6]=>1010010
[1,4,2,8,5,3,6,7]=>0110100
[3,5,1,4,8,2,6,7]=>1100000
[1,5,2,8,4,3,6,7]=>0111000
[1,2,5,4,3,8,6,7]=>0011010
[1,2,4,8,5,3,7,6]=>0010110
[1,5,2,7,8,4,3,6]=>0111000
[5,1,2,7,4,8,3,6]=>1011000
[8,3,5,1,4,7,2,6]=>1110000
[1,2,8,5,7,4,3,6]=>0011100
[1,2,4,8,7,5,3,6]=>0010101
[2,8,1,4,3,7,6,5]=>1010110
[7,6,1,4,2,8,3,5]=>1110010
[7,1,6,2,8,4,3,5]=>1111000
[1,4,2,7,8,5,3,6]=>0110100
[6,1,2,8,4,3,7,5]=>1011100
[6,4,1,2,8,3,7,5]=>1011100
[7,6,1,3,2,4,8,5]=>1100110
[6,7,1,3,2,4,8,5]=>1100100
[1,2,7,3,5,8,4,6]=>0011000
[5,8,1,3,7,2,4,6]=>1100000
[1,2,5,8,7,3,4,6]=>0010001
[8,6,1,3,2,4,7,5]=>1100110
[4,2,8,1,7,3,6,5]=>1110100
[7,1,2,8,4,3,6,5]=>1011100
[1,2,8,4,7,5,3,6]=>0011100
[1,2,8,7,4,5,3,6]=>0011001
[2,8,1,7,5,3,4,6]=>1010100
[8,3,7,1,5,2,4,6]=>1110000
[8,6,1,4,2,7,3,5]=>1110010
[7,1,2,8,6,4,3,5]=>1011010
[3,7,4,8,1,6,2,5]=>1101000
[3,4,8,7,1,6,2,5]=>1100001
[4,2,8,1,7,6,3,5]=>1110010
[2,8,1,7,6,4,3,5]=>1011010
[7,8,3,4,1,5,2,6]=>1110000
[6,8,3,4,1,7,2,5]=>1110000
[5,7,3,4,1,8,2,6]=>1110000
[5,8,3,4,1,7,2,6]=>1110000
[4,7,3,5,1,6,2,8]=>1110000
[4,8,3,5,1,6,2,7]=>1110000
[4,8,3,5,1,7,2,6]=>1110000
[4,7,3,5,1,8,2,6]=>1110000
[5,6,2,3,1,7,4,8]=>1101000
[5,6,2,4,1,8,3,7]=>1110000
[5,6,2,4,1,7,3,8]=>1110000
[4,6,2,5,1,7,3,8]=>1110000
[4,6,2,5,1,8,3,7]=>1110000
[4,5,1,8,3,7,2,6]=>1110000
[4,6,2,7,3,8,1,5]=>1110000
[5,6,2,7,3,8,1,4]=>1110000
[5,6,2,8,4,7,1,3]=>1101000
[5,6,2,8,3,7,1,4]=>1110000
[4,6,2,8,3,7,1,5]=>1110000
[4,5,1,7,3,6,2,8]=>1110000
[4,5,1,8,3,6,2,7]=>1110000
[6,5,3,2,1,4,8,7]=>1110101
[8,7,3,5,2,4,1,6]=>1110001
[6,8,2,4,5,7,3,1]=>1110000
[3,6,1,4,5,2,8,7]=>1100001
[8,3,7,4,5,2,1,6]=>1111000
[6,3,8,4,5,7,2,1]=>1111000
[8,1,7,4,3,6,2,5]=>1111000
[8,7,3,5,1,4,2,6]=>1110001
[2,1,6,8,5,7,4,3]=>1011100
[6,8,3,5,1,7,4,2]=>1111000
[2,5,8,4,7,6,3,1]=>1011010
[4,3,8,1,5,6,7,2]=>1110000
[4,8,3,6,1,2,7,5]=>1010100
[3,8,7,4,1,6,2,5]=>1101001
[3,8,1,2,5,6,7,4]=>1001000
[2,8,7,4,5,1,3,6]=>1001001
[8,7,2,4,1,6,3,5]=>1110001
[5,8,3,6,2,4,7,1]=>1110000
[8,6,3,2,1,4,7,5]=>1110110
[8,7,3,5,2,1,4,6]=>1110001
[5,8,3,6,2,1,7,4]=>1111000
[6,1,8,4,5,7,2,3]=>1101000
[6,8,3,5,1,7,2,4]=>1110000
[5,8,3,6,1,2,7,4]=>1011000
[5,8,1,4,7,6,2,3]=>1100010
[4,5,3,8,6,1,7,2]=>1110010
[4,5,7,6,2,3,8,1]=>1100010
[3,5,7,2,6,4,8,1]=>1101000
[2,5,7,3,6,4,8,1]=>1011000
[8,4,3,7,6,1,5,2]=>1111010
[6,7,2,3,5,4,8,1]=>1101000
[5,2,7,3,6,4,8,1]=>1111000
[8,3,4,7,6,1,5,2]=>1110010
[8,2,4,7,1,6,5,3]=>1110100
[3,1,4,7,6,8,5,2]=>1100110
[5,1,7,3,6,8,4,2]=>1111000
[6,7,1,3,5,8,4,2]=>1101000
[4,8,3,7,6,1,5,2]=>1110010
[2,8,4,7,1,6,5,3]=>1011100
[8,1,4,7,2,6,5,3]=>1110100
[8,1,3,2,7,6,5,4]=>1101110
[2,8,3,1,7,6,5,4]=>1011110
[6,7,1,2,8,5,4,3]=>1011100
[8,2,3,1,7,6,5,4]=>1101110
[1,4,2,7,8,6,5,3]=>0110110
[8,4,2,7,1,6,5,3]=>1111100
[8,5,7,2,1,6,4,3]=>1111100
[1,5,7,2,8,6,4,3]=>0111010
[2,5,7,1,8,6,4,3]=>1011010
[3,5,7,1,6,8,4,2]=>1101000
[6,7,4,5,8,1,3,2]=>1101000
[2,5,7,8,1,6,4,3]=>1011000
[1,5,7,8,2,6,4,3]=>0111000
[8,5,7,1,2,6,4,3]=>1011100
[8,4,1,7,2,6,5,3]=>1111100
[6,7,2,8,1,5,4,3]=>1111000
[5,2,7,8,1,6,4,3]=>1111000
[4,2,8,7,1,6,5,3]=>1110101
[1,3,8,2,7,6,5,4]=>0101110
[8,3,1,2,7,6,5,4]=>1011110
[8,2,1,3,7,6,5,4]=>1101110
[2,1,8,3,7,6,5,4]=>1011110
[5,1,7,8,2,6,4,3]=>1111000
[6,7,1,8,2,5,4,3]=>1111000
[4,8,1,7,2,6,5,3]=>1110100
[3,8,1,2,7,6,5,4]=>1001110
[1,8,2,3,7,6,5,4]=>0101110
[3,7,1,5,8,2,6,4]=>1101000
[2,7,1,5,8,3,6,4]=>1011000
[2,6,5,1,8,3,7,4]=>1011100
[5,6,4,1,8,7,2,3]=>1101001
[8,1,4,5,7,6,2,3]=>1100010
[6,4,5,1,8,7,2,3]=>1101001
[5,4,6,1,8,7,2,3]=>1101001
[3,5,6,1,8,2,7,4]=>1101000
[2,5,6,1,8,3,7,4]=>1011000
[2,4,6,1,3,8,7,5]=>1000101
[3,4,6,1,2,8,7,5]=>1000101
[5,3,6,1,8,2,7,4]=>1111000
[7,3,1,5,8,2,6,4]=>1111000
[8,1,3,5,7,2,6,4]=>1101000
[8,1,2,5,7,3,6,4]=>1011000
[7,2,1,5,8,3,6,4]=>1111000
[6,2,5,1,8,3,7,4]=>1111000
[4,2,6,1,3,8,7,5]=>1100101
[4,2,5,3,1,8,7,6]=>1110011
[6,2,4,1,3,8,7,5]=>1100101
[7,2,1,4,3,8,6,5]=>1110110
[8,1,2,4,3,7,6,5]=>1010110
[8,1,3,4,2,7,6,5]=>1100110
[7,3,1,4,2,8,6,5]=>1110110
[4,6,3,1,2,8,7,5]=>1010101
[2,6,4,1,3,8,7,5]=>1001101
[2,7,1,4,3,8,6,5]=>1010110
[8,1,6,7,2,3,5,4]=>1101000
[4,7,1,2,3,8,6,5]=>1000110
[3,7,1,2,4,8,6,5]=>1000110
[2,6,3,1,4,8,7,5]=>1010101
[3,6,2,1,4,8,7,5]=>1100101
[5,6,2,1,8,3,7,4]=>1111000
[6,5,2,1,8,3,7,4]=>1111100
[8,1,4,2,3,7,6,5]=>1100110
[7,4,1,2,3,8,6,5]=>1001110
[5,4,2,3,1,8,7,6]=>1101011
[3,5,2,4,1,8,7,6]=>1100011
[7,3,1,2,4,8,6,5]=>1010110
[8,1,3,2,4,7,6,5]=>1100110
[7,2,1,3,4,8,6,5]=>1100110
[2,4,3,6,1,5,8,7]=>1010001
[2,4,3,6,5,8,1,7]=>1010100
[2,4,6,3,5,8,7,1]=>1010001
[2,4,6,3,5,1,8,7]=>1010001
[2,4,6,3,1,5,8,7]=>1010001
[2,4,1,6,5,3,8,7]=>1010101
[2,4,6,1,5,3,8,7]=>1010001
[4,2,6,5,3,1,8,7]=>1110101
[4,2,6,5,1,3,8,7]=>1100101
[4,2,6,5,8,1,7,3]=>1110100
[4,2,6,5,8,1,3,7]=>1100100
[4,2,6,5,8,3,1,7]=>1110100
[2,4,1,6,5,8,3,7]=>1010100
[2,1,4,6,5,8,3,7]=>1010100
[2,4,1,6,5,8,7,3]=>1010101
[2,4,6,1,5,8,7,3]=>1010001
[4,2,6,5,3,8,7,1]=>1110101
[2,6,4,3,8,7,5,1]=>1011101
[4,2,6,8,5,3,7,1]=>1110100
[2,4,6,8,1,5,7,3]=>1010000
[2,4,1,6,8,5,7,3]=>1010100
[2,1,4,6,8,5,3,7]=>1010100
[2,4,6,1,8,5,3,7]=>1010100
[2,4,6,8,1,5,3,7]=>1010000
[2,4,6,8,3,5,7,1]=>1010000
[2,4,6,8,3,1,5,7]=>1010000
[2,4,6,3,8,5,7,1]=>1010100
[2,4,3,6,8,5,7,1]=>1010100
[2,4,3,6,8,5,1,7]=>1010100
[2,4,3,6,8,1,5,7]=>1010000
[2,4,3,6,1,8,5,7]=>1010100
[2,4,3,1,6,8,5,7]=>1010100
[2,4,1,3,6,8,7,5]=>1000101
[2,4,3,6,8,1,7,5]=>1010100
[4,6,5,2,8,7,1,3]=>1100101
[4,6,2,5,8,7,1,3]=>1100001
[4,6,2,5,8,7,3,1]=>1110001
[2,4,6,3,1,8,7,5]=>1010101
[2,4,1,6,3,8,7,5]=>1010101
[2,1,4,6,3,8,7,5]=>1010101
[2,4,1,6,8,3,7,5]=>1010100
[2,4,6,8,1,3,7,5]=>1000100
[4,6,2,8,5,7,3,1]=>1110100
[4,6,2,8,5,7,1,3]=>1100100
[6,2,4,8,7,1,3,5]=>1100001
[2,6,4,8,1,7,5,3]=>1011100
[2,6,4,1,8,7,5,3]=>1011101
[2,1,6,4,8,7,3,5]=>1011001
[2,6,4,1,8,7,3,5]=>1011001
[2,6,4,8,1,7,3,5]=>1011000
[6,2,4,8,7,3,5,1]=>1110001
[6,2,4,8,7,3,1,5]=>1110001
[1,3,7,4,5,8,2,6]=>0101000
[1,7,6,3,4,8,2,5]=>0110010
[8,1,6,3,7,2,4,5]=>1110000
[1,2,7,4,8,3,5,6]=>0011000
[6,1,7,3,4,8,2,5]=>1110000
[2,1,7,4,5,8,3,6]=>1011000
[5,1,4,7,3,8,2,6]=>1110000
[4,3,1,7,5,8,2,6]=>1110100
[2,8,6,3,7,1,4,5]=>1010010
[6,8,1,3,7,2,4,5]=>1100000
[5,8,2,1,7,3,4,6]=>1110000
[5,7,2,1,8,3,4,6]=>1110000
[6,7,1,3,8,2,4,5]=>1100000
[8,5,1,3,7,2,4,6]=>1100100
[1,5,3,2,8,4,6,7]=>0111000
[2,6,4,8,7,1,3,5]=>1001001
[1,6,4,8,7,2,3,5]=>0101001
[4,3,2,8,7,1,5,6]=>1110001
[5,2,4,8,7,1,3,6]=>1100001
[6,2,8,3,7,1,4,5]=>1110000
[5,1,4,8,7,2,3,6]=>1100001
[3,7,2,1,5,4,8,6]=>1101010
[3,8,2,1,5,4,7,6]=>1101010
[8,3,2,1,5,4,6,7]=>1111000
[8,3,2,1,6,4,5,7]=>1111000
[8,4,2,5,1,6,3,7]=>1111000
[8,3,2,1,4,6,5,7]=>1110100
[3,8,2,1,4,5,7,6]=>1100010
[3,2,7,1,4,6,8,5]=>1100100
[3,2,8,1,4,6,7,5]=>1100100
[3,8,2,1,4,7,5,6]=>1100100
[3,8,2,1,5,7,4,6]=>1101000
[4,8,2,5,1,7,3,6]=>1110000
[4,7,2,5,1,8,3,6]=>1110000
[3,7,2,1,5,8,4,6]=>1101000
[3,7,2,1,4,8,5,6]=>1100100
[3,2,1,7,5,8,6,4]=>1101110
[4,2,7,6,1,8,3,5]=>1110010
[4,3,7,6,8,1,2,5]=>1010010
[4,3,8,6,7,1,2,5]=>1010010
[3,8,2,1,7,4,5,6]=>1101000
[3,2,8,1,6,4,7,5]=>1101100
[3,2,7,1,6,4,8,5]=>1101100
[4,2,7,6,1,3,8,5]=>1100110
[4,2,8,6,1,3,7,5]=>1100110
[5,7,8,3,4,1,2,6]=>1010000
[4,2,6,8,1,3,7,5]=>1100100
[4,2,6,7,1,3,8,5]=>1100100
[3,2,6,1,8,4,7,5]=>1101100
[3,7,2,1,8,5,4,6]=>1101100
[4,7,3,8,5,1,2,6]=>1010100
[4,3,7,8,6,1,2,5]=>1010010
[3,2,7,1,8,6,4,5]=>1101010
[3,2,1,6,8,5,7,4]=>1101100
[3,2,6,1,8,7,4,5]=>1101001
[4,2,6,8,1,7,3,5]=>1110000
[4,3,6,8,7,1,2,5]=>1010001
[4,2,6,7,1,8,3,5]=>1110000
[3,2,6,1,7,8,4,5]=>1101000
[5,3,6,4,8,7,1,2]=>1011001
[1,4,6,2,7,8,5,3]=>0110100
[3,1,8,5,4,2,6,7]=>1101100
[1,2,7,5,4,8,6,3]=>0011110
[6,3,7,5,4,8,1,2]=>1011100
[1,6,2,5,4,8,7,3]=>0111001
[1,8,2,5,7,3,6,4]=>0111000
[6,2,1,5,4,8,7,3]=>1111001
[4,1,6,2,8,7,5,3]=>1110101
[7,8,3,1,4,2,6,5]=>1110100
[4,3,6,1,8,2,7,5]=>1110100
[7,5,1,6,4,3,2,8]=>1111100
[6,1,5,7,4,3,2,8]=>1111000
[1,5,8,6,4,3,2,7]=>0111010
[7,8,5,1,6,3,2,4]=>1110100
[2,6,1,5,7,3,8,4]=>1011000
[1,6,8,7,4,3,2,5]=>0111001
[6,8,1,7,4,3,2,5]=>1111000
[5,6,1,7,4,3,2,8]=>1111000
[5,1,7,6,4,3,2,8]=>1111010
[6,1,7,8,4,3,2,5]=>1111000
[7,1,8,6,4,3,2,5]=>1111010
[7,2,1,5,4,6,8,3]=>1111000
[1,2,8,5,6,3,7,4]=>0011100
[6,1,2,5,7,3,8,4]=>1011000
[4,3,6,1,5,7,2,8]=>1110000
[1,3,6,8,5,7,2,4]=>0100100
[1,3,6,4,8,7,2,5]=>0101001
[4,1,6,7,3,8,2,5]=>1110000
[5,4,6,1,3,7,2,8]=>1101000
[6,4,1,5,2,3,7,8]=>1101000
[4,1,7,5,2,3,8,6]=>1100110
[2,8,3,5,4,1,7,6]=>1011010
[7,8,1,4,6,3,2,5]=>1110000
[5,1,8,7,4,3,2,6]=>1111001
[6,5,1,8,4,3,2,7]=>1111100
[6,5,7,1,4,3,2,8]=>1110100
[7,5,8,1,4,3,2,6]=>1110100
[1,5,7,8,4,3,2,6]=>0111000
[2,4,7,5,1,3,8,6]=>1000110
[7,8,4,6,1,3,2,5]=>1101000
[1,6,5,8,4,3,2,7]=>0111100
[6,8,5,1,4,3,2,7]=>1110100
[3,6,2,5,4,1,7,8]=>1101000
[4,3,6,2,8,1,5,7]=>1110000
[6,1,2,5,4,7,8,3]=>1011000
[6,2,4,5,1,3,7,8]=>1100000
[4,2,8,5,1,3,7,6]=>1100110
[4,3,6,8,1,7,2,5]=>1110000
[5,3,6,4,1,7,2,8]=>1111000
[1,6,7,4,8,3,5,2]=>0111000
[1,4,6,3,7,5,8,2]=>0110100
[4,6,7,2,5,8,1,3]=>1100000
[2,4,6,1,7,5,3,8]=>1010100
[2,7,5,4,1,6,3,8]=>1011100
[1,7,5,4,3,8,6,2]=>0111110
[1,5,8,4,3,6,7,2]=>0111000
[5,4,6,2,7,8,1,3]=>1101000
[2,5,4,1,6,7,3,8]=>1011000
[5,6,3,2,7,1,4,8]=>1110000
[5,6,3,2,7,1,8,4]=>1111000
[8,5,6,3,2,7,1,4]=>1110100
[5,4,6,2,8,1,7,3]=>1111000
[2,4,1,7,8,5,3,6]=>1010100
[5,6,3,2,1,8,4,7]=>1111000
[3,5,2,1,6,4,7,8]=>1101000
[6,8,4,3,2,1,5,7]=>1111000
[5,3,8,2,1,6,4,7]=>1111000
[7,3,2,8,5,1,6,4]=>1111100
[8,4,6,3,2,1,7,5]=>1111100
[5,4,7,2,1,8,6,3]=>1111010
[5,7,3,2,1,6,8,4]=>1111000
[6,3,7,2,5,1,8,4]=>1111000
[6,7,8,3,5,2,1,4]=>1110000
[6,2,5,7,8,4,1,3]=>1101000
[2,1,5,7,8,6,3,4]=>1010010
[3,6,7,2,8,1,4,5]=>1100000
[3,2,6,1,7,4,5,8]=>1101000
[2,5,8,4,1,3,7,6]=>1001010
[2,4,1,7,8,3,6,5]=>1010100
[3,6,8,2,1,7,4,5]=>1101000
[5,3,8,2,1,4,7,6]=>1110010
[4,8,7,3,2,1,5,6]=>1110001
[4,7,3,2,1,5,6,8]=>1110000
[8,4,7,3,2,1,5,6]=>1111000
[8,3,5,2,1,4,7,6]=>1110010
[3,5,2,1,4,6,8,7]=>1100001
[2,7,6,5,1,8,3,4]=>1010110
[2,7,6,5,1,8,4,3]=>1011110
[2,3,6,5,1,4,8,7]=>1000101
[2,3,6,4,1,5,8,7]=>1001001
[2,7,6,1,4,8,5,3]=>1010110
[7,3,5,1,8,4,2,6]=>1111000
[2,7,6,1,5,8,4,3]=>1011010
[2,7,6,4,1,8,5,3]=>1011110
[2,7,6,4,1,8,3,5]=>1011010
[7,3,5,1,8,6,2,4]=>1110010
[2,3,4,8,7,6,1,5]=>1000011
[2,3,4,8,5,7,1,6]=>1000100
[7,3,5,4,8,1,2,6]=>1011000
[6,4,3,5,8,7,2,1]=>1111001
[2,1,4,5,8,7,3,6]=>1010001
[6,4,3,5,8,7,1,2]=>1011001
[2,3,4,8,7,5,1,6]=>1000101
[2,7,6,5,4,8,1,3]=>1001110
[7,3,5,6,8,1,2,4]=>1010000
[6,4,1,5,8,7,2,3]=>1101001
[6,4,1,5,8,7,3,2]=>1111001
[6,4,1,5,8,3,7,2]=>1111000
[5,7,1,6,3,8,2,4]=>1110000
[6,4,1,5,8,3,2,7]=>1111000
[6,3,5,7,8,2,1,4]=>1110000
[5,7,3,6,1,8,4,2]=>1111000
[7,3,5,4,8,6,2,1]=>1111010
[2,3,4,8,5,6,1,7]=>1000100
[2,3,4,8,7,1,6,5]=>1000101
[2,3,4,8,5,1,7,6]=>1000110
[7,4,3,5,8,2,1,6]=>1111000
[7,4,3,5,8,2,6,1]=>1111000
[6,3,5,4,8,2,1,7]=>1111000
[2,3,4,8,5,1,6,7]=>1000100
[6,1,4,2,8,5,7,3]=>1110100
[4,8,6,5,3,2,7,1]=>1110110
[8,6,5,1,2,4,7,3]=>1010110
[1,7,5,8,2,6,4,3]=>0111100
[1,3,8,5,7,6,2,4]=>0100110
[6,3,8,5,7,1,2,4]=>1010100
[6,8,5,2,1,4,7,3]=>1110100
[3,8,2,5,6,1,7,4]=>1101000
[8,1,2,5,6,3,7,4]=>1011000
[8,6,1,5,7,2,3,4]=>1100010
[3,8,6,5,7,1,2,4]=>1000110
[5,1,7,6,8,4,2,3]=>1101010
[5,1,3,7,8,6,2,4]=>1100010
[7,2,5,8,1,6,4,3]=>1111000
[3,2,8,5,7,6,1,4]=>1100110
[8,2,1,5,7,6,3,4]=>1110010
[5,2,8,6,1,7,3,4]=>1110010
[1,2,8,6,5,7,3,4]=>0010110
[8,2,5,6,3,7,1,4]=>1110000
[7,2,6,5,4,1,8,3]=>1111100
[6,1,3,5,4,7,8,2]=>1101000
[6,1,5,3,4,7,8,2]=>1110000
[7,5,6,2,4,1,8,3]=>1110100
[8,5,2,6,3,7,1,4]=>1110100
[8,1,6,5,7,3,2,4]=>1110100
[3,5,8,6,2,7,1,4]=>1100010
[1,8,5,6,3,7,2,4]=>0110100
[1,7,6,5,4,2,8,3]=>0111110
[5,7,6,1,4,2,8,3]=>1110010
[7,1,4,2,6,5,8,3]=>1110100
[2,7,4,1,5,6,8,3]=>1011000
[5,7,6,4,1,2,8,3]=>1011010
[4,7,6,1,5,2,8,3]=>1110010
[1,7,6,4,5,2,8,3]=>0111010
[3,8,1,6,5,7,2,4]=>1100100
[8,1,3,5,7,6,2,4]=>1100010
[7,8,5,4,1,6,2,3]=>1101100
[6,1,5,4,3,7,8,2]=>1111000
[7,5,6,4,2,1,8,3]=>1111100
[8,3,2,6,5,7,1,4]=>1110100
[7,4,6,2,5,1,8,3]=>1111000
[6,1,4,3,5,7,8,2]=>1110000
[6,1,3,4,5,7,8,2]=>1100000
[7,2,6,4,5,1,8,3]=>1111000
[8,2,3,6,5,7,1,4]=>1100100
[3,8,2,7,6,1,5,4]=>1101010
[4,8,7,2,6,5,3,1]=>1110101
[4,8,7,3,1,6,5,2]=>1110101
[4,8,7,3,2,6,1,5]=>1110001
[4,8,7,3,2,6,5,1]=>1110101
[4,8,7,3,6,2,5,1]=>1110001
[4,8,7,3,6,1,5,2]=>1110001
[5,8,7,6,3,4,2,1]=>1110011
[5,8,7,6,3,1,4,2]=>1110011
[5,8,7,6,2,4,3,1]=>1110011
[5,8,7,6,4,2,1,3]=>1101011
[5,8,7,6,4,1,3,2]=>1101011
[5,8,7,6,4,3,1,2]=>1011011
[7,3,4,2,1,6,5,8]=>1110100
[7,3,5,2,6,1,4,8]=>1110000
[7,3,5,2,6,4,1,8]=>1111000
[7,2,1,5,6,4,3,8]=>1111000
[7,3,5,1,6,4,2,8]=>1111000
[7,4,5,6,1,3,2,8]=>1101000
[1,4,5,7,3,2,8,6]=>0110010
[6,4,5,7,3,1,8,2]=>1111000
[6,3,5,1,7,4,8,2]=>1111000
[6,2,1,5,7,4,8,3]=>1111000
[3,2,1,5,7,4,8,6]=>1101010
[2,4,6,7,3,8,1,5]=>1010000
[1,4,6,7,3,8,5,2]=>0110100
[2,5,6,7,8,3,1,4]=>1010000
[3,2,1,6,7,8,4,5]=>1101000
[5,2,1,6,7,8,4,3]=>1111000
[5,3,6,1,7,8,4,2]=>1111000
[5,4,6,7,1,8,3,2]=>1111000
[6,4,5,7,2,1,8,3]=>1111000
[5,4,6,7,2,8,3,1]=>1111000
[5,3,6,2,7,8,4,1]=>1111000
[5,3,6,2,7,8,1,4]=>1110000
[6,3,5,2,7,1,8,4]=>1111000
[5,3,4,1,2,7,8,6]=>1010010
[4,3,6,2,7,8,1,5]=>1110000
[4,3,6,2,7,8,5,1]=>1110100
[1,3,6,2,7,8,5,4]=>0101100
[1,4,6,7,2,8,5,3]=>0110100
[3,4,6,7,2,8,5,1]=>1100100
[3,4,5,7,2,1,8,6]=>1100010
[4,2,1,5,7,3,8,6]=>1110010
[4,2,1,6,7,8,3,5]=>1110000
[4,3,6,1,7,8,2,5]=>1110000
[1,5,6,7,8,2,4,3]=>0110000
[1,5,6,7,8,4,2,3]=>0101000
[4,3,6,1,7,8,5,2]=>1110100
[4,2,1,6,7,8,5,3]=>1110100
[2,4,6,7,1,8,5,3]=>1010100
[2,5,6,7,8,1,4,3]=>1010000
[1,4,3,6,2,5,7,8]=>0110000
[1,4,3,7,2,5,6,8]=>0110000
[1,4,3,7,6,8,2,5]=>0110010
[1,4,3,7,5,8,2,6]=>0110100
[1,5,3,7,4,8,2,6]=>0111000
[1,5,4,8,2,6,3,7]=>0111000
[1,5,4,8,3,7,2,6]=>0111000
[1,2,3,6,5,8,4,7]=>0001100
[6,8,2,4,5,7,1,3]=>1100000
[3,7,8,4,5,2,6,1]=>1101000
[7,8,1,4,5,3,6,2]=>1110000
[5,8,1,4,7,6,3,2]=>1110010
[7,5,1,8,6,2,4,3]=>1110110
[7,4,1,8,2,6,3,5]=>1111000
[7,1,8,4,2,6,3,5]=>1111000
[7,3,1,8,4,2,6,5]=>1111100
[7,2,8,3,6,5,1,4]=>1110100
[7,2,8,3,6,1,5,4]=>1111000
[6,1,2,8,3,5,4,7]=>1011000
[5,2,3,8,1,4,7,6]=>1100010
[6,2,4,1,8,7,3,5]=>1110001
[3,1,6,4,2,8,5,7]=>1101100
[2,6,3,8,7,1,5,4]=>1011001
[2,6,3,8,5,1,4,7]=>1010100
[2,5,1,8,3,4,7,6]=>1010010
[1,2,5,3,8,4,7,6]=>0011010
[1,2,4,8,3,7,6,5]=>0010110
[2,4,8,3,7,1,6,5]=>1010100
[2,4,8,3,7,6,1,5]=>1010010
[2,5,3,8,1,7,4,6]=>1011000
[2,5,4,1,3,8,7,6]=>1001011
[3,1,5,4,8,2,7,6]=>1101010
[5,3,1,4,8,2,7,6]=>1110010
[5,2,3,8,4,7,1,6]=>1101000
[4,8,2,3,7,6,1,5]=>1100010
[4,8,2,3,7,1,6,5]=>1100100
[4,8,1,2,3,7,6,5]=>1000110
[1,4,8,3,7,2,6,5]=>0110100
[6,3,8,1,5,2,4,7]=>1110000
[5,3,8,1,2,4,7,6]=>1010010
[5,1,3,8,2,4,7,6]=>1100010
[1,5,3,8,2,4,7,6]=>0110010
[1,5,4,8,2,7,6,3]=>0111010
[5,1,4,8,2,7,6,3]=>1110010
[5,4,8,1,2,7,6,3]=>1011010
[6,5,1,2,8,7,4,3]=>1011101
[4,1,5,8,2,7,6,3]=>1110010
[4,1,2,5,8,7,6,3]=>1010011
[1,4,2,5,8,7,6,3]=>0110011
[1,3,5,2,8,7,4,6]=>0101001
[3,5,1,2,8,7,4,6]=>1001001
[4,2,6,1,8,7,3,5]=>1110001
[4,3,1,5,8,2,7,6]=>1110010
[3,5,2,8,7,1,4,6]=>1100001
[3,4,8,7,2,6,1,5]=>1100001
[3,4,8,1,7,2,6,5]=>1100100
[1,3,4,8,7,2,6,5]=>0100101
[1,3,4,8,2,7,6,5]=>0100110
[3,4,8,1,2,7,6,5]=>1000110
[3,4,8,2,7,1,6,5]=>1100100
[3,4,8,2,7,6,1,5]=>1100010
[4,2,5,8,1,7,6,3]=>1110010
[4,3,1,2,5,8,7,6]=>1010011
[3,1,4,2,5,8,7,6]=>1100011
[2,3,5,1,8,7,6,4]=>1001011
[7,8,2,1,5,3,6,4]=>1111000
[6,4,1,2,7,3,5,8]=>1011000
[2,3,7,5,4,1,8,6]=>1001110
[6,3,1,5,4,2,7,8]=>1111000
[7,8,1,5,4,2,6,3]=>1111000
[7,8,3,5,4,1,6,2]=>1111000
[7,8,2,5,4,1,3,6]=>1101000
[7,8,2,5,4,6,1,3]=>1101000
[6,2,1,5,4,7,3,8]=>1111000
[5,3,6,2,4,7,1,8]=>1110000
[6,4,2,1,7,3,8,5]=>1111100
[2,7,6,5,3,1,4,8]=>1010110
[3,7,6,4,8,5,1,2]=>1001110
[5,7,6,3,8,4,1,2]=>1011010
[5,1,6,2,4,8,3,7]=>1110000
[4,7,6,5,2,1,3,8]=>1100110
[4,7,6,5,2,8,1,3]=>1100110
[4,7,6,5,1,8,3,2]=>1110110
[1,7,6,5,2,8,3,4]=>0110110
[1,7,6,5,3,2,8,4]=>0111110
[4,7,6,5,1,2,8,3]=>1010110
[4,7,6,5,3,1,8,2]=>1110110
[5,2,6,3,4,1,7,8]=>1110000
[5,1,6,2,4,7,8,3]=>1110000
[1,7,2,4,8,3,6,5]=>0110100
[4,7,2,1,5,3,6,8]=>1110000
[4,7,1,6,2,3,8,5]=>1100100
[1,7,2,6,8,3,5,4]=>0111000
[1,2,6,7,4,8,5,3]=>0011100
[3,1,6,7,4,2,8,5]=>1101100
[3,2,8,5,4,6,1,7]=>1101100
[4,7,6,3,5,8,1,2]=>1010010
[3,7,6,5,2,4,1,8]=>1100110
[3,7,6,5,2,1,8,4]=>1101110
[1,7,6,5,8,2,4,3]=>0110110
[3,7,6,5,8,1,4,2]=>1100110
[3,7,6,5,1,2,4,8]=>1000110
[3,1,6,8,4,2,5,7]=>1101000
[4,7,6,8,3,5,1,2]=>1010010
[2,7,6,5,8,1,3,4]=>1000110
[2,7,6,5,8,4,1,3]=>1001110
[3,7,5,8,2,4,1,6]=>1100100
[5,1,7,8,4,3,2,6]=>1111000
[5,1,2,6,4,3,8,7]=>1011001
[5,1,2,4,6,3,8,7]=>1010001
[4,1,5,7,8,3,2,6]=>1110000
[4,7,1,8,3,6,2,5]=>1110000
[4,1,7,8,5,2,3,6]=>1100100
[5,1,7,4,8,2,3,6]=>1101000
[5,1,8,4,7,2,3,6]=>1101000
[4,1,8,7,5,2,3,6]=>1100101
[4,7,1,6,3,2,8,5]=>1110100
[7,1,2,3,8,6,5,4]=>1001110
[6,8,1,4,3,7,2,5]=>1110000
[8,7,3,2,4,1,6,5]=>1110101
[6,7,1,4,3,8,2,5]=>1110000
[8,1,2,3,5,7,6,4]=>1001010
[7,1,2,3,6,8,5,4]=>1001100
[7,1,8,5,4,3,2,6]=>1111100
[7,8,2,6,3,4,1,5]=>1110000
[6,7,2,8,3,4,1,5]=>1110000
[3,8,7,1,4,2,6,5]=>1100101
[3,7,8,1,4,2,6,5]=>1100100
[3,6,8,1,4,2,7,5]=>1100100
[3,5,7,8,2,4,1,6]=>1100000
[3,6,7,1,4,2,8,5]=>1100100
[8,6,2,7,3,1,4,5]=>1110010
[8,1,7,5,4,3,2,6]=>1111100
[8,1,7,4,5,3,2,6]=>1111000
[5,8,3,7,1,4,2,6]=>1110000
[2,1,7,3,4,6,8,5]=>1010100
[6,7,3,2,4,1,8,5]=>1110100
[8,7,2,4,3,6,1,5]=>1110001
[7,1,2,3,5,6,8,4]=>1001000
[6,1,2,3,8,7,4,5]=>1001001
[5,1,2,3,7,8,6,4]=>1001010
[8,6,2,4,3,1,7,5]=>1110110
[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]=>1110110
[7,8,1,2,6,3,5,4]=>1011000
[1,4,8,2,7,3,5,6]=>0110000
[1,2,8,5,4,7,3,6]=>0011100
[2,3,6,8,4,7,1,5]=>1001000
[1,3,6,8,4,7,5,2]=>0101100
[2,4,8,1,7,3,6,5]=>1010100
[3,4,8,5,7,6,1,2]=>1000110
[1,2,6,8,4,5,7,3]=>0011000
[7,5,1,2,4,3,6,8]=>1010100
[7,4,6,1,5,2,3,8]=>1101000
[6,8,1,4,7,2,3,5]=>1100000
[1,6,4,2,8,3,5,7]=>0111000
[1,6,3,8,5,4,2,7]=>0111100
[7,1,3,6,5,4,2,8]=>1101100
[7,2,1,4,6,3,5,8]=>1110000
[7,2,3,6,5,1,4,8]=>1100100
[7,1,2,3,6,5,4,8]=>1001100
[6,8,1,2,7,3,5,4]=>1011000
[1,6,2,3,8,5,4,7]=>0101100
[1,5,8,2,7,6,3,4]=>0110010
[5,8,2,7,6,3,4,1]=>1110010
[6,2,8,1,7,3,5,4]=>1111000
[3,6,4,1,2,8,5,7]=>1001100
[2,5,1,8,7,6,3,4]=>1010011
[1,2,5,3,8,7,4,6]=>0011001
[2,5,3,8,7,1,6,4]=>1011001
[2,5,8,4,1,7,6,3]=>1011010
[3,5,8,7,1,4,2,6]=>1100001
[5,3,8,4,1,7,6,2]=>1111010
[4,2,8,7,6,3,5,1]=>1110011
[6,3,1,8,7,2,5,4]=>1111001
[5,1,3,8,7,6,2,4]=>1100011
[1,5,3,8,7,6,2,4]=>0110011
[5,1,8,4,7,2,6,3]=>1111000
[5,8,7,4,6,1,2,3]=>1001001
[6,8,5,1,2,4,7,3]=>1010100
[4,5,8,1,7,2,6,3]=>1110000
[1,3,2,5,8,7,4,6]=>0101001
[3,5,1,8,7,4,6,2]=>1101001
[4,3,6,1,2,8,5,7]=>1010100
[4,5,8,3,1,7,2,6]=>1110000
[4,5,2,8,7,1,3,6]=>1100001
[3,2,5,8,7,1,6,4]=>1101001
[3,4,8,7,6,2,1,5]=>1100011
[3,4,8,7,6,5,1,2]=>1000111
[1,3,4,8,7,6,2,5]=>0100011
[3,4,8,7,6,2,5,1]=>1100011
[3,2,5,8,7,4,6,1]=>1101001
[2,1,3,5,8,7,4,6]=>1001001
[1,2,7,5,8,6,4,3]=>0011110
[6,8,1,3,7,5,2,4]=>1100100
[1,3,7,8,2,6,5,4]=>0101100
[2,7,8,1,3,6,5,4]=>1001100
[8,1,2,6,7,3,5,4]=>1011000
[8,1,2,6,7,5,3,4]=>1010100
[8,2,5,7,1,3,6,4]=>1101000
[2,8,1,6,7,3,5,4]=>1011000
[2,6,8,3,7,1,5,4]=>1011000
[2,8,6,4,7,1,5,3]=>1011010
[6,8,3,4,1,7,5,2]=>1110100
[6,8,3,7,4,1,5,2]=>1111000
[8,2,5,7,1,6,3,4]=>1110000
[8,4,7,2,3,6,1,5]=>1101000
[8,5,7,4,2,6,1,3]=>1101100
[8,3,5,7,4,1,6,2]=>1111000
[8,5,2,4,7,1,6,3]=>1110100
[8,2,4,7,3,6,1,5]=>1110000
[8,2,7,1,4,6,3,5]=>1110000
[8,7,1,2,4,6,3,5]=>1010001
[8,7,1,4,6,2,3,5]=>1100001
[8,4,7,1,3,6,2,5]=>1101000
[8,3,5,7,1,2,6,4]=>1011000
[5,8,7,1,3,6,2,4]=>1100001
[8,5,4,7,1,6,2,3]=>1101100
[8,5,4,7,1,2,6,3]=>1011100
[8,5,1,4,7,2,6,3]=>1110100
[8,5,6,3,1,7,4,2]=>1111100
[1,8,4,5,7,2,6,3]=>0111000
[5,8,7,3,6,1,2,4]=>1010001
[8,3,5,7,1,6,2,4]=>1110000
[1,6,8,3,7,5,2,4]=>0110100
[6,3,8,2,7,5,1,4]=>1110100
[8,6,4,7,3,1,5,2]=>1111010
[8,4,5,7,3,1,6,2]=>1111000
[8,3,4,7,2,6,1,5]=>1110000
[8,7,1,3,4,6,2,5]=>1100001
[8,3,7,2,4,6,1,5]=>1110000
[2,8,4,5,7,1,6,3]=>1011000
[8,7,3,4,5,1,6,2]=>1110001
[8,7,4,5,2,6,1,3]=>1101001
[8,7,2,3,4,6,1,5]=>1100001
[8,6,5,1,3,2,7,4]=>1101110
[8,6,3,1,7,2,4,5]=>1110010
[8,7,3,1,5,2,4,6]=>1110001
[8,6,1,2,4,7,3,5]=>1010010
[8,6,1,5,3,4,7,2]=>1110010
[8,6,1,5,2,4,7,3]=>1110010
[8,6,1,2,5,7,3,4]=>1010010
[5,1,4,2,3,8,6,7]=>1100010
[5,1,4,2,7,3,6,8]=>1110000
[5,7,8,1,2,4,6,3]=>1010000
[5,7,8,1,3,4,6,2]=>1100000
[5,8,1,7,3,4,6,2]=>1110000
[8,1,5,7,2,4,6,3]=>1110000
[1,4,2,3,8,7,5,6]=>0100101
[1,4,2,7,6,3,5,8]=>0110010
[6,1,2,8,7,5,3,4]=>1010101
[6,1,2,4,8,7,5,3]=>1010101
[3,1,8,4,6,7,5,2]=>1101100
[3,1,7,6,4,8,5,2]=>1101110
[7,1,2,4,6,8,5,3]=>1010100
[7,1,2,6,8,5,3,4]=>1010100
[7,1,5,3,2,8,6,4]=>1111010
[8,1,7,5,3,2,6,4]=>1111100
[8,3,7,1,2,6,4,5]=>1011000
[3,1,2,8,4,7,5,6]=>1001100
[1,4,2,3,8,6,5,7]=>0100110
[1,4,2,3,8,5,7,6]=>0100110
[5,8,1,7,2,4,6,3]=>1110000
[5,8,1,3,4,7,6,2]=>1100010
[3,1,8,6,4,7,5,2]=>1101110
[8,1,2,6,7,4,5,3]=>1011000
[1,2,3,5,8,4,7,6]=>0001010
[1,2,3,5,8,6,4,7]=>0001010
[7,1,2,8,3,6,5,4]=>1011100
[7,1,2,8,6,4,5,3]=>1011010
[3,1,7,8,4,6,5,2]=>1101100
[8,1,2,7,4,6,5,3]=>1011100
[8,1,2,7,3,6,5,4]=>1011100
[1,2,3,6,8,5,4,7]=>0001100
[3,6,2,5,4,1,8,7]=>1101001
[3,5,2,8,4,7,6,1]=>1101010
[5,4,7,3,2,8,6,1]=>1111010
[5,4,8,3,2,7,6,1]=>1111010
[5,3,2,6,4,1,8,7]=>1111001
[4,5,8,3,2,7,6,1]=>1110010
[4,7,6,3,8,5,2,1]=>1110110
[4,8,6,3,7,5,2,1]=>1110110
[5,3,2,8,4,7,6,1]=>1111010
[2,1,5,8,4,7,6,3]=>1011010
[5,3,2,7,4,8,6,1]=>1111010
[5,7,4,3,2,8,6,1]=>1111010
[4,7,5,3,2,8,6,1]=>1110110
[4,7,8,3,6,5,2,1]=>1110100
[4,6,8,3,7,5,2,1]=>1110100
[7,6,4,3,8,5,2,1]=>1111110
[8,3,2,6,7,5,4,1]=>1111100
[8,6,4,3,7,5,2,1]=>1111110
[8,4,5,3,2,7,6,1]=>1111010
[8,4,6,3,7,5,2,1]=>1111100
[7,4,6,3,8,5,2,1]=>1111100
[3,7,2,6,8,5,4,1]=>1101100
[3,8,2,6,7,5,4,1]=>1101100
[3,7,2,8,6,5,4,1]=>1101110
[3,6,2,8,7,5,4,1]=>1101101
[7,4,5,3,2,8,6,1]=>1111010
[2,1,7,5,4,8,6,3]=>1011110
[7,3,2,8,6,5,4,1]=>1111110
[7,8,4,3,6,5,2,1]=>1111100
[6,3,2,8,7,5,4,1]=>1111101
[6,3,2,7,8,5,4,1]=>1111100
[1,6,4,8,2,5,3,7]=>0111000
[1,6,5,8,2,4,3,7]=>0110100
[1,6,8,2,4,3,7,5]=>0110100
[1,6,2,4,3,7,8,5]=>0110100
[1,5,6,2,4,7,3,8]=>0110000
[1,5,6,2,4,7,8,3]=>0110000
[1,6,7,2,4,3,8,5]=>0110100
[1,5,8,2,4,6,7,3]=>0110000
[1,5,7,8,3,2,4,6]=>0110000
[1,5,8,3,2,4,6,7]=>0110000
[1,5,6,2,4,8,3,7]=>0110000
[1,7,3,4,2,8,6,5]=>0110110
[1,5,6,2,4,8,7,3]=>0110001
[1,5,8,7,3,2,4,6]=>0110001
[1,7,4,2,8,6,5,3]=>0111110
[1,5,8,3,2,4,7,6]=>0110010
[1,6,5,2,3,7,4,8]=>0101100
[1,6,5,2,3,7,8,4]=>0101100
[1,6,8,4,2,3,7,5]=>0101100
[1,6,8,5,2,3,7,4]=>0101100
[1,6,4,2,3,7,5,8]=>0101100
[1,5,8,6,2,4,7,3]=>0110010
[1,7,5,2,8,6,4,3]=>0111110
[3,7,5,6,1,4,8,2]=>1100100
[8,6,1,4,2,7,5,3]=>1110110
[1,6,7,4,3,5,8,2]=>0111000
[6,7,1,4,3,5,8,2]=>1110000
[4,7,1,6,3,5,8,2]=>1110000
[3,1,4,7,6,5,8,2]=>1100110
[6,1,7,4,3,5,8,2]=>1111000
[7,1,6,4,3,5,8,2]=>1111000
[1,7,6,4,3,5,8,2]=>0111010
[8,1,6,4,2,7,5,3]=>1111100
[4,7,1,3,8,2,5,6]=>1100000
[7,4,1,3,8,2,5,6]=>1101000
[1,3,6,4,2,8,5,7]=>0101100
[4,7,3,1,2,8,5,6]=>1010100
[4,7,8,1,2,6,5,3]=>1010100
[1,8,6,4,2,7,5,3]=>0111110
[4,8,1,3,7,2,5,6]=>1100000
[8,7,1,3,6,2,5,4]=>1101001
[1,8,4,3,7,2,5,6]=>0111000
[3,7,4,6,8,2,1,5]=>1101000
[2,4,3,7,8,6,1,5]=>1010010
[1,4,7,3,8,2,5,6]=>0110000
[5,7,6,8,3,2,1,4]=>1110010
[6,1,4,3,8,2,5,7]=>1110000
[4,1,7,3,8,2,5,6]=>1110000
[8,1,4,3,7,2,5,6]=>1110000
[4,2,3,7,8,6,1,5]=>1100010
[2,7,5,6,3,8,1,4]=>1010100
[5,7,2,6,8,4,1,3]=>1101000
[7,2,5,6,8,4,1,3]=>1101000
[5,2,3,8,7,6,1,4]=>1100011
[8,2,3,7,5,6,1,4]=>1100100
[6,1,8,3,7,2,5,4]=>1111000
[1,7,8,4,2,6,5,3]=>0111100
[4,7,1,8,2,5,6,3]=>1110000
[1,4,8,3,6,2,5,7]=>0110000
[3,7,5,8,6,2,1,4]=>1100110
[3,7,8,6,5,2,1,4]=>1100110
[6,8,7,5,3,2,1,4]=>1110101
[5,7,6,8,3,4,1,2]=>1010010
[3,7,6,8,4,5,1,2]=>1001010
[1,5,4,7,6,8,2,3]=>0101010
[1,7,4,6,5,8,2,3]=>0101100
[3,7,4,6,5,8,1,2]=>1001100
[3,5,4,8,6,7,1,2]=>1001010
[3,8,4,6,5,7,1,2]=>1001100
[3,6,4,7,5,8,1,2]=>1001100
[1,6,2,7,5,8,3,4]=>0110100
[1,6,4,8,5,7,2,3]=>0101100
[1,8,4,6,5,7,2,3]=>0101100
[1,5,4,8,6,7,2,3]=>0101010
[7,8,1,5,4,6,2,3]=>1101000
[1,8,2,6,5,7,3,4]=>0110100
[1,7,2,8,5,6,3,4]=>0110100
[1,7,2,6,5,8,3,4]=>0110100
[1,5,2,7,6,8,3,4]=>0110010
[1,7,6,8,2,5,3,4]=>0110010
[1,7,6,8,4,5,2,3]=>0101010
[7,8,5,6,1,3,2,4]=>1100100
[5,8,6,7,1,3,2,4]=>1100010
[1,3,2,7,6,8,4,5]=>0101010
[1,7,6,8,2,4,3,5]=>0110010
[1,3,2,8,6,7,4,5]=>0101010
[7,8,1,3,2,6,4,5]=>1101000
[7,8,1,6,2,4,3,5]=>1110000
[1,8,6,7,2,4,3,5]=>0110010
[7,8,1,4,2,6,3,5]=>1110000
[6,4,8,5,2,7,1,3]=>1101100
[8,4,7,5,2,6,1,3]=>1101100
[5,4,6,8,2,1,7,3]=>1111000
[4,8,7,5,6,1,3,2]=>1100101
[2,7,5,1,8,4,3,6]=>1011100
[2,8,6,7,4,3,5,1]=>1011010
[3,8,7,1,4,6,5,2]=>1100101
[5,7,1,2,4,3,8,6]=>1010010
[4,3,7,6,8,2,5,1]=>1110010
[5,3,6,8,1,7,2,4]=>1110000
[3,2,6,8,5,7,1,4]=>1100100
[7,4,8,6,5,2,1,3]=>1101110
[7,1,8,2,5,4,3,6]=>1111000
[2,5,3,7,4,1,8,6]=>1011010
[3,6,4,7,5,1,8,2]=>1101100
[8,4,7,1,2,5,6,3]=>1011000
[4,2,8,7,3,5,6,1]=>1110001
[6,4,1,5,8,2,7,3]=>1111000
[8,3,5,6,7,4,1,2]=>1011000
[7,4,3,2,8,5,6,1]=>1111100
[4,2,7,1,8,5,6,3]=>1110100
[4,7,8,3,1,5,6,2]=>1110000
[3,7,1,4,8,5,6,2]=>1100100
[2,6,3,5,8,7,1,4]=>1010001
[7,6,2,1,5,8,4,3]=>1111010
[4,5,2,7,6,1,8,3]=>1110010
[3,6,8,7,5,2,1,4]=>1100101
[7,4,8,6,5,2,3,1]=>1101110
[8,1,6,4,7,3,2,5]=>1111000
[7,6,4,1,2,3,8,5]=>1001110
[2,6,4,8,5,3,7,1]=>1011100
[4,8,7,5,6,1,2,3]=>1000101
[6,1,4,8,7,3,5,2]=>1110001
[4,7,8,1,3,5,6,2]=>1100000
[8,7,3,4,1,5,6,2]=>1110001
[4,8,2,7,3,5,6,1]=>1110000
[3,1,8,7,2,5,6,4]=>1101001
[8,2,3,7,1,5,6,4]=>1101000
[6,4,8,7,1,3,2,5]=>1101001
[7,8,2,4,3,5,6,1]=>1110000
[2,8,3,7,1,5,6,4]=>1011000
[5,3,8,6,2,1,4,7]=>1110010
[4,6,5,2,8,3,1,7]=>1110100
[4,3,7,5,1,8,2,6]=>1110100
[6,8,5,2,7,4,3,1]=>1111100
[3,6,8,1,4,5,2,7]=>1100000
[6,8,1,2,4,5,3,7]=>1010000
[4,1,6,5,8,2,3,7]=>1100100
[4,3,8,6,2,5,1,7]=>1110010
[8,3,6,1,4,5,2,7]=>1110000
[6,3,8,7,4,2,5,1]=>1111001
[5,8,4,3,7,6,1,2]=>1011010
[8,7,4,3,1,6,2,5]=>1111001
[1,7,4,3,8,6,2,5]=>0111010
[7,1,5,3,4,8,2,6]=>1110000
[2,8,6,1,7,4,5,3]=>1011010
[4,7,6,8,2,1,5,3]=>1110010
[6,1,8,7,4,3,5,2]=>1111001
[8,5,4,3,1,6,7,2]=>1111100
[1,5,8,6,3,4,7,2]=>0110010
[2,5,8,6,3,4,7,1]=>1010010
[4,6,5,2,8,1,7,3]=>1110100
[1,8,5,2,3,6,7,4]=>0101100
[4,8,3,2,5,6,7,1]=>1110000
[2,1,8,3,5,6,7,4]=>1011000
[4,2,7,1,8,6,3,5]=>1110010
[3,8,4,1,2,6,7,5]=>1001100
[5,8,3,6,7,4,1,2]=>1011000
[2,3,1,6,8,4,7,5]=>1001100
[2,4,3,7,1,8,5,6]=>1010100
[2,4,1,8,6,3,7,5]=>1010110
[8,4,1,3,6,2,7,5]=>1101100
[6,8,5,1,7,2,3,4]=>1100100
[7,3,6,5,8,2,1,4]=>1110100
[7,6,3,5,8,2,1,4]=>1110010
[4,5,8,7,3,6,1,2]=>1010001
[8,6,5,4,1,2,7,3]=>1011110
[6,1,5,3,8,7,2,4]=>1110001
[2,8,6,3,7,1,5,4]=>1011010
[7,6,1,5,8,2,3,4]=>1100010
[3,6,8,5,1,2,7,4]=>1001100
[6,5,2,4,8,1,7,3]=>1110100
[5,1,4,8,2,6,7,3]=>1110000
[3,4,8,5,2,6,7,1]=>1100100
[4,2,1,8,5,6,7,3]=>1110100
[1,5,4,8,2,6,7,3]=>0111000
[7,2,1,5,8,6,3,4]=>1110010
[2,8,4,5,1,6,7,3]=>1011000
[5,4,8,3,7,6,1,2]=>1011010
[3,1,5,8,6,2,7,4]=>1101010
[6,3,4,8,5,1,7,2]=>1110100
[5,3,4,8,1,6,7,2]=>1110000
[6,5,4,8,7,1,3,2]=>1101101
[6,5,4,8,1,2,7,3]=>1011100
[7,5,1,6,8,2,4,3]=>1110100
[6,5,4,1,8,2,7,3]=>1111100
[6,5,4,7,1,2,8,3]=>1011100
[6,5,4,7,8,1,3,2]=>1101100
[6,5,3,7,1,4,2,8]=>1110100
[7,5,1,4,8,3,2,6]=>1110100
[8,1,6,4,7,3,5,2]=>1111000
[7,5,1,4,8,3,6,2]=>1110100
[7,4,1,5,3,8,6,2]=>1111010
[8,1,5,4,3,7,6,2]=>1111010
[8,1,5,4,3,7,2,6]=>1111000
[6,5,3,8,1,4,2,7]=>1110100
[8,1,7,2,5,4,6,3]=>1111000
[7,6,1,2,5,4,8,3]=>1011010
[6,5,3,8,1,4,7,2]=>1110100
[6,5,3,1,2,7,8,4]=>1011100
[8,1,6,4,2,5,7,3]=>1111000
[8,1,5,4,3,2,7,6]=>1111010
[7,4,1,5,3,2,8,6]=>1111010
[6,4,3,1,5,2,8,7]=>1111001
[6,4,3,1,5,7,2,8]=>1111000
[7,4,1,5,3,6,2,8]=>1111000
[6,4,3,1,5,7,8,2]=>1111000
[7,1,5,8,4,6,2,3]=>1101000
[8,6,7,1,4,2,5,3]=>1110010
[8,6,3,7,5,1,2,4]=>1010110
[8,6,1,7,3,2,5,4]=>1111010
[7,6,1,8,3,5,2,4]=>1110010
[7,6,1,3,8,5,2,4]=>1100110
[7,6,8,2,4,5,1,3]=>1100010
[7,6,2,8,3,5,1,4]=>1110010
[8,7,1,5,2,6,3,4]=>1110001
[8,7,1,5,2,3,6,4]=>1101001
[8,5,2,3,1,7,6,4]=>1101110
[8,6,2,3,7,1,5,4]=>1101010
[8,6,2,7,3,1,5,4]=>1111010
[8,6,7,2,4,1,5,3]=>1110010
[6,8,7,3,4,1,5,2]=>1110001
[8,7,2,5,1,6,3,4]=>1110001
[8,7,2,1,4,6,3,5]=>1110001
[8,4,2,1,7,6,3,5]=>1111010
[8,5,2,7,1,6,3,4]=>1110100
[8,5,7,2,1,4,3,6]=>1110100
[5,8,7,3,1,4,2,6]=>1110001
[8,5,7,2,1,4,6,3]=>1110100
[8,5,2,7,1,3,6,4]=>1101100
[8,7,4,1,2,3,6,5]=>1001101
[8,7,4,1,2,6,3,5]=>1011001
[8,4,3,1,7,2,6,5]=>1111100
[8,4,3,1,2,7,6,5]=>1011110
[8,6,1,3,7,2,5,4]=>1101010
[8,5,1,3,2,7,6,4]=>1101110
[8,5,7,4,1,6,2,3]=>1101100
[8,5,7,4,1,2,6,3]=>1011100
[8,1,5,4,2,7,6,3]=>1111010
[8,1,6,4,7,2,5,3]=>1111000
[6,1,5,8,4,2,7,3]=>1111000
[5,8,3,6,4,1,2,7]=>1011000
[8,4,7,5,1,6,2,3]=>1101100
[8,4,7,5,1,2,6,3]=>1011100
[8,4,7,5,1,2,3,6]=>1001100
[8,3,2,6,5,1,4,7]=>1110100
[4,8,6,3,5,1,2,7]=>1010010
[4,8,7,3,1,5,2,6]=>1110001
[8,4,7,2,1,5,3,6]=>1111000
[8,3,2,7,1,5,4,6]=>1111000
[8,3,2,1,7,6,4,5]=>1111010
[8,7,3,1,6,2,4,5]=>1110001
[8,7,3,1,2,4,6,5]=>1010101
[8,3,2,1,7,4,6,5]=>1111100
[8,4,7,2,1,5,6,3]=>1111000
[8,7,2,1,3,6,4,5]=>1101001
[8,7,2,1,3,4,6,5]=>1100101
[1,2,7,3,5,4,8,6]=>0011010
[1,5,7,2,3,6,4,8]=>0101000
[1,3,8,2,4,5,7,6]=>0100010
[1,2,3,8,4,6,7,5]=>0001100
[1,7,8,2,3,6,4,5]=>0101000
[1,6,7,8,2,3,5,4]=>0101000
[1,7,8,2,5,3,6,4]=>0111000
[1,8,2,3,6,4,5,7]=>0101000
[1,2,7,8,3,6,4,5]=>0011000
[1,5,2,7,8,3,6,4]=>0111000
[1,3,2,8,4,6,7,5]=>0101100
[1,8,2,3,4,6,7,5]=>0100100
[1,7,8,2,4,3,6,5]=>0110100
[7,6,3,1,5,2,4,8]=>1110010
[6,7,3,1,5,2,8,4]=>1111000
[6,8,3,1,5,2,7,4]=>1111000
[6,8,4,5,1,2,7,3]=>1011000
[6,7,4,5,1,2,8,3]=>1011000
[7,2,1,6,5,3,4,8]=>1110100
[7,3,6,1,5,2,4,8]=>1110000
[7,4,6,5,1,2,3,8]=>1001100
[6,7,5,4,1,2,8,3]=>1011100
[5,8,6,4,1,7,2,3]=>1101010
[5,7,6,4,1,8,2,3]=>1101010
[5,6,7,4,1,8,2,3]=>1101000
[6,5,7,4,1,2,8,3]=>1011100
[6,2,1,7,5,3,8,4]=>1111100
[6,3,8,1,5,2,7,4]=>1111000
[6,4,8,5,1,2,7,3]=>1011100
[6,5,8,4,1,2,7,3]=>1011100
[5,6,8,4,1,7,2,3]=>1101000
[4,6,8,5,7,1,2,3]=>1000100
[4,5,8,6,7,1,2,3]=>1000010
[5,2,1,7,6,8,3,4]=>1110010
[4,5,7,6,8,1,2,3]=>1000010
[4,6,7,5,8,1,2,3]=>1000100
[4,7,5,6,8,1,2,3]=>1000100
[4,6,5,7,8,1,2,3]=>1000100
[5,7,4,6,1,8,2,3]=>1101000
[5,8,3,1,6,7,2,4]=>1110000
[5,7,3,1,6,8,2,4]=>1110000
[5,6,3,1,7,8,2,4]=>1110000
[5,8,3,1,7,6,2,4]=>1110010
[5,7,4,8,1,6,2,3]=>1101000
[5,2,1,6,8,7,3,4]=>1110001
[5,4,6,8,1,7,2,3]=>1101000
[4,5,6,8,7,1,2,3]=>1000001
[4,7,5,8,6,1,2,3]=>1000110
[4,8,5,7,6,1,2,3]=>1000110
[4,8,6,7,5,1,2,3]=>1000110
[4,7,6,8,5,1,2,3]=>1000110
[4,6,7,8,5,1,2,3]=>1000100
[4,5,7,8,6,1,2,3]=>1000010
[5,4,7,8,1,6,2,3]=>1101000
[5,3,7,1,8,6,2,4]=>1110010
[5,2,1,7,8,6,3,4]=>1110010
[5,3,8,1,7,6,2,4]=>1110010
[5,4,8,7,1,6,2,3]=>1101001
[4,6,8,7,5,1,2,3]=>1000101
[4,7,8,6,5,1,2,3]=>1000110
[4,8,7,6,5,1,2,3]=>1000111
[2,5,4,7,3,6,1,8]=>1011000
[4,2,7,3,6,5,1,8]=>1110100
[4,2,6,3,1,5,8,7]=>1110001
[2,5,3,1,6,4,8,7]=>1011001
[2,5,3,7,6,4,1,8]=>1011010
[2,6,5,3,7,4,1,8]=>1011100
[4,2,7,6,3,5,1,8]=>1110010
[2,7,5,3,6,4,1,8]=>1011100
[2,6,3,7,5,4,1,8]=>1011100
[1,7,5,2,3,8,4,6]=>0101100
[2,1,3,7,5,4,8,6]=>1001110
[2,3,1,8,6,5,4,7]=>1001110
[2,5,3,1,8,6,4,7]=>1011010
[4,2,8,3,1,6,5,7]=>1110100
[8,3,2,6,4,1,5,7]=>1111000
[3,6,8,2,1,4,5,7]=>1100000
[1,2,6,3,8,7,4,5]=>0011001
[1,2,7,6,3,4,8,5]=>0010110
[2,1,3,8,7,5,4,6]=>1001101
[1,2,3,8,6,4,7,5]=>0001110
[1,2,3,7,4,8,6,5]=>0001110
[1,2,7,6,3,8,4,5]=>0011010
[1,2,3,6,4,8,7,5]=>0001101
[1,2,3,7,6,4,8,5]=>0001110
[2,1,3,8,5,4,7,6]=>1001110
[7,1,8,4,2,3,5,6]=>1101000
[4,2,6,3,1,8,5,7]=>1110100
[5,4,2,8,3,1,6,7]=>1111000
[2,5,4,8,3,1,6,7]=>1011000
[1,8,7,4,2,3,5,6]=>0101001
[1,5,2,8,7,3,4,6]=>0110001
[1,2,7,3,6,4,8,5]=>0011100
[1,2,8,6,3,7,4,5]=>0011010
[1,2,6,3,8,4,7,5]=>0011100
[4,2,1,8,3,7,5,6]=>1110100
[8,3,2,1,7,4,5,6]=>1111000
[1,2,3,8,7,4,6,5]=>0001101
[1,2,3,8,7,6,4,5]=>0001011
[2,6,5,7,1,4,3,8]=>1010100
[2,6,5,7,1,3,8,4]=>1001100
[3,8,5,7,1,2,6,4]=>1001100
[3,8,5,7,2,6,4,1]=>1101100
[3,4,8,6,2,5,7,1]=>1100010
[3,4,8,6,1,2,5,7]=>1000010
[2,5,7,1,4,8,6,3]=>1010010
[2,8,1,7,5,6,4,3]=>1011100
[2,3,8,1,6,5,7,4]=>1001100
[3,5,7,6,1,2,4,8]=>1000010
[4,8,6,7,2,3,5,1]=>1100010
[4,8,6,7,1,3,5,2]=>1100010
[3,4,8,6,1,5,7,2]=>1100010
[3,8,5,7,1,6,4,2]=>1101100
[3,8,5,7,2,1,6,4]=>1101100
[3,4,8,6,2,1,5,7]=>1100010
[3,5,7,6,2,1,4,8]=>1100010
[5,8,6,7,3,4,2,1]=>1110010
[5,8,6,7,2,1,3,4]=>1100010
[4,8,6,7,2,1,5,3]=>1110010
[4,3,1,7,5,2,8,6]=>1110110
[4,3,2,8,5,1,7,6]=>1110110
[4,3,8,5,1,6,7,2]=>1110100
[5,8,6,7,2,3,4,1]=>1100010
[5,8,6,7,2,4,3,1]=>1110010
[5,8,6,7,1,2,4,3]=>1010010
[3,2,5,7,6,1,4,8]=>1100010
[4,8,6,7,1,3,2,5]=>1100010
[4,8,6,7,1,2,5,3]=>1010010
[4,8,6,7,2,5,3,1]=>1110010
[4,3,8,5,2,6,7,1]=>1110100
[4,2,6,7,5,1,3,8]=>1100100
[3,8,4,7,1,5,2,6]=>1101000
[3,5,1,7,4,6,2,8]=>1101000
[3,8,4,7,2,5,1,6]=>1101000
[4,1,3,8,5,2,6,7]=>1100100
[4,2,6,7,5,3,8,1]=>1110100
[4,8,6,7,3,2,5,1]=>1110010
[4,8,6,7,3,1,2,5]=>1010010
[3,1,5,7,6,2,4,8]=>1100010
[3,4,1,7,5,6,2,8]=>1100100
[4,1,7,5,2,8,6,3]=>1110110
[4,1,6,7,5,2,3,8]=>1100100
[5,8,6,7,3,2,4,1]=>1110010
[5,8,6,7,4,2,3,1]=>1101010
[5,8,6,7,4,1,2,3]=>1001010
[5,8,6,7,4,1,3,2]=>1101010
[5,8,6,7,3,1,4,2]=>1110010
[4,8,6,7,3,1,5,2]=>1110010
[4,1,6,7,5,3,8,2]=>1110100
[4,1,7,5,3,2,8,6]=>1110110
[4,2,8,5,3,1,7,6]=>1110110
[4,2,1,6,7,5,3,8]=>1110100
[4,8,6,7,3,2,1,5]=>1110010
[5,8,6,7,4,2,1,3]=>1101010
[5,8,6,7,4,3,1,2]=>1011010
[6,1,5,2,8,4,7,3]=>1111000
[4,6,1,8,5,7,2,3]=>1100100
[4,7,1,2,8,5,6,3]=>1010100
[1,4,7,2,8,5,6,3]=>0110100
[1,7,3,5,8,6,2,4]=>0110010
[7,3,5,8,6,1,2,4]=>1010010
[6,8,1,5,7,2,3,4]=>1100000
[7,1,2,5,8,6,3,4]=>1010010
[1,7,2,5,8,6,3,4]=>0110010
[1,7,6,8,2,3,5,4]=>0101010
[7,6,8,1,2,3,5,4]=>1001010
[2,7,1,5,8,6,3,4]=>1010010
[2,4,7,1,8,5,6,3]=>1010100
[4,7,5,8,3,1,6,2]=>1110100
[4,7,2,1,8,5,6,3]=>1110100
[7,3,5,8,6,2,1,4]=>1110010
[7,6,8,2,1,3,5,4]=>1101010
[1,2,7,6,8,3,5,4]=>0011010
[3,7,6,8,2,1,5,4]=>1101010
[6,7,4,1,8,5,3,2]=>1111100
[6,7,4,3,1,8,5,2]=>1111100
[2,7,4,1,6,8,5,3]=>1011100
[3,1,7,6,8,2,5,4]=>1101010
[1,3,7,6,8,2,5,4]=>0101010
[1,7,4,2,6,8,5,3]=>0111100
[7,1,4,2,8,5,6,3]=>1110100
[7,1,8,2,5,4,6,3]=>1111000
[7,1,6,8,5,4,2,3]=>1101100
[7,1,2,6,8,5,4,3]=>1011100
[1,7,2,6,8,5,4,3]=>0111100
[1,7,6,8,3,2,5,4]=>0111010
[7,6,8,3,1,2,5,4]=>1011010
[7,1,5,8,6,3,2,4]=>1110010
[3,6,7,1,8,5,4,2]=>1101100
[7,2,6,8,5,4,1,3]=>1101100
[7,6,8,2,3,1,5,4]=>1101010
[2,7,6,8,3,1,5,4]=>1011010
[2,7,1,6,8,5,4,3]=>1011100
[6,7,3,1,8,5,4,2]=>1111100
[6,7,1,8,5,4,3,2]=>1111100
[7,2,1,6,8,5,4,3]=>1111100
[7,8,4,2,1,6,5,3]=>1111100
[6,2,3,4,8,7,1,5]=>1100001
[6,2,3,4,7,8,1,5]=>1100000
[7,8,3,6,4,2,1,5]=>1111000
[7,8,3,5,6,2,1,4]=>1110000
[5,2,6,3,8,1,7,4]=>1111000
[6,3,2,5,8,7,1,4]=>1110001
[6,3,2,8,4,7,1,5]=>1111000
[6,4,3,8,7,5,1,2]=>1011101
[6,4,3,7,8,5,1,2]=>1011100
[6,3,2,7,4,8,1,5]=>1111000
[6,3,2,5,7,8,1,4]=>1110000
[5,8,2,3,6,1,7,4]=>1101000
[4,5,6,8,3,2,1,7]=>1110000
[4,6,8,5,3,2,1,7]=>1110100
[5,6,1,4,2,3,7,8]=>1100000
[5,6,8,4,3,7,1,2]=>1011000
[5,6,1,4,2,3,8,7]=>1100001
[5,2,8,3,4,1,7,6]=>1110010
[4,5,8,6,3,2,1,7]=>1110010
[4,7,5,6,3,2,1,8]=>1110100
[5,1,4,3,6,2,8,7]=>1110001
[5,1,4,3,8,2,7,6]=>1110010
[5,6,2,4,1,8,7,3]=>1110001
[5,7,2,4,1,8,6,3]=>1110010
[6,1,4,2,8,7,5,3]=>1110101
[5,8,2,4,1,7,6,3]=>1110010
[5,4,1,3,7,2,6,8]=>1101000
[5,8,1,4,2,3,7,6]=>1100010
[5,1,6,3,4,2,7,8]=>1110000
[4,8,6,5,3,2,1,7]=>1110110
[5,4,7,8,3,2,1,6]=>1111000
[4,7,8,5,3,2,1,6]=>1110100
[5,7,1,3,4,2,6,8]=>1100000
[5,1,8,4,2,3,6,7]=>1101000
[5,1,7,4,2,3,6,8]=>1101000
[5,8,1,3,4,2,6,7]=>1100000
[4,8,7,5,3,2,1,6]=>1110101
[4,7,8,6,3,2,1,5]=>1110010
[4,8,2,3,6,7,5,1]=>1100100
[4,8,3,1,6,7,5,2]=>1110100
[4,3,8,1,6,2,5,7]=>1110000
[1,4,8,7,3,5,2,6]=>0110001
[4,3,8,7,2,5,1,6]=>1110001
[5,8,1,4,7,2,6,3]=>1110000
[6,8,1,2,4,3,5,7]=>1010000
[5,8,7,1,3,4,2,6]=>1100001
[4,8,7,6,3,1,2,5]=>1010011
[5,8,4,7,3,1,2,6]=>1011000
[4,3,8,2,7,5,6,1]=>1110100
[1,4,8,3,7,5,6,2]=>0110100
[1,4,3,8,2,6,5,7]=>0110100
[4,1,3,8,2,6,5,7]=>1100100
[4,1,8,7,3,5,2,6]=>1110001
[3,4,8,1,6,2,5,7]=>1100000
[3,4,8,7,2,5,1,6]=>1100001
[3,4,8,2,7,5,6,1]=>1100100
[1,2,4,3,8,6,5,7]=>0010110
[3,4,2,1,8,6,5,7]=>1100110
[3,4,1,8,2,6,5,7]=>1100100
[3,6,7,8,4,1,2,5]=>1001000
[4,1,2,8,3,6,5,7]=>1010100
[1,4,3,2,8,6,5,7]=>0110110
[4,2,3,1,8,6,5,7]=>1100110
[3,7,8,2,6,4,5,1]=>1101000
[4,2,3,8,1,6,5,7]=>1100100
[4,3,1,8,2,6,5,7]=>1110100
[1,4,7,8,5,3,2,6]=>0110100
[4,2,8,6,3,1,5,7]=>1110010
[2,4,8,6,3,1,5,7]=>1010010
[7,3,6,8,4,2,1,5]=>1111000
[1,7,3,8,4,6,5,2]=>0111100
[1,3,4,8,2,6,5,7]=>0100100
[3,2,4,8,1,6,5,7]=>1100100
[7,3,8,2,6,4,5,1]=>1111000
[6,2,8,7,4,3,5,1]=>1111001
[7,4,1,8,5,2,6,3]=>1111100
[7,3,2,8,4,6,5,1]=>1111100
[1,3,4,2,8,6,5,7]=>0100110
[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]=>1100110
[3,1,4,8,2,6,5,7]=>1100100
[7,3,4,8,5,1,6,2]=>1110100
[3,7,4,8,5,1,2,6]=>1001100
[6,7,2,8,3,5,4,1]=>1111000
[2,3,1,4,8,6,5,7]=>1000110
[2,1,3,4,8,6,5,7]=>1000110
[3,5,7,8,6,1,2,4]=>1000010
[3,1,5,6,8,2,7,4]=>1101000
[5,1,6,3,8,4,7,2]=>1111000
[2,5,1,6,8,3,7,4]=>1011000
[5,1,2,6,8,3,7,4]=>1011000
[1,5,2,7,8,6,3,4]=>0110010
[6,1,7,5,2,8,3,4]=>1110100
[2,6,7,5,1,8,3,4]=>1010100
[5,7,2,8,6,1,3,4]=>1100010
[3,5,7,8,6,2,1,4]=>1100010
[3,2,5,7,8,6,1,4]=>1100010
[6,2,7,5,1,8,3,4]=>1110100
[1,2,6,7,5,8,3,4]=>0010100
[6,2,7,5,4,1,8,3]=>1111100
[6,7,5,2,4,1,8,3]=>1110100
[6,7,2,5,3,8,1,4]=>1110000
[5,1,7,8,6,3,2,4]=>1110010
[1,6,7,5,3,8,2,4]=>0110100
[1,6,7,5,4,2,8,3]=>0111100
[5,7,8,6,4,1,2,3]=>1001010
[6,7,4,1,5,2,8,3]=>1111000
[1,6,7,4,5,2,8,3]=>0111000
[6,3,1,7,5,8,2,4]=>1110100
[2,5,3,7,8,6,1,4]=>1010010
[6,3,2,7,5,8,1,4]=>1110100
[6,7,4,2,5,1,8,3]=>1111000
[6,2,7,4,5,1,8,3]=>1111000
[6,2,3,7,5,8,1,4]=>1100100
[7,5,1,6,3,8,2,4]=>1110100
[7,5,1,6,3,8,4,2]=>1111100
[2,7,6,1,3,8,4,5]=>1001010
[2,7,6,1,3,8,5,4]=>1001110
[2,6,7,1,5,8,3,4]=>1010000
[2,6,7,4,1,8,3,5]=>1011000
[2,1,6,7,3,8,5,4]=>1011100
[2,6,7,4,1,8,5,3]=>1011100
[2,6,7,1,5,8,4,3]=>1011000
[3,6,5,1,8,4,2,7]=>1101100
[3,7,5,4,8,1,6,2]=>1101100
[3,7,5,4,8,1,2,6]=>1001100
[4,6,1,5,8,7,3,2]=>1110001
[4,6,1,5,8,7,2,3]=>1100001
[4,6,1,5,8,2,7,3]=>1110000
[7,5,1,6,2,8,3,4]=>1110100
[4,6,1,5,8,2,3,7]=>1100000
[4,7,1,5,8,3,6,2]=>1110000
[8,3,4,6,2,1,5,7]=>1110000
[3,5,6,2,1,8,4,7]=>1101000
[7,5,3,2,8,4,1,6]=>1111100
[7,5,3,2,8,4,6,1]=>1111100
[4,2,5,6,8,3,1,7]=>1110000
[5,3,6,8,1,4,2,7]=>1110000
[4,5,6,8,1,3,2,7]=>1100000
[1,4,5,6,8,3,2,7]=>0110000
[4,5,3,7,2,8,6,1]=>1110010
[6,4,7,3,2,8,5,1]=>1111100
[6,1,4,7,3,2,8,5]=>1110100
[5,1,7,3,8,4,2,6]=>1111000
[5,3,7,1,4,8,6,2]=>1110010
[6,4,3,1,7,8,5,2]=>1111100
[5,6,1,3,7,8,4,2]=>1101000
[5,6,1,7,8,3,4,2]=>1110000
[1,6,3,7,4,8,5,2]=>0111100
[6,7,2,4,1,8,5,3]=>1110100
[6,7,2,1,4,3,8,5]=>1110100
[6,4,7,3,1,2,8,5]=>1011100
[5,6,3,1,2,7,8,4]=>1011000
[5,6,1,3,2,7,8,4]=>1101000
[5,6,3,2,1,7,8,4]=>1111000
[5,6,3,2,7,8,4,1]=>1111000
[2,5,6,3,7,8,4,1]=>1011000
[2,5,6,3,1,7,8,4]=>1011000
[2,6,4,7,3,1,8,5]=>1011100
[6,3,7,2,8,4,1,5]=>1111000
[6,3,2,7,1,8,4,5]=>1111000
[7,5,3,2,1,8,4,6]=>1111100
[7,3,8,4,2,1,5,6]=>1111000
[4,7,2,1,3,8,6,5]=>1100110
[1,3,7,8,6,4,2,5]=>0101010
[5,7,3,8,2,1,6,4]=>1111000
[4,6,2,7,8,5,3,1]=>1110100
[2,5,1,7,3,8,6,4]=>1011010
[6,7,2,1,3,8,5,4]=>1101100
[5,1,6,7,8,2,4,3]=>1110000
[6,3,7,1,8,5,2,4]=>1110100
[6,2,1,7,3,8,5,4]=>1111100
[6,2,7,1,8,5,4,3]=>1111100
[6,3,1,7,8,5,4,2]=>1111100
[5,3,2,1,8,4,7,6]=>1111010
[4,5,2,1,3,8,7,6]=>1100011
[3,2,6,4,5,8,1,7]=>1101000
[2,4,6,5,8,1,3,7]=>1000100
[1,3,4,6,5,8,2,7]=>0100100
[1,6,3,4,5,8,2,7]=>0110000
[3,4,1,8,5,2,7,6]=>1100110
[2,8,4,1,7,6,3,5]=>1011010
[1,5,3,2,8,7,4,6]=>0111001
[8,2,1,7,5,3,4,6]=>1110100
[1,7,6,4,5,8,3,2]=>0111010
[5,8,7,4,6,2,1,3]=>1101001
[3,4,2,5,8,6,7,1]=>1100010
[4,1,3,5,6,8,7,2]=>1100001
[2,4,8,6,7,1,3,5]=>1000010
[3,7,4,8,2,1,6,5]=>1101100
[2,3,5,8,6,7,1,4]=>1000010
[3,2,5,6,8,7,1,4]=>1100001
[7,2,4,8,5,3,1,6]=>1110100
[4,8,3,1,2,7,6,5]=>1010110
[8,4,2,3,7,1,5,6]=>1101000
[3,5,2,7,6,1,8,4]=>1101010
[5,8,7,3,4,6,2,1]=>1110001
[5,8,2,7,4,1,6,3]=>1111000
[5,1,4,2,8,7,6,3]=>1110011
[5,2,6,8,7,1,3,4]=>1100001
[6,3,2,1,8,5,7,4]=>1111100
[2,7,5,4,1,8,6,3]=>1011110
[4,2,5,6,8,7,1,3]=>1100001
[1,8,4,2,5,6,7,3]=>0111000
[3,8,4,1,5,6,7,2]=>1101000
[4,2,8,5,6,7,1,3]=>1100100
[5,2,4,7,1,8,6,3]=>1110010
[8,1,3,6,5,2,4,7]=>1100100
[8,3,2,4,6,5,1,7]=>1110100
[8,3,6,4,1,5,2,7]=>1111000
[1,3,4,8,5,7,2,6]=>0100100
[5,8,4,7,6,2,3,1]=>1101010
[1,3,4,7,5,8,2,6]=>0100100
[1,3,5,2,4,8,7,6]=>0100011
[2,6,5,1,3,8,7,4]=>1001101
[2,8,5,1,4,7,6,3]=>1010110
[4,3,1,5,8,6,7,2]=>1110010
[5,4,2,1,6,8,7,3]=>1111001
[6,8,4,3,2,7,1,5]=>1111000
[5,1,3,2,8,6,7,4]=>1101010
[5,3,1,2,8,6,7,4]=>1011010
[5,2,3,1,6,8,7,4]=>1101001
[5,3,2,1,8,6,7,4]=>1111010
[5,2,1,3,6,8,7,4]=>1101001
[2,7,4,5,8,3,1,6]=>1011000
[1,8,4,3,7,2,6,5]=>0111100
[3,4,8,7,2,1,6,5]=>1100101
[5,4,7,8,3,6,2,1]=>1111000
[6,3,8,7,4,1,2,5]=>1011001
[8,4,7,2,3,1,5,6]=>1101000
[8,6,4,1,3,2,7,5]=>1101110
[3,5,7,2,6,1,8,4]=>1101000
[6,1,3,8,5,7,2,4]=>1100100
[2,8,1,5,4,7,6,3]=>1011010
[1,7,2,4,6,5,8,3]=>0110100
[5,8,2,6,1,3,7,4]=>1101000
[6,3,5,8,7,2,1,4]=>1110001
[2,5,7,8,4,1,6,3]=>1011000
[4,1,5,2,6,8,7,3]=>1110001
[4,1,8,5,2,6,7,3]=>1110100
[2,7,1,8,5,4,6,3]=>1011100
[5,8,6,2,1,3,7,4]=>1101010
[3,4,5,1,8,6,7,2]=>1100010
[5,1,3,6,4,8,7,2]=>1101001
[1,3,2,7,5,8,6,4]=>0101110
[1,4,2,5,8,3,7,6]=>0110010
[1,4,2,7,8,5,6,3]=>0110100
[5,1,2,6,8,4,7,3]=>1011000
[3,1,2,6,5,8,4,7]=>1001100
[4,1,2,6,8,5,3,7]=>1010100
[1,5,2,4,8,7,6,3]=>0110011
[1,2,7,4,8,6,5,3]=>0011110
[1,3,2,7,5,8,4,6]=>0101100
[2,3,1,7,5,4,8,6]=>1001110
[1,3,2,8,5,7,4,6]=>0101100
[1,2,6,4,8,7,3,5]=>0011001
[1,2,6,8,5,7,3,4]=>0010100
[1,5,6,8,2,7,3,4]=>0110000
[1,3,8,2,6,7,4,5]=>0101000
[1,4,7,2,8,6,3,5]=>0110010
[1,6,7,8,2,5,3,4]=>0110000
[1,2,6,8,3,7,5,4]=>0011100
[1,5,7,8,2,3,6,4]=>0101000
[1,4,7,2,8,3,6,5]=>0110100
[1,6,7,3,4,8,5,2]=>0110100
[1,5,3,7,4,8,6,2]=>0111010
[1,3,6,4,2,8,7,5]=>0101101
[1,3,7,4,2,8,6,5]=>0101110
[1,2,8,4,7,3,6,5]=>0011100
[1,5,2,4,8,3,7,6]=>0110010
[1,8,4,5,7,2,3,6]=>0101000
[1,8,3,5,2,7,4,6]=>0111000
[2,8,3,5,1,4,7,6]=>1010010
[2,3,8,6,1,4,7,5]=>1000110
[1,4,8,6,7,2,3,5]=>0100010
[1,5,6,8,7,2,3,4]=>0100001
[1,2,7,8,5,3,6,4]=>0011100
[1,2,5,8,7,3,6,4]=>0011001
[1,2,6,8,7,3,5,4]=>0011001
[1,2,7,8,6,3,5,4]=>0011010
[1,5,7,8,6,2,3,4]=>0100010
[1,3,7,6,2,8,4,5]=>0101010
[1,2,8,4,7,6,3,5]=>0011010
[1,2,5,8,7,6,3,4]=>0010011
[1,2,6,8,7,5,3,4]=>0010101
[1,2,7,8,6,5,3,4]=>0010110
[5,2,6,7,3,4,8,1]=>1110000
[5,6,2,1,7,8,3,4]=>1110000
[5,6,2,1,4,8,7,3]=>1110001
[2,6,1,4,5,8,7,3]=>1010001
[5,4,2,7,6,3,8,1]=>1111010
[2,3,7,6,4,5,8,1]=>1001010
[2,6,1,7,5,8,3,4]=>1010100
[5,1,2,7,8,4,3,6]=>1011000
[2,6,1,7,4,8,3,5]=>1011000
[3,6,4,1,7,8,2,5]=>1101000
[5,4,6,1,7,8,2,3]=>1101000
[5,4,6,1,3,8,7,2]=>1101001
[3,6,4,1,5,8,7,2]=>1101001
[2,6,1,5,4,8,7,3]=>1011001
[2,6,1,4,7,8,5,3]=>1010100
[5,1,2,4,8,7,6,3]=>1010011
[2,1,5,3,8,6,4,7]=>1011010
[5,1,2,4,8,6,3,7]=>1010010
[5,6,3,1,4,8,2,7]=>1110000
[2,5,4,3,1,8,6,7]=>1011010
[5,4,6,3,1,8,7,2]=>1111001
[2,1,3,7,8,6,4,5]=>1001010
[5,1,4,2,8,6,7,3]=>1110010
[1,2,3,8,6,7,4,5]=>0001010
[1,2,3,8,7,5,4,6]=>0001101
[1,2,3,8,7,4,5,6]=>0001001
[2,1,3,6,8,7,4,5]=>1001001
[3,1,6,2,8,7,5,4]=>1101101
[6,8,1,3,2,5,4,7]=>1101000
[6,8,1,4,2,5,3,7]=>1110000
[7,8,3,6,1,4,2,5]=>1110000
[7,8,2,5,1,4,3,6]=>1110000
[7,8,1,4,3,6,2,5]=>1110000
[5,8,1,4,3,7,2,6]=>1110000
[6,8,2,5,1,4,3,7]=>1110000
[6,8,2,5,3,7,1,4]=>1110000
[2,5,4,7,6,8,1,3]=>1001010
[2,6,1,4,3,7,5,8]=>1010100
[2,6,1,5,3,7,4,8]=>1011000
[2,6,4,7,5,8,1,3]=>1001100
[5,8,2,6,4,7,1,3]=>1101000
[6,8,3,7,1,4,2,5]=>1110000
[5,8,1,3,2,6,4,7]=>1101000
[5,8,4,7,1,3,2,6]=>1101000
[6,8,4,7,1,3,2,5]=>1101000
[6,8,5,7,1,3,2,4]=>1100100
[5,7,6,8,2,4,1,3]=>1100010
[4,7,5,8,1,3,2,6]=>1100100
[4,7,1,3,2,6,5,8]=>1100100
[3,7,1,4,2,6,5,8]=>1100100
[3,7,6,8,1,4,2,5]=>1100010
[4,7,6,8,2,5,1,3]=>1100010
[4,7,5,8,3,6,1,2]=>1010100
[4,7,5,8,2,6,1,3]=>1100100
[3,7,4,8,2,6,1,5]=>1101000
[3,7,1,5,2,6,4,8]=>1101000
[3,7,2,6,1,5,4,8]=>1101000
[3,7,2,6,5,8,1,4]=>1100100
[4,7,3,6,5,8,1,2]=>1010100
[2,6,5,8,4,7,1,3]=>1001100
[2,6,3,7,1,5,4,8]=>1011000
[7,6,4,8,5,2,3,1]=>1101110
[6,7,4,3,5,1,8,2]=>1111000
[6,7,3,5,4,8,2,1]=>1111000
[6,8,3,7,5,2,4,1]=>1110100
[7,6,3,5,8,2,4,1]=>1110010
[7,6,2,8,4,1,5,3]=>1111010
[7,6,3,4,8,2,5,1]=>1110010
[6,8,3,7,4,5,2,1]=>1111000
[6,7,3,5,8,4,2,1]=>1111000
[5,7,8,3,6,2,1,4]=>1110000
[6,3,4,8,7,2,5,1]=>1110001
[6,3,8,4,7,2,1,5]=>1111000
[6,3,4,7,5,8,2,1]=>1110100
[6,3,5,7,8,4,2,1]=>1111000
[5,7,3,6,8,2,1,4]=>1110000
[5,6,7,3,4,1,8,2]=>1110000
[4,6,7,8,3,5,2,1]=>1110000
[4,7,3,5,6,8,2,1]=>1110000
[5,3,4,7,8,2,1,6]=>1110000
[5,3,8,2,4,1,6,7]=>1110000
[5,3,4,8,2,6,1,7]=>1110000
[4,8,3,6,2,5,7,1]=>1110000
[4,8,3,5,7,2,6,1]=>1110000
[4,8,3,5,6,7,2,1]=>1110000
[4,7,8,3,5,6,2,1]=>1110000
[4,7,8,3,6,2,5,1]=>1110000
[4,8,3,6,7,2,5,1]=>1110000
[4,8,3,7,2,5,6,1]=>1110000
[5,8,3,7,2,6,4,1]=>1111000
[5,7,3,4,8,2,1,6]=>1110000
[5,8,4,2,3,1,6,7]=>1101000
[5,8,4,2,3,1,7,6]=>1101010
[6,4,8,5,3,7,2,1]=>1111100
[6,4,2,7,3,1,8,5]=>1111100
[6,4,3,7,8,5,2,1]=>1111100
[6,4,5,3,7,1,8,2]=>1111000
[5,7,4,2,3,1,6,8]=>1101000
[5,6,3,7,1,8,2,4]=>1110000
[5,6,3,4,8,2,1,7]=>1110000
[6,3,5,7,4,8,2,1]=>1111000
[6,3,5,4,7,8,2,1]=>1111000
[6,4,3,5,7,1,8,2]=>1111000
[6,4,2,5,1,7,3,8]=>1111000
[5,3,4,7,2,6,1,8]=>1110000
[4,7,3,6,2,5,8,1]=>1110000
[4,7,3,6,8,2,5,1]=>1110000
[4,6,7,3,5,8,2,1]=>1110000
[4,5,7,8,3,6,2,1]=>1110000
[4,5,8,3,7,2,6,1]=>1110000
[5,3,4,6,8,2,1,7]=>1110000
[5,3,6,7,1,8,2,4]=>1110000
[5,3,4,6,7,1,8,2]=>1110000
[4,6,3,5,7,8,2,1]=>1110000
[4,5,7,3,6,8,2,1]=>1110000
[7,1,5,8,4,2,3,6]=>1101000
[8,1,5,7,4,2,3,6]=>1101000
[7,1,4,5,8,2,3,6]=>1100000
[7,4,1,6,2,8,3,5]=>1111000
[8,4,1,7,2,6,3,5]=>1111000
[8,1,4,7,5,2,3,6]=>1100100
[8,1,5,4,7,2,3,6]=>1101000
[2,1,7,5,8,3,4,6]=>1010100
[7,1,5,4,8,2,3,6]=>1101000
[7,1,4,8,5,2,3,6]=>1100100
[7,8,3,1,2,4,6,5]=>1010100
[8,7,1,6,4,2,3,5]=>1101001
[8,6,1,7,4,2,3,5]=>1101010
[7,6,1,8,4,2,3,5]=>1101010
[7,3,8,1,2,4,6,5]=>1010100
[8,3,7,1,2,4,6,5]=>1010100
[8,3,6,1,2,4,7,5]=>1010100
[8,3,7,5,1,2,4,6]=>1010100
[7,3,6,1,2,4,8,5]=>1010100
[6,7,1,8,4,2,3,5]=>1101000
[6,8,1,7,4,2,3,5]=>1101000
[7,1,8,4,5,2,3,6]=>1101000
[7,6,3,1,2,4,8,5]=>1010110
[6,1,2,3,8,7,5,4]=>1001101
[6,8,3,1,2,7,4,5]=>1011000
[6,7,3,1,2,8,4,5]=>1011000
[6,7,1,4,2,3,8,5]=>1100100
[4,3,6,8,5,7,1,2]=>1010100
[6,1,2,5,4,8,3,7]=>1011000
[3,2,8,5,4,1,7,6]=>1101110
[7,8,2,1,4,6,3,5]=>1110000
[2,4,8,5,1,3,6,7]=>1000100
[3,5,6,1,8,4,2,7]=>1101000
[1,3,6,8,7,4,2,5]=>0101001
[1,2,8,5,7,3,4,6]=>0010100
[3,1,5,6,4,8,7,2]=>1101001
[1,3,6,2,5,7,8,4]=>0101000
[3,6,1,4,2,7,8,5]=>1100100
[1,3,6,5,2,7,8,4]=>0101100
[1,2,6,4,3,8,5,7]=>0011100
[1,2,6,3,5,8,7,4]=>0011001
[2,3,5,1,8,4,7,6]=>1001010
[1,2,7,4,6,8,3,5]=>0011000
[2,3,7,5,1,8,4,6]=>1001100
[4,7,2,5,3,8,6,1]=>1110010
[3,1,7,5,4,8,6,2]=>1101110
[1,2,7,6,4,8,5,3]=>0011110
[1,2,7,3,6,8,5,4]=>0011100
[3,1,5,4,8,7,6,2]=>1101011
[1,2,6,8,5,4,7,3]=>0011100
[3,5,7,4,8,2,1,6]=>1101000
[2,4,7,6,8,3,1,5]=>1010010
[1,4,6,8,3,5,2,7]=>0110000
[1,3,6,8,5,2,4,7]=>0100100
[1,2,6,8,5,4,3,7]=>0011100
[1,2,5,8,4,3,7,6]=>0011010
[1,3,6,8,2,5,4,7]=>0101000
[1,4,6,8,3,2,5,7]=>0110000
[2,3,6,5,8,1,7,4]=>1001100
[3,5,4,6,8,2,1,7]=>1101000
[3,5,4,6,8,1,2,7]=>1001000
[1,2,4,7,5,8,3,6]=>0010100
[3,6,4,7,1,8,5,2]=>1101100
[1,2,6,7,3,8,5,4]=>0011100
[1,2,5,7,3,8,6,4]=>0011010
[3,1,5,7,6,8,4,2]=>1101010
[3,5,4,6,8,2,7,1]=>1101000
[4,2,6,1,8,7,5,3]=>1110101
[1,2,7,4,6,8,5,3]=>0011100
[1,2,7,5,6,8,4,3]=>0011100
[3,1,6,7,5,8,4,2]=>1101100
[4,6,2,7,5,8,3,1]=>1110100
[3,5,7,4,8,2,6,1]=>1101000
[1,3,6,8,2,5,7,4]=>0101000
[1,3,5,8,2,7,4,6]=>0101000
[1,2,5,8,4,7,6,3]=>0011010
[1,2,4,8,7,3,6,5]=>0010101
[1,2,5,8,7,4,3,6]=>0011001
[1,3,5,8,7,2,4,6]=>0100001
[2,3,7,6,8,5,1,4]=>1000110
[5,7,1,2,8,6,4,3]=>1011010
[3,1,7,6,8,5,4,2]=>1101110
[1,2,6,8,5,7,4,3]=>0011100
[1,2,5,8,7,4,6,3]=>0011001
[1,2,4,8,7,6,3,5]=>0010011
[3,2,7,4,6,8,1,5]=>1101000
[5,3,6,2,7,1,4,8]=>1110000
[2,6,3,4,7,1,5,8]=>1010000
[2,7,3,4,5,8,1,6]=>1010000
[4,7,6,2,3,8,1,5]=>1100010
[7,3,5,2,4,8,1,6]=>1110000
[7,6,2,4,5,8,1,3]=>1100010
[6,5,2,3,4,8,1,7]=>1100100
[5,3,1,2,8,4,7,6]=>1011010
[6,5,2,3,7,1,4,8]=>1100100
[5,2,1,7,3,4,6,8]=>1110000
[5,2,1,8,3,4,6,7]=>1110000
[6,3,2,8,4,5,7,1]=>1111000
[7,3,1,2,8,4,6,5]=>1011100
[6,2,3,1,8,4,7,5]=>1101100
[8,3,5,2,7,1,4,6]=>1110000
[8,6,2,4,7,1,5,3]=>1110010
[8,2,1,7,3,4,5,6]=>1110000
[8,6,3,7,2,4,5,1]=>1110010
[8,2,7,3,4,5,6,1]=>1110000
[8,1,6,2,3,4,5,7]=>1100000
[8,1,7,3,4,5,6,2]=>1110000
[8,6,1,7,2,4,5,3]=>1110010
[1,7,5,8,2,3,6,4]=>0101100
[7,2,1,8,3,4,5,6]=>1110000
[1,7,8,3,4,5,6,2]=>0110000
[1,6,2,8,4,5,7,3]=>0111000
[4,1,3,6,8,2,7,5]=>1100100
[4,6,3,8,7,1,2,5]=>1010001
[6,4,5,8,7,1,2,3]=>1001001
[5,3,4,8,7,1,2,6]=>1010001
[3,2,8,7,1,4,6,5]=>1100101
[3,1,8,7,2,4,6,5]=>1100101
[5,3,7,6,1,2,4,8]=>1010010
[1,8,3,7,2,4,5,6]=>0110000
[3,8,1,7,2,4,5,6]=>1100000
[6,8,2,3,5,1,4,7]=>1100000
[4,7,8,2,6,1,3,5]=>1100000
[6,2,8,7,1,4,5,3]=>1110001
[3,8,7,1,4,5,6,2]=>1100001
[2,8,6,1,3,4,5,7]=>1000010
[2,7,6,1,3,4,5,8]=>1000010
[1,7,6,2,3,4,5,8]=>0100010
[1,8,6,2,3,4,5,7]=>0100010
[2,8,7,3,4,5,6,1]=>1010001
[3,8,7,2,4,5,6,1]=>1100001
[7,8,3,6,2,4,5,1]=>1110000
[1,5,8,7,2,3,6,4]=>0101001
[1,7,3,6,5,2,8,4]=>0111100
[8,6,2,5,4,1,7,3]=>1111010
[3,2,6,4,7,5,1,8]=>1101100
[6,2,3,7,5,4,1,8]=>1101100
[1,3,4,7,6,2,8,5]=>0100110
[2,8,3,6,1,7,5,4]=>1011100
[8,7,2,5,1,6,4,3]=>1111001
[3,8,2,6,5,1,7,4]=>1101100
[7,8,2,5,4,1,6,3]=>1111000
[4,8,5,2,6,1,7,3]=>1110100
[4,5,1,3,7,2,8,6]=>1100010
[6,1,3,7,5,2,8,4]=>1101100
[7,1,3,6,2,8,5,4]=>1101100
[8,1,3,6,2,7,5,4]=>1101100
[1,2,4,7,3,8,6,5]=>0010110
[7,1,8,2,6,5,4,3]=>1111100
[4,1,7,8,2,6,5,3]=>1110100
[3,4,8,6,5,1,7,2]=>1100110
[8,3,7,5,1,6,4,2]=>1111100
[1,4,8,6,2,7,5,3]=>0110110
[8,4,6,7,1,5,3,2]=>1111000
[3,4,6,5,1,2,8,7]=>1000101
[7,3,5,1,2,8,6,4]=>1011010
[1,4,6,2,3,8,7,5]=>0100101
[1,3,2,7,4,8,6,5]=>0101110
[7,2,1,6,3,8,5,4]=>1111100
[4,5,2,1,7,3,8,6]=>1110010
[5,6,7,1,2,8,4,3]=>1011000
[4,7,5,1,2,8,6,3]=>1010110
[3,7,1,6,2,8,5,4]=>1101100
[7,6,1,2,8,5,4,3]=>1011110
[2,7,1,3,8,6,5,4]=>1001110
[8,6,1,2,7,5,4,3]=>1011110
[1,7,2,3,8,6,5,4]=>0101110
[8,7,1,2,6,5,4,3]=>1011101
[7,8,1,2,6,5,4,3]=>1011100
[3,8,1,6,2,7,5,4]=>1101100
[4,8,5,1,2,7,6,3]=>1010110
[1,8,2,7,4,3,5,6]=>0111000
[1,8,6,4,7,2,3,5]=>0101010
[1,8,4,2,6,3,5,7]=>0111000
[7,4,8,1,5,2,3,6]=>1101000
[4,1,7,2,6,3,5,8]=>1110000
[5,1,7,4,3,6,2,8]=>1111000
[1,8,5,4,3,7,2,6]=>0111100
[1,8,4,2,5,3,7,6]=>0111010
[1,8,5,4,2,6,7,3]=>0111100
[7,4,8,2,1,3,5,6]=>1101000
[4,1,7,3,2,5,6,8]=>1110000
[7,5,4,8,2,3,6,1]=>1101100
[6,4,8,2,1,3,7,5]=>1101100
[7,3,8,1,5,6,2,4]=>1110000
[3,1,7,2,6,8,4,5]=>1101000
[5,1,7,4,2,6,8,3]=>1111000
[5,4,3,7,1,2,8,6]=>1011010
[4,3,1,6,2,5,7,8]=>1110000
[6,5,4,3,7,1,8,2]=>1111100
[5,4,2,7,1,6,8,3]=>1111000
[6,5,1,7,3,8,2,4]=>1110100
[6,3,2,8,5,7,1,4]=>1110100
[6,5,4,2,8,3,7,1]=>1111100
[5,4,8,2,1,7,3,6]=>1111000
[5,4,3,8,1,6,2,7]=>1111000
[5,4,3,7,1,6,2,8]=>1111000
[7,2,8,6,3,1,4,5]=>1110010
[2,1,7,8,3,6,4,5]=>1011000
[4,2,1,6,7,3,5,8]=>1110000
[4,3,1,5,2,7,6,8]=>1110010
[5,4,2,7,3,8,1,6]=>1111000
[3,1,6,2,8,7,4,5]=>1101001
[6,3,1,7,8,5,2,4]=>1110100
[5,4,1,7,8,2,6,3]=>1111000
[6,5,4,1,7,8,3,2]=>1111100
[5,4,3,1,6,7,2,8]=>1111000
[5,4,2,6,3,8,7,1]=>1111001
[4,3,1,5,2,6,8,7]=>1110001
[5,4,2,1,6,7,8,3]=>1111000
[5,4,3,1,6,7,8,2]=>1111000
[7,8,2,4,5,1,3,6]=>1100000
[4,6,7,2,5,1,3,8]=>1100000
[7,8,1,3,2,4,5,6]=>1100000
[7,8,4,1,5,2,3,6]=>1101000
[3,6,7,2,1,4,5,8]=>1100000
[5,2,3,6,1,4,7,8]=>1100000
[2,5,3,6,1,4,7,8]=>1010000
[6,4,7,1,5,2,3,8]=>1101000
[6,2,7,3,1,4,5,8]=>1110000
[3,5,4,6,7,8,1,2]=>1001000
[1,5,4,6,7,2,3,8]=>0101000
[1,6,7,3,2,4,5,8]=>0110000
[1,5,3,6,2,4,7,8]=>0110000
[5,1,3,6,2,4,7,8]=>1100000
[5,2,4,6,7,1,3,8]=>1100000
[2,6,7,4,5,1,3,8]=>1001000
[4,2,5,6,7,1,3,8]=>1100000
[4,5,2,6,7,1,3,8]=>1100000
[5,3,1,6,2,4,7,8]=>1110000
[6,1,7,3,2,4,5,8]=>1110000
[6,1,7,4,5,2,3,8]=>1101000
[6,3,7,4,5,8,1,2]=>1011000
[5,4,1,6,7,2,3,8]=>1101000
[5,2,1,6,3,4,7,8]=>1110000
[1,3,6,7,5,2,8,4]=>0101100
[7,3,4,1,6,2,5,8]=>1110000
[7,3,4,1,6,5,2,8]=>1110100
[7,3,4,1,5,2,6,8]=>1110000
[1,3,6,7,2,5,8,4]=>0101000
[4,3,1,7,2,6,8,5]=>1110100
[5,6,1,4,7,3,8,2]=>1110000
[5,3,2,1,7,4,8,6]=>1111010
[1,3,4,5,8,7,2,6]=>0100001
[6,3,4,5,8,1,7,2]=>1110000
[2,4,5,1,6,8,7,3]=>1010001
[3,1,2,5,6,8,7,4]=>1001001
[4,3,2,5,6,8,1,7]=>1110000
[3,1,4,6,5,8,2,7]=>1100100
[2,3,4,5,8,6,1,7]=>1000010
[4,3,1,7,6,5,8,2]=>1110110
[1,4,5,2,6,8,7,3]=>0110001
[3,7,5,2,6,8,1,4]=>1100100
[3,7,5,2,6,8,4,1]=>1101100
[5,6,1,2,7,4,8,3]=>1011000
[6,3,5,2,4,7,8,1]=>1110000
[5,3,2,1,4,7,8,6]=>1110010
[5,3,1,4,2,7,8,6]=>1110010
[5,3,1,2,4,7,8,6]=>1010010
[7,1,5,2,6,8,4,3]=>1111000
[7,1,5,2,6,8,3,4]=>1110000
[1,7,4,6,5,8,3,2]=>0111100
[2,7,4,6,1,8,3,5]=>1011000
[2,7,4,6,1,8,5,3]=>1011100
[2,3,6,7,1,5,8,4]=>1001000
[2,3,6,7,5,1,8,4]=>1001100
[4,3,2,6,7,1,8,5]=>1110100
[7,3,2,5,6,8,1,4]=>1110000
[7,1,5,4,6,8,2,3]=>1101000
[2,7,4,6,5,8,1,3]=>1001100
[7,3,4,5,8,1,2,6]=>1010000
[1,3,4,5,8,6,2,7]=>0100010
[1,3,4,5,8,2,7,6]=>0100010
[7,1,5,4,6,8,3,2]=>1111000
[7,3,2,5,6,8,4,1]=>1111000
[5,7,4,6,1,8,3,2]=>1111000
[6,3,4,5,8,1,2,7]=>1010000
[7,3,4,5,8,2,6,1]=>1110000
[6,2,1,7,3,5,4,8]=>1111000
[2,1,8,6,3,5,4,7]=>1011010
[2,7,3,1,5,4,6,8]=>1011000
[2,6,3,1,4,8,5,7]=>1010100
[4,2,1,8,3,6,7,5]=>1110100
[6,2,1,7,3,5,8,4]=>1111000
[2,7,3,1,4,8,5,6]=>1010100
[3,2,1,5,7,8,4,6]=>1101000
[2,4,7,5,1,6,8,3]=>1010100
[4,3,6,8,5,1,7,2]=>1110100
[2,1,6,8,3,7,4,5]=>1011000
[3,2,1,5,6,8,4,7]=>1101000
[2,1,7,3,6,4,5,8]=>1011000
[2,1,6,3,5,8,4,7]=>1011000
[2,6,1,8,3,5,4,7]=>1011000
[2,7,3,1,5,6,4,8]=>1011000
[2,4,7,5,1,6,3,8]=>1010100
[8,2,4,1,7,5,3,6]=>1110100
[2,4,7,1,8,5,3,6]=>1010100
[2,4,8,5,1,6,3,7]=>1010100
[6,2,1,7,3,4,8,5]=>1110100
[6,2,1,7,8,3,5,4]=>1111000
[2,7,1,8,3,5,6,4]=>1011000
[3,2,1,6,7,4,5,8]=>1101000
[3,2,1,7,4,5,6,8]=>1101000
[2,1,8,3,7,4,5,6]=>1011000
[2,4,8,5,1,6,7,3]=>1010100
[4,3,8,5,6,1,7,2]=>1110100
[3,2,1,8,4,5,6,7]=>1101000
[1,6,8,3,7,2,4,5]=>0110000
[3,8,1,5,7,2,4,6]=>1100000
[1,2,6,8,4,7,3,5]=>0011000
[6,1,5,8,2,4,7,3]=>1110000
[1,2,4,8,3,6,7,5]=>0010100
[4,1,2,7,8,3,6,5]=>1010100
[5,3,8,4,7,6,1,2]=>1011010
[8,7,1,2,5,4,6,3]=>1011001
[5,8,1,2,3,7,6,4]=>1001010
[1,2,8,4,3,5,7,6]=>0011010
[1,2,5,3,7,6,4,8]=>0011010
[6,1,2,8,7,4,5,3]=>1011001
[7,1,6,2,8,4,5,3]=>1111000
[1,2,6,3,8,5,4,7]=>0011100
[1,2,8,5,3,6,4,7]=>0011100
[1,2,7,3,8,5,4,6]=>0011100
[1,6,2,8,4,3,5,7]=>0111000
[1,6,4,2,7,3,5,8]=>0111000
[1,8,6,3,2,4,5,7]=>0110010
[3,1,7,8,6,2,4,5]=>1100010
[1,8,7,3,5,6,2,4]=>0110001
[1,3,2,8,7,4,5,6]=>0101001
[1,2,8,4,3,7,5,6]=>0011100
[8,5,1,7,2,4,6,3]=>1110100
[3,8,6,4,7,5,1,2]=>1001110
[6,1,8,2,7,4,5,3]=>1111000
[1,2,7,5,3,6,4,8]=>0011100
[1,2,6,3,7,5,4,8]=>0011100
[1,2,3,7,5,4,8,6]=>0001110
[3,7,4,8,6,5,1,2]=>1001110
[1,8,2,7,6,4,5,3]=>0111010
[7,4,6,3,8,5,1,2]=>1011100
[8,4,6,2,7,5,3,1]=>1111100
[6,5,7,8,4,1,3,2]=>1101100
[7,5,6,8,2,4,1,3]=>1100100
[7,4,6,2,8,5,1,3]=>1101100
[4,3,2,6,8,5,1,7]=>1110100
[3,5,6,8,2,4,1,7]=>1100000
[2,6,7,8,1,4,5,3]=>1010000
[3,6,7,8,1,4,2,5]=>1100000
[3,5,7,8,2,1,4,6]=>1100000
[2,6,7,8,1,4,3,5]=>1010000
[2,5,7,8,3,1,4,6]=>1010000
[2,4,7,3,8,1,5,6]=>1010000
[6,4,7,3,8,1,5,2]=>1111000
[6,4,7,3,8,1,2,5]=>1011000
[7,4,6,3,8,2,1,5]=>1111000
[6,3,2,5,4,8,1,7]=>1111000
[6,4,5,2,3,8,1,7]=>1101000
[5,4,6,3,8,2,1,7]=>1111000
[5,4,7,3,8,1,6,2]=>1111000
[2,5,7,8,3,1,6,4]=>1011000
[4,5,7,8,3,1,2,6]=>1010000
[4,5,6,8,2,3,1,7]=>1100000
[5,4,6,2,8,3,1,7]=>1111000
[5,3,2,6,8,4,1,7]=>1111000
[5,4,7,2,8,1,3,6]=>1101000
[4,5,7,8,2,1,3,6]=>1100000
[4,6,7,8,1,3,2,5]=>1100000
[4,6,7,8,1,3,5,2]=>1100000
[2,6,7,8,1,3,5,4]=>1001000
[2,6,7,8,1,5,3,4]=>1010000
[4,6,7,8,1,5,2,3]=>1100000
[4,6,7,8,1,2,5,3]=>1010000
[5,3,2,7,8,1,6,4]=>1111000
[4,3,2,7,8,1,6,5]=>1110100
[3,5,7,8,2,1,6,4]=>1101000
[3,6,7,8,1,5,4,2]=>1101000
[2,6,7,8,1,5,4,3]=>1011000
[4,5,8,3,6,7,1,2]=>1010000
[4,5,8,3,7,6,1,2]=>1010010
[4,2,8,3,7,1,6,5]=>1110100
[7,2,3,4,8,1,5,6]=>1100000
[7,6,3,4,8,5,1,2]=>1010110
[7,6,3,5,8,4,1,2]=>1011010
[7,6,3,8,4,5,1,2]=>1011010
[7,2,3,8,5,1,4,6]=>1100100
[2,6,4,8,1,5,7,3]=>1011000
[7,2,3,8,4,1,5,6]=>1101000
[7,8,2,3,6,1,4,5]=>1100000
[4,2,6,3,7,1,5,8]=>1110000
[7,2,3,5,8,1,6,4]=>1101000
[7,2,3,8,4,1,6,5]=>1101100
[2,6,4,8,1,3,7,5]=>1001100
[3,6,4,8,1,7,5,2]=>1101100
[7,6,5,1,2,3,8,4]=>1001110
[7,6,5,1,4,2,8,3]=>1110110
[7,8,5,4,1,2,6,3]=>1011100
[3,5,6,4,1,2,8,7]=>1001001
[7,6,5,1,2,4,3,8]=>1010110
[7,6,5,1,2,4,8,3]=>1010110
[7,6,5,1,3,2,4,8]=>1100110
[2,6,4,3,1,8,7,5]=>1011101
[3,5,8,4,1,2,7,6]=>1001010
[3,5,8,4,1,2,6,7]=>1001000
[3,5,8,4,1,6,2,7]=>1101000
[2,5,8,4,1,7,3,6]=>1011000
[3,6,4,2,1,7,5,8]=>1101100
[3,5,6,4,1,8,7,2]=>1101001
[2,6,4,5,1,3,7,8]=>1001000
[7,6,5,1,4,3,8,2]=>1110110
[7,6,5,1,2,8,3,4]=>1010110
[7,6,5,1,8,2,4,3]=>1110110
[7,6,5,1,8,2,3,4]=>1100110
[7,6,5,1,8,3,2,4]=>1110110
[7,6,5,1,4,8,2,3]=>1100110
[3,6,4,5,1,7,2,8]=>1101000
[2,5,6,4,1,7,8,3]=>1011000
[2,5,6,4,1,7,3,8]=>1011000
[3,6,4,5,1,7,8,2]=>1101000
[7,6,5,1,4,8,3,2]=>1110110
[7,6,5,1,8,3,4,2]=>1110110
[7,6,5,1,8,4,2,3]=>1101110
[6,7,4,2,5,3,1,8]=>1111000
[7,6,4,8,3,1,5,2]=>1111010
[7,4,8,5,6,1,3,2]=>1101100
[7,4,2,5,6,3,1,8]=>1111000
[4,2,7,5,6,3,1,8]=>1110100
[4,7,3,5,6,2,1,8]=>1110000
[1,6,8,5,2,7,4,3]=>0111100
[6,2,8,5,1,7,4,3]=>1111100
[6,7,4,8,2,1,5,3]=>1111000
[3,2,7,8,6,1,5,4]=>1101010
[6,8,4,1,2,3,7,5]=>1001100
[1,8,2,5,6,4,3,7]=>0111000
[6,1,8,5,3,7,4,2]=>1111100
[3,8,1,5,2,7,6,4]=>1101010
[8,2,1,5,3,7,6,4]=>1111010
[8,1,6,5,3,7,2,4]=>1110100
[7,1,4,6,3,2,8,5]=>1110100
[3,2,6,4,1,7,8,5]=>1101100
[7,6,4,3,1,2,8,5]=>1011110
[8,6,3,5,1,7,2,4]=>1110010
[4,5,3,1,6,7,8,2]=>1110000
[3,5,2,1,6,7,8,4]=>1101000
[5,2,3,1,6,7,8,4]=>1101000
[1,5,3,2,6,7,8,4]=>0111000
[8,2,7,5,6,1,3,4]=>1100100
[1,7,4,6,2,3,8,5]=>0101100
[7,6,4,2,1,5,8,3]=>1111010
[5,7,4,6,1,3,8,2]=>1101000
[8,6,4,7,3,1,2,5]=>1011010
[5,2,4,3,7,1,8,6]=>1110010
[8,6,4,1,3,5,2,7]=>1101010
[6,7,4,1,5,3,8,2]=>1111000
[7,5,4,1,2,6,8,3]=>1011100
[1,8,2,5,3,7,6,4]=>0111010
[3,8,1,5,6,4,2,7]=>1101000
[7,6,4,1,5,2,8,3]=>1111010
[8,6,1,5,4,7,2,3]=>1101010
[5,2,1,4,6,7,8,3]=>1110000
[5,4,1,3,6,7,8,2]=>1101000
[8,4,1,5,3,7,2,6]=>1111000
[7,5,4,1,3,2,8,6]=>1101110
[3,2,5,1,4,7,8,6]=>1100010
[5,1,3,4,6,7,8,2]=>1100000
[3,8,1,7,5,6,4,2]=>1101100
[8,2,5,7,3,6,4,1]=>1111000
[1,8,6,7,5,3,4,2]=>0110110
[8,2,6,7,5,3,4,1]=>1110100
[5,4,8,6,2,3,7,1]=>1101010
[2,7,6,1,3,5,4,8]=>1001010
[2,8,6,1,3,5,4,7]=>1001010
[5,7,4,1,8,6,3,2]=>1111010
[5,6,4,2,8,3,7,1]=>1111000
[5,6,4,2,7,3,1,8]=>1111000
[5,8,1,4,6,3,7,2]=>1110000
[3,6,7,4,5,8,2,1]=>1101000
[5,4,6,1,7,8,3,2]=>1111000
[5,6,4,1,8,7,3,2]=>1111001
[3,5,8,4,6,7,2,1]=>1101000
[3,6,8,4,5,7,2,1]=>1101000
[3,7,8,4,5,6,2,1]=>1101000
[3,7,1,5,4,6,2,8]=>1101000
[3,8,1,5,4,6,7,2]=>1101000
[3,7,1,5,4,6,8,2]=>1101000
[6,7,1,4,5,3,8,2]=>1110000
[5,7,1,4,6,3,8,2]=>1110000
[5,4,7,2,8,3,1,6]=>1111000
[5,4,7,2,8,3,6,1]=>1111000
[5,6,4,2,8,3,1,7]=>1111000
[5,8,1,4,6,3,2,7]=>1110000
[3,8,1,5,4,6,2,7]=>1101000
[3,6,1,5,4,2,7,8]=>1101000
[3,6,1,5,4,8,2,7]=>1101000
[6,8,3,1,4,2,5,7]=>1110000
[7,3,8,1,4,2,5,6]=>1110000
[3,6,1,5,4,7,8,2]=>1101000
[3,4,1,2,7,6,5,8]=>1000110
[3,4,1,2,6,8,7,5]=>1000101
[7,8,1,4,5,3,2,6]=>1110000
[3,8,1,5,4,7,2,6]=>1101000
[3,6,1,5,4,8,7,2]=>1101001
[3,6,1,5,4,7,2,8]=>1101000
[6,7,3,1,4,2,5,8]=>1110000
[6,8,3,1,4,2,7,5]=>1110100
[7,8,3,1,4,6,2,5]=>1110000
[7,8,4,2,6,5,1,3]=>1101100
[6,5,8,7,3,4,2,1]=>1110101
[7,8,3,1,4,6,5,2]=>1110100
[6,7,3,1,4,5,2,8]=>1110000
[3,7,1,5,4,2,6,8]=>1101000
[3,8,1,5,4,2,7,6]=>1101010
[5,8,1,4,7,3,6,2]=>1110000
[6,3,7,1,4,8,5,2]=>1110100
[3,7,1,5,4,8,6,2]=>1101010
[3,7,1,5,4,2,8,6]=>1101010
[6,7,3,1,4,5,8,2]=>1110000
[7,3,8,1,4,5,2,6]=>1110000
[6,8,3,1,4,5,2,7]=>1110000
[3,8,1,5,4,2,6,7]=>1101000
[2,3,5,4,1,8,6,7]=>1001010
[2,3,6,4,8,1,5,7]=>1001000
[1,8,4,6,3,5,2,7]=>0111000
[5,4,8,6,2,1,3,7]=>1101010
[2,3,6,8,1,5,4,7]=>1001000
[2,5,6,1,4,7,8,3]=>1010000
[2,5,6,1,4,7,3,8]=>1010000
[2,7,6,1,8,5,4,3]=>1011110
[2,7,6,8,1,4,5,3]=>1010010
[5,7,8,6,2,3,4,1]=>1100010
[2,7,6,1,8,5,3,4]=>1010110
[6,3,5,1,7,2,4,8]=>1110000
[2,3,4,7,6,1,5,8]=>1000010
[7,3,5,8,4,1,2,6]=>1011000
[1,8,4,5,2,7,3,6]=>0111000
[1,8,4,5,2,7,6,3]=>0111010
[7,3,5,8,4,1,6,2]=>1111000
[2,7,6,4,8,5,1,3]=>1001110
[7,3,5,4,6,8,1,2]=>1011000
[6,3,5,4,7,1,8,2]=>1111000
[6,3,5,4,7,1,2,8]=>1011000
[3,7,1,6,8,5,2,4]=>1100100
[2,3,1,8,6,4,7,5]=>1001110
[1,8,4,3,6,2,5,7]=>0111000
[2,3,1,8,6,4,5,7]=>1001010
[3,7,1,6,8,5,4,2]=>1101100
[6,3,5,4,7,2,1,8]=>1111000
[7,3,5,4,6,8,2,1]=>1111000
[2,7,6,4,8,5,3,1]=>1011110
[1,8,4,5,2,6,3,7]=>0111000
[6,4,8,5,3,1,2,7]=>1011100
[7,3,5,8,4,6,2,1]=>1111000
[2,3,4,6,5,8,1,7]=>1000100
[2,3,4,7,5,1,8,6]=>1000110
[2,3,4,7,5,1,6,8]=>1000100
[2,3,4,7,1,6,5,8]=>1000100
[2,3,4,7,1,6,8,5]=>1000100
[2,3,4,6,1,8,7,5]=>1000101
[6,3,5,8,4,2,7,1]=>1111000
[1,8,4,5,2,3,6,7]=>0101000
[7,4,8,5,3,2,6,1]=>1111100
[3,4,8,7,5,2,6,1]=>1100101
[3,2,8,6,1,5,4,7]=>1101010
[8,7,3,6,4,2,5,1]=>1111001
[3,8,7,2,5,4,6,1]=>1101001
[8,7,2,4,5,6,3,1]=>1110001
[5,3,6,2,4,8,7,1]=>1110001
[3,5,2,8,6,1,4,7]=>1100010
[3,7,2,5,1,4,8,6]=>1100010
[5,1,8,6,2,3,4,7]=>1100010
[2,5,4,1,8,6,3,7]=>1011010
[3,7,6,1,8,2,5,4]=>1101010
[8,2,3,6,1,4,7,5]=>1100100
[1,8,2,6,3,4,7,5]=>0110100
[7,1,3,6,4,8,2,5]=>1101000
[8,2,1,3,5,7,4,6]=>1101000
[7,5,4,1,3,8,2,6]=>1101100
[7,3,8,5,4,1,2,6]=>1011100
[7,2,3,6,1,4,8,5]=>1100100
[1,3,7,2,5,8,4,6]=>0101000
[1,7,2,3,5,8,4,6]=>0101000
[7,4,8,1,3,6,2,5]=>1101000
[8,6,1,4,7,3,2,5]=>1110010
[2,6,3,7,1,4,8,5]=>1010100
[2,6,3,8,1,4,7,5]=>1010100
[7,5,4,8,1,3,2,6]=>1101100
[8,5,4,7,1,3,2,6]=>1101100
[2,3,1,8,5,4,6,7]=>1001100
[8,5,1,7,6,3,4,2]=>1110110
[3,4,7,6,1,8,5,2]=>1100110
[3,5,2,6,7,1,8,4]=>1101000
[3,2,8,4,7,5,1,6]=>1101100
[8,4,7,5,1,3,2,6]=>1101100
[6,8,3,1,7,2,4,5]=>1110000
[3,7,2,5,6,1,8,4]=>1101000
[6,8,4,2,5,1,7,3]=>1111000
[2,7,5,3,8,4,1,6]=>1011100
[8,3,1,4,7,2,6,5]=>1110100
[8,3,2,1,5,7,4,6]=>1111000
[2,8,3,6,4,7,1,5]=>1011000
[7,3,6,4,8,1,2,5]=>1011000
[8,3,6,4,7,1,2,5]=>1011000
[1,2,8,3,5,7,4,6]=>0011000
[1,8,3,2,5,7,4,6]=>0111000
[6,5,1,7,4,2,8,3]=>1111100
[7,3,6,4,8,2,1,5]=>1111000
[4,6,1,7,3,5,2,8]=>1110000
[5,6,1,7,3,4,2,8]=>1110000
[6,1,7,3,4,2,8,5]=>1110100
[7,3,8,1,6,5,2,4]=>1110100
[8,3,7,1,6,5,2,4]=>1110100
[2,8,1,7,6,5,3,4]=>1010110
[4,2,8,6,5,1,7,3]=>1110110
[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]=>1101001
[4,2,3,8,7,5,1,6]=>1100101
[3,8,7,1,6,5,2,4]=>1100101
[2,4,3,8,1,6,7,5]=>1010100
[2,4,3,7,1,6,8,5]=>1010100
[4,2,3,7,8,5,1,6]=>1100100
[5,1,6,4,2,3,7,8]=>1101000
[6,4,7,8,1,5,2,3]=>1101000
[8,7,4,6,1,5,2,3]=>1101001
[6,5,7,8,1,4,2,3]=>1100100
[4,7,8,6,1,5,2,3]=>1100010
[3,2,4,8,7,1,5,6]=>1100001
[4,8,7,6,1,5,2,3]=>1100011
[5,8,7,6,1,4,2,3]=>1100011
[8,6,5,7,1,4,2,3]=>1100110
[5,1,6,7,4,2,3,8]=>1101000
[6,7,4,8,1,5,2,3]=>1101000
[8,4,7,6,1,5,2,3]=>1101010
[8,3,2,4,7,1,5,6]=>1110000
[7,3,2,4,8,1,5,6]=>1110000
[2,5,3,7,1,6,4,8]=>1011000
[8,4,6,7,1,5,2,3]=>1101000
[5,1,6,8,4,2,3,7]=>1101000
[4,2,3,7,5,1,6,8]=>1100100
[2,4,3,7,1,6,5,8]=>1010100
[2,4,7,1,5,8,6,3]=>1010010
[3,2,4,7,6,1,5,8]=>1100010
[4,7,6,8,1,5,2,3]=>1100010
[8,5,6,7,1,4,2,3]=>1100100
[8,6,7,5,1,4,2,3]=>1100110
[6,8,7,5,1,4,2,3]=>1100101
[5,6,8,7,1,4,2,3]=>1100001
[4,6,8,7,1,5,2,3]=>1100001
[3,2,4,6,1,5,7,8]=>1100000
[6,7,8,5,1,4,2,3]=>1100100
[7,8,6,5,1,4,2,3]=>1100110
[2,1,8,5,4,6,3,7]=>1011100
[4,1,8,5,2,3,6,7]=>1100100
[5,4,1,3,6,7,2,8]=>1101000
[8,4,1,2,6,3,7,5]=>1011100
[8,2,7,1,5,3,4,6]=>1110000
[3,2,7,1,5,8,4,6]=>1101000
[7,3,8,1,5,4,2,6]=>1111000
[7,1,5,3,8,4,2,6]=>1111000
[3,6,8,1,5,4,2,7]=>1101000
[6,8,3,1,5,4,2,7]=>1111000
[7,6,3,1,5,4,2,8]=>1111010
[3,6,2,1,5,8,4,7]=>1101000
[8,6,2,1,5,3,4,7]=>1110010
[2,3,8,1,5,7,4,6]=>1001000
[7,1,3,2,8,6,4,5]=>1101010
[4,7,1,2,6,3,8,5]=>1010100
[2,7,8,1,5,3,4,6]=>1010000
[6,7,2,1,5,3,4,8]=>1110000
[4,7,2,1,8,5,3,6]=>1110100
[8,7,2,1,4,5,3,6]=>1110001
[5,7,8,6,1,4,3,2]=>1110010
[2,7,4,1,6,5,3,8]=>1011100
[7,1,6,4,5,8,3,2]=>1111000
[2,6,4,1,7,5,3,8]=>1011100
[5,6,8,7,1,4,3,2]=>1110001
[4,2,8,1,6,5,3,7]=>1110100
[6,2,4,1,8,5,3,7]=>1110100
[8,3,1,4,5,6,7,2]=>1110000
[5,3,1,4,8,6,7,2]=>1110010
[7,5,1,6,3,4,8,2]=>1110100
[7,1,5,8,4,3,6,2]=>1111000
[5,8,1,6,4,3,7,2]=>1111000
[5,3,1,8,4,6,7,2]=>1111000
[8,3,1,5,4,6,7,2]=>1111000
[8,2,6,1,4,5,3,7]=>1110000
[6,2,8,1,4,5,3,7]=>1110000
[7,2,6,1,5,3,4,8]=>1110000
[2,8,6,1,5,3,4,7]=>1010010
[4,2,1,5,6,3,8,7]=>1110001
[7,1,2,5,8,3,4,6]=>1010000
[7,1,4,5,6,8,3,2]=>1110000
[2,6,7,1,4,5,3,8]=>1010000
[3,5,1,7,4,6,8,2]=>1101000
[7,1,5,6,4,8,3,2]=>1111000
[7,1,6,5,4,8,3,2]=>1111100
[2,7,6,1,4,5,3,8]=>1010010
[5,7,6,8,1,4,3,2]=>1110010
[7,8,6,5,1,4,3,2]=>1110110
[5,3,1,2,4,8,7,6]=>1010011
[5,3,6,2,1,8,7,4]=>1111001
[5,3,7,2,8,4,1,6]=>1111000
[7,2,4,5,8,3,1,6]=>1110000
[7,2,4,5,1,3,6,8]=>1100000
[6,2,4,5,1,8,7,3]=>1110001
[3,1,4,5,2,8,7,6]=>1100011
[1,6,4,5,2,8,7,3]=>0111001
[3,7,4,5,1,2,6,8]=>1001000
[1,7,4,2,6,3,5,8]=>0111000
[8,7,4,5,2,1,6,3]=>1111001
[6,3,7,1,8,4,2,5]=>1111000
[5,7,4,1,6,3,2,8]=>1111000
[1,7,4,8,6,3,2,5]=>0111010
[5,7,4,8,6,3,1,2]=>1011010
[4,8,3,5,6,7,1,2]=>1010000
[1,8,3,5,6,7,2,4]=>0110000
[4,8,1,5,6,7,2,3]=>1100000
[4,1,3,5,6,7,2,8]=>1100000
[5,8,4,3,6,1,2,7]=>1011000
[5,3,8,4,1,7,2,6]=>1111000
[1,5,8,4,6,7,3,2]=>0111000
[1,4,8,3,6,7,5,2]=>0110100
[4,3,8,2,1,7,5,6]=>1110100
[3,8,4,2,6,1,5,7]=>1101000
[3,8,1,5,6,7,4,2]=>1101000
[3,8,2,5,6,7,1,4]=>1100000
[8,2,1,5,6,7,4,3]=>1111000
[8,1,3,5,6,7,4,2]=>1101000
[7,1,4,3,6,2,5,8]=>1110000
[7,8,4,3,6,2,1,5]=>1111000
[4,3,1,8,5,7,6,2]=>1110110
[6,3,5,8,2,7,1,4]=>1110000
[7,5,4,8,6,2,1,3]=>1101110
[7,1,4,8,6,2,3,5]=>1100010
[7,5,4,1,6,2,3,8]=>1101100
[1,6,4,5,8,2,3,7]=>0101000
[1,8,5,3,6,7,4,2]=>0111100
[8,3,5,2,1,7,4,6]=>1111000
[4,1,8,5,6,7,3,2]=>1110100
[1,2,8,5,6,7,3,4]=>0010100
[4,2,1,5,6,7,3,8]=>1110000
[1,5,3,8,6,7,4,2]=>0111010
[1,4,8,5,6,7,2,3]=>0100100
[6,2,4,3,8,7,5,1]=>1110101
[7,3,5,4,1,8,6,2]=>1111010
[5,2,7,1,3,4,8,6]=>1100010
[2,6,5,7,3,1,4,8]=>1010100
[2,6,5,7,3,1,8,4]=>1011100
[6,3,1,4,7,8,5,2]=>1110100
[6,8,2,1,3,4,5,7]=>1100000
[3,7,1,8,4,5,2,6]=>1101000
[6,3,2,4,7,5,8,1]=>1110100
[6,3,2,4,7,5,1,8]=>1110100
[4,2,1,6,3,7,5,8]=>1110100
[4,2,1,6,3,7,8,5]=>1110100
[7,4,3,5,8,6,1,2]=>1011010
[2,7,6,8,3,1,4,5]=>1010010
[7,4,3,5,8,6,2,1]=>1111010
[4,2,1,7,3,8,6,5]=>1110110
[4,2,1,3,7,8,6,5]=>1100110
[5,8,1,7,4,3,6,2]=>1111000
[5,8,1,7,4,3,2,6]=>1111000
[3,7,8,6,2,1,4,5]=>1100010
[4,2,1,8,3,5,6,7]=>1110000
[4,2,1,3,6,7,5,8]=>1100100
[4,2,1,3,7,5,6,8]=>1100100
[7,3,2,4,8,6,5,1]=>1110110
[4,2,1,7,3,5,6,8]=>1110000
[3,6,7,5,2,1,4,8]=>1100100
[3,6,7,5,2,1,8,4]=>1101100
[7,3,4,2,6,8,5,1]=>1110100
[4,8,6,2,7,3,5,1]=>1110010
[7,3,4,2,6,8,1,5]=>1110000
[3,6,7,5,2,4,8,1]=>1100100
[3,6,7,5,2,4,1,8]=>1100100
[4,2,1,7,3,6,8,5]=>1110100
[3,7,6,8,4,2,5,1]=>1101010
[5,8,1,7,4,2,6,3]=>1111000
[3,7,8,6,2,4,5,1]=>1100010
[4,2,1,3,8,6,7,5]=>1100110
[4,2,1,3,5,7,6,8]=>1100010
[4,8,1,7,3,6,5,2]=>1110100
[4,2,1,8,3,7,6,5]=>1110110
[4,2,1,3,5,6,8,7]=>1100001
[7,8,2,4,1,3,6,5]=>1100100
[2,6,1,5,4,7,8,3]=>1011000
[4,6,3,5,8,7,1,2]=>1010001
[2,3,6,8,4,1,5,7]=>1001000
[2,7,5,1,8,3,4,6]=>1010100
[4,7,5,2,1,3,6,8]=>1100100
[3,5,6,2,4,1,7,8]=>1100000
[3,1,8,5,2,7,6,4]=>1101110
[8,3,7,6,1,4,5,2]=>1110010
[3,1,7,8,2,5,6,4]=>1101000
[4,8,1,5,2,7,3,6]=>1110000
[4,1,2,5,3,8,7,6]=>1010011
[4,3,6,8,7,5,1,2]=>1010101
[6,4,8,1,2,5,3,7]=>1011000
[6,7,3,1,4,8,5,2]=>1110100
[6,5,1,2,3,4,8,7]=>1000101
[6,7,4,1,2,5,3,8]=>1011000
[1,2,6,7,5,3,8,4]=>0011100
[1,7,5,3,2,8,4,6]=>0111100
[1,6,5,7,2,3,8,4]=>0101100
[1,3,8,2,6,5,7,4]=>0101100
[1,2,5,7,6,3,4,8]=>0010010
[1,3,4,8,2,5,7,6]=>0100010
[1,5,7,6,2,3,4,8]=>0100010
[1,5,3,8,2,6,4,7]=>0111000
[1,4,8,3,2,5,7,6]=>0110010
[1,2,4,8,3,5,7,6]=>0010010
[1,3,8,4,2,6,7,5]=>0101100
[1,4,8,2,3,5,7,6]=>0100010
[4,2,6,7,5,8,3,1]=>1110100
[6,7,5,2,1,8,4,3]=>1111100
[3,4,8,7,5,2,1,6]=>1100101
[1,7,5,2,8,4,6,3]=>0111100
[5,6,8,3,1,7,2,4]=>1110000
[6,1,4,8,3,2,7,5]=>1110100
[3,4,7,1,8,6,2,5]=>1100010
[3,4,6,8,2,1,5,7]=>1100000
[3,8,2,5,6,1,4,7]=>1100000
[3,5,2,8,6,4,1,7]=>1101010
[4,2,5,7,3,8,6,1]=>1110010
[7,4,2,5,3,8,1,6]=>1111000
[1,5,6,8,3,4,2,7]=>0110000
[4,5,1,6,8,3,2,7]=>1110000
[4,5,7,3,8,2,6,1]=>1110000
[6,4,3,7,8,2,5,1]=>1111000
[6,4,3,1,7,8,2,5]=>1111000
[4,5,3,1,7,8,2,6]=>1110000
[7,1,3,5,4,8,2,6]=>1101000
[7,5,2,8,1,4,3,6]=>1110100
[1,4,5,7,3,8,6,2]=>0110010
[4,6,3,7,8,5,2,1]=>1110100
[1,5,3,6,7,8,4,2]=>0111000
[4,6,1,7,3,8,5,2]=>1110100
[6,7,2,4,8,1,5,3]=>1110000
[5,2,3,6,7,8,4,1]=>1101000
[6,4,2,7,1,8,3,5]=>1111000
[4,2,6,3,7,8,5,1]=>1110100
[6,7,3,8,2,4,5,1]=>1110000
[3,6,2,7,4,1,8,5]=>1101100
[6,7,3,2,1,4,8,5]=>1110100
[7,2,4,8,6,1,3,5]=>1100010
[3,5,7,2,1,8,6,4]=>1101010
[6,7,8,3,2,5,1,4]=>1110000
[6,3,7,8,2,5,4,1]=>1111000
[2,6,7,4,8,5,3,1]=>1011100
[6,2,4,7,1,8,5,3]=>1110100
[1,7,4,8,5,2,6,3]=>0111100
[1,3,7,8,5,2,6,4]=>0101100
[2,5,7,8,1,6,3,4]=>1010000
[1,6,4,7,8,2,5,3]=>0111000
[2,5,6,1,7,8,4,3]=>1011000
[5,6,1,2,7,8,4,3]=>1011000
[6,7,2,1,8,5,3,4]=>1110100
[6,4,5,2,3,8,7,1]=>1101001
[4,6,5,2,3,1,8,7]=>1100101
[6,4,2,5,3,1,8,7]=>1111001
[6,4,2,5,3,8,7,1]=>1111001
[8,6,4,7,5,2,3,1]=>1101110
[8,6,2,7,4,5,3,1]=>1111010
[6,4,2,5,8,7,3,1]=>1111001
[4,6,5,2,3,8,7,1]=>1100101
[6,8,2,7,4,5,3,1]=>1111000
[8,6,4,7,2,5,3,1]=>1111010
[8,6,2,4,7,5,3,1]=>1110110
[6,8,2,4,7,5,3,1]=>1110100
[4,8,2,6,7,5,3,1]=>1110100
[2,8,4,6,7,5,3,1]=>1011100
[2,8,6,7,4,5,3,1]=>1011010
[6,8,7,2,4,5,3,1]=>1110001
[2,6,4,5,8,7,3,1]=>1011001
[2,6,4,8,7,5,3,1]=>1011101
[4,6,2,8,7,5,3,1]=>1110101
[8,2,4,6,7,5,3,1]=>1110100
[6,2,4,8,7,5,3,1]=>1110101
[4,2,6,8,7,5,3,1]=>1110101
[4,2,6,5,8,7,3,1]=>1110101
[6,2,4,5,8,7,3,1]=>1110001
[8,2,6,7,4,5,3,1]=>1111000
[8,6,7,2,4,5,3,1]=>1110010
[6,4,5,8,7,2,3,1]=>1101001
[8,6,7,4,2,5,3,1]=>1111010
[8,4,6,7,2,5,3,1]=>1111000
[6,4,8,7,2,5,3,1]=>1111001
[6,2,8,7,4,5,3,1]=>1111001
[4,6,5,8,7,2,3,1]=>1100101
[2,1,6,8,7,4,5,3]=>1011001
[2,6,8,7,4,5,3,1]=>1011001
[2,4,8,6,7,5,3,1]=>1010110
[6,2,8,4,7,5,3,1]=>1111100
[8,2,6,4,7,5,3,1]=>1111100
[4,6,8,2,7,5,3,1]=>1110100
[2,6,8,4,7,5,3,1]=>1011100
[4,6,8,7,2,5,3,1]=>1110001
[4,6,5,8,2,7,3,1]=>1110100
[2,1,6,8,4,7,5,3]=>1011100
[2,1,8,6,4,7,5,3]=>1011110
[6,8,7,4,2,5,3,1]=>1111001
[2,8,6,4,7,5,3,1]=>1011110
[4,8,6,2,7,5,3,1]=>1110110
[3,7,8,5,6,1,2,4]=>1000100
[3,6,1,8,4,7,2,5]=>1101000
[3,1,6,8,4,7,2,5]=>1101000
[4,1,6,8,3,2,7,5]=>1110100
[4,6,1,8,3,2,7,5]=>1110100
[4,7,8,1,3,2,6,5]=>1100100
[4,7,8,3,1,2,6,5]=>1010100
[2,7,8,3,4,6,5,1]=>1010100
[4,7,8,2,1,3,6,5]=>1100100
[4,6,1,8,2,3,7,5]=>1100100
[4,5,2,1,8,3,7,6]=>1110010
[4,6,2,8,1,3,7,5]=>1100100
[3,6,2,8,4,7,1,5]=>1101000
[2,3,6,8,4,7,5,1]=>1001100
[3,2,6,8,4,7,1,5]=>1101000
[4,2,6,8,3,1,7,5]=>1110100
[4,2,5,1,8,3,7,6]=>1110010
[5,1,2,4,3,8,7,6]=>1010011
[5,2,4,1,3,8,7,6]=>1100011
[4,2,5,3,8,1,7,6]=>1110010
[3,2,5,4,8,7,1,6]=>1101001
[3,5,2,4,8,7,1,6]=>1100001
[5,1,4,2,3,8,7,6]=>1100011
[5,4,3,1,2,8,7,6]=>1011011
[4,5,3,1,8,2,7,6]=>1110010
[4,5,1,3,8,2,7,6]=>1100010
[3,1,5,4,8,7,2,6]=>1101001
[3,5,4,1,8,7,2,6]=>1101001
[3,6,5,8,7,1,2,4]=>1000101
[3,4,1,5,8,7,2,6]=>1100001
[4,1,3,5,8,2,7,6]=>1100010
[4,3,6,8,2,1,7,5]=>1110100
[2,4,6,8,3,7,5,1]=>1010100
[3,4,5,2,8,7,1,6]=>1100001
[5,3,1,4,2,8,7,6]=>1110011
[5,1,3,4,2,8,7,6]=>1100011
[5,1,3,2,4,8,7,6]=>1100011
[5,3,2,1,4,8,7,6]=>1110011
[4,3,2,5,8,1,7,6]=>1110010
[3,4,2,5,8,7,1,6]=>1100001
[3,2,4,5,8,7,1,6]=>1100001
[4,2,3,5,8,1,7,6]=>1100010
[5,2,3,1,4,8,7,6]=>1100011
[5,2,1,3,4,8,7,6]=>1100011
[1,7,2,3,5,6,8,4]=>0101000
[3,7,4,2,1,5,6,8]=>1101000
[3,4,6,2,8,5,7,1]=>1100100
[4,2,1,7,5,8,3,6]=>1110100
[4,7,2,6,5,1,3,8]=>1100100
[3,7,4,1,2,5,8,6]=>1001010
[4,7,1,6,5,2,8,3]=>1110100
[4,7,3,6,5,1,8,2]=>1110100
[4,3,7,1,6,8,5,2]=>1110100
[4,2,1,7,5,6,8,3]=>1110100
[4,2,6,8,7,3,1,5]=>1110001
[3,4,6,1,8,5,2,7]=>1100100
[4,1,6,7,5,8,2,3]=>1100100
[4,3,6,7,5,1,2,8]=>1010100
[4,3,7,1,6,8,2,5]=>1110000
[4,3,7,5,6,8,2,1]=>1110100
[4,1,7,3,6,5,2,8]=>1110100
[2,8,7,4,5,3,1,6]=>1011001
[2,8,7,4,3,5,1,6]=>1011001
[4,1,7,3,6,2,5,8]=>1110000
[5,8,7,6,1,2,4,3]=>1010011
[4,1,7,2,6,8,5,3]=>1110100
[4,2,7,3,6,1,8,5]=>1110100
[4,2,7,3,6,5,8,1]=>1110100
[3,8,5,6,2,4,1,7]=>1100100
[2,8,6,5,3,7,1,4]=>1010110
[3,8,6,5,1,4,7,2]=>1100110
[3,8,2,1,4,6,7,5]=>1100100
[3,8,2,5,4,6,7,1]=>1101000
[4,2,6,7,5,3,1,8]=>1110100
[3,2,6,1,4,5,8,7]=>1100001
[2,8,7,3,4,5,1,6]=>1010001
[5,8,7,6,1,3,4,2]=>1100011
[5,8,7,6,2,3,4,1]=>1100011
[4,1,7,5,6,2,3,8]=>1100100
[3,8,1,5,2,6,4,7]=>1101000
[2,8,7,5,3,4,1,6]=>1010101
[2,8,7,5,4,3,1,6]=>1011101
[4,1,7,5,6,3,2,8]=>1110100
[5,8,7,6,1,3,2,4]=>1100011
[5,8,7,6,4,1,2,3]=>1001011
[8,1,7,2,4,5,3,6]=>1110000
[8,1,3,6,2,5,4,7]=>1101000
[7,2,1,6,3,5,4,8]=>1111000
[2,7,1,6,3,5,4,8]=>1011000
[2,7,1,5,4,3,6,8]=>1011000
[7,2,1,5,4,3,6,8]=>1111000
[8,1,3,5,4,2,6,7]=>1101000
[8,1,5,3,4,2,6,7]=>1110000
[8,1,5,6,2,3,7,4]=>1101000
[8,1,4,5,3,2,6,7]=>1110000
[8,1,4,3,5,2,6,7]=>1110000
[7,2,1,4,5,3,6,8]=>1110000
[2,7,1,4,5,3,6,8]=>1010000
[2,6,3,1,5,4,7,8]=>1011000
[6,3,2,1,5,4,7,8]=>1111000
[7,3,1,4,5,2,6,8]=>1110000
[7,3,1,5,4,2,6,8]=>1111000
[7,3,1,6,2,5,4,8]=>1111000
[3,7,1,6,2,5,4,8]=>1101000
[3,7,1,4,5,2,6,8]=>1100000
[2,3,6,1,5,4,7,8]=>1001000
[6,3,4,1,5,2,7,8]=>1110000
[6,2,4,1,5,3,7,8]=>1110000
[2,6,4,1,5,3,7,8]=>1011000
[2,6,5,1,3,7,4,8]=>1001100
[6,5,2,1,3,7,4,8]=>1101100
[7,6,1,2,4,5,3,8]=>1010010
[6,7,1,2,8,3,5,4]=>1011000
[6,7,1,2,5,4,3,8]=>1011000
[5,6,2,1,3,7,4,8]=>1101000
[5,2,6,1,3,7,4,8]=>1101000
[2,4,6,1,5,3,7,8]=>1010000
[4,7,1,3,5,2,6,8]=>1100000
[4,7,1,5,3,2,6,8]=>1110000
[5,7,1,6,2,3,8,4]=>1101000
[5,6,3,1,2,7,4,8]=>1011000
[4,2,5,3,1,6,7,8]=>1110000
[8,5,6,2,7,1,4,3]=>1110100
[6,5,1,2,7,8,4,3]=>1011100
[4,7,6,1,5,3,8,2]=>1110010
[5,7,6,4,1,3,8,2]=>1101010
[7,6,2,4,5,3,8,1]=>1110010
[6,1,7,5,3,8,4,2]=>1111100
[8,6,7,5,3,1,4,2]=>1110110
[8,5,2,7,1,6,4,3]=>1111100
[5,6,2,4,7,8,1,3]=>1100000
[3,4,8,6,7,1,5,2]=>1100010
[4,8,5,6,7,2,3,1]=>1100100
[5,8,6,4,1,2,7,3]=>1011010
[5,8,7,3,2,6,4,1]=>1111001
[5,8,1,7,2,6,4,3]=>1111000
[8,1,5,7,2,6,4,3]=>1111000
[8,1,7,2,5,6,3,4]=>1110000
[6,8,7,2,5,1,3,4]=>1100001
[5,8,7,2,1,6,3,4]=>1110001
[4,8,1,5,2,6,7,3]=>1110000
[3,7,8,5,1,6,2,4]=>1100100
[6,5,2,7,8,1,4,3]=>1110100
[7,1,2,8,5,6,3,4]=>1010100
[8,7,2,1,5,6,3,4]=>1110001
[8,6,7,1,5,2,3,4]=>1100010
[6,1,7,8,5,2,3,4]=>1100100
[7,5,6,2,1,8,4,3]=>1111100
[8,7,5,2,1,6,4,3]=>1111101
[7,1,3,5,8,6,2,4]=>1100010
[5,1,3,4,6,8,7,2]=>1100001
[8,4,3,1,2,6,7,5]=>1011100
[8,5,1,6,3,4,7,2]=>1110100
[5,1,8,6,3,4,7,2]=>1110010
[4,6,8,1,5,3,7,2]=>1110000
[6,4,5,8,3,2,7,1]=>1111000
[3,6,4,8,7,1,5,2]=>1101001
[6,5,8,1,3,4,7,2]=>1100100
[6,1,8,3,5,2,7,4]=>1111000
[7,6,8,3,5,2,1,4]=>1110010
[8,6,1,3,5,2,7,4]=>1101010
[8,7,1,3,5,6,2,4]=>1100001
[5,8,2,4,3,6,7,1]=>1110000
[5,8,2,3,1,6,7,4]=>1101000
[6,8,2,3,5,1,7,4]=>1101000
[7,8,2,3,5,6,1,4]=>1100000
[8,6,5,1,4,3,7,2]=>1110110
[2,4,8,6,1,3,7,5]=>1000110
[6,7,1,8,4,3,5,2]=>1111000
[2,7,8,6,1,4,3,5]=>1010010
[2,7,3,8,1,6,4,5]=>1011000
[7,5,1,8,2,4,6,3]=>1110100
[2,7,8,4,1,6,3,5]=>1011000
[2,6,5,4,1,3,8,7]=>1001101
[4,1,7,6,3,8,2,5]=>1110010
[4,8,2,5,7,6,3,1]=>1110010
[3,4,6,5,1,8,2,7]=>1100100
[4,6,1,5,2,3,8,7]=>1100001
[2,6,7,5,1,8,4,3]=>1011100
[7,6,5,2,8,3,4,1]=>1110110
[2,4,7,6,5,8,1,3]=>1000110
[2,1,4,8,7,6,3,5]=>1010011
[8,1,3,5,7,4,6,2]=>1101000
[3,2,8,7,5,1,6,4]=>1101101
[4,8,5,1,6,7,2,3]=>1100100
[7,8,6,1,3,5,2,4]=>1100010
[2,5,1,8,6,7,4,3]=>1011010
[3,5,1,8,6,7,4,2]=>1101010
[8,3,5,4,6,7,1,2]=>1011000
[5,1,3,8,6,7,4,2]=>1101010
[5,6,3,2,8,1,4,7]=>1110000
[8,1,6,3,5,2,7,4]=>1111000
[4,7,6,8,3,2,5,1]=>1110010
[2,7,5,8,1,3,4,6]=>1000100
[8,1,3,7,5,2,6,4]=>1101100
[3,4,8,7,5,1,6,2]=>1100101
[6,3,8,1,4,2,5,7]=>1110000
[3,6,8,2,4,1,7,5]=>1100100
[4,5,8,2,6,7,3,1]=>1110000
[2,5,8,4,6,7,3,1]=>1011000
[8,4,3,2,6,7,1,5]=>1111000
[4,2,8,1,6,7,3,5]=>1110000
[2,4,8,1,6,7,3,5]=>1010000
[5,1,8,2,6,7,3,4]=>1110000
[3,4,8,7,2,1,5,6]=>1100001
[5,8,4,1,6,7,2,3]=>1101000
[3,8,1,4,6,7,2,5]=>1100000
[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]=>0110000
[1,6,3,4,2,5,7,8]=>0110000
[1,7,3,4,2,5,6,8]=>0110000
[1,8,5,7,3,4,2,6]=>0110100
[1,7,3,4,2,6,5,8]=>0110100
[1,5,2,8,4,7,3,6]=>0111000
[1,4,2,8,5,7,3,6]=>0110100
[1,7,3,5,2,6,4,8]=>0111000
[1,8,4,7,3,5,2,6]=>0111000
[1,7,3,6,2,5,4,8]=>0111000
[1,7,3,6,2,4,5,8]=>0110000
[1,7,4,6,2,3,5,8]=>0101000
[1,8,5,6,2,3,4,7]=>0100100
[1,8,5,6,2,4,3,7]=>0110100
[1,3,2,8,5,6,4,7]=>0101100
[1,4,2,8,5,6,3,7]=>0110100
[1,5,2,8,4,6,3,7]=>0111000
[1,6,2,8,4,5,3,7]=>0111000
[8,6,4,7,2,1,3,5]=>1101010
[1,6,4,7,2,8,3,5]=>0111000
[1,4,7,3,5,8,2,6]=>0110000
[8,4,6,2,3,5,1,7]=>1101000
[5,4,8,2,3,6,1,7]=>1101000
[7,4,8,5,2,3,1,6]=>1101100
[3,8,6,2,4,5,1,7]=>1100010
[4,8,6,2,3,5,1,7]=>1100010
[1,7,5,3,4,8,2,6]=>0110100
[1,7,6,4,8,2,3,5]=>0101010
[5,8,7,4,1,2,3,6]=>1001001
[6,8,5,3,4,1,2,7]=>1010100
[6,8,3,7,2,1,4,5]=>1110000
[8,5,1,6,3,7,2,4]=>1110100
[6,1,3,7,4,8,2,5]=>1101000
[4,1,7,3,5,8,2,6]=>1110000
[7,1,6,4,8,2,3,5]=>1101000
[5,1,7,3,8,2,4,6]=>1110000
[6,1,5,7,8,2,3,4]=>1100000
[7,4,8,6,1,2,3,5]=>1001010
[3,8,7,5,1,2,4,6]=>1000101
[3,7,6,1,2,4,5,8]=>1000010
[4,7,6,1,2,3,5,8]=>1000010
[1,6,5,8,2,3,4,7]=>0100100
[6,5,8,4,1,2,3,7]=>1001100
[8,5,7,4,1,2,3,6]=>1001100
[1,5,7,4,8,2,3,6]=>0101000
[7,6,2,3,8,1,4,5]=>1100010
[7,4,8,5,1,6,2,3]=>1101100
[8,6,2,3,1,7,4,5]=>1101010
[8,6,4,1,2,7,3,5]=>1011010
[1,7,2,8,6,3,4,5]=>0110010
[7,5,8,1,3,6,2,4]=>1100100
[5,4,1,8,2,3,6,7]=>1101000
[1,4,8,7,2,3,5,6]=>0100001
[1,5,8,7,2,3,4,6]=>0100001
[6,5,1,8,2,3,4,7]=>1100100
[5,7,1,3,8,2,4,6]=>1100000
[7,6,8,1,5,2,3,4]=>1100010
[7,1,5,8,6,2,3,4]=>1100010
[4,1,8,7,2,3,5,6]=>1100001
[5,1,8,7,2,3,4,6]=>1100001
[7,1,5,8,3,4,2,6]=>1110000
[7,1,4,3,2,5,6,8]=>1110000
[6,4,2,3,8,5,7,1]=>1101100
[6,4,2,7,5,8,3,1]=>1111100
[7,1,4,6,5,2,3,8]=>1100100
[7,1,4,6,5,8,2,3]=>1100100
[7,1,4,6,3,8,2,5]=>1110000
[7,1,4,3,2,5,8,6]=>1110010
[7,1,4,6,5,2,8,3]=>1110100
[7,1,4,6,5,3,8,2]=>1110100
[7,1,4,6,5,3,2,8]=>1110100
[6,4,2,7,5,3,8,1]=>1111100
[3,4,7,2,6,8,5,1]=>1100100
[3,4,7,1,6,8,2,5]=>1100000
[3,4,7,1,6,8,5,2]=>1100100
[2,4,1,7,5,3,6,8]=>1010100
[3,4,1,7,8,6,2,5]=>1100010
[6,4,2,3,8,5,1,7]=>1101100
[6,4,2,7,5,3,1,8]=>1111100
[3,4,7,2,6,8,1,5]=>1100000
[5,4,7,3,6,8,2,1]=>1111000
[3,4,7,2,6,5,1,8]=>1100100
[4,8,7,3,5,1,2,6]=>1010001
[4,8,7,1,3,5,2,6]=>1100001
[4,8,3,1,2,6,5,7]=>1010100
[3,4,7,1,6,2,5,8]=>1100000
[3,4,7,1,6,2,8,5]=>1100100
[3,4,7,2,6,5,8,1]=>1100100
[4,8,3,1,2,6,7,5]=>1010100
[5,8,1,6,3,4,2,7]=>1110000
[6,8,5,1,3,7,2,4]=>1100100
[6,8,5,1,3,4,7,2]=>1100100
[5,8,3,4,2,6,7,1]=>1110000
[6,4,3,7,5,1,2,8]=>1011100
[3,8,7,4,1,5,2,6]=>1101001
[2,4,7,3,6,1,5,8]=>1010000
[5,8,3,2,1,6,4,7]=>1111000
[5,8,7,4,3,1,2,6]=>1011001
[5,3,6,2,4,7,8,1]=>1110000
[5,3,6,1,4,8,7,2]=>1110001
[5,3,7,2,4,6,8,1]=>1110000
[4,2,1,5,8,6,3,7]=>1110010
[4,2,1,5,8,6,7,3]=>1110010
[4,3,1,5,7,8,6,2]=>1110010
[4,3,1,7,5,8,6,2]=>1110110
[6,7,3,1,4,8,2,5]=>1110000
[5,3,7,1,4,8,2,6]=>1110000
[4,3,1,5,7,8,2,6]=>1110000
[3,2,1,8,5,4,6,7]=>1101100
[3,2,1,8,5,7,4,6]=>1101100
[6,7,2,1,8,4,5,3]=>1111000
[3,2,1,8,5,6,4,7]=>1101100
[4,3,1,6,7,8,5,2]=>1110100
[4,2,1,6,8,5,7,3]=>1110100
[4,2,1,6,8,5,3,7]=>1110100
[5,2,6,1,8,4,3,7]=>1111000
[5,2,6,1,8,7,3,4]=>1110001
[5,2,6,1,8,3,4,7]=>1110000
[4,2,1,6,8,3,7,5]=>1110100
[4,3,1,6,7,8,2,5]=>1110000
[4,2,1,7,8,6,3,5]=>1110010
[3,2,1,8,6,4,7,5]=>1101110
[3,2,1,8,6,4,5,7]=>1101010
[3,2,1,8,4,6,5,7]=>1101100
[3,2,1,8,4,6,7,5]=>1101100
[4,2,1,7,8,3,6,5]=>1110100
[5,2,7,1,8,3,6,4]=>1111000
[6,7,2,1,8,3,5,4]=>1111000
[5,2,7,1,8,3,4,6]=>1110000
[4,2,1,7,8,3,5,6]=>1110000
[3,2,1,8,4,5,7,6]=>1101010
[7,4,8,6,2,5,3,1]=>1111010
[7,3,8,6,2,4,5,1]=>1110010
[7,4,3,1,8,2,5,6]=>1111000
[7,4,2,8,5,6,1,3]=>1101100
[7,3,8,5,2,4,6,1]=>1110100
[6,3,8,2,4,5,1,7]=>1110000
[6,3,8,2,5,7,4,1]=>1111000
[5,6,7,3,8,2,4,1]=>1110000
[5,3,8,2,4,6,7,1]=>1110000
[6,3,8,2,4,7,5,1]=>1110100
[5,7,4,2,6,8,1,3]=>1101000
[6,5,3,1,4,2,7,8]=>1110100
[5,7,4,2,6,1,3,8]=>1101000
[5,6,4,2,3,8,1,7]=>1101000
[5,6,3,7,8,2,4,1]=>1110000
[5,6,3,8,2,4,7,1]=>1110000
[6,3,7,2,4,5,1,8]=>1110000
[6,3,7,2,5,8,4,1]=>1111000
[5,3,6,8,2,4,7,1]=>1110000
[5,4,6,2,3,8,1,7]=>1101000
[5,3,6,7,8,2,4,1]=>1110000
[3,6,4,2,1,5,8,7]=>1101001
[3,5,8,6,4,2,1,7]=>1101010
[5,8,6,3,4,2,1,7]=>1110010
[5,6,3,4,2,1,8,7]=>1110001
[6,3,4,2,1,5,8,7]=>1110001
[5,6,4,2,1,3,8,7]=>1101001
[2,7,8,5,4,1,6,3]=>1011100
[2,8,5,4,1,6,3,7]=>1011100
[2,6,3,8,5,4,1,7]=>1011100
[2,8,6,3,5,4,1,7]=>1011010
[5,8,6,4,2,1,3,7]=>1101010
[4,2,1,5,7,8,6,3]=>1110010
[2,7,8,6,3,5,4,1]=>1011010
[4,3,8,5,7,6,2,1]=>1110110
[2,1,8,5,6,4,3,7]=>1011100
[4,2,1,8,5,6,3,7]=>1110100
[6,3,4,2,1,8,5,7]=>1110100
[3,8,5,6,4,2,1,7]=>1101100
[3,6,4,2,1,8,5,7]=>1101100
[8,5,3,7,6,2,4,1]=>1110110
[7,6,2,4,1,8,5,3]=>1110110
[8,5,4,1,7,6,2,3]=>1101110
[7,6,2,3,8,5,4,1]=>1101110
[2,1,7,8,6,4,3,5]=>1011010
[2,1,6,4,3,7,8,5]=>1011100
[6,3,7,8,4,2,1,5]=>1111000
[7,8,4,2,1,6,3,5]=>1111000
[5,7,6,2,3,8,4,1]=>1101010
[2,6,1,8,4,3,7,5]=>1011100
[2,6,1,7,5,8,4,3]=>1011100
[8,4,2,3,7,5,6,1]=>1101100
[8,5,7,6,2,1,4,3]=>1110110
[4,8,5,7,6,2,1,3]=>1100110
[4,7,6,2,1,3,8,5]=>1100110
[7,5,6,1,8,4,2,3]=>1101100
[2,7,5,8,4,3,6,1]=>1011100
[2,8,4,3,6,1,7,5]=>1011100
[8,4,2,6,3,1,7,5]=>1111100
[1,5,3,7,4,2,8,6]=>0111010
[1,6,7,3,4,2,8,5]=>0110100
[8,6,5,2,3,1,7,4]=>1101110
[1,7,6,3,4,2,8,5]=>0110110
[1,8,6,3,2,5,7,4]=>0111010
[8,7,5,2,1,4,6,3]=>1110101
[7,8,5,2,1,4,6,3]=>1110100
[6,8,5,2,3,1,7,4]=>1101100
[5,8,6,2,3,1,7,4]=>1101010
[4,8,2,6,3,1,7,5]=>1110100
[3,2,8,6,4,1,7,5]=>1101110
[3,2,1,7,5,4,8,6]=>1101110
[4,1,3,7,5,2,8,6]=>1100110
[7,1,6,3,2,5,8,4]=>1111000
[1,2,7,4,3,6,8,5]=>0011100
[6,1,8,2,4,5,7,3]=>1110000
[5,1,8,3,2,6,7,4]=>1111000
[4,8,2,7,1,5,6,3]=>1110000
[5,8,7,2,1,4,6,3]=>1110001
[6,8,7,1,3,4,5,2]=>1100001
[7,8,6,1,3,4,5,2]=>1100010
[1,7,8,2,4,5,6,3]=>0110000
[8,6,7,1,3,4,5,2]=>1100010
[7,6,8,1,3,4,5,2]=>1100010
[6,5,8,2,3,1,7,4]=>1101100
[1,6,8,3,2,5,7,4]=>0111000
[8,4,2,7,1,5,6,3]=>1111000
[7,4,2,8,1,5,6,3]=>1111000
[6,4,2,8,3,1,7,5]=>1111100
[5,4,2,3,8,1,7,6]=>1101010
[4,5,2,3,1,6,8,7]=>1100001
[7,4,2,1,3,6,8,5]=>1101100
[8,4,2,1,3,6,7,5]=>1101100
[1,5,3,2,4,7,8,6]=>0110010
[8,5,1,3,2,6,7,4]=>1101100
[5,6,1,3,4,2,8,7]=>1100001
[4,7,2,1,3,6,8,5]=>1100100
[5,7,1,3,2,6,8,4]=>1101000
[6,7,1,2,4,5,8,3]=>1010000
[1,8,2,3,5,6,7,4]=>0101000
[5,8,1,3,2,6,7,4]=>1101000
[4,8,2,1,3,6,7,5]=>1100100
[4,1,3,2,5,7,8,6]=>1100010
[5,1,2,4,3,7,8,6]=>1010010
[8,7,5,2,6,3,4,1]=>1110101
[8,6,5,2,7,3,4,1]=>1110110
[1,2,6,4,7,5,8,3]=>0011100
[3,1,7,5,4,2,6,8]=>1101100
[6,3,8,5,4,7,1,2]=>1011100
[1,6,2,5,4,7,8,3]=>0111000
[1,2,6,4,8,5,7,3]=>0011100
[7,8,3,1,4,2,5,6]=>1110000
[4,8,1,5,2,3,6,7]=>1100000
[7,4,1,5,2,3,6,8]=>1101000
[5,6,1,8,4,3,2,7]=>1111000
[5,1,8,6,4,3,2,7]=>1111010
[5,1,6,3,8,7,2,4]=>1110001
[6,1,2,5,8,3,7,4]=>1011000
[6,1,8,7,4,3,2,5]=>1111001
[7,1,2,5,4,8,6,3]=>1011010
[1,2,7,5,8,3,6,4]=>0011100
[4,1,6,3,7,5,2,8]=>1110100
[1,3,6,7,8,5,2,4]=>0100100
[1,2,6,4,7,8,5,3]=>0011100
[4,1,6,3,7,8,2,5]=>1110000
[3,1,6,4,8,2,7,5]=>1101100
[7,8,4,1,6,3,2,5]=>1111000
[4,1,6,3,8,7,2,5]=>1110001
[7,5,1,8,4,3,2,6]=>1111100
[6,5,1,7,4,3,2,8]=>1111100
[4,1,8,5,2,3,7,6]=>1100110
[4,1,6,8,3,7,2,5]=>1110000
[6,5,8,1,4,3,2,7]=>1110100
[1,6,3,2,7,4,8,5]=>0111100
[1,3,7,2,5,4,8,6]=>0101010
[2,6,1,7,4,3,8,5]=>1011100
[1,4,7,3,5,2,8,6]=>0110010
[1,3,7,5,2,4,8,6]=>0100110
[2,5,7,4,3,8,1,6]=>1011000
[2,5,3,7,4,8,1,6]=>1011000
[1,4,7,2,3,8,6,5]=>0100110
[1,4,6,3,8,2,7,5]=>0110100
[1,3,5,2,8,7,6,4]=>0101011
[1,4,7,3,8,2,6,5]=>0110100
[3,2,6,7,8,1,5,4]=>1101000
[4,3,6,7,8,2,1,5]=>1110000
[3,5,2,7,8,4,1,6]=>1101000
[1,5,7,4,8,3,2,6]=>0111000
[2,5,1,6,8,4,7,3]=>1011000
[5,3,6,4,7,8,2,1]=>1111000
[3,5,2,6,8,4,7,1]=>1101000
[2,5,4,6,8,7,1,3]=>1001001
[1,3,6,2,8,7,5,4]=>0101101
[1,4,6,3,8,7,2,5]=>0110001
[2,5,7,4,3,8,6,1]=>1011010
[1,5,7,2,4,8,6,3]=>0110010
[4,6,3,7,2,8,5,1]=>1110100
[4,3,6,7,8,2,5,1]=>1110000
[1,4,7,3,8,6,2,5]=>0110010
[3,2,6,7,8,5,1,4]=>1100100
[1,3,7,2,8,6,5,4]=>0101110
[5,1,6,8,2,4,3,7]=>1110000
[5,3,7,8,2,4,1,6]=>1110000
[8,5,3,7,2,4,1,6]=>1110100
[8,2,4,7,3,1,5,6]=>1110000
[2,4,7,8,3,1,5,6]=>1010000
[6,3,1,5,8,2,4,7]=>1110000
[6,5,3,4,2,8,1,7]=>1110100
[5,2,4,3,8,1,6,7]=>1110000
[3,2,4,8,1,5,6,7]=>1100000
[8,1,5,7,3,2,4,6]=>1110000
[8,4,6,7,2,3,1,5]=>1101000
[4,6,7,8,2,3,1,5]=>1100000
[7,4,6,8,2,3,1,5]=>1101000
[7,2,4,8,3,1,5,6]=>1110000
[5,3,8,7,2,4,1,6]=>1110001
[2,4,8,7,3,1,5,6]=>1010001
[4,6,8,7,2,3,1,5]=>1100001
[6,4,8,7,2,3,1,5]=>1101001
[3,1,7,4,2,8,6,5]=>1101110
[3,2,8,4,1,7,6,5]=>1101110
[7,6,4,8,2,3,1,5]=>1101010
[5,7,6,8,2,3,1,4]=>1100010
[4,7,6,8,2,3,1,5]=>1100010
[8,6,4,7,2,3,1,5]=>1101010
[8,2,3,7,4,1,6,5]=>1101100
[3,7,4,8,2,5,1,6]=>1101000
[2,3,7,4,1,6,8,5]=>1001100
[8,1,6,4,2,3,7,5]=>1101100
[4,7,8,6,2,3,1,5]=>1100010
[6,3,1,7,4,2,8,5]=>1111100
[8,5,7,6,2,3,1,4]=>1100110
[7,1,6,4,2,3,8,5]=>1101100
[3,1,7,6,4,2,8,5]=>1101110
[4,8,7,6,2,3,1,5]=>1100011
[6,8,7,5,2,3,1,4]=>1100101
[4,3,6,1,5,8,7,2]=>1110001
[4,3,6,5,1,8,7,2]=>1110101
[4,6,3,5,1,8,7,2]=>1110001
[4,6,3,1,5,8,7,2]=>1110001
[4,1,6,5,3,8,7,2]=>1110101
[4,6,1,5,3,8,7,2]=>1110001
[2,6,5,3,1,8,7,4]=>1011101
[2,6,5,8,3,1,7,4]=>1011100
[2,6,5,3,8,1,7,4]=>1011100
[4,6,1,5,8,3,7,2]=>1110000
[4,1,6,5,8,3,7,2]=>1110100
[1,4,6,5,8,3,7,2]=>0110100
[4,1,6,5,8,7,3,2]=>1110101
[6,4,3,8,7,1,5,2]=>1111001
[6,4,8,3,7,1,5,2]=>1111000
[2,6,8,5,3,7,1,4]=>1010100
[4,6,8,1,5,7,3,2]=>1110000
[4,6,1,8,5,7,3,2]=>1110100
[1,4,6,8,5,7,3,2]=>0110100
[1,4,6,8,5,3,7,2]=>0110100
[4,6,1,8,5,3,7,2]=>1110100
[4,6,3,8,5,7,1,2]=>1010100
[4,3,6,8,1,5,7,2]=>1110000
[4,3,6,1,8,5,7,2]=>1110100
[4,3,1,6,8,5,7,2]=>1110100
[4,1,3,6,8,7,5,2]=>1100101
[4,3,6,1,8,7,5,2]=>1110101
[4,3,6,8,1,7,5,2]=>1110100
[6,5,2,8,7,3,1,4]=>1110101
[6,5,2,8,7,1,3,4]=>1100101
[6,2,5,8,7,1,3,4]=>1100001
[6,2,5,8,7,3,1,4]=>1110001
[4,6,3,8,1,7,5,2]=>1110100
[4,6,3,1,8,7,5,2]=>1110101
[4,1,6,3,8,7,5,2]=>1110101
[1,4,6,3,8,7,5,2]=>0110101
[4,1,6,8,3,7,5,2]=>1110100
[4,6,1,8,3,7,5,2]=>1110100
[4,6,8,1,3,7,5,2]=>1100100
[6,2,8,5,7,3,1,4]=>1110100
[6,2,8,5,7,1,3,4]=>1100100
[2,4,8,7,1,5,3,6]=>1010001
[6,4,1,8,7,5,3,2]=>1111101
[6,1,4,8,7,5,3,2]=>1110101
[1,6,4,8,7,3,5,2]=>0111001
[6,4,1,8,7,3,5,2]=>1111001
[4,2,8,7,5,1,3,6]=>1100101
[2,4,8,7,3,5,1,6]=>1010001
[1,5,3,2,6,4,7,8]=>0111000
[1,5,3,2,6,7,4,8]=>0111000
[1,7,3,2,8,5,4,6]=>0111100
[1,7,3,2,5,8,4,6]=>0111000
[6,4,2,5,3,7,1,8]=>1111000
[5,4,7,6,2,3,1,8]=>1101010
[3,6,4,8,2,1,5,7]=>1101000
[1,6,2,8,5,3,4,7]=>0110100
[4,6,2,3,7,5,1,8]=>1100100
[4,7,2,3,6,5,1,8]=>1100100
[5,3,2,6,4,7,1,8]=>1111000
[3,5,2,1,6,8,4,7]=>1101000
[1,5,2,6,8,4,3,7]=>0111000
[1,5,7,2,8,4,3,6]=>0111000
[3,5,2,1,8,6,4,7]=>1101010
[3,6,8,4,2,1,5,7]=>1101000
[4,3,2,6,1,8,5,7]=>1110100
[1,5,8,2,7,4,3,6]=>0111000
[1,7,2,3,4,8,6,5]=>0100110
[6,8,2,3,4,1,7,5]=>1100100
[2,3,1,8,4,5,7,6]=>1001010
[7,3,2,1,4,5,8,6]=>1110010
[7,8,1,4,3,5,2,6]=>1110000
[1,8,2,3,4,7,6,5]=>0100110
[3,8,2,1,6,5,4,7]=>1101100
[1,7,8,3,5,4,2,6]=>0111000
[7,4,1,8,3,5,2,6]=>1111000
[8,4,1,7,3,5,2,6]=>1111000
[3,8,4,6,2,1,5,7]=>1101000
[8,4,2,5,3,1,6,7]=>1111000
[4,3,2,5,1,8,6,7]=>1110010
[3,5,2,4,1,8,6,7]=>1100010
[2,4,7,8,1,5,3,6]=>1010000
[1,8,7,3,5,4,2,6]=>0111001
[5,1,8,2,7,4,3,6]=>1111000
[5,1,7,2,8,4,3,6]=>1111000
[6,1,2,8,5,3,4,7]=>1010100
[6,3,2,1,8,4,5,7]=>1111000
[7,3,2,8,4,5,1,6]=>1111000
[2,7,8,4,3,5,1,6]=>1011000
[7,1,8,3,5,4,2,6]=>1111000
[7,8,2,3,4,6,1,5]=>1100000
[6,8,1,3,4,7,2,5]=>1100000
[8,6,2,3,4,1,7,5]=>1100110
[8,3,2,7,4,5,1,6]=>1111000
[6,7,2,3,4,1,8,5]=>1100100
[8,6,2,3,4,7,1,5]=>1100010
[4,8,7,3,5,6,1,2]=>1010001
[4,8,7,5,3,6,1,2]=>1010101
[5,8,7,3,4,6,1,2]=>1010001
[5,8,4,2,1,6,7,3]=>1111000
[5,8,4,1,2,6,7,3]=>1011000
[5,3,7,2,6,1,8,4]=>1111000
[5,2,8,1,6,3,7,4]=>1111000
[5,8,2,1,4,7,6,3]=>1110010
[4,8,2,5,1,7,6,3]=>1110010
[7,8,4,1,2,6,5,3]=>1011100
[4,8,1,5,2,7,6,3]=>1110010
[5,8,1,2,4,7,6,3]=>1010010
[5,2,8,3,6,7,1,4]=>1110000
[2,8,7,6,4,1,3,5]=>1001011
[7,8,2,6,5,1,3,4]=>1100100
[1,8,7,6,2,4,3,5]=>0110011
[2,8,1,4,5,6,7,3]=>1010000
[2,1,7,3,6,5,8,4]=>1011100
[3,2,7,1,6,5,8,4]=>1101100
[6,1,2,8,5,7,3,4]=>1010100
[6,2,1,8,5,7,3,4]=>1110100
[6,3,1,8,5,7,2,4]=>1110100
[6,4,2,1,7,5,8,3]=>1111100
[6,1,3,8,5,2,7,4]=>1101100
[1,3,7,2,6,8,5,4]=>0101100
[7,8,2,6,5,3,1,4]=>1110100
[3,2,6,7,5,8,1,4]=>1100100
[1,2,7,5,6,3,8,4]=>0011100
[2,8,7,6,4,3,1,5]=>1011011
[3,8,7,6,1,2,5,4]=>1001011
[4,8,7,6,2,1,3,5]=>1100011
[4,8,7,6,1,3,2,5]=>1100011
[3,8,7,6,4,1,2,5]=>1001011
[7,8,3,6,5,1,2,4]=>1010100
[2,3,7,5,6,8,1,4]=>1000100
[3,8,7,6,4,2,1,5]=>1101011
[3,4,2,6,7,8,1,5]=>1100000
[3,1,4,2,6,8,7,5]=>1100101
[8,3,4,2,6,1,7,5]=>1110100
[2,6,7,3,5,4,1,8]=>1011000
[2,7,8,3,5,4,1,6]=>1011000
[2,6,8,3,5,4,1,7]=>1011000
[4,7,1,2,8,5,3,6]=>1010100
[4,8,1,2,7,5,3,6]=>1010100
[2,1,6,3,7,5,4,8]=>1011100
[2,7,1,3,6,8,4,5]=>1001000
[7,4,1,2,8,5,3,6]=>1011100
[8,7,4,2,1,5,3,6]=>1111001
[7,4,1,2,6,5,3,8]=>1011100
[7,4,3,1,5,6,8,2]=>1111000
[6,7,4,1,5,8,3,2]=>1111000
[4,7,5,1,6,8,3,2]=>1110100
[4,5,3,1,7,6,8,2]=>1110010
[4,6,1,2,7,5,3,8]=>1010100
[4,6,1,2,8,5,3,7]=>1010100
[4,5,3,1,8,6,7,2]=>1110010
[4,8,5,6,3,1,7,2]=>1110100
[5,1,3,4,8,6,7,2]=>1100010
[5,4,3,8,1,6,7,2]=>1111000
[8,5,3,4,1,6,7,2]=>1110100
[6,4,8,2,1,5,3,7]=>1111000
[6,7,3,2,5,1,4,8]=>1110000
[6,8,3,2,5,1,4,7]=>1110000
[5,7,1,4,6,8,3,2]=>1110000
[5,1,3,4,7,6,8,2]=>1100010
[5,4,3,7,1,6,8,2]=>1111000
[6,7,5,4,1,8,3,2]=>1111100
[7,6,4,2,1,5,3,8]=>1111010
[8,5,6,1,3,2,4,7]=>1100100
[8,6,1,5,3,2,4,7]=>1110010
[7,8,1,5,3,2,4,6]=>1110000
[8,1,7,5,3,2,4,6]=>1110100
[8,6,1,4,5,2,3,7]=>1100010
[8,6,3,1,5,2,4,7]=>1110010
[8,4,6,1,5,2,3,7]=>1101000
[8,6,2,1,5,4,3,7]=>1111010
[8,5,2,6,1,4,3,7]=>1110100
[8,5,2,1,7,4,3,6]=>1111100
[8,2,7,5,1,3,4,6]=>1100100
[8,4,1,7,5,2,3,6]=>1101100
[8,2,6,1,7,4,3,5]=>1111000
[8,1,7,4,3,2,6,5]=>1111100
[8,1,5,7,3,2,6,4]=>1111000
[5,7,8,1,3,2,6,4]=>1101000
[8,2,6,1,5,7,3,4]=>1110000
[5,8,1,6,7,2,3,4]=>1100000
[5,7,6,1,8,2,3,4]=>1100010
[8,1,5,6,7,2,3,4]=>1100000
[6,5,7,1,8,2,3,4]=>1100100
[8,1,6,4,7,2,3,5]=>1101000
[7,5,8,1,3,2,4,6]=>1100100
[7,8,4,1,3,2,5,6]=>1101000
[8,3,7,4,1,2,5,6]=>1011000
[8,5,1,7,3,2,4,6]=>1110100
[6,8,1,7,3,2,4,5]=>1110000
[7,1,8,4,3,6,2,5]=>1111000
[7,3,1,8,6,4,2,5]=>1111010
[8,3,1,7,4,6,2,5]=>1111000
[8,4,5,1,7,2,3,6]=>1101000
[5,6,8,1,7,2,3,4]=>1100000
[6,5,8,1,2,7,3,4]=>1010100
[7,3,1,8,5,6,2,4]=>1110100
[6,2,7,8,3,1,5,4]=>1111000
[5,8,1,7,3,2,6,4]=>1111000
[8,4,1,7,3,2,6,5]=>1111100
[8,3,4,7,1,2,6,5]=>1010100
[7,4,8,2,1,3,6,5]=>1101100
[7,4,3,8,1,2,6,5]=>1011100
[8,2,3,6,7,1,5,4]=>1101000
[2,6,8,7,1,5,4,3]=>1011001
[7,8,5,2,3,6,4,1]=>1101100
[8,7,5,2,3,1,6,4]=>1101101
[6,8,5,2,3,4,7,1]=>1100100
[5,7,3,4,6,8,1,2]=>1010000
[5,7,3,4,6,1,2,8]=>1010000
[7,3,5,6,1,2,8,4]=>1011000
[5,7,3,1,4,6,8,2]=>1110000
[5,7,3,1,4,8,6,2]=>1110010
[5,7,3,1,4,8,2,6]=>1110000
[5,3,7,4,1,2,8,6]=>1011010
[5,3,7,4,1,2,6,8]=>1011000
[5,3,7,1,4,2,6,8]=>1110000
[5,3,7,1,4,2,8,6]=>1110010
[3,7,5,1,2,8,6,4]=>1001110
[7,8,3,5,1,2,6,4]=>1011000
[7,3,8,5,1,2,6,4]=>1011100
[7,3,5,8,1,2,6,4]=>1011000
[3,7,5,1,2,6,4,8]=>1001100
[3,7,5,1,2,6,8,4]=>1001100
[3,6,8,7,2,5,1,4]=>1100001
[3,5,7,2,8,6,1,4]=>1100010
[2,5,7,4,8,6,1,3]=>1001010
[1,6,3,7,5,2,8,4]=>0111100
[2,6,4,8,7,5,1,3]=>1001101
[3,6,2,5,8,7,1,4]=>1100001
[5,2,8,4,7,6,1,3]=>1101010
[7,2,4,8,6,5,1,3]=>1100110
[6,2,4,8,7,5,1,3]=>1100101
[2,3,5,7,6,1,8,4]=>1001010
[1,3,4,6,2,8,7,5]=>0100101
[5,2,3,6,1,8,7,4]=>1101001
[4,2,7,3,8,1,6,5]=>1110100
[2,5,1,4,7,3,8,6]=>1010010
[6,1,3,8,7,2,5,4]=>1101001
[3,1,5,6,2,8,7,4]=>1101001
[1,2,4,6,3,8,7,5]=>0010101
[7,1,4,2,8,6,5,3]=>1110110
[5,1,3,7,2,8,6,4]=>1101010
[4,1,5,3,2,8,7,6]=>1110011
[2,6,1,4,3,8,7,5]=>1010101
[3,6,2,4,1,8,7,5]=>1100101
[7,2,3,5,1,8,6,4]=>1101010
[7,3,4,1,8,6,5,2]=>1110110
[6,3,4,1,8,7,5,2]=>1110101
[3,4,5,1,8,7,6,2]=>1100011
[1,4,5,2,8,7,6,3]=>0110011
[1,6,4,2,8,7,5,3]=>0111101
[4,6,2,7,5,1,8,3]=>1110100
[4,5,2,6,1,8,7,3]=>1110001
[1,5,3,6,2,8,7,4]=>0111001
[1,5,8,3,2,7,6,4]=>0111010
[2,5,8,3,1,7,6,4]=>1011010
[3,6,2,5,1,4,8,7]=>1100001
[5,2,8,4,1,3,7,6]=>1101010
[2,4,8,7,1,3,6,5]=>1000101
[2,5,8,1,3,7,6,4]=>1001010
[2,3,8,1,4,7,6,5]=>1000110
[3,4,1,7,2,8,6,5]=>1100110
[3,5,2,1,7,4,8,6]=>1101010
[6,3,1,7,2,8,5,4]=>1111100
[7,5,1,2,8,6,4,3]=>1011110
[4,6,1,2,8,7,5,3]=>1010101
[1,6,2,3,8,7,5,4]=>0101101
[1,5,2,3,8,7,6,4]=>0101011
[4,5,1,2,8,7,6,3]=>1010011
[6,4,1,2,8,7,5,3]=>1011101
[7,4,1,2,8,6,5,3]=>1011110
[5,3,1,7,2,8,6,4]=>1111010
[5,2,8,1,3,7,6,4]=>1101010
[4,1,2,8,3,7,6,5]=>1010110
[3,5,8,7,2,6,4,1]=>1101001
[5,8,2,7,1,6,4,3]=>1111000
[2,1,6,4,5,8,3,7]=>1011000
[8,6,3,7,5,2,1,4]=>1110110
[4,6,3,8,5,2,1,7]=>1110100
[4,6,3,7,5,2,8,1]=>1110100
[3,5,7,8,2,6,1,4]=>1100000
[4,2,3,6,1,5,8,7]=>1100001
[3,8,6,4,5,1,2,7]=>1001010
[4,8,3,7,5,2,1,6]=>1110100
[8,7,3,6,5,1,2,4]=>1010101
[5,2,8,3,7,6,1,4]=>1110010
[8,2,7,3,1,6,4,5]=>1111000
[8,6,7,4,1,5,3,2]=>1111010
[4,8,6,7,5,1,3,2]=>1100110
[7,1,8,4,6,5,2,3]=>1101100
[8,7,1,5,4,6,2,3]=>1101001
[8,5,7,1,4,6,3,2]=>1110100
[6,4,8,5,1,7,3,2]=>1111100
[8,4,7,1,5,6,3,2]=>1111000
[8,7,5,1,4,6,2,3]=>1100101
[8,7,2,5,1,4,6,3]=>1110001
[4,8,7,2,5,1,6,3]=>1110001
[8,7,1,4,2,5,6,3]=>1110001
[8,7,5,1,2,4,6,3]=>1010101
[7,1,8,5,6,2,3,4]=>1100100
[3,5,8,7,1,2,6,4]=>1001001
[2,3,8,5,7,1,6,4]=>1001100
[3,8,7,1,5,6,2,4]=>1100001
[3,5,8,7,1,6,2,4]=>1100001
[2,3,8,6,7,5,1,4]=>1000110
[3,2,8,6,7,5,1,4]=>1100110
[4,1,8,6,2,7,5,3]=>1110110
[8,7,4,1,2,6,5,3]=>1011101
[1,3,8,6,7,5,2,4]=>0100110
[5,7,1,8,2,6,3,4]=>1110000
[2,8,7,1,5,6,3,4]=>1010001
[8,7,1,5,2,4,6,3]=>1110001
[7,1,8,2,4,6,5,3]=>1110100
[1,6,2,8,4,7,5,3]=>0111100
[1,3,8,5,7,2,6,4]=>0101100
[1,8,3,7,2,5,6,4]=>0111000
[2,8,7,1,3,5,6,4]=>1001001
[5,7,1,8,2,3,6,4]=>1101000
[7,1,8,2,3,5,6,4]=>1101000
[8,6,3,7,4,1,5,2]=>1111010
[4,2,8,6,7,5,1,3]=>1100110
[8,4,2,7,5,6,1,3]=>1101100
[4,8,3,6,1,7,5,2]=>1110100
[8,3,4,7,5,1,6,2]=>1110100
[8,3,7,4,5,1,6,2]=>1111000
[8,7,4,2,5,6,1,3]=>1101001
[8,7,5,1,6,2,3,4]=>1100101
[8,7,2,4,1,5,6,3]=>1110001
[4,8,6,1,7,2,5,3]=>1110010
[4,2,8,6,7,1,5,3]=>1110010
[8,7,4,1,2,5,6,3]=>1011001
[8,2,7,1,6,3,4,5]=>1110000
[8,2,7,1,3,6,4,5]=>1101000
[2,8,3,6,7,1,5,4]=>1011000
[8,7,2,1,3,5,6,4]=>1101001
[1,8,7,2,3,6,4,5]=>0101001
[1,8,7,2,6,3,4,5]=>0110001
[8,2,7,3,6,1,4,5]=>1110000
[1,8,7,3,6,2,4,5]=>0110001
[1,8,2,7,6,3,4,5]=>0110010
[8,2,7,4,1,5,6,3]=>1111000
[8,2,1,7,5,6,3,4]=>1110100
[8,7,3,1,5,6,2,4]=>1110001
[2,8,7,3,5,6,1,4]=>1010001
[8,3,1,6,7,5,2,4]=>1110100
[8,5,2,1,6,7,4,3]=>1111100
[1,5,2,8,6,7,4,3]=>0111010
[1,2,8,6,7,5,3,4]=>0010110
[1,8,3,6,7,5,2,4]=>0110100
[8,2,3,6,7,5,1,4]=>1100100
[8,3,7,2,5,6,1,4]=>1110000
[8,1,3,7,5,6,2,4]=>1100100
[8,4,1,2,7,5,6,3]=>1011100
[8,1,4,2,6,7,5,3]=>1110100
[1,2,8,6,7,3,5,4]=>0011010
[8,1,2,7,3,6,4,5]=>1011000
[8,1,7,3,6,2,4,5]=>1110000
[8,1,7,2,6,3,4,5]=>1110000
[8,1,7,2,3,6,4,5]=>1101000
[8,1,3,7,2,5,6,4]=>1101000
[1,8,3,6,7,2,5,4]=>0111000
[1,7,8,2,3,6,5,4]=>0101100
[8,3,7,1,2,5,6,4]=>1011000
[7,4,2,6,1,5,3,8]=>1111000
[7,4,2,5,6,1,3,8]=>1101000
[7,3,5,6,4,2,1,8]=>1111000
[7,4,3,1,5,6,2,8]=>1111000
[7,4,5,2,6,1,3,8]=>1101000
[5,3,7,2,8,6,4,1]=>1111010
[5,3,8,2,6,7,4,1]=>1111000
[6,3,8,2,5,4,7,1]=>1111000
[6,4,3,1,8,2,7,5]=>1111100
[5,3,7,8,2,6,4,1]=>1111000
[4,7,8,5,6,3,2,1]=>1110100
[5,3,7,6,8,2,4,1]=>1110010
[5,7,8,4,6,2,1,3]=>1101000
[5,8,4,3,6,7,1,2]=>1011000
[5,8,6,4,7,2,1,3]=>1101010
[5,3,8,6,2,7,4,1]=>1111010
[4,7,5,8,6,3,2,1]=>1110110
[6,3,8,7,2,4,1,5]=>1110001
[5,3,8,7,2,6,4,1]=>1111001
[5,3,8,6,7,2,4,1]=>1110010
[5,3,7,8,6,2,4,1]=>1110010
[5,7,6,4,8,2,1,3]=>1101010
[5,8,4,6,7,2,1,3]=>1101000
[6,4,2,8,1,7,3,5]=>1111000
[6,5,2,4,3,7,8,1]=>1110100
[5,4,6,2,8,7,1,3]=>1101001
[5,6,3,8,7,2,4,1]=>1110001
[6,7,4,3,1,8,2,5]=>1111000
[5,7,4,3,6,8,1,2]=>1011000
[5,7,3,8,6,2,4,1]=>1110010
[4,5,8,6,7,3,2,1]=>1110010
[4,6,8,5,7,3,2,1]=>1110100
[5,6,8,3,7,2,4,1]=>1110000
[5,4,6,8,2,7,1,3]=>1101000
[7,8,4,5,1,3,2,6]=>1101000
[6,7,1,3,2,5,4,8]=>1101000
[6,7,1,4,3,5,2,8]=>1110000
[7,8,2,3,1,5,4,6]=>1101000
[7,8,2,4,3,5,1,6]=>1110000
[7,8,2,4,1,5,3,6]=>1110000
[1,4,2,6,5,7,3,8]=>0110100
[5,6,1,4,2,7,3,8]=>1110000
[6,7,2,4,1,5,3,8]=>1110000
[6,7,2,4,3,5,1,8]=>1110000
[6,7,2,3,1,5,4,8]=>1101000
[6,7,3,5,4,8,1,2]=>1011000
[2,4,1,6,5,7,3,8]=>1010100
[1,5,2,6,4,7,3,8]=>0111000
[2,5,1,6,4,7,3,8]=>1011000
[5,6,2,4,3,7,1,8]=>1110000
[4,5,2,6,1,7,3,8]=>1110000
[4,5,1,6,3,7,2,8]=>1110000
[4,5,3,6,1,7,2,8]=>1110000
[5,6,3,4,1,7,2,8]=>1110000
[5,6,1,4,3,7,2,8]=>1110000
[5,6,1,3,2,7,4,8]=>1101000
[5,6,4,7,1,3,2,8]=>1101000
[6,7,4,5,1,3,2,8]=>1101000
[6,7,5,8,1,3,2,4]=>1100100
[4,5,1,3,2,7,6,8]=>1100010
[4,6,5,7,1,3,2,8]=>1100100
[4,6,1,3,2,7,5,8]=>1100100
[1,4,3,6,2,7,5,8]=>0110100
[4,5,2,3,1,7,6,8]=>1100010
[4,5,3,7,6,8,1,2]=>1010010
[4,6,5,7,3,8,1,2]=>1010100
[4,6,5,7,2,3,1,8]=>1100100
[3,5,4,6,1,7,2,8]=>1101000
[3,5,1,6,4,7,2,8]=>1101000
[1,5,3,6,4,7,2,8]=>0111000
[1,5,3,6,2,7,4,8]=>0111000
[3,5,2,6,1,7,4,8]=>1101000
[3,5,2,6,4,7,1,8]=>1101000
[3,4,2,6,1,7,5,8]=>1100100
[4,6,2,3,1,7,5,8]=>1100100
[2,4,3,6,1,7,5,8]=>1010100
[2,5,3,6,4,7,1,8]=>1011000
[2,5,3,6,1,7,4,8]=>1011000
[4,6,2,7,3,5,8,1]=>1110000
[3,6,2,7,5,4,8,1]=>1101100
[4,6,1,7,3,8,2,5]=>1110000
[2,4,7,1,3,8,6,5]=>1000110
[5,2,6,7,4,3,8,1]=>1111000
[3,5,2,7,6,4,8,1]=>1101010
[1,5,7,4,3,8,2,6]=>0111000
[2,5,7,3,1,8,6,4]=>1011010
[1,5,7,2,8,3,6,4]=>0111000
[2,5,7,3,1,8,4,6]=>1011000
[1,5,7,3,4,8,2,6]=>0110000
[5,2,6,7,1,8,4,3]=>1111000
[1,3,7,2,8,5,6,4]=>0101100
[2,3,1,5,8,4,7,6]=>1001010
[2,1,5,6,8,4,3,7]=>1011000
[2,3,1,5,8,6,4,7]=>1001010
[2,4,7,3,1,8,5,6]=>1010100
[1,3,7,2,8,5,4,6]=>0101100
[2,3,1,6,8,5,4,7]=>1001100
[4,6,2,7,1,8,3,5]=>1110000
[1,5,4,3,6,8,2,7]=>0111000
[1,6,4,5,7,8,3,2]=>0111000
[2,5,1,7,8,6,3,4]=>1010010
[1,3,6,2,8,7,4,5]=>0101001
[2,1,5,6,8,4,7,3]=>1011000
[1,3,6,2,8,4,7,5]=>0101100
[2,1,5,6,8,7,3,4]=>1010001
[3,6,5,2,7,8,4,1]=>1101100
[6,2,4,7,5,8,3,1]=>1110100
[1,5,7,8,4,2,6,3]=>0111000
[3,7,4,1,8,6,2,5]=>1101010
[3,4,6,8,5,7,2,1]=>1100100
[4,5,6,2,8,7,3,1]=>1110001
[4,5,6,1,8,7,3,2]=>1110001
[4,5,6,3,1,8,7,2]=>1110001
[4,3,6,2,1,7,5,8]=>1110100
[4,6,3,2,1,7,5,8]=>1110100
[4,6,3,1,7,5,2,8]=>1110100
[4,5,3,7,6,1,8,2]=>1110010
[4,5,1,7,3,8,6,2]=>1110010
[2,5,7,1,4,3,8,6]=>1010010
[4,3,5,7,6,1,8,2]=>1110010
[4,3,6,1,7,5,2,8]=>1110100
[4,3,2,6,1,7,5,8]=>1110100
[5,3,2,1,6,4,7,8]=>1111000
[5,3,1,6,2,7,4,8]=>1111000
[5,1,6,3,2,7,4,8]=>1111000
[2,6,1,4,7,5,3,8]=>1010100
[3,6,1,7,4,2,5,8]=>1101000
[4,6,1,7,5,3,2,8]=>1110100
[5,1,6,3,7,4,2,8]=>1111000
[5,3,6,4,2,1,7,8]=>1111000
[5,3,2,6,4,1,7,8]=>1111000
[5,2,1,6,3,7,4,8]=>1111000
[5,2,6,3,1,7,4,8]=>1111000
[4,2,6,3,1,7,8,5]=>1110100
[3,6,2,1,7,4,5,8]=>1101000
[3,6,2,7,4,1,5,8]=>1101000
[3,5,7,2,8,6,4,1]=>1101010
[2,6,1,3,7,5,4,8]=>1001100
[3,6,1,7,5,2,4,8]=>1100100
[5,1,6,2,7,4,3,8]=>1111000
[5,2,6,4,3,1,7,8]=>1111000
[5,2,1,6,4,3,7,8]=>1111000
[5,4,2,1,6,3,7,8]=>1111000
[5,4,1,6,2,7,3,8]=>1111000
[5,1,6,4,2,7,3,8]=>1111000
[3,6,1,7,5,4,8,2]=>1101100
[2,6,1,5,4,3,7,8]=>1011000
[3,1,6,2,5,4,7,8]=>1101000
[4,1,6,3,2,7,8,5]=>1110100
[5,1,6,4,3,2,7,8]=>1111000
[5,4,1,6,3,2,7,8]=>1111000
[5,4,3,1,6,2,7,8]=>1111000
[1,2,8,7,4,6,3,5]=>0011001
[3,7,4,8,6,1,5,2]=>1101010
[4,5,1,8,7,6,2,3]=>1100011
[1,5,2,8,7,6,3,4]=>0110011
[5,1,2,8,7,6,3,4]=>1010011
[4,1,5,8,7,6,2,3]=>1100011
[2,3,6,8,7,4,5,1]=>1001001
[2,3,7,8,6,4,5,1]=>1001010
[4,5,7,8,2,6,3,1]=>1110000
[4,5,6,8,2,7,3,1]=>1110000
[5,2,6,8,3,7,4,1]=>1111000
[3,1,6,8,7,4,5,2]=>1101001
[6,1,4,8,7,2,5,3]=>1110001
[6,1,8,4,7,3,5,2]=>1111000
[5,8,3,4,7,1,6,2]=>1110000
[6,8,3,5,7,1,4,2]=>1110000
[5,2,7,8,3,6,4,1]=>1111000
[4,6,7,8,2,5,3,1]=>1110000
[7,5,8,4,2,6,3,1]=>1111100
[6,8,4,5,2,7,3,1]=>1111000
[6,8,2,5,3,7,4,1]=>1111000
[6,3,8,4,2,7,5,1]=>1111100
[7,2,5,3,8,6,4,1]=>1111010
[3,4,7,5,8,6,2,1]=>1100110
[3,6,7,4,8,5,2,1]=>1101100
[6,7,4,2,8,5,3,1]=>1111100
[4,7,5,2,8,6,3,1]=>1110110
[5,6,2,8,3,7,4,1]=>1111000
[5,7,8,3,2,6,4,1]=>1111000
[5,6,8,3,2,7,4,1]=>1111000
[3,6,8,4,2,7,5,1]=>1101100
[1,5,8,2,7,3,6,4]=>0111000
[5,8,4,7,2,3,6,1]=>1101000
[5,6,8,1,3,7,4,2]=>1101000
[6,7,4,8,1,5,3,2]=>1111000
[5,7,2,8,3,6,4,1]=>1111000
[1,7,4,8,6,2,5,3]=>0111010
[7,4,2,8,6,1,5,3]=>1111010
[6,8,5,3,7,2,4,1]=>1110100
[6,8,5,2,3,7,4,1]=>1101100
[7,5,3,8,2,6,4,1]=>1111100
[3,7,4,5,8,6,2,1]=>1101010
[7,4,2,5,8,6,3,1]=>1111010
[6,1,8,3,4,7,5,2]=>1110100
[6,8,4,2,5,7,3,1]=>1111000
[7,5,8,3,4,6,2,1]=>1110100
[7,4,5,8,1,6,3,2]=>1111000
[6,3,4,7,8,5,2,1]=>1110100
[3,6,8,4,5,7,1,2]=>1001000
[1,6,8,4,7,2,3,5]=>0101000
[1,4,5,7,8,2,6,3]=>0110000
[1,4,5,8,7,2,3,6]=>0100001
[1,2,5,8,3,6,4,7]=>0011000
[7,8,1,4,6,2,3,5]=>1100000
[1,6,7,4,8,2,5,3]=>0111000
[1,4,5,6,8,2,7,3]=>0110000
[1,4,5,8,6,2,7,3]=>0110010
[1,2,5,8,3,4,7,6]=>0010010
[7,8,1,2,3,5,4,6]=>1001000
[1,6,7,2,3,5,4,8]=>0101000
[1,4,5,7,6,2,3,8]=>0100010
[1,2,5,7,3,6,4,8]=>0011000
[1,2,5,7,3,6,8,4]=>0011000
[1,6,8,2,3,5,7,4]=>0101000
[1,6,8,4,5,2,3,7]=>0101000
[1,6,8,2,3,4,7,5]=>0100100
[1,6,8,2,3,7,4,5]=>0101000
[1,4,5,7,6,2,8,3]=>0110010
[7,8,1,4,5,2,6,3]=>1110000
[1,6,7,2,3,8,5,4]=>0101100
[1,2,5,6,3,8,7,4]=>0011001
[2,7,4,8,3,5,1,6]=>1011000
[2,7,4,8,3,5,6,1]=>1011000
[7,2,8,4,3,5,1,6]=>1111000
[8,4,2,1,5,3,6,7]=>1111000
[8,4,1,5,3,2,6,7]=>1111000
[6,7,3,8,4,2,5,1]=>1111000
[6,7,3,8,4,2,1,5]=>1111000
[7,1,8,4,3,5,2,6]=>1111000
[1,7,8,4,3,5,2,6]=>0111000
[7,1,4,8,3,5,2,6]=>1110000
[7,1,8,4,3,5,6,2]=>1111000
[6,7,3,1,8,4,5,2]=>1111000
[6,7,1,4,8,3,5,2]=>1110000
[6,7,4,1,3,8,2,5]=>1101000
[1,6,7,8,4,3,2,5]=>0111000
[7,2,1,8,4,5,3,6]=>1111000
[6,2,7,1,8,4,3,5]=>1111000
[6,2,7,8,4,3,1,5]=>1111000
[6,2,7,8,4,3,5,1]=>1111000
[2,6,7,4,8,3,5,1]=>1011000
[2,6,7,4,8,3,1,5]=>1011000
[7,8,1,3,6,2,4,5]=>1100000
[1,2,7,8,6,3,4,5]=>0010010
[2,6,7,1,8,5,3,4]=>1010100
[2,6,7,8,5,3,4,1]=>1010100
[6,2,7,8,4,5,3,1]=>1111000
[1,7,2,8,4,5,6,3]=>0111000
[6,3,7,8,1,5,2,4]=>1110000
[6,7,1,2,8,5,3,4]=>1010100
[1,6,7,8,4,2,5,3]=>0111000
[3,1,2,7,6,5,8,4]=>1001110
[6,1,2,4,7,3,8,5]=>1010100
[1,7,5,3,6,4,8,2]=>0111100
[5,1,2,6,7,4,8,3]=>1011000
[4,1,5,7,3,2,6,8]=>1110000
[4,6,1,7,3,2,5,8]=>1110000
[4,6,1,8,3,2,5,7]=>1110000
[4,1,7,8,6,2,3,5]=>1100010
[1,6,5,7,8,3,4,2]=>0110100
[1,6,5,8,7,3,4,2]=>0110101
[4,1,8,7,6,2,3,5]=>1100011
[4,8,1,7,3,5,2,6]=>1110000
[4,8,1,6,3,2,5,7]=>1110000
[4,7,1,6,3,2,5,8]=>1110000
[6,1,2,3,7,5,4,8]=>1001100
[6,8,1,5,3,7,2,4]=>1110000
[8,7,5,2,4,1,6,3]=>1110101
[1,5,8,3,4,7,6,2]=>0110010
[7,8,5,2,4,1,6,3]=>1110100
[7,1,2,3,5,6,4,8]=>1001000
[7,1,8,4,6,3,2,5]=>1111000
[6,8,2,4,3,1,5,7]=>1110000
[6,7,2,4,3,1,5,8]=>1110000
[3,7,1,8,6,4,2,5]=>1101010
[1,6,4,3,7,5,8,2]=>0111100
[3,1,2,6,7,5,8,4]=>1001100
[3,8,1,7,6,4,2,5]=>1101010
[7,6,2,4,3,1,5,8]=>1110010
[8,7,2,4,3,5,1,6]=>1110001
[8,1,7,4,6,3,2,5]=>1111000
[8,1,7,6,5,3,2,4]=>1110110
[1,5,7,3,4,6,8,2]=>0110000
[8,7,2,5,3,6,1,4]=>1110001
[7,1,2,3,5,4,8,6]=>1001010
[6,1,2,3,5,8,4,7]=>1001000
[6,1,2,3,5,7,4,8]=>1001000
[5,1,2,3,7,6,4,8]=>1001010
[5,1,2,3,8,6,4,7]=>1001010
[1,5,6,3,4,7,8,2]=>0110000
[8,6,5,2,4,7,1,3]=>1100110
[7,6,2,5,3,1,8,4]=>1111010
[6,7,3,5,1,4,8,2]=>1110000
[5,7,8,4,2,6,3,1]=>1111000
[5,4,7,6,2,8,3,1]=>1111010
[5,7,4,1,6,8,3,2]=>1111000
[6,8,4,5,7,1,3,2]=>1101000
[5,8,4,6,1,7,3,2]=>1111000
[5,6,1,4,7,8,3,2]=>1110000
[5,6,7,2,4,8,3,1]=>1110000
[5,3,6,7,4,8,2,1]=>1111000
[5,3,2,8,6,7,4,1]=>1111010
[5,4,8,2,6,7,3,1]=>1111000
[5,4,8,6,2,7,3,1]=>1111010
[6,4,8,5,7,2,3,1]=>1101100
[4,6,8,5,7,2,3,1]=>1100100
[5,6,8,2,4,7,3,1]=>1110000
[5,6,3,8,4,7,2,1]=>1111000
[4,6,3,5,8,7,2,1]=>1110001
[4,6,3,2,8,7,5,1]=>1110101
[5,6,3,8,2,7,4,1]=>1111000
[3,6,5,8,7,2,4,1]=>1100101
[5,3,6,8,2,7,4,1]=>1111000
[4,3,7,2,8,6,5,1]=>1110110
[5,4,7,2,6,8,3,1]=>1111000
[5,3,2,7,6,8,4,1]=>1111010
[6,7,3,8,5,2,4,1]=>1110100
[6,3,2,7,5,4,8,1]=>1111100
[6,4,7,2,5,3,8,1]=>1111000
[6,2,7,5,1,4,8,3]=>1110100
[2,7,8,5,3,6,1,4]=>1010100
[6,3,7,8,4,2,5,1]=>1111000
[3,5,7,8,4,6,2,1]=>1101000
[5,7,8,2,4,6,3,1]=>1110000
[2,5,8,4,3,7,6,1]=>1011010
[2,6,8,4,7,3,5,1]=>1011000
[3,7,4,8,6,2,1,5]=>1101010
[3,6,4,8,7,2,5,1]=>1101001
[3,5,4,8,2,7,6,1]=>1101010
[4,5,7,3,8,6,2,1]=>1110010
[6,3,1,8,7,5,4,2]=>1111101
[5,4,8,1,7,6,3,2]=>1111010
[5,8,4,1,7,6,3,2]=>1111010
[7,5,4,1,8,6,3,2]=>1111110
[8,5,4,1,7,6,3,2]=>1111110
[1,8,2,5,6,3,4,7]=>0110000
[7,2,8,4,5,1,3,6]=>1101000
[1,3,7,5,6,2,4,8]=>0100100
[1,6,7,4,3,5,2,8]=>0111000
[1,8,2,5,3,6,7,4]=>0111000
[2,6,8,4,3,5,7,1]=>1011000
[7,2,8,4,1,5,6,3]=>1111000
[7,5,8,1,2,6,3,4]=>1010100
[1,5,2,6,4,7,8,3]=>0111000
[1,5,4,6,2,3,7,8]=>0101000
[6,2,5,7,1,4,8,3]=>1110000
[6,5,4,3,8,1,7,2]=>1111100
[2,6,5,8,3,4,1,7]=>1010100
[2,6,5,7,3,4,1,8]=>1010100
[6,2,5,7,4,1,3,8]=>1101000
[6,2,5,8,4,1,3,7]=>1101000
[2,7,8,4,6,1,3,5]=>1001000
[6,1,2,8,5,4,7,3]=>1011100
[6,2,5,7,8,1,3,4]=>1100000
[1,5,4,2,6,7,3,8]=>0111000
[2,6,5,7,3,8,1,4]=>1010100
[1,6,2,7,5,8,4,3]=>0111100
[1,3,2,7,8,5,6,4]=>0101100
[1,6,2,4,8,7,3,5]=>0110001
[6,5,2,1,8,7,3,4]=>1110101
[2,6,5,3,7,8,4,1]=>1011100
[6,5,2,3,8,7,1,4]=>1100101
[5,1,4,2,3,7,8,6]=>1100010
[1,5,4,2,6,3,8,7]=>0111001
[5,1,6,3,8,2,7,4]=>1111000
[6,5,8,7,4,3,1,2]=>1011101
[6,4,2,7,8,5,1,3]=>1101100
[6,1,4,8,7,5,2,3]=>1100101
[1,6,4,8,7,5,2,3]=>0101101
[1,8,6,2,4,7,3,5]=>0110010
[8,1,6,2,4,7,3,5]=>1110000
[6,4,1,7,8,5,2,3]=>1101100
[7,6,1,2,4,8,3,5]=>1010010
[1,8,6,3,4,7,2,5]=>0110010
[1,7,2,5,4,8,3,6]=>0111000
[7,1,2,5,4,8,3,6]=>1011000
[2,7,1,5,4,8,3,6]=>1011000
[2,8,6,1,4,7,3,5]=>1010010
[7,2,1,5,4,8,3,6]=>1111000
[1,2,7,5,4,8,3,6]=>0011100
[3,2,7,5,4,8,1,6]=>1101100
[2,5,8,4,7,3,1,6]=>1011000
[2,3,7,5,4,8,1,6]=>1001100
[6,8,3,2,4,7,1,5]=>1110000
[3,7,2,5,4,8,1,6]=>1101000
[3,1,7,5,4,8,2,6]=>1101100
[1,3,7,5,4,8,2,6]=>0101100
[1,5,8,4,7,3,2,6]=>0111000
[5,1,8,4,7,3,2,6]=>1111000
[5,8,2,4,7,3,1,6]=>1110000
[6,8,4,3,7,5,1,2]=>1011100
[8,5,2,4,7,3,1,6]=>1110100
[8,1,5,4,7,3,2,6]=>1111000
[1,8,5,4,7,3,2,6]=>0111100
[1,7,3,5,4,8,2,6]=>0111000
[8,6,3,1,4,7,2,5]=>1110010
[8,6,4,1,7,2,5,3]=>1111010
[5,3,7,4,6,8,2,1]=>1111000
[4,1,3,2,7,8,5,6]=>1100100
[1,4,3,2,7,8,5,6]=>0110100
[2,4,3,1,7,8,5,6]=>1010100
[2,7,3,5,4,8,1,6]=>1011000
[2,8,5,4,7,3,1,6]=>1011100
[5,7,3,4,6,8,2,1]=>1110000
[8,2,5,4,7,3,1,6]=>1111000
[7,2,3,5,4,8,1,6]=>1101000
[3,2,1,4,7,8,5,6]=>1100100
[8,1,7,6,4,3,5,2]=>1111010
[8,6,4,5,2,7,1,3]=>1101010
[7,1,8,6,4,3,5,2]=>1111010
[7,4,2,5,1,6,3,8]=>1111000
[7,3,6,5,2,1,4,8]=>1110100
[8,3,6,5,2,1,7,4]=>1111100
[7,3,6,5,2,1,8,4]=>1111100
[5,4,2,8,1,3,7,6]=>1101010
[5,8,2,6,4,1,3,7]=>1101000
[6,4,2,5,1,8,3,7]=>1111000
[6,3,5,2,1,4,7,8]=>1110000
[2,3,5,8,1,4,7,6]=>1000010
[2,3,6,8,1,5,7,4]=>1001000
[6,3,8,5,2,7,1,4]=>1110100
[6,3,7,5,2,1,4,8]=>1110100
[2,5,7,6,3,1,4,8]=>1010010
[2,8,7,6,3,1,5,4]=>1011011
[2,5,8,7,6,3,1,4]=>1010011
[2,4,8,1,6,5,7,3]=>1010100
[2,8,7,3,6,1,4,5]=>1010001
[8,4,2,5,1,3,7,6]=>1101010
[2,3,6,8,1,4,7,5]=>1000100
[2,7,8,6,3,1,4,5]=>1010010
[2,8,6,3,1,4,5,7]=>1010010
[8,3,5,2,1,4,6,7]=>1110000
[2,5,8,1,7,3,6,4]=>1011000
[2,8,1,5,7,3,6,4]=>1011000
[2,6,8,1,5,7,3,4]=>1010000
[2,7,1,5,8,3,4,6]=>1010000
[3,7,5,8,1,2,6,4]=>1001100
[7,3,6,1,2,8,4,5]=>1011000
[7,4,8,1,6,5,2,3]=>1101100
[6,8,4,5,1,7,2,3]=>1101000
[5,1,8,7,6,2,3,4]=>1100011
[4,6,1,8,7,5,2,3]=>1100101
[3,4,8,7,1,2,5,6]=>1000001
[6,4,8,7,1,2,5,3]=>1011001
[5,6,8,3,7,1,4,2]=>1110000
[6,4,7,1,2,8,5,3]=>1011100
[6,5,1,8,2,7,3,4]=>1110100
[6,5,1,8,7,2,3,4]=>1100101
[6,5,1,7,2,8,3,4]=>1110100
[6,5,1,7,2,3,8,4]=>1101100
[5,6,8,7,4,1,2,3]=>1001001
[6,8,5,7,4,1,2,3]=>1001100
[6,8,3,1,5,2,4,7]=>1110000
[4,2,7,1,6,3,5,8]=>1110000
[5,1,7,4,2,6,3,8]=>1111000
[6,8,4,2,1,5,3,7]=>1111000
[5,8,2,1,4,7,3,6]=>1110000
[6,8,4,3,1,5,7,2]=>1111000
[6,8,4,2,1,5,7,3]=>1111000
[6,8,3,2,1,4,5,7]=>1110000
[5,4,7,2,1,6,8,3]=>1111000
[5,2,1,7,3,4,8,6]=>1110010
[6,4,3,1,7,5,8,2]=>1111100
[5,3,1,7,2,6,8,4]=>1111000
[3,2,1,7,6,4,8,5]=>1101110
[4,2,1,6,5,8,3,7]=>1110100
[4,2,1,8,5,7,3,6]=>1110100
[7,4,3,1,8,5,6,2]=>1111100
[6,3,2,1,7,4,5,8]=>1111000
[6,4,2,1,7,5,3,8]=>1111100
[6,1,8,4,2,7,3,5]=>1111000
[6,2,1,8,3,7,4,5]=>1111000
[5,2,1,7,3,6,4,8]=>1111000
[5,3,2,7,6,1,4,8]=>1110010
[5,3,2,8,6,1,4,7]=>1110010
[6,3,2,8,7,1,4,5]=>1110001
[4,2,8,1,7,3,5,6]=>1110000
[4,3,8,7,2,1,5,6]=>1110001
[2,1,5,8,4,7,3,6]=>1011000
[4,3,2,5,8,1,6,7]=>1110000
[4,3,2,5,7,1,6,8]=>1110000
[4,3,1,6,2,7,5,8]=>1110100
[4,3,1,7,2,8,5,6]=>1110100
[5,4,1,7,2,8,6,3]=>1111010
[6,5,3,1,7,8,4,2]=>1111100
[6,4,2,1,7,8,3,5]=>1111000
[5,4,2,1,6,7,3,8]=>1111000
[5,3,2,1,6,7,4,8]=>1111000
[6,4,2,1,7,8,5,3]=>1111100
[5,3,2,6,8,1,7,4]=>1111000
[3,2,1,4,8,7,5,6]=>1100101
[3,2,1,4,6,8,5,7]=>1100100
[4,3,2,6,1,7,8,5]=>1110100
[5,3,2,1,6,7,8,4]=>1111000
[8,6,1,4,5,7,2,3]=>1100010
[3,8,6,4,5,7,1,2]=>1001010
[5,2,8,3,7,4,6,1]=>1111000
[6,2,8,5,4,7,3,1]=>1111100
[5,2,8,4,3,6,7,1]=>1111000
[5,4,2,7,3,6,1,8]=>1111000
[5,4,2,8,3,6,1,7]=>1111000
[6,5,3,8,4,7,2,1]=>1111100
[5,2,8,4,3,7,1,6]=>1111000
[6,2,8,3,7,4,1,5]=>1111000
[5,4,2,7,3,1,8,6]=>1111010
[6,4,3,7,1,2,8,5]=>1011100
[6,4,3,8,1,2,7,5]=>1011100
[7,2,8,4,3,1,5,6]=>1111000
[7,5,3,8,4,2,6,1]=>1111100
[6,4,2,7,3,1,5,8]=>1111000
[7,6,4,8,2,3,5,1]=>1101010
[5,3,1,7,8,4,6,2]=>1111000
[5,3,2,7,8,4,6,1]=>1111000
[6,5,1,7,8,2,3,4]=>1100100
[6,3,1,7,8,4,2,5]=>1111000
[5,4,1,7,3,8,2,6]=>1111000
[6,3,2,7,8,4,1,5]=>1111000
[6,1,5,4,3,2,8,7]=>1111001
[8,7,6,1,3,5,2,4]=>1100011
[8,1,6,5,7,3,4,2]=>1110100
[8,4,1,5,7,6,2,3]=>1101010
[7,8,6,2,5,3,1,4]=>1110010
[6,1,3,5,2,8,4,7]=>1101000
[8,1,3,7,4,2,5,6]=>1101000
[4,3,8,7,5,2,1,6]=>1110101
[6,7,1,8,5,3,4,2]=>1110100
[2,7,6,4,8,3,5,1]=>1011010
[6,5,2,7,1,4,8,3]=>1110100
[7,4,6,1,3,2,8,5]=>1101100
[7,5,2,1,3,8,4,6]=>1101100
[8,4,7,6,3,1,5,2]=>1111010
[7,4,1,5,6,3,8,2]=>1111000
[3,4,7,5,6,1,8,2]=>1100100
[2,7,6,1,3,4,8,5]=>1000110
[5,7,2,1,6,3,8,4]=>1111000
[4,7,2,5,6,3,8,1]=>1110000
[8,6,2,5,7,1,4,3]=>1110010
[2,7,4,5,3,8,1,6]=>1011000
[6,8,7,1,3,2,5,4]=>1101001
[2,8,6,5,7,1,4,3]=>1010110
[5,8,4,3,2,6,7,1]=>1111000
[1,8,5,6,2,4,7,3]=>0110100
[8,1,5,6,2,4,7,3]=>1110000
[6,4,8,1,3,2,7,5]=>1101100
[5,4,1,2,8,6,7,3]=>1011010
[8,4,5,2,1,6,7,3]=>1111000
[3,1,2,6,8,4,7,5]=>1001100
[5,1,3,2,7,8,4,6]=>1101000
[4,6,7,8,3,1,5,2]=>1110000
[5,2,8,6,3,4,7,1]=>1110010
[5,6,8,4,3,2,7,1]=>1111000
[5,3,8,1,7,2,4,6]=>1110000
[3,6,7,8,4,2,1,5]=>1101000
[6,5,1,8,4,3,7,2]=>1111100
[6,3,8,4,2,1,7,5]=>1111100
[2,5,8,3,1,6,7,4]=>1011000
[3,5,8,1,2,6,7,4]=>1001000
[3,2,7,8,4,6,1,5]=>1101000
[5,1,8,3,4,6,7,2]=>1110000
[4,8,7,2,1,6,3,5]=>1110001
[2,8,1,6,3,4,7,5]=>1010100
[3,6,1,2,5,8,4,7]=>1001000
[1,4,5,8,2,3,7,6]=>0100010
[1,5,2,4,6,8,3,7]=>0110000
[3,6,1,5,8,2,4,7]=>1100000
[2,6,5,1,4,8,3,7]=>1010100
[2,5,1,8,4,7,3,6]=>1011000
[2,7,1,4,3,6,8,5]=>1010100
[1,3,7,5,8,2,4,6]=>0100100
[8,2,1,5,7,3,4,6]=>1110000
[2,5,4,8,1,3,7,6]=>1001010
[2,4,1,3,8,6,7,5]=>1000110
[8,4,3,7,1,2,6,5]=>1011100
[1,7,3,5,8,2,6,4]=>0111000
[1,8,4,2,6,7,3,5]=>0111000
[3,1,6,8,7,2,4,5]=>1100001
[7,2,1,6,8,3,4,5]=>1110000
[4,1,7,2,6,8,3,5]=>1110000
[5,1,7,2,3,6,8,4]=>1101000
[7,2,1,6,3,5,8,4]=>1111000
[2,6,1,7,3,5,8,4]=>1011000
[8,1,3,2,4,6,7,5]=>1100100
[7,3,1,2,4,6,8,5]=>1010100
[1,8,3,4,7,2,5,6]=>0110000
[3,5,8,1,2,7,4,6]=>1001000
[3,6,8,1,2,4,7,5]=>1000100
[4,1,3,8,7,2,6,5]=>1100101
[1,3,7,4,8,2,6,5]=>0101100
[1,4,6,8,2,3,7,5]=>0100100
[3,5,8,1,7,2,4,6]=>1100000
[2,6,8,1,7,3,4,5]=>1010000
[1,8,3,2,7,5,6,4]=>0111100
[2,6,7,3,8,1,5,4]=>1011000
[8,4,1,7,3,6,2,5]=>1111000
[3,7,2,8,6,1,5,4]=>1101010
[6,2,3,8,7,1,5,4]=>1101001
[5,1,7,8,4,2,6,3]=>1111000
[5,1,8,7,4,2,6,3]=>1111001
[4,7,2,8,3,6,5,1]=>1110100
[4,1,7,8,5,3,6,2]=>1110100
[5,1,7,4,8,3,6,2]=>1111000
[4,1,8,7,5,3,6,2]=>1110101
[4,8,2,7,3,6,5,1]=>1110100
[4,7,2,6,3,5,8,1]=>1110000
[6,8,2,4,3,7,5,1]=>1110100
[6,7,2,4,3,8,5,1]=>1110100
[3,8,7,2,4,1,5,6]=>1100001
[3,7,8,2,4,1,5,6]=>1100000
[3,6,8,2,4,5,7,1]=>1100000
[3,6,7,2,4,5,8,1]=>1100000
[1,7,5,3,8,2,4,6]=>0110100
[1,7,2,4,5,8,3,6]=>0110000
[1,7,4,5,8,3,2,6]=>0111000
[2,6,4,7,8,3,5,1]=>1011000
[1,2,6,4,7,8,3,5]=>0011000
[2,7,4,5,8,1,3,6]=>1001000
[2,7,5,3,1,8,4,6]=>1011100
[6,1,4,7,8,3,5,2]=>1110000
[3,6,4,7,8,1,5,2]=>1101000
[4,3,6,7,1,8,5,2]=>1110100
[4,3,6,7,1,8,2,5]=>1110000
[3,7,4,5,2,1,8,6]=>1101010
[1,3,6,4,7,2,8,5]=>0101100
[3,6,4,7,2,8,5,1]=>1101100
[6,1,7,3,8,2,5,4]=>1111000
[1,6,7,3,8,2,5,4]=>0111000
[6,1,4,7,8,5,2,3]=>1100100
[6,3,2,1,7,8,5,4]=>1111100
[6,2,7,3,1,8,5,4]=>1111100
[6,2,4,7,8,1,5,3]=>1110000
[2,6,7,3,1,8,5,4]=>1011100
[8,6,5,1,3,2,4,7]=>1100110
[6,4,7,8,3,2,5,1]=>1111000
[3,8,4,7,1,2,5,6]=>1001000
[4,8,6,1,5,3,2,7]=>1110010
[5,8,6,4,1,3,2,7]=>1101010
[8,3,6,4,5,2,1,7]=>1111000
[6,8,5,7,4,2,3,1]=>1101100
[2,3,8,7,1,6,4,5]=>1001001
[4,3,7,8,1,6,2,5]=>1110000
[3,5,8,7,4,1,2,6]=>1001001
[7,3,8,4,1,2,5,6]=>1011000
[4,8,1,2,7,3,5,6]=>1010000
[6,8,1,2,7,4,5,3]=>1011000
[5,6,8,4,1,3,7,2]=>1101000
[8,5,4,7,1,6,3,2]=>1111100
[2,5,8,7,3,6,4,1]=>1011001
[2,4,8,7,5,6,1,3]=>1000101
[3,7,4,8,5,6,2,1]=>1101100
[6,4,8,7,5,1,2,3]=>1001101
[3,8,5,2,4,6,7,1]=>1100100
[5,7,1,8,4,6,2,3]=>1101000
[6,3,8,7,2,1,4,5]=>1110001
[2,3,7,8,5,6,1,4]=>1000100
[3,7,6,8,5,1,2,4]=>1000110
[2,6,7,8,5,1,3,4]=>1000100
[2,4,7,8,1,6,3,5]=>1010000
[5,4,7,8,2,6,3,1]=>1111000
[2,8,3,4,1,5,7,6]=>1010010
[6,8,3,4,1,2,7,5]=>1010100
[6,8,7,1,5,2,3,4]=>1100001
[2,5,3,1,8,6,7,4]=>1011010
[4,5,3,2,8,6,7,1]=>1110010
[3,5,8,6,1,4,7,2]=>1100010
[2,8,5,6,1,4,7,3]=>1010100
[4,8,6,1,5,2,7,3]=>1110010
[5,8,2,3,7,6,1,4]=>1100010
[4,6,8,5,3,2,7,1]=>1110100
[2,6,4,8,5,1,7,3]=>1011100
[7,6,4,8,5,2,1,3]=>1101110
[3,4,8,6,5,2,7,1]=>1100110
[3,4,8,7,5,6,2,1]=>1100101
[7,5,3,2,8,6,1,4]=>1110110
[2,5,1,3,8,6,7,4]=>1001010
[4,5,1,2,8,6,7,3]=>1010010
[5,4,8,1,3,6,7,2]=>1101000
[8,3,5,4,1,6,7,2]=>1111000
[5,1,6,4,3,2,8,7]=>1111001
[8,3,7,1,4,6,5,2]=>1110100
[2,8,3,6,4,7,5,1]=>1011100
[6,2,1,7,5,8,3,4]=>1110100
[6,7,2,1,5,8,4,3]=>1111000
[1,6,4,8,3,2,5,7]=>0111000
[1,8,3,5,6,2,4,7]=>0110000
[1,4,8,5,6,2,3,7]=>0100100
[6,1,4,8,2,3,5,7]=>1100000
[8,7,2,5,6,1,4,3]=>1110001
[1,8,2,5,4,7,3,6]=>0111000
[5,7,4,1,2,3,8,6]=>1001010
[1,7,4,2,5,3,8,6]=>0111010
[6,7,4,2,1,3,8,5]=>1101100
[6,4,3,8,5,7,1,2]=>1011100
[7,4,3,6,2,1,5,8]=>1111000
[7,2,5,3,4,1,6,8]=>1110000
[8,3,7,4,5,6,1,2]=>1011000
[2,7,4,3,1,5,6,8]=>1011000
[6,8,4,2,3,1,5,7]=>1101000
[2,1,7,4,8,3,5,6]=>1011000
[5,2,8,6,1,3,4,7]=>1100010
[2,8,3,1,4,5,6,7]=>1010000
[7,4,8,2,3,1,5,6]=>1101000
[4,2,7,3,1,5,6,8]=>1110000
[8,3,7,2,1,4,5,6]=>1110000
[6,5,2,4,7,1,3,8]=>1100100
[6,5,7,4,1,8,2,3]=>1101100
[8,6,4,1,3,7,2,5]=>1101010
[6,4,3,1,8,2,5,7]=>1111000
[4,8,1,3,5,7,2,6]=>1100000
[7,8,4,1,3,6,2,5]=>1101000
[6,5,8,1,3,7,2,4]=>1100100
[5,3,6,1,8,2,4,7]=>1110000
[4,7,3,1,8,2,5,6]=>1110000
[8,3,1,7,2,4,5,6]=>1110000
[2,8,1,4,7,3,5,6]=>1010000
[3,1,8,5,4,7,6,2]=>1101110
[4,1,5,8,3,7,6,2]=>1110010
[4,1,5,3,8,7,6,2]=>1110011
[4,5,1,8,2,7,6,3]=>1110010
[4,8,5,3,1,7,6,2]=>1110110
[4,5,2,8,1,7,6,3]=>1110010
[4,6,2,8,7,1,5,3]=>1110001
[4,8,6,3,7,1,5,2]=>1110010
[4,6,8,2,7,5,1,3]=>1100100
[4,6,2,8,7,5,1,3]=>1100101
[5,6,2,7,4,1,8,3]=>1111000
[5,6,7,2,3,1,8,4]=>1101000
[5,6,7,2,8,3,1,4]=>1110000
[5,6,7,2,1,8,3,4]=>1110000
[5,6,7,2,1,3,8,4]=>1101000
[5,6,1,7,8,2,4,3]=>1110000
[5,6,1,7,2,4,8,3]=>1110000
[4,1,6,8,7,3,5,2]=>1110001
[4,1,6,8,7,5,3,2]=>1110101
[5,6,1,7,8,4,2,3]=>1101000
[4,6,8,1,7,5,2,3]=>1100100
[4,8,6,1,7,5,3,2]=>1110110
[5,6,7,1,8,3,2,4]=>1110000
[5,6,7,1,3,8,2,4]=>1100000
[5,6,7,1,3,2,8,4]=>1101000
[5,6,7,3,1,2,8,4]=>1011000
[5,6,8,7,4,2,1,3]=>1101001
[7,8,1,3,5,6,2,4]=>1100000
[7,8,3,1,5,6,2,4]=>1110000
[7,1,3,8,5,6,2,4]=>1100100
[5,1,7,8,3,4,6,2]=>1110000
[1,5,7,8,3,4,6,2]=>0110000
[3,7,1,5,8,6,2,4]=>1100010
[1,3,7,8,2,5,6,4]=>0101000
[3,1,7,8,5,2,6,4]=>1101100
[1,3,7,5,8,2,6,4]=>0101100
[3,1,7,5,8,2,6,4]=>1101100
[3,5,7,1,8,4,6,2]=>1101000
[3,5,7,8,1,4,6,2]=>1100000
[5,3,7,8,4,6,1,2]=>1011000
[5,3,7,8,4,1,6,2]=>1111000
[5,3,7,8,1,4,6,2]=>1110000
[5,3,7,1,8,4,6,2]=>1111000
[1,5,3,7,8,4,2,6]=>0111000
[5,1,3,7,8,4,2,6]=>1101000
[3,6,2,1,4,5,8,7]=>1100001
[8,6,2,7,4,5,1,3]=>1101010
[5,2,8,1,7,3,4,6]=>1110000
[2,1,5,8,4,3,6,7]=>1011000
[5,8,3,2,7,1,4,6]=>1110000
[5,1,8,3,7,2,4,6]=>1110000
[5,1,8,4,6,2,3,7]=>1101000
[3,8,4,2,1,5,6,7]=>1101000
[3,4,2,8,1,5,6,7]=>1100000
[4,8,5,2,6,1,3,7]=>1100100
[4,1,7,5,6,2,8,3]=>1110100
[5,7,4,3,8,1,6,2]=>1111000
[5,7,4,3,8,2,6,1]=>1111000
[3,8,4,2,6,7,5,1]=>1101100
[3,8,4,1,6,7,5,2]=>1101100
[6,1,7,5,2,8,4,3]=>1111100
[5,6,4,3,2,8,1,7]=>1111000
[2,6,7,5,3,8,4,1]=>1011100
[2,1,6,7,5,3,8,4]=>1011100
[3,8,4,2,1,6,7,5]=>1101100
[5,7,4,3,8,2,1,6]=>1111000
[6,7,4,8,1,2,5,3]=>1011000
[6,7,5,8,1,2,4,3]=>1010100
[6,7,4,8,3,1,2,5]=>1011000
[6,1,3,4,8,2,5,7]=>1100000
[6,2,3,4,8,1,5,7]=>1100000
[3,4,8,2,1,5,7,6]=>1100010
[6,7,5,8,3,1,4,2]=>1110100
[2,5,7,6,1,4,8,3]=>1010010
[6,7,4,8,2,3,5,1]=>1101000
[6,7,4,8,1,3,5,2]=>1101000
[2,6,7,5,1,3,8,4]=>1001100
[6,3,1,4,8,2,5,7]=>1110000
[6,7,4,8,1,3,2,5]=>1101000
[6,7,5,8,4,1,3,2]=>1101100
[6,7,4,8,2,1,3,5]=>1101000
[6,7,4,8,1,2,3,5]=>1001000
[7,8,3,2,6,1,4,5]=>1110000
[3,4,8,2,6,1,7,5]=>1100100
[7,8,4,1,5,6,3,2]=>1111000
[7,8,1,2,6,3,4,5]=>1010000
[7,8,5,1,4,6,3,2]=>1110100
[5,3,8,4,1,6,7,2]=>1111000
[6,2,4,8,1,5,3,7]=>1110000
[3,4,8,5,1,6,7,2]=>1100100
[5,3,8,1,4,6,7,2]=>1110000
[4,2,6,8,1,5,3,7]=>1110000
[7,4,2,8,1,5,3,6]=>1111000
[6,1,7,5,8,4,3,2]=>1111100
[1,2,7,8,5,3,4,6]=>0010100
[6,3,7,8,5,4,1,2]=>1011100
[6,1,5,7,8,4,3,2]=>1111000
[1,7,5,6,8,4,3,2]=>0111100
[3,1,8,4,5,6,7,2]=>1101000
[4,2,1,8,6,5,3,7]=>1110110
[3,2,7,8,5,1,4,6]=>1100100
[2,3,7,8,5,1,4,6]=>1000100
[2,7,3,8,5,1,4,6]=>1010100
[3,6,2,8,5,1,4,7]=>1100100
[1,4,2,8,7,5,3,6]=>0110101
[7,3,6,8,5,4,1,2]=>1011100
[7,2,1,8,5,3,4,6]=>1110100
[1,2,6,8,4,5,3,7]=>0011000
[7,1,6,5,8,4,3,2]=>1111100
[6,5,7,1,8,4,3,2]=>1111100
[5,7,6,1,8,4,3,2]=>1111010
[6,7,1,5,8,4,3,2]=>1111000
[7,1,2,8,4,5,3,6]=>1011000
[7,6,1,5,8,4,3,2]=>1111010
[7,5,6,1,8,4,3,2]=>1111100
[7,1,6,5,3,2,4,8]=>1110100
[1,8,7,5,3,2,4,6]=>0110101
[1,8,7,4,2,5,3,6]=>0111001
[8,7,4,2,5,3,6,1]=>1111001
[7,1,6,4,2,5,3,8]=>1111000
[2,6,5,4,7,1,3,8]=>1001100
[7,1,5,3,6,4,2,8]=>1111000
[5,3,7,1,6,4,2,8]=>1111000
[5,3,6,4,2,7,1,8]=>1111000
[1,5,3,8,7,4,2,6]=>0111001
[7,4,2,8,6,3,5,1]=>1111010
[5,3,6,1,8,7,4,2]=>1111001
[6,1,5,3,8,7,4,2]=>1111001
[2,8,7,5,4,6,1,3]=>1001101
[2,3,1,8,7,5,4,6]=>1001101
[7,4,2,1,8,6,3,5]=>1111010
[1,8,6,3,5,7,4,2]=>0111010
[6,3,8,5,2,1,7,4]=>1111100
[8,6,3,7,4,2,1,5]=>1111010
[2,8,6,4,7,5,1,3]=>1001110
[5,1,8,6,3,7,4,2]=>1111010
[6,3,7,4,1,8,5,2]=>1111100
[8,5,2,6,3,7,4,1]=>1111100
[6,1,8,7,4,2,5,3]=>1111001
[8,6,3,7,4,2,5,1]=>1111010
[1,8,6,3,2,4,7,5]=>0110110
[8,6,3,2,4,7,5,1]=>1110110
[7,5,1,8,6,3,2,4]=>1110110
[6,1,8,7,5,3,2,4]=>1110101
[2,4,5,1,3,8,7,6]=>1000011
[1,7,5,8,6,3,2,4]=>0110110
[1,7,4,2,5,8,6,3]=>0111010
[8,6,3,1,7,4,2,5]=>1111010
[8,7,4,2,5,3,1,6]=>1111001
[5,3,1,8,7,4,2,6]=>1111001
[4,1,8,7,5,3,2,6]=>1110101
[2,8,6,4,1,3,7,5]=>1001110
[4,1,8,6,3,2,7,5]=>1110110
[7,4,2,8,6,3,1,5]=>1111010
[6,3,1,8,5,2,7,4]=>1111100
[8,5,2,6,3,1,7,4]=>1111100
[7,4,8,5,2,6,3,1]=>1111100
[1,8,5,2,7,4,6,3]=>0111100
[7,4,6,3,1,8,5,2]=>1111100
[6,3,1,7,4,8,5,2]=>1111100
[4,1,7,5,8,6,3,2]=>1110110
[2,3,1,7,5,8,6,4]=>1001110
[7,4,8,5,2,1,6,3]=>1111100
[1,7,4,6,3,8,5,2]=>0111100
[3,6,5,2,1,4,8,7]=>1100101
[3,5,6,2,1,4,8,7]=>1100001
[3,5,7,8,1,4,2,6]=>1100000
[4,1,8,5,7,3,2,6]=>1110100
[4,1,7,5,8,3,2,6]=>1110100
[2,1,5,8,7,4,3,6]=>1011001
[5,1,7,4,8,3,2,6]=>1111000
[4,7,2,8,3,6,1,5]=>1110000
[4,6,2,7,3,1,8,5]=>1110100
[3,7,8,2,4,1,6,5]=>1100100
[3,8,7,2,4,1,6,5]=>1100101
[3,8,6,2,4,1,7,5]=>1100110
[6,2,8,4,1,7,3,5]=>1111000
[7,3,4,8,1,6,2,5]=>1110000
[6,3,4,8,1,7,2,5]=>1110000
[5,3,4,8,1,2,7,6]=>1010010
[4,3,5,8,1,2,7,6]=>1010010
[1,8,5,4,2,3,7,6]=>0101110
[3,5,4,8,1,2,7,6]=>1001010
[4,5,3,8,1,2,7,6]=>1010010
[6,4,3,8,1,7,2,5]=>1111000
[7,4,3,8,1,6,2,5]=>1111000
[6,5,3,8,7,1,2,4]=>1010101
[5,6,3,8,7,1,2,4]=>1010001
[4,6,3,8,1,7,2,5]=>1110000
[2,6,8,4,1,7,3,5]=>1011000
[1,8,7,4,2,6,3,5]=>0111001
[5,7,3,8,6,1,2,4]=>1010010
[3,7,5,8,6,1,2,4]=>1000110
[2,7,8,5,6,1,3,4]=>1000100
[1,8,7,5,6,2,3,4]=>0100101
[2,6,8,5,7,1,3,4]=>1000100
[5,3,6,8,7,1,2,4]=>1010001
[7,2,8,5,6,1,3,4]=>1100100
[5,2,8,6,7,1,3,4]=>1100010
[1,8,3,2,7,6,4,5]=>0111010
[5,2,8,7,6,1,3,4]=>1100011
[6,2,8,7,5,1,3,4]=>1100101
[3,4,7,8,1,6,2,5]=>1100000
[1,8,5,7,6,2,3,4]=>0100110
[2,5,8,7,6,1,3,4]=>1000011
[7,4,6,5,8,1,2,3]=>1001100
[2,6,8,7,5,1,3,4]=>1000101
[1,8,6,7,5,2,3,4]=>0100110
[2,7,8,6,5,1,3,4]=>1000110
[5,7,6,4,8,1,2,3]=>1001010
[6,1,3,2,4,8,7,5]=>1100101
[8,7,4,2,3,6,1,5]=>1101001
[8,7,1,5,4,2,3,6]=>1101001
[3,7,1,5,2,8,6,4]=>1101010
[8,7,2,5,4,1,3,6]=>1101001
[5,2,8,7,1,4,3,6]=>1110001
[7,1,8,6,2,4,3,5]=>1110010
[8,1,6,2,7,5,3,4]=>1110100
[7,1,6,2,8,5,3,4]=>1110100
[7,2,4,3,5,1,8,6]=>1110010
[5,1,7,2,3,8,6,4]=>1101010
[8,2,3,5,1,7,6,4]=>1101010
[7,6,3,1,4,8,2,5]=>1110010
[7,2,8,1,6,5,3,4]=>1110100
[7,2,6,4,3,8,1,5]=>1111000
[5,1,7,4,3,8,2,6]=>1111000
[5,3,1,7,4,8,2,6]=>1111000
[7,4,8,2,1,5,3,6]=>1111000
[8,2,4,1,6,3,7,5]=>1110100
[8,2,7,5,1,6,4,3]=>1111100
[6,1,7,3,2,8,5,4]=>1111100
[4,7,2,1,6,3,8,5]=>1110100
[6,2,1,5,3,8,4,7]=>1111000
[5,3,1,6,2,8,4,7]=>1111000
[6,1,5,2,8,4,3,7]=>1111000
[7,4,3,8,1,5,2,6]=>1111000
[7,4,8,1,5,3,2,6]=>1111000
[6,1,5,3,2,8,4,7]=>1111000
[6,3,2,8,4,1,5,7]=>1111000
[7,3,4,2,8,5,1,6]=>1110100
[8,5,1,3,7,4,2,6]=>1101100
[3,8,6,1,5,2,7,4]=>1101010
[4,8,5,6,1,7,3,2]=>1110100
[6,7,1,3,8,5,2,4]=>1100100
[3,6,7,1,5,2,8,4]=>1101000
[7,1,3,8,4,2,6,5]=>1101100
[5,6,2,7,1,3,8,4]=>1101000
[5,6,2,8,1,3,7,4]=>1101000
[6,1,8,3,7,5,2,4]=>1110100
[7,4,2,1,5,8,3,6]=>1111000
[7,4,1,5,8,3,2,6]=>1111000
[7,3,2,6,4,8,1,5]=>1111000
[6,4,2,7,3,8,1,5]=>1111000
[7,4,8,3,1,5,2,6]=>1111000
[5,2,1,7,4,8,3,6]=>1111000
[6,1,8,4,5,2,7,3]=>1111000
[7,1,6,4,5,2,8,3]=>1111000
[3,5,2,7,1,6,8,4]=>1101000
[4,5,7,3,1,6,8,2]=>1110000
[4,5,7,2,8,6,1,3]=>1100010
[4,5,7,2,8,1,3,6]=>1100000
[4,6,7,2,1,5,8,3]=>1110000
[4,6,7,1,3,8,5,2]=>1100100
[3,6,1,5,7,8,4,2]=>1101000
[4,6,7,1,5,8,3,2]=>1110000
[6,1,4,2,5,3,7,8]=>1110000
[1,3,7,5,4,2,8,6]=>0101110
[6,1,3,5,4,2,7,8]=>1101000
[6,1,2,5,4,7,3,8]=>1011000
[5,2,6,3,4,7,1,8]=>1110000
[2,4,7,1,5,3,8,6]=>1010010
[2,3,6,7,4,8,1,5]=>1001000
[1,3,6,7,4,8,5,2]=>0101100
[2,7,6,5,3,1,8,4]=>1011110
[5,2,6,1,4,7,8,3]=>1110000
[4,7,6,5,2,1,8,3]=>1110110
[6,3,1,5,4,7,8,2]=>1111000
[5,3,6,1,4,2,7,8]=>1110000
[1,7,4,2,6,3,8,5]=>0111100
[5,7,4,1,2,3,6,8]=>1001000
[6,4,1,2,5,3,7,8]=>1011000
[4,7,6,3,8,5,1,2]=>1010110
[3,7,6,5,2,8,1,4]=>1100110
[3,7,6,5,1,2,8,4]=>1001110
[4,7,2,6,1,3,8,5]=>1100100
[2,7,6,5,8,1,4,3]=>1010110
[4,2,6,8,3,1,5,7]=>1110000
[3,7,6,2,4,5,1,8]=>1100010
[2,3,6,5,8,1,4,7]=>1000100
[2,3,5,8,6,1,4,7]=>1000010
[4,2,3,8,6,1,5,7]=>1100010
[1,2,3,7,4,6,8,5]=>0001100
[3,2,7,1,4,5,8,6]=>1100010
[2,1,5,3,8,7,4,6]=>1011001
[5,8,3,2,4,1,6,7]=>1110000
[4,2,7,1,8,3,5,6]=>1110000
[1,2,7,5,3,8,4,6]=>0011100
[3,2,7,1,4,8,5,6]=>1100100
[1,2,3,7,6,8,4,5]=>0001010
[1,2,3,6,8,7,4,5]=>0001001
[1,2,3,7,8,4,6,5]=>0001100
[1,2,3,6,8,4,7,5]=>0001100
[6,2,8,3,7,5,1,4]=>1110100
[4,2,8,3,7,5,6,1]=>1110100
[7,3,4,8,6,5,1,2]=>1010110
[5,3,4,8,7,2,6,1]=>1110001
[4,6,3,8,5,7,2,1]=>1110100
[7,5,3,8,6,2,4,1]=>1110110
[2,6,8,3,7,4,5,1]=>1011000
[2,5,8,3,7,4,6,1]=>1011000
[7,4,3,8,6,2,5,1]=>1111010
[3,5,4,8,7,2,6,1]=>1101001
[4,5,3,8,6,7,2,1]=>1110010
[3,6,7,8,4,5,2,1]=>1101000
[1,8,5,6,4,7,3,2]=>0111100
[2,5,8,6,4,7,3,1]=>1011010
[6,3,7,8,4,5,2,1]=>1111000
[4,3,7,8,5,6,2,1]=>1110100
[4,2,8,6,5,7,3,1]=>1110110
[3,2,8,6,7,4,5,1]=>1101010
[2,3,8,7,5,4,6,1]=>1001101
[1,8,2,7,4,5,6,3]=>0111000
[7,2,8,6,3,4,5,1]=>1110010
[6,2,8,4,5,7,3,1]=>1111000
[5,2,8,4,6,7,3,1]=>1111000
[4,3,6,8,5,7,2,1]=>1110100
[3,4,6,8,7,2,5,1]=>1100001
[7,3,5,8,6,2,4,1]=>1110010
[1,8,3,5,7,4,6,2]=>0111000
[2,7,8,4,5,6,3,1]=>1011000
[3,7,5,8,4,6,2,1]=>1101100
[5,7,4,6,8,3,2,1]=>1111000
[3,6,5,8,4,7,2,1]=>1101100
[2,6,8,4,5,7,3,1]=>1011000
[4,2,7,1,3,8,5,6]=>1100100
[4,2,5,1,3,8,6,7]=>1100010
[5,3,6,1,7,2,4,8]=>1110000
[3,7,1,2,5,8,6,4]=>1001010
[3,7,4,1,2,8,5,6]=>1001100
[7,5,1,3,4,8,6,2]=>1100110
[7,5,1,2,4,8,6,3]=>1010110
[6,4,2,3,7,1,5,8]=>1101000
[7,6,3,8,1,2,5,4]=>1011010
[7,4,2,3,8,1,6,5]=>1101100
[4,7,5,2,8,1,3,6]=>1100100
[8,2,6,3,7,1,4,5]=>1110000
[8,6,1,2,7,4,5,3]=>1011010
[8,4,7,1,2,3,6,5]=>1001100
[8,5,7,1,2,4,6,3]=>1010100
[3,8,5,6,1,2,4,7]=>1000100
[3,7,5,8,1,2,4,6]=>1000100
[7,6,4,8,1,3,5,2]=>1101010
[6,5,8,1,2,4,7,3]=>1010100
[3,6,8,1,2,5,7,4]=>1001000
[4,6,3,8,1,2,5,7]=>1010000
[4,6,3,7,1,2,5,8]=>1010000
[4,1,7,8,2,3,6,5]=>1100100
[5,1,2,8,6,3,4,7]=>1010010
[5,3,8,1,6,2,4,7]=>1110000
[6,1,8,5,2,3,4,7]=>1100100
[6,1,7,5,2,3,4,8]=>1100100
[6,8,1,3,7,4,5,2]=>1101000
[7,2,8,1,6,3,4,5]=>1110000
[4,7,8,2,5,1,3,6]=>1100000
[6,8,2,7,1,4,5,3]=>1110000
[4,8,7,1,3,5,6,2]=>1100001
[3,8,7,1,2,4,6,5]=>1000101
[4,8,7,1,2,3,6,5]=>1000101
[5,8,7,1,2,4,6,3]=>1010001
[5,8,7,1,3,4,6,2]=>1100001
[7,1,8,6,2,3,5,4]=>1101010
[5,8,6,4,1,2,3,7]=>1001010
[5,1,3,4,6,7,2,8]=>1100000
[1,3,4,8,7,5,2,6]=>0100101
[8,2,4,1,7,3,5,6]=>1110000
[8,6,1,4,2,3,7,5]=>1100110
[3,6,1,4,2,8,7,5]=>1100101
[1,6,8,4,3,7,2,5]=>0111000
[3,1,4,7,8,5,2,6]=>1100100
[6,1,7,4,3,8,2,5]=>1111000
[1,8,7,4,3,6,2,5]=>0111001
[7,4,1,3,8,2,6,5]=>1101100
[4,8,2,3,1,5,7,6]=>1100010
[4,8,6,2,1,3,7,5]=>1100110
[2,7,4,1,8,3,5,6]=>1011000
[1,7,8,4,2,3,6,5]=>0101100
[8,7,1,3,4,2,6,5]=>1100101
[1,7,4,3,6,2,8,5]=>0111100
[3,8,6,4,5,2,1,7]=>1101010
[3,8,4,6,5,2,1,7]=>1101100
[2,4,3,7,5,8,1,6]=>1010100
[1,4,7,3,6,2,8,5]=>0110100
[6,4,1,3,7,2,8,5]=>1101100
[8,1,4,3,6,2,7,5]=>1110100
[4,2,3,8,5,7,1,6]=>1100100
[2,8,5,7,3,4,1,6]=>1010100
[5,8,2,6,4,3,1,7]=>1111000
[7,2,5,8,4,3,1,6]=>1111000
[4,2,3,5,8,7,1,6]=>1100001
[8,2,3,5,4,7,1,6]=>1101000
[6,1,8,3,4,2,7,5]=>1110100
[1,8,6,4,2,3,7,5]=>0101110
[3,8,4,5,6,2,1,7]=>1101000
[3,8,6,5,4,2,1,7]=>1101110
[6,3,1,4,2,8,7,5]=>1110101
[7,3,8,1,2,6,4,5]=>1011000
[7,1,4,5,3,2,6,8]=>1110000
[1,8,4,2,6,5,3,7]=>0111100
[5,1,4,8,6,3,2,7]=>1110010
[5,3,1,8,4,7,2,6]=>1111000
[4,3,8,1,5,7,2,6]=>1110000
[6,3,1,2,5,7,4,8]=>1011000
[7,1,4,2,6,5,3,8]=>1110100
[3,8,4,1,6,5,2,7]=>1101100
[7,5,3,6,4,8,2,1]=>1111100
[7,3,6,4,5,8,2,1]=>1111000
[8,7,2,4,5,1,6,3]=>1110001
[7,1,5,4,8,6,3,2]=>1111010
[5,8,3,7,4,1,6,2]=>1111000
[8,1,7,4,2,6,5,3]=>1111100
[5,6,3,1,8,4,7,2]=>1111000
[5,7,1,4,8,6,3,2]=>1110010
[5,3,7,4,8,6,2,1]=>1111010
[8,5,3,6,1,4,7,2]=>1110100
[5,4,3,6,8,2,7,1]=>1111000
[6,5,3,7,4,8,2,1]=>1111100
[2,7,8,4,5,1,6,3]=>1011000
[5,6,3,8,1,4,7,2]=>1110000
[8,4,1,2,5,6,7,3]=>1011000
[6,8,3,1,2,5,7,4]=>1011000
[8,7,1,4,5,2,6,3]=>1110001
[8,7,3,1,5,4,2,6]=>1111001
[3,5,4,7,6,1,2,8]=>1001010
[3,5,7,4,6,1,8,2]=>1101000
[3,5,7,4,6,1,2,8]=>1001000
[3,5,7,4,6,2,1,8]=>1101000
[3,5,2,7,6,4,1,8]=>1101010
[3,5,7,2,6,4,1,8]=>1101000
[5,3,7,6,1,2,8,4]=>1011010
[5,3,7,6,1,4,2,8]=>1110010
[5,3,7,6,4,1,2,8]=>1011010
[3,5,7,2,6,1,4,8]=>1100000
[3,5,2,7,6,1,4,8]=>1100010
[5,3,7,6,4,1,8,2]=>1111010
[3,7,5,4,1,8,2,6]=>1101100
[3,7,5,4,1,8,6,2]=>1101110
[3,7,5,1,4,8,6,2]=>1100110
[3,7,5,1,4,8,2,6]=>1100100
[3,5,7,1,2,6,8,4]=>1001000
[3,5,7,2,1,6,4,8]=>1101000
[5,3,7,1,6,2,4,8]=>1110000
[3,5,7,1,4,6,8,2]=>1100000
[3,5,7,1,4,2,6,8]=>1100000
[3,5,7,4,1,2,6,8]=>1001000
[3,5,4,7,1,6,8,2]=>1101000
[3,5,4,7,1,2,6,8]=>1001000
[3,5,4,7,2,1,6,8]=>1101000
[3,5,4,2,7,1,6,8]=>1101000
[3,5,4,7,2,1,8,6]=>1101010
[3,5,4,7,1,2,8,6]=>1001010
[5,7,6,3,1,8,4,2]=>1111010
[5,7,6,3,1,8,2,4]=>1110010
[3,5,7,4,1,2,8,6]=>1001010
[3,5,7,4,2,1,8,6]=>1101010
[3,2,5,7,4,1,8,6]=>1101010
[3,2,5,7,1,4,8,6]=>1100010
[3,5,2,7,1,4,8,6]=>1100010
[3,5,7,2,1,4,8,6]=>1100010
[3,5,7,1,4,2,8,6]=>1100010
[3,7,5,2,1,8,6,4]=>1101110
[3,7,2,5,1,8,6,4]=>1101010
[3,2,7,5,1,8,6,4]=>1101110
[3,2,7,5,1,8,4,6]=>1101100
[3,7,2,5,1,8,4,6]=>1101000
[3,7,5,2,1,8,4,6]=>1101100
[5,8,3,4,1,7,6,2]=>1110010
[5,8,7,2,4,1,6,3]=>1110001
[3,8,6,4,1,7,5,2]=>1101110
[4,3,5,6,8,1,7,2]=>1110000
[3,7,6,4,1,8,5,2]=>1101110
[3,7,4,1,8,6,5,2]=>1101110
[3,8,4,1,7,6,5,2]=>1101110
[3,2,7,6,1,5,4,8]=>1101010
[5,7,8,2,4,1,6,3]=>1110000
[4,2,5,8,1,6,7,3]=>1110000
[5,8,2,4,1,6,3,7]=>1110000
[8,4,2,6,5,1,3,7]=>1101100
[3,2,6,8,1,5,4,7]=>1101000
[8,3,2,5,6,1,4,7]=>1110000
[3,2,8,6,7,1,5,4]=>1101010
[3,2,6,8,7,1,5,4]=>1101001
[3,2,6,7,1,5,4,8]=>1101000
[8,7,3,2,5,6,1,4]=>1110001
[7,2,8,1,5,3,6,4]=>1111000
[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]=>1110100
[7,5,3,4,2,8,1,6]=>1110100
[8,5,3,6,2,4,7,1]=>1110100
[8,5,6,3,7,4,2,1]=>1111100
[8,5,6,2,7,4,3,1]=>1111100
[8,7,6,3,4,1,5,2]=>1110011
[1,7,2,3,6,8,5,4]=>0101100
[3,5,6,4,8,2,7,1]=>1101000
[3,5,1,4,8,2,7,6]=>1100010
[1,7,5,4,8,2,6,3]=>0111100
[3,7,5,1,6,4,8,2]=>1101100
[2,7,5,4,8,1,3,6]=>1001100
[2,7,5,4,8,6,1,3]=>1001110
[1,7,5,4,8,6,3,2]=>0111110
[2,5,1,4,8,7,3,6]=>1010001
[3,6,4,2,8,7,1,5]=>1101001
[3,5,2,4,8,1,6,7]=>1100000
[4,5,6,1,7,3,8,2]=>1110000
[3,5,6,4,8,1,2,7]=>1001000
[1,5,6,4,8,7,2,3]=>0101001
[3,6,4,1,8,7,2,5]=>1101001
[3,6,4,5,8,7,2,1]=>1101001
[1,6,4,3,8,5,2,7]=>0111100
[7,6,1,4,5,3,8,2]=>1110010
[7,6,1,3,5,4,8,2]=>1101010
[7,1,3,2,5,8,4,6]=>1101000
[1,6,4,2,8,5,3,7]=>0111100
[7,6,5,8,3,1,4,2]=>1110110
[2,6,4,3,8,1,7,5]=>1011100
[2,6,4,3,8,5,7,1]=>1011100
[7,2,3,1,5,8,6,4]=>1101010
[7,1,5,6,3,8,4,2]=>1111000
[7,3,6,5,1,4,8,2]=>1110100
[7,2,6,5,3,8,1,4]=>1110100
[7,2,3,1,4,8,6,5]=>1100110
[7,2,3,5,4,8,6,1]=>1101010
[2,6,4,5,8,1,7,3]=>1011000
[1,5,6,4,8,3,7,2]=>0111000
[2,5,6,4,8,3,1,7]=>1011000
[3,5,6,1,4,7,8,2]=>1100000
[7,6,1,3,4,5,8,2]=>1100010
[7,1,3,2,4,8,5,6]=>1100100
[7,6,1,5,3,4,8,2]=>1110010
[7,6,1,5,4,3,8,2]=>1111010
[1,6,4,5,8,3,2,7]=>0111000
[7,6,5,8,1,3,2,4]=>1100110
[3,4,6,8,7,2,1,5]=>1100001
[3,5,6,8,2,1,7,4]=>1101000
[4,2,1,5,3,7,8,6]=>1110010
[4,2,5,6,3,1,8,7]=>1110001
[3,5,6,8,1,7,2,4]=>1100000
[4,1,5,6,3,2,8,7]=>1110001
[4,5,3,1,7,2,8,6]=>1110010
[4,1,3,5,2,7,8,6]=>1100010
[2,5,4,7,3,8,6,1]=>1011010
[3,5,7,1,8,4,2,6]=>1101000
[4,1,5,3,2,7,8,6]=>1110010
[4,5,3,7,1,2,8,6]=>1010010
[4,3,6,1,2,7,5,8]=>1010100
[5,1,3,2,4,6,7,8]=>1100000
[3,6,1,7,4,5,2,8]=>1101000
[5,3,1,4,2,6,7,8]=>1110000
[4,5,2,3,7,1,8,6]=>1100010
[4,2,6,1,3,7,5,8]=>1100100
[4,6,2,1,3,7,5,8]=>1100100
[3,6,2,1,7,4,8,5]=>1101100
[3,1,4,7,6,5,2,8]=>1100110
[3,6,2,7,1,5,8,4]=>1101000
[4,6,2,7,1,3,5,8]=>1100000
[3,5,7,1,8,2,6,4]=>1101000
[5,1,4,2,3,6,7,8]=>1100000
[2,6,5,3,4,7,8,1]=>1010100
[3,6,1,7,5,4,2,8]=>1101100
[5,1,4,3,2,6,7,8]=>1110000
[5,4,1,3,2,6,7,8]=>1101000
[6,4,2,5,3,8,1,7]=>1111000
[4,6,2,3,5,1,8,7]=>1100001
[6,2,4,5,1,8,3,7]=>1110000
[8,2,6,7,1,4,5,3]=>1110000
[8,2,6,7,4,1,5,3]=>1111000
[4,6,2,3,5,8,1,7]=>1100000
[2,6,4,1,5,8,3,7]=>1011000
[2,8,1,6,7,4,5,3]=>1011000
[2,8,6,1,4,7,5,3]=>1010110
[2,8,1,6,4,7,5,3]=>1011100
[2,6,1,4,8,5,3,7]=>1010100
[6,4,5,2,8,3,1,7]=>1111000
[4,2,3,6,1,8,5,7]=>1100100
[4,2,3,1,6,8,5,7]=>1100100
[4,2,3,8,6,1,7,5]=>1100110
[6,4,5,8,2,3,7,1]=>1101000
[6,4,8,5,2,3,7,1]=>1101100
[2,4,8,1,3,6,7,5]=>1000100
[2,4,1,8,3,6,7,5]=>1010100
[2,1,4,8,6,3,7,5]=>1010110
[6,4,8,2,5,3,7,1]=>1111000
[8,6,2,4,7,5,1,3]=>1100110
[4,6,8,2,3,5,7,1]=>1100000
[2,1,6,8,4,5,7,3]=>1011000
[2,8,1,4,6,7,3,5]=>1010000
[4,8,6,2,3,7,5,1]=>1100110
[8,4,2,6,7,3,1,5]=>1111000
[5,1,8,3,6,4,7,2]=>1111000
[5,1,3,8,7,6,4,2]=>1101011
[3,8,5,6,1,7,2,4]=>1100100
[3,4,8,1,7,6,2,5]=>1100010
[4,7,6,8,5,1,3,2]=>1100110
[6,7,4,8,5,1,3,2]=>1101100
[5,3,6,8,7,1,4,2]=>1110001
[1,8,4,6,7,2,5,3]=>0111000
[5,2,8,3,7,1,6,4]=>1111000
[7,4,5,8,6,1,3,2]=>1101010
[4,3,6,8,7,1,5,2]=>1110001
[6,4,8,3,1,7,5,2]=>1111100
[6,2,8,4,3,7,5,1]=>1111100
[3,6,5,8,7,1,4,2]=>1100101
[5,6,8,3,1,7,4,2]=>1111000
[4,6,3,8,2,7,5,1]=>1110100
[5,3,8,1,7,2,6,4]=>1111000
[6,5,8,1,3,7,4,2]=>1101100
[6,5,3,8,2,7,4,1]=>1111100
[6,4,8,1,3,7,5,2]=>1101100
[6,2,8,3,4,7,5,1]=>1110100
[6,3,4,8,2,7,5,1]=>1110100
[7,6,3,1,4,2,5,8]=>1110010
[1,5,4,3,7,8,2,6]=>0111000
[7,8,4,2,5,3,1,6]=>1111000
[4,2,7,8,5,3,1,6]=>1110100
[4,2,5,3,1,7,8,6]=>1110010
[4,2,8,7,6,3,1,5]=>1110011
[4,2,7,6,3,1,5,8]=>1110010
[6,3,1,8,7,5,2,4]=>1110101
[4,2,7,6,3,1,8,5]=>1110110
[7,6,3,1,8,4,2,5]=>1111010
[7,6,4,2,1,8,3,5]=>1111010
[1,8,2,7,6,4,3,5]=>0111010
[8,4,2,5,7,6,3,1]=>1111010
[7,5,2,4,8,6,3,1]=>1110110
[8,7,5,2,4,6,3,1]=>1110101
[7,5,2,4,6,3,1,8]=>1110100
[5,2,8,6,3,7,4,1]=>1111010
[8,4,7,5,2,6,3,1]=>1111100
[8,3,6,4,7,5,2,1]=>1111100
[7,5,2,1,8,3,6,4]=>1111100
[7,5,2,6,3,1,8,4]=>1111100
[5,2,7,4,1,8,6,3]=>1111010
[5,2,8,7,4,1,6,3]=>1111001
[8,7,4,1,5,2,6,3]=>1111001
[7,4,1,5,2,8,6,3]=>1111010
[7,6,3,1,4,2,8,5]=>1110110
[7,5,2,8,6,3,1,4]=>1110110
[7,5,2,1,3,6,4,8]=>1101100
[8,7,5,2,1,3,6,4]=>1101101
[1,3,7,6,5,8,2,4]=>0100110
[8,6,4,7,5,2,1,3]=>1101110
[6,4,7,5,2,1,3,8]=>1101100
[6,3,1,4,7,5,2,8]=>1110100
[6,3,1,4,8,7,5,2]=>1110101
[8,6,3,1,4,7,5,2]=>1110110
[1,8,2,6,4,7,5,3]=>0111100
[7,5,2,1,6,4,8,3]=>1111100
[6,3,8,7,4,1,5,2]=>1111001
[6,3,7,4,1,5,2,8]=>1111000
[7,4,1,6,3,5,2,8]=>1111000
[7,4,1,8,6,3,5,2]=>1111010
[8,4,6,3,1,7,5,2]=>1111100
[6,4,7,5,2,1,8,3]=>1111100
[1,6,4,7,5,3,8,2]=>0111100
[6,3,5,2,7,4,1,8]=>1111000
[4,6,7,2,5,3,1,8]=>1110000
[3,6,7,4,8,1,5,2]=>1101000
[3,4,6,8,7,1,5,2]=>1100001
[1,4,7,8,2,6,5,3]=>0110100
[2,4,7,8,1,6,5,3]=>1010100
[4,2,6,8,7,1,5,3]=>1110001
[3,1,7,8,2,6,5,4]=>1101100
[6,1,3,8,2,7,5,4]=>1101100
[5,1,8,4,2,7,6,3]=>1111010
[8,2,6,1,7,5,4,3]=>1111100
[6,8,3,7,1,5,4,2]=>1111000
[2,7,3,8,1,6,5,4]=>1011100
[2,6,8,4,1,7,5,3]=>1011100
[4,5,8,6,3,1,7,2]=>1110010
[4,6,7,1,2,8,5,3]=>1010100
[3,6,1,8,2,7,5,4]=>1101100
[5,7,4,1,2,8,6,3]=>1011010
[6,3,7,1,2,8,5,4]=>1011100
[6,2,1,8,3,7,5,4]=>1111100
[1,8,2,3,6,5,4,7]=>0101100
[3,5,8,4,7,2,6,1]=>1101000
[1,8,5,4,6,2,3,7]=>0101100
[3,8,5,4,6,1,2,7]=>1001100
[3,8,5,1,6,4,2,7]=>1101100
[2,8,5,4,6,1,3,7]=>1001100
[2,8,5,4,6,3,1,7]=>1011100
[1,8,5,4,6,3,2,7]=>0111100
[2,5,8,4,7,3,6,1]=>1011000
[3,6,4,2,7,8,5,1]=>1101100
[3,6,4,2,7,8,1,5]=>1101000
[3,5,4,1,6,2,7,8]=>1101000
[4,5,8,1,7,6,2,3]=>1100010
[3,5,8,4,7,1,6,2]=>1101000
[1,5,8,4,7,3,6,2]=>0111000
[3,6,4,1,7,8,5,2]=>1101100
[3,6,4,8,7,5,2,1]=>1101101
[1,6,4,3,7,8,5,2]=>0111100
[7,6,1,3,8,4,2,5]=>1101010
[1,6,4,2,7,8,3,5]=>0111000
[2,6,4,3,7,1,8,5]=>1011100
[2,6,4,1,7,8,3,5]=>1011000
[7,2,3,4,8,6,5,1]=>1100110
[7,2,3,1,8,6,4,5]=>1101010
[7,2,3,4,1,6,8,5]=>1100100
[1,2,4,3,8,5,7,6]=>0010110
[7,3,8,6,1,4,2,5]=>1110010
[7,2,8,6,3,4,1,5]=>1110010
[7,2,3,1,5,6,8,4]=>1101000
[7,2,3,8,5,6,4,1]=>1101100
[2,6,4,8,7,1,5,3]=>1011001
[1,5,8,4,7,6,2,3]=>0101010
[3,5,8,1,6,7,2,4]=>1100000
[7,6,1,3,5,8,2,4]=>1100010
[7,1,3,2,5,6,8,4]=>1101000
[7,1,3,8,2,6,5,4]=>1101100
[7,6,1,8,5,4,2,3]=>1101110
[3,2,6,5,8,4,7,1]=>1101100
[4,3,7,1,6,5,8,2]=>1110100
[5,2,6,4,8,3,7,1]=>1111000
[5,2,6,4,8,1,7,3]=>1111000
[4,3,7,5,8,2,6,1]=>1110100
[5,3,7,4,8,2,6,1]=>1111000
[5,3,7,4,8,1,6,2]=>1111000
[4,3,7,1,6,2,8,5]=>1110100
[5,4,8,2,6,3,7,1]=>1111000
[4,1,7,8,6,3,2,5]=>1110010
[1,2,6,8,3,7,4,5]=>0011000
[6,8,3,2,1,4,7,5]=>1110100
[6,8,2,4,1,3,7,5]=>1100100
[6,1,2,7,5,8,4,3]=>1011100
[4,2,7,3,8,5,6,1]=>1110100
[4,5,2,6,8,3,7,1]=>1110000
[4,8,3,2,5,7,6,1]=>1110010
[8,4,7,6,2,3,5,1]=>1101010
[6,8,4,1,5,3,7,2]=>1111000
[8,3,4,7,6,2,5,1]=>1110010
[1,8,3,5,2,6,7,4]=>0111000
[5,8,2,4,3,7,6,1]=>1110010
[6,5,3,8,4,2,7,1]=>1111100
[7,4,5,1,6,2,8,3]=>1111000
[4,7,3,5,6,2,8,1]=>1110000
[6,7,8,4,1,3,5,2]=>1101000
[3,1,6,8,4,7,5,2]=>1101100
[8,3,6,1,5,7,4,2]=>1111000
[3,2,7,5,8,6,1,4]=>1100110
[2,4,6,7,8,1,5,3]=>1010000
[2,4,6,8,1,7,5,3]=>1010100
[7,4,3,8,6,2,1,5]=>1111010
[4,3,6,2,1,8,5,7]=>1110100
[4,6,2,3,7,5,8,1]=>1100100
[5,8,4,2,3,6,7,1]=>1101000
[8,4,5,3,2,1,7,6]=>1111010
[6,8,4,2,3,7,5,1]=>1101100
[6,4,8,3,2,7,1,5]=>1111000
[5,8,3,7,2,1,6,4]=>1111000
[2,5,6,4,7,1,8,3]=>1011000
[2,5,4,8,1,6,7,3]=>1011000
[1,2,6,5,8,7,3,4]=>0010101
[5,6,3,4,8,7,2,1]=>1110001
[6,5,3,4,8,7,2,1]=>1110101
[7,5,3,8,4,6,2,1]=>1111100
[8,5,3,7,4,6,2,1]=>1111100
[5,8,1,2,3,4,7,6]=>1000010
[4,3,8,7,5,6,2,1]=>1110101
[5,8,3,7,4,6,2,1]=>1111000
[6,8,7,3,4,5,2,1]=>1110001
[8,6,1,2,3,4,7,5]=>1000110
[8,6,2,3,5,1,4,7]=>1100010
[8,2,4,5,7,3,1,6]=>1110000
[2,6,3,8,7,5,4,1]=>1011101
[8,2,3,7,5,4,1,6]=>1101100
[8,2,6,3,5,4,1,7]=>1111000
[8,6,1,5,2,4,3,7]=>1110010
[8,6,2,4,1,5,3,7]=>1110010
[8,4,1,6,5,3,2,7]=>1111100
[8,3,6,1,5,4,2,7]=>1111000
[8,3,2,6,5,4,1,7]=>1111100
[8,3,2,5,7,4,1,6]=>1111000
[8,3,1,7,5,4,2,6]=>1111100
[6,1,3,8,7,5,4,2]=>1101101
[3,6,1,8,7,5,4,2]=>1101101
[3,8,1,5,7,6,4,2]=>1101010
[3,5,2,8,7,6,4,1]=>1101011
[3,4,8,2,7,6,5,1]=>1100110
[3,4,8,7,1,6,5,2]=>1100101
[8,1,3,5,7,6,4,2]=>1101010
[4,1,8,5,7,6,3,2]=>1110110
[8,2,7,1,4,5,6,3]=>1110000
[8,1,7,3,4,6,2,5]=>1110000
[8,3,1,7,2,6,5,4]=>1111100
[3,8,2,4,7,6,5,1]=>1100110
[2,8,3,7,4,6,5,1]=>1011100
[8,2,3,7,1,6,5,4]=>1101100
[8,2,7,1,3,6,5,4]=>1101100
[8,1,7,2,6,4,3,5]=>1111000
[8,1,7,5,2,4,3,6]=>1110100
[8,2,3,7,4,6,1,5]=>1101000
[2,4,8,5,7,6,3,1]=>1010110
[8,2,4,3,7,6,1,5]=>1110010
[8,2,7,3,5,1,4,6]=>1110000
[8,2,7,4,3,1,5,6]=>1111000
[8,2,1,5,7,6,4,3]=>1111010
[6,1,8,2,7,5,4,3]=>1111100
[8,1,5,2,7,6,4,3]=>1111010
[8,1,7,2,4,6,5,3]=>1110100
[8,2,4,1,7,6,5,3]=>1110110
[4,2,8,3,7,6,5,1]=>1110110
[4,8,2,1,7,6,5,3]=>1110110
[5,1,8,7,2,6,4,3]=>1111001
[5,8,1,3,7,6,2,4]=>1100010
[8,2,5,4,1,7,6,3]=>1111010
[5,1,4,8,7,6,3,2]=>1110011
[8,1,4,3,7,6,5,2]=>1110110
[4,8,1,3,7,6,5,2]=>1100110
[4,3,8,1,7,6,5,2]=>1110110
[6,2,8,1,5,7,3,4]=>1110000
[7,2,5,4,1,8,6,3]=>1111010
[7,3,2,8,5,6,1,4]=>1110100
[4,7,6,5,1,3,8,2]=>1100110
[5,4,6,8,7,2,1,3]=>1101001
[1,7,6,3,2,8,4,5]=>0111010
[5,4,2,1,7,3,6,8]=>1111000
[6,5,8,3,4,1,7,2]=>1110100
[4,1,2,8,5,3,6,7]=>1010100
[3,5,8,2,6,1,7,4]=>1101000
[3,7,6,2,8,4,5,1]=>1101010
[4,3,6,8,5,1,2,7]=>1010100
[2,7,1,5,8,4,3,6]=>1011000
[2,7,6,1,8,4,3,5]=>1011010
[7,1,2,6,3,5,4,8]=>1011000
[7,2,6,3,4,5,1,8]=>1110000
[6,7,8,4,2,5,3,1]=>1111000
[4,1,2,7,8,5,3,6]=>1010100
[4,7,3,1,2,6,8,5]=>1010100
[3,8,5,6,4,2,7,1]=>1101100
[3,2,6,4,7,8,5,1]=>1101100
[4,2,7,5,8,3,1,6]=>1110100
[5,2,1,4,7,8,3,6]=>1110000
[5,6,2,7,3,4,8,1]=>1110000
[1,5,8,6,4,2,3,7]=>0101010
[2,5,8,6,4,1,7,3]=>1011010
[1,6,2,3,5,8,7,4]=>0101001
[4,7,2,3,1,6,8,5]=>1100100
[7,4,6,2,8,3,5,1]=>1111000
[3,4,6,5,1,2,7,8]=>1000100
[4,3,8,2,5,7,1,6]=>1110000
[4,1,6,2,5,3,7,8]=>1110000
[4,2,6,1,5,3,8,7]=>1110001
[6,7,2,3,1,5,8,4]=>1101000
[2,1,5,7,8,3,6,4]=>1011000
[4,7,5,8,6,3,1,2]=>1010110
[7,3,2,5,8,1,6,4]=>1111000
[2,4,8,3,7,1,5,6]=>1010000
[5,2,8,4,1,6,3,7]=>1111000
[7,6,5,2,1,8,4,3]=>1111110
[2,7,5,1,8,3,6,4]=>1011100
[5,1,8,7,4,3,6,2]=>1111001
[3,8,7,2,4,6,1,5]=>1100001
[5,7,1,3,2,4,8,6]=>1100010
[4,2,7,6,3,5,8,1]=>1110010
[8,4,7,6,3,5,1,2]=>1011010
[8,1,7,4,2,3,5,6]=>1101000
[6,5,1,3,8,7,4,2]=>1101101
[6,1,8,5,3,7,2,4]=>1110100
[5,1,6,8,3,7,4,2]=>1111000
[8,6,5,1,7,4,3,2]=>1111110
[7,6,4,1,3,5,8,2]=>1101010
[8,2,3,7,1,4,5,6]=>1100000
[5,6,2,7,4,3,1,8]=>1111000
[3,7,8,2,6,1,4,5]=>1100000
[3,7,8,5,2,1,4,6]=>1100100
[4,8,6,5,1,2,7,3]=>1010110
[4,8,6,5,1,2,3,7]=>1000110
[3,8,7,6,5,1,2,4]=>1000111
[5,8,2,6,1,4,7,3]=>1110000
[3,8,7,5,6,1,4,2]=>1100101
[7,4,6,5,1,3,8,2]=>1101100
[4,6,3,8,7,5,1,2]=>1010101
[2,8,4,1,5,7,6,3]=>1011010
[1,8,4,2,5,7,6,3]=>0111010
[2,8,5,4,1,7,6,3]=>1011110
[2,5,8,3,7,1,6,4]=>1011000
[1,8,5,2,4,7,6,3]=>0110110
[1,4,6,2,8,7,5,3]=>0110101
[7,8,2,4,1,6,5,3]=>1110100
[2,4,6,1,8,7,5,3]=>1010101
[2,8,4,5,1,7,6,3]=>1011010
[3,5,8,1,7,6,2,4]=>1100010
[3,5,8,2,7,6,1,4]=>1100010
[2,1,6,8,7,5,3,4]=>1010101
[1,8,2,4,5,7,6,3]=>0110010
[1,3,8,2,5,7,6,4]=>0101010
[2,3,8,1,5,7,6,4]=>1001010
[2,6,1,8,7,5,3,4]=>1010101
[1,6,2,8,7,5,3,4]=>0110101
[1,6,3,8,7,5,2,4]=>0110101
[2,6,3,8,7,5,1,4]=>1010101
[3,2,8,1,5,7,6,4]=>1101010
[3,1,8,2,5,7,6,4]=>1101010
[2,1,8,3,5,7,6,4]=>1011010
[7,8,2,1,4,6,5,3]=>1110100
[2,3,6,8,7,5,1,4]=>1000101
[3,1,6,8,7,2,5,4]=>1101001
[3,8,4,5,1,6,2,7]=>1101000
[6,1,4,5,7,2,3,8]=>1100000
[8,1,4,7,6,3,2,5]=>1110010
[8,3,1,6,4,7,2,5]=>1111000
[5,3,8,6,2,7,1,4]=>1110010
[8,3,6,1,5,7,2,4]=>1110000
[8,4,6,3,1,2,5,7]=>1011000
[6,8,1,4,5,2,3,7]=>1100000
[1,5,8,4,6,2,3,7]=>0101000
[5,6,8,1,4,2,3,7]=>1100000
[5,7,4,8,1,2,3,6]=>1001000
[4,7,8,1,2,6,3,5]=>1010000
[8,7,1,5,6,2,3,4]=>1100001
[1,6,5,8,7,2,3,4]=>0100101
[3,7,1,6,2,4,8,5]=>1100100
[5,1,2,7,6,8,3,4]=>1010010
[1,7,6,5,8,2,3,4]=>0100110
[1,6,8,5,7,2,3,4]=>0100100
[7,5,1,2,6,8,3,4]=>1010100
[6,1,5,2,7,8,3,4]=>1110000
[5,1,2,6,8,7,3,4]=>1010001
[1,8,6,2,5,7,3,4]=>0110010
[5,7,8,1,2,6,3,4]=>1010000
[8,1,5,7,6,2,3,4]=>1100010
[3,7,1,2,8,4,6,5]=>1001100
[1,5,8,7,6,2,3,4]=>0100011
[7,8,6,1,5,2,3,4]=>1100010
[4,5,7,2,3,1,8,6]=>1100010
[3,7,8,1,4,6,5,2]=>1100100
[2,5,8,7,4,1,3,6]=>1001001
[2,6,4,7,5,3,8,1]=>1011100
[6,2,4,7,1,3,8,5]=>1100100
[7,3,5,1,4,2,8,6]=>1110010
[5,4,7,1,3,2,8,6]=>1101010
[6,1,4,7,5,3,8,2]=>1110100
[8,7,4,3,1,5,6,2]=>1111001
[8,7,1,4,3,5,6,2]=>1110001
[6,1,8,4,7,3,2,5]=>1111000
[4,7,3,6,1,2,8,5]=>1010100
[5,2,1,7,4,3,8,6]=>1111010
[4,7,6,2,3,1,8,5]=>1100110
[7,6,8,2,5,3,4,1]=>1110010
[2,3,6,1,8,7,5,4]=>1001101
[2,6,8,7,5,3,1,4]=>1010101
[6,4,1,7,5,2,8,3]=>1111100
[5,7,8,2,3,6,1,4]=>1100000
[4,8,7,1,2,5,6,3]=>1010001
[2,8,7,4,1,5,6,3]=>1011001
[8,6,2,1,5,7,4,3]=>1111010
[3,8,6,7,5,2,1,4]=>1100110
[6,1,3,7,5,8,2,4]=>1100100
[4,7,3,1,8,5,6,2]=>1110100
[1,3,8,5,2,7,4,6]=>0101100
[1,3,8,6,7,2,4,5]=>0100010
[2,8,3,7,6,1,4,5]=>1010010
[1,3,8,7,6,2,4,5]=>0100011
[1,4,6,8,7,2,3,5]=>0100001
[7,6,4,8,5,1,3,2]=>1101110
[7,2,6,5,8,1,3,4]=>1100100
[3,6,7,5,2,8,4,1]=>1101100
[4,6,5,7,2,8,1,3]=>1100100
[5,3,6,7,8,1,4,2]=>1110000
[6,3,2,8,5,4,1,7]=>1111100
[3,8,4,1,5,2,6,7]=>1101000
[2,5,7,4,3,1,6,8]=>1011000
[5,3,4,2,7,1,6,8]=>1110000
[3,7,5,4,1,2,6,8]=>1001100
[4,2,5,1,3,8,7,6]=>1100011
[4,3,5,1,2,7,6,8]=>1010010
[5,3,4,1,7,2,6,8]=>1110000
[4,1,6,3,5,2,7,8]=>1110000
[3,1,7,2,5,6,4,8]=>1101000
[3,7,5,4,2,1,6,8]=>1101100
[7,3,2,1,6,4,5,8]=>1111000
[2,8,6,1,7,4,3,5]=>1011010
[2,5,4,6,1,3,7,8]=>1001000
[2,5,6,4,1,3,7,8]=>1001000
[8,5,2,6,1,3,7,4]=>1101100
[7,1,5,6,3,2,4,8]=>1110000
[7,1,2,5,4,6,3,8]=>1011000
[2,4,1,6,5,3,7,8]=>1010100
[4,1,2,7,5,6,3,8]=>1010100
[7,1,2,6,5,4,3,8]=>1011100
[8,2,1,5,6,3,7,4]=>1111000
[2,8,5,1,6,4,7,3]=>1011100
[6,1,4,5,3,2,7,8]=>1110000
[3,1,6,5,4,2,7,8]=>1101100
[3,1,4,6,5,2,7,8]=>1100100
[5,6,3,8,7,4,1,2]=>1011001
[5,2,6,8,7,4,1,3]=>1101001
[5,2,3,1,4,8,6,7]=>1100010
[5,4,1,3,2,8,6,7]=>1101010
[5,1,3,4,2,8,6,7]=>1100010
[4,2,7,3,8,5,1,6]=>1110100
[5,3,1,2,4,8,6,7]=>1010010
[1,3,2,6,4,8,7,5]=>0101101
[1,6,2,5,3,8,7,4]=>0111001
[1,8,2,6,3,7,5,4]=>0111100
[1,8,3,6,4,7,5,2]=>0111100
[1,7,2,6,3,8,5,4]=>0111100
[1,5,2,7,4,8,6,3]=>0111010
[1,4,2,8,5,7,6,3]=>0110110
[4,8,1,3,2,6,5,7]=>1100100
[1,5,3,8,4,7,6,2]=>0111010
[2,6,3,8,1,5,4,7]=>1011000
[8,3,1,4,2,6,5,7]=>1110100
[6,8,7,3,5,2,4,1]=>1110001
[8,3,5,1,2,6,4,7]=>1011000
[8,6,3,1,5,4,2,7]=>1111010
[8,6,4,1,5,3,2,7]=>1111010
[8,6,5,4,1,3,2,7]=>1101110
[5,3,8,7,4,6,2,1]=>1111001
[2,3,8,7,4,6,1,5]=>1001001
[8,3,5,7,4,1,2,6]=>1011000
[4,8,5,3,1,2,7,6]=>1010110
[6,8,7,3,1,5,4,2]=>1111001
[6,8,5,4,1,3,7,2]=>1101100
[2,5,8,7,4,6,3,1]=>1011001
[4,8,7,6,5,1,3,2]=>1100111
[3,8,7,5,1,6,2,4]=>1100101
[2,3,8,7,5,6,1,4]=>1000101
[2,8,7,1,3,6,4,5]=>1001001
[8,5,4,7,2,1,3,6]=>1101100
[6,8,7,3,5,2,1,4]=>1110001
[3,5,8,6,4,2,7,1]=>1101010
[6,8,4,1,5,2,7,3]=>1111000
[6,8,2,1,7,5,3,4]=>1110100
[5,8,4,6,1,2,7,3]=>1011000
[2,4,8,6,5,1,7,3]=>1010110
[4,8,7,6,5,2,1,3]=>1100111
[4,8,7,5,1,6,2,3]=>1100101
[4,5,2,1,8,6,7,3]=>1110010
[2,8,3,5,6,7,1,4]=>1010000
[5,6,2,4,7,1,8,3]=>1110000
[2,7,5,4,6,1,8,3]=>1011100
[3,7,5,4,6,2,8,1]=>1101100
[2,6,7,4,1,3,8,5]=>1001100
[6,5,7,4,1,3,8,2]=>1101100
[2,4,6,3,5,7,8,1]=>1010000
[3,6,4,2,5,7,8,1]=>1101000
[2,3,6,1,5,7,8,4]=>1001000
[4,3,6,2,5,7,8,1]=>1110000
[4,6,1,2,5,7,8,3]=>1010000
[2,6,4,1,5,7,8,3]=>1011000
[2,4,1,6,5,7,8,3]=>1010100
[7,8,4,1,6,3,5,2]=>1111000
[8,7,5,6,1,3,4,2]=>1100101
[1,4,5,8,6,3,2,7]=>0110010
[8,4,5,7,2,6,1,3]=>1101000
[8,1,7,5,3,6,2,4]=>1110100
[5,2,6,3,1,7,8,4]=>1111000
[5,7,6,1,2,3,8,4]=>1001010
[5,3,2,1,8,6,4,7]=>1111010
[4,3,6,2,1,8,7,5]=>1110101
[5,3,6,4,8,2,1,7]=>1111000
[3,7,4,5,1,6,2,8]=>1101000
[3,6,4,5,8,2,1,7]=>1101000
[6,1,4,5,2,8,7,3]=>1110001
[7,2,4,5,1,6,3,8]=>1110000
[7,5,4,1,6,3,2,8]=>1111100
[1,5,4,8,6,3,2,7]=>0111010
[7,5,4,8,6,3,1,2]=>1011110
[1,8,7,5,3,6,4,2]=>0111101
[8,3,7,4,1,6,2,5]=>1111000
[8,5,4,1,6,3,2,7]=>1111100
[1,7,4,2,6,5,3,8]=>0111100
[8,2,1,5,6,7,3,4]=>1110000
[6,3,1,8,4,7,2,5]=>1111000
[7,1,4,8,6,3,2,5]=>1110010
[4,1,8,5,6,7,2,3]=>1100100
[5,7,4,8,6,2,1,3]=>1101010
[5,3,6,8,2,7,1,4]=>1110000
[6,3,7,4,8,2,1,5]=>1111000
[5,3,6,1,4,7,2,8]=>1110000
[4,3,6,8,2,7,1,5]=>1110000
[5,3,7,4,8,2,1,6]=>1111000
[5,3,8,4,1,6,2,7]=>1111000
[5,3,8,1,4,7,2,6]=>1110000
[5,8,4,1,6,3,2,7]=>1111000
[7,3,8,4,1,6,2,5]=>1111000
[1,5,8,3,6,7,4,2]=>0111000
[1,8,2,5,6,7,3,4]=>0110000
[7,8,4,1,6,5,2,3]=>1101100
[6,3,8,1,5,7,2,4]=>1110000
[8,3,1,2,5,7,4,6]=>1011000
[8,1,4,2,6,5,3,7]=>1110100
[3,8,5,6,2,7,1,4]=>1100100
[2,4,5,8,7,3,1,6]=>1010001
[4,3,1,5,6,2,8,7]=>1110001
[4,1,5,8,6,7,2,3]=>1100010
[4,3,7,6,1,2,8,5]=>1010110
[4,7,5,6,1,2,8,3]=>1010100
[4,5,1,8,6,7,3,2]=>1110010
[3,4,5,8,6,7,2,1]=>1100010
[2,1,5,8,6,7,4,3]=>1011010
[3,4,5,8,7,1,2,6]=>1000001
[4,7,1,5,6,2,8,3]=>1110000
[2,6,4,7,1,3,8,5]=>1001100
[5,3,8,6,4,7,2,1]=>1111010
[6,4,1,5,7,8,3,2]=>1111000
[3,6,4,7,2,1,8,5]=>1101100
[3,8,4,6,1,7,2,5]=>1101000
[3,8,5,6,4,7,2,1]=>1101100
[3,8,6,5,2,7,4,1]=>1101110
[3,8,7,5,2,1,4,6]=>1100101
[6,4,1,7,3,2,8,5]=>1111100
[5,1,4,6,7,2,8,3]=>1110000
[6,5,4,7,1,3,8,2]=>1101100
[2,1,6,5,3,7,8,4]=>1011100
[6,1,4,7,2,3,8,5]=>1100100
[1,6,2,5,4,8,3,7]=>0111000
[4,1,2,7,5,8,3,6]=>1010100
[6,1,3,5,8,2,4,7]=>1100000
[5,6,4,3,1,8,2,7]=>1111000
[6,2,3,5,8,1,4,7]=>1100000
[6,7,2,3,8,4,5,1]=>1101000
[6,7,2,1,3,8,4,5]=>1101000
[5,7,4,1,8,3,2,6]=>1111000
[4,1,7,5,8,3,6,2]=>1110100
[6,7,1,3,8,4,5,2]=>1101000
[1,6,7,4,3,8,5,2]=>0111100
[6,1,7,4,2,8,5,3]=>1111100
[2,1,6,7,4,3,8,5]=>1011100
[6,7,3,2,1,8,4,5]=>1111000
[2,5,7,3,1,4,8,6]=>1010010
[6,7,3,2,8,4,5,1]=>1111000
[2,6,7,4,3,8,5,1]=>1011100
[1,2,6,7,4,3,8,5]=>0011100
[1,7,5,8,2,4,3,6]=>0110100
[2,7,1,8,4,6,3,5]=>1011000
[2,7,5,8,1,6,3,4]=>1010100
[1,6,7,3,8,5,4,2]=>0111100
[6,7,1,8,4,5,3,2]=>1111000
[8,6,1,5,4,3,2,7]=>1111010
[2,4,3,8,5,1,6,7]=>1010100
[1,5,6,7,3,8,2,4]=>0110000
[1,6,5,4,8,3,2,7]=>0111100
[3,8,7,2,4,6,5,1]=>1100101
[1,3,7,6,4,8,5,2]=>0101110
[3,1,8,7,6,4,2,5]=>1101011
[3,1,8,7,5,4,2,6]=>1101101
[3,1,7,6,5,4,2,8]=>1101110
[4,7,1,6,5,3,2,8]=>1110100
[4,8,1,6,5,3,2,7]=>1110100
[4,8,1,7,5,3,2,6]=>1110100
[8,4,1,7,6,3,2,5]=>1111010
[5,4,1,8,6,3,2,7]=>1111010
[5,4,1,7,6,3,2,8]=>1111010
[6,4,1,7,5,3,2,8]=>1111100
[6,4,1,8,5,3,2,7]=>1111100
[8,4,1,7,5,3,2,6]=>1111100
[7,4,1,6,5,3,2,8]=>1111100
[7,5,6,1,4,3,2,8]=>1110100
[8,5,6,1,4,3,2,7]=>1110100
[5,7,6,1,4,3,2,8]=>1110010
[5,8,6,1,4,3,2,7]=>1110010
[6,7,5,1,4,3,2,8]=>1110100
[8,7,5,1,4,3,2,6]=>1110101
[8,6,5,1,4,3,2,7]=>1110110
[1,8,6,3,4,2,5,7]=>0110010
[3,1,6,4,5,8,7,2]=>1101001
[3,1,6,4,5,7,2,8]=>1101000
[7,6,3,8,4,5,2,1]=>1111010
[8,2,7,6,1,4,3,5]=>1110010
[5,2,7,8,1,4,3,6]=>1110000
[8,2,7,6,1,4,5,3]=>1110010
[5,2,3,7,1,6,8,4]=>1101000
[1,7,5,2,6,4,8,3]=>0111100
[7,1,3,6,8,2,4,5]=>1100000
[1,2,5,7,8,4,6,3]=>0011000
[3,1,2,7,5,4,8,6]=>1001110
[6,7,4,1,3,2,8,5]=>1101100
[1,7,2,8,4,3,5,6]=>0111000
[4,1,6,5,7,8,2,3]=>1100100
[1,6,3,5,7,8,2,4]=>0110000
[8,6,1,7,5,2,4,3]=>1110110
[7,6,4,1,8,3,2,5]=>1111010
[8,4,1,6,5,2,7,3]=>1111100
[1,5,3,4,7,8,2,6]=>0110000
[4,2,1,5,7,8,3,6]=>1110000
[5,1,4,6,7,8,2,3]=>1100000
[4,1,5,3,7,8,2,6]=>1110000
[8,1,4,6,5,2,7,3]=>1110100
[7,1,5,4,6,3,2,8]=>1111000
[8,2,1,6,7,5,4,3]=>1111100
[1,2,4,7,6,3,8,5]=>0010110
[6,7,4,1,8,5,2,3]=>1101100
[8,6,4,1,5,7,3,2]=>1111010
[5,2,4,3,7,1,6,8]=>1110000
[6,1,5,4,8,3,2,7]=>1111000
[1,2,8,7,4,3,6,5]=>0011101
[3,2,1,7,5,8,4,6]=>1101100
[8,1,7,6,4,2,5,3]=>1111010
[1,3,6,4,7,8,2,5]=>0101000
[5,1,3,4,7,8,2,6]=>1100000
[4,5,1,3,7,8,2,6]=>1100000
[5,2,3,1,7,8,4,6]=>1101000
[1,6,4,3,7,8,2,5]=>0111000
[7,6,4,3,1,5,2,8]=>1111010
[3,2,6,4,1,8,5,7]=>1101100
[7,5,4,6,1,3,2,8]=>1101100
[8,4,6,5,1,2,7,3]=>1011100
[1,5,6,3,7,8,2,4]=>0110000
[4,2,5,1,7,8,3,6]=>1110000
[4,7,8,1,6,5,3,2]=>1110100
[3,5,8,6,1,4,2,7]=>1100010
[1,8,4,2,7,6,3,5]=>0111010
[3,7,2,8,1,5,4,6]=>1101000
[7,3,8,1,6,5,4,2]=>1111100
[2,4,1,8,7,3,6,5]=>1010101
[7,3,8,6,1,5,4,2]=>1111010
[3,5,1,7,8,2,6,4]=>1101000
[5,4,7,8,2,1,6,3]=>1111000
[5,3,6,1,8,4,2,7]=>1111000
[6,4,7,1,5,3,2,8]=>1111000
[3,4,6,2,1,8,5,7]=>1100100
[5,6,4,8,3,2,1,7]=>1111000
[5,7,4,8,2,1,6,3]=>1111000
[4,7,5,8,2,1,6,3]=>1110100
[4,7,3,2,8,1,5,6]=>1110000
[7,1,2,6,3,8,5,4]=>1011100
[8,1,2,6,3,7,5,4]=>1011100
[8,1,2,7,6,3,5,4]=>1011010
[4,8,7,3,1,6,2,5]=>1110001
[4,7,8,3,1,6,2,5]=>1110000
[7,4,3,1,6,2,8,5]=>1111100
[7,4,3,1,8,6,2,5]=>1111010
[6,8,3,2,1,7,4,5]=>1111000
[3,7,6,2,4,8,1,5]=>1100010
[4,3,7,2,8,6,1,5]=>1110010
[5,1,2,6,3,8,7,4]=>1011001
[5,1,2,7,3,8,6,4]=>1011010
[6,1,2,7,3,5,8,4]=>1011000
[6,2,5,4,1,8,7,3]=>1111001
[4,6,3,2,1,8,7,5]=>1110101
[8,4,3,2,7,6,1,5]=>1111010
[1,5,8,4,7,6,3,2]=>0111010
[3,2,7,4,8,6,1,5]=>1101010
[7,4,3,2,8,6,1,5]=>1111010
[6,4,3,8,5,2,1,7]=>1111100
[8,2,5,4,7,6,1,3]=>1101010
[7,2,5,4,8,6,1,3]=>1101010
[6,2,8,7,5,4,1,3]=>1101101
[4,5,3,2,8,6,1,7]=>1110010
[3,2,5,4,8,6,1,7]=>1101010
[3,2,8,6,5,4,1,7]=>1101110
[8,4,3,6,5,2,1,7]=>1111100
[8,4,3,7,5,2,1,6]=>1111100
[3,2,7,8,5,4,1,6]=>1101100
[6,8,7,4,3,2,1,5]=>1111001
[6,3,2,1,8,7,4,5]=>1111001
[6,2,3,1,8,7,4,5]=>1101001
[3,4,8,1,7,5,6,2]=>1100100
[7,2,1,5,8,4,6,3]=>1111000
[7,3,1,5,2,8,6,4]=>1111010
[7,1,6,4,2,8,5,3]=>1111100
[3,7,4,1,5,8,6,2]=>1101010
[6,7,1,4,3,8,5,2]=>1110100
[7,1,6,4,8,3,5,2]=>1111000
[8,5,3,6,1,7,4,2]=>1111100
[8,5,6,1,2,7,4,3]=>1011100
[3,6,1,5,7,8,2,4]=>1100000
[2,1,5,8,6,3,7,4]=>1011010
[3,7,8,5,2,6,1,4]=>1100100
[3,7,8,5,4,1,6,2]=>1101100
[7,8,2,3,5,4,1,6]=>1101000
[4,6,5,1,7,3,8,2]=>1110100
[5,7,3,1,2,4,8,6]=>1010010
[6,3,2,5,1,7,4,8]=>1111000
[6,1,2,4,8,5,3,7]=>1010100
[6,3,1,7,2,5,8,4]=>1111000
[3,7,2,8,5,1,4,6]=>1100100
[3,6,5,2,4,7,1,8]=>1100100
[1,5,7,8,3,4,2,6]=>0110000
[6,8,4,3,1,7,2,5]=>1111000
[8,4,1,3,7,5,6,2]=>1101100
[4,8,1,3,7,5,6,2]=>1100100
[1,8,5,7,4,2,3,6]=>0101100
[2,1,6,8,5,3,4,7]=>1010100
[4,5,1,3,8,6,7,2]=>1100010
[1,2,6,8,5,3,4,7]=>0010100
[5,6,8,7,3,1,2,4]=>1010001
[6,3,2,4,7,1,8,5]=>1110100
[1,5,6,8,4,2,3,7]=>0101000
[5,7,8,3,6,1,2,4]=>1010000
[1,5,8,6,2,4,3,7]=>0110010
[1,5,3,7,2,6,8,4]=>0111000
[1,5,2,4,8,6,7,3]=>0110010
[1,5,4,2,6,8,7,3]=>0111001
[5,7,6,3,8,1,2,4]=>1010010
[5,7,6,8,3,1,2,4]=>1010010
[1,2,5,3,6,8,7,4]=>0011001
[7,1,5,6,2,3,8,4]=>1101000
[8,2,1,4,6,7,3,5]=>1110000
[7,2,6,1,3,4,8,5]=>1100100
[4,1,3,7,2,5,8,6]=>1100010
[6,2,7,5,1,3,8,4]=>1101100
[1,7,5,6,2,3,8,4]=>0101100
[3,7,6,1,2,4,8,5]=>1000110
[8,6,1,3,5,7,2,4]=>1100010
[1,7,4,3,8,2,5,6]=>0111000
[6,1,5,3,4,8,2,7]=>1110000
[3,6,7,5,2,8,1,4]=>1100100
[7,8,4,1,5,6,2,3]=>1101000
[5,8,1,3,6,7,2,4]=>1100000
[2,8,4,3,7,1,5,6]=>1011000
[3,8,4,6,7,1,2,5]=>1001000
[6,3,8,4,7,1,2,5]=>1011000
[1,2,5,4,8,3,6,7]=>0011000
[7,1,3,8,2,4,5,6]=>1100000
[8,1,3,7,2,4,5,6]=>1100000
[3,5,4,7,8,1,2,6]=>1001000
[8,3,1,4,7,2,5,6]=>1110000
[1,6,4,7,8,2,3,5]=>0101000
[1,3,7,8,5,6,2,4]=>0100100
[7,5,4,8,6,1,2,3]=>1001110
[8,2,6,7,5,1,3,4]=>1100100
[8,1,7,4,6,2,3,5]=>1101000
[2,5,8,4,7,1,3,6]=>1001000
[4,5,8,7,1,2,3,6]=>1000001
[4,1,8,5,7,2,3,6]=>1100100
[1,8,7,4,6,2,3,5]=>0101001
[2,6,5,4,1,8,3,7]=>1011100
[6,2,5,1,4,8,3,7]=>1110000
[6,5,4,1,3,8,2,7]=>1101100
[6,3,5,4,2,8,1,7]=>1111000
[1,3,8,7,4,2,6,5]=>0101101
[8,7,4,3,1,5,2,6]=>1111001
[8,2,5,1,4,6,7,3]=>1110000
[3,8,4,5,1,6,7,2]=>1101000
[8,5,4,1,3,6,7,2]=>1101100
[8,3,1,7,5,6,4,2]=>1111100
[8,4,7,6,5,3,1,2]=>1011110
[8,1,3,7,5,6,4,2]=>1101100
[8,1,4,5,7,6,3,2]=>1110010
[2,4,1,8,5,7,6,3]=>1010110
[8,2,1,4,7,6,3,5]=>1110010
[8,3,1,7,4,2,6,5]=>1111100
[8,2,7,3,1,6,5,4]=>1111100
[1,8,4,2,3,7,6,5]=>0101110
[3,1,2,8,7,4,6,5]=>1001101
[8,5,1,2,4,3,7,6]=>1010110
[2,8,3,7,4,1,6,5]=>1011100
[2,3,1,8,7,6,4,5]=>1001011
[4,2,8,7,3,1,5,6]=>1110001
[1,3,4,8,7,2,5,6]=>0100001
[8,1,3,4,6,7,2,5]=>1100000
[3,4,8,2,6,7,1,5]=>1100000
[3,6,8,2,5,1,7,4]=>1101000
[3,8,2,5,7,4,6,1]=>1101000
[8,4,2,1,7,5,6,3]=>1111100
[8,2,7,5,6,4,1,3]=>1101100
[6,2,8,5,4,1,7,3]=>1111100
[6,8,5,4,1,7,2,3]=>1101100
[2,8,1,5,7,6,3,4]=>1010010
[3,1,8,2,7,5,6,4]=>1101100
[8,5,7,1,6,4,2,3]=>1101100
[8,4,7,6,5,1,2,3]=>1001110
[2,8,4,7,3,6,5,1]=>1011100
[8,4,7,2,1,6,5,3]=>1111100
[1,8,4,7,6,5,2,3]=>0101110
[8,2,5,7,1,4,6,3]=>1110000
[3,5,8,1,7,4,6,2]=>1101000
[8,4,7,1,3,6,5,2]=>1101100
[5,1,7,8,3,4,2,6]=>1110000
[5,3,6,1,4,2,8,7]=>1110001
[5,7,2,1,4,3,8,6]=>1110010
[7,1,8,3,5,2,4,6]=>1110000
[7,2,4,8,1,5,6,3]=>1110000
[7,1,8,4,2,5,6,3]=>1111000
[6,4,2,5,8,1,7,3]=>1111000
[2,1,7,5,8,3,6,4]=>1011100
[7,3,8,5,6,2,1,4]=>1110100
[2,7,4,8,1,5,6,3]=>1011000
[7,4,8,3,1,5,6,2]=>1111000
[6,1,5,8,3,7,4,2]=>1111000
[2,6,3,5,8,7,4,1]=>1011001
[6,8,1,2,5,7,4,3]=>1011000
[8,6,5,3,7,2,1,4]=>1110110
[4,8,5,3,7,2,1,6]=>1110100
[7,4,8,6,5,3,2,1]=>1111110
[6,4,7,1,3,2,8,5]=>1101100
[7,8,4,1,3,5,6,2]=>1101000
[7,8,3,4,1,5,6,2]=>1110000
[7,3,1,8,2,5,6,4]=>1111000
[7,2,3,8,1,5,6,4]=>1101000
[2,7,4,8,6,3,1,5]=>1011010
[6,4,8,2,3,1,7,5]=>1101100
[7,2,1,8,3,5,6,4]=>1111000
[5,1,6,3,8,2,4,7]=>1110000
[3,5,6,8,1,4,2,7]=>1100000
[4,3,5,8,2,1,6,7]=>1110000
[6,4,7,2,3,1,5,8]=>1101000
[6,8,1,5,4,2,7,3]=>1111000
[7,8,6,3,1,4,2,5]=>1110010
[7,8,6,3,5,1,2,4]=>1010010
[7,2,8,5,4,6,3,1]=>1111100
[6,1,8,4,7,2,3,5]=>1101000
[6,5,3,7,2,4,8,1]=>1110100
[5,6,2,8,4,3,7,1]=>1111000
[4,6,2,7,8,3,5,1]=>1110000
[3,1,2,4,8,5,7,6]=>1000110
[5,1,2,4,6,7,8,3]=>1010000
[4,6,3,5,2,8,7,1]=>1110001
[5,3,2,6,8,4,7,1]=>1111000
[5,6,3,4,8,2,7,1]=>1110000
[5,2,6,4,1,7,8,3]=>1111000
[5,8,4,6,3,2,7,1]=>1111000
[5,4,3,8,6,2,7,1]=>1111010
[5,7,8,2,4,3,6,1]=>1110000
[5,6,2,4,8,3,7,1]=>1110000
[5,4,2,8,6,3,7,1]=>1111010
[5,7,4,2,6,3,8,1]=>1111000
[6,4,7,8,2,3,5,1]=>1101000
[3,7,5,2,4,8,1,6]=>1100100
[4,7,5,2,3,8,6,1]=>1100110
[6,4,7,3,2,5,8,1]=>1111000
[6,3,7,8,2,4,5,1]=>1110000
[5,7,3,2,8,4,6,1]=>1111000
[5,3,7,2,8,4,6,1]=>1111000
[4,3,7,2,5,8,6,1]=>1110010
[4,7,3,2,5,8,6,1]=>1110010
[4,7,3,2,6,8,5,1]=>1110100
[7,5,3,2,6,4,8,1]=>1111100
[5,7,3,2,6,4,8,1]=>1111000
[5,3,2,8,6,4,7,1]=>1111010
[8,5,2,6,7,3,4,1]=>1110100
[8,4,2,6,3,7,5,1]=>1111100
[7,4,6,2,3,8,5,1]=>1101100
[7,5,6,2,8,3,4,1]=>1110100
[6,3,7,5,2,4,8,1]=>1110100
[5,7,6,2,8,3,4,1]=>1110010
[4,7,6,2,3,8,5,1]=>1100110
[7,6,3,2,5,8,1,4]=>1110010
[7,6,4,2,5,8,3,1]=>1111010
[6,3,8,5,4,7,2,1]=>1111100
[4,8,3,7,1,6,5,2]=>1110100
[8,7,2,6,5,1,4,3]=>1110101
[5,8,3,2,1,7,6,4]=>1111010
[5,4,3,8,1,7,6,2]=>1111010
[6,5,3,8,7,1,4,2]=>1110101
[4,3,8,2,7,6,5,1]=>1110110
[4,8,2,7,6,5,3,1]=>1110110
[7,8,2,6,5,4,1,3]=>1101100
[3,8,7,6,2,5,1,4]=>1100011
[4,8,3,7,2,1,6,5]=>1110100
[8,6,3,1,7,5,4,2]=>1111110
[8,6,3,7,1,5,4,2]=>1111010
[4,8,3,7,6,2,5,1]=>1110010
[5,8,2,7,6,4,1,3]=>1101010
[8,4,2,1,7,6,5,3]=>1111110
[1,6,4,2,5,3,7,8]=>0111000
[1,6,7,2,5,3,4,8]=>0110000
[1,8,6,2,7,3,4,5]=>0110010
[1,5,2,6,4,3,7,8]=>0111000
[1,5,2,4,6,3,7,8]=>0110000
[1,8,6,2,3,7,4,5]=>0101010
[1,5,2,8,6,3,4,7]=>0110010
[1,7,3,2,6,8,4,5]=>0111000
[1,3,6,8,2,7,4,5]=>0101000
[1,4,3,8,2,5,6,7]=>0110000
[1,7,2,3,8,5,4,6]=>0101100
[1,6,2,8,5,4,3,7]=>0111100
[1,7,2,3,8,6,4,5]=>0101010
[1,5,3,8,2,7,4,6]=>0111000
[1,7,2,5,3,4,8,6]=>0110010
[1,4,8,2,5,6,3,7]=>0110000
[1,2,7,3,6,8,4,5]=>0011000
[1,7,2,3,6,8,4,5]=>0101000
[1,4,8,3,2,5,6,7]=>0110000
[1,7,2,5,8,3,4,6]=>0110000
[1,5,6,3,4,2,7,8]=>0110000
[1,5,6,3,4,7,2,8]=>0110000
[1,5,3,6,4,2,7,8]=>0111000
[1,7,5,6,8,3,4,2]=>0110100
[1,7,5,6,3,8,4,2]=>0111100
[1,3,7,5,2,8,6,4]=>0101110
[1,3,7,2,5,8,6,4]=>0101010
[1,5,3,7,4,6,2,8]=>0111000
[1,5,3,7,6,4,2,8]=>0111010
[1,5,3,6,7,4,2,8]=>0111000
[1,5,6,3,7,4,2,8]=>0111000
[1,5,7,6,3,4,8,2]=>0110010
[1,5,7,3,6,4,8,2]=>0111000
[1,3,7,2,5,6,8,4]=>0101000
[1,3,7,5,6,2,8,4]=>0101100
[2,5,7,4,1,3,8,6]=>1001010
[6,7,3,1,8,5,2,4]=>1110100
[8,3,5,1,7,6,2,4]=>1110010
[3,5,6,1,8,7,2,4]=>1100001
[2,4,6,8,7,3,1,5]=>1010001
[7,2,4,8,6,3,1,5]=>1110010
[2,3,6,4,1,8,7,5]=>1001101
[4,7,5,2,1,8,6,3]=>1110110
[8,5,3,6,2,1,7,4]=>1111100
[4,5,7,3,1,2,8,6]=>1010010
[4,5,1,8,3,2,7,6]=>1110010
[3,6,1,2,4,8,7,5]=>1000101
[2,5,3,8,4,1,7,6]=>1011010
[8,6,2,3,1,7,5,4]=>1101110
[6,3,1,2,4,8,7,5]=>1010101
[2,6,4,5,8,1,3,7]=>1001000
[6,4,1,3,5,8,2,7]=>1101000
[3,1,6,4,8,7,5,2]=>1101101
[4,2,6,1,3,7,8,5]=>1100100
[8,5,4,2,7,6,3,1]=>1111110
[2,8,4,6,7,1,3,5]=>1001000
[5,8,2,1,4,6,7,3]=>1110000
[3,7,8,4,2,6,5,1]=>1101100
[7,1,3,8,4,5,6,2]=>1101000
[7,8,1,4,3,5,6,2]=>1110000
[3,6,7,1,8,2,5,4]=>1101000
[3,1,5,7,2,8,6,4]=>1101010
[4,1,8,3,2,7,6,5]=>1110110
[3,8,2,4,7,1,6,5]=>1100100
[3,2,4,8,7,1,6,5]=>1100101
[3,2,5,7,1,8,6,4]=>1101010
[4,2,8,3,1,7,6,5]=>1110110
[4,8,2,1,3,7,6,5]=>1100110
[4,2,8,1,3,7,6,5]=>1100110
[2,4,6,5,1,3,8,7]=>1000101
[2,3,4,6,8,7,1,5]=>1000001
[2,1,4,6,8,7,3,5]=>1010001
[6,7,2,8,3,1,4,5]=>1110000
[6,3,7,8,4,1,2,5]=>1011000
[7,8,5,2,4,1,3,6]=>1100100
[7,6,2,3,1,8,4,5]=>1101010
[4,1,3,7,8,5,2,6]=>1100100
[4,3,1,8,5,2,7,6]=>1110110
[3,1,8,5,4,2,7,6]=>1101110
[5,1,3,2,4,7,8,6]=>1100010
[2,3,7,8,5,4,1,6]=>1001100
[2,4,8,5,6,1,7,3]=>1010100
[2,8,7,4,5,1,6,3]=>1011001
[1,3,8,5,2,6,7,4]=>0101100
[8,6,2,4,1,5,7,3]=>1110010
[1,6,4,3,2,7,8,5]=>0111100
[8,5,3,2,1,6,7,4]=>1111100
[1,7,5,2,3,6,8,4]=>0101100
[8,1,2,5,3,6,7,4]=>1011000
[8,2,6,4,3,5,1,7]=>1111000
[8,3,1,4,6,5,2,7]=>1110100
[5,8,3,1,2,6,4,7]=>1011000
[4,8,1,7,5,2,3,6]=>1100100
[4,8,1,7,5,2,6,3]=>1110100
[8,5,1,4,2,6,3,7]=>1110100
[8,4,1,3,5,6,2,7]=>1101000
[8,5,3,2,1,6,4,7]=>1111100
[8,1,5,4,2,6,3,7]=>1111000
[8,5,2,4,1,6,3,7]=>1110100
[4,8,7,1,5,2,6,3]=>1110001
[4,8,7,1,5,2,3,6]=>1100001
[7,6,8,4,1,3,2,5]=>1101010
[7,6,8,4,1,3,5,2]=>1101010
[8,4,2,7,5,1,6,3]=>1111100
[3,8,7,5,4,1,2,6]=>1001101
[7,6,8,4,1,5,2,3]=>1101010
[8,7,6,1,5,2,3,4]=>1100011
[7,1,4,8,6,3,5,2]=>1110010
[8,1,6,5,3,4,7,2]=>1110100
[8,6,2,5,3,4,7,1]=>1110010
[8,6,5,1,3,4,7,2]=>1100110
[8,7,5,1,3,6,2,4]=>1100101
[8,7,1,5,3,6,2,4]=>1110001
[8,6,1,3,5,4,7,2]=>1101010
[8,1,6,3,5,4,7,2]=>1111000
[7,1,4,8,3,6,5,2]=>1110100
[8,3,2,7,4,6,5,1]=>1111100
[7,8,5,2,4,3,6,1]=>1110100
[7,3,8,2,5,4,6,1]=>1111000
[8,4,2,5,3,7,6,1]=>1111010
[4,8,1,5,3,7,6,2]=>1110010
[7,4,8,2,6,3,5,1]=>1111000
[7,4,8,2,6,3,1,5]=>1111000
[8,7,3,1,6,4,2,5]=>1111001
[8,7,3,1,6,4,5,2]=>1111001
[8,7,3,1,4,6,5,2]=>1110101
[8,4,3,2,7,5,6,1]=>1111100
[6,4,1,7,8,5,3,2]=>1111100
[7,6,3,4,1,8,5,2]=>1110110
[8,7,3,1,6,2,5,4]=>1111001
[7,8,6,4,2,5,1,3]=>1101010
[7,8,2,4,6,5,1,3]=>1100100
[8,1,7,3,5,6,2,4]=>1110000
[8,7,1,6,5,2,3,4]=>1100101
[8,7,5,2,4,6,1,3]=>1100101
[8,1,7,5,4,6,2,3]=>1101100
[8,7,3,2,6,1,5,4]=>1111001
[8,1,7,6,5,2,3,4]=>1100110
[8,7,2,6,5,1,3,4]=>1100101
[1,4,8,6,7,5,3,2]=>0110110
[8,6,2,5,7,4,3,1]=>1111010
[7,1,3,6,8,5,4,2]=>1101100
[8,1,7,6,4,5,3,2]=>1111010
[7,1,8,6,4,5,3,2]=>1111010
[6,7,2,5,8,1,4,3]=>1110000
[6,3,7,5,8,2,4,1]=>1110100
[6,5,7,3,8,1,4,2]=>1110100
[6,3,7,4,8,2,5,1]=>1111000
[6,3,7,4,8,1,5,2]=>1111000
[6,2,7,4,8,1,5,3]=>1111000
[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]=>1111000
[6,7,5,1,4,3,8,2]=>1110100
[2,7,6,8,3,5,1,4]=>1010010
[7,2,1,5,3,8,6,4]=>1111010
[5,8,2,7,6,1,3,4]=>1100010
[4,2,3,1,5,8,6,7]=>1100010
[1,5,7,3,6,8,2,4]=>0110000
[8,4,6,2,5,7,1,3]=>1101000
[1,3,4,7,6,8,2,5]=>0100010
[8,1,3,6,7,4,2,5]=>1101000
[1,2,4,7,8,5,3,6]=>0010100
[2,1,4,7,8,5,3,6]=>1010100
[3,1,4,7,6,8,2,5]=>1100010
[4,1,3,7,6,8,2,5]=>1100010
[5,1,7,3,6,8,2,4]=>1110000
[6,7,8,2,4,5,1,3]=>1100000
[5,8,6,2,4,7,1,3]=>1100010
[3,8,2,6,5,7,1,4]=>1100100
[2,8,3,6,7,4,1,5]=>1011000
[1,8,3,6,7,4,2,5]=>0111000
[8,7,2,5,6,3,1,4]=>1110001
[8,7,1,6,4,3,2,5]=>1111001
[1,8,2,7,5,4,3,6]=>0111100
[3,8,1,7,5,4,2,6]=>1101100
[4,8,1,6,7,3,2,5]=>1110000
[5,8,6,1,7,3,2,4]=>1110010
[6,7,1,2,8,4,3,5]=>1011000
[2,1,3,8,6,5,4,7]=>1001110
[8,2,1,7,5,4,3,6]=>1111100
[1,3,2,8,6,5,4,7]=>0101110
[3,4,1,7,6,8,2,5]=>1100010
[2,5,7,1,8,4,3,6]=>1011000
[3,5,7,1,6,8,2,4]=>1100000
[4,5,7,6,1,8,2,3]=>1100010
[5,4,7,6,8,3,1,2]=>1011010
[1,5,7,8,6,3,2,4]=>0110010
[8,4,6,7,5,2,1,3]=>1101100
[8,3,7,5,6,2,1,4]=>1110100
[1,4,8,6,7,3,2,5]=>0110010
[2,4,8,6,7,3,1,5]=>1010010
[2,3,8,7,5,4,1,6]=>1001101
[1,3,8,7,5,4,2,6]=>0101101
[8,2,7,6,4,3,1,5]=>1111010
[8,1,7,6,4,3,2,5]=>1111010
[4,1,8,6,7,3,2,5]=>1110010
[4,8,7,5,6,2,1,3]=>1100101
[8,1,7,2,5,6,4,3]=>1111000
[8,1,3,5,2,7,6,4]=>1101010
[8,1,7,4,3,6,5,2]=>1111100
[2,7,1,5,4,8,6,3]=>1011010
[8,6,2,4,3,7,5,1]=>1110110
[8,1,4,5,6,3,7,2]=>1110000
[8,1,4,5,6,2,7,3]=>1110000
[8,1,4,7,6,2,5,3]=>1110010
[2,5,1,7,8,6,4,3]=>1011010
[3,5,6,2,8,7,4,1]=>1101001
[3,5,6,1,8,7,4,2]=>1101001
[2,4,5,1,7,6,3,8]=>1010010
[7,3,1,5,6,4,2,8]=>1111000
[8,6,2,4,7,3,1,5]=>1110010
[8,4,7,3,5,2,1,6]=>1111000
[8,4,5,3,7,6,2,1]=>1111010
[3,4,5,6,2,8,1,7]=>1100000
[3,7,4,2,8,5,1,6]=>1101100
[7,3,4,1,6,8,2,5]=>1110000
[2,6,3,1,4,7,5,8]=>1010100
[7,2,1,6,3,4,8,5]=>1110100
[7,3,4,1,6,5,8,2]=>1110100
[3,7,4,2,5,8,6,1]=>1101010
[2,3,5,1,4,8,7,6]=>1000011
[2,7,1,3,6,8,5,4]=>1001100
[2,7,1,3,8,4,6,5]=>1001100
[3,8,7,1,6,2,5,4]=>1101001
[3,8,7,1,4,5,2,6]=>1100001
[3,7,4,2,1,8,6,5]=>1101110
[4,8,5,7,2,6,3,1]=>1110100
[8,4,5,7,3,2,6,1]=>1111000
[8,3,7,2,4,1,5,6]=>1110000
[8,6,7,2,1,4,3,5]=>1110010
[8,3,7,5,1,2,6,4]=>1011100
[7,3,4,6,2,1,5,8]=>1110000
[3,7,4,6,1,5,2,8]=>1101000
[3,4,7,6,1,2,8,5]=>1000110
[4,5,8,7,6,1,3,2]=>1100011
[8,6,3,7,5,1,4,2]=>1110110
[8,7,3,5,6,1,4,2]=>1110001
[7,6,3,8,1,4,5,2]=>1110010
[8,5,2,7,6,1,3,4]=>1100110
[7,6,4,8,1,2,5,3]=>1011010
[8,7,3,1,4,5,2,6]=>1110001
[6,4,7,2,1,5,8,3]=>1111000
[8,4,2,5,1,6,7,3]=>1111000
[8,5,3,1,6,4,7,2]=>1111100
[8,7,3,1,4,5,6,2]=>1110001
[8,7,4,1,5,6,2,3]=>1101001
[8,6,4,1,7,5,2,3]=>1101110
[8,6,3,1,7,4,5,2]=>1111010
[8,5,3,1,6,7,4,2]=>1111100
[8,5,3,7,1,6,4,2]=>1111100
[7,6,3,8,1,4,2,5]=>1110010
[7,4,8,2,6,1,5,3]=>1111000
[8,5,3,1,6,4,2,7]=>1111100
[8,7,4,1,5,2,3,6]=>1101001
[8,7,5,1,2,6,3,4]=>1010101
[8,6,4,1,2,7,5,3]=>1011110
[8,7,3,1,4,2,5,6]=>1110001
[8,7,4,1,2,5,3,6]=>1011001
[8,7,5,1,2,3,6,4]=>1001101
[1,6,7,3,2,8,4,5]=>0111000
[1,8,6,3,2,7,4,5]=>0111010
[1,5,3,7,2,8,4,6]=>0111000
[1,4,6,2,8,5,3,7]=>0110100
[1,5,6,2,8,4,3,7]=>0111000
[3,5,2,6,4,7,8,1]=>1101000
[1,2,5,3,8,6,7,4]=>0011010
[2,4,6,3,1,7,5,8]=>1010100
[3,4,8,6,5,7,2,1]=>1100110
[2,3,8,6,7,1,5,4]=>1001010
[1,2,5,7,4,6,8,3]=>0011000
[1,2,4,7,6,8,3,5]=>0010010
[2,3,6,8,1,7,4,5]=>1001000
[2,4,8,5,6,7,1,3]=>1000100
[1,4,8,5,6,7,3,2]=>0110100
[6,1,3,5,4,2,8,7]=>1101001
[2,1,5,8,6,4,7,3]=>1011010
[1,8,3,5,6,2,7,4]=>0111000
[8,3,2,5,6,1,7,4]=>1111000
[4,2,5,1,6,8,7,3]=>1110001
[5,4,2,7,8,6,1,3]=>1101010
[6,7,1,8,3,2,4,5]=>1110000
[6,7,2,8,1,3,4,5]=>1100000
[1,7,8,5,2,6,3,4]=>0110100
[5,8,7,2,6,3,4,1]=>1110001
[7,6,2,4,8,1,5,3]=>1110010
[4,8,3,1,7,6,5,2]=>1110110
[5,3,8,7,1,6,4,2]=>1111001
[5,8,7,3,1,6,4,2]=>1111001
[5,3,8,2,1,7,6,4]=>1111010
[3,8,7,2,6,5,1,4]=>1100101
[7,4,1,8,6,5,3,2]=>1111110
[5,4,2,8,1,7,6,3]=>1111010
[5,8,4,7,1,6,3,2]=>1111000
[8,5,6,1,4,7,2,3]=>1100100
[6,7,4,1,2,5,8,3]=>1011000
[3,6,7,5,8,1,2,4]=>1000100
[6,5,8,7,4,2,3,1]=>1101101
[5,7,6,2,8,3,1,4]=>1110010
[2,5,6,3,1,4,8,7]=>1010001
[3,8,7,2,1,5,4,6]=>1101001
[4,8,5,6,7,3,1,2]=>1010100
[3,7,6,2,8,5,1,4]=>1100110
[6,1,7,3,8,5,2,4]=>1110100
[4,8,5,6,7,2,1,3]=>1100100
[5,8,6,2,7,4,1,3]=>1101010
[4,6,5,8,7,3,1,2]=>1010101
[8,3,1,7,2,6,4,5]=>1111000
[8,4,5,1,7,6,2,3]=>1101010
[8,5,6,1,7,2,4,3]=>1110100
[7,5,6,1,3,8,4,2]=>1101100
[5,7,6,1,3,8,4,2]=>1101010
[6,7,1,4,2,8,5,3]=>1110100
[2,1,6,4,8,3,7,5]=>1011100
[7,4,5,1,3,8,6,2]=>1101010
[5,8,7,4,6,2,3,1]=>1101001
[6,8,7,1,5,3,4,2]=>1110001
[2,7,8,4,6,5,1,3]=>1001100
[3,7,8,5,4,6,2,1]=>1101100
[2,8,7,5,3,6,4,1]=>1011101
[1,8,7,3,6,4,5,2]=>0111001
[2,8,7,4,6,1,5,3]=>1011001
[4,8,7,2,5,6,3,1]=>1110001
[4,7,8,5,3,6,2,1]=>1110100
[6,4,8,1,5,7,3,2]=>1111000
[4,5,8,6,3,7,2,1]=>1110010
[2,6,7,8,4,5,1,3]=>1001000
[6,1,2,8,4,7,5,3]=>1011100
[4,7,1,8,5,6,3,2]=>1110100
[5,7,1,8,2,6,4,3]=>1111000
[7,2,1,8,6,4,5,3]=>1111010
[5,3,8,4,7,6,2,1]=>1111010
[2,5,8,1,7,4,6,3]=>1011000
[4,5,8,3,7,6,2,1]=>1110010
[1,7,2,8,6,4,5,3]=>0111010
[2,4,7,8,5,6,1,3]=>1000100
[2,4,8,5,7,6,1,3]=>1000110
[2,6,3,8,5,1,7,4]=>1011100
[4,1,5,8,6,7,3,2]=>1110010
[3,4,6,8,2,1,7,5]=>1100100
[5,3,4,7,6,1,2,8]=>1010010
[2,8,7,1,4,3,6,5]=>1010101
[1,2,7,8,4,3,6,5]=>0011100
[2,8,5,4,1,3,7,6]=>1001110
[4,2,8,7,1,3,5,6]=>1100001
[5,4,6,3,1,7,2,8]=>1111000
[4,3,6,5,1,8,2,7]=>1110100
[1,5,6,8,7,3,2,4]=>0110001
[1,4,8,3,6,5,2,7]=>0110100
[1,2,8,6,4,3,7,5]=>0011110
[6,5,1,8,7,3,2,4]=>1110101
[8,3,2,6,1,7,4,5]=>1111000
[6,5,1,8,7,4,3,2]=>1111101
[7,5,1,8,6,4,3,2]=>1111110
[8,5,1,7,6,4,3,2]=>1111110
[8,5,3,7,6,1,4,2]=>1110110
[3,8,7,6,1,5,4,2]=>1101011
[8,5,2,6,1,4,7,3]=>1110100
[2,7,5,8,1,4,6,3]=>1010100
[8,5,6,1,7,3,2,4]=>1110100
[3,2,6,7,1,8,5,4]=>1101100
[3,4,6,7,8,2,1,5]=>1100000
[6,7,1,3,8,5,4,2]=>1101100
[6,7,1,8,5,2,4,3]=>1110100
[1,6,2,7,8,5,3,4]=>0110100
[1,2,6,7,8,5,3,4]=>0010100
[1,6,7,4,8,3,2,5]=>0111000
[1,4,6,7,8,3,2,5]=>0110000
[8,6,1,2,7,3,4,5]=>1010010
[3,6,8,2,7,1,5,4]=>1101000
[2,8,6,1,4,5,7,3]=>1010010
[6,8,7,2,5,4,1,3]=>1101001
[3,7,2,1,8,4,6,5]=>1101100
[3,7,2,4,1,8,6,5]=>1100110
[3,2,6,4,8,7,5,1]=>1101101
[4,7,2,8,6,5,1,3]=>1100110
[4,7,1,8,6,5,3,2]=>1110110
[2,7,4,8,3,6,1,5]=>1011000
[4,7,3,8,6,1,5,2]=>1110010
[4,7,3,8,6,2,1,5]=>1110010
[4,3,6,8,7,2,5,1]=>1110001
[4,3,8,2,5,7,6,1]=>1110010
[4,3,8,1,5,7,6,2]=>1110010
[4,1,2,6,8,7,5,3]=>1010101
[2,4,3,6,8,7,1,5]=>1010001
[3,1,6,4,8,7,2,5]=>1101001
[4,1,6,8,7,5,2,3]=>1100101
[3,8,1,4,5,7,2,6]=>1100000
[3,8,1,4,2,5,7,6]=>1100010
[4,1,8,3,5,2,7,6]=>1110010
[4,2,3,6,8,7,1,5]=>1100001
[4,2,8,3,5,7,6,1]=>1110010
[3,8,2,4,5,7,6,1]=>1100010
[3,8,2,4,1,5,7,6]=>1100010
[3,8,2,5,1,4,7,6]=>1100010
[4,2,8,5,7,1,3,6]=>1100100
[3,8,1,5,2,4,7,6]=>1100010
[7,5,6,4,1,3,2,8]=>1101100
[7,8,6,4,1,3,2,5]=>1101010
[7,1,4,2,5,6,3,8]=>1110000
[7,3,2,1,4,6,5,8]=>1110100
[7,6,1,4,3,2,5,8]=>1110010
[7,4,1,3,5,6,2,8]=>1101000
[7,3,1,2,5,6,4,8]=>1011000
[2,7,1,3,5,6,8,4]=>1001000
[3,6,2,1,5,8,7,4]=>1101001
[2,3,6,1,5,8,7,4]=>1001001
[3,1,7,2,5,6,8,4]=>1101000
[3,4,7,1,5,6,8,2]=>1100000
[3,6,7,4,1,2,8,5]=>1001100
[4,3,2,7,1,6,8,5]=>1110100
[7,3,2,8,1,6,4,5]=>1111000
[7,4,8,1,5,6,3,2]=>1111000
[2,6,8,1,5,3,7,4]=>1011000
[6,8,2,1,5,3,7,4]=>1111000
[4,8,2,5,3,6,7,1]=>1110000
[4,5,8,2,3,6,7,1]=>1100000
[2,4,8,5,3,6,7,1]=>1010100
[4,1,8,6,5,3,7,2]=>1110110
[5,7,8,4,6,3,2,1]=>1111000
[5,3,2,6,4,8,7,1]=>1111001
[2,4,5,3,8,6,7,1]=>1010010
[4,3,5,2,8,6,7,1]=>1110010
[4,5,2,3,8,6,7,1]=>1100010
[4,8,5,3,2,6,7,1]=>1110100
[3,8,4,5,2,6,7,1]=>1101000
[3,5,4,2,8,6,7,1]=>1101010
[4,1,2,7,5,6,8,3]=>1010100
[4,8,1,6,5,2,7,3]=>1110100
[5,6,7,4,2,8,3,1]=>1111000
[2,5,7,4,6,8,3,1]=>1011000
[7,3,5,4,2,8,6,1]=>1111010
[7,5,2,4,3,8,6,1]=>1110110
[6,8,1,2,5,4,7,3]=>1011000
[6,4,1,8,5,2,7,3]=>1111100
[2,6,1,8,5,4,7,3]=>1011100
[7,1,2,8,5,6,4,3]=>1011100
[4,3,2,6,8,5,7,1]=>1110100
[3,7,6,4,8,5,2,1]=>1101110
[3,1,6,8,5,4,7,2]=>1101100
[2,3,5,8,4,6,7,1]=>1001000
[3,4,5,8,2,6,7,1]=>1100000
[5,4,2,8,3,6,7,1]=>1111000
[5,3,4,8,2,6,7,1]=>1110000
[2,5,4,8,3,6,7,1]=>1011000
[6,3,2,5,8,4,7,1]=>1111000
[6,1,8,3,5,4,7,2]=>1111000
[5,4,8,3,2,6,7,1]=>1111000
[5,8,2,3,4,6,7,1]=>1100000
[3,4,5,2,7,1,6,8]=>1100000
[7,5,6,1,2,3,8,4]=>1001100
[1,5,7,6,3,2,8,4]=>0111010
[8,4,6,7,3,2,5,1]=>1111000
[8,4,6,2,3,1,5,7]=>1101000
[7,5,2,1,4,3,8,6]=>1110110
[3,1,7,8,5,4,2,6]=>1101100
[3,4,5,2,1,8,6,7]=>1100010
[7,6,4,8,3,1,2,5]=>1011010
[6,2,8,5,1,3,4,7]=>1100100
[3,2,7,8,6,1,4,5]=>1100010
[6,8,2,5,1,3,7,4]=>1101000
[6,7,4,2,1,5,3,8]=>1111000
[5,7,4,1,6,8,2,3]=>1101000
[5,6,8,1,3,7,2,4]=>1100000
[3,7,4,8,6,1,2,5]=>1001010
[1,6,8,5,3,2,4,7]=>0110100
[7,2,8,4,6,1,3,5]=>1101000
[4,1,6,8,7,3,2,5]=>1110001
[5,1,4,6,7,3,8,2]=>1110000
[7,1,3,4,6,2,8,5]=>1100100
[5,8,7,4,2,1,3,6]=>1101001
[3,1,5,2,7,8,6,4]=>1101010
[1,8,7,3,2,5,4,6]=>0111001
[1,2,5,4,8,7,3,6]=>0011001
[1,2,4,8,6,3,5,7]=>0010010
[8,5,3,2,1,4,7,6]=>1110110
[1,2,7,6,8,4,3,5]=>0011010
[1,7,3,4,2,6,8,5]=>0110100
[1,6,3,5,8,4,2,7]=>0111000
[1,5,6,3,2,8,4,7]=>0111000
[1,2,5,8,4,6,3,7]=>0011000
[1,2,7,8,4,5,3,6]=>0011000
[1,5,3,2,7,8,4,6]=>0111000
[4,1,8,6,2,3,7,5]=>1100110
[1,7,6,4,3,8,5,2]=>0111110
[1,8,5,7,6,3,2,4]=>0110110
[1,6,3,5,7,8,4,2]=>0111000
[1,5,6,3,2,7,8,4]=>0111000
[1,8,4,7,5,3,2,6]=>0111100
[7,6,2,5,3,4,1,8]=>1110010
[7,6,2,4,5,3,1,8]=>1110010
[7,6,2,4,3,5,1,8]=>1110010
[7,6,2,3,5,4,1,8]=>1101010
[8,4,2,7,1,6,3,5]=>1111000
[8,7,6,1,5,3,2,4]=>1110011
[8,7,6,1,3,5,4,2]=>1101011
[8,7,6,1,5,4,2,3]=>1101011
[4,5,3,8,2,1,6,7]=>1110000
[8,3,5,4,2,1,6,7]=>1111000
[7,8,4,3,1,5,2,6]=>1111000
[7,5,8,2,1,4,3,6]=>1110100
[8,6,3,7,1,5,2,4]=>1110010
[8,7,6,1,2,5,3,4]=>1010011
[8,7,6,1,2,5,4,3]=>1011011
[8,7,6,1,4,2,5,3]=>1110011
[2,4,7,3,5,6,1,8]=>1010000
[5,7,6,4,2,3,1,8]=>1101010
[3,1,4,8,5,6,2,7]=>1100100
[5,8,2,4,6,1,3,7]=>1100000
[2,4,1,8,5,6,3,7]=>1010100
[6,1,4,8,5,2,7,3]=>1110100
[4,1,2,8,5,3,7,6]=>1010110
[2,4,6,8,5,1,7,3]=>1010100
[3,1,6,8,5,2,7,4]=>1101100
[2,3,8,1,5,6,4,7]=>1001000
[5,1,8,2,4,6,7,3]=>1110000
[5,8,2,7,3,4,1,6]=>1110000
[3,8,7,5,2,6,1,4]=>1100101
[5,3,8,1,6,7,4,2]=>1111000
[5,8,2,1,3,7,6,4]=>1101010
[4,8,2,1,3,5,6,7]=>1100000
[5,1,8,3,6,7,4,2]=>1111000
[8,4,1,6,5,2,3,7]=>1101100
[6,8,7,3,2,4,1,5]=>1110001
[3,2,4,7,5,8,1,6]=>1100100
[1,2,7,4,6,3,8,5]=>0011100
[2,8,7,6,4,5,1,3]=>1001011
[3,5,2,4,7,6,8,1]=>1100010
[3,5,2,4,6,7,8,1]=>1100000
[5,3,2,6,4,7,8,1]=>1111000
[5,3,2,6,7,4,8,1]=>1111000
[5,3,2,7,6,4,8,1]=>1111010
[7,3,5,2,8,4,6,1]=>1111000
[3,2,5,7,4,6,8,1]=>1101000
[2,3,5,7,4,6,8,1]=>1001000
[3,2,7,5,4,8,6,1]=>1101110
[3,7,5,2,4,8,6,1]=>1100110
[7,5,3,2,8,6,4,1]=>1111110
[2,3,7,5,4,8,6,1]=>1001110
[2,4,8,7,5,1,3,6]=>1000101
[3,5,7,6,1,8,4,2]=>1101010
[3,5,7,6,2,8,4,1]=>1101010
[2,4,6,3,8,7,5,1]=>1010101
[1,5,3,2,8,7,6,4]=>0111011
[6,3,1,8,7,4,2,5]=>1111001
[5,3,6,2,8,7,4,1]=>1111001
[5,8,3,1,7,6,4,2]=>1111010
[6,3,5,2,1,8,7,4]=>1111001
[3,8,1,4,7,6,5,2]=>1100110
[6,2,3,8,7,5,4,1]=>1101101
[4,1,3,5,8,7,6,2]=>1100011
[4,2,5,3,7,6,1,8]=>1110010
[6,2,4,3,7,5,1,8]=>1110100
[1,3,6,4,7,5,2,8]=>0101100
[8,2,5,3,6,4,1,7]=>1111000
[7,2,5,3,6,4,1,8]=>1111000
[6,2,5,3,7,4,1,8]=>1111000
[4,2,6,3,7,5,1,8]=>1110100
[5,2,7,3,6,4,1,8]=>1111000
[7,3,6,2,5,4,1,8]=>1111000
[6,3,8,2,5,4,1,7]=>1111000
[7,3,1,4,6,5,2,8]=>1110100
[8,3,7,2,5,4,1,6]=>1111000
[5,2,8,3,6,4,1,7]=>1111000
[4,2,8,3,6,5,1,7]=>1110100
[3,2,8,4,6,5,1,7]=>1101100
[1,4,7,3,6,5,2,8]=>0110100
[8,2,5,4,1,6,3,7]=>1111000
[1,3,6,5,2,7,4,8]=>0101100
[8,2,6,4,1,5,3,7]=>1111000
[1,4,8,3,7,5,2,6]=>0110100
[6,2,1,4,8,5,3,7]=>1110100
[5,2,1,4,8,6,3,7]=>1110010
[3,2,1,5,8,6,4,7]=>1101010
[4,2,8,3,7,5,1,6]=>1110100
[5,2,8,3,7,4,1,6]=>1111000
[8,3,7,2,6,4,1,5]=>1111000
[7,3,1,4,8,5,2,6]=>1110100
[1,3,7,4,8,5,2,6]=>0101100
[8,2,6,3,7,4,1,5]=>1111000
[7,2,6,3,8,4,1,5]=>1111000
[5,2,7,3,8,4,1,6]=>1111000
[3,2,7,4,8,5,1,6]=>1101100
[5,2,6,3,8,4,1,7]=>1111000
[6,2,5,3,8,4,1,7]=>1111000
[7,2,5,3,8,4,1,6]=>1111000
[8,2,5,3,7,4,1,6]=>1111000
[1,3,6,4,8,5,2,7]=>0101100
[1,3,5,4,8,6,2,7]=>0101010
[8,2,4,3,7,5,1,6]=>1110100
[7,2,4,3,8,5,1,6]=>1110100
[6,2,4,3,8,5,1,7]=>1110100
[5,2,4,3,8,6,1,7]=>1110010
[4,2,5,3,8,6,1,7]=>1110010
[4,2,5,3,1,7,6,8]=>1110010
[6,2,4,3,1,7,5,8]=>1110100
[7,2,4,3,1,6,5,8]=>1110100
[8,5,1,3,6,4,2,7]=>1101100
[8,4,1,3,6,5,2,7]=>1101100
[1,5,2,4,7,6,3,8]=>0110010
[7,2,5,3,1,6,4,8]=>1111000
[6,2,5,3,1,7,4,8]=>1111000
[4,2,6,3,1,7,5,8]=>1110100
[3,2,6,4,1,7,5,8]=>1101100
[5,2,7,3,1,6,4,8]=>1111000
[6,2,7,3,1,5,4,8]=>1111000
[7,2,6,3,1,5,4,8]=>1111000
[1,5,2,4,8,6,3,7]=>0110010
[8,4,1,3,7,5,2,6]=>1101100
[6,2,1,5,3,7,4,8]=>1111000
[3,2,1,6,4,7,5,8]=>1101100
[3,2,8,5,1,6,4,7]=>1101100
[4,2,8,5,1,6,3,7]=>1110100
[6,2,8,4,1,5,3,7]=>1111000
[1,4,8,5,2,6,3,7]=>0110100
[8,3,7,4,1,5,2,6]=>1111000
[7,1,3,2,5,6,4,8]=>1101000
[1,5,2,8,7,4,3,6]=>0111001
[5,7,2,8,1,4,3,6]=>1110000
[2,7,1,5,6,4,3,8]=>1011000
[7,1,5,3,2,6,8,4]=>1111000
[1,7,3,4,5,2,8,6]=>0110010
[8,6,7,3,5,2,1,4]=>1110010
[3,2,1,7,8,5,4,6]=>1101100
[7,3,4,2,1,5,8,6]=>1110010
[1,7,6,3,2,4,8,5]=>0110110
[1,8,5,3,2,4,7,6]=>0110110
[1,2,8,4,6,3,5,7]=>0011000
[2,6,1,5,4,7,3,8]=>1011000
[1,2,8,5,4,6,3,7]=>0011100
[1,3,8,5,4,2,6,7]=>0101100
[1,3,6,8,4,5,7,2]=>0101000
[1,2,8,4,6,3,7,5]=>0011100
[4,6,3,5,7,8,1,2]=>1010000
[2,7,6,5,1,4,8,3]=>1010110
[2,7,4,8,1,3,6,5]=>1001100
[2,3,6,8,4,1,7,5]=>1001100
[1,2,6,8,4,7,5,3]=>0011100
[1,7,2,8,6,3,5,4]=>0111010
[2,3,8,5,4,7,1,6]=>1001100
[2,7,4,1,6,3,5,8]=>1011000
[1,2,8,4,7,3,5,6]=>0011000
[2,6,1,4,8,3,7,5]=>1010100
[3,7,6,5,2,1,4,8]=>1100110
[2,5,6,1,4,8,7,3]=>1010001
[7,1,5,2,6,4,3,8]=>1111000
[1,8,5,6,2,7,4,3]=>0111100
[4,2,7,6,1,8,5,3]=>1110110
[7,3,2,1,6,4,8,5]=>1111100
[6,7,2,4,3,5,8,1]=>1110000
[4,5,3,7,2,1,6,8]=>1110000
[4,3,8,2,1,5,7,6]=>1110010
[4,3,2,8,1,6,7,5]=>1110100
[4,5,8,3,2,7,1,6]=>1110000
[5,4,7,8,2,3,6,1]=>1101000
[4,3,8,2,1,6,7,5]=>1110100
[4,6,7,2,5,3,8,1]=>1110000
[6,4,7,8,3,1,5,2]=>1111000
[8,4,7,3,1,5,6,2]=>1111000
[5,6,7,1,8,3,4,2]=>1110000
[7,1,8,6,2,5,4,3]=>1111010
[8,5,1,7,6,4,2,3]=>1101110
[1,5,8,2,6,4,7,3]=>0111000
[1,5,7,4,6,8,3,2]=>0111000
[3,1,8,6,5,2,7,4]=>1101110
[2,3,7,6,5,8,1,4]=>1000110
[2,3,7,6,5,1,8,4]=>1001110
[7,3,5,2,1,6,8,4]=>1111000
[3,7,2,6,8,1,5,4]=>1101000
[2,7,6,8,5,1,4,3]=>1010110
[1,5,4,7,8,6,2,3]=>0101010
[7,3,1,6,8,2,5,4]=>1111000
[7,1,6,8,5,2,4,3]=>1110100
[2,7,6,4,8,1,5,3]=>1011010
[3,6,2,1,4,7,8,5]=>1100100
[6,3,8,7,5,4,2,1]=>1111101
[6,8,2,7,5,4,3,1]=>1111100
[5,8,1,7,6,4,3,2]=>1111010
[4,2,6,3,8,5,7,1]=>1110100
[8,2,6,5,7,3,4,1]=>1110100
[5,1,8,3,7,4,6,2]=>1111000
[8,3,7,1,5,4,6,2]=>1111000
[8,4,7,1,5,3,6,2]=>1111000
[8,2,7,4,5,1,6,3]=>1111000
[5,8,7,1,4,2,3,6]=>1100001
[1,7,5,2,4,8,6,3]=>0110110
[2,6,3,7,1,4,5,8]=>1010000
[7,2,8,5,3,1,6,4]=>1111100
[4,7,6,1,5,8,3,2]=>1110010
[4,7,3,8,6,2,5,1]=>1110010
[5,4,7,3,8,2,1,6]=>1111000
[4,3,5,7,2,6,1,8]=>1110000
[1,7,2,8,5,4,3,6]=>0111100
[5,4,8,3,6,2,1,7]=>1111000
[6,8,3,5,7,2,4,1]=>1110000
[3,8,6,2,7,5,1,4]=>1100110
[4,7,3,2,5,1,6,8]=>1110000
[4,2,5,3,8,7,1,6]=>1110001
[7,2,5,3,8,4,6,1]=>1111000
[6,7,3,2,5,4,1,8]=>1111000
[8,7,3,2,5,4,6,1]=>1111001
[4,5,6,2,7,3,1,8]=>1110000
[7,3,4,8,2,1,6,5]=>1110100
[7,4,8,6,5,1,2,3]=>1001110
[3,8,1,7,5,2,4,6]=>1100100
[4,5,8,2,7,3,1,6]=>1110000
[6,5,8,2,7,3,1,4]=>1110100
[6,4,8,2,7,3,1,5]=>1111000
[7,8,1,3,6,4,2,5]=>1101000
[4,3,8,2,7,5,1,6]=>1110100
[4,5,7,8,3,2,1,6]=>1110000
[8,1,5,4,6,2,7,3]=>1111000
[5,3,7,2,1,8,6,4]=>1111010
[5,4,8,3,2,7,1,6]=>1111000
[5,4,3,7,2,1,6,8]=>1111000
[5,4,3,7,8,2,6,1]=>1111000
[5,4,3,8,2,6,7,1]=>1111000
[5,4,3,7,8,2,1,6]=>1111000
[6,1,3,5,8,7,4,2]=>1101001
[6,8,5,7,3,4,2,1]=>1110100
[5,3,6,8,4,2,1,7]=>1111000
[5,1,6,8,4,7,3,2]=>1111000
[6,2,8,3,4,1,5,7]=>1110000
[2,4,1,8,7,6,3,5]=>1010011
[1,3,5,8,4,7,2,6]=>0101000
[2,3,8,7,5,1,6,4]=>1001101
[8,5,4,7,6,1,3,2]=>1101110
[5,8,7,2,4,1,3,6]=>1100001
[4,1,3,5,6,2,8,7]=>1100001
[6,3,8,5,1,7,4,2]=>1111100
[5,2,4,6,1,3,8,7]=>1100001
[8,2,4,6,1,3,7,5]=>1100100
[6,4,8,7,3,5,2,1]=>1111001
[8,2,3,5,6,1,4,7]=>1100000
[4,3,5,6,8,2,7,1]=>1110000
[8,2,3,4,6,1,7,5]=>1100100
[1,7,4,3,5,2,8,6]=>0111010
[2,7,4,3,8,1,5,6]=>1011000
[5,3,6,2,1,8,4,7]=>1111000
[4,3,8,6,2,7,1,5]=>1110010
[8,2,1,4,6,3,7,5]=>1110100
[3,1,6,8,2,7,5,4]=>1101100
[5,3,8,6,7,2,1,4]=>1110010
[5,8,7,2,4,6,1,3]=>1100001
[1,5,2,8,7,6,4,3]=>0111011
[2,7,1,4,6,5,3,8]=>1010100
[4,7,1,2,6,5,8,3]=>1010100
[3,2,4,5,1,8,6,7]=>1100010
[4,2,5,6,8,7,3,1]=>1110001
[8,2,5,1,6,3,7,4]=>1111000
[8,3,4,5,1,6,7,2]=>1110000
[7,8,1,5,6,3,2,4]=>1110000
[1,7,8,3,2,5,4,6]=>0111000
[7,8,1,3,5,4,2,6]=>1101000
[7,8,1,3,2,5,6,4]=>1101000
[7,8,1,3,5,4,6,2]=>1101000
[7,8,1,3,5,2,4,6]=>1100000
[1,3,7,8,5,2,4,6]=>0100100
[1,7,8,3,5,2,6,4]=>0111000
[1,7,8,3,2,5,6,4]=>0111000
[3,5,7,6,4,8,1,2]=>1001010
[1,3,7,8,5,4,6,2]=>0101100
[1,3,7,8,5,4,2,6]=>0101100
[1,3,7,8,2,5,4,6]=>0101000
[1,7,8,5,6,3,2,4]=>0110100
[5,7,6,8,1,3,4,2]=>1100010
[1,5,7,6,8,3,2,4]=>0110010
[3,5,4,7,8,6,1,2]=>1001010
[3,5,7,6,8,4,1,2]=>1001010
[1,5,7,6,8,3,4,2]=>0110010
[3,5,7,4,6,8,1,2]=>1001000
[7,2,8,6,5,1,4,3]=>1110110
[4,2,7,5,3,1,8,6]=>1110110
[7,3,2,5,4,1,8,6]=>1111010
[3,6,4,1,8,2,7,5]=>1101100
[4,6,3,8,7,2,1,5]=>1110001
[4,3,5,1,8,7,2,6]=>1110001
[8,4,3,2,7,5,1,6]=>1111100
[7,5,2,8,4,3,1,6]=>1111100
[1,7,2,4,5,3,6,8]=>0110000
[1,7,4,5,3,2,6,8]=>0111000
[1,6,4,7,3,5,2,8]=>0111000
[8,3,5,6,1,4,7,2]=>1110000
[1,6,4,7,5,2,3,8]=>0101100
[1,5,2,6,7,4,3,8]=>0111000
[8,5,6,1,4,3,7,2]=>1110100
[5,4,7,8,3,1,2,6]=>1011000
[2,5,4,7,8,3,1,6]=>1011000
[6,4,5,8,2,3,1,7]=>1101000
[8,6,1,3,2,5,7,4]=>1101010
[7,5,8,1,4,6,3,2]=>1110100
[4,2,6,7,8,1,5,3]=>1110000
[3,4,6,7,8,1,5,2]=>1100000
[4,3,2,7,5,8,1,6]=>1110100
[4,8,5,3,2,6,1,7]=>1110100
[2,8,4,5,3,6,1,7]=>1011000
[8,1,5,3,2,4,7,6]=>1110010
[8,1,2,4,5,3,7,6]=>1010010
[8,1,4,5,3,2,7,6]=>1110010
[7,8,4,1,3,6,5,2]=>1101100
[8,6,1,3,2,7,4,5]=>1101010
[7,3,8,2,4,1,6,5]=>1110100
[6,2,3,7,8,1,5,4]=>1101000
[6,3,7,8,1,5,4,2]=>1111000
[2,6,3,7,8,1,5,4]=>1011000
[7,5,8,1,6,4,2,3]=>1101100
[7,4,3,2,5,8,1,6]=>1111000
[7,2,4,3,5,8,1,6]=>1110000
[1,3,6,4,2,5,7,8]=>0101000
[1,7,6,4,2,3,5,8]=>0101010
[1,2,3,7,6,4,5,8]=>0001010
[1,3,2,5,8,6,4,7]=>0101010
[4,8,2,7,1,3,6,5]=>1100100
[7,1,8,4,6,3,5,2]=>1111000
[1,7,4,6,8,3,5,2]=>0111000
[4,1,5,2,3,8,7,6]=>1100011
[6,3,5,8,2,4,7,1]=>1110000
[2,8,7,1,4,6,3,5]=>1010001
[3,1,2,8,5,7,4,6]=>1001100
[6,4,1,5,3,2,8,7]=>1111001
[6,3,8,1,2,5,4,7]=>1011000
[2,1,8,6,3,7,5,4]=>1011110
[1,6,5,3,2,4,7,8]=>0110100
[1,7,2,4,6,5,3,8]=>0110100
[1,4,7,2,6,5,3,8]=>0110100
[1,3,7,2,4,6,5,8]=>0100100
[1,7,2,6,4,3,5,8]=>0111000
[1,2,6,8,7,4,3,5]=>0011001
[1,2,7,4,3,5,8,6]=>0011010
[1,8,6,3,5,2,7,4]=>0111010
[1,6,2,8,7,4,3,5]=>0111001
[1,3,8,7,5,4,6,2]=>0101101
[1,2,8,6,3,5,7,4]=>0011010
[1,8,5,2,3,6,4,7]=>0101100
[1,7,4,8,5,2,3,6]=>0101100
[1,4,7,5,8,6,3,2]=>0110110
[1,4,7,5,2,8,6,3]=>0110110
[1,6,3,7,4,2,8,5]=>0111100
[1,8,5,2,7,4,3,6]=>0111100
[1,4,8,6,3,2,7,5]=>0110110
[1,4,8,7,5,3,2,6]=>0110101
[1,2,5,8,6,3,7,4]=>0011010
[1,2,4,7,5,8,6,3]=>0010110
[1,3,5,8,7,6,2,4]=>0100011
[1,5,2,4,3,6,8,7]=>0110001
[1,6,8,7,5,3,2,4]=>0110101
[1,2,5,7,4,3,8,6]=>0011010
[1,5,3,2,6,8,7,4]=>0111001
[1,4,2,6,8,7,5,3]=>0110101
[1,5,8,6,3,2,7,4]=>0111010
[1,8,5,2,6,3,4,7]=>0110100
[1,7,4,6,3,2,8,5]=>0111100
[1,6,3,2,8,5,4,7]=>0111100
[1,4,2,8,6,3,5,7]=>0110010
[1,3,8,6,4,2,5,7]=>0101010
[1,5,7,4,2,3,8,6]=>0101010
[8,2,7,3,1,5,4,6]=>1111000
[8,4,7,2,5,3,1,6]=>1111000
[8,3,4,5,2,1,7,6]=>1110010
[8,6,1,4,7,3,5,2]=>1110010
[5,3,6,7,2,8,4,1]=>1111000
[5,3,6,7,2,4,8,1]=>1110000
[1,3,8,2,5,6,7,4]=>0101000
[5,4,2,3,6,1,8,7]=>1101001
[5,1,7,4,3,6,8,2]=>1111000
[7,1,3,6,5,2,8,4]=>1101100
[6,1,8,5,2,7,3,4]=>1110100
[8,7,2,6,3,1,4,5]=>1110001
[5,4,1,3,7,2,8,6]=>1101010
[8,3,4,7,6,2,1,5]=>1110010
[3,1,8,7,5,2,4,6]=>1100101
[6,5,8,7,2,4,3,1]=>1110101
[4,3,6,5,8,2,1,7]=>1110100
[3,2,6,8,7,1,4,5]=>1100001
[4,7,3,1,8,5,2,6]=>1110100
[5,1,7,8,6,2,3,4]=>1100010
[8,5,1,6,7,2,3,4]=>1100100
[1,8,3,6,4,5,7,2]=>0111000
[7,1,6,2,5,3,4,8]=>1110000
[8,1,7,2,5,3,4,6]=>1110000
[8,1,6,7,5,2,3,4]=>1100100
[8,1,6,4,2,3,5,7]=>1101000
[8,3,1,2,4,6,7,5]=>1010100
[7,1,8,2,5,3,4,6]=>1110000
[5,1,7,2,6,3,4,8]=>1110000
[1,6,3,8,4,5,7,2]=>0111000
[2,7,4,3,8,5,1,6]=>1011100
[2,4,7,3,5,1,6,8]=>1010000
[2,5,8,4,6,3,1,7]=>1011000
[2,4,8,6,3,5,1,7]=>1010010
[2,3,7,5,4,1,6,8]=>1001100
[3,4,6,2,1,5,8,7]=>1100001
[2,6,8,3,5,1,4,7]=>1010000
[2,3,6,1,5,8,4,7]=>1001000
[2,3,7,1,6,5,8,4]=>1001100
[2,4,7,1,3,6,8,5]=>1000100
[5,4,7,8,1,3,2,6]=>1101000
[2,5,7,1,4,6,3,8]=>1010000
[2,4,7,1,6,3,5,8]=>1010000
[2,3,7,1,6,5,4,8]=>1001100
[2,5,7,1,4,3,6,8]=>1010000
[2,5,7,3,1,4,6,8]=>1010000
[3,4,7,2,1,6,8,5]=>1100100
[5,7,3,2,8,1,4,6]=>1110000
[3,6,8,5,4,1,7,2]=>1101100
[5,4,7,8,1,3,6,2]=>1101000
[2,5,7,1,4,6,8,3]=>1010000
[2,4,7,1,6,3,8,5]=>1010100
[2,4,7,1,6,8,3,5]=>1010000
[2,4,8,3,1,7,6,5]=>1010110
[8,6,5,1,2,4,3,7]=>1010110
[7,6,1,4,2,3,5,8]=>1100010
[7,5,4,8,3,2,6,1]=>1111100
[8,7,5,1,4,2,3,6]=>1100101
[8,4,1,2,5,3,6,7]=>1011000
[4,3,8,1,5,2,6,7]=>1110000
[8,6,1,4,2,5,3,7]=>1110010
[2,8,3,7,4,5,6,1]=>1011000
[8,7,5,2,4,3,6,1]=>1110101
[6,8,3,2,4,5,1,7]=>1110000
[3,8,5,2,4,6,1,7]=>1100100
[8,2,4,5,3,1,6,7]=>1110000
[4,8,2,5,3,1,6,7]=>1110000
[4,3,7,5,2,1,6,8]=>1110100
[1,6,7,4,3,2,5,8]=>0111000
[1,4,5,7,3,2,6,8]=>0110000
[3,5,1,4,7,2,6,8]=>1100000
[2,5,4,7,8,1,3,6]=>1001000
[2,5,1,4,7,8,3,6]=>1010000
[4,3,7,1,5,2,6,8]=>1110000
[3,5,1,6,4,2,7,8]=>1101000
[6,4,3,1,7,2,5,8]=>1111000
[6,2,7,4,3,1,5,8]=>1111000
[2,6,4,1,7,3,5,8]=>1011000
[6,3,2,7,4,5,1,8]=>1111000
[7,2,4,1,3,6,8,5]=>1100100
[6,3,2,5,7,1,4,8]=>1110000
[3,2,6,5,7,1,4,8]=>1100100
[1,7,3,2,5,6,4,8]=>0111000
[2,1,7,3,5,6,8,4]=>1011000
[2,1,6,3,5,7,8,4]=>1011000
[1,6,3,2,5,7,4,8]=>0111000
[5,6,2,1,4,3,7,8]=>1110000
[2,5,1,6,4,3,7,8]=>1011000
[2,5,4,1,6,3,7,8]=>1011000
[4,6,1,5,2,7,3,8]=>1110000
[1,6,5,3,7,2,4,8]=>0110100
[2,6,1,8,5,4,3,7]=>1011100
[5,8,6,2,3,4,1,7]=>1100010
[4,5,8,6,2,1,3,7]=>1100010
[6,3,7,4,2,5,8,1]=>1111000
[7,5,6,2,4,3,8,1]=>1110100
[6,2,5,7,4,3,8,1]=>1111000
[4,6,2,5,7,3,8,1]=>1110000
[4,2,8,5,3,6,1,7]=>1110100
[8,1,7,4,5,6,2,3]=>1101000
[8,4,6,2,5,3,7,1]=>1111000
[5,6,3,2,8,1,7,4]=>1111000
[8,2,6,3,1,5,7,4]=>1111000
[8,2,5,6,7,4,3,1]=>1111000
[8,2,5,3,4,7,6,1]=>1110010
[7,5,3,2,4,1,8,6]=>1110110
[6,5,3,2,4,8,1,7]=>1110100
[3,1,8,4,6,5,7,2]=>1101100
[3,4,7,5,8,2,6,1]=>1100100
[8,7,1,4,6,5,2,3]=>1100101
[8,3,7,6,4,5,1,2]=>1011010
[5,3,8,6,4,1,7,2]=>1111010
[6,4,7,1,8,5,2,3]=>1101100
[5,7,4,2,3,8,6,1]=>1101010
[3,8,2,5,1,7,4,6]=>1101000
[5,8,4,2,3,7,1,6]=>1101000
[4,8,5,2,1,7,3,6]=>1110100
[8,5,7,6,1,2,4,3]=>1010110
[7,8,6,5,2,4,3,1]=>1110110
[7,8,4,2,6,3,5,1]=>1111000
[5,7,6,8,4,1,3,2]=>1101010
[7,3,1,6,8,5,4,2]=>1111100
[5,3,1,7,4,8,6,2]=>1111010
[7,3,1,8,6,4,5,2]=>1111010
[8,6,4,1,7,3,2,5]=>1111010
[4,6,8,3,7,1,2,5]=>1010000
[3,5,2,8,4,7,1,6]=>1101000
[3,7,2,8,6,4,5,1]=>1101010
[8,6,5,7,1,3,2,4]=>1100110
[6,4,8,3,7,2,1,5]=>1111000
[3,6,2,8,7,4,1,5]=>1101001
[6,8,4,2,7,3,1,5]=>1111000
[3,4,7,8,5,1,2,6]=>1000100
[5,7,2,4,3,6,8,1]=>1110000
[4,7,3,2,5,6,8,1]=>1110000
[3,2,7,6,4,5,8,1]=>1101010
[1,7,3,6,8,4,2,5]=>0111000
[8,3,1,2,6,4,7,5]=>1011100
[1,7,8,2,4,3,5,6]=>0110000
[3,6,4,7,1,2,8,5]=>1001100
[2,4,7,8,5,1,3,6]=>1000100
[5,7,4,8,1,3,2,6]=>1101000
[4,3,7,8,1,5,2,6]=>1110000
[8,5,4,2,6,1,7,3]=>1111100
[3,2,6,8,7,4,1,5]=>1101001
[2,3,7,5,1,8,6,4]=>1001110
[6,3,1,2,8,7,4,5]=>1011001
[5,2,1,3,8,7,6,4]=>1101011
[7,2,1,5,3,8,4,6]=>1111000
[1,5,8,2,4,3,6,7]=>0110000
[4,3,6,8,1,5,2,7]=>1110000
[2,4,6,8,5,1,3,7]=>1000100
[1,6,8,2,4,3,5,7]=>0110000
[5,4,6,8,3,1,7,2]=>1111000
[8,6,1,7,2,4,3,5]=>1110010
[7,3,1,2,8,6,4,5]=>1011010
[2,3,7,6,1,8,5,4]=>1001110
[3,2,7,8,6,4,1,5]=>1101010
[6,2,8,3,1,4,7,5]=>1110100
[3,1,2,8,7,4,5,6]=>1001001
[2,1,3,8,7,4,6,5]=>1001101
[2,1,3,8,7,4,5,6]=>1001001
[8,5,1,7,2,4,3,6]=>1110100
[8,3,1,6,2,7,5,4]=>1111100
[1,3,2,8,7,6,4,5]=>0101011
[2,1,3,8,7,6,4,5]=>1001011
[5,7,2,8,4,1,3,6]=>1101000
[3,5,8,2,4,1,7,6]=>1100010
[2,4,8,3,1,6,7,5]=>1010100
[1,3,6,8,5,4,2,7]=>0101100
[1,4,2,5,7,6,3,8]=>0110010
[1,4,2,6,8,5,3,7]=>0110100
[1,5,3,2,6,8,4,7]=>0111000
[1,5,4,2,3,6,8,7]=>0101001
[1,6,8,3,5,4,2,7]=>0111000
[1,5,3,2,4,6,8,7]=>0110001
[1,5,8,7,6,3,2,4]=>0110011
[1,5,7,6,3,2,4,8]=>0110010
[1,6,3,2,4,7,5,8]=>0110100
[1,6,3,2,4,8,7,5]=>0110101
[1,2,7,6,4,3,5,8]=>0011010
[1,8,7,5,2,4,6,3]=>0110101
[1,7,5,2,4,6,3,8]=>0110100
[1,7,4,2,5,3,6,8]=>0111000
[1,8,4,7,5,2,6,3]=>0111100
[1,7,5,2,3,6,4,8]=>0101100
[1,7,5,2,6,3,4,8]=>0110100
[1,6,3,7,4,2,5,8]=>0111000
[1,6,3,2,7,5,4,8]=>0111100
[1,4,8,7,5,2,6,3]=>0110101
[1,4,7,5,2,6,3,8]=>0110100
[1,3,6,4,8,7,5,2]=>0101101
[1,3,7,6,4,2,5,8]=>0101010
[1,3,8,7,5,2,4,6]=>0100101
[1,4,6,3,2,7,5,8]=>0110100
[1,4,6,3,2,8,7,5]=>0110101
[1,5,7,6,4,2,3,8]=>0101010
[1,2,6,4,7,5,3,8]=>0011100
[1,6,3,2,8,4,7,5]=>0111100
[1,5,2,7,4,3,6,8]=>0111000
[1,6,3,5,2,7,4,8]=>0111000
[1,6,3,5,2,8,7,4]=>0111001
[1,8,3,7,5,2,4,6]=>0110100
[1,8,4,6,3,2,7,5]=>0111100
[6,4,7,1,5,3,8,2]=>1111000
[5,3,8,2,6,4,7,1]=>1111000
[4,3,8,2,6,5,7,1]=>1110100
[2,6,1,8,3,4,7,5]=>1010100
[6,5,7,1,4,3,8,2]=>1110100
[4,8,3,5,7,6,1,2]=>1010010
[5,7,6,1,2,4,8,3]=>1010010
[4,8,3,5,7,6,2,1]=>1110010
[5,7,6,2,4,8,3,1]=>1110010
[6,7,5,2,3,8,4,1]=>1101100
[6,7,5,3,8,4,2,1]=>1111100
[3,2,1,4,8,5,7,6]=>1100110
[7,3,1,4,2,6,5,8]=>1110100
[7,4,1,6,2,5,3,8]=>1111000
[5,4,1,8,2,6,3,7]=>1111000
[4,7,1,5,2,6,3,8]=>1110000
[6,5,1,4,2,7,3,8]=>1110100
[5,4,1,6,2,8,3,7]=>1111000
[8,4,2,3,1,6,5,7]=>1101100
[4,8,6,2,3,1,7,5]=>1100110
[2,8,6,4,5,1,7,3]=>1011010
[8,2,4,6,7,1,5,3]=>1110000
[2,8,3,1,4,5,7,6]=>1010010
[6,1,7,2,8,4,5,3]=>1111000
[8,3,2,1,5,6,7,4]=>1111000
[8,7,4,5,1,6,3,2]=>1111001
[7,2,8,1,4,5,6,3]=>1110000
[8,2,3,7,4,5,6,1]=>1101000
[8,6,2,5,4,7,3,1]=>1111010
[8,5,7,2,3,6,4,1]=>1101100
[7,5,2,1,6,8,3,4]=>1110100
[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]=>1010001
[6,5,1,3,7,2,8,4]=>1101100
[1,8,7,3,4,5,2,6]=>0110001
[8,2,7,3,4,5,1,6]=>1110000
[1,7,8,3,4,5,2,6]=>0110000
[8,1,7,3,4,5,2,6]=>1110000
[6,8,7,3,4,2,1,5]=>1110001
[1,8,5,3,4,6,2,7]=>0110100
[7,1,6,5,4,3,8,2]=>1111100
[7,1,3,6,4,5,8,2]=>1101000
[7,1,5,3,6,4,8,2]=>1111000
[6,1,5,3,7,8,2,4]=>1110000
[5,7,1,3,2,8,6,4]=>1101010
[5,8,7,1,2,6,3,4]=>1010001
[6,8,2,3,4,7,1,5]=>1100000
[6,7,2,3,4,8,1,5]=>1100000
[5,1,7,3,8,6,2,4]=>1110010
[6,1,3,2,4,7,8,5]=>1100100
[6,2,1,3,4,7,8,5]=>1100100
[3,2,5,8,7,4,1,6]=>1101001
[4,2,5,8,7,3,1,6]=>1110001
[8,3,4,1,6,5,2,7]=>1110100
[3,4,8,5,7,2,1,6]=>1100100
[3,6,4,8,5,7,2,1]=>1101100
[5,8,4,7,3,6,2,1]=>1111000
[4,2,8,7,3,1,6,5]=>1110101
[6,5,8,2,1,7,4,3]=>1111100
[6,1,4,3,8,7,2,5]=>1110001
[5,1,3,2,6,8,7,4]=>1101001
[6,1,3,8,7,2,4,5]=>1100001
[1,2,8,4,5,7,3,6]=>0011000
[4,2,1,8,7,6,3,5]=>1110011
[3,2,5,8,7,1,4,6]=>1100001
[5,6,3,8,7,2,1,4]=>1110001
[2,5,8,4,7,1,6,3]=>1011000
[1,6,2,4,8,5,7,3]=>0110100
[3,1,6,5,8,7,2,4]=>1100101
[4,8,5,3,6,7,1,2]=>1010100
[1,8,5,3,4,7,6,2]=>0110110
[1,4,6,2,5,3,7,8]=>0110000
[4,3,6,5,1,2,7,8]=>1010100
[1,3,8,7,6,5,2,4]=>0100111
[1,8,7,2,6,3,5,4]=>0111001
[8,7,1,2,4,3,6,5]=>1010101
[2,8,7,1,6,3,4,5]=>1010001
[6,2,1,8,7,5,3,4]=>1110101
[3,2,1,4,5,8,6,7]=>1100010
[1,3,7,5,4,8,6,2]=>0101110
[5,2,1,4,3,6,8,7]=>1110001
[1,5,6,3,8,4,2,7]=>0111000
[2,6,5,3,8,4,1,7]=>1011100
[5,7,3,8,4,2,6,1]=>1111000
[2,3,6,5,4,8,1,7]=>1001100
[2,7,5,1,8,4,6,3]=>1011100
[1,7,6,4,8,2,5,3]=>0111010
[6,3,8,7,2,4,5,1]=>1110001
[2,4,3,8,7,1,6,5]=>1010101
[2,8,7,6,1,5,3,4]=>1010011
[5,4,7,6,3,1,2,8]=>1011010
[3,6,4,8,1,5,2,7]=>1101000
[3,6,8,4,1,5,2,7]=>1101000
[7,8,1,4,2,3,5,6]=>1100000
[8,7,1,4,2,3,5,6]=>1100001
[3,8,6,4,1,5,2,7]=>1101010
[3,8,4,6,1,5,2,7]=>1101000
[8,3,7,2,1,6,5,4]=>1111100
[8,4,7,3,6,2,1,5]=>1111000
[3,8,7,5,6,4,1,2]=>1001101
[3,8,7,5,6,2,1,4]=>1100101
[3,8,7,5,6,2,4,1]=>1100101
[2,8,7,5,6,4,1,3]=>1001101
[3,6,2,4,8,7,1,5]=>1100001
[1,5,6,3,8,2,7,4]=>0111000
[2,6,3,8,4,7,1,5]=>1011000
[2,6,3,5,7,8,1,4]=>1010000
[1,5,6,3,7,2,8,4]=>0111000
[1,7,5,3,6,2,8,4]=>0111100
[1,5,7,3,4,2,8,6]=>0110010
[1,5,8,3,4,2,7,6]=>0110010
[1,4,5,3,8,2,7,6]=>0110010
[6,5,1,4,2,7,8,3]=>1110100
[6,5,1,4,2,8,7,3]=>1110101
[1,7,5,4,2,8,6,3]=>0111110
[5,1,6,8,3,7,2,4]=>1110000
[3,8,5,2,1,4,7,6]=>1100110
[3,5,4,8,2,6,7,1]=>1101000
[1,4,8,2,6,5,3,7]=>0110100
[7,5,1,8,3,4,2,6]=>1110100
[1,4,8,2,6,7,3,5]=>0110000
[1,2,5,6,8,7,3,4]=>0010001
[1,5,6,8,2,7,4,3]=>0111000
[2,6,7,3,4,1,8,5]=>1010100
[1,6,5,7,8,2,4,3]=>0110100
[1,5,6,7,2,8,4,3]=>0111000
[1,3,7,2,6,4,8,5]=>0101100
[1,5,8,6,7,3,4,2]=>0110010
[1,6,5,8,7,2,4,3]=>0110101
[1,5,7,6,2,8,3,4]=>0110010
[1,2,5,8,6,7,4,3]=>0011010
[1,2,6,5,7,3,8,4]=>0011100
[1,7,5,8,6,4,2,3]=>0101110
[7,6,1,2,3,5,4,8]=>1001010
[8,5,2,6,4,3,1,7]=>1111100
[5,8,3,7,1,4,6,2]=>1110000
[3,8,7,4,2,6,5,1]=>1101101
[5,8,3,2,4,7,6,1]=>1110010
[6,1,3,4,2,5,7,8]=>1100000
[5,3,8,2,4,6,1,7]=>1110000
[4,1,5,6,3,2,7,8]=>1110000
[4,5,8,3,2,6,1,7]=>1110000
[5,8,2,1,4,6,3,7]=>1110000
[4,1,5,8,3,6,2,7]=>1110000
[4,5,8,3,6,1,2,7]=>1010000
[1,6,3,4,7,8,5,2]=>0110100
[8,1,3,4,2,6,5,7]=>1100100
[4,7,8,5,2,3,1,6]=>1100100
[4,1,5,8,6,2,3,7]=>1100010
[5,8,2,1,6,3,4,7]=>1110000
[2,7,1,3,8,5,4,6]=>1001100
[2,6,7,8,4,1,3,5]=>1001000
[2,6,7,8,4,3,1,5]=>1011000
[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]=>0111110
[1,7,4,3,6,2,5,8]=>0111000
[1,7,8,5,4,2,3,6]=>0101100
[8,1,5,3,6,4,7,2]=>1111000
[3,6,4,5,2,8,1,7]=>1101000
[8,1,5,4,7,3,6,2]=>1111000
[3,6,4,1,5,7,2,8]=>1101000
[8,1,5,4,7,6,3,2]=>1111010
[2,5,1,4,6,7,3,8]=>1010000
[8,6,3,5,4,1,2,7]=>1011010
[8,2,6,5,4,1,3,7]=>1101100
[8,2,6,5,4,3,1,7]=>1111100
[8,3,2,6,1,5,4,7]=>1111000
[8,1,6,5,4,3,2,7]=>1111100
[4,8,1,7,6,3,5,2]=>1110010
[8,5,1,7,4,3,6,2]=>1111100
[8,5,7,6,2,1,3,4]=>1100110
[5,4,8,3,1,7,2,6]=>1111000
[5,1,4,8,3,2,7,6]=>1110010
[4,8,1,7,6,5,2,3]=>1100110
[4,3,8,7,2,6,1,5]=>1110001
[3,8,7,2,6,4,1,5]=>1101001
[8,2,7,6,4,1,5,3]=>1111010
[4,3,8,7,2,6,5,1]=>1110101
[8,2,5,7,4,3,6,1]=>1111000
[3,8,7,4,6,1,2,5]=>1001001
[8,3,7,5,4,1,6,2]=>1111100
[2,8,4,7,6,1,5,3]=>1011010
[2,5,4,8,3,1,7,6]=>1011010
[5,4,8,2,1,3,7,6]=>1101010
[3,8,7,2,6,1,5,4]=>1101001
[1,8,4,7,6,3,5,2]=>0111010
[1,8,3,7,6,5,2,4]=>0110110
[1,4,3,8,7,2,6,5]=>0110101
[8,1,2,7,6,5,4,3]=>1011110
[7,8,1,3,6,4,5,2]=>1101000
[7,2,6,8,4,5,3,1]=>1111000
[7,3,6,8,5,1,4,2]=>1110100
[7,5,8,1,6,2,4,3]=>1110100
[5,7,8,1,6,3,2,4]=>1110000
[7,2,6,8,5,1,4,3]=>1110100
[6,7,8,3,5,4,2,1]=>1111000
[6,7,8,4,2,1,5,3]=>1111000
[7,2,6,8,4,3,1,5]=>1111000
[7,5,2,4,8,3,1,6]=>1110100
[5,6,2,4,3,8,1,7]=>1110000
[7,8,3,1,6,2,5,4]=>1111000
[6,7,8,4,3,1,5,2]=>1111000
[7,8,2,6,3,5,4,1]=>1111000
[7,8,3,6,4,1,5,2]=>1111000
[6,1,5,2,4,8,3,7]=>1110000
[1,5,6,3,8,2,4,7]=>0110000
[7,3,8,1,6,4,5,2]=>1111000
[7,2,6,8,4,3,5,1]=>1111000
[7,5,2,4,8,3,6,1]=>1110100
[1,7,5,8,2,4,6,3]=>0110100
[7,5,2,8,1,4,6,3]=>1110100
[3,7,8,2,6,5,1,4]=>1100100
[3,7,8,2,1,6,4,5]=>1101000
[7,2,8,1,6,4,3,5]=>1111000
[7,8,1,6,3,5,4,2]=>1111000
[6,7,8,3,2,5,4,1]=>1111000
[6,7,8,2,5,4,3,1]=>1111000
[6,7,8,3,1,5,4,2]=>1111000
[7,8,1,6,2,5,4,3]=>1111000
[5,6,1,4,3,8,2,7]=>1110000
[1,6,4,5,2,7,3,8]=>0111000
[1,4,7,3,2,5,6,8]=>0110000
[6,2,1,5,7,3,4,8]=>1110000
[1,6,7,4,2,8,3,5]=>0111000
[1,5,8,7,4,3,2,6]=>0111001
[1,4,7,2,3,6,8,5]=>0100100
[3,1,2,6,7,8,5,4]=>1001100
[1,6,3,4,7,8,2,5]=>0110000
[3,1,5,7,6,2,8,4]=>1101010
[6,3,1,4,2,7,8,5]=>1110100
[2,4,3,7,6,1,8,5]=>1010110
[3,1,6,5,2,8,7,4]=>1101101
[3,1,7,6,5,2,8,4]=>1101110
[1,4,7,6,8,3,2,5]=>0110010
[7,2,1,5,6,3,8,4]=>1111000
[4,3,1,8,6,2,7,5]=>1110110
[3,1,5,2,8,7,6,4]=>1101011
[1,2,8,4,3,7,6,5]=>0011110
[1,8,5,4,2,7,3,6]=>0111100
[3,1,8,5,4,7,2,6]=>1101100
[2,6,1,8,7,4,3,5]=>1011001
[7,5,1,8,3,2,6,4]=>1111100
[4,7,6,3,1,8,2,5]=>1110010
[5,3,1,8,6,2,4,7]=>1110010
[5,1,8,6,3,2,4,7]=>1110010
[1,5,4,2,8,6,3,7]=>0111010
[8,3,1,6,4,2,5,7]=>1111000
[3,6,7,1,8,4,2,5]=>1101000
[1,7,4,8,3,5,2,6]=>0111000
[7,3,2,4,8,5,1,6]=>1110100
[6,3,4,7,1,8,5,2]=>1110100
[5,7,8,1,4,2,6,3]=>1110000
[5,7,1,2,3,8,6,4]=>1001010
[7,2,8,1,4,3,6,5]=>1110100
[2,6,3,8,1,7,5,4]=>1011100
[1,8,3,6,4,7,2,5]=>0111000
[2,8,6,4,1,7,3,5]=>1011010
[1,8,4,2,7,5,3,6]=>0111100
[6,5,1,7,2,8,4,3]=>1111100
[2,8,1,7,5,3,6,4]=>1011100
[1,2,8,7,6,4,3,5]=>0011011
[4,1,7,8,6,3,5,2]=>1110010
[1,6,5,7,8,4,2,3]=>0101100
[1,6,5,8,7,4,2,3]=>0101101
[4,1,8,7,6,3,5,2]=>1110011
[4,8,2,6,3,5,1,7]=>1110000
[6,7,2,5,3,8,4,1]=>1111000
[4,3,5,7,1,6,2,8]=>1110000
[4,2,8,5,3,6,7,1]=>1110100
[4,1,8,5,3,6,2,7]=>1110100
[6,4,2,5,3,1,7,8]=>1111000
[3,1,5,8,2,7,4,6]=>1101000
[6,4,1,5,3,2,7,8]=>1111000
[6,2,1,5,4,3,7,8]=>1111000
[3,1,8,5,4,6,2,7]=>1101100
[6,2,8,4,5,3,7,1]=>1111000
[6,1,8,4,5,3,2,7]=>1111000
[4,5,2,7,1,6,3,8]=>1110000
[4,3,5,7,1,6,8,2]=>1110000
[4,1,8,5,3,6,7,2]=>1110100
[6,3,8,4,5,1,7,2]=>1111000
[3,1,6,8,5,7,4,2]=>1101100
[2,6,1,8,5,7,4,3]=>1011100
[6,5,8,7,1,3,2,4]=>1100101
[6,5,8,7,2,3,4,1]=>1100101
[6,5,8,7,3,2,4,1]=>1110101
[6,3,8,4,5,2,7,1]=>1111000
[3,1,6,8,5,7,2,4]=>1100100
[2,1,6,8,5,3,7,4]=>1011100
[3,1,6,8,5,4,2,7]=>1101100
[3,2,6,8,5,4,7,1]=>1101100
[4,1,8,5,2,6,3,7]=>1110100
[3,1,6,8,5,2,4,7]=>1100100
[6,2,8,4,5,1,3,7]=>1101000
[6,5,8,7,4,1,2,3]=>1001101
[6,5,8,7,4,2,1,3]=>1101101
[6,5,8,7,2,4,1,3]=>1100101
[6,2,8,4,5,7,1,3]=>1101000
[6,1,8,4,5,7,3,2]=>1111000
[4,2,7,3,5,8,6,1]=>1110010
[3,6,2,4,8,5,7,1]=>1100100
[2,7,5,4,3,8,6,1]=>1011110
[3,5,1,8,4,7,6,2]=>1101010
[2,4,8,3,7,6,5,1]=>1010110
[3,6,8,5,2,4,7,1]=>1100100
[2,6,8,5,4,3,7,1]=>1011100
[3,6,8,2,5,4,7,1]=>1101000
[4,6,8,3,2,5,7,1]=>1110000
[4,6,2,8,3,5,7,1]=>1110000
[3,6,1,8,5,7,4,2]=>1101100
[4,6,3,8,7,2,5,1]=>1110001
[3,5,8,2,7,4,6,1]=>1101000
[2,4,8,7,3,6,5,1]=>1010101
[2,5,8,7,4,3,6,1]=>1011001
[2,4,8,7,6,3,5,1]=>1010011
[4,7,2,5,6,3,1,8]=>1110000
[6,1,2,8,7,3,4,5]=>1010001
[4,1,3,5,7,8,2,6]=>1100000
[6,1,5,8,4,3,2,7]=>1111000
[3,2,6,1,5,8,4,7]=>1101000
[4,5,2,1,7,8,3,6]=>1110000
[2,3,7,8,5,1,6,4]=>1001100
[8,1,3,2,5,6,4,7]=>1101000
[3,2,5,8,4,7,1,6]=>1101000
[8,6,4,1,5,2,3,7]=>1101010
[2,5,8,1,3,4,7,6]=>1000010
[3,5,1,8,7,4,2,6]=>1101001
[4,6,1,3,8,2,7,5]=>1100100
[8,1,5,2,3,7,6,4]=>1101010
[6,2,1,8,5,7,4,3]=>1111100
[5,4,7,1,3,8,6,2]=>1101010
[6,5,7,8,1,3,4,2]=>1100100
[6,4,7,2,8,3,1,5]=>1111000
[4,8,1,2,7,6,5,3]=>1010110
[3,7,4,8,5,2,6,1]=>1101100
[8,1,2,6,5,3,4,7]=>1010100
[3,4,2,8,6,7,5,1]=>1100110
[3,7,8,6,1,4,2,5]=>1100010
[3,6,1,5,2,7,8,4]=>1101000
[7,1,6,8,3,4,2,5]=>1110000
[6,2,8,4,7,1,3,5]=>1101000
[1,8,4,3,7,6,2,5]=>0111010
[4,3,8,7,1,2,6,5]=>1010101
[1,8,3,6,7,2,4,5]=>0110000
[1,8,4,5,7,6,2,3]=>0101010
[4,3,8,5,7,1,6,2]=>1110100
[6,3,4,8,7,2,1,5]=>1110001
[5,3,8,4,7,1,6,2]=>1111000
[5,2,8,7,1,4,6,3]=>1110001
[3,2,8,7,1,6,4,5]=>1101001
[2,7,8,3,1,6,4,5]=>1011000
[3,5,8,7,4,1,6,2]=>1101001
[7,4,6,8,3,5,1,2]=>1011000
[7,2,8,4,1,3,6,5]=>1101100
[2,7,8,1,3,6,4,5]=>1001000
[2,7,8,1,5,4,6,3]=>1011000
[2,7,8,1,4,5,6,3]=>1010000
[3,6,7,8,2,4,1,5]=>1100000
[4,5,7,8,6,3,1,2]=>1010010
[5,4,6,8,7,3,1,2]=>1011001
[4,5,8,6,7,1,3,2]=>1100010
[5,7,6,8,2,1,3,4]=>1100010
[3,7,6,8,2,4,1,5]=>1100010
[5,4,7,8,6,3,1,2]=>1011010
[3,6,7,8,2,1,4,5]=>1100000
[4,5,6,8,7,3,1,2]=>1010001
[4,2,5,3,7,8,6,1]=>1110010
[5,3,6,2,4,1,8,7]=>1110001
[7,8,6,2,3,5,4,1]=>1101010
[5,8,2,6,3,7,4,1]=>1111000
[4,8,2,3,7,5,6,1]=>1100100
[7,5,6,2,3,8,4,1]=>1101100
[2,7,5,6,4,3,8,1]=>1011100
[2,8,4,3,7,5,6,1]=>1011100
[2,7,5,6,3,8,4,1]=>1011100
[7,6,3,8,5,4,2,1]=>1111110
[3,8,5,7,6,4,2,1]=>1101110
[7,8,6,3,5,4,2,1]=>1111010
[2,7,6,3,8,5,4,1]=>1011110
[4,2,8,5,3,7,6,1]=>1110110
[7,4,2,5,6,3,8,1]=>1111000
[6,2,7,5,3,8,4,1]=>1111100
[2,4,8,3,7,5,6,1]=>1010100
[4,8,3,7,5,6,2,1]=>1110100
[6,2,5,8,3,7,4,1]=>1111000
[7,6,2,5,3,8,4,1]=>1111010
[4,7,3,8,2,5,6,1]=>1110000
[8,2,5,6,3,7,4,1]=>1111000
[4,5,3,7,1,2,6,8]=>1010000
[6,7,2,8,4,3,1,5]=>1111000
[6,7,3,2,8,4,1,5]=>1111000
[4,5,8,1,3,2,6,7]=>1100000
[4,5,8,1,3,7,2,6]=>1100000
[2,6,7,4,3,8,1,5]=>1011000
[3,7,6,4,5,8,1,2]=>1001010
[5,7,2,8,3,4,6,1]=>1110000
[3,1,5,8,6,4,7,2]=>1101010
[3,6,2,8,7,4,5,1]=>1101001
[3,6,2,8,4,7,5,1]=>1101100
[2,3,8,6,7,5,4,1]=>1001110
[8,3,5,1,6,4,2,7]=>1111000
[5,7,8,3,4,6,2,1]=>1110000
[3,1,5,8,6,2,4,7]=>1100010
[1,5,8,6,3,4,2,7]=>0110010
[5,3,7,8,4,2,6,1]=>1111000
[5,1,6,4,3,8,7,2]=>1111001
[4,7,1,3,2,5,6,8]=>1100000
[4,7,6,8,3,1,5,2]=>1110010
[5,4,8,6,1,7,3,2]=>1111010
[3,5,4,7,1,8,6,2]=>1101010
[1,8,5,4,2,3,6,7]=>0101100
[7,1,5,4,2,3,6,8]=>1101000
[7,1,3,6,4,5,2,8]=>1101000
[6,1,3,8,4,5,2,7]=>1101000
[5,8,6,3,1,2,7,4]=>1011010
[5,8,2,7,1,3,6,4]=>1101000
[2,6,5,4,1,3,7,8]=>1001100
[4,1,5,7,6,3,2,8]=>1110010
[7,6,3,2,8,5,1,4]=>1110110
[5,3,8,2,7,1,6,4]=>1111000
[6,3,4,2,1,8,7,5]=>1110101
[4,5,1,7,6,3,2,8]=>1110010
[1,5,3,7,4,2,6,8]=>0111000
[1,2,7,4,3,8,6,5]=>0011110
[1,5,4,2,3,8,7,6]=>0101011
[1,5,4,2,3,8,6,7]=>0101010
[1,5,3,2,4,6,7,8]=>0110000
[1,5,4,2,3,7,8,6]=>0101010
[3,6,5,2,4,1,7,8]=>1100100
[4,6,7,2,5,1,8,3]=>1110000
[3,6,2,5,1,7,8,4]=>1101000
[3,4,2,7,8,6,1,5]=>1100010
[3,4,2,7,8,1,5,6]=>1100000
[3,8,5,2,4,7,1,6]=>1100100
[6,4,3,2,8,1,7,5]=>1111100
[6,2,4,3,8,1,7,5]=>1110100
[8,7,3,6,2,1,5,4]=>1111001
[3,7,5,4,6,1,2,8]=>1001100
[5,3,4,7,6,8,1,2]=>1010010
[5,3,7,4,6,1,2,8]=>1011000
[7,3,5,4,6,1,2,8]=>1011000
[7,8,3,5,4,1,2,6]=>1011000
[7,3,5,4,1,2,6,8]=>1011000
[5,7,6,3,1,2,4,8]=>1010010
[5,7,6,3,4,1,2,8]=>1010010
[7,5,6,8,1,3,2,4]=>1100100
[3,5,4,1,2,7,6,8]=>1001010
[5,7,6,1,3,2,4,8]=>1100010
[3,5,4,1,7,2,6,8]=>1101000
[5,3,4,1,2,7,6,8]=>1010010
[7,8,3,1,2,5,4,6]=>1011000
[7,8,5,1,3,2,4,6]=>1100100
[7,5,6,1,3,2,4,8]=>1100100
[7,1,3,8,2,5,4,6]=>1101000
[5,1,3,7,6,2,4,8]=>1100010
[6,7,1,8,3,4,5,2]=>1110000
[3,7,1,6,8,4,5,2]=>1101000
[8,7,1,5,3,2,6,4]=>1111001
[3,7,1,6,5,2,8,4]=>1101100
[8,6,7,2,5,3,1,4]=>1110010
[1,8,2,6,5,3,4,7]=>0110100
[8,6,1,5,2,3,4,7]=>1100010
[8,5,1,6,2,3,4,7]=>1100100
[8,1,4,2,3,5,7,6]=>1100010
[1,7,8,2,5,3,4,6]=>0110000
[2,7,8,4,1,3,5,6]=>1001000
[6,8,1,2,3,7,4,5]=>1001000
[1,2,8,6,4,5,3,7]=>0011010
[1,5,8,7,6,3,4,2]=>0110011
[1,2,7,8,4,3,5,6]=>0011000
[1,5,7,8,4,2,3,6]=>0101000
[1,6,8,5,4,2,3,7]=>0101100
[1,2,3,7,5,4,6,8]=>0001100
[1,3,4,8,5,2,7,6]=>0100110
[4,6,5,2,1,7,8,3]=>1110100
[4,6,1,7,5,8,3,2]=>1110100
[3,5,6,2,1,4,7,8]=>1100000
[4,3,6,5,1,7,8,2]=>1110100
[4,6,5,3,1,7,8,2]=>1110100
[5,1,3,4,8,2,6,7]=>1100000
[5,8,1,4,2,3,6,7]=>1100000
[4,3,1,8,5,2,6,7]=>1110100
[4,5,8,2,3,1,6,7]=>1100000
[3,5,4,8,1,7,2,6]=>1101000
[5,3,6,8,1,4,7,2]=>1110000
[5,1,6,8,3,4,7,2]=>1110000
[3,5,1,8,6,4,7,2]=>1101010
[6,4,8,1,5,7,2,3]=>1101000
[4,7,2,8,3,1,6,5]=>1110100
[1,2,5,6,8,3,7,4]=>0011000
[5,1,6,8,7,2,3,4]=>1100001
[1,5,6,8,3,7,2,4]=>0110000
[5,6,8,1,2,3,7,4]=>1001000
[2,8,1,3,5,7,4,6]=>1001000
[7,4,8,1,5,2,6,3]=>1111000
[8,3,2,1,6,5,7,4]=>1111100
[4,1,5,6,8,7,2,3]=>1100001
[1,2,5,6,8,4,7,3]=>0011000
[1,5,6,8,4,7,2,3]=>0101000
[6,8,1,4,5,7,2,3]=>1100000
[4,3,5,1,8,6,7,2]=>1110010
[1,3,5,6,8,4,7,2]=>0101000
[5,6,8,1,3,4,7,2]=>1100000
[5,6,8,2,3,4,7,1]=>1100000
[5,7,8,3,2,6,1,4]=>1110000
[7,5,8,6,4,1,3,2]=>1101110
[5,1,8,6,4,2,7,3]=>1111010
[2,7,6,3,8,5,1,4]=>1010110
[2,3,1,8,4,6,5,7]=>1001100
[2,3,1,7,6,8,4,5]=>1001010
[2,3,1,8,4,6,7,5]=>1001100
[2,7,4,1,3,6,8,5]=>1001100
[6,3,2,8,1,7,5,4]=>1111100
[2,6,8,7,1,3,5,4]=>1001001
[3,7,6,1,4,5,2,8]=>1100010
[4,1,6,2,7,5,3,8]=>1110100
[7,6,2,5,3,1,4,8]=>1110010
[4,3,1,7,6,2,5,8]=>1110010
[4,5,3,1,2,8,6,7]=>1010010
[2,4,5,3,1,8,6,7]=>1010010
[5,7,6,2,3,1,4,8]=>1100010
[4,1,3,7,5,2,6,8]=>1100100
[4,1,6,3,2,7,5,8]=>1110100
[2,7,5,4,1,3,6,8]=>1001100
[7,5,4,1,3,2,6,8]=>1101100
[2,4,8,5,6,3,1,7]=>1010100
[2,5,7,4,1,3,6,8]=>1001000
[5,7,4,1,3,2,6,8]=>1101000
[6,2,4,5,7,3,1,8]=>1110000
[2,6,8,4,5,3,1,7]=>1011000
[2,5,3,8,4,1,6,7]=>1011000
[5,2,3,7,4,1,6,8]=>1101000
[4,5,1,6,3,2,7,8]=>1110000
[5,1,6,3,2,4,7,8]=>1110000
[4,2,5,1,6,3,7,8]=>1110000
[5,1,6,2,4,3,7,8]=>1110000
[4,3,5,1,6,2,7,8]=>1110000
[6,2,1,7,5,8,4,3]=>1111100
[1,5,7,8,6,4,2,3]=>0101010
[1,6,4,8,5,3,7,2]=>0111100
[1,6,5,3,4,7,8,2]=>0110100
[4,2,6,7,8,1,3,5]=>1100000
[4,5,1,7,6,3,8,2]=>1110010
[4,6,5,1,3,7,8,2]=>1100100
[5,2,1,7,6,4,8,3]=>1111010
[6,8,5,2,7,3,1,4]=>1110100
[6,1,2,4,3,7,8,5]=>1010100
[8,1,5,4,2,3,6,7]=>1101000
[7,1,2,4,6,3,8,5]=>1010100
[7,1,2,6,5,3,8,4]=>1011100
[7,5,6,1,2,4,8,3]=>1010100
[7,1,4,5,2,3,6,8]=>1100000
[6,1,4,8,7,2,3,5]=>1100001
[6,1,8,5,7,2,3,4]=>1100100
[1,6,7,5,8,3,4,2]=>0110100
[6,1,7,5,8,2,3,4]=>1100100
[6,1,4,7,8,2,3,5]=>1100000
[5,8,6,1,2,4,7,3]=>1010010
[1,6,8,7,5,3,4,2]=>0110101
[6,8,7,5,1,2,4,3]=>1010101
[6,1,8,7,5,2,3,4]=>1100101
[8,3,1,2,4,6,5,7]=>1010100
[8,3,1,2,4,5,7,6]=>1010010
[6,3,1,2,4,7,5,8]=>1010100
[6,7,1,4,2,3,5,8]=>1100000
[6,1,7,4,8,2,3,5]=>1101000
[6,7,8,5,1,2,4,3]=>1010100
[4,6,8,2,3,5,1,7]=>1100000
[6,8,2,1,3,5,4,7]=>1101000
[3,5,1,6,4,8,2,7]=>1101000
[3,5,8,6,2,1,4,7]=>1100010
[2,4,8,5,6,1,3,7]=>1000100
[5,3,8,4,2,7,6,1]=>1111010
[2,8,5,3,1,4,7,6]=>1010110
[3,7,8,5,1,4,2,6]=>1100100
[1,7,8,4,6,3,2,5]=>0111000
[8,7,2,4,6,3,1,5]=>1110001
[7,8,3,4,6,5,2,1]=>1110100
[8,7,3,6,5,2,4,1]=>1110101
[3,1,2,8,6,5,7,4]=>1001110
[3,8,2,7,5,4,6,1]=>1101100
[8,7,1,4,5,3,6,2]=>1110001
[2,8,7,4,6,3,5,1]=>1011001
[2,8,7,4,6,3,1,5]=>1011001
[8,3,4,1,2,5,7,6]=>1010010
[8,4,1,3,2,5,7,6]=>1101010
[7,4,8,2,3,5,1,6]=>1101000
[7,3,8,6,2,1,4,5]=>1110010
[7,2,8,4,6,5,1,3]=>1101100
[5,8,6,4,7,2,3,1]=>1101010
[4,7,2,6,5,8,3,1]=>1110100
[3,6,8,5,7,4,2,1]=>1101100
[6,7,5,2,4,8,3,1]=>1110100
[8,7,2,4,6,1,5,3]=>1110001
[8,1,2,7,5,6,3,4]=>1010100
[8,2,7,3,4,6,1,5]=>1110000
[6,7,5,4,8,1,3,2]=>1101100
[2,5,1,4,7,3,6,8]=>1010000
[3,1,6,5,7,2,4,8]=>1100100
[2,5,7,1,6,3,4,8]=>1010000
[2,5,7,1,6,3,8,4]=>1011000
[2,6,1,5,7,4,3,8]=>1011000
[3,1,6,5,2,4,7,8]=>1100100
[3,6,5,1,4,2,7,8]=>1100100
[3,5,6,2,8,1,7,4]=>1101000
[3,6,5,1,7,2,4,8]=>1100100
[3,6,5,2,1,4,7,8]=>1100100
[4,5,2,7,6,1,3,8]=>1100010
[4,6,5,3,1,2,7,8]=>1010100
[5,4,1,6,3,7,2,8]=>1111000
[5,4,2,6,3,7,8,1]=>1111000
[3,6,5,7,1,4,2,8]=>1100100
[3,6,5,1,4,7,2,8]=>1100100
[4,3,6,5,7,1,2,8]=>1010100
[4,2,6,5,1,3,7,8]=>1100100
[4,1,6,5,3,7,8,2]=>1110100
[4,1,5,7,6,3,8,2]=>1110010
[4,2,5,7,6,1,3,8]=>1100010
[3,4,7,6,1,2,5,8]=>1000010
[3,4,7,6,8,2,5,1]=>1100010
[4,2,5,7,6,3,8,1]=>1110010
[4,1,6,5,2,7,3,8]=>1110100
[4,2,6,5,7,3,1,8]=>1110100
[3,6,5,7,2,1,4,8]=>1100100
[3,5,7,6,2,4,1,8]=>1100010
[5,4,2,6,3,7,1,8]=>1111000
[4,6,5,2,7,3,1,8]=>1110100
[4,5,2,7,6,3,8,1]=>1110010
[4,6,5,2,1,7,3,8]=>1110100
[3,5,8,2,1,4,6,7]=>1100000
[3,5,8,2,4,6,7,1]=>1100000
[5,3,8,2,1,4,6,7]=>1110000
[5,3,1,8,2,4,6,7]=>1110000
[1,5,3,8,2,4,6,7]=>0110000
[1,5,8,4,2,3,6,7]=>0101000
[5,8,2,1,4,3,6,7]=>1110000
[5,8,2,4,6,3,1,7]=>1110000
[5,8,2,4,3,6,1,7]=>1110000
[5,8,1,4,6,2,3,7]=>1100000
[1,5,8,4,6,7,2,3]=>0101000
[5,1,8,4,6,7,2,3]=>1101000
[5,8,2,4,6,3,7,1]=>1110000
[3,8,4,6,7,2,1,5]=>1101000
[3,8,4,6,7,2,5,1]=>1101000
[8,4,3,6,7,2,5,1]=>1111000
[8,4,3,6,7,2,1,5]=>1111000
[8,6,2,4,5,3,7,1]=>1110010
[8,6,4,1,5,7,2,3]=>1101010
[1,8,6,4,5,7,2,3]=>0101010
[8,1,6,4,5,2,3,7]=>1101000
[8,6,2,4,5,3,1,7]=>1110010
[1,8,6,4,2,3,5,7]=>0101010
[3,8,1,6,2,4,5,7]=>1100000
[1,3,8,6,2,4,5,7]=>0100010
[3,8,6,2,1,4,5,7]=>1100010
[3,8,6,2,4,1,5,7]=>1100010
[3,8,6,2,4,5,7,1]=>1100010
[8,3,6,2,4,5,1,7]=>1110000
[1,8,3,6,2,4,5,7]=>0110000
[8,1,3,6,2,4,5,7]=>1100000
[8,3,6,7,2,1,4,5]=>1110000
[2,5,8,4,6,1,7,3]=>1011000
[3,8,6,7,2,1,4,5]=>1100010
[3,1,8,6,7,2,4,5]=>1100010
[8,2,6,4,5,1,7,3]=>1111000
[8,4,6,1,7,2,5,3]=>1111000
[1,8,4,6,7,5,2,3]=>0101100
[8,1,4,6,7,5,2,3]=>1100100
[8,4,6,1,3,7,2,5]=>1101000
[8,1,4,6,3,7,2,5]=>1110000
[8,4,1,6,3,7,2,5]=>1111000
[8,2,4,6,1,7,5,3]=>1110100
[8,4,6,2,3,7,5,1]=>1101100
[8,4,7,3,1,6,2,5]=>1111000
[8,4,7,2,1,3,6,5]=>1101100
[8,4,2,1,5,3,7,6]=>1111010
[8,2,1,4,7,3,6,5]=>1110100
[3,2,1,7,4,5,8,6]=>1101010
[2,8,4,1,7,5,3,6]=>1011100
[2,6,8,5,1,7,4,3]=>1011100
[4,7,3,1,8,6,2,5]=>1110010
[2,1,5,8,7,3,6,4]=>1011001
[3,2,1,6,7,4,8,5]=>1101100
[4,3,1,7,8,5,2,6]=>1110100
[5,6,8,2,4,3,7,1]=>1110000
[5,8,2,6,4,3,7,1]=>1111000
[2,8,5,3,6,4,7,1]=>1011100
[1,2,8,6,4,7,3,5]=>0011010
[4,2,7,8,3,5,6,1]=>1110000
[2,8,3,7,1,4,6,5]=>1010100
[2,8,7,1,5,3,6,4]=>1011001
[3,8,4,2,7,6,5,1]=>1101110
[3,8,4,2,5,1,7,6]=>1101010
[4,8,3,2,7,5,6,1]=>1110100
[3,2,4,8,7,5,6,1]=>1100101
[3,5,2,6,4,8,1,7]=>1101000
[2,6,8,1,5,3,4,7]=>1010000
[8,1,5,2,4,6,3,7]=>1110000
[3,8,1,6,4,5,2,7]=>1101000
[8,1,3,6,5,4,2,7]=>1101100
[7,4,3,6,2,1,8,5]=>1111100
[1,2,4,8,6,3,7,5]=>0010110
[7,2,1,5,3,4,8,6]=>1110010
[5,7,2,3,1,4,8,6]=>1100010
[7,1,5,2,4,6,8,3]=>1110000
[8,4,2,7,3,5,6,1]=>1111000
[1,8,6,4,7,5,3,2]=>0111110
[7,4,1,5,8,6,3,2]=>1111010
[8,6,3,2,7,4,1,5]=>1111010
[4,5,8,7,3,1,2,6]=>1010001
[1,3,8,7,6,4,2,5]=>0101011
[8,6,4,7,5,1,2,3]=>1001110
[2,8,5,1,7,4,6,3]=>1011100
[1,8,6,4,7,5,2,3]=>0101110
[2,7,4,6,3,8,5,1]=>1011100
[1,2,8,6,4,7,5,3]=>0011110
[8,6,2,1,5,7,3,4]=>1110010
[1,6,5,4,3,8,2,7]=>0111100
[6,4,2,1,5,7,3,8]=>1111000
[3,1,5,8,7,2,4,6]=>1100001
[3,2,5,7,8,4,1,6]=>1101000
[3,2,5,7,8,4,6,1]=>1101000
[5,3,7,4,2,6,8,1]=>1111000
[5,3,7,4,2,6,1,8]=>1111000
[5,2,8,4,3,1,6,7]=>1111000
[5,1,8,4,3,2,6,7]=>1111000
[5,2,7,4,3,6,1,8]=>1111000
[5,2,7,4,3,6,8,1]=>1111000
[5,3,7,4,1,6,8,2]=>1111000
[3,1,5,7,8,4,2,6]=>1101000
[1,2,8,6,4,5,7,3]=>0011010
[6,2,3,7,4,1,8,5]=>1101100
[5,2,7,4,1,3,8,6]=>1101010
[6,2,3,7,4,8,5,1]=>1101100
[6,2,3,7,4,8,1,5]=>1101000
[6,1,3,7,4,2,8,5]=>1101100
[6,2,3,7,4,5,1,8]=>1101000
[6,2,3,7,4,5,8,1]=>1101000
[6,1,3,7,4,5,8,2]=>1101000
[1,2,8,6,4,3,5,7]=>0011010
[6,1,3,7,4,5,2,8]=>1101000
[1,8,6,3,5,4,2,7]=>0111010
[2,5,4,1,8,6,7,3]=>1011010
[1,8,5,3,2,6,7,4]=>0111100
[5,6,8,3,4,2,7,1]=>1110000
[6,3,8,2,4,1,7,5]=>1110100
[5,1,7,8,2,4,3,6]=>1110000
[5,3,2,4,8,1,7,6]=>1110010
[5,3,2,4,8,1,6,7]=>1110000
[5,3,2,4,7,1,8,6]=>1110010
[8,4,5,3,7,1,2,6]=>1011000
[4,8,1,7,3,5,6,2]=>1110000
[5,3,2,4,6,8,1,7]=>1110000
[7,6,4,2,8,3,1,5]=>1111010
[1,2,6,4,7,3,5,8]=>0011000
[8,5,2,4,3,7,1,6]=>1110100
[7,5,4,1,3,6,8,2]=>1101100
[4,2,5,7,8,6,3,1]=>1110010
[6,7,2,4,5,1,8,3]=>1110000
[5,2,7,8,3,6,1,4]=>1110000
[8,2,3,4,7,1,5,6]=>1100000
[2,7,8,5,6,1,4,3]=>1010100
[2,4,7,8,1,3,6,5]=>1000100
[5,2,8,3,1,4,7,6]=>1110010
[8,7,2,5,1,4,3,6]=>1110001
[8,3,5,1,2,4,7,6]=>1010010
[8,6,5,1,7,4,2,3]=>1101110
[8,3,6,5,4,1,2,7]=>1011100
[8,7,4,5,1,2,6,3]=>1011001
[3,4,8,2,1,7,6,5]=>1100110
[8,3,5,2,7,4,6,1]=>1111000
[8,3,1,7,5,6,2,4]=>1110100
[8,4,1,7,5,2,6,3]=>1111100
[8,3,4,2,7,5,6,1]=>1110100
[8,3,2,7,5,6,1,4]=>1110100
[8,4,2,7,5,3,1,6]=>1111100
[8,2,6,5,7,1,3,4]=>1100100
[8,4,3,7,5,1,2,6]=>1011100
[8,5,7,6,4,3,1,2]=>1011110
[8,5,7,6,4,1,2,3]=>1001110
[8,2,4,7,1,5,6,3]=>1110000
[8,4,7,6,5,2,1,3]=>1101110
[8,3,1,4,7,6,2,5]=>1110010
[1,5,2,6,8,3,7,4]=>0111000
[7,2,8,4,1,3,5,6]=>1101000
[6,7,8,5,2,1,4,3]=>1110100
[1,6,2,7,8,4,3,5]=>0111000
[4,3,8,6,5,2,7,1]=>1110110
[2,3,8,6,5,1,7,4]=>1001110
[7,3,2,6,1,4,8,5]=>1110100
[3,2,5,6,8,4,1,7]=>1101000
[2,6,8,1,5,4,3,7]=>1011000
[8,4,7,1,2,5,3,6]=>1011000
[8,5,6,7,2,1,4,3]=>1110100
[8,5,6,7,3,1,4,2]=>1110100
[1,8,3,2,5,4,6,7]=>0111000
[5,1,7,3,2,8,4,6]=>1111000
[8,2,5,3,1,7,4,6]=>1111000
[1,4,8,5,3,2,6,7]=>0110100
[5,8,3,1,4,2,6,7]=>1110000
[1,5,4,8,2,3,6,7]=>0101000
[1,5,4,8,2,3,7,6]=>0101010
[5,7,8,1,3,2,4,6]=>1100000
[8,2,7,5,1,4,6,3]=>1110100
[8,2,4,1,6,7,3,5]=>1110000
[8,7,3,6,2,4,1,5]=>1110001
[1,7,4,8,3,6,2,5]=>0111000
[7,8,6,1,3,5,4,2]=>1101010
[1,7,5,8,4,3,2,6]=>0111100
[6,3,1,2,7,8,5,4]=>1011100
[7,1,8,5,3,4,2,6]=>1110100
[1,2,7,8,3,5,6,4]=>0011000
[8,2,7,5,3,4,1,6]=>1110100
[6,3,1,2,8,7,5,4]=>1011101
[8,4,7,2,6,3,1,5]=>1111000
[8,2,4,7,6,3,1,5]=>1110010
[1,2,5,7,8,3,6,4]=>0011000
[7,6,3,4,2,1,8,5]=>1110110
[8,2,4,6,3,7,1,5]=>1110000
[3,4,5,8,1,7,2,6]=>1100000
[8,6,3,4,7,2,1,5]=>1110010
[4,3,8,6,7,5,1,2]=>1010110
[4,5,6,2,7,8,3,1]=>1110000
[4,5,6,2,7,1,8,3]=>1110000
[4,5,6,2,1,7,3,8]=>1110000
[4,5,6,1,7,8,3,2]=>1110000
[4,5,1,6,7,8,3,2]=>1110000
[4,5,1,6,7,3,8,2]=>1110000
[4,5,1,6,7,3,2,8]=>1110000
[4,5,6,1,7,3,2,8]=>1110000
[8,6,4,3,7,2,1,5]=>1111010
[5,8,1,4,3,2,7,6]=>1110010
[1,6,4,3,8,2,7,5]=>0111100
[7,8,1,4,3,2,5,6]=>1110000
[1,7,8,4,5,3,6,2]=>0111000
[2,7,6,3,4,1,8,5]=>1010110
[8,1,7,4,3,5,6,2]=>1111000
[7,1,8,4,5,3,6,2]=>1111000
[4,3,1,8,6,5,7,2]=>1110110
[4,3,2,7,5,1,8,6]=>1110110
[5,2,3,7,4,1,8,6]=>1101010
[2,1,7,4,3,6,8,5]=>1011100
[7,1,2,4,5,6,8,3]=>1010000
[2,8,7,1,4,5,6,3]=>1010001
[8,7,1,3,4,5,6,2]=>1100001
[7,8,1,3,4,5,6,2]=>1100000
[1,7,2,5,4,6,8,3]=>0111000
[2,5,3,8,1,6,7,4]=>1011000
[1,6,4,2,5,7,8,3]=>0111000
[8,5,3,1,4,6,7,2]=>1110100
[6,5,3,4,1,7,8,2]=>1110100
[5,6,3,4,1,7,8,2]=>1110000
[2,5,3,1,4,7,8,6]=>1010010
[2,6,1,4,3,7,8,5]=>1010100
[6,8,2,3,1,5,7,4]=>1101000
[6,1,3,4,2,7,8,5]=>1100100
[4,3,1,5,2,7,8,6]=>1110010
[5,2,3,1,4,7,8,6]=>1100010
[7,2,1,3,5,6,8,4]=>1101000
[5,2,4,7,8,6,3,1]=>1110010
[8,4,2,7,6,1,5,3]=>1111010
[5,3,7,6,1,8,4,2]=>1111010
[8,6,4,1,2,5,3,7]=>1011010
[8,6,1,4,2,5,7,3]=>1110010
[8,6,4,1,2,5,7,3]=>1011010
[8,6,1,4,7,2,5,3]=>1110010
[4,8,6,2,3,1,5,7]=>1100010
[2,5,3,7,6,4,8,1]=>1011010
[3,1,5,7,6,4,2,8]=>1101010
[3,1,6,5,4,7,2,8]=>1101100
[2,5,6,8,3,4,7,1]=>1010000
[4,1,3,6,5,2,7,8]=>1100100
[3,6,2,4,5,7,1,8]=>1100000
[3,6,2,5,4,7,1,8]=>1101000
[3,5,1,7,6,4,2,8]=>1101010
[3,6,1,4,5,7,2,8]=>1100000
[4,3,1,6,5,2,7,8]=>1110100
[4,1,2,6,5,3,7,8]=>1010100
[3,6,4,2,5,7,1,8]=>1101000
[4,2,6,3,5,1,7,8]=>1110000
[3,4,6,8,7,1,2,5]=>1000001
[3,4,7,6,5,1,2,8]=>1000110
[4,5,2,7,1,3,6,8]=>1100000
[4,6,1,2,5,3,7,8]=>1010000
[2,5,4,8,3,7,6,1]=>1011010
[1,3,6,2,5,8,7,4]=>0101001
[1,3,5,8,6,4,7,2]=>0101010
[5,8,7,1,4,6,3,2]=>1110001
[6,2,5,1,3,4,8,7]=>1100001
[2,6,5,1,3,4,8,7]=>1000101
[4,6,5,1,2,7,3,8]=>1010100
[5,6,4,1,2,7,3,8]=>1011000
[8,1,5,6,2,4,3,7]=>1110000
[6,4,5,1,2,7,3,8]=>1011000
[5,4,6,1,3,2,7,8]=>1101000
[5,7,1,4,3,2,6,8]=>1110000
[2,6,4,1,3,7,5,8]=>1001100
[6,3,2,5,7,4,8,1]=>1111000
[5,7,3,8,1,2,4,6]=>1010000
[4,5,2,7,6,3,1,8]=>1110010
[4,5,2,1,7,6,3,8]=>1110010
[5,4,1,6,7,2,8,3]=>1111000
[4,1,6,5,2,7,8,3]=>1110100
[5,4,6,2,7,8,3,1]=>1111000
[3,5,2,6,7,8,4,1]=>1101000
[6,3,2,5,1,7,8,4]=>1111000
[4,6,3,7,8,2,1,5]=>1110000
[5,6,7,1,8,4,2,3]=>1101000
[5,6,7,2,8,4,1,3]=>1101000
[1,7,8,4,6,5,2,3]=>0101100
[6,4,1,8,7,2,5,3]=>1111001
[3,7,2,8,6,5,1,4]=>1100110
[2,7,8,1,6,5,3,4]=>1010100
[2,5,8,1,7,6,3,4]=>1010010
[2,8,4,7,6,3,1,5]=>1011010
[4,5,8,7,1,6,2,3]=>1100001
[6,4,8,7,2,1,5,3]=>1111001
[3,2,8,7,6,4,1,5]=>1101011
[2,5,1,8,4,7,6,3]=>1011010
[2,4,5,8,1,7,6,3]=>1010010
[2,6,8,1,4,3,7,5]=>1010100
[4,1,8,2,6,7,3,5]=>1110000
[2,6,1,5,8,7,3,4]=>1010001
[8,1,7,3,5,2,4,6]=>1110000
[8,1,3,2,7,6,4,5]=>1101010
[7,5,8,1,6,2,3,4]=>1100100
[6,7,5,3,2,8,4,1]=>1111100
[7,6,1,3,5,2,4,8]=>1100010
[6,2,4,5,3,8,1,7]=>1110000
[6,1,5,4,7,2,3,8]=>1101000
[1,2,5,4,7,8,3,6]=>0011000
[3,6,2,4,7,8,5,1]=>1100100
[1,8,5,4,6,7,2,3]=>0101100
[1,3,5,4,8,7,2,6]=>0101001
[1,6,2,4,8,3,7,5]=>0110100
[7,1,4,2,3,8,6,5]=>1100110
[1,7,3,2,4,6,5,8]=>0110100
[8,1,3,2,6,5,7,4]=>1101100
[1,5,7,3,2,6,4,8]=>0111000
[5,1,3,7,2,6,4,8]=>1101000
[1,7,8,5,4,2,6,3]=>0111100
[8,1,7,5,4,2,6,3]=>1111100
[1,5,2,8,6,4,7,3]=>0111010
[1,6,5,2,7,4,8,3]=>0111100
[5,1,6,7,4,2,8,3]=>1111000
[1,5,4,2,8,6,7,3]=>0111010
[1,6,3,5,2,7,8,4]=>0111000
[5,8,4,1,6,2,7,3]=>1111000
[3,1,2,6,8,7,5,4]=>1001101
[6,4,8,2,3,5,7,1]=>1101000
[6,4,8,2,5,7,1,3]=>1101000
[6,8,2,4,7,3,5,1]=>1110000
[8,6,2,4,5,1,3,7]=>1100010
[6,8,4,2,7,1,3,5]=>1101000
[6,8,2,4,1,7,3,5]=>1110000
[2,5,4,7,6,1,3,8]=>1001010
[5,2,3,7,6,1,4,8]=>1100010
[4,2,3,7,6,1,5,8]=>1100010
[4,2,7,3,5,1,6,8]=>1110000
[5,6,2,3,8,4,7,1]=>1101000
[5,6,2,3,1,7,8,4]=>1101000
[5,7,2,3,4,1,6,8]=>1100000
[6,2,7,3,5,1,4,8]=>1110000
[7,2,6,3,5,1,4,8]=>1110000
[6,5,2,3,1,7,8,4]=>1101100
[6,5,2,3,8,4,7,1]=>1101100
[7,5,2,1,4,6,8,3]=>1110100
[8,5,2,1,4,6,7,3]=>1110100
[8,5,2,3,1,6,4,7]=>1101100
[8,6,2,3,1,5,4,7]=>1101010
[8,2,6,3,1,7,4,5]=>1111000
[1,6,3,4,2,7,5,8]=>0110100
[8,5,2,7,3,4,6,1]=>1110100
[1,7,2,4,5,6,8,3]=>0110000
[1,8,3,2,5,6,4,7]=>0111000
[8,6,1,3,4,5,7,2]=>1100010
[6,8,1,3,4,5,7,2]=>1100000
[7,2,8,1,4,6,3,5]=>1110000
[2,7,8,1,5,6,3,4]=>1010000
[6,8,2,3,1,5,4,7]=>1101000
[5,8,2,3,1,6,4,7]=>1101000
[5,7,2,1,4,6,8,3]=>1110000
[4,2,3,8,1,7,5,6]=>1100100
[5,2,3,8,1,7,4,6]=>1101000
[2,5,4,8,1,7,3,6]=>1011000
[2,5,4,1,3,8,6,7]=>1001010
[4,2,1,5,3,7,6,8]=>1110010
[5,1,3,2,6,7,8,4]=>1101000
[5,1,3,4,2,7,6,8]=>1100010
[6,1,3,4,2,7,5,8]=>1100100
[7,2,1,3,5,8,4,6]=>1101000
[6,1,2,4,5,7,8,3]=>1010000
[6,8,7,2,3,4,5,1]=>1100001
[3,7,2,8,1,4,5,6]=>1100000
[5,2,3,7,4,6,1,8]=>1101000
[2,5,3,7,4,6,1,8]=>1011000
[2,6,7,3,4,5,1,8]=>1010000
[6,2,7,3,4,5,1,8]=>1110000
[6,2,8,3,5,1,4,7]=>1110000
[3,8,4,5,2,1,6,7]=>1101000
[8,2,6,3,5,1,4,7]=>1110000
[2,7,6,3,4,5,1,8]=>1010010
[2,8,6,3,5,1,4,7]=>1010010
[2,8,7,5,1,3,4,6]=>1000101
[1,5,7,3,6,2,8,4]=>0111000
[1,6,5,7,2,8,3,4]=>0110100
[7,5,2,6,1,8,4,3]=>1111100
[6,1,5,2,7,8,4,3]=>1111000
[1,6,5,7,2,8,4,3]=>0111100
[1,5,4,6,2,8,7,3]=>0111001
[1,5,4,6,2,8,3,7]=>0111000
[1,5,6,4,8,2,3,7]=>0101000
[6,2,1,5,8,4,7,3]=>1111000
[8,3,7,5,1,4,2,6]=>1110100
[8,3,7,1,6,4,2,5]=>1111000
[4,2,6,5,3,1,7,8]=>1110100
[4,3,7,5,1,6,2,8]=>1110100
[3,5,2,8,6,7,4,1]=>1101010
[5,3,7,4,2,8,6,1]=>1111010
[5,6,2,8,7,1,4,3]=>1110001
[4,3,7,5,2,6,1,8]=>1110100
[4,6,3,5,2,7,8,1]=>1110000
[4,1,6,3,5,7,2,8]=>1110000
[3,1,5,7,4,6,8,2]=>1101000
[7,2,5,8,6,1,4,3]=>1110010
[7,8,4,5,1,3,6,2]=>1101000
[4,3,6,1,5,7,8,2]=>1110000
[6,4,7,1,3,5,2,8]=>1101000
[3,5,4,1,2,6,7,8]=>1001000
[5,3,1,4,6,7,8,2]=>1110000
[6,2,1,4,7,5,8,3]=>1110100
[4,6,7,1,3,5,8,2]=>1100000
[5,6,1,3,4,7,2,8]=>1100000
[2,5,3,7,8,4,6,1]=>1011000
[4,5,7,2,3,6,1,8]=>1100000
[4,6,2,1,3,7,8,5]=>1100100
[3,6,2,4,1,7,5,8]=>1100100
[3,2,6,7,4,8,5,1]=>1101100
[7,3,4,8,5,2,1,6]=>1110100
[7,1,8,3,4,6,2,5]=>1110000
[6,3,2,7,5,8,4,1]=>1111100
[6,2,7,1,4,5,3,8]=>1110000
[4,2,6,1,5,7,3,8]=>1110000
[2,7,5,8,6,3,4,1]=>1010110
[2,5,4,1,3,6,7,8]=>1001000
[5,4,1,2,6,7,3,8]=>1011000
[6,5,2,7,4,1,3,8]=>1101100
[6,5,7,3,1,4,2,8]=>1110100
[6,7,4,3,1,5,8,2]=>1111000
[5,4,2,3,6,8,1,7]=>1101000
[6,4,1,2,7,8,3,5]=>1011000
[5,1,8,3,4,6,2,7]=>1110000
[4,5,8,2,3,7,1,6]=>1100000
[5,1,4,7,2,6,8,3]=>1110000
[2,6,5,3,8,1,4,7]=>1010100
[5,2,6,8,3,7,1,4]=>1110000
[1,7,6,5,3,8,2,4]=>0110110
[1,7,2,4,3,5,8,6]=>0110010
[4,6,1,3,7,8,5,2]=>1100100
[8,4,1,5,2,6,7,3]=>1111000
[6,3,1,8,5,4,7,2]=>1111100
[6,1,3,8,7,4,5,2]=>1101001
[2,8,4,6,5,1,7,3]=>1011100
[7,4,1,3,6,5,2,8]=>1101100
[5,7,2,8,1,3,6,4]=>1101000
[5,4,1,2,6,3,8,7]=>1011001
[2,3,8,4,1,7,6,5]=>1001110
[6,5,1,4,7,3,2,8]=>1110100
[2,7,8,4,1,3,6,5]=>1001100
[3,6,5,1,4,8,2,7]=>1100100
[3,6,4,1,2,7,8,5]=>1001100
[4,1,7,3,8,6,2,5]=>1110010
[4,8,2,7,6,5,1,3]=>1100110
[5,4,2,8,7,6,1,3]=>1101011
[7,4,2,8,6,5,1,3]=>1101110
[6,5,8,2,7,4,1,3]=>1101100
[8,6,5,2,7,1,4,3]=>1110110
[7,8,5,2,1,6,4,3]=>1111100
[6,8,5,2,7,1,4,3]=>1110100
[6,5,8,2,7,1,4,3]=>1110100
[7,5,8,2,1,6,4,3]=>1111100
[3,2,1,6,5,8,4,7]=>1101100
[6,3,1,4,5,8,2,7]=>1110000
[3,4,8,5,2,1,7,6]=>1100110
[4,8,7,1,3,2,6,5]=>1100101
[3,5,1,4,2,8,7,6]=>1100011
[5,8,7,4,6,1,3,2]=>1101001
[5,1,8,7,4,6,3,2]=>1111001
[3,4,1,8,7,6,2,5]=>1100011
[3,5,2,8,6,4,7,1]=>1101010
[2,8,7,5,4,1,6,3]=>1011101
[4,2,5,8,6,7,1,3]=>1100010
[8,1,5,7,4,2,6,3]=>1111000
[8,4,5,3,1,6,7,2]=>1111000
[5,8,7,3,4,1,6,2]=>1110001
[2,4,5,8,1,3,7,6]=>1000010
[7,1,4,3,8,5,6,2]=>1110100
[6,3,2,5,8,4,1,7]=>1111000
[8,7,1,4,6,3,2,5]=>1110001
[8,4,1,3,7,6,5,2]=>1101110
[2,7,8,6,5,3,1,4]=>1010110
[5,1,6,4,7,8,2,3]=>1101000
[2,8,3,5,6,1,4,7]=>1010000
[1,3,6,4,2,7,5,8]=>0101100
[3,2,8,5,6,1,4,7]=>1100100
[7,2,5,8,1,4,6,3]=>1110000
[4,7,5,8,1,2,6,3]=>1010100
[5,4,7,8,2,1,3,6]=>1101000
[4,7,5,8,1,2,3,6]=>1000100
[3,4,7,5,2,8,1,6]=>1100100
[4,3,2,5,7,8,1,6]=>1110000
[5,4,8,6,2,3,1,7]=>1101010
[2,4,7,5,8,3,1,6]=>1010100
[7,2,5,8,1,6,3,4]=>1110000
[3,7,8,4,2,1,6,5]=>1101100
[8,5,4,7,6,3,1,2]=>1011110
[1,5,4,8,7,6,2,3]=>0101011
[3,2,4,5,8,1,6,7]=>1100000
[2,4,6,8,3,7,1,5]=>1010000
[1,4,7,6,3,8,2,5]=>0110010
[3,6,5,1,7,2,8,4]=>1101100
[6,4,1,7,2,8,5,3]=>1111100
[7,4,1,6,2,8,5,3]=>1111100
[2,8,3,7,5,1,6,4]=>1011100
[1,3,6,8,2,4,7,5]=>0100100
[8,5,4,1,6,2,7,3]=>1111100
[4,7,2,8,5,1,6,3]=>1110100
[8,6,2,7,3,5,1,4]=>1110010
[5,7,3,2,4,8,6,1]=>1110010
[2,8,4,6,3,5,1,7]=>1011000
[2,7,8,3,6,4,5,1]=>1011000
[4,5,2,6,7,1,8,3]=>1110000
[4,7,5,2,6,3,8,1]=>1110100
[3,5,6,2,8,1,4,7]=>1100000
[5,7,2,1,8,4,3,6]=>1111000
[6,1,8,2,4,3,5,7]=>1110000
[1,6,8,2,5,3,4,7]=>0110000
[8,7,6,2,4,5,1,3]=>1100011
[8,7,3,5,1,4,6,2]=>1110001
[8,6,3,5,2,1,4,7]=>1110010
[8,7,3,2,6,5,1,4]=>1110101
[8,4,2,7,6,5,1,3]=>1101110
[5,2,8,7,6,4,1,3]=>1101011
[8,7,1,4,5,6,2,3]=>1100001
[4,1,3,8,5,6,2,7]=>1100100
[3,2,4,8,5,7,1,6]=>1100100
[6,3,8,5,4,2,7,1]=>1111100
[7,4,6,1,3,5,2,8]=>1101000
[6,2,3,8,5,4,7,1]=>1101100
[1,5,3,8,7,4,6,2]=>0111001
[5,1,3,8,7,4,6,2]=>1101001
[2,5,3,8,7,4,1,6]=>1011001
[5,2,1,8,7,4,6,3]=>1111001
[6,8,3,5,1,2,7,4]=>1011000
[5,8,2,7,4,6,3,1]=>1111000
[6,8,7,3,1,2,4,5]=>1010001
[4,5,2,8,3,7,1,6]=>1110000
[4,5,8,1,3,7,6,2]=>1100010
[7,8,5,1,6,4,3,2]=>1111100
[8,7,5,1,6,4,3,2]=>1111101
[4,5,8,3,1,2,7,6]=>1010010
[4,6,8,3,2,1,7,5]=>1110100
[4,6,8,3,5,1,2,7]=>1010000
[7,1,6,8,5,4,3,2]=>1111100
[5,8,1,3,4,2,7,6]=>1100010
[1,4,6,3,7,5,2,8]=>0110100
[4,5,2,6,8,7,3,1]=>1110001
[3,2,8,7,4,5,6,1]=>1101001
[6,4,2,5,1,7,8,3]=>1111000
[1,3,2,8,7,4,6,5]=>0101101
[7,5,2,8,3,1,6,4]=>1111100
[5,4,2,7,3,8,6,1]=>1111010
[6,7,1,3,2,5,8,4]=>1101000
[8,3,5,4,7,1,2,6]=>1011000
[6,3,5,4,8,1,2,7]=>1011000
[6,2,5,4,1,7,8,3]=>1111000
[4,1,5,6,3,8,7,2]=>1110001
[6,8,7,4,3,2,5,1]=>1111001
[8,1,5,4,6,7,3,2]=>1111000
[2,8,5,1,3,7,6,4]=>1001110
[2,4,5,8,3,7,6,1]=>1010010
[5,6,4,1,8,2,7,3]=>1111000
[6,1,3,5,4,8,2,7]=>1101000
[1,3,8,7,2,5,6,4]=>0101001
[2,5,4,1,8,3,7,6]=>1011010
[6,1,5,4,3,8,2,7]=>1111000
[1,4,8,3,2,7,6,5]=>0110110
[5,1,4,8,3,7,6,2]=>1110010
[3,5,8,2,1,4,7,6]=>1100010
[8,4,1,2,7,6,5,3]=>1011110
[4,8,3,2,7,6,5,1]=>1110110
[2,4,8,1,7,6,5,3]=>1010110
[8,7,3,2,1,4,6,5]=>1110101
[1,4,8,5,2,3,6,7]=>0100100
[1,4,8,5,2,3,7,6]=>0100110
[6,1,4,2,8,7,3,5]=>1110001
[1,5,8,7,2,4,3,6]=>0110001
[1,2,8,7,3,5,4,6]=>0011001
[8,7,1,3,2,5,4,6]=>1101001
[6,7,4,2,8,1,3,5]=>1101000
[4,7,5,6,2,8,3,1]=>1110100
[8,4,3,6,7,5,2,1]=>1111100
[6,7,5,2,8,4,3,1]=>1111100
[6,8,4,3,2,7,5,1]=>1111100
[6,1,5,8,7,4,3,2]=>1111001
[8,5,1,4,7,6,3,2]=>1110110
[8,2,1,7,5,3,6,4]=>1111100
[8,1,3,7,2,4,6,5]=>1100100
[2,6,7,3,5,8,4,1]=>1011000
[2,6,7,3,5,8,1,4]=>1010000
[5,3,1,6,4,8,2,7]=>1111000
[2,5,6,7,1,4,8,3]=>1010000
[6,4,8,3,5,2,1,7]=>1111000
[1,4,2,7,5,8,3,6]=>0110100
[4,7,5,2,8,6,1,3]=>1100110
[1,6,5,7,3,8,4,2]=>0111100
[5,8,1,2,7,4,3,6]=>1011000
[4,6,3,7,8,1,5,2]=>1110000
[2,1,4,7,5,8,6,3]=>1010110
[8,6,3,5,2,1,7,4]=>1111010
[6,8,3,1,2,5,4,7]=>1011000
[5,8,6,4,7,1,2,3]=>1001010
[2,5,1,8,7,3,4,6]=>1010001
[6,8,1,7,5,4,2,3]=>1101100
[4,8,2,7,5,3,6,1]=>1110100
[7,2,4,3,8,6,1,5]=>1110010
[5,8,4,3,1,6,7,2]=>1111000
[6,8,7,4,5,1,3,2]=>1101001
[1,4,7,3,6,8,2,5]=>0110000
[2,4,7,3,6,8,1,5]=>1010000
[2,7,3,1,8,5,4,6]=>1011100
[2,3,1,6,8,7,4,5]=>1001001
[6,4,8,2,1,7,3,5]=>1111000
[2,3,1,7,8,5,6,4]=>1001100
[2,3,1,8,7,5,6,4]=>1001101
[8,7,4,5,1,3,2,6]=>1101001
[8,5,1,2,7,4,3,6]=>1011100
[1,3,7,6,8,4,2,5]=>0101010
[4,5,7,8,6,2,1,3]=>1100010
[2,1,5,7,4,6,8,3]=>1011000
[2,3,5,7,8,1,6,4]=>1001000
[1,6,4,2,3,5,7,8]=>0101000
[1,5,7,4,2,3,6,8]=>0101000
[8,1,7,2,4,6,3,5]=>1110000
[1,5,7,2,3,6,8,4]=>0101000
[2,4,7,8,6,1,3,5]=>1000010
[2,4,7,8,3,5,1,6]=>1010000
[1,3,6,2,5,8,4,7]=>0101000
[1,5,3,6,8,2,4,7]=>0110000
[2,8,5,1,4,3,7,6]=>1010110
[6,1,5,8,3,2,7,4]=>1111000
[1,8,6,2,4,3,7,5]=>0110110
[4,8,5,1,3,2,6,7]=>1100100
[5,4,3,1,2,7,6,8]=>1011010
[4,1,6,5,2,3,7,8]=>1100100
[7,1,5,2,3,6,4,8]=>1101000
[4,1,6,3,7,2,5,8]=>1110000
[4,6,1,2,8,3,7,5]=>1010100
[4,1,3,6,7,2,5,8]=>1100000
[2,6,5,1,3,4,7,8]=>1000100
[2,6,7,4,3,1,5,8]=>1011000
[2,6,3,1,7,4,5,8]=>1011000
[2,3,6,7,1,5,4,8]=>1001000
[3,7,5,6,2,1,4,8]=>1100100
[2,7,5,8,1,3,6,4]=>1001100
[5,1,6,7,3,2,4,8]=>1110000
[5,1,3,6,7,4,2,8]=>1101000
[2,5,6,3,8,4,7,1]=>1011000
[7,4,1,2,3,6,8,5]=>1001100
[8,5,6,2,1,4,7,3]=>1110100
[2,7,4,1,5,8,3,6]=>1011000
[6,1,7,3,4,2,5,8]=>1110000
[2,6,4,7,8,5,3,1]=>1011100
[5,2,8,4,6,7,1,3]=>1101000
[1,3,5,8,4,6,7,2]=>0101000
[8,2,7,6,3,4,5,1]=>1110010
[1,8,3,7,4,2,5,6]=>0111000
[8,5,7,2,4,3,6,1]=>1110100
[7,8,6,2,4,1,3,5]=>1100010
[6,8,7,3,2,1,4,5]=>1110001
[3,4,8,2,7,1,5,6]=>1100000
[7,2,6,1,4,8,3,5]=>1110000
[7,8,1,2,4,6,3,5]=>1010000
[7,2,8,3,4,5,1,6]=>1110000
[6,1,8,3,4,2,5,7]=>1110000
[6,8,4,3,1,5,2,7]=>1111000
[5,8,2,1,7,4,3,6]=>1111000
[1,7,2,6,3,4,8,5]=>0110100
[7,5,1,2,4,3,8,6]=>1010110
[7,6,8,1,4,2,3,5]=>1100010
[6,3,5,2,1,8,4,7]=>1111000
[3,2,4,8,6,1,7,5]=>1100110
[2,1,3,8,4,5,7,6]=>1001010
[1,4,7,5,2,3,8,6]=>0100110
[2,1,3,7,8,4,6,5]=>1001100
[2,1,3,8,4,7,6,5]=>1001110
[3,1,2,8,4,5,7,6]=>1001010
[1,2,8,7,5,4,6,3]=>0011101
[1,3,6,8,2,7,5,4]=>0101100
[3,2,7,5,6,8,1,4]=>1100100
[6,1,5,4,2,3,8,7]=>1101001
[6,4,5,1,2,8,3,7]=>1011000
[8,4,1,5,7,6,3,2]=>1111010
[8,1,6,3,5,2,4,7]=>1110000
[4,6,2,5,3,8,1,7]=>1110000
[4,6,5,2,1,8,3,7]=>1110100
[5,8,4,3,6,7,2,1]=>1111000
[6,8,2,1,5,3,4,7]=>1110000
[2,5,3,8,6,7,4,1]=>1011010
[3,2,6,5,1,8,4,7]=>1101100
[6,4,5,1,8,3,2,7]=>1111000
[3,6,8,2,5,1,4,7]=>1100000
[7,4,5,8,1,6,2,3]=>1101000
[4,5,8,1,6,7,3,2]=>1110000
[5,1,8,4,6,7,3,2]=>1111000
[4,8,3,1,6,7,2,5]=>1110000
[7,2,4,6,3,8,5,1]=>1110100
[2,8,3,7,6,1,5,4]=>1011010
[5,4,2,6,8,7,3,1]=>1111001
[3,7,2,5,8,6,4,1]=>1101010
[5,4,3,7,2,8,6,1]=>1111010
[4,6,5,3,8,1,7,2]=>1110100
[2,4,8,7,6,1,5,3]=>1010011
[4,8,5,2,7,6,3,1]=>1110110
[2,8,6,5,7,1,3,4]=>1000110
[4,1,8,6,2,5,7,3]=>1110010
[3,8,4,7,2,1,6,5]=>1101100
[1,8,7,4,5,2,3,6]=>0101001
[5,8,1,7,6,2,3,4]=>1100010
[6,8,2,1,3,4,7,5]=>1100100
[4,8,1,3,7,6,2,5]=>1100010
[5,2,1,7,6,4,3,8]=>1111010
[7,4,8,3,6,5,1,2]=>1011100
[6,4,8,5,1,7,2,3]=>1101100
[5,2,8,1,3,6,7,4]=>1101000
[5,2,7,1,3,8,6,4]=>1101010
[6,3,7,2,5,4,8,1]=>1111000
[5,2,1,7,6,3,8,4]=>1111010
[6,3,2,7,4,5,8,1]=>1111000
[7,4,3,8,5,6,1,2]=>1011100
[7,3,2,8,4,6,1,5]=>1111000
[6,2,1,8,7,4,5,3]=>1111001
[6,2,1,8,7,3,5,4]=>1111001
[5,2,1,7,6,3,4,8]=>1110010
[7,4,3,8,5,6,2,1]=>1111100
[4,2,8,3,6,7,5,1]=>1110100
[4,2,6,8,5,7,1,3]=>1100100
[4,2,1,6,5,7,8,3]=>1110100
[8,6,1,4,3,5,2,7]=>1110010
[6,1,8,4,3,5,2,7]=>1111000
[5,1,6,4,8,2,3,7]=>1101000
[2,8,6,4,1,5,3,7]=>1011010
[8,1,4,2,5,3,6,7]=>1110000
[2,8,4,1,5,3,6,7]=>1011000
[8,4,1,3,5,2,6,7]=>1101000
[3,4,8,1,5,2,6,7]=>1100000
[4,1,8,3,5,2,6,7]=>1110000
[8,3,1,2,5,4,6,7]=>1011000
[2,8,1,3,5,4,6,7]=>1001000
[1,7,6,2,4,3,8,5]=>0110110
[1,4,5,8,3,2,6,7]=>0110000
[5,6,8,7,1,3,2,4]=>1100001
[2,8,6,5,7,4,3,1]=>1011110
[6,3,7,5,1,4,2,8]=>1110100
[2,8,6,5,7,4,1,3]=>1001110
[6,5,2,7,4,3,1,8]=>1111100
[6,5,2,8,4,3,7,1]=>1111100
[7,5,8,3,4,2,1,6]=>1110100
[6,3,7,5,1,4,8,2]=>1110100
[5,3,7,2,4,1,8,6]=>1110010
[5,1,2,8,6,3,7,4]=>1011010
[6,5,2,8,4,7,1,3]=>1101100
[6,5,8,3,1,2,7,4]=>1011100
[6,1,5,7,2,4,3,8]=>1110000
[7,1,6,8,2,5,4,3]=>1111000
[4,1,8,2,6,5,7,3]=>1110100
[6,1,4,7,8,5,3,2]=>1110100
[5,1,4,6,7,3,2,8]=>1110000
[6,1,5,7,8,4,2,3]=>1101000
[1,8,4,5,6,7,2,3]=>0101000
[4,2,8,6,7,1,3,5]=>1100010
[6,4,2,7,1,5,8,3]=>1111000
[5,6,2,7,4,8,3,1]=>1111000
[5,3,6,7,4,2,8,1]=>1111000
[2,6,3,7,5,4,8,1]=>1011100
[1,7,3,2,4,8,6,5]=>0110110
[6,4,1,3,8,7,5,2]=>1101101
[4,3,1,8,2,6,7,5]=>1110100
[4,8,1,3,2,5,7,6]=>1100010
[7,2,6,5,8,3,4,1]=>1110100
[1,7,5,3,8,6,2,4]=>0110110
[2,5,3,8,1,4,7,6]=>1010010
[4,2,5,8,1,3,7,6]=>1100010
[8,1,2,4,3,5,7,6]=>1010010
[2,4,3,8,1,5,7,6]=>1010010
[7,5,2,3,8,4,6,1]=>1101100
[2,7,5,1,4,8,3,6]=>1010100
[3,1,7,4,8,6,5,2]=>1101110
[6,4,5,3,2,8,7,1]=>1111001
[2,7,3,8,5,1,6,4]=>1011100
[8,7,3,2,5,6,4,1]=>1111001
[1,5,8,2,6,4,3,7]=>0111000
[3,1,8,2,6,5,4,7]=>1101100
[7,6,2,8,1,4,5,3]=>1110010
[8,4,2,3,1,5,7,6]=>1101010
[8,2,3,4,1,5,7,6]=>1100010
[7,1,6,2,4,8,3,5]=>1110000
[4,5,2,6,1,3,8,7]=>1100001
[2,7,8,1,4,3,6,5]=>1010100
[6,5,8,1,3,2,4,7]=>1100100
[5,7,2,1,8,4,6,3]=>1111000
[2,1,8,5,3,4,6,7]=>1010100
[7,8,1,5,2,4,6,3]=>1110000
[7,4,1,8,2,5,6,3]=>1111000
[2,1,6,7,4,8,3,5]=>1011000
[2,8,6,3,1,5,4,7]=>1011010
[5,8,6,3,2,1,4,7]=>1110010
[5,7,2,8,4,1,6,3]=>1111000
[2,5,6,3,8,1,4,7]=>1010000
[7,3,5,6,1,8,4,2]=>1111000
[7,4,5,6,8,1,3,2]=>1101000
[7,5,1,8,4,6,3,2]=>1111100
[2,8,1,7,4,5,3,6]=>1011000
[7,3,6,2,5,4,8,1]=>1111000
[6,1,5,3,8,4,7,2]=>1111000
[1,6,5,3,8,4,7,2]=>0111100
[7,6,2,3,5,4,8,1]=>1101010
[7,6,2,3,5,1,4,8]=>1100010
[6,1,5,2,3,4,8,7]=>1100001
[6,2,5,3,4,8,1,7]=>1110000
[6,2,5,3,4,8,7,1]=>1110001
[2,6,5,3,4,8,7,1]=>1010101
[2,6,5,3,4,8,1,7]=>1010100
[2,5,1,4,8,3,7,6]=>1010010
[1,2,5,4,8,3,7,6]=>0011010
[5,3,4,8,1,7,2,6]=>1110000
[5,1,3,4,8,7,2,6]=>1100001
[1,5,3,4,8,7,2,6]=>0110001
[5,1,3,8,4,7,6,2]=>1101010
[5,3,8,1,4,7,6,2]=>1110010
[4,3,5,8,1,7,6,2]=>1110010
[3,6,5,4,8,1,2,7]=>1001100
[3,6,5,4,8,2,7,1]=>1101100
[4,3,5,8,2,1,7,6]=>1110010
[3,5,2,4,8,7,6,1]=>1100011
[2,3,6,5,8,4,1,7]=>1001100
[5,2,3,8,7,4,1,6]=>1101001
[2,3,1,7,4,8,6,5]=>1001110
[2,3,8,7,6,4,1,5]=>1001011
[7,5,2,3,1,6,4,8]=>1101100
[4,2,8,5,1,3,6,7]=>1100100
[7,4,1,3,6,2,5,8]=>1101000
[7,4,6,3,1,2,5,8]=>1011000
[7,2,5,8,1,3,6,4]=>1101000
[1,2,6,5,3,4,7,8]=>0010100
[1,4,6,5,7,2,3,8]=>0100100
[2,4,6,5,7,1,8,3]=>1010100
[3,5,2,1,7,8,6,4]=>1101010
[1,2,7,8,6,4,5,3]=>0011010
[7,1,6,3,2,4,8,5]=>1110100
[8,5,1,2,3,6,7,4]=>1001100
[6,4,8,1,2,3,7,5]=>1001100
[4,3,5,1,7,8,6,2]=>1110010
[4,6,7,2,3,8,5,1]=>1100100
[2,3,5,8,7,4,1,6]=>1001001
[2,3,5,8,7,4,6,1]=>1001001
[4,5,3,7,8,1,2,6]=>1010000
[1,7,4,5,8,3,6,2]=>0111000
[7,3,6,8,5,2,1,4]=>1110100
[7,1,5,2,4,8,3,6]=>1110000
[8,1,5,2,4,7,3,6]=>1110000
[7,5,8,1,4,2,3,6]=>1100100
[1,7,5,8,4,2,3,6]=>0101100
[1,3,4,8,5,6,2,7]=>0100100
[4,8,3,6,1,7,2,5]=>1110000
[4,6,3,1,2,5,7,8]=>1010000
[7,4,6,8,3,1,2,5]=>1011000
[8,5,4,7,3,1,2,6]=>1011100
[7,3,2,1,5,4,8,6]=>1111010
[2,5,6,4,8,1,3,7]=>1001000
[5,4,1,6,2,3,7,8]=>1101000
[1,5,6,4,2,3,7,8]=>0101000
[1,3,6,5,2,4,7,8]=>0100100
[1,5,6,3,2,4,7,8]=>0110000
[5,7,8,1,2,4,3,6]=>1010000
[6,5,1,2,4,3,8,7]=>1010101
[2,5,1,4,6,3,8,7]=>1010001
[5,8,7,3,1,2,4,6]=>1010001
[2,7,8,1,4,5,3,6]=>1010000
[4,3,7,1,2,6,8,5]=>1010100
[4,1,2,8,7,3,6,5]=>1010101
[8,7,5,1,2,4,3,6]=>1010101
[6,1,2,4,3,8,7,5]=>1010101
[3,7,8,1,2,4,6,5]=>1000100
[7,8,5,1,2,4,3,6]=>1010100
[8,3,4,1,2,6,7,5]=>1010100
[2,1,4,7,3,6,8,5]=>1010100
[7,3,4,1,2,6,8,5]=>1010100
[8,4,3,1,2,6,5,7]=>1011100
[3,8,2,7,4,5,1,6]=>1101000
[8,6,2,3,5,4,1,7]=>1101010
[8,2,6,1,3,5,4,7]=>1101000
[8,5,3,4,2,7,1,6]=>1110100
[8,4,3,7,2,5,6,1]=>1111000
[5,3,4,1,8,2,7,6]=>1110010
[8,3,1,7,4,5,2,6]=>1111000
[8,2,4,5,1,7,3,6]=>1110000
[4,3,8,1,7,5,6,2]=>1110100
[8,4,3,7,1,5,6,2]=>1111000
[8,3,4,7,2,6,5,1]=>1110100
[8,1,3,7,6,4,5,2]=>1101010
[8,1,4,3,7,5,6,2]=>1110100
[8,3,7,1,4,5,6,2]=>1110000
[8,7,3,6,1,2,5,4]=>1011001
[8,3,7,6,2,4,5,1]=>1110010
[8,7,2,3,6,1,5,4]=>1101001
[8,7,1,2,6,5,3,4]=>1010101
[8,2,7,1,3,4,6,5]=>1100100
[5,1,8,4,2,3,7,6]=>1101010
[8,2,4,7,3,1,6,5]=>1110100
[8,2,7,6,3,1,4,5]=>1110010
[6,8,1,4,7,3,2,5]=>1110000
[8,5,7,2,6,3,1,4]=>1110100
[5,8,2,7,3,1,6,4]=>1111000
[8,1,2,6,7,5,4,3]=>1011100
[6,2,8,5,1,7,3,4]=>1110100
[8,4,1,7,5,6,2,3]=>1101100
[8,1,2,4,7,6,5,3]=>1010110
[8,2,4,7,6,5,1,3]=>1100110
[8,2,7,6,4,5,1,3]=>1101010
[8,4,7,2,3,6,5,1]=>1101100
[8,2,4,7,3,6,5,1]=>1110100
[8,1,7,6,4,5,2,3]=>1101010
[8,1,2,7,6,4,5,3]=>1011010
[8,1,4,2,7,5,6,3]=>1110100
[8,1,5,7,3,6,4,2]=>1111000
[8,1,4,7,3,6,5,2]=>1110100
[1,7,3,8,6,2,5,4]=>0111010
[5,8,2,3,7,4,1,6]=>1101000
[4,2,8,3,7,6,1,5]=>1110010
[1,2,4,6,8,3,7,5]=>0010100
[1,3,5,6,4,8,2,7]=>0101000
[3,1,7,8,5,2,4,6]=>1100100
[6,3,5,7,1,4,2,8]=>1110000
[6,3,5,2,8,4,7,1]=>1111000
[1,6,3,5,2,8,4,7]=>0111000
[1,5,4,8,6,3,7,2]=>0111010
[5,4,8,6,3,7,2,1]=>1111010
[5,4,8,6,3,7,1,2]=>1011010
[6,4,5,8,3,1,7,2]=>1111000
[6,4,5,8,1,3,7,2]=>1101000
[6,3,5,1,8,4,7,2]=>1111000
[2,6,3,1,5,8,4,7]=>1011000
[2,5,4,8,6,3,1,7]=>1011010
[1,2,5,4,8,6,3,7]=>0011010
[2,4,8,5,6,7,3,1]=>1010100
[4,8,5,6,7,1,3,2]=>1100100
[6,4,5,8,2,1,7,3]=>1111000
[5,3,8,2,6,7,1,4]=>1110000
[6,3,5,2,8,1,7,4]=>1111000
[5,3,4,1,2,6,8,7]=>1010001
[4,3,5,2,8,6,1,7]=>1110010
[1,4,3,5,2,8,6,7]=>0110010
[1,3,5,4,8,2,6,7]=>0101000
[3,5,4,8,2,6,1,7]=>1101000
[3,6,4,5,1,2,8,7]=>1001001
[4,3,5,1,8,6,2,7]=>1110010
[3,5,4,8,1,6,2,7]=>1101000
[3,4,8,5,6,1,2,7]=>1000100
[3,4,8,5,6,2,1,7]=>1100100
[3,4,8,5,6,2,7,1]=>1100100
[3,5,4,8,1,6,7,2]=>1101000
[2,4,3,1,5,8,6,7]=>1010010
[1,7,6,2,5,4,8,3]=>0111010
[3,7,2,1,5,6,8,4]=>1101000
[8,1,6,4,3,5,2,7]=>1111000
[1,3,7,8,2,6,4,5]=>0101000
[4,6,8,5,1,3,7,2]=>1100100
[4,6,8,3,7,1,5,2]=>1110000
[4,3,1,8,5,7,2,6]=>1110100
[4,8,3,6,1,5,2,7]=>1110000
[8,3,2,4,7,1,6,5]=>1110100
[7,3,2,4,8,1,6,5]=>1110100
[8,3,2,4,6,1,7,5]=>1110100
[8,3,2,4,5,7,1,6]=>1110000
[8,3,6,2,4,1,7,5]=>1110100
[7,4,6,2,1,3,8,5]=>1101100
[3,2,4,5,7,8,1,6]=>1100000
[3,6,7,2,4,1,8,5]=>1100100
[5,3,2,8,7,6,4,1]=>1111011
[4,3,6,1,8,5,2,7]=>1110100
[4,3,7,5,8,2,1,6]=>1110100
[7,3,5,2,8,1,4,6]=>1110000
[2,6,8,4,5,1,7,3]=>1011000
[1,5,8,7,4,2,3,6]=>0101001
[1,5,2,7,6,4,8,3]=>0111010
[1,4,6,8,7,2,5,3]=>0110001
[1,3,6,8,7,2,5,4]=>0101001
[1,4,3,6,8,7,2,5]=>0110001
[1,6,2,7,5,3,4,8]=>0110100
[1,7,2,5,4,3,8,6]=>0111010
[1,6,3,7,2,4,5,8]=>0110000
[1,3,2,6,8,5,4,7]=>0101100
[1,6,3,2,7,4,5,8]=>0111000
[1,5,8,6,2,7,4,3]=>0111010
[1,3,7,2,6,4,5,8]=>0101000
[1,3,7,5,8,6,2,4]=>0100110
[1,7,3,2,8,5,6,4]=>0111100
[1,6,5,2,4,8,3,7]=>0110100
[1,4,7,6,2,3,5,8]=>0100010
[1,7,3,8,4,2,5,6]=>0111000
[1,6,2,4,7,5,8,3]=>0110100
[1,6,2,7,4,3,8,5]=>0111100
[1,5,8,2,3,6,4,7]=>0101000
[2,6,7,3,4,8,1,5]=>1010000
[4,1,3,8,7,5,2,6]=>1100101
[3,6,7,2,1,5,8,4]=>1101000
[2,5,6,1,3,8,7,4]=>1001001
[2,1,3,8,6,7,4,5]=>1001010
[3,8,5,2,1,6,4,7]=>1101100
[5,4,7,8,1,6,3,2]=>1111000
[7,3,4,2,8,5,6,1]=>1110100
[7,2,8,3,6,4,5,1]=>1111000
[1,7,8,4,3,6,5,2]=>0111100
[1,7,8,3,6,5,4,2]=>0111100
[6,4,5,8,7,2,1,3]=>1101001
[1,8,4,2,3,7,5,6]=>0101100
[6,4,2,3,8,7,5,1]=>1101101
[6,5,1,3,8,4,2,7]=>1101100
[6,1,4,2,7,8,3,5]=>1110000
[6,5,1,3,7,8,4,2]=>1101100
[6,4,2,3,7,8,5,1]=>1101100
[5,6,8,2,4,7,1,3]=>1100000
[6,7,4,2,3,8,5,1]=>1101100
[5,1,3,2,6,8,4,7]=>1101000
[5,7,1,4,6,8,2,3]=>1100000
[5,7,8,3,2,4,6,1]=>1110000
[1,5,7,3,6,4,2,8]=>0111000
[1,6,3,5,7,4,8,2]=>0111000
[1,7,2,4,8,3,5,6]=>0110000
[1,6,7,2,4,8,3,5]=>0110000
[1,6,7,8,2,4,3,5]=>0110000
[3,1,6,7,8,4,2,5]=>1101000
[3,1,6,7,8,4,5,2]=>1101000
[1,6,7,8,2,4,5,3]=>0110000
[4,2,7,6,8,5,1,3]=>1100110
[5,3,4,1,7,8,6,2]=>1110010
[3,7,5,6,1,8,4,2]=>1101100
[1,2,6,8,4,3,5,7]=>0011000
[2,4,7,5,8,3,6,1]=>1010100
[6,8,7,4,2,5,1,3]=>1101001
[7,6,3,1,2,8,5,4]=>1011110
[3,1,8,6,4,7,2,5]=>1101010
[6,2,7,8,3,4,5,1]=>1110000
[8,1,3,5,6,4,7,2]=>1101000
[2,3,7,5,8,4,6,1]=>1001100
[2,5,7,4,6,1,3,8]=>1001000
[4,8,2,6,5,3,7,1]=>1110100
[5,8,6,4,7,3,2,1]=>1111010
[8,5,2,3,1,6,7,4]=>1101100
[8,5,4,2,1,6,7,3]=>1111100
[8,3,5,2,1,6,7,4]=>1111000
[2,8,6,3,5,1,7,4]=>1011010
[8,3,2,6,4,1,7,5]=>1111100
[8,4,1,5,3,6,7,2]=>1111000
[8,3,5,1,4,6,7,2]=>1110000
[8,5,1,3,4,6,7,2]=>1100100
[2,8,6,1,5,4,7,3]=>1011010
[8,3,2,6,1,5,7,4]=>1111000
[3,8,6,4,7,1,2,5]=>1001010
[3,8,6,2,5,4,7,1]=>1101010
[3,8,4,6,5,2,7,1]=>1101100
[2,8,6,4,7,3,1,5]=>1011010
[8,3,5,4,2,7,1,6]=>1111000
[8,1,7,4,2,5,3,6]=>1111000
[8,3,2,5,1,4,7,6]=>1110010
[8,4,1,3,2,6,7,5]=>1101100
[8,4,5,1,2,6,7,3]=>1011000
[8,1,5,2,4,6,7,3]=>1110000
[8,3,1,5,2,6,7,4]=>1111000
[2,8,1,6,5,3,7,4]=>1011100
[8,3,2,1,6,4,7,5]=>1111100
[5,2,6,4,1,3,8,7]=>1101001
[2,1,8,5,4,3,7,6]=>1011110
[6,2,8,5,4,1,3,7]=>1101100
[7,2,8,5,4,1,3,6]=>1101100
[3,7,5,8,4,1,2,6]=>1001100
[5,2,4,7,8,1,3,6]=>1100000
[1,7,6,2,8,5,3,4]=>0110110
[5,6,2,8,1,7,3,4]=>1110000
[3,1,2,4,8,6,7,5]=>1000110
[1,8,7,2,3,4,5,6]=>0100001
[8,6,3,2,5,4,7,1]=>1111010
[8,6,4,2,5,3,7,1]=>1111010
[8,6,5,2,4,3,7,1]=>1110110
[8,5,6,2,4,3,7,1]=>1110100
[6,2,5,3,7,4,8,1]=>1111000
[8,4,5,2,6,3,7,1]=>1111000
[8,5,4,2,6,3,7,1]=>1111100
[8,5,3,2,6,4,7,1]=>1111100
[7,4,6,5,8,2,3,1]=>1101100
[7,3,6,5,8,2,4,1]=>1110100
[7,3,6,4,8,2,5,1]=>1111000
[7,3,5,4,8,2,6,1]=>1111000
[3,7,5,2,8,1,4,6]=>1100100
[1,2,7,4,8,5,6,3]=>0011100
[2,6,7,1,8,4,5,3]=>1011000
[5,6,3,4,2,8,7,1]=>1110001
[3,2,7,5,8,1,6,4]=>1101100
[3,6,5,8,2,7,4,1]=>1101100
[2,7,1,8,5,6,4,3]=>1011100
[4,3,6,8,5,2,1,7]=>1110100
[4,3,6,8,5,2,7,1]=>1110100
[4,5,3,2,1,8,6,7]=>1110010
[3,6,5,8,1,7,4,2]=>1101100
[3,6,5,8,1,2,7,4]=>1001100
[4,1,6,8,5,2,3,7]=>1100100
[4,5,2,8,6,7,3,1]=>1110010
[3,5,8,6,2,4,7,1]=>1100010
[3,2,4,5,8,6,1,7]=>1100010
[3,4,5,8,6,2,1,7]=>1100010
[3,4,5,8,6,2,7,1]=>1100010
[4,5,2,1,3,8,6,7]=>1100010
[4,2,3,6,8,5,1,7]=>1100100
[4,1,3,6,8,5,2,7]=>1100100
[3,1,4,5,8,6,2,7]=>1100010
[4,5,1,3,2,8,6,7]=>1100010
[3,4,5,8,6,1,7,2]=>1100010
[3,4,5,8,6,1,2,7]=>1000010
[8,2,5,4,1,3,7,6]=>1101010
[8,2,6,4,1,3,7,5]=>1101100
[1,5,8,2,4,3,7,6]=>0110010
[4,3,7,8,2,6,5,1]=>1110100
[7,3,8,4,1,5,6,2]=>1111000
[8,6,7,1,4,3,2,5]=>1110010
[3,8,5,1,2,6,7,4]=>1001100
[3,7,8,2,5,4,6,1]=>1101000
[2,4,7,8,3,6,5,1]=>1010100
[5,4,7,8,3,6,1,2]=>1011000
[6,8,1,3,2,5,7,4]=>1101000
[2,4,8,3,5,7,1,6]=>1010000
[1,4,8,5,7,2,3,6]=>0100100
[1,8,7,3,2,4,5,6]=>0110001
[2,8,4,3,5,7,1,6]=>1011000
[5,6,2,7,8,3,1,4]=>1110000
[8,6,2,7,3,4,1,5]=>1110010
[8,6,2,7,3,4,5,1]=>1110010
[5,6,2,7,8,3,4,1]=>1110000
[5,6,3,2,8,7,1,4]=>1110001
[6,8,5,3,1,7,2,4]=>1110100
[8,6,1,7,3,4,2,5]=>1110010
[5,1,6,7,8,3,2,4]=>1110000
[1,5,6,3,7,2,4,8]=>0110000
[6,2,4,8,3,7,1,5]=>1110000
[1,6,8,7,5,2,3,4]=>0100101
[1,5,6,7,4,2,3,8]=>0101000
[5,1,6,7,3,4,2,8]=>1110000
[8,6,1,7,3,4,5,2]=>1110010
[6,1,8,7,4,5,2,3]=>1101001
[2,6,8,4,7,5,1,3]=>1001100
[6,8,5,1,7,4,2,3]=>1101100
[4,6,5,7,2,3,8,1]=>1100100
[5,3,7,4,6,2,8,1]=>1111000
[3,6,7,2,5,8,4,1]=>1101000
[3,5,7,6,8,2,1,4]=>1100010
[5,3,6,7,4,8,1,2]=>1011000
[3,5,7,6,8,1,4,2]=>1100010
[4,2,7,8,3,6,5,1]=>1110100
[5,4,3,7,8,1,6,2]=>1111000
[5,3,6,7,8,2,1,4]=>1110000
[3,5,7,8,4,2,1,6]=>1101000
[4,6,7,8,2,1,3,5]=>1100000
[4,6,7,3,2,8,1,5]=>1110000
[4,6,5,3,7,8,1,2]=>1010100
[4,6,5,2,7,8,3,1]=>1110100
[3,7,5,2,8,6,1,4]=>1100110
[5,6,2,4,7,8,3,1]=>1110000
[5,4,6,2,8,3,7,1]=>1111000
[5,6,3,2,8,4,7,1]=>1111000
[5,6,2,8,3,4,7,1]=>1110000
[3,7,4,8,1,6,5,2]=>1101100
[5,2,6,4,8,7,3,1]=>1111001
[2,4,7,8,6,5,1,3]=>1000110
[2,5,7,8,6,1,4,3]=>1010010
[1,3,6,4,8,2,7,5]=>0101100
[2,4,5,3,8,7,1,6]=>1010001
[8,6,3,7,2,4,1,5]=>1110010
[8,4,6,7,3,5,2,1]=>1111000
[4,8,5,3,2,7,1,6]=>1110100
[5,4,8,1,3,7,2,6]=>1101000
[8,4,5,3,1,7,2,6]=>1111000
[7,4,5,3,1,8,6,2]=>1111010
[5,6,8,7,2,4,3,1]=>1110001
[8,4,6,3,7,5,1,2]=>1011100
[5,7,8,6,4,2,3,1]=>1101010
[6,8,7,5,1,3,2,4]=>1100101
[3,8,2,6,7,5,1,4]=>1100100
[4,7,6,3,8,2,5,1]=>1110010
[6,7,4,1,8,2,5,3]=>1111000
[6,8,4,1,7,5,2,3]=>1101100
[7,5,4,2,1,8,6,3]=>1111110
[5,7,6,8,3,2,4,1]=>1110010
[7,6,4,2,8,1,5,3]=>1111010
[7,4,6,3,8,1,5,2]=>1111000
[3,4,6,8,2,5,7,1]=>1100000
[1,8,5,6,4,2,3,7]=>0101100
[1,8,4,5,6,2,3,7]=>0101000
[6,4,8,5,7,3,1,2]=>1011100
[1,7,6,2,3,5,8,4]=>0101010
[7,2,5,4,6,8,1,3]=>1101000
[7,2,4,5,6,8,1,3]=>1100000
[8,1,6,5,2,7,4,3]=>1111100
[2,7,1,5,3,8,6,4]=>1011010
[3,5,7,2,8,4,1,6]=>1101000
[7,3,2,1,4,8,6,5]=>1110110
[8,3,7,2,6,5,1,4]=>1110100
[7,8,6,1,4,5,2,3]=>1100010
[7,5,8,2,6,1,4,3]=>1110100
[8,5,1,3,2,4,6,7]=>1100100
[3,8,5,1,2,4,6,7]=>1000100
[5,1,3,2,4,6,8,7]=>1100001
[5,3,8,1,4,2,6,7]=>1110000
[5,8,4,1,2,3,6,7]=>1001000
[5,1,7,8,4,2,3,6]=>1101000
[1,5,7,8,2,4,3,6]=>0110000
[3,5,8,1,4,2,7,6]=>1100010
[2,8,5,7,1,4,3,6]=>1010100
[4,8,7,5,1,2,3,6]=>1000101
[8,6,4,1,2,3,7,5]=>1001110
[8,1,2,4,6,3,7,5]=>1010100
[6,3,8,4,1,7,2,5]=>1111000
[7,6,1,4,2,3,8,5]=>1100110
[1,7,5,2,3,4,8,6]=>0100110
[7,8,1,2,5,3,4,6]=>1010000
[1,8,7,5,2,3,4,6]=>0100101
[7,1,4,8,2,3,6,5]=>1100100
[1,8,4,7,5,2,3,6]=>0101100
[7,3,4,1,8,6,2,5]=>1110010
[8,4,7,2,1,6,3,5]=>1111000
[7,1,5,3,6,8,2,4]=>1110000
[8,1,5,3,6,7,2,4]=>1110000
[3,6,5,2,4,7,8,1]=>1100100
[2,7,5,4,6,8,1,3]=>1001100
[1,7,5,4,6,8,2,3]=>0101100
[2,7,5,3,6,8,1,4]=>1010100
[4,7,8,2,5,6,1,3]=>1100000
[2,8,5,4,6,7,1,3]=>1001100
[4,7,5,3,8,1,2,6]=>1010100
[4,2,7,6,8,1,3,5]=>1100010
[3,1,7,8,5,6,2,4]=>1100100
[1,3,8,5,6,7,2,4]=>0100100
[3,4,7,8,6,1,2,5]=>1000010
[6,8,3,2,4,1,5,7]=>1110000
[7,6,1,8,2,5,4,3]=>1111010
[7,6,1,8,2,5,3,4]=>1110010
[5,8,4,2,1,6,3,7]=>1111000
[7,6,4,1,2,5,3,8]=>1011010
[8,7,2,6,4,5,3,1]=>1111001
[5,2,3,7,1,8,4,6]=>1101000
[4,8,6,5,1,3,7,2]=>1100110
[1,7,5,4,8,6,2,3]=>0101110
[4,5,1,6,8,2,7,3]=>1110000
[1,6,3,7,2,4,8,5]=>0110100
[8,7,2,4,1,5,3,6]=>1110001
[5,2,4,1,8,3,6,7]=>1110000
[4,3,1,6,7,2,5,8]=>1110000
[6,3,1,5,7,2,4,8]=>1110000
[6,1,8,2,4,5,3,7]=>1110000
[4,5,2,1,3,7,6,8]=>1100010
[8,2,7,4,1,6,5,3]=>1111100
[3,7,6,4,1,5,8,2]=>1101010
[2,7,6,4,5,1,8,3]=>1011010
[4,6,8,1,7,3,5,2]=>1110000
[2,8,4,6,3,1,5,7]=>1011000
[2,8,3,1,6,7,4,5]=>1011000
[1,3,7,6,5,2,4,8]=>0100110
[1,3,6,7,5,2,4,8]=>0100100
[1,5,2,6,8,7,3,4]=>0110001
[4,8,5,7,1,2,3,6]=>1000100
[7,8,6,1,4,3,2,5]=>1110010
[7,4,8,3,6,2,1,5]=>1111000
[1,5,7,4,8,6,2,3]=>0101010
[4,8,7,5,2,3,1,6]=>1100101
[1,2,7,8,6,4,3,5]=>0011010
[3,5,1,7,8,6,2,4]=>1100010
[1,8,6,7,4,2,3,5]=>0101010
[7,1,3,2,6,5,8,4]=>1101100
[2,4,6,5,8,3,1,7]=>1010100
[2,4,6,5,8,1,7,3]=>1010100
[2,4,6,3,8,7,1,5]=>1010001
[1,5,4,7,3,8,6,2]=>0111010
[2,5,6,4,1,3,8,7]=>1001001
[7,2,3,1,6,8,4,5]=>1101000
[5,7,8,1,6,2,3,4]=>1100000
[1,4,8,3,2,7,5,6]=>0110100
[1,6,3,8,2,7,4,5]=>0111000
[1,6,4,2,7,3,8,5]=>0111100
[1,4,2,5,8,6,3,7]=>0110010
[4,8,2,1,5,7,3,6]=>1110000
[5,2,7,1,6,3,4,8]=>1110000
[4,8,2,5,1,6,3,7]=>1110000
[5,8,1,2,4,6,3,7]=>1010000
[5,1,7,3,6,4,2,8]=>1111000
[3,1,7,5,6,2,4,8]=>1100100
[3,2,7,5,6,1,4,8]=>1100100
[3,2,7,1,6,4,5,8]=>1101000
[6,3,1,7,5,4,2,8]=>1111100
[5,8,3,2,4,1,7,6]=>1110010
[6,1,4,3,7,5,8,2]=>1110100
[2,7,5,6,8,3,1,4]=>1010100
[1,7,8,6,3,4,2,5]=>0110010
[6,4,1,8,2,7,5,3]=>1111100
[1,5,6,8,4,2,7,3]=>0111000
[7,3,2,1,4,6,8,5]=>1110100
[7,8,5,3,2,1,6,4]=>1111100
[4,7,2,6,1,8,3,5]=>1110000
[8,7,3,5,2,1,6,4]=>1111001
[3,8,6,2,1,7,4,5]=>1101010
[2,5,7,1,3,6,4,8]=>1001000
[1,4,7,2,5,3,6,8]=>0110000
[4,5,1,3,8,2,6,7]=>1100000
[4,1,5,3,2,7,6,8]=>1110010
[7,3,5,1,4,2,6,8]=>1110000
[7,5,2,4,1,3,8,6]=>1100110
[6,2,1,7,4,3,8,5]=>1111100
[2,4,3,6,7,1,5,8]=>1010000
[3,1,7,4,2,6,8,5]=>1101100
[7,3,5,2,1,6,4,8]=>1111000
[4,6,5,2,1,3,7,8]=>1100100
[1,4,7,2,5,6,3,8]=>0110000
[7,2,5,6,1,3,8,4]=>1101000
[2,5,6,1,4,3,7,8]=>1010000
[6,1,5,3,7,2,4,8]=>1110000
[3,6,5,4,1,7,2,8]=>1101100
[1,7,4,5,6,8,2,3]=>0101000
[6,8,5,7,2,1,4,3]=>1110100
[1,6,8,7,3,4,2,5]=>0110001
[1,4,2,6,7,8,5,3]=>0110100
[5,6,4,2,1,8,3,7]=>1111000
[4,1,2,6,7,8,5,3]=>1010100
[5,6,2,7,8,1,3,4]=>1100000
[3,7,8,2,1,4,5,6]=>1100000
[3,7,8,1,5,2,6,4]=>1101000
[1,5,4,7,8,3,6,2]=>0111000
[5,1,4,7,8,3,6,2]=>1110000
[5,6,4,1,7,3,8,2]=>1111000
[8,3,7,5,4,2,6,1]=>1111100
[4,3,7,8,2,5,1,6]=>1110000
[2,7,1,6,5,8,3,4]=>1010100
[3,7,8,5,4,2,1,6]=>1101100
[1,7,4,5,6,8,3,2]=>0111000
[2,7,4,5,6,8,3,1]=>1011000
[2,8,3,5,6,4,1,7]=>1011000
[2,4,7,8,3,1,6,5]=>1010100
[5,4,3,6,8,1,7,2]=>1111000
[3,7,4,5,8,1,2,6]=>1001000
[3,7,4,5,8,1,6,2]=>1101000
[1,4,3,5,6,8,2,7]=>0110000
[1,4,6,5,8,2,7,3]=>0110100
[2,4,3,5,8,1,6,7]=>1010000
[4,6,1,7,3,2,8,5]=>1110100
[1,7,3,6,4,2,8,5]=>0111100
[1,3,7,6,2,4,8,5]=>0100110
[4,7,3,5,1,2,8,6]=>1010010
[2,5,1,8,3,7,4,6]=>1011000
[5,1,2,4,3,6,8,7]=>1010001
[4,8,3,5,2,1,6,7]=>1110000
[8,7,3,1,5,2,6,4]=>1111001
[3,8,4,1,7,5,2,6]=>1101100
[7,8,5,3,6,2,1,4]=>1110100
[6,7,1,5,2,8,4,3]=>1111000
[2,7,6,4,8,3,1,5]=>1011010
[2,6,3,7,5,8,4,1]=>1011100
[4,7,3,2,6,5,1,8]=>1110100
[4,7,5,2,3,6,1,8]=>1100100
[4,3,7,8,2,1,6,5]=>1110100
[4,8,7,2,1,5,6,3]=>1110001
[7,3,8,2,5,1,6,4]=>1111000
[4,5,3,8,2,1,7,6]=>1110010
[4,5,3,8,6,1,2,7]=>1010010
[7,3,8,4,5,1,2,6]=>1011000
[4,8,7,5,1,3,2,6]=>1100101
[4,8,7,5,1,2,6,3]=>1010101
[7,8,4,6,1,3,5,2]=>1101000
[4,8,7,5,1,3,6,2]=>1100101
[4,5,3,6,8,1,2,7]=>1010000
[7,8,6,2,1,4,3,5]=>1110010
[4,7,5,8,2,1,3,6]=>1100100
[4,8,5,7,1,3,2,6]=>1100100
[7,8,6,3,1,2,5,4]=>1011010
[4,1,3,6,5,7,2,8]=>1100100
[4,1,3,5,7,2,8,6]=>1100010
[5,1,8,2,4,6,3,7]=>1110000
[6,8,2,1,4,5,3,7]=>1110000
[2,1,4,7,5,3,8,6]=>1010110
[6,8,1,3,5,7,4,2]=>1101000
[5,8,3,2,7,4,6,1]=>1111000
[4,1,3,7,5,6,2,8]=>1100100
[5,1,7,2,4,6,3,8]=>1110000
[4,2,7,3,6,8,5,1]=>1110100
[5,8,4,7,1,3,6,2]=>1101000
[3,1,5,8,6,7,2,4]=>1100010
[6,8,2,1,4,5,7,3]=>1110000
[5,3,1,2,4,6,8,7]=>1010001
[3,6,7,5,8,4,1,2]=>1001100
[6,1,5,2,8,7,4,3]=>1111001
[3,2,6,1,5,8,7,4]=>1101001
[4,5,2,1,6,7,8,3]=>1110000
[8,4,6,3,1,2,7,5]=>1011100
[3,7,6,4,1,5,2,8]=>1101010
[3,8,6,4,1,5,7,2]=>1101010
[8,7,1,4,5,2,3,6]=>1100001
[8,7,1,4,2,5,3,6]=>1110001
[4,8,7,3,1,2,6,5]=>1010101
[3,8,6,4,5,1,7,2]=>1101010
[3,7,6,4,5,1,2,8]=>1001010
[8,4,6,2,1,7,3,5]=>1111000
[7,4,6,3,1,2,8,5]=>1011100
[4,6,3,5,7,1,8,2]=>1110000
[4,6,2,5,7,8,1,3]=>1100000
[4,7,3,5,8,1,6,2]=>1110000
[4,6,3,5,7,1,2,8]=>1010000
[4,7,3,5,8,6,1,2]=>1010010
[4,7,3,5,6,1,2,8]=>1010000
[4,8,3,5,7,1,6,2]=>1110000
[4,8,3,5,6,1,2,7]=>1010000
[4,7,2,5,6,8,1,3]=>1100000
[4,8,2,5,6,7,1,3]=>1100000
[1,4,7,2,6,5,8,3]=>0110100
[1,2,7,8,3,5,4,6]=>0011000
[1,6,7,8,3,2,5,4]=>0111000
[1,7,6,2,8,5,4,3]=>0111110
[1,6,7,8,3,2,4,5]=>0110000
[1,2,7,8,3,4,6,5]=>0010100
[1,7,6,8,3,4,2,5]=>0110010
[8,4,7,3,1,2,6,5]=>1011100
[4,2,8,1,6,5,7,3]=>1110100
[3,1,8,2,6,5,7,4]=>1101100
[2,8,4,3,1,6,5,7]=>1011100
[2,4,3,8,6,5,1,7]=>1010110
[2,8,6,4,3,1,7,5]=>1011110
[7,4,5,8,1,3,6,2]=>1101000
[1,4,6,3,2,5,8,7]=>0110001
[4,2,5,7,1,6,8,3]=>1110000
[4,5,3,7,1,6,8,2]=>1110000
[6,8,4,1,5,7,3,2]=>1111000
[6,8,4,1,5,7,2,3]=>1101000
[5,2,6,7,4,1,8,3]=>1111000
[5,6,7,4,3,1,8,2]=>1111000
[8,5,6,4,1,7,3,2]=>1111100
[5,8,2,6,1,7,4,3]=>1111000
[7,8,3,1,6,4,5,2]=>1111000
[5,8,2,6,3,1,7,4]=>1111000
[4,5,8,1,6,3,7,2]=>1110000
[8,1,4,6,2,5,7,3]=>1110000
[4,8,1,3,6,2,7,5]=>1100100
[4,5,8,1,6,2,7,3]=>1110000
[5,2,6,8,1,4,3,7]=>1110000
[6,2,7,3,8,1,4,5]=>1110000
[6,7,3,8,2,1,4,5]=>1110000
[6,2,7,8,3,1,4,5]=>1110000
[8,7,3,1,2,5,6,4]=>1011001
[2,8,3,6,4,1,7,5]=>1011100
[6,1,3,7,2,8,5,4]=>1101100
[5,4,3,6,1,7,8,2]=>1111000
[4,8,3,2,1,7,5,6]=>1110100
[1,2,4,6,5,8,3,7]=>0010100
[2,4,8,6,3,1,7,5]=>1010110
[3,4,8,1,6,7,2,5]=>1100000
[3,6,7,8,4,1,5,2]=>1101000
[2,3,7,8,4,6,1,5]=>1001000
[1,3,7,8,4,6,2,5]=>0101000
[3,1,7,8,4,6,2,5]=>1101000
[4,8,7,3,6,1,2,5]=>1010001
[5,8,4,3,7,1,2,6]=>1011000
[4,1,8,3,7,5,2,6]=>1110100
[2,4,8,3,6,7,1,5]=>1010000
[2,4,8,6,5,7,1,3]=>1000110
[1,6,5,8,7,3,2,4]=>0110101
[5,6,4,8,7,2,1,3]=>1101001
[7,2,6,8,3,5,1,4]=>1110000
[7,2,8,6,5,3,1,4]=>1110110
[4,8,3,7,6,1,2,5]=>1010010
[4,1,7,8,6,5,2,3]=>1100110
[2,1,8,7,3,5,4,6]=>1011001
[1,7,6,2,3,8,5,4]=>0101110
[1,8,5,3,2,7,4,6]=>0111100
[4,5,1,3,7,6,2,8]=>1100010
[7,2,3,8,6,4,5,1]=>1101010
[3,5,8,1,7,4,2,6]=>1101000
[5,8,1,2,7,6,4,3]=>1011010
[8,7,1,3,2,6,4,5]=>1101001
[1,3,8,5,2,4,6,7]=>0100100
[7,8,6,1,3,2,4,5]=>1100010
[8,1,6,3,7,5,4,2]=>1111100
[8,5,1,3,7,6,4,2]=>1101110
[1,6,4,7,3,8,5,2]=>0111100
[2,8,1,5,6,4,3,7]=>1011000
[1,2,6,8,3,4,7,5]=>0010100
[1,6,7,5,8,4,2,3]=>0101100
[7,4,1,6,5,2,8,3]=>1111100
[5,3,8,2,7,6,1,4]=>1110010
[7,4,2,8,6,5,3,1]=>1111110
[5,8,2,7,6,1,4,3]=>1110010
[7,4,8,3,1,6,5,2]=>1111100
[5,8,7,2,6,4,3,1]=>1111001
[6,8,7,5,2,1,4,3]=>1110101
[6,8,7,3,5,1,4,2]=>1110001
[1,8,6,4,7,3,2,5]=>0111010
[7,2,5,4,1,3,8,6]=>1101010
[8,6,7,2,3,5,4,1]=>1101010
[5,4,8,6,7,3,1,2]=>1011010
[4,2,7,3,1,6,8,5]=>1110100
[7,2,6,8,5,1,3,4]=>1100100
[7,3,6,4,2,1,8,5]=>1111100
[4,8,5,2,7,3,1,6]=>1110100
[5,8,6,3,2,1,7,4]=>1111010
[6,4,3,1,8,5,2,7]=>1111100
[7,4,3,1,5,8,6,2]=>1111010
[7,4,8,6,5,3,1,2]=>1011110
[7,8,5,2,6,4,3,1]=>1111100
[7,3,2,1,8,5,6,4]=>1111100
[1,5,7,2,4,3,8,6]=>0110010
[1,2,7,5,8,4,3,6]=>0011100
[5,1,3,8,2,7,4,6]=>1101000
[5,7,1,3,2,8,4,6]=>1101000
[7,1,6,3,2,8,4,5]=>1111000
[8,1,7,2,3,6,5,4]=>1101100
[1,7,2,5,8,4,3,6]=>0111000
[7,1,2,6,4,3,8,5]=>1011100
[1,4,7,8,3,2,5,6]=>0110000
[8,7,1,3,2,4,6,5]=>1100101
[8,1,6,3,2,4,7,5]=>1110100
[1,8,2,7,6,3,5,4]=>0111010
[1,8,6,2,7,4,3,5]=>0111010
[8,1,6,3,2,7,4,5]=>1111000
[8,2,1,7,6,3,4,5]=>1110010
[6,8,4,3,5,1,2,7]=>1011000
[8,7,3,5,4,1,2,6]=>1011001
[8,5,3,6,4,2,1,7]=>1111100
[6,3,8,5,7,2,1,4]=>1110100
[8,7,3,6,4,1,2,5]=>1011001
[5,2,7,4,6,1,3,8]=>1101000
[8,7,2,3,5,1,4,6]=>1100001
[6,4,5,3,1,7,8,2]=>1111000
[6,4,5,3,1,8,7,2]=>1111001
[8,7,3,2,5,1,6,4]=>1111001
[6,3,5,2,8,1,4,7]=>1110000
[6,4,5,3,1,7,2,8]=>1111000
[8,7,2,4,3,1,5,6]=>1110001
[7,6,2,3,1,4,8,5]=>1100110
[4,7,6,2,3,1,5,8]=>1100010
[1,8,2,3,5,6,4,7]=>0101000
[2,8,1,3,5,6,4,7]=>1001000
[2,5,7,4,8,3,6,1]=>1011000
[2,6,3,4,7,8,5,1]=>1010100
[2,3,5,4,7,1,8,6]=>1001010
[7,4,1,3,6,8,5,2]=>1101100
[7,2,1,3,6,8,4,5]=>1101000
[7,4,2,3,6,8,5,1]=>1101100
[7,2,3,6,8,5,4,1]=>1101100
[7,6,3,1,8,5,2,4]=>1110110
[7,2,1,3,6,8,5,4]=>1101100
[7,6,3,8,1,5,2,4]=>1110010
[1,6,4,7,8,5,3,2]=>0111100
[7,2,5,1,6,4,3,8]=>1111000
[1,2,4,6,8,5,7,3]=>0010100
[8,5,2,3,7,4,1,6]=>1101100
[2,6,3,7,4,1,8,5]=>1011100
[6,1,3,2,8,5,7,4]=>1101100
[3,8,5,1,2,4,7,6]=>1000110
[1,8,3,7,5,2,6,4]=>0111100
[8,1,3,6,5,2,7,4]=>1101100
[7,1,3,8,5,2,6,4]=>1101100
[4,7,1,5,2,6,8,3]=>1110000
[7,4,1,5,2,6,8,3]=>1111000
[3,1,6,7,5,2,8,4]=>1101100
[8,6,2,4,5,1,7,3]=>1110010
[4,6,2,5,3,1,7,8]=>1110000
[7,1,4,5,2,6,8,3]=>1110000
[5,7,6,8,2,1,4,3]=>1110010
[3,5,4,7,8,2,6,1]=>1101000
[5,1,4,7,6,8,3,2]=>1110010
[5,2,4,7,6,8,3,1]=>1110010
[5,6,4,7,1,8,3,2]=>1111000
[3,6,7,5,1,4,8,2]=>1100100
[6,3,7,1,2,5,8,4]=>1011000
[5,1,4,7,8,2,6,3]=>1110000
[6,3,7,5,1,2,8,4]=>1011100
[5,3,7,4,6,1,8,2]=>1111000
[5,4,1,7,6,8,3,2]=>1111010
[4,2,5,3,6,7,8,1]=>1110000
[4,5,1,3,6,7,8,2]=>1100000
[3,6,7,1,5,4,8,2]=>1101000
[3,6,4,7,5,8,2,1]=>1101100
[6,4,7,1,5,2,8,3]=>1111000
[3,5,6,2,1,7,8,4]=>1101000
[2,5,6,7,1,8,4,3]=>1011000
[8,1,4,3,5,2,7,6]=>1110010
[4,8,1,3,5,2,7,6]=>1100010
[4,5,1,6,2,8,7,3]=>1110001
[3,2,5,8,6,1,7,4]=>1101010
[4,5,1,7,2,8,6,3]=>1110010
[7,1,4,3,6,8,2,5]=>1110000
[5,6,3,2,7,4,1,8]=>1111000
[5,2,6,7,4,3,1,8]=>1111000
[8,5,1,6,4,3,2,7]=>1111100
[8,5,1,6,4,3,7,2]=>1111100
[8,5,2,1,6,4,3,7]=>1111100
[8,6,3,5,2,7,1,4]=>1110010
[8,4,6,2,1,5,7,3]=>1111000
[5,6,2,1,8,4,7,3]=>1111000
[8,5,2,1,6,4,7,3]=>1111100
[1,7,2,8,5,4,6,3]=>0111100
[6,7,1,4,8,5,3,2]=>1110100
[7,4,8,2,1,5,6,3]=>1111000
[7,3,2,8,5,1,4,6]=>1110100
[6,7,1,4,3,2,8,5]=>1110100
[4,1,7,3,2,8,5,6]=>1110100
[8,3,5,2,4,7,1,6]=>1110000
[4,3,7,8,6,1,5,2]=>1110010
[6,2,8,4,3,7,1,5]=>1111000
[1,2,6,3,7,8,5,4]=>0011100
[6,1,3,2,7,8,5,4]=>1101100
[6,7,1,3,2,8,5,4]=>1101100
[2,6,4,7,5,3,1,8]=>1011100
[5,6,3,7,2,8,4,1]=>1111000
[4,5,1,8,6,2,7,3]=>1110010
[5,6,1,8,7,2,3,4]=>1100001
[4,5,1,6,8,7,3,2]=>1110001
[2,4,6,3,5,1,7,8]=>1010000
[4,1,6,2,5,8,3,7]=>1110000
[1,8,2,5,7,3,4,6]=>0110000
[3,8,2,5,4,1,6,7]=>1101000
[1,4,6,3,8,5,2,7]=>0110100
[4,5,6,3,1,7,2,8]=>1110000
[3,4,6,2,5,1,7,8]=>1100000
[6,2,1,5,8,3,4,7]=>1110000
[1,5,7,3,6,2,4,8]=>0110000
[1,4,7,5,2,3,6,8]=>0100100
[1,4,6,5,8,2,3,7]=>0100100
[1,5,8,6,2,3,4,7]=>0100010
[1,4,8,3,7,6,2,5]=>0110010
[1,4,5,3,7,2,6,8]=>0110000
[1,4,8,7,3,6,2,5]=>0110001
[8,3,5,1,6,4,7,2]=>1111000
[5,8,4,3,6,2,7,1]=>1111000
[4,6,5,8,3,2,7,1]=>1110100
[3,4,7,5,6,8,2,1]=>1100100
[3,4,7,8,5,2,6,1]=>1100100
[2,3,8,4,7,1,6,5]=>1001100
[1,8,7,5,2,6,3,4]=>0110101
[1,8,7,5,4,3,2,6]=>0111101
[1,7,6,3,4,5,8,2]=>0110010
[1,8,7,4,5,6,2,3]=>0101001
[1,8,7,3,6,4,2,5]=>0111001
[1,8,7,2,4,6,3,5]=>0110001
[1,4,7,8,6,2,5,3]=>0110010
[1,7,6,4,2,5,3,8]=>0111010
[1,4,7,5,8,2,3,6]=>0100100
[1,4,7,5,8,2,6,3]=>0110100
[1,6,8,3,4,2,5,7]=>0110000
[1,4,7,2,3,6,5,8]=>0100100
[1,3,2,6,8,4,7,5]=>0101100
[1,7,2,5,6,3,4,8]=>0110000
[1,5,8,3,6,4,7,2]=>0111000
[1,2,6,5,8,3,4,7]=>0010100
[1,6,8,2,7,3,4,5]=>0110000
[1,4,5,8,2,6,3,7]=>0110000
[3,5,6,7,2,4,1,8]=>1100000
[6,4,7,5,2,3,1,8]=>1101100
[1,5,6,4,8,3,2,7]=>0111000
[5,2,6,4,8,7,1,3]=>1101001
[2,1,5,6,4,8,3,7]=>1011000
[5,1,4,7,8,6,2,3]=>1100010
[2,5,7,1,8,6,3,4]=>1010010
[1,6,7,2,8,5,4,3]=>0111100
[4,6,1,7,8,5,3,2]=>1110100
[5,3,2,1,7,8,6,4]=>1111010
[7,4,3,8,6,1,5,2]=>1111010
[4,3,7,1,5,8,6,2]=>1110010
[8,2,4,5,3,1,7,6]=>1110010
[8,5,3,2,4,1,7,6]=>1110110
[1,4,3,2,7,5,8,6]=>0110110
[4,8,7,2,6,1,3,5]=>1100001
[4,5,8,2,1,7,3,6]=>1110000
[6,8,4,1,7,3,2,5]=>1111000
[7,6,2,8,4,5,3,1]=>1111010
[7,8,2,6,4,5,3,1]=>1111000
[2,8,3,1,7,5,6,4]=>1011100
[1,8,3,5,2,6,4,7]=>0111000
[2,5,8,4,6,1,3,7]=>1001000
[1,8,4,5,6,2,7,3]=>0111000
[2,3,8,7,4,5,1,6]=>1001001
[2,4,8,5,7,3,1,6]=>1010100
[1,8,3,5,7,4,2,6]=>0111000
[2,5,8,4,6,7,1,3]=>1001000
[3,5,6,8,4,7,1,2]=>1001000
[3,5,6,8,4,2,7,1]=>1101000
[2,5,8,4,6,3,7,1]=>1011000
[1,8,4,5,6,3,2,7]=>0111000
[7,2,5,3,4,6,1,8]=>1110000
[7,1,2,6,4,3,5,8]=>1011000
[7,1,2,6,3,4,5,8]=>1010000
[7,1,2,6,4,5,3,8]=>1011000
[7,1,2,6,5,3,4,8]=>1010100
[5,3,1,4,7,2,8,6]=>1110010
[7,1,3,8,2,6,4,5]=>1101000
[1,8,3,7,2,4,6,5]=>0110100
[2,7,5,6,4,8,1,3]=>1001100
[2,8,3,6,5,7,1,4]=>1010100
[7,4,3,1,6,5,2,8]=>1111100
[3,5,1,2,6,8,7,4]=>1001001
[1,5,2,4,3,8,7,6]=>0110011
[3,1,2,4,8,7,5,6]=>1000101
[5,2,1,6,3,8,7,4]=>1111001
[3,4,6,7,2,1,5,8]=>1100000
[2,5,7,4,6,8,1,3]=>1001000
[4,6,2,7,5,8,1,3]=>1100100
[4,7,2,5,3,8,1,6]=>1110000
[2,4,7,6,3,8,1,5]=>1010010
[5,8,3,6,4,1,7,2]=>1111000
[4,6,8,5,1,2,3,7]=>1000100
[4,6,5,7,1,2,3,8]=>1000100
[4,6,5,7,1,3,8,2]=>1100100
[3,4,7,6,1,8,2,5]=>1100010
[8,5,6,7,4,1,3,2]=>1101100
[1,6,5,7,3,8,2,4]=>0110100
[7,2,4,8,6,1,5,3]=>1110010
[7,1,4,8,6,5,2,3]=>1100110
[8,6,2,1,3,7,5,4]=>1101110
[8,1,4,6,7,2,5,3]=>1110000
[8,1,4,6,2,7,5,3]=>1110100
[8,6,1,3,2,7,5,4]=>1101110
[8,1,7,5,2,4,6,3]=>1110100
[8,6,2,7,5,3,1,4]=>1110110
[8,2,7,5,4,1,6,3]=>1111100
[8,2,1,6,7,4,5,3]=>1111000
[8,7,2,1,5,3,6,4]=>1111001
[8,6,1,2,7,3,5,4]=>1011010
[8,1,6,2,4,7,5,3]=>1110100
[5,2,6,7,4,8,3,1]=>1111000
[6,2,3,8,7,4,5,1]=>1101001
[4,3,7,1,2,8,5,6]=>1010100
[8,5,7,1,4,2,6,3]=>1110100
[2,6,7,1,4,3,8,5]=>1010100
[4,5,2,1,6,3,8,7]=>1110001
[4,5,2,1,6,7,3,8]=>1110000
[5,3,8,6,2,4,7,1]=>1110010
[2,5,1,6,4,3,8,7]=>1011001
[3,6,2,8,5,7,1,4]=>1100100
[4,6,8,1,5,7,2,3]=>1100000
[4,1,2,5,7,6,3,8]=>1010010
[5,2,3,8,7,1,6,4]=>1101001
[3,2,8,1,7,5,4,6]=>1101100
[4,8,5,1,3,7,2,6]=>1100100
[4,6,5,8,1,7,3,2]=>1110100
[2,1,3,6,4,8,7,5]=>1001101
[4,8,2,1,6,7,5,3]=>1110100
[4,8,1,2,7,5,6,3]=>1010100
[5,2,8,1,7,4,6,3]=>1111000
[5,7,4,8,1,2,6,3]=>1011000
[8,1,6,7,3,4,2,5]=>1110000
[4,5,1,6,8,7,2,3]=>1100001
[3,4,7,2,5,8,6,1]=>1100010
[3,4,7,1,5,8,2,6]=>1100000
[6,2,7,4,5,3,1,8]=>1111000
[6,8,7,5,4,1,2,3]=>1001101
[4,3,8,6,1,2,5,7]=>1010010
[4,8,6,5,7,1,3,2]=>1100110
[4,8,1,5,3,6,7,2]=>1110000
[8,4,6,7,5,1,3,2]=>1101100
[8,3,4,2,7,6,1,5]=>1110010
[8,7,5,6,4,1,3,2]=>1101101
[8,7,4,2,3,6,5,1]=>1101101
[8,4,2,3,7,6,5,1]=>1101110
[8,6,4,7,5,1,3,2]=>1101110
[5,3,6,4,1,2,8,7]=>1011001
[5,4,1,7,8,6,2,3]=>1101010
[6,1,4,7,5,8,2,3]=>1100100
[2,1,7,5,8,6,3,4]=>1010110
[5,3,4,7,8,1,6,2]=>1110000
[5,1,4,8,2,3,7,6]=>1100010
[5,8,6,3,1,2,4,7]=>1010010
[4,5,2,3,8,6,1,7]=>1100010
[4,5,1,3,2,6,8,7]=>1100001
[4,7,1,8,5,3,6,2]=>1110100
[6,4,7,5,1,3,2,8]=>1101100
[6,7,2,4,1,8,3,5]=>1110000
[5,1,6,3,2,7,8,4]=>1111000
[2,3,7,8,5,4,6,1]=>1001100
[7,4,5,1,2,6,8,3]=>1011000
[6,7,8,2,1,5,3,4]=>1110000
[5,2,1,6,4,7,3,8]=>1111000
[6,7,2,5,4,1,3,8]=>1101000
[7,4,8,6,3,5,1,2]=>1011010
[8,4,1,6,2,7,5,3]=>1111100
[4,2,7,1,5,8,3,6]=>1110000
[4,6,3,5,1,8,2,7]=>1110000
[8,5,7,6,2,3,4,1]=>1100110
[8,4,2,3,6,7,5,1]=>1101100
[2,4,7,5,8,6,3,1]=>1010110
[4,1,7,6,2,8,3,5]=>1110010
[2,7,5,3,1,4,8,6]=>1010110
[4,1,7,2,8,5,3,6]=>1110100
[2,6,5,3,8,4,7,1]=>1011100
[7,1,4,3,6,5,8,2]=>1110100
[7,1,6,3,5,4,8,2]=>1111000
[5,7,3,2,8,4,1,6]=>1111000
[2,8,7,1,6,5,3,4]=>1010101
[2,8,6,1,7,5,3,4]=>1010110
[8,1,5,2,7,4,3,6]=>1111000
[2,6,8,1,7,5,3,4]=>1010100
[1,4,6,5,3,8,2,7]=>0110100
[2,4,5,8,7,1,3,6]=>1000001
[3,1,6,8,7,5,4,2]=>1101101
[3,1,8,7,5,6,4,2]=>1101101
[5,1,8,7,6,3,4,2]=>1110011
[1,3,8,4,7,2,6,5]=>0101100
[1,8,2,4,7,3,6,5]=>0110100
[8,2,7,5,3,6,4,1]=>1111100
[8,4,1,3,6,7,2,5]=>1101000
[8,7,2,3,1,5,6,4]=>1101001
[1,2,8,6,7,5,4,3]=>0011110
[2,8,5,7,6,1,3,4]=>1000110
[1,8,7,2,6,4,5,3]=>0111001
[8,7,2,1,6,4,5,3]=>1111001
[8,7,2,4,3,6,5,1]=>1110101
[4,2,8,7,3,6,5,1]=>1110101
[8,7,1,6,4,3,5,2]=>1111001
[8,4,1,7,3,6,5,2]=>1111100
[4,5,1,8,7,3,6,2]=>1110001
[4,3,8,5,2,6,1,7]=>1110100
[4,3,8,5,2,7,1,6]=>1110100
[5,6,8,2,3,4,1,7]=>1100000
[3,6,4,7,5,2,1,8]=>1101100
[5,7,4,1,2,6,8,3]=>1011000
[2,8,6,7,5,3,1,4]=>1010110
[7,4,5,2,6,3,1,8]=>1111000
[8,4,5,3,6,1,7,2]=>1111000
[8,6,3,4,5,1,7,2]=>1110010
[8,6,3,5,4,1,7,2]=>1111010
[8,7,4,5,1,3,6,2]=>1101001
[8,4,5,2,6,1,7,3]=>1111000
[8,6,2,5,3,1,4,7]=>1110010
[8,4,7,3,1,2,5,6]=>1011000
[8,7,3,5,1,6,4,2]=>1111001
[8,6,2,3,5,1,7,4]=>1101010
[4,8,3,2,6,1,7,5]=>1110100
[5,2,6,3,7,8,4,1]=>1111000
[3,6,2,5,7,8,4,1]=>1101000
[2,7,4,6,8,3,5,1]=>1011000
[2,7,3,6,8,5,4,1]=>1011100
[3,7,6,8,1,5,4,2]=>1101010
[4,7,6,8,2,3,5,1]=>1100010
[3,7,5,6,8,2,4,1]=>1100100
[3,7,2,6,8,4,5,1]=>1101000
[1,5,7,6,8,4,2,3]=>0101010
[2,7,5,6,8,4,3,1]=>1011100
[3,7,6,8,5,1,4,2]=>1100110
[7,1,3,8,6,2,4,5]=>1100010
[2,7,1,8,6,5,3,4]=>1010110
[8,1,5,2,6,4,7,3]=>1111000
[5,3,4,7,6,2,1,8]=>1110010
[8,7,2,6,4,5,1,3]=>1101001
[3,1,2,8,7,5,4,6]=>1001101
[3,1,2,8,7,6,4,5]=>1001011
[7,1,4,6,8,5,3,2]=>1110100
[7,2,5,1,6,4,8,3]=>1111000
[2,7,1,5,6,4,8,3]=>1011000
[1,5,7,8,4,6,3,2]=>0111000
[1,4,8,5,7,6,3,2]=>0110110
[2,8,1,5,6,4,7,3]=>1011000
[8,2,1,5,6,4,7,3]=>1111000
[2,8,5,1,6,4,3,7]=>1011100
[3,7,2,8,1,5,6,4]=>1101000
[7,3,2,5,1,6,8,4]=>1111000
[8,7,2,1,3,6,5,4]=>1101101
[7,3,2,8,1,4,6,5]=>1110100
[2,7,8,1,5,4,3,6]=>1011000
[3,6,2,1,8,4,7,5]=>1101100
[4,5,2,6,7,3,8,1]=>1110000
[3,5,1,6,7,4,8,2]=>1101000
[6,5,8,1,4,3,7,2]=>1110100
[6,4,1,2,5,7,8,3]=>1011000
[6,1,5,4,2,7,3,8]=>1111000
[6,4,2,3,1,7,5,8]=>1101100
[4,6,1,3,5,7,2,8]=>1100000
[2,4,5,7,3,6,1,8]=>1010000
[3,4,6,1,8,2,7,5]=>1100100
[2,4,1,7,5,6,3,8]=>1010100
[5,3,1,4,7,6,2,8]=>1110010
[6,4,5,2,7,1,3,8]=>1101000
[7,4,3,5,1,6,2,8]=>1111000
[7,5,3,6,2,1,4,8]=>1110100
[6,4,3,7,1,8,2,5]=>1111000
[3,1,2,7,6,4,5,8]=>1001010
[5,1,2,7,6,3,4,8]=>1010010
[5,6,1,7,2,4,3,8]=>1110000
[2,6,5,7,1,3,4,8]=>1000100
[2,3,7,1,5,6,4,8]=>1001000
[5,6,1,3,2,4,7,8]=>1100000
[2,6,5,3,4,1,7,8]=>1010100
[2,6,1,3,5,4,7,8]=>1001000
[3,6,7,1,4,2,5,8]=>1100000
[3,6,5,2,7,1,4,8]=>1100100
[7,1,5,4,2,6,3,8]=>1111000
[4,6,1,5,2,8,7,3]=>1110001
[6,1,5,4,2,7,8,3]=>1111000
[4,6,1,5,2,7,8,3]=>1110000
[4,5,1,7,6,2,8,3]=>1110010
[2,8,6,5,1,3,7,4]=>1001110
[5,1,8,6,2,7,4,3]=>1111010
[3,6,8,2,7,5,1,4]=>1100100
[7,8,5,3,2,6,1,4]=>1110100
[6,8,3,2,7,5,1,4]=>1110100
[5,6,4,1,7,2,8,3]=>1111000
[3,8,6,1,5,7,4,2]=>1101010
[1,6,7,2,4,3,5,8]=>0110000
[8,1,3,2,4,6,5,7]=>1100100
[6,4,2,3,7,8,1,5]=>1101000
[5,4,3,1,7,2,8,6]=>1111010
[5,3,1,6,4,7,2,8]=>1111000
[6,5,2,4,1,7,8,3]=>1110100
[4,3,6,2,5,8,1,7]=>1110000
[1,6,2,7,8,4,5,3]=>0111000
[1,6,7,8,3,4,2,5]=>0110000
[7,2,1,8,3,6,4,5]=>1111000
[5,4,2,3,1,7,8,6]=>1101010
[2,1,3,8,6,4,7,5]=>1001110
[4,6,1,3,2,8,5,7]=>1100100
[4,6,5,3,8,2,1,7]=>1110100
[8,2,5,4,3,7,1,6]=>1111000
[5,8,4,3,7,6,2,1]=>1111010
[8,1,5,3,4,7,2,6]=>1110000
[6,1,8,7,4,5,3,2]=>1111001
[1,5,8,6,4,3,7,2]=>0111010
[2,5,8,6,4,3,7,1]=>1011010
[8,5,4,1,2,3,7,6]=>1001110
[8,5,2,4,1,3,7,6]=>1100110
[4,5,8,7,3,6,2,1]=>1110001
[5,8,6,4,2,1,7,3]=>1111010
[2,6,1,8,4,7,5,3]=>1011100
[5,3,8,6,1,2,7,4]=>1011010
[5,8,1,4,6,2,7,3]=>1110000
[6,3,2,8,4,5,1,7]=>1111000
[5,4,7,2,1,3,8,6]=>1101010
[8,4,6,5,2,7,3,1]=>1111100
[6,4,7,5,8,3,1,2]=>1011100
[4,6,7,5,1,8,3,2]=>1110100
[2,6,4,5,7,1,8,3]=>1011000
[4,1,7,6,5,2,8,3]=>1110110
[3,7,4,6,1,5,8,2]=>1101000
[3,4,6,5,2,8,1,7]=>1100100
[4,6,7,5,8,2,1,3]=>1100100
[6,4,7,1,2,3,8,5]=>1001100
[8,2,3,1,6,4,7,5]=>1101100
[3,1,8,5,7,2,6,4]=>1101100
[5,6,4,2,1,7,3,8]=>1111000
[6,5,7,1,2,8,3,4]=>1010100
[6,4,7,1,2,5,3,8]=>1011000
[5,7,6,3,1,2,8,4]=>1011010
[1,2,4,8,5,7,3,6]=>0010100
[1,2,7,5,8,6,3,4]=>0010110
[7,4,5,1,6,8,2,3]=>1101000
[1,7,8,4,2,6,3,5]=>0111000
[6,3,2,5,7,4,1,8]=>1111000
[6,4,7,5,3,8,1,2]=>1011100
[6,2,1,5,3,7,8,4]=>1111000
[7,5,6,1,4,3,8,2]=>1110100
[4,1,7,8,3,6,5,2]=>1110100
[6,3,2,4,8,5,1,7]=>1110100
[6,4,2,1,7,3,5,8]=>1111000
[5,7,4,2,1,6,3,8]=>1111000
[5,8,4,2,1,3,6,7]=>1101000
[2,7,3,8,5,6,4,1]=>1011100
[8,3,2,6,5,1,7,4]=>1111100
[1,8,5,6,4,3,7,2]=>0111100
[1,7,5,8,4,6,3,2]=>0111100
[8,3,5,6,1,7,2,4]=>1110000
[1,5,3,7,8,4,6,2]=>0111000
[1,4,7,3,5,8,6,2]=>0110010
[1,6,3,7,8,5,4,2]=>0111100
[8,5,6,1,7,4,2,3]=>1101100
[8,6,1,4,3,7,2,5]=>1110010
[3,7,8,2,5,1,6,4]=>1101000
[8,1,3,5,6,4,2,7]=>1101000
[8,6,1,4,3,2,7,5]=>1110110
[7,3,8,2,4,1,5,6]=>1110000
[6,3,7,8,1,2,5,4]=>1011000
[7,5,8,1,2,3,6,4]=>1001100
[8,6,1,5,3,7,2,4]=>1110010
[8,1,7,5,6,4,2,3]=>1101100
[8,1,4,7,6,5,2,3]=>1100110
[6,1,4,8,2,7,5,3]=>1110100
[4,6,8,5,1,2,7,3]=>1010100
[2,8,4,6,1,3,7,5]=>1001100
[5,2,7,8,4,1,3,6]=>1101000
[4,6,8,5,3,1,2,7]=>1010100
[8,6,4,2,7,3,5,1]=>1111010
[6,8,7,5,2,1,3,4]=>1100101
[7,6,1,5,2,3,8,4]=>1101010
[5,1,8,6,7,2,3,4]=>1100010
[5,7,1,6,8,2,3,4]=>1100000
[5,1,7,6,8,2,3,4]=>1100010
[6,1,5,7,2,8,3,4]=>1110000
[6,8,4,2,1,7,3,5]=>1111000
[5,8,6,1,7,2,3,4]=>1100010
[6,3,2,8,1,7,4,5]=>1111000
[1,4,7,8,3,5,2,6]=>0110000
[2,5,6,8,1,4,7,3]=>1010000
[8,4,5,1,6,7,2,3]=>1101000
[7,3,6,1,4,2,8,5]=>1110100
[7,4,1,6,5,2,3,8]=>1101100
[4,1,6,5,2,3,8,7]=>1100101
[4,5,1,7,8,6,2,3]=>1100010
[8,3,1,4,6,2,7,5]=>1110100
[2,5,3,4,6,8,1,7]=>1010000
[8,3,6,1,5,2,4,7]=>1110000
[4,7,1,2,5,6,3,8]=>1010000
[6,7,3,1,8,2,4,5]=>1110000
[7,3,1,4,6,2,8,5]=>1110100
[7,4,1,2,5,6,3,8]=>1011000
[4,5,1,3,6,8,7,2]=>1100001
[8,4,1,2,5,7,3,6]=>1011000
[8,4,1,3,6,7,5,2]=>1101100
[5,4,1,6,3,7,8,2]=>1111000
[6,7,3,1,5,2,4,8]=>1110000
[5,4,1,3,6,8,7,2]=>1101001
[6,4,1,2,5,8,3,7]=>1011000
[5,7,4,8,1,6,3,2]=>1111000
[7,5,3,6,4,2,1,8]=>1111100
[4,3,1,2,6,5,7,8]=>1010100
[4,3,1,2,5,7,6,8]=>1010010
[4,7,3,1,5,2,8,6]=>1110010
[8,3,6,5,7,4,2,1]=>1111100
[8,2,6,5,7,4,3,1]=>1111100
[8,1,4,2,6,5,7,3]=>1110100
[8,4,7,1,5,2,6,3]=>1111000
[8,2,6,3,7,4,5,1]=>1111000
[8,2,6,3,7,5,4,1]=>1111100
[8,2,5,3,7,6,4,1]=>1111010
[8,6,7,1,4,3,5,2]=>1110010
[8,5,7,1,4,3,6,2]=>1110100
[4,5,3,6,8,7,1,2]=>1010001
[6,5,1,2,7,4,8,3]=>1011100
[6,8,5,1,7,3,4,2]=>1110100
[5,3,8,1,4,2,7,6]=>1110010
[6,5,3,4,1,8,2,7]=>1110100
[3,1,8,4,2,7,6,5]=>1101110
[2,8,7,4,1,3,6,5]=>1001101
[8,2,3,1,7,6,4,5]=>1101010
[5,2,4,1,6,8,3,7]=>1110000
[8,7,2,3,1,6,4,5]=>1101001
[6,2,3,1,7,8,4,5]=>1101000
[7,2,5,8,3,1,4,6]=>1110000
[6,8,2,3,1,7,4,5]=>1101000
[8,2,5,7,3,1,4,6]=>1110000
[2,5,8,7,3,1,4,6]=>1010001
[2,8,7,3,1,4,5,6]=>1010001
[8,2,3,1,6,7,4,5]=>1101000
[2,8,4,1,3,6,7,5]=>1001100
[2,7,3,1,4,5,8,6]=>1010010
[7,2,8,3,1,4,5,6]=>1110000
[2,7,8,3,1,4,5,6]=>1010000
[5,3,2,8,7,1,6,4]=>1111001
[6,8,7,2,1,5,4,3]=>1111001
[8,2,5,4,1,6,7,3]=>1111000
[7,2,4,6,8,1,5,3]=>1110000
[6,2,5,4,7,8,1,3]=>1101000
[6,3,5,2,7,1,4,8]=>1110000
[8,5,6,3,7,2,1,4]=>1110100
[3,8,2,6,1,7,4,5]=>1101000
[5,7,1,3,6,2,4,8]=>1100000
[3,6,4,1,2,5,7,8]=>1001000
[3,6,4,1,2,5,8,7]=>1001001
[4,7,1,3,2,5,8,6]=>1100010
[4,7,1,3,2,6,8,5]=>1100100
[5,7,1,3,6,2,8,4]=>1101000
[6,8,2,5,7,3,1,4]=>1110000
[4,8,5,2,3,6,1,7]=>1100100
[5,8,6,3,4,7,2,1]=>1110010
[3,7,5,4,2,8,1,6]=>1101100
[4,6,5,1,7,8,2,3]=>1100100
[4,7,1,3,2,8,5,6]=>1100100
[3,6,5,1,8,2,4,7]=>1100100
[5,8,7,3,4,2,6,1]=>1110001
[3,8,5,4,2,1,6,7]=>1101100
[4,8,5,3,6,1,7,2]=>1110100
[6,3,1,5,4,8,2,7]=>1111000
[8,4,2,6,5,7,3,1]=>1111100
[4,7,6,3,5,2,8,1]=>1110010
[1,7,5,3,4,8,6,2]=>0110110
[4,8,6,2,5,7,3,1]=>1110010
[8,7,3,2,6,4,5,1]=>1111001
[8,3,1,4,7,5,2,6]=>1110100
[5,3,1,6,4,8,7,2]=>1111001
[3,4,8,5,7,2,6,1]=>1100100
[4,1,7,8,3,2,5,6]=>1110000
[8,5,1,2,7,6,4,3]=>1011110
[4,6,5,3,1,8,7,2]=>1110101
[8,1,6,7,4,5,3,2]=>1111000
[6,4,8,1,5,3,7,2]=>1111000
[6,4,7,2,5,3,1,8]=>1111000
[4,3,6,1,2,7,8,5]=>1010100
[2,7,4,6,3,8,1,5]=>1011000
[7,3,5,6,4,1,8,2]=>1111000
[5,7,6,3,4,2,1,8]=>1110010
[3,7,5,6,4,2,1,8]=>1101100
[5,7,3,6,4,2,1,8]=>1111000
[5,7,3,6,4,1,8,2]=>1111000
[3,7,5,6,4,1,8,2]=>1101100
[5,7,6,3,4,1,8,2]=>1110010
[3,2,7,5,6,1,8,4]=>1101100
[5,3,4,7,6,1,8,2]=>1110010
[5,3,4,2,7,1,8,6]=>1110010
[3,5,4,1,7,8,6,2]=>1101010
[2,4,6,5,1,8,7,3]=>1010101
[2,4,6,5,1,8,3,7]=>1010100
[2,4,6,1,8,7,3,5]=>1010001
[2,4,6,5,8,3,7,1]=>1010100
[2,4,6,8,5,3,1,7]=>1010100
[2,4,6,8,5,3,7,1]=>1010100
[2,4,6,8,5,7,3,1]=>1010100
[2,4,6,5,3,8,1,7]=>1010100
[2,4,6,5,8,7,1,3]=>1000101
[2,4,6,8,7,5,1,3]=>1000101
[2,4,6,8,5,7,1,3]=>1000100
[2,4,6,8,7,1,5,3]=>1010001
[2,4,6,8,7,1,3,5]=>1000001
[2,4,6,8,1,7,3,5]=>1010000
[2,7,6,4,3,8,5,1]=>1011110
[2,6,7,5,3,8,1,4]=>1010100
[3,6,7,5,8,2,4,1]=>1100100
[4,5,2,6,8,7,1,3]=>1100001
[4,5,2,6,8,3,1,7]=>1110000
[4,5,3,6,8,2,1,7]=>1110000
[3,1,2,7,5,8,4,6]=>1001100
[4,8,1,6,2,5,3,7]=>1110000
[1,5,8,3,4,6,2,7]=>0110000
[7,5,8,2,4,3,6,1]=>1110100
[8,1,5,3,4,6,2,7]=>1110000
[8,1,2,4,7,5,6,3]=>1010100
[2,7,3,8,4,5,6,1]=>1011000
[1,7,8,6,4,5,3,2]=>0111010
[5,8,7,2,4,3,6,1]=>1110001
[1,8,2,4,7,5,6,3]=>0110100
[1,7,2,4,8,5,6,3]=>0110100
[5,8,2,3,7,4,6,1]=>1101000
[7,8,2,3,5,4,6,1]=>1101000
[8,4,1,3,2,6,5,7]=>1101100
[2,8,3,1,4,6,5,7]=>1010100
[8,7,2,3,5,4,6,1]=>1101001
[1,7,6,8,4,5,3,2]=>0111010
[8,5,2,3,7,4,6,1]=>1101100
[7,4,1,3,8,5,6,2]=>1101100
[2,7,3,1,8,5,6,4]=>1011100
[2,8,6,1,5,7,4,3]=>1011010
[8,3,5,1,7,6,4,2]=>1111010
[8,3,5,4,7,1,6,2]=>1111000
[6,4,1,5,7,8,2,3]=>1101000
[8,4,1,5,6,2,7,3]=>1111000
[1,8,5,3,2,4,6,7]=>0110100
[4,8,5,1,2,3,6,7]=>1000100
[3,5,1,4,2,6,8,7]=>1100001
[4,8,7,1,2,5,3,6]=>1010001
[8,7,2,6,1,4,3,5]=>1110001
[1,7,6,8,4,2,3,5]=>0101010
[1,7,4,8,2,5,3,6]=>0111000
[6,1,7,3,8,2,4,5]=>1110000
[1,5,8,2,3,4,7,6]=>0100010
[8,4,2,7,1,3,6,5]=>1101100
[7,1,8,6,4,2,3,5]=>1101010
[1,7,8,6,4,2,3,5]=>0101010
[3,1,2,5,7,6,8,4]=>1001010
[7,1,3,2,4,6,8,5]=>1100100
[7,4,2,3,1,6,8,5]=>1101100
[5,1,7,3,2,6,8,4]=>1111000
[4,8,2,3,7,5,1,6]=>1100100
[6,8,5,3,4,2,1,7]=>1110100
[8,7,2,4,3,5,6,1]=>1110001
[8,1,3,6,4,5,2,7]=>1101000
[8,1,3,7,4,5,6,2]=>1101000
[8,1,3,2,7,5,4,6]=>1101100
[8,1,2,4,7,3,5,6]=>1010000
[7,1,2,4,8,3,5,6]=>1010000
[7,6,2,8,4,5,1,3]=>1101010
[8,7,5,3,2,6,4,1]=>1111101
[4,8,3,2,5,1,6,7]=>1110000
[4,3,8,5,1,2,7,6]=>1010110
[3,1,8,4,5,2,7,6]=>1101010
[8,3,6,2,1,5,4,7]=>1111000
[8,2,1,6,5,3,4,7]=>1110100
[2,3,7,6,1,8,4,5]=>1001010
[4,7,8,2,1,3,5,6]=>1100000
[4,8,5,2,1,3,7,6]=>1100110
[2,3,7,4,1,8,6,5]=>1001110
[5,8,4,2,1,3,7,6]=>1101010
[4,5,2,3,8,7,1,6]=>1100001
[4,6,7,5,2,3,1,8]=>1100100
[6,5,2,3,1,8,7,4]=>1101101
[6,2,5,3,1,8,7,4]=>1111001
[6,2,5,3,8,7,1,4]=>1110001
[6,4,5,3,8,7,1,2]=>1011001
[1,6,4,5,8,7,3,2]=>0111001
[8,4,7,5,2,3,1,6]=>1101100
[8,2,7,4,5,3,1,6]=>1111000
[6,2,4,7,5,3,1,8]=>1110100
[8,2,4,7,5,3,1,6]=>1110100
[8,2,6,7,5,3,1,4]=>1110100
[8,4,6,7,5,3,1,2]=>1011100
[6,4,5,8,7,3,1,2]=>1011001
[6,2,8,7,5,3,1,4]=>1110101
[2,4,8,7,5,3,1,6]=>1010101
[4,6,8,7,5,3,1,2]=>1010101
[4,6,5,3,8,7,1,2]=>1010101
[2,6,5,8,7,3,1,4]=>1010101
[6,7,2,4,5,3,1,8]=>1110000
[4,5,8,7,2,3,1,6]=>1100001
[4,8,7,2,5,3,1,6]=>1110001
[6,8,7,4,5,3,1,2]=>1011001
[2,8,4,7,5,3,1,6]=>1011100
[4,8,2,7,5,3,1,6]=>1110100
[6,8,2,7,5,3,1,4]=>1110100
[7,4,3,8,1,6,5,2]=>1111100
[3,7,4,6,2,1,8,5]=>1101100
[2,6,5,7,8,3,1,4]=>1010100
[3,4,8,6,2,1,7,5]=>1100110
[1,6,2,3,8,5,7,4]=>0101100
[1,2,7,3,8,5,6,4]=>0011100
[2,3,6,5,8,4,7,1]=>1001100
[3,4,2,6,8,5,7,1]=>1100100
[2,4,7,3,8,5,1,6]=>1010100
[1,2,8,3,5,4,7,6]=>0011010
[1,3,6,7,4,5,8,2]=>0101000
[7,4,1,3,6,8,2,5]=>1101000
[5,1,7,3,4,6,8,2]=>1110000
[6,1,7,3,5,8,2,4]=>1110000
[6,8,1,2,7,3,4,5]=>1010000
[5,6,2,1,8,3,4,7]=>1110000
[6,4,1,3,7,8,2,5]=>1101000
[1,6,2,8,7,3,4,5]=>0110001
[5,2,8,4,7,1,3,6]=>1101000
[3,8,7,2,6,1,4,5]=>1100001
[2,5,1,8,3,6,4,7]=>1011000
[2,3,8,1,4,6,5,7]=>1000100
[1,3,8,2,5,4,7,6]=>0101010
[3,1,8,4,6,2,5,7]=>1101000
[6,3,2,4,8,7,1,5]=>1110001
[1,4,8,6,2,3,5,7]=>0100010
[3,1,8,4,5,6,2,7]=>1101000
[4,5,8,3,6,1,7,2]=>1110000
[3,5,4,8,6,1,7,2]=>1101010
[4,2,7,8,6,3,1,5]=>1110010
[7,1,4,2,8,6,3,5]=>1110010
[2,3,7,4,8,1,6,5]=>1001100
[1,6,2,7,4,5,3,8]=>0111000
[1,7,5,4,6,2,3,8]=>0101100
[5,2,8,6,3,1,4,7]=>1110010
[5,2,8,6,3,1,7,4]=>1111010
[7,1,5,6,3,2,8,4]=>1111000
[6,2,7,5,3,1,4,8]=>1110100
[6,1,7,4,8,5,2,3]=>1101100
[8,2,4,6,3,1,7,5]=>1110100
[8,3,1,2,5,4,7,6]=>1011010
[6,5,1,2,8,4,7,3]=>1011100
[8,1,5,3,7,4,2,6]=>1111000
[1,3,4,8,6,2,7,5]=>0100110
[1,2,4,8,6,7,3,5]=>0010010
[8,1,2,6,5,7,3,4]=>1010100
[7,1,2,6,5,8,3,4]=>1010100
[7,1,6,8,3,2,4,5]=>1110000
[7,4,8,3,5,6,2,1]=>1111000
[2,6,1,4,7,5,8,3]=>1010100
[5,1,4,3,7,8,6,2]=>1110010
[6,4,1,3,7,8,5,2]=>1101100
[3,1,5,7,2,6,8,4]=>1101000
[7,2,4,8,5,1,6,3]=>1110100
[3,1,7,5,2,6,8,4]=>1101100
[3,2,7,5,1,6,8,4]=>1101100
[5,2,7,3,1,6,8,4]=>1111000
[6,7,2,1,3,4,8,5]=>1100100
[4,6,3,1,2,7,8,5]=>1010100
[6,7,3,1,2,4,8,5]=>1010100
[3,8,5,2,1,6,7,4]=>1101100
[6,8,2,3,5,7,4,1]=>1101000
[5,3,8,4,6,7,2,1]=>1111000
[6,2,8,1,7,4,5,3]=>1111000
[4,2,6,7,8,5,3,1]=>1110100
[4,3,5,8,6,7,2,1]=>1110010
[6,2,4,7,8,5,3,1]=>1110100
[3,2,7,8,5,6,4,1]=>1101100
[4,7,3,8,5,6,2,1]=>1110100
[7,1,4,8,5,6,3,2]=>1110100
[4,3,8,7,2,5,6,1]=>1110001
[1,7,3,8,6,4,5,2]=>0111010
[3,4,8,2,6,7,5,1]=>1100100
[1,2,6,8,7,4,5,3]=>0011001
[1,6,3,8,7,4,5,2]=>0111001
[1,4,5,8,7,6,2,3]=>0100011
[6,4,7,8,3,5,1,2]=>1011000
[6,4,7,8,1,2,5,3]=>1011000
[3,5,6,7,1,8,4,2]=>1101000
[1,7,4,5,2,8,6,3]=>0111010
[1,7,3,8,2,5,4,6]=>0111000
[2,7,8,3,6,1,5,4]=>1011000
[1,7,8,3,6,2,5,4]=>0111000
[1,4,7,5,8,3,6,2]=>0110100
[3,4,7,5,8,2,1,6]=>1100100
[7,2,6,4,1,8,5,3]=>1111100
[7,4,3,5,8,1,6,2]=>1111000
[7,3,6,4,1,8,5,2]=>1111100
[7,8,4,3,6,1,5,2]=>1111000
[7,1,6,4,3,8,5,2]=>1111100
[8,7,3,4,1,5,2,6]=>1110001
[7,2,6,4,3,8,5,1]=>1111100
[1,7,5,4,3,8,2,6]=>0111100
[8,6,4,5,1,3,7,2]=>1101010
[7,5,8,4,1,3,6,2]=>1101100
[4,7,5,3,6,8,1,2]=>1010100
[4,8,5,3,7,1,2,6]=>1010100
[2,8,1,6,5,7,3,4]=>1010100
[4,7,5,3,8,1,6,2]=>1110100
[7,4,8,5,3,6,1,2]=>1011100
[7,4,5,3,8,1,6,2]=>1111000
[8,4,6,5,1,3,7,2]=>1101100
[6,3,5,8,1,7,4,2]=>1111000
[7,3,6,1,5,8,4,2]=>1111000
[4,5,3,8,7,1,2,6]=>1010001
[8,5,4,7,6,1,2,3]=>1001110
[3,7,6,1,5,8,4,2]=>1101010
[8,2,3,6,4,1,7,5]=>1101100
[2,7,3,6,4,1,8,5]=>1011100
[2,3,7,8,1,4,6,5]=>1000100
[2,7,3,5,4,1,8,6]=>1011010
[8,2,3,5,4,1,7,6]=>1101010
[7,1,3,8,2,4,6,5]=>1100100
[7,2,3,6,4,1,8,5]=>1101100
[6,5,2,4,1,8,3,7]=>1110100
[5,7,2,4,1,3,8,6]=>1100010
[6,2,5,4,1,8,3,7]=>1111000
[8,1,2,5,3,7,6,4]=>1011010
[1,6,4,3,7,5,2,8]=>0111100
[1,6,7,5,4,8,2,3]=>0101100
[1,8,5,4,2,6,3,7]=>0111100
[4,2,8,1,5,7,6,3]=>1110010
[6,7,3,5,4,1,2,8]=>1011000
[5,7,3,6,2,1,4,8]=>1110000
[5,6,8,4,2,7,1,3]=>1101000
[6,8,7,3,2,1,5,4]=>1111001
[3,6,8,7,2,4,1,5]=>1100001
[3,7,6,4,2,8,1,5]=>1101010
[2,8,6,4,7,3,5,1]=>1011010
[3,8,6,4,2,7,1,5]=>1101010
[5,7,3,6,2,1,8,4]=>1111000
[2,4,8,6,5,7,3,1]=>1010110
[3,6,5,2,4,8,1,7]=>1100100
[4,6,3,2,5,1,8,7]=>1110001
[8,3,6,5,4,2,1,7]=>1111100
[5,4,8,7,6,2,3,1]=>1101011
[6,8,4,7,5,1,3,2]=>1101100
[6,5,8,3,7,1,4,2]=>1110100
[7,4,6,1,5,3,8,2]=>1111000
[6,1,5,4,7,3,8,2]=>1111000
[7,1,5,4,6,3,8,2]=>1111000
[2,5,4,7,1,8,3,6]=>1011000
[1,5,4,7,3,8,2,6]=>0111000
[1,5,6,8,3,2,4,7]=>0110000
[1,2,6,7,3,5,4,8]=>0011000
[1,5,6,7,2,4,3,8]=>0110000
[1,7,2,5,6,8,3,4]=>0110000
[4,1,7,5,6,8,2,3]=>1100100
[5,7,3,4,2,8,6,1]=>1110010
[5,8,3,4,2,7,6,1]=>1110010
[7,6,4,2,3,8,5,1]=>1101110
[7,3,8,4,2,6,5,1]=>1111100
[3,5,6,8,2,4,7,1]=>1100000
[8,4,7,3,2,5,6,1]=>1111000
[4,8,7,3,2,5,6,1]=>1110001
[8,5,7,3,2,4,6,1]=>1110100
[3,7,4,2,6,8,5,1]=>1101100
[7,2,8,4,5,6,3,1]=>1111000
[6,2,8,3,7,4,5,1]=>1111000
[4,3,7,8,6,2,5,1]=>1110010
[1,5,8,3,2,7,4,6]=>0111000
[8,1,4,3,6,7,2,5]=>1110000
[8,3,1,4,6,7,2,5]=>1110000
[7,8,5,1,2,6,3,4]=>1010100
[8,3,6,7,5,1,2,4]=>1010100
[7,6,4,2,5,3,1,8]=>1111010
[1,8,6,5,2,7,4,3]=>0111110
[8,2,6,5,1,7,4,3]=>1111100
[6,1,4,7,2,5,8,3]=>1110000
[6,8,2,5,1,7,4,3]=>1111000
[1,6,4,7,2,5,8,3]=>0111000
[7,6,4,1,2,5,8,3]=>1011010
[6,8,1,5,2,7,4,3]=>1111000
[8,6,5,2,1,7,4,3]=>1111110
[1,6,5,2,8,7,4,3]=>0111101
[1,8,5,2,7,6,4,3]=>0111110
[1,8,6,7,2,5,4,3]=>0111010
[1,7,6,8,2,5,4,3]=>0111010
[1,7,8,6,2,5,4,3]=>0111010
[8,1,7,6,2,5,4,3]=>1111010
[5,2,4,7,3,8,6,1]=>1110010
[1,5,6,3,2,8,7,4]=>0111001
[4,6,5,7,1,8,2,3]=>1100100
[6,7,5,3,8,2,1,4]=>1110100
[7,2,5,6,4,8,3,1]=>1111000
[7,4,6,2,8,5,3,1]=>1111100
[7,2,6,3,8,5,4,1]=>1111100
[1,2,6,5,3,8,4,7]=>0011100
[6,5,3,4,8,2,1,7]=>1110100
[1,7,8,6,3,5,4,2]=>0111010
[1,4,2,3,7,8,6,5]=>0100110
[1,8,4,2,3,6,5,7]=>0101100
[1,3,8,5,6,4,2,7]=>0101100
[1,6,3,7,8,4,2,5]=>0111000
[1,6,3,8,4,2,5,7]=>0111000
[1,7,8,4,2,3,5,6]=>0101000
[1,7,8,5,6,4,2,3]=>0101100
[1,6,3,4,2,5,8,7]=>0110001
[1,3,5,8,6,4,2,7]=>0101010
[1,7,6,2,3,8,4,5]=>0101010
[1,5,7,6,2,3,8,4]=>0101010
[1,3,7,6,2,4,5,8]=>0100010
[1,4,3,7,6,2,5,8]=>0110010
[1,5,8,4,3,7,6,2]=>0111010
[1,7,5,8,4,3,6,2]=>0111100
[4,1,5,7,3,8,2,6]=>1110000
[1,3,7,4,6,8,5,2]=>0101100
[1,5,2,6,8,7,4,3]=>0111001
[1,3,7,6,4,8,2,5]=>0101010
[6,5,1,4,3,8,7,2]=>1110101
[5,6,1,4,3,8,7,2]=>1110001
[5,8,6,4,3,1,7,2]=>1111010
[4,1,3,7,8,6,5,2]=>1100110
[8,5,6,4,3,1,7,2]=>1111100
[8,4,3,1,7,6,5,2]=>1111110
[3,2,7,1,8,6,5,4]=>1101110
[2,1,4,3,6,5,8,7,10,9]=>101010101
[2,4,6,8,10,1,3,5,7,9]=>100000000
[10,9,8,7,6,1,2,3,4,5]=>100001111
[9,10,7,8,5,6,3,4,1,2]=>101010100
[5,4,3,2,1,6,7,8,9,10]=>111100000
[6,4,3,2,7,1,5,8,9,10]=>111100000
[7,5,3,8,2,6,1,4,9,10]=>111010000
[8,6,9,4,7,2,5,1,3,10]=>110101000
[6,7,8,9,10,5,4,3,2,1]=>111110000
[5,7,8,9,4,10,6,3,2,1]=>111101000
[4,6,8,3,9,5,10,7,2,1]=>111010100
[3,5,2,7,4,9,6,10,8,1]=>110101010
[3,1,5,2,7,4,9,6,8,10]=>110101000
[1,2,3,4,5,10,9,8,7,6]=>000001111
[10,9,8,5,1,7,2,3,4,6]=>110010011
[10,9,4,1,6,2,8,3,5,7]=>111100001
[10,3,1,5,2,7,4,9,6,8]=>111101000
[1,4,2,6,3,8,5,10,7,9]=>011010100
[10,8,6,4,2,1,3,5,7,9]=>110101010
[6,5,4,3,7,8,9,10,1,2]=>101110000
[10,1,2,3,4,6,7,8,9,5]=>100010000
[2,1,7,8,9,10,6,5,4,3]=>101111000
[9,8,7,6,1,2,3,4,5,10]=>100001110
[3,2,5,4,7,6,9,8,1,10]=>110101010
[1,4,3,6,5,8,7,10,9,2]=>011010101
[3,4,2,1,6,5,8,7,10,9]=>110010101
[3,5,2,6,4,1,8,7,10,9]=>110100101
[3,5,2,7,4,8,6,1,10,9]=>110101001
[2,1,5,6,4,3,8,7,10,9]=>101100101
[4,5,6,3,2,1,8,7,10,9]=>111000101
[4,5,7,3,2,8,6,1,10,9]=>111001001
[4,5,7,3,2,9,6,10,8,1]=>111001010
[2,1,5,7,4,8,6,3,10,9]=>101101001
[4,6,7,3,8,5,2,1,10,9]=>111010001
[4,6,7,3,9,5,2,10,8,1]=>111010010
[2,1,5,7,4,9,6,10,8,3]=>101101010
[2,1,4,3,7,8,6,5,10,9]=>101011001
[3,4,2,1,7,8,6,5,10,9]=>110011001
[3,6,2,7,8,5,4,1,10,9]=>110110001
[3,6,2,7,9,5,4,10,8,1]=>110110010
[2,1,6,7,8,5,4,3,10,9]=>101110001
[5,6,7,8,4,3,2,1,10,9]=>111100001
[5,6,7,9,4,3,2,10,8,1]=>111100010
[2,1,6,7,9,5,4,10,8,3]=>101110010
[5,6,8,9,4,3,10,7,2,1]=>111100100
[2,1,4,3,7,9,6,10,8,5]=>101011010
[3,4,2,1,7,9,6,10,8,5]=>110011010
[3,6,2,8,9,5,10,7,4,1]=>110110100
[2,1,6,8,9,5,10,7,4,3]=>101110100
[2,1,4,3,6,5,9,10,8,7]=>101010110
[3,4,2,1,6,5,9,10,8,7]=>110010110
[3,5,2,6,4,1,9,10,8,7]=>110100110
[3,5,2,8,4,9,10,7,6,1]=>110101100
[2,1,5,6,4,3,9,10,8,7]=>101100110
[4,5,6,3,2,1,9,10,8,7]=>111000110
[4,5,8,3,2,9,10,7,6,1]=>111001100
[2,1,5,8,4,9,10,7,6,3]=>101101100
[4,7,8,3,9,10,6,5,2,1]=>111011000
[2,1,4,3,8,9,10,7,6,5]=>101011100
[3,4,2,1,8,9,10,7,6,5]=>110011100
[3,7,2,8,9,10,6,5,4,1]=>110111000
[7,8,10,9,5,6,3,4,1,2]=>101010001
[9,10,5,6,8,7,3,4,1,2]=>101010100
[5,8,10,6,9,7,3,4,1,2]=>101001100
[5,6,7,10,9,8,3,4,1,2]=>101000011
[9,10,7,8,3,4,6,5,1,2]=>101010100
[7,8,10,9,3,4,6,5,1,2]=>101010001
[9,10,3,6,8,4,7,5,1,2]=>101110000
[3,8,10,6,9,4,7,5,1,2]=>100111000
[3,6,7,10,9,4,8,5,1,2]=>100110001
[9,10,3,4,5,8,7,6,1,2]=>101001100
[3,8,10,4,5,9,7,6,1,2]=>100101100
[3,4,7,10,5,9,8,6,1,2]=>100011010
[3,4,5,6,10,9,8,7,1,2]=>100000111
[9,10,7,8,5,6,1,2,4,3]=>101010100
[7,8,10,9,5,6,1,2,4,3]=>101010001
[9,10,5,6,8,7,1,2,4,3]=>101010100
[5,8,10,6,9,7,1,2,4,3]=>101001100
[5,6,7,10,9,8,1,2,4,3]=>101000011
[9,10,7,8,1,4,6,2,5,3]=>111000100
[7,8,10,9,1,4,6,2,5,3]=>111000001
[9,10,1,6,8,4,7,2,5,3]=>111100000
[1,8,10,6,9,4,7,2,5,3]=>011101000
[1,6,7,10,9,4,8,2,5,3]=>011100001
[9,10,1,4,5,8,7,2,6,3]=>111000100
[1,8,10,4,5,9,7,2,6,3]=>011100100
[1,4,7,10,5,9,8,2,6,3]=>011010010
[1,4,5,6,10,9,8,2,7,3]=>011000011
[9,10,7,8,1,2,3,6,5,4]=>100110100
[7,8,10,9,1,2,3,6,5,4]=>100110001
[9,10,1,6,8,2,3,7,5,4]=>110110000
[1,8,10,6,9,2,3,7,5,4]=>010111000
[1,6,7,10,9,2,3,8,5,4]=>010110001
[9,10,1,2,5,8,3,7,6,4]=>101101000
[1,8,10,2,5,9,3,7,6,4]=>011101000
[1,2,7,10,5,9,3,8,6,4]=>001111000
[1,2,5,6,10,9,3,8,7,4]=>001100101
[9,10,1,2,3,4,8,7,6,5]=>100011100
[1,8,10,2,3,4,9,7,6,5]=>010011100
[1,2,7,10,3,4,9,8,6,5]=>001011010
[1,2,3,6,10,4,9,8,7,5]=>000110110
[2,1,4,3,6,5,10,9,7,8]=>101010101
[2,1,4,3,8,7,5,6,10,9]=>101010101
[2,1,4,3,10,7,5,9,6,8]=>101011100
[2,1,4,3,10,9,8,5,6,7]=>101010011
[2,1,6,5,3,4,8,7,10,9]=>101010101
[2,1,6,5,3,4,10,9,7,8]=>101010101
[2,1,8,5,3,7,4,6,10,9]=>101110001
[2,1,10,5,3,7,4,9,6,8]=>101111000
[2,1,10,5,3,9,8,4,6,7]=>101110010
[2,1,8,7,6,3,4,5,10,9]=>101001101
[2,1,10,7,6,3,4,9,5,8]=>101011100
[2,1,10,9,6,3,8,4,5,7]=>101101001
[2,1,10,9,8,7,3,4,5,6]=>101000111
[4,3,1,2,6,5,8,7,10,9]=>101010101
[4,3,1,2,6,5,10,9,7,8]=>101010101
[4,3,1,2,8,7,5,6,10,9]=>101010101
[4,3,1,2,10,7,5,9,6,8]=>101011100
[4,3,1,2,10,9,8,5,6,7]=>101010011
[6,3,1,5,2,4,8,7,10,9]=>111000101
[6,3,1,5,2,4,10,9,7,8]=>111000101
[8,3,1,5,2,7,4,6,10,9]=>111100001
[10,3,1,5,2,9,8,4,6,7]=>111100010
[8,3,1,7,6,2,4,5,10,9]=>111001001
[10,3,1,7,6,2,4,9,5,8]=>111011000
[10,3,1,9,6,2,8,4,5,7]=>111101000
[10,3,1,9,8,7,2,4,5,6]=>111000110
[6,5,4,1,2,3,8,7,10,9]=>100110101
[6,5,4,1,2,3,10,9,7,8]=>100110101
[8,5,4,1,2,7,3,6,10,9]=>101110001
[10,5,4,1,2,7,3,9,6,8]=>101111000
[10,5,4,1,2,9,8,3,6,7]=>101110010
[8,7,4,1,6,2,3,5,10,9]=>110100101
[10,7,4,1,6,2,3,9,5,8]=>110110100
[10,9,4,1,8,7,2,3,5,6]=>110100101
[8,7,6,5,1,2,3,4,10,9]=>100011101
[10,7,6,5,1,2,3,9,4,8]=>100111100
[10,9,6,5,1,2,8,3,4,7]=>101011001
[9,10,7,8,5,6,2,1,3,4]=>110010100
[9,10,7,8,4,3,5,6,1,2]=>101100100
[9,10,7,8,4,2,5,1,3,6]=>110100100
[9,10,7,8,3,2,1,4,5,6]=>111000100
[9,10,6,5,7,8,3,4,1,2]=>101011000
[9,10,6,5,7,8,2,1,3,4]=>110011000
[9,10,6,4,7,3,5,8,1,2]=>101101000
[9,10,6,4,7,2,5,1,3,8]=>110101000
[9,10,6,3,7,2,1,4,5,8]=>111001000
[9,10,5,4,3,6,7,8,1,2]=>101110000
[9,10,5,4,2,6,7,1,3,8]=>110110000
[9,10,5,3,2,6,1,4,7,8]=>111010000
[9,10,4,3,2,1,5,6,7,8]=>111100000
[8,7,9,10,5,6,3,4,1,2]=>101010100
[8,7,9,10,5,6,2,1,3,4]=>110010100
[8,7,9,10,4,3,5,6,1,2]=>101100100
[8,7,9,10,4,2,5,1,3,6]=>110100100
[8,7,9,10,3,2,1,4,5,6]=>111000100
[8,6,9,5,7,10,3,4,1,2]=>101011000
[8,6,9,5,7,10,2,1,3,4]=>110011000
[8,6,9,4,7,3,5,10,1,2]=>101101000
[8,6,9,3,7,2,1,4,5,10]=>111001000
[8,5,9,4,3,6,7,10,1,2]=>101110000
[8,5,9,4,2,6,7,1,3,10]=>110110000
[8,5,9,3,2,6,1,4,7,10]=>111010000
[8,4,9,3,2,1,5,6,7,10]=>111100000
[7,6,5,8,9,10,3,4,1,2]=>101011000
[7,6,5,8,9,10,2,1,3,4]=>110011000
[7,6,4,8,9,3,5,10,1,2]=>101101000
[7,6,4,8,9,2,5,1,3,10]=>110101000
[7,6,3,8,9,2,1,4,5,10]=>111001000
[7,5,4,8,3,6,9,10,1,2]=>101110000
[7,5,4,8,2,6,9,1,3,10]=>110110000
[7,4,3,8,2,1,5,6,9,10]=>111100000
[6,5,4,2,7,8,9,1,3,10]=>110110000
[6,5,3,2,7,8,1,4,9,10]=>111010000
[3,2,5,4,7,6,1,10,8,9]=>110101010
[3,2,5,4,9,8,6,7,1,10]=>110101010
[3,2,5,4,1,8,6,10,7,9]=>110101100
[3,2,5,4,1,10,9,6,7,8]=>110101001
[3,2,7,6,4,5,9,8,1,10]=>110101010
[3,2,7,6,4,5,1,10,8,9]=>110101010
[3,2,9,6,4,8,5,7,1,10]=>110111000
[3,2,1,6,4,8,5,10,7,9]=>110110100
[3,2,1,6,4,10,9,5,7,8]=>110110001
[3,2,9,8,7,4,5,6,1,10]=>110100110
[3,2,1,8,7,4,5,10,6,9]=>110101100
[3,2,1,10,7,4,9,5,6,8]=>110110100
[3,2,1,10,9,8,4,5,6,7]=>110100011
[5,4,2,3,7,6,9,8,1,10]=>110101010
[5,4,2,3,7,6,1,10,8,9]=>110101010
[5,4,2,3,9,8,6,7,1,10]=>110101010
[5,4,2,3,1,8,6,10,7,9]=>110101100
[5,4,2,3,1,10,9,6,7,8]=>110101001
[7,4,2,6,3,5,9,8,1,10]=>111100010
[7,4,2,6,3,5,1,10,8,9]=>111100010
[9,4,2,6,3,8,5,7,1,10]=>111110000
[1,4,2,6,3,10,9,5,7,8]=>011010001
[9,4,2,8,7,3,5,6,1,10]=>111100100
[1,4,2,8,7,3,5,10,6,9]=>011001100
[1,4,2,10,7,3,9,5,6,8]=>011010100
[1,4,2,10,9,8,3,5,6,7]=>011000011
[7,6,5,2,3,4,9,8,1,10]=>110011010
[7,6,5,2,3,4,1,10,8,9]=>110011010
[9,6,5,2,3,8,4,7,1,10]=>110111000
[1,6,5,2,3,8,4,10,7,9]=>010110100
[1,6,5,2,3,10,9,4,7,8]=>010110001
[9,8,5,2,7,3,4,6,1,10]=>111010010
[1,8,5,2,7,3,4,10,6,9]=>011011000
[1,10,5,2,7,3,9,4,6,8]=>011110000
[1,10,5,2,9,8,3,4,6,7]=>011010010
[9,8,7,6,2,3,4,5,1,10]=>110001110
[1,8,7,6,2,3,4,10,5,9]=>010011100
[1,10,7,6,2,3,9,4,5,8]=>010101100
[1,10,9,6,2,8,3,4,5,7]=>011001001
[1,10,9,8,7,2,3,4,5,6]=>010000111
[2,1,4,3,6,5,8,10,9,7]=>101010101
[2,1,4,3,6,8,7,5,10,9]=>101010101
[2,1,4,3,8,10,7,9,5,6]=>101010100
[2,1,4,3,6,7,10,8,9,5]=>101010010
[2,1,4,6,5,3,8,7,10,9]=>101010101
[2,1,4,6,5,3,8,10,9,7]=>101010101
[2,1,6,8,5,7,3,4,10,9]=>101010001
[2,1,8,7,5,10,4,9,3,6]=>101110100
[2,1,6,7,5,10,8,4,9,3]=>101110010
[2,1,4,5,8,6,7,3,10,9]=>101001001
[2,1,8,5,10,6,7,9,3,4]=>101011000
[2,1,4,7,10,6,9,8,3,5]=>101001010
[2,1,4,5,6,10,7,8,9,3]=>101000100
[2,4,3,1,6,5,8,7,10,9]=>101010101
[2,4,3,1,6,5,8,10,9,7]=>101010101
[2,4,3,1,6,8,7,5,10,9]=>101010101
[2,4,3,1,8,10,7,9,5,6]=>101010100
[2,4,3,1,6,7,10,8,9,5]=>101010010
[4,6,3,5,1,2,8,7,10,9]=>101000101
[4,6,3,5,1,2,8,10,9,7]=>101000101
[6,5,3,8,2,7,1,4,10,9]=>111010001
[8,5,3,7,2,10,4,9,1,6]=>111110000
[6,5,3,7,2,10,8,4,9,1]=>111110010
[4,5,3,8,6,2,7,1,10,9]=>111001001
[8,6,3,5,10,2,7,9,1,4]=>111001000
[4,7,3,6,10,1,9,8,2,5]=>111000010
[4,5,3,6,10,7,1,8,9,2]=>111000100
[2,3,6,4,5,1,8,7,10,9]=>100100101
[2,3,6,4,5,1,8,10,9,7]=>100100101
[6,3,8,4,5,7,1,2,10,9]=>101100001
[8,3,7,4,5,10,2,9,1,6]=>111100000
[6,3,7,4,5,10,8,2,9,1]=>111100010
[2,5,8,4,7,6,1,3,10,9]=>100101001
[8,5,10,4,7,6,2,9,1,3]=>110111000
[2,7,10,4,8,6,9,5,1,3]=>100111000
[2,5,6,4,10,8,7,3,9,1]=>101100110
[2,3,4,8,5,6,7,1,10,9]=>100010001
[8,3,4,10,5,6,7,9,1,2]=>101010000
[2,7,4,10,5,6,9,8,1,3]=>100110010
[2,3,6,10,5,9,7,8,1,4]=>100010100
[2,3,4,5,10,6,7,8,9,1]=>100001000
[1,4,3,6,5,10,9,7,8,2]=>011010101
[1,4,3,8,7,5,6,10,9,2]=>011010101
[1,4,3,10,7,5,9,6,8,2]=>011011100
[1,4,3,10,9,8,5,6,7,2]=>011010011
[1,6,5,3,4,8,7,10,9,2]=>011010101
[1,6,5,3,4,10,9,7,8,2]=>011010101
[1,8,5,3,7,4,6,10,9,2]=>011110001
[1,10,5,3,7,4,9,6,8,2]=>011111000
[1,10,5,3,9,8,4,6,7,2]=>011110010
[1,8,7,6,3,4,5,10,9,2]=>011001101
[1,10,7,6,3,4,9,5,8,2]=>011011100
[1,10,9,6,3,8,4,5,7,2]=>011101001
[1,10,9,8,7,3,4,5,6,2]=>011000111
[3,1,2,6,5,8,7,10,9,4]=>100110101
[3,1,2,6,5,10,9,7,8,4]=>100110101
[3,1,2,8,7,5,6,10,9,4]=>100110101
[3,1,2,10,7,5,9,6,8,4]=>100111100
[3,1,2,10,9,8,5,6,7,4]=>100110011
[3,1,5,2,4,8,7,10,9,6]=>110001101
[3,1,5,2,4,10,9,7,8,6]=>110001101
[3,1,5,2,7,4,6,10,9,8]=>110100011
[3,1,5,2,9,8,4,6,7,10]=>110100010
[3,1,7,6,2,4,5,10,9,8]=>110001011
[3,1,7,6,2,4,9,5,8,10]=>110011000
[3,1,9,6,2,8,4,5,7,10]=>110101000
[3,1,9,8,7,2,4,5,6,10]=>110000110
[5,4,1,2,3,8,7,10,9,6]=>100101101
[5,4,1,2,3,10,9,7,8,6]=>100101101
[5,4,1,2,7,3,6,10,9,8]=>101100011
[5,4,1,2,7,3,9,6,8,10]=>101101000
[5,4,1,2,9,8,3,6,7,10]=>101100010
[7,4,1,6,2,3,5,10,9,8]=>110100011
[7,4,1,6,2,3,9,5,8,10]=>110110000
[9,4,1,6,2,8,3,5,7,10]=>111100000
[9,4,1,8,7,2,3,5,6,10]=>110100100
[7,6,5,1,2,3,4,10,9,8]=>100011011
[7,6,5,1,2,3,9,4,8,10]=>100111000
[9,6,5,1,2,8,3,4,7,10]=>101011000
[9,8,5,1,7,2,3,4,6,10]=>110010010
[9,10,6,4,2,1,3,5,8,7]=>110101100
[10,7,8,4,2,1,3,6,5,9]=>110110100
[9,7,10,4,2,1,3,6,8,5]=>110110100
[8,9,10,4,2,1,3,7,6,5]=>110111000
[10,8,5,6,2,1,4,3,7,9]=>111010010
[9,10,5,6,2,1,4,3,8,7]=>111010100
[10,7,5,8,2,1,4,6,3,9]=>111010100
[9,7,5,10,2,1,4,6,8,3]=>111010100
[8,9,5,10,2,1,4,7,6,3]=>111011000
[10,6,7,8,2,1,5,4,3,9]=>111101000
[9,6,7,10,2,1,5,4,8,3]=>111101000
[8,6,9,10,2,1,5,7,4,3]=>111101000
[7,8,9,10,2,1,6,5,4,3]=>111110000
[10,8,6,3,4,2,1,5,7,9]=>111001010
[9,10,6,3,4,2,1,5,8,7]=>111001100
[10,7,8,3,4,2,1,6,5,9]=>111010100
[9,7,10,3,4,2,1,6,8,5]=>111010100
[8,9,10,3,4,2,1,7,6,5]=>111011000
[10,8,5,3,6,2,4,1,7,9]=>111010010
[9,10,5,3,6,2,4,1,8,7]=>111010100
[10,7,5,3,8,2,4,6,1,9]=>111010100
[9,7,5,3,10,2,4,6,8,1]=>111010100
[8,9,5,3,10,2,4,7,6,1]=>111011000
[10,6,7,3,8,2,5,4,1,9]=>111101000
[9,6,7,3,10,2,5,4,8,1]=>111101000
[8,6,9,3,10,2,5,7,4,1]=>111101000
[7,8,9,3,10,2,6,5,4,1]=>111110000
[10,8,4,5,6,3,2,1,7,9]=>111100010
[9,10,4,5,6,3,2,1,8,7]=>111100100
[10,7,4,5,8,3,2,6,1,9]=>111100100
[9,7,4,5,10,3,2,6,8,1]=>111100100
[8,9,4,5,10,3,2,7,6,1]=>111101000
[10,6,4,7,8,3,5,2,1,9]=>111101000
[9,6,4,7,10,3,5,2,8,1]=>111101000
[8,6,4,9,10,3,5,7,2,1]=>111101000
[7,8,4,9,10,3,6,5,2,1]=>111110000
[10,5,6,7,8,4,3,2,1,9]=>111110000
[9,5,6,7,10,4,3,2,8,1]=>111110000
[8,5,6,9,10,4,3,7,2,1]=>111110000
[7,5,8,9,10,4,6,3,2,1]=>111110000
[9,10,2,4,6,8,1,3,5,7]=>110000000
[7,8,2,4,6,10,1,3,5,9]=>110000000
[9,7,10,2,4,6,8,1,3,5]=>110000100
[8,9,10,7,2,4,6,1,3,5]=>110000100
[5,6,2,4,8,10,1,3,7,9]=>110000000
[5,6,9,10,2,4,8,1,3,7]=>110000000
[7,5,8,2,4,6,10,1,3,9]=>110010000
[7,9,5,10,2,4,6,8,1,3]=>110010000
[5,8,9,10,7,2,4,6,1,3]=>110000100
[6,7,8,5,2,4,10,1,3,9]=>110010000
[9,6,7,5,10,2,4,8,1,3]=>110011000
[8,9,6,10,5,7,2,4,1,3]=>110011000
[7,8,9,10,6,5,2,4,1,3]=>110011000
[3,4,2,6,8,10,1,5,7,9]=>110000000
[3,4,9,10,2,6,8,1,5,7]=>110000000
[3,4,7,8,2,6,10,1,5,9]=>110000000
[9,3,4,7,10,2,6,8,1,5]=>111000000
[8,9,10,3,4,7,2,6,1,5]=>111000000
[5,3,6,2,4,8,10,1,7,9]=>111000000
[5,3,6,9,10,2,4,8,1,7]=>111000000
[5,7,3,8,2,4,6,10,1,9]=>111000000
[5,7,9,3,10,2,4,6,8,1]=>111000000
[8,5,9,10,3,7,2,4,6,1]=>111010000
[3,6,7,8,5,2,4,10,1,9]=>110010000
[9,3,6,7,5,10,2,4,8,1]=>111010000
[6,8,3,9,10,5,7,2,4,1]=>111010000
[7,8,9,10,3,6,5,2,4,1]=>111010000
[4,5,6,3,2,8,10,1,7,9]=>111000000
[4,5,6,3,9,10,2,8,1,7]=>111000000
[7,4,5,3,8,2,6,10,1,9]=>111100000
[7,4,5,9,3,10,2,6,8,1]=>111100000
[4,8,5,9,10,3,7,2,6,1]=>111010000
[6,7,4,8,3,5,2,10,1,9]=>111100000
[6,7,9,4,3,5,10,2,8,1]=>111100000
[8,6,9,4,10,3,5,7,2,1]=>111101000
[7,4,8,9,10,6,3,5,2,1]=>111101000
[5,6,7,8,4,3,2,10,1,9]=>111100000
[9,5,6,7,4,3,10,2,8,1]=>111110000
[8,9,5,6,4,10,3,7,2,1]=>111110000
[7,8,9,5,10,4,6,3,2,1]=>111110000
[2,1,4,3,6,5,10,7,9,8]=>101010110
[2,1,4,3,8,5,7,6,10,9]=>101011001
[2,1,4,3,10,9,7,5,6,8]=>101010101
[2,1,4,3,10,5,6,8,9,7]=>101010100
[2,1,6,3,5,4,8,7,10,9]=>101100101
[2,1,6,3,5,4,10,7,9,8]=>101100110
[2,1,8,7,5,3,4,6,10,9]=>101010101
[2,1,10,7,5,9,4,3,6,8]=>101110100
[2,1,10,8,5,3,6,4,9,7]=>101110110
[2,1,8,3,4,6,7,5,10,9]=>101010001
[2,1,10,9,4,6,7,3,5,8]=>101100001
[2,1,10,3,9,6,4,8,5,7]=>101111000
[2,1,10,3,4,5,7,8,9,6]=>101001000
[4,1,3,2,6,5,8,7,10,9]=>110010101
[4,1,3,2,6,5,10,7,9,8]=>110010110
[4,1,3,2,8,5,7,6,10,9]=>110011001
[4,1,3,2,10,9,7,5,6,8]=>110010101
[4,1,3,2,10,5,6,8,9,7]=>110010100
[6,5,3,1,2,4,8,7,10,9]=>101010101
[6,5,3,1,2,4,10,7,9,8]=>101010110
[8,5,3,7,2,1,4,6,10,9]=>111010001
[10,5,3,7,2,9,4,1,6,8]=>111110000
[10,5,3,8,2,1,6,4,9,7]=>111110100
[8,6,3,1,4,2,7,5,10,9]=>111011001
[10,6,3,9,4,2,7,1,5,8]=>111101000
[10,6,3,1,9,2,4,8,5,7]=>111011000
[10,7,3,1,4,5,2,8,9,6]=>111001100
[6,1,2,4,5,3,8,7,10,9]=>101000101
[6,1,2,4,5,3,10,7,9,8]=>101000110
[8,7,2,4,5,1,3,6,10,9]=>110000101
[10,7,2,4,5,9,3,1,6,8]=>111000100
[10,8,2,4,5,1,6,3,9,7]=>111000110
[8,1,7,4,2,6,3,5,10,9]=>111100001
[10,9,7,4,2,6,3,1,5,8]=>111100101
[10,1,8,4,9,6,2,3,5,7]=>110101000
[10,1,8,4,2,5,7,3,9,6]=>111101000
[8,1,2,3,5,6,7,4,10,9]=>100100001
[10,9,2,3,5,6,7,1,4,8]=>110000001
[10,1,9,3,5,6,2,8,4,7]=>111100000
[10,1,2,9,5,3,7,8,4,6]=>101110000
[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]=>10000000000
[11,12,9,10,7,8,5,6,3,4,1,2]=>10101010100
[12,10,8,6,4,2,1,3,5,7,9,11]=>11010101010
[3,2,5,4,7,6,9,8,11,10,1,12]=>11010101010
[1,4,3,6,5,8,7,10,9,12,11,2]=>01101010101
[2,1,4,3,6,5,8,7,11,12,10,9]=>10101010110
[2,1,4,3,6,5,9,10,8,7,12,11]=>10101011001
[2,1,4,3,6,5,9,11,8,12,10,7]=>10101011010
[2,1,4,3,6,5,10,11,12,9,8,7]=>10101011100
[2,1,4,3,7,8,6,5,10,9,12,11]=>10101100101
[2,1,4,3,7,8,6,5,11,12,10,9]=>10101100110
[2,1,4,3,7,9,6,10,8,5,12,11]=>10101101001
[2,1,4,3,7,9,6,11,8,12,10,5]=>10101101010
[2,1,4,3,7,10,6,11,12,9,8,5]=>10101101100
[2,1,4,3,8,9,10,7,6,5,12,11]=>10101110001
[2,1,4,3,8,9,11,7,6,12,10,5]=>10101110010
[2,1,4,3,8,10,11,7,12,9,6,5]=>10101110100
[2,1,4,3,9,10,11,12,8,7,6,5]=>10101111000
[2,1,5,6,4,3,8,7,10,9,12,11]=>10110010101
[2,1,5,6,4,3,8,7,11,12,10,9]=>10110010110
[2,1,5,6,4,3,9,10,8,7,12,11]=>10110011001
[2,1,5,6,4,3,9,11,8,12,10,7]=>10110011010
[2,1,5,6,4,3,10,11,12,9,8,7]=>10110011100
[2,1,5,7,4,8,6,3,10,9,12,11]=>10110100101
[2,1,5,7,4,8,6,3,11,12,10,9]=>10110100110
[2,1,5,7,4,9,6,10,8,3,12,11]=>10110101001
[2,1,5,7,4,9,6,11,8,12,10,3]=>10110101010
[2,1,5,7,4,10,6,11,12,9,8,3]=>10110101100
[2,1,5,8,4,9,10,7,6,3,12,11]=>10110110001
[2,1,5,8,4,9,11,7,6,12,10,3]=>10110110010
[2,1,5,8,4,10,11,7,12,9,6,3]=>10110110100
[2,1,5,9,4,10,11,12,8,7,6,3]=>10110111000
[2,1,6,7,8,5,4,3,10,9,12,11]=>10111000101
[2,1,6,7,8,5,4,3,11,12,10,9]=>10111000110
[2,1,6,7,9,5,4,10,8,3,12,11]=>10111001001
[2,1,6,7,9,5,4,11,8,12,10,3]=>10111001010
[2,1,6,7,10,5,4,11,12,9,8,3]=>10111001100
[2,1,6,8,9,5,10,7,4,3,12,11]=>10111010001
[2,1,6,8,9,5,11,7,4,12,10,3]=>10111010010
[2,1,6,8,10,5,11,7,12,9,4,3]=>10111010100
[2,1,6,9,10,5,11,12,8,7,4,3]=>10111011000
[2,1,7,8,9,10,6,5,4,3,12,11]=>10111100001
[2,1,7,8,9,11,6,5,4,12,10,3]=>10111100010
[2,1,7,8,10,11,6,5,12,9,4,3]=>10111100100
[2,1,7,9,10,11,6,12,8,5,4,3]=>10111101000
[2,1,8,9,10,11,12,7,6,5,4,3]=>10111110000
[3,4,2,1,6,5,8,7,10,9,12,11]=>11001010101
[3,4,2,1,6,5,8,7,11,12,10,9]=>11001010110
[3,4,2,1,6,5,9,10,8,7,12,11]=>11001011001
[3,4,2,1,6,5,9,11,8,12,10,7]=>11001011010
[3,4,2,1,6,5,10,11,12,9,8,7]=>11001011100
[3,4,2,1,7,8,6,5,10,9,12,11]=>11001100101
[3,4,2,1,7,8,6,5,11,12,10,9]=>11001100110
[3,4,2,1,7,9,6,10,8,5,12,11]=>11001101001
[3,4,2,1,7,9,6,11,8,12,10,5]=>11001101010
[3,4,2,1,7,10,6,11,12,9,8,5]=>11001101100
[3,4,2,1,8,9,10,7,6,5,12,11]=>11001110001
[3,4,2,1,8,9,11,7,6,12,10,5]=>11001110010
[3,4,2,1,8,10,11,7,12,9,6,5]=>11001110100
[3,4,2,1,9,10,11,12,8,7,6,5]=>11001111000
[3,5,2,6,4,1,8,7,10,9,12,11]=>11010010101
[3,5,2,6,4,1,8,7,11,12,10,9]=>11010010110
[3,5,2,6,4,1,9,10,8,7,12,11]=>11010011001
[3,5,2,6,4,1,9,11,8,12,10,7]=>11010011010
[3,5,2,6,4,1,10,11,12,9,8,7]=>11010011100
[3,5,2,7,4,8,6,1,10,9,12,11]=>11010100101
[3,5,2,7,4,8,6,1,11,12,10,9]=>11010100110
[3,5,2,7,4,9,6,10,8,1,12,11]=>11010101001
[3,5,2,7,4,9,6,11,8,12,10,1]=>11010101010
[3,5,2,7,4,10,6,11,12,9,8,1]=>11010101100
[3,5,2,8,4,9,10,7,6,1,12,11]=>11010110001
[3,5,2,8,4,9,11,7,6,12,10,1]=>11010110010
[3,5,2,8,4,10,11,7,12,9,6,1]=>11010110100
[3,5,2,9,4,10,11,12,8,7,6,1]=>11010111000
[3,6,2,7,8,5,4,1,10,9,12,11]=>11011000101
[3,6,2,7,8,5,4,1,11,12,10,9]=>11011000110
[3,6,2,7,9,5,4,10,8,1,12,11]=>11011001001
[3,6,2,7,9,5,4,11,8,12,10,1]=>11011001010
[3,6,2,7,10,5,4,11,12,9,8,1]=>11011001100
[3,6,2,8,9,5,10,7,4,1,12,11]=>11011010001
[3,6,2,8,9,5,11,7,4,12,10,1]=>11011010010
[3,6,2,8,10,5,11,7,12,9,4,1]=>11011010100
[3,6,2,9,10,5,11,12,8,7,4,1]=>11011011000
[3,7,2,8,9,10,6,5,4,1,12,11]=>11011100001
[3,7,2,8,9,11,6,5,4,12,10,1]=>11011100010
[3,7,2,8,10,11,6,5,12,9,4,1]=>11011100100
[3,7,2,9,10,11,6,12,8,5,4,1]=>11011101000
[3,8,2,9,10,11,12,7,6,5,4,1]=>11011110000
[4,5,6,3,2,1,8,7,10,9,12,11]=>11100010101
[4,5,6,3,2,1,8,7,11,12,10,9]=>11100010110
[4,5,6,3,2,1,9,10,8,7,12,11]=>11100011001
[4,5,6,3,2,1,9,11,8,12,10,7]=>11100011010
[4,5,6,3,2,1,10,11,12,9,8,7]=>11100011100
[4,5,7,3,2,8,6,1,10,9,12,11]=>11100100101
[4,5,7,3,2,8,6,1,11,12,10,9]=>11100100110
[4,5,7,3,2,9,6,10,8,1,12,11]=>11100101001
[4,5,7,3,2,9,6,11,8,12,10,1]=>11100101010
[4,5,7,3,2,10,6,11,12,9,8,1]=>11100101100
[4,5,8,3,2,9,10,7,6,1,12,11]=>11100110001
[4,5,8,3,2,9,11,7,6,12,10,1]=>11100110010
[4,5,8,3,2,10,11,7,12,9,6,1]=>11100110100
[4,5,9,3,2,10,11,12,8,7,6,1]=>11100111000
[4,6,7,3,8,5,2,1,10,9,12,11]=>11101000101
[4,6,7,3,8,5,2,1,11,12,10,9]=>11101000110
[4,6,7,3,9,5,2,10,8,1,12,11]=>11101001001
[4,6,7,3,9,5,2,11,8,12,10,1]=>11101001010
[4,6,7,3,10,5,2,11,12,9,8,1]=>11101001100
[4,6,8,3,9,5,10,7,2,1,12,11]=>11101010001
[4,6,8,3,9,5,11,7,2,12,10,1]=>11101010010
[4,6,8,3,10,5,11,7,12,9,2,1]=>11101010100
[4,6,9,3,10,5,11,12,8,7,2,1]=>11101011000
[4,7,8,3,9,10,6,5,2,1,12,11]=>11101100001
[4,7,8,3,9,11,6,5,2,12,10,1]=>11101100010
[4,7,8,3,10,11,6,5,12,9,2,1]=>11101100100
[4,7,9,3,10,11,6,12,8,5,2,1]=>11101101000
[4,8,9,3,10,11,12,7,6,5,2,1]=>11101110000
[5,6,7,8,4,3,2,1,10,9,12,11]=>11110000101
[5,6,7,8,4,3,2,1,11,12,10,9]=>11110000110
[5,6,7,9,4,3,2,10,8,1,12,11]=>11110001001
[5,6,7,9,4,3,2,11,8,12,10,1]=>11110001010
[5,6,7,10,4,3,2,11,12,9,8,1]=>11110001100
[5,6,8,9,4,3,10,7,2,1,12,11]=>11110010001
[5,6,8,9,4,3,11,7,2,12,10,1]=>11110010010
[5,6,8,10,4,3,11,7,12,9,2,1]=>11110010100
[5,6,9,10,4,3,11,12,8,7,2,1]=>11110011000
[5,7,8,9,4,10,6,3,2,1,12,11]=>11110100001
[5,7,8,9,4,11,6,3,2,12,10,1]=>11110100010
[5,7,8,10,4,11,6,3,12,9,2,1]=>11110100100
[5,7,9,10,4,11,6,12,8,3,2,1]=>11110101000
[5,8,9,10,4,11,12,7,6,3,2,1]=>11110110000
[6,7,8,9,10,5,4,3,2,1,12,11]=>11111000001
[6,7,8,9,11,5,4,3,2,12,10,1]=>11111000010
[6,7,8,10,11,5,4,3,12,9,2,1]=>11111000100
[6,7,9,10,11,5,4,12,8,3,2,1]=>11111001000
[6,8,9,10,11,5,12,7,4,3,2,1]=>11111010000
[7,8,9,10,11,12,6,5,4,3,2,1]=>11111100000
[9,10,12,11,7,8,5,6,3,4,1,2]=>10101010001
[11,12,7,8,10,9,5,6,3,4,1,2]=>10101010100
[7,10,12,8,11,9,5,6,3,4,1,2]=>10101001100
[7,8,9,12,11,10,5,6,3,4,1,2]=>10101000011
[11,12,9,10,5,6,8,7,3,4,1,2]=>10101010100
[9,10,12,11,5,6,8,7,3,4,1,2]=>10101010001
[11,12,5,8,10,6,9,7,3,4,1,2]=>10101110000
[5,10,12,8,11,6,9,7,3,4,1,2]=>10100111000
[5,8,9,12,11,6,10,7,3,4,1,2]=>10100110001
[11,12,5,6,7,10,9,8,3,4,1,2]=>10101001100
[5,10,12,6,7,11,9,8,3,4,1,2]=>10100101100
[5,6,9,12,7,11,10,8,3,4,1,2]=>10100011010
[5,6,7,8,12,11,10,9,3,4,1,2]=>10100000111
[11,12,9,10,7,8,3,4,6,5,1,2]=>10101010100
[9,10,12,11,7,8,3,4,6,5,1,2]=>10101010001
[11,12,7,8,10,9,3,4,6,5,1,2]=>10101010100
[7,10,12,8,11,9,3,4,6,5,1,2]=>10101001100
[7,8,9,12,11,10,3,4,6,5,1,2]=>10101000011
[11,12,9,10,3,6,8,4,7,5,1,2]=>10111000100
[9,10,12,11,3,6,8,4,7,5,1,2]=>10111000001
[11,12,3,8,10,6,9,4,7,5,1,2]=>10111100000
[3,10,12,8,11,6,9,4,7,5,1,2]=>10011101000
[3,8,9,12,11,6,10,4,7,5,1,2]=>10011100001
[11,12,3,6,7,10,9,4,8,5,1,2]=>10111000100
[3,10,12,6,7,11,9,4,8,5,1,2]=>10011100100
[3,6,9,12,7,11,10,4,8,5,1,2]=>10011010010
[3,6,7,8,12,11,10,4,9,5,1,2]=>10011000011
[11,12,9,10,3,4,5,8,7,6,1,2]=>10100110100
[9,10,12,11,3,4,5,8,7,6,1,2]=>10100110001
[11,12,3,8,10,4,5,9,7,6,1,2]=>10110110000
[3,10,12,8,11,4,5,9,7,6,1,2]=>10010111000
[3,8,9,12,11,4,5,10,7,6,1,2]=>10010110001
[11,12,3,4,7,10,5,9,8,6,1,2]=>10101101000
[3,10,12,4,7,11,5,9,8,6,1,2]=>10011101000
[3,4,9,12,7,11,5,10,8,6,1,2]=>10001111000
[3,4,7,8,12,11,5,10,9,6,1,2]=>10001100101
[11,12,3,4,5,6,10,9,8,7,1,2]=>10100011100
[3,10,12,4,5,6,11,9,8,7,1,2]=>10010011100
[3,4,9,12,5,6,11,10,8,7,1,2]=>10001011010
[3,4,5,8,12,6,11,10,9,7,1,2]=>10000110110
[3,4,5,6,7,12,11,10,9,8,1,2]=>10000001111
[11,12,9,10,7,8,5,6,1,2,4,3]=>10101010100
[9,10,12,11,7,8,5,6,1,2,4,3]=>10101010001
[11,12,7,8,10,9,5,6,1,2,4,3]=>10101010100
[7,10,12,8,11,9,5,6,1,2,4,3]=>10101001100
[7,8,9,12,11,10,5,6,1,2,4,3]=>10101000011
[11,12,9,10,5,6,8,7,1,2,4,3]=>10101010100
[9,10,12,11,5,6,8,7,1,2,4,3]=>10101010001
[11,12,5,8,10,6,9,7,1,2,4,3]=>10101110000
[5,10,12,8,11,6,9,7,1,2,4,3]=>10100111000
[5,8,9,12,11,6,10,7,1,2,4,3]=>10100110001
[11,12,5,6,7,10,9,8,1,2,4,3]=>10101001100
[5,10,12,6,7,11,9,8,1,2,4,3]=>10100101100
[5,6,9,12,7,11,10,8,1,2,4,3]=>10100011010
[5,6,7,8,12,11,10,9,1,2,4,3]=>10100000111
[11,12,9,10,7,8,1,4,6,2,5,3]=>11100010100
[9,10,12,11,7,8,1,4,6,2,5,3]=>11100010001
[11,12,7,8,10,9,1,4,6,2,5,3]=>11100010100
[7,10,12,8,11,9,1,4,6,2,5,3]=>11100001100
[7,8,9,12,11,10,1,4,6,2,5,3]=>11100000011
[11,12,9,10,1,6,8,4,7,2,5,3]=>11110000100
[9,10,12,11,1,6,8,4,7,2,5,3]=>11110000001
[11,12,1,8,10,6,9,4,7,2,5,3]=>11110100000
[1,10,12,8,11,6,9,4,7,2,5,3]=>01110101000
[1,8,9,12,11,6,10,4,7,2,5,3]=>01110100001
[11,12,1,6,7,10,9,4,8,2,5,3]=>11110000100
[1,10,12,6,7,11,9,4,8,2,5,3]=>01110100100
[1,6,9,12,7,11,10,4,8,2,5,3]=>01110010010
[1,6,7,8,12,11,10,4,9,2,5,3]=>01110000011
[11,12,9,10,1,4,5,8,7,2,6,3]=>11100010100
[9,10,12,11,1,4,5,8,7,2,6,3]=>11100010001
[11,12,1,8,10,4,5,9,7,2,6,3]=>11110010000
[1,10,12,8,11,4,5,9,7,2,6,3]=>01110011000
[1,8,9,12,11,4,5,10,7,2,6,3]=>01110010001
[11,12,1,4,7,10,5,9,8,2,6,3]=>11101001000
[1,10,12,4,7,11,5,9,8,2,6,3]=>01111001000
[1,4,9,12,7,11,5,10,8,2,6,3]=>01101011000
[1,4,7,8,12,11,5,10,9,2,6,3]=>01101000101
[11,12,1,4,5,6,10,9,8,2,7,3]=>11100001100
[1,10,12,4,5,6,11,9,8,2,7,3]=>01110001100
[1,4,9,12,5,6,11,10,8,2,7,3]=>01101001010
[1,4,5,8,12,6,11,10,9,2,7,3]=>01100100110
[1,4,5,6,7,12,11,10,9,2,8,3]=>01100000111
[11,12,9,10,7,8,1,2,3,6,5,4]=>10011010100
[9,10,12,11,7,8,1,2,3,6,5,4]=>10011010001
[11,12,7,8,10,9,1,2,3,6,5,4]=>10011010100
[7,10,12,8,11,9,1,2,3,6,5,4]=>10011001100
[7,8,9,12,11,10,1,2,3,6,5,4]=>10011000011
[11,12,9,10,1,6,8,2,3,7,5,4]=>11011000100
[9,10,12,11,1,6,8,2,3,7,5,4]=>11011000001
[11,12,1,8,10,6,9,2,3,7,5,4]=>11011100000
[1,10,12,8,11,6,9,2,3,7,5,4]=>01011101000
[1,8,9,12,11,6,10,2,3,7,5,4]=>01011100001
[11,12,1,6,7,10,9,2,3,8,5,4]=>11011000100
[1,10,12,6,7,11,9,2,3,8,5,4]=>01011100100
[1,6,9,12,7,11,10,2,3,8,5,4]=>01011010010
[1,6,7,8,12,11,10,2,3,9,5,4]=>01011000011
[11,12,9,10,1,2,5,8,3,7,6,4]=>10110100100
[9,10,12,11,1,2,5,8,3,7,6,4]=>10110100001
[11,12,1,8,10,2,5,9,3,7,6,4]=>11110100000
[1,10,12,8,11,2,5,9,3,7,6,4]=>01110101000
[1,8,9,12,11,2,5,10,3,7,6,4]=>01110100001
[11,12,1,2,7,10,5,9,3,8,6,4]=>10111100000
[1,10,12,2,7,11,5,9,3,8,6,4]=>01111100000
[1,2,9,12,7,11,5,10,3,8,6,4]=>00111110000
[1,2,7,8,12,11,5,10,3,9,6,4]=>00111100001
[11,12,1,2,5,6,10,9,3,8,7,4]=>10110010100
[1,10,12,2,5,6,11,9,3,8,7,4]=>01110010100
[1,2,9,12,5,6,11,10,3,8,7,4]=>00111010010
[1,2,5,8,12,6,11,10,3,9,7,4]=>00110110010
[1,2,5,6,7,12,11,10,3,9,8,4]=>00110001011
[11,12,9,10,1,2,3,4,8,7,6,5]=>10001110100
[9,10,12,11,1,2,3,4,8,7,6,5]=>10001110001
[11,12,1,8,10,2,3,4,9,7,6,5]=>11001110000
[1,10,12,8,11,2,3,4,9,7,6,5]=>01001111000
[1,8,9,12,11,2,3,4,10,7,6,5]=>01001110001
[11,12,1,2,7,10,3,4,9,8,6,5]=>10101101000
[1,10,12,2,7,11,3,4,9,8,6,5]=>01101101000
[1,2,9,12,7,11,3,4,10,8,6,5]=>00101111000
[1,2,7,8,12,11,3,4,10,9,6,5]=>00101100101
[11,12,1,2,3,6,10,4,9,8,7,5]=>10011011000
[1,10,12,2,3,6,11,4,9,8,7,5]=>01011011000
[1,2,9,12,3,6,11,4,10,8,7,5]=>00111011000
[1,2,3,8,12,6,11,4,10,9,7,5]=>00011110100
[1,2,3,6,7,12,11,4,10,9,8,5]=>00011001101
[11,12,1,2,3,4,5,10,9,8,7,6]=>10000111100
[1,10,12,2,3,4,5,11,9,8,7,6]=>01000111100
[1,2,9,12,3,4,5,11,10,8,7,6]=>00100111010
[1,2,3,8,12,4,5,11,10,9,7,6]=>00010110110
[1,2,3,4,7,12,5,11,10,9,8,6]=>00001101110
[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]=>10101010101
[2,1,4,3,6,5,10,9,7,8,12,11]=>10101010101
[2,1,4,3,6,5,12,9,7,11,8,10]=>10101011100
[2,1,4,3,6,5,12,11,10,7,8,9]=>10101010011
[2,1,4,3,8,7,5,6,10,9,12,11]=>10101010101
[2,1,4,3,8,7,5,6,12,11,9,10]=>10101010101
[2,1,4,3,10,7,5,9,6,8,12,11]=>10101110001
[2,1,4,3,12,7,5,9,6,11,8,10]=>10101111000
[2,1,4,3,12,7,5,11,10,6,8,9]=>10101110010
[2,1,4,3,10,9,8,5,6,7,12,11]=>10101001101
[2,1,4,3,12,9,8,5,6,11,7,10]=>10101011100
[2,1,4,3,12,11,8,5,10,6,7,9]=>10101101001
[2,1,4,3,12,11,10,9,5,6,7,8]=>10101000111
[2,1,6,5,3,4,8,7,10,9,12,11]=>10101010101
[2,1,6,5,3,4,8,7,12,11,9,10]=>10101010101
[2,1,6,5,3,4,10,9,7,8,12,11]=>10101010101
[2,1,6,5,3,4,12,9,7,11,8,10]=>10101011100
[2,1,6,5,3,4,12,11,10,7,8,9]=>10101010011
[2,1,8,5,3,7,4,6,10,9,12,11]=>10111000101
[2,1,8,5,3,7,4,6,12,11,9,10]=>10111000101
[2,1,10,5,3,7,4,9,6,8,12,11]=>10111100001
[2,1,12,5,3,7,4,9,6,11,8,10]=>10111101000
[2,1,12,5,3,7,4,11,10,6,8,9]=>10111100010
[2,1,10,5,3,9,8,4,6,7,12,11]=>10111001001
[2,1,12,5,3,9,8,4,6,11,7,10]=>10111011000
[2,1,12,5,3,11,8,4,10,6,7,9]=>10111101000
[2,1,12,5,3,11,10,9,4,6,7,8]=>10111000110
[2,1,8,7,6,3,4,5,10,9,12,11]=>10100110101
[2,1,8,7,6,3,4,5,12,11,9,10]=>10100110101
[2,1,10,7,6,3,4,9,5,8,12,11]=>10101110001
[2,1,12,7,6,3,4,9,5,11,8,10]=>10101111000
[2,1,12,7,6,3,4,11,10,5,8,9]=>10101110010
[2,1,10,9,6,3,8,4,5,7,12,11]=>10110100101
[2,1,12,9,6,3,8,4,5,11,7,10]=>10110110100
[2,1,12,11,6,3,8,4,10,5,7,9]=>10111100001
[2,1,12,11,6,3,10,9,4,5,7,8]=>10110100101
[2,1,10,9,8,7,3,4,5,6,12,11]=>10100011101
[2,1,12,9,8,7,3,4,5,11,6,10]=>10100111100
[2,1,12,11,8,7,3,4,10,5,6,9]=>10101011001
[2,1,12,11,10,7,3,9,4,5,6,8]=>10110010011
[2,1,12,11,10,9,8,3,4,5,6,7]=>10100001111
[4,3,1,2,6,5,8,7,10,9,12,11]=>10101010101
[4,3,1,2,6,5,8,7,12,11,9,10]=>10101010101
[4,3,1,2,6,5,10,9,7,8,12,11]=>10101010101
[4,3,1,2,6,5,12,9,7,11,8,10]=>10101011100
[4,3,1,2,6,5,12,11,10,7,8,9]=>10101010011
[4,3,1,2,8,7,5,6,10,9,12,11]=>10101010101
[4,3,1,2,8,7,5,6,12,11,9,10]=>10101010101
[4,3,1,2,10,7,5,9,6,8,12,11]=>10101110001
[4,3,1,2,12,7,5,9,6,11,8,10]=>10101111000
[4,3,1,2,12,7,5,11,10,6,8,9]=>10101110010
[4,3,1,2,10,9,8,5,6,7,12,11]=>10101001101
[4,3,1,2,12,9,8,5,6,11,7,10]=>10101011100
[4,3,1,2,12,11,8,5,10,6,7,9]=>10101101001
[4,3,1,2,12,11,10,9,5,6,7,8]=>10101000111
[6,3,1,5,2,4,8,7,10,9,12,11]=>11100010101
[6,3,1,5,2,4,8,7,12,11,9,10]=>11100010101
[6,3,1,5,2,4,10,9,7,8,12,11]=>11100010101
[6,3,1,5,2,4,12,9,7,11,8,10]=>11100011100
[6,3,1,5,2,4,12,11,10,7,8,9]=>11100010011
[8,3,1,5,2,7,4,6,10,9,12,11]=>11110000101
[8,3,1,5,2,7,4,6,12,11,9,10]=>11110000101
[10,3,1,5,2,7,4,9,6,8,12,11]=>11110100001
[12,3,1,5,2,7,4,9,6,11,8,10]=>11110101000
[12,3,1,5,2,7,4,11,10,6,8,9]=>11110100010
[10,3,1,5,2,9,8,4,6,7,12,11]=>11110001001
[12,3,1,5,2,9,8,4,6,11,7,10]=>11110011000
[12,3,1,5,2,11,8,4,10,6,7,9]=>11110101000
[12,3,1,5,2,11,10,9,4,6,7,8]=>11110000110
[8,3,1,7,6,2,4,5,10,9,12,11]=>11100100101
[8,3,1,7,6,2,4,5,12,11,9,10]=>11100100101
[10,3,1,7,6,2,4,9,5,8,12,11]=>11101100001
[12,3,1,7,6,2,4,9,5,11,8,10]=>11101101000
[12,3,1,7,6,2,4,11,10,5,8,9]=>11101100010
[10,3,1,9,6,2,8,4,5,7,12,11]=>11110100001
[12,3,1,9,6,2,8,4,5,11,7,10]=>11110110000
[12,3,1,11,6,2,8,4,10,5,7,9]=>11111100000
[12,3,1,11,6,2,10,9,4,5,7,8]=>11110100100
[10,3,1,9,8,7,2,4,5,6,12,11]=>11100011001
[12,3,1,9,8,7,2,4,5,11,6,10]=>11100111000
[12,3,1,11,8,7,2,4,10,5,6,9]=>11101011000
[12,3,1,11,10,7,2,9,4,5,6,8]=>11110010010
[12,3,1,11,10,9,8,2,4,5,6,7]=>11100001110
[6,5,4,1,2,3,8,7,10,9,12,11]=>10011010101
[6,5,4,1,2,3,8,7,12,11,9,10]=>10011010101
[6,5,4,1,2,3,10,9,7,8,12,11]=>10011010101
[6,5,4,1,2,3,12,9,7,11,8,10]=>10011011100
[6,5,4,1,2,3,12,11,10,7,8,9]=>10011010011
[8,5,4,1,2,7,3,6,10,9,12,11]=>10111000101
[8,5,4,1,2,7,3,6,12,11,9,10]=>10111000101
[10,5,4,1,2,7,3,9,6,8,12,11]=>10111100001
[12,5,4,1,2,7,3,9,6,11,8,10]=>10111101000
[12,5,4,1,2,7,3,11,10,6,8,9]=>10111100010
[10,5,4,1,2,9,8,3,6,7,12,11]=>10111001001
[12,5,4,1,2,9,8,3,6,11,7,10]=>10111011000
[12,5,4,1,2,11,8,3,10,6,7,9]=>10111101000
[12,5,4,1,2,11,10,9,3,6,7,8]=>10111000110
[8,7,4,1,6,2,3,5,10,9,12,11]=>11010010101
[8,7,4,1,6,2,3,5,12,11,9,10]=>11010010101
[10,7,4,1,6,2,3,9,5,8,12,11]=>11011010001
[12,7,4,1,6,2,3,9,5,11,8,10]=>11011011000
[12,7,4,1,6,2,3,11,10,5,8,9]=>11011010010
[10,9,4,1,6,2,8,3,5,7,12,11]=>11110000101
[12,9,4,1,6,2,8,3,5,11,7,10]=>11110010100
[12,11,4,1,6,2,8,3,10,5,7,9]=>11111000001
[12,11,4,1,6,2,10,9,3,5,7,8]=>11110000101
[10,9,4,1,8,7,2,3,5,6,12,11]=>11010010101
[12,9,4,1,8,7,2,3,5,11,6,10]=>11010110100
[12,11,4,1,8,7,2,3,10,5,6,9]=>11011010001
[12,11,4,1,10,7,2,9,3,5,6,8]=>11110010001
[12,11,4,1,10,9,8,2,3,5,6,7]=>11010001101
[8,7,6,5,1,2,3,4,10,9,12,11]=>10001110101
[8,7,6,5,1,2,3,4,12,11,9,10]=>10001110101
[10,7,6,5,1,2,3,9,4,8,12,11]=>10011110001
[12,7,6,5,1,2,3,9,4,11,8,10]=>10011111000
[12,7,6,5,1,2,3,11,10,4,8,9]=>10011110010
[10,9,6,5,1,2,8,3,4,7,12,11]=>10101100101
[12,9,6,5,1,2,8,3,4,11,7,10]=>10101110100
[12,11,6,5,1,2,8,3,10,4,7,9]=>10111100001
[12,11,6,5,1,2,10,9,3,4,7,8]=>10101100101
[10,9,8,5,1,7,2,3,4,6,12,11]=>11001001101
[12,9,8,5,1,7,2,3,4,11,6,10]=>11001101100
[12,11,8,5,1,7,2,3,10,4,6,9]=>11011001001
[12,11,10,5,1,7,2,9,3,4,6,8]=>11101000011
[12,11,10,5,1,9,8,2,3,4,6,7]=>11001001011
[10,9,8,7,6,1,2,3,4,5,12,11]=>10000111101
[12,9,8,7,6,1,2,3,4,11,5,10]=>10001111100
[12,11,8,7,6,1,2,3,10,4,5,9]=>10010111001
[12,11,10,7,6,1,2,9,3,4,5,8]=>10100110011
[12,11,10,9,6,1,8,2,3,4,5,7]=>11000100111
[12,11,10,9,8,7,1,2,3,4,5,6]=>10000011111
[11,12,9,10,7,8,5,6,2,1,3,4]=>11001010100
[11,12,9,10,7,8,4,3,5,6,1,2]=>10110010100
[11,12,9,10,7,8,4,2,5,1,3,6]=>11010010100
[11,12,9,10,7,8,3,2,1,4,5,6]=>11100010100
[11,12,9,10,6,5,7,8,3,4,1,2]=>10101100100
[11,12,9,10,6,5,7,8,2,1,3,4]=>11001100100
[11,12,9,10,6,4,7,3,5,8,1,2]=>10110100100
[11,12,9,10,6,4,7,2,5,1,3,8]=>11010100100
[11,12,9,10,6,3,7,2,1,4,5,8]=>11100100100
[11,12,9,10,5,4,3,6,7,8,1,2]=>10111000100
[11,12,9,10,5,4,2,6,7,1,3,8]=>11011000100
[11,12,9,10,5,3,2,6,1,4,7,8]=>11101000100
[11,12,9,10,4,3,2,1,5,6,7,8]=>11110000100
[11,12,8,7,9,10,5,6,3,4,1,2]=>10101011000
[11,12,8,7,9,10,5,6,2,1,3,4]=>11001011000
[11,12,8,7,9,10,4,3,5,6,1,2]=>10110011000
[11,12,8,7,9,10,4,2,5,1,3,6]=>11010011000
[11,12,8,7,9,10,3,2,1,4,5,6]=>11100011000
[11,12,8,6,9,5,7,10,3,4,1,2]=>10101101000
[11,12,8,6,9,5,7,10,2,1,3,4]=>11001101000
[11,12,8,6,9,4,7,3,5,10,1,2]=>10110101000
[11,12,8,6,9,4,7,2,5,1,3,10]=>11010101000
[11,12,8,6,9,3,7,2,1,4,5,10]=>11100101000
[11,12,8,5,9,4,3,6,7,10,1,2]=>10111001000
[11,12,8,5,9,4,2,6,7,1,3,10]=>11011001000
[11,12,8,5,9,3,2,6,1,4,7,10]=>11101001000
[11,12,8,4,9,3,2,1,5,6,7,10]=>11110001000
[11,12,7,6,5,8,9,10,3,4,1,2]=>10101110000
[11,12,7,6,5,8,9,10,2,1,3,4]=>11001110000
[11,12,7,6,4,8,9,3,5,10,1,2]=>10110110000
[11,12,7,6,4,8,9,2,5,1,3,10]=>11010110000
[11,12,7,6,3,8,9,2,1,4,5,10]=>11100110000
[11,12,7,5,4,8,3,6,9,10,1,2]=>10111010000
[11,12,7,5,4,8,2,6,9,1,3,10]=>11011010000
[11,12,7,5,3,8,2,6,1,4,9,10]=>11101010000
[11,12,7,4,3,8,2,1,5,6,9,10]=>11110010000
[11,12,6,5,4,3,7,8,9,10,1,2]=>10111100000
[11,12,6,5,4,2,7,8,9,1,3,10]=>11011100000
[11,12,6,5,3,2,7,8,1,4,9,10]=>11101100000
[11,12,6,4,3,2,7,1,5,8,9,10]=>11110100000
[11,12,5,4,3,2,1,6,7,8,9,10]=>11111000000
[10,9,11,12,7,8,5,6,3,4,1,2]=>10101010100
[10,9,11,12,7,8,5,6,2,1,3,4]=>11001010100
[10,9,11,12,7,8,4,3,5,6,1,2]=>10110010100
[10,9,11,12,7,8,4,2,5,1,3,6]=>11010010100
[10,9,11,12,7,8,3,2,1,4,5,6]=>11100010100
[10,9,11,12,6,5,7,8,3,4,1,2]=>10101100100
[10,9,11,12,6,5,7,8,2,1,3,4]=>11001100100
[10,9,11,12,6,4,7,3,5,8,1,2]=>10110100100
[10,9,11,12,6,4,7,2,5,1,3,8]=>11010100100
[10,9,11,12,6,3,7,2,1,4,5,8]=>11100100100
[10,9,11,12,5,4,3,6,7,8,1,2]=>10111000100
[10,9,11,12,5,4,2,6,7,1,3,8]=>11011000100
[10,9,11,12,5,3,2,6,1,4,7,8]=>11101000100
[10,9,11,12,4,3,2,1,5,6,7,8]=>11110000100
[10,8,11,7,9,12,5,6,3,4,1,2]=>10101011000
[10,8,11,7,9,12,5,6,2,1,3,4]=>11001011000
[10,8,11,7,9,12,4,3,5,6,1,2]=>10110011000
[10,8,11,7,9,12,4,2,5,1,3,6]=>11010011000
[10,8,11,7,9,12,3,2,1,4,5,6]=>11100011000
[10,8,11,6,9,5,7,12,3,4,1,2]=>10101101000
[10,8,11,6,9,5,7,12,2,1,3,4]=>11001101000
[10,8,11,6,9,4,7,3,5,12,1,2]=>10110101000
[10,8,11,6,9,4,7,2,5,1,3,12]=>11010101000
[10,8,11,6,9,3,7,2,1,4,5,12]=>11100101000
[10,8,11,5,9,4,3,6,7,12,1,2]=>10111001000
[10,8,11,5,9,4,2,6,7,1,3,12]=>11011001000
[10,8,11,5,9,3,2,6,1,4,7,12]=>11101001000
[10,8,11,4,9,3,2,1,5,6,7,12]=>11110001000
[10,7,11,6,5,8,9,12,3,4,1,2]=>10101110000
[10,7,11,6,5,8,9,12,2,1,3,4]=>11001110000
[10,7,11,6,4,8,9,3,5,12,1,2]=>10110110000
[10,7,11,6,4,8,9,2,5,1,3,12]=>11010110000
[10,7,11,6,3,8,9,2,1,4,5,12]=>11100110000
[10,7,11,5,4,8,3,6,9,12,1,2]=>10111010000
[10,7,11,5,4,8,2,6,9,1,3,12]=>11011010000
[10,7,11,5,3,8,2,6,1,4,9,12]=>11101010000
[10,7,11,4,3,8,2,1,5,6,9,12]=>11110010000
[10,6,11,5,4,3,7,8,9,12,1,2]=>10111100000
[10,6,11,5,4,2,7,8,9,1,3,12]=>11011100000
[10,6,11,5,3,2,7,8,1,4,9,12]=>11101100000
[10,6,11,4,3,2,7,1,5,8,9,12]=>11110100000
[10,5,11,4,3,2,1,6,7,8,9,12]=>11111000000
[9,8,7,10,11,12,5,6,3,4,1,2]=>10101011000
[9,8,7,10,11,12,5,6,2,1,3,4]=>11001011000
[9,8,7,10,11,12,4,3,5,6,1,2]=>10110011000
[9,8,7,10,11,12,4,2,5,1,3,6]=>11010011000
[9,8,7,10,11,12,3,2,1,4,5,6]=>11100011000
[9,8,6,10,11,5,7,12,3,4,1,2]=>10101101000
[9,8,6,10,11,5,7,12,2,1,3,4]=>11001101000
[9,8,6,10,11,4,7,3,5,12,1,2]=>10110101000
[9,8,6,10,11,4,7,2,5,1,3,12]=>11010101000
[9,8,6,10,11,3,7,2,1,4,5,12]=>11100101000
[9,8,5,10,11,4,3,6,7,12,1,2]=>10111001000
[9,8,5,10,11,4,2,6,7,1,3,12]=>11011001000
[9,8,5,10,11,3,2,6,1,4,7,12]=>11101001000
[9,8,4,10,11,3,2,1,5,6,7,12]=>11110001000
[9,7,6,10,5,8,11,12,3,4,1,2]=>10101110000
[9,7,6,10,5,8,11,12,2,1,3,4]=>11001110000
[9,7,6,10,4,8,11,3,5,12,1,2]=>10110110000
[9,7,6,10,4,8,11,2,5,1,3,12]=>11010110000
[9,7,6,10,3,8,11,2,1,4,5,12]=>11100110000
[9,7,5,10,4,8,3,6,11,12,1,2]=>10111010000
[9,7,5,10,4,8,2,6,11,1,3,12]=>11011010000
[9,7,5,10,3,8,2,6,1,4,11,12]=>11101010000
[9,7,4,10,3,8,2,1,5,6,11,12]=>11110010000
[9,6,5,10,4,3,7,8,11,12,1,2]=>10111100000
[9,6,5,10,4,2,7,8,11,1,3,12]=>11011100000
[9,6,5,10,3,2,7,8,1,4,11,12]=>11101100000
[9,6,4,10,3,2,7,1,5,8,11,12]=>11110100000
[9,5,4,10,3,2,1,6,7,8,11,12]=>11111000000
[8,7,6,5,9,10,11,12,3,4,1,2]=>10101110000
[8,7,6,5,9,10,11,12,2,1,3,4]=>11001110000
[8,7,6,4,9,10,11,3,5,12,1,2]=>10110110000
[8,7,6,4,9,10,11,2,5,1,3,12]=>11010110000
[8,7,6,3,9,10,11,2,1,4,5,12]=>11100110000
[8,7,5,4,9,10,3,6,11,12,1,2]=>10111010000
[8,7,5,4,9,10,2,6,11,1,3,12]=>11011010000
[8,7,5,3,9,10,2,6,1,4,11,12]=>11101010000
[8,7,4,3,9,10,2,1,5,6,11,12]=>11110010000
[8,6,5,4,9,3,7,10,11,12,1,2]=>10111100000
[8,6,5,4,9,2,7,10,11,1,3,12]=>11011100000
[8,6,5,3,9,2,7,10,1,4,11,12]=>11101100000
[8,6,4,3,9,2,7,1,5,10,11,12]=>11110100000
[8,5,4,3,9,2,1,6,7,10,11,12]=>11111000000
[7,6,5,4,3,8,9,10,11,12,1,2]=>10111100000
[7,6,5,4,2,8,9,10,11,1,3,12]=>11011100000
[7,6,5,3,2,8,9,10,1,4,11,12]=>11101100000
[7,6,4,3,2,8,9,1,5,10,11,12]=>11110100000
[7,5,4,3,2,8,1,6,9,10,11,12]=>11111000000
[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]=>11010101010
[3,2,5,4,7,6,11,10,8,9,1,12]=>11010101010
[3,2,5,4,7,6,1,10,8,12,9,11]=>11010101100
[3,2,5,4,7,6,1,12,11,8,9,10]=>11010101001
[3,2,5,4,9,8,6,7,11,10,1,12]=>11010101010
[3,2,5,4,9,8,6,7,1,12,10,11]=>11010101010
[3,2,5,4,11,8,6,10,7,9,1,12]=>11010111000
[3,2,5,4,1,8,6,10,7,12,9,11]=>11010110100
[3,2,5,4,1,8,6,12,11,7,9,10]=>11010110001
[3,2,5,4,11,10,9,6,7,8,1,12]=>11010100110
[3,2,5,4,1,10,9,6,7,12,8,11]=>11010101100
[3,2,5,4,1,12,9,6,11,7,8,10]=>11010110100
[3,2,5,4,1,12,11,10,6,7,8,9]=>11010100011
[3,2,7,6,4,5,9,8,11,10,1,12]=>11010101010
[3,2,7,6,4,5,9,8,1,12,10,11]=>11010101010
[3,2,7,6,4,5,11,10,8,9,1,12]=>11010101010
[3,2,7,6,4,5,1,10,8,12,9,11]=>11010101100
[3,2,7,6,4,5,1,12,11,8,9,10]=>11010101001
[3,2,9,6,4,8,5,7,11,10,1,12]=>11011100010
[3,2,9,6,4,8,5,7,1,12,10,11]=>11011100010
[3,2,11,6,4,8,5,10,7,9,1,12]=>11011110000
[3,2,1,6,4,8,5,10,7,12,9,11]=>11011010100
[3,2,1,6,4,8,5,12,11,7,9,10]=>11011010001
[3,2,11,6,4,10,9,5,7,8,1,12]=>11011100100
[3,2,1,6,4,10,9,5,7,12,8,11]=>11011001100
[3,2,1,6,4,12,9,5,11,7,8,10]=>11011010100
[3,2,1,6,4,12,11,10,5,7,8,9]=>11011000011
[3,2,9,8,7,4,5,6,11,10,1,12]=>11010011010
[3,2,9,8,7,4,5,6,1,12,10,11]=>11010011010
[3,2,11,8,7,4,5,10,6,9,1,12]=>11010111000
[3,2,1,8,7,4,5,10,6,12,9,11]=>11010110100
[3,2,1,8,7,4,5,12,11,6,9,10]=>11010110001
[3,2,11,10,7,4,9,5,6,8,1,12]=>11011010010
[3,2,1,10,7,4,9,5,6,12,8,11]=>11011011000
[3,2,1,12,7,4,9,5,11,6,8,10]=>11011110000
[3,2,1,12,7,4,11,10,5,6,8,9]=>11011010010
[3,2,11,10,9,8,4,5,6,7,1,12]=>11010001110
[3,2,1,10,9,8,4,5,6,12,7,11]=>11010011100
[3,2,1,12,9,8,4,5,11,6,7,10]=>11010101100
[3,2,1,12,11,8,4,10,5,6,7,9]=>11011001001
[3,2,1,12,11,10,9,4,5,6,7,8]=>11010000111
[5,4,2,3,7,6,9,8,11,10,1,12]=>11010101010
[5,4,2,3,7,6,9,8,1,12,10,11]=>11010101010
[5,4,2,3,7,6,11,10,8,9,1,12]=>11010101010
[5,4,2,3,7,6,1,10,8,12,9,11]=>11010101100
[5,4,2,3,7,6,1,12,11,8,9,10]=>11010101001
[5,4,2,3,9,8,6,7,11,10,1,12]=>11010101010
[5,4,2,3,9,8,6,7,1,12,10,11]=>11010101010
[5,4,2,3,11,8,6,10,7,9,1,12]=>11010111000
[5,4,2,3,1,8,6,10,7,12,9,11]=>11010110100
[5,4,2,3,1,8,6,12,11,7,9,10]=>11010110001
[5,4,2,3,11,10,9,6,7,8,1,12]=>11010100110
[5,4,2,3,1,10,9,6,7,12,8,11]=>11010101100
[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]=>11010100011
[7,4,2,6,3,5,9,8,11,10,1,12]=>11110001010
[7,4,2,6,3,5,9,8,1,12,10,11]=>11110001010
[7,4,2,6,3,5,11,10,8,9,1,12]=>11110001010
[7,4,2,6,3,5,1,10,8,12,9,11]=>11110001100
[7,4,2,6,3,5,1,12,11,8,9,10]=>11110001001
[9,4,2,6,3,8,5,7,11,10,1,12]=>11111000010
[9,4,2,6,3,8,5,7,1,12,10,11]=>11111000010
[11,4,2,6,3,8,5,10,7,9,1,12]=>11111010000
[1,4,2,6,3,8,5,10,7,12,9,11]=>01101010100
[1,4,2,6,3,8,5,12,11,7,9,10]=>01101010001
[11,4,2,6,3,10,9,5,7,8,1,12]=>11111000100
[1,4,2,6,3,10,9,5,7,12,8,11]=>01101001100
[1,4,2,6,3,12,9,5,11,7,8,10]=>01101010100
[1,4,2,6,3,12,11,10,5,7,8,9]=>01101000011
[9,4,2,8,7,3,5,6,11,10,1,12]=>11110010010
[9,4,2,8,7,3,5,6,1,12,10,11]=>11110010010
[11,4,2,8,7,3,5,10,6,9,1,12]=>11110110000
[1,4,2,8,7,3,5,10,6,12,9,11]=>01100110100
[1,4,2,8,7,3,5,12,11,6,9,10]=>01100110001
[11,4,2,10,7,3,9,5,6,8,1,12]=>11111010000
[1,4,2,10,7,3,9,5,6,12,8,11]=>01101011000
[1,4,2,12,7,3,9,5,11,6,8,10]=>01101110000
[1,4,2,12,7,3,11,10,5,6,8,9]=>01101010010
[11,4,2,10,9,8,3,5,6,7,1,12]=>11110001100
[1,4,2,10,9,8,3,5,6,12,7,11]=>01100011100
[1,4,2,12,9,8,3,5,11,6,7,10]=>01100101100
[1,4,2,12,11,8,3,10,5,6,7,9]=>01101001001
[1,4,2,12,11,10,9,3,5,6,7,8]=>01100000111
[7,6,5,2,3,4,9,8,11,10,1,12]=>11001101010
[7,6,5,2,3,4,9,8,1,12,10,11]=>11001101010
[7,6,5,2,3,4,11,10,8,9,1,12]=>11001101010
[7,6,5,2,3,4,1,10,8,12,9,11]=>11001101100
[7,6,5,2,3,4,1,12,11,8,9,10]=>11001101001
[9,6,5,2,3,8,4,7,11,10,1,12]=>11011100010
[9,6,5,2,3,8,4,7,1,12,10,11]=>11011100010
[11,6,5,2,3,8,4,10,7,9,1,12]=>11011110000
[1,6,5,2,3,8,4,10,7,12,9,11]=>01011010100
[1,6,5,2,3,8,4,12,11,7,9,10]=>01011010001
[11,6,5,2,3,10,9,4,7,8,1,12]=>11011100100
[1,6,5,2,3,10,9,4,7,12,8,11]=>01011001100
[1,6,5,2,3,12,9,4,11,7,8,10]=>01011010100
[1,6,5,2,3,12,11,10,4,7,8,9]=>01011000011
[9,8,5,2,7,3,4,6,11,10,1,12]=>11101001010
[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]=>11101101000
[1,8,5,2,7,3,4,10,6,12,9,11]=>01101100100
[1,8,5,2,7,3,4,12,11,6,9,10]=>01101100001
[11,10,5,2,7,3,9,4,6,8,1,12]=>11111000010
[1,10,5,2,7,3,9,4,6,12,8,11]=>01111001000
[1,12,5,2,7,3,9,4,11,6,8,10]=>01111100000
[1,12,5,2,7,3,11,10,4,6,8,9]=>01111000010
[11,10,5,2,9,8,3,4,6,7,1,12]=>11101001010
[1,10,5,2,9,8,3,4,6,12,7,11]=>01101011000
[1,12,5,2,9,8,3,4,11,6,7,10]=>01101101000
[1,12,5,2,11,8,3,10,4,6,7,9]=>01111001000
[1,12,5,2,11,10,9,3,4,6,7,8]=>01101000110
[9,8,7,6,2,3,4,5,11,10,1,12]=>11000111010
[9,8,7,6,2,3,4,5,1,12,10,11]=>11000111010
[11,8,7,6,2,3,4,10,5,9,1,12]=>11001111000
[1,8,7,6,2,3,4,10,5,12,9,11]=>01001110100
[1,8,7,6,2,3,4,12,11,5,9,10]=>01001110001
[11,10,7,6,2,3,9,4,5,8,1,12]=>11010110010
[1,10,7,6,2,3,9,4,5,12,8,11]=>01010111000
[1,12,7,6,2,3,9,4,11,5,8,10]=>01011110000
[1,12,7,6,2,3,11,10,4,5,8,9]=>01010110010
[11,10,9,6,2,8,3,4,5,7,1,12]=>11100100110
[1,10,9,6,2,8,3,4,5,12,7,11]=>01100110100
[1,12,9,6,2,8,3,4,11,5,7,10]=>01101100100
[1,12,11,6,2,8,3,10,4,5,7,9]=>01110100001
[1,12,11,6,2,10,9,3,4,5,7,8]=>01100100101
[11,10,9,8,7,2,3,4,5,6,1,12]=>11000011110
[1,10,9,8,7,2,3,4,5,12,6,11]=>01000111100
[1,12,9,8,7,2,3,4,11,5,6,10]=>01001011100
[1,12,11,8,7,2,3,10,4,5,6,9]=>01010011001
[1,12,11,10,7,2,9,3,4,5,6,8]=>01100010011
[1,12,11,10,9,8,2,3,4,5,6,7]=>01000001111
[2,1,4,3,6,5,8,7,10,12,11,9]=>10101010101
[2,1,4,3,6,5,8,10,9,7,12,11]=>10101010101
[2,1,4,3,6,5,10,12,9,11,7,8]=>10101010100
[2,1,4,3,6,5,8,9,12,10,11,7]=>10101010010
[2,1,4,3,6,8,7,5,10,9,12,11]=>10101010101
[2,1,4,3,6,8,7,5,10,12,11,9]=>10101010101
[2,1,4,3,8,10,7,9,5,6,12,11]=>10101010001
[2,1,4,3,10,9,7,12,6,11,5,8]=>10101110100
[2,1,4,3,8,9,7,12,10,6,11,5]=>10101110010
[2,1,4,3,6,7,10,8,9,5,12,11]=>10101001001
[2,1,4,3,10,7,12,8,9,11,5,6]=>10101011000
[2,1,4,3,6,9,12,8,11,10,5,7]=>10101001010
[2,1,4,3,6,7,8,12,9,10,11,5]=>10101000100
[2,1,4,6,5,3,8,7,10,9,12,11]=>10101010101
[2,1,4,6,5,3,8,7,10,12,11,9]=>10101010101
[2,1,4,6,5,3,8,10,9,7,12,11]=>10101010101
[2,1,4,6,5,3,10,12,9,11,7,8]=>10101010100
[2,1,4,6,5,3,8,9,12,10,11,7]=>10101010010
[2,1,6,8,5,7,3,4,10,9,12,11]=>10101000101
[2,1,6,8,5,7,3,4,10,12,11,9]=>10101000101
[2,1,8,7,5,10,4,9,3,6,12,11]=>10111010001
[2,1,10,7,5,9,4,12,6,11,3,8]=>10111110000
[2,1,8,7,5,9,4,12,10,6,11,3]=>10111110010
[2,1,6,7,5,10,8,4,9,3,12,11]=>10111001001
[2,1,10,8,5,7,12,4,9,11,3,6]=>10111001000
[2,1,6,9,5,8,12,3,11,10,4,7]=>10111000010
[2,1,6,7,5,8,12,9,3,10,11,4]=>10111000100
[2,1,4,5,8,6,7,3,10,9,12,11]=>10100100101
[2,1,4,5,8,6,7,3,10,12,11,9]=>10100100101
[2,1,8,5,10,6,7,9,3,4,12,11]=>10101100001
[2,1,10,5,9,6,7,12,4,11,3,8]=>10111100000
[2,1,8,5,9,6,7,12,10,4,11,3]=>10111100010
[2,1,4,7,10,6,9,8,3,5,12,11]=>10100101001
[2,1,10,7,12,6,9,8,4,11,3,5]=>10110111000
[2,1,4,9,12,6,10,8,11,7,3,5]=>10100111000
[2,1,4,7,8,6,12,10,9,5,11,3]=>10101100110
[2,1,4,5,6,10,7,8,9,3,12,11]=>10100010001
[2,1,10,5,6,12,7,8,9,11,3,4]=>10101010000
[2,1,4,9,6,12,7,8,11,10,3,5]=>10100110010
[2,1,4,5,8,12,7,11,9,10,3,6]=>10100010100
[2,1,4,5,6,7,12,8,9,10,11,3]=>10100001000
[2,4,3,1,6,5,8,7,10,9,12,11]=>10101010101
[2,4,3,1,6,5,8,7,10,12,11,9]=>10101010101
[2,4,3,1,6,5,8,10,9,7,12,11]=>10101010101
[2,4,3,1,6,5,10,12,9,11,7,8]=>10101010100
[2,4,3,1,6,5,8,9,12,10,11,7]=>10101010010
[2,4,3,1,6,8,7,5,10,9,12,11]=>10101010101
[2,4,3,1,6,8,7,5,10,12,11,9]=>10101010101
[2,4,3,1,8,10,7,9,5,6,12,11]=>10101010001
[2,4,3,1,10,9,7,12,6,11,5,8]=>10101110100
[2,4,3,1,8,9,7,12,10,6,11,5]=>10101110010
[2,4,3,1,6,7,10,8,9,5,12,11]=>10101001001
[2,4,3,1,10,7,12,8,9,11,5,6]=>10101011000
[2,4,3,1,6,9,12,8,11,10,5,7]=>10101001010
[2,4,3,1,6,7,8,12,9,10,11,5]=>10101000100
[4,6,3,5,1,2,8,7,10,9,12,11]=>10100010101
[4,6,3,5,1,2,8,7,10,12,11,9]=>10100010101
[4,6,3,5,1,2,8,10,9,7,12,11]=>10100010101
[4,6,3,5,1,2,10,12,9,11,7,8]=>10100010100
[4,6,3,5,1,2,8,9,12,10,11,7]=>10100010010
[6,5,3,8,2,7,1,4,10,9,12,11]=>11101000101
[6,5,3,8,2,7,1,4,10,12,11,9]=>11101000101
[8,5,3,7,2,10,4,9,1,6,12,11]=>11111000001
[10,5,3,7,2,9,4,12,6,11,1,8]=>11111100000
[8,5,3,7,2,9,4,12,10,6,11,1]=>11111100010
[6,5,3,7,2,10,8,4,9,1,12,11]=>11111001001
[10,5,3,8,2,7,12,4,9,11,1,6]=>11111000000
[6,5,3,9,2,8,12,1,11,10,4,7]=>11111000010
[6,5,3,7,2,8,12,9,1,10,11,4]=>11111000100
[4,5,3,8,6,2,7,1,10,9,12,11]=>11100100101
[4,5,3,8,6,2,7,1,10,12,11,9]=>11100100101
[8,6,3,5,10,2,7,9,1,4,12,11]=>11100100001
[10,6,3,5,9,2,7,12,4,11,1,8]=>11110100000
[8,6,3,5,9,2,7,12,10,4,11,1]=>11110100010
[4,7,3,6,10,1,9,8,2,5,12,11]=>11100001001
[10,6,3,7,12,2,9,8,4,11,1,5]=>11110101000
[4,9,3,6,12,1,10,8,11,7,2,5]=>11100011000
[4,7,3,6,8,1,12,10,9,5,11,2]=>11101000110
[4,5,3,6,10,7,1,8,9,2,12,11]=>11100010001
[10,7,3,5,6,12,2,8,9,11,1,4]=>11100010000
[4,9,3,7,6,12,1,8,11,10,2,5]=>11100100010
[4,5,3,8,7,12,2,11,9,10,1,6]=>11100010100
[4,5,3,6,7,12,8,2,9,10,11,1]=>11100001000
[2,3,6,4,5,1,8,7,10,9,12,11]=>10010010101
[2,3,6,4,5,1,8,7,10,12,11,9]=>10010010101
[2,3,6,4,5,1,8,10,9,7,12,11]=>10010010101
[2,3,6,4,5,1,10,12,9,11,7,8]=>10010010100
[2,3,6,4,5,1,8,9,12,10,11,7]=>10010010010
[6,3,8,4,5,7,1,2,10,9,12,11]=>10110000101
[6,3,8,4,5,7,1,2,10,12,11,9]=>10110000101
[8,3,7,4,5,10,2,9,1,6,12,11]=>11110000001
[10,3,7,4,5,9,2,12,6,11,1,8]=>11110100000
[8,3,7,4,5,9,2,12,10,6,11,1]=>11110100010
[6,3,7,4,5,10,8,2,9,1,12,11]=>11110001001
[10,3,8,4,5,7,12,2,9,11,1,6]=>11110000000
[6,3,9,4,5,8,12,1,11,10,2,7]=>11110000010
[6,3,7,4,5,8,12,9,1,10,11,2]=>11110000100
[2,5,8,4,7,6,1,3,10,9,12,11]=>10010100101
[2,5,8,4,7,6,1,3,10,12,11,9]=>10010100101
[8,5,10,4,7,6,2,9,1,3,12,11]=>11011100001
[10,5,9,4,7,6,2,12,3,11,1,8]=>11111100000
[8,5,9,4,7,6,2,12,10,3,11,1]=>11111100010
[2,7,10,4,8,6,9,5,1,3,12,11]=>10011100001
[10,7,12,4,8,6,9,5,2,11,1,3]=>11011110000
[2,9,8,4,12,6,10,3,11,7,1,5]=>10110111000
[2,7,8,4,12,6,9,10,1,3,11,5]=>10011100000
[2,5,6,4,10,8,7,3,9,1,12,11]=>10110011001
[10,5,6,4,12,8,7,3,9,11,1,2]=>10111011000
[2,9,8,4,6,12,7,3,11,10,1,5]=>10110011010
[2,5,8,4,12,9,7,11,6,10,3,1]=>10110110100
[2,5,6,4,7,12,9,8,1,10,11,3]=>10110001100
[2,3,4,8,5,6,7,1,10,9,12,11]=>10001000101
[2,3,4,8,5,6,7,1,10,12,11,9]=>10001000101
[8,3,4,10,5,6,7,9,1,2,12,11]=>10101000001
[10,3,4,9,5,6,7,12,2,11,1,8]=>11101000000
[8,3,4,9,5,6,7,12,10,2,11,1]=>11101000010
[2,7,4,10,5,6,9,8,1,3,12,11]=>10011001001
[10,7,4,12,5,6,9,8,2,11,1,3]=>11011011000
[2,9,4,12,5,6,10,8,11,7,1,3]=>10011011000
[2,7,4,8,5,6,12,10,9,3,11,1]=>10111000110
[2,3,6,10,5,9,7,8,1,4,12,11]=>10001010001
[10,3,6,12,5,9,7,8,2,11,1,4]=>11101010000
[2,9,6,12,5,11,7,8,10,1,3,4]=>10001110000
[2,3,8,12,5,10,7,11,9,6,1,4]=>10001110100
[2,3,6,7,5,12,10,8,9,4,11,1]=>10011001010
[2,3,4,5,10,6,7,8,9,1,12,11]=>10000100001
[10,3,4,5,12,6,7,8,9,11,1,2]=>10100100000
[2,9,4,5,12,6,7,8,11,10,1,3]=>10010100010
[2,3,8,5,12,6,7,11,9,10,1,4]=>10001100100
[2,3,4,7,12,6,11,8,9,10,1,5]=>10000101000
[2,3,4,5,6,12,7,8,9,10,11,1]=>10000010000
[1,4,3,6,5,8,7,12,11,9,10,2]=>01101010101
[1,4,3,6,5,10,9,7,8,12,11,2]=>01101010101
[1,4,3,6,5,12,9,7,11,8,10,2]=>01101011100
[1,4,3,6,5,12,11,10,7,8,9,2]=>01101010011
[1,4,3,8,7,5,6,10,9,12,11,2]=>01101010101
[1,4,3,8,7,5,6,12,11,9,10,2]=>01101010101
[1,4,3,10,7,5,9,6,8,12,11,2]=>01101110001
[1,4,3,12,7,5,9,6,11,8,10,2]=>01101111000
[1,4,3,12,7,5,11,10,6,8,9,2]=>01101110010
[1,4,3,10,9,8,5,6,7,12,11,2]=>01101001101
[1,4,3,12,9,8,5,6,11,7,10,2]=>01101011100
[1,4,3,12,11,8,5,10,6,7,9,2]=>01101101001
[1,4,3,12,11,10,9,5,6,7,8,2]=>01101000111
[1,6,5,3,4,8,7,10,9,12,11,2]=>01101010101
[1,6,5,3,4,8,7,12,11,9,10,2]=>01101010101
[1,6,5,3,4,10,9,7,8,12,11,2]=>01101010101
[1,6,5,3,4,12,9,7,11,8,10,2]=>01101011100
[1,6,5,3,4,12,11,10,7,8,9,2]=>01101010011
[1,8,5,3,7,4,6,10,9,12,11,2]=>01111000101
[1,8,5,3,7,4,6,12,11,9,10,2]=>01111000101
[1,10,5,3,7,4,9,6,8,12,11,2]=>01111100001
[1,12,5,3,7,4,9,6,11,8,10,2]=>01111101000
[1,12,5,3,7,4,11,10,6,8,9,2]=>01111100010
[1,10,5,3,9,8,4,6,7,12,11,2]=>01111001001
[1,12,5,3,9,8,4,6,11,7,10,2]=>01111011000
[1,12,5,3,11,8,4,10,6,7,9,2]=>01111101000
[1,12,5,3,11,10,9,4,6,7,8,2]=>01111000110
[1,8,7,6,3,4,5,10,9,12,11,2]=>01100110101
[1,8,7,6,3,4,5,12,11,9,10,2]=>01100110101
[1,10,7,6,3,4,9,5,8,12,11,2]=>01101110001
[1,12,7,6,3,4,9,5,11,8,10,2]=>01101111000
[1,12,7,6,3,4,11,10,5,8,9,2]=>01101110010
[1,10,9,6,3,8,4,5,7,12,11,2]=>01110100101
[1,12,9,6,3,8,4,5,11,7,10,2]=>01110110100
[1,12,11,6,3,8,4,10,5,7,9,2]=>01111100001
[1,12,11,6,3,10,9,4,5,7,8,2]=>01110100101
[1,10,9,8,7,3,4,5,6,12,11,2]=>01100011101
[1,12,9,8,7,3,4,5,11,6,10,2]=>01100111100
[1,12,11,8,7,3,4,10,5,6,9,2]=>01101011001
[1,12,11,10,7,3,9,4,5,6,8,2]=>01110010011
[1,12,11,10,9,8,3,4,5,6,7,2]=>01100001111
[3,1,2,6,5,8,7,10,9,12,11,4]=>10011010101
[3,1,2,6,5,8,7,12,11,9,10,4]=>10011010101
[3,1,2,6,5,10,9,7,8,12,11,4]=>10011010101
[3,1,2,6,5,12,9,7,11,8,10,4]=>10011011100
[3,1,2,6,5,12,11,10,7,8,9,4]=>10011010011
[3,1,2,8,7,5,6,10,9,12,11,4]=>10011010101
[3,1,2,8,7,5,6,12,11,9,10,4]=>10011010101
[3,1,2,10,7,5,9,6,8,12,11,4]=>10011110001
[3,1,2,12,7,5,9,6,11,8,10,4]=>10011111000
[3,1,2,12,7,5,11,10,6,8,9,4]=>10011110010
[3,1,2,10,9,8,5,6,7,12,11,4]=>10011001101
[3,1,2,12,9,8,5,6,11,7,10,4]=>10011011100
[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]=>10011000111
[3,1,5,2,4,8,7,10,9,12,11,6]=>11000110101
[3,1,5,2,4,8,7,12,11,9,10,6]=>11000110101
[3,1,5,2,4,10,9,7,8,12,11,6]=>11000110101
[3,1,5,2,4,12,9,7,11,8,10,6]=>11000111100
[3,1,5,2,4,12,11,10,7,8,9,6]=>11000110011
[3,1,5,2,7,4,6,10,9,12,11,8]=>11010001101
[3,1,5,2,7,4,6,12,11,9,10,8]=>11010001101
[3,1,5,2,7,4,9,6,8,12,11,10]=>11010100011
[3,1,5,2,7,4,9,6,11,8,10,12]=>11010101000
[3,1,5,2,7,4,11,10,6,8,9,12]=>11010100010
[3,1,5,2,9,8,4,6,7,12,11,10]=>11010001011
[3,1,5,2,9,8,4,6,11,7,10,12]=>11010011000
[3,1,5,2,11,8,4,10,6,7,9,12]=>11010101000
[3,1,5,2,11,10,9,4,6,7,8,12]=>11010000110
[3,1,7,6,2,4,5,10,9,12,11,8]=>11000101101
[3,1,7,6,2,4,5,12,11,9,10,8]=>11000101101
[3,1,7,6,2,4,9,5,8,12,11,10]=>11001100011
[3,1,7,6,2,4,9,5,11,8,10,12]=>11001101000
[3,1,7,6,2,4,11,10,5,8,9,12]=>11001100010
[3,1,9,6,2,8,4,5,7,12,11,10]=>11010100011
[3,1,9,6,2,8,4,5,11,7,10,12]=>11010110000
[3,1,11,6,2,8,4,10,5,7,9,12]=>11011100000
[3,1,11,6,2,10,9,4,5,7,8,12]=>11010100100
[3,1,9,8,7,2,4,5,6,12,11,10]=>11000011011
[3,1,9,8,7,2,4,5,11,6,10,12]=>11000111000
[3,1,11,8,7,2,4,10,5,6,9,12]=>11001011000
[3,1,11,10,7,2,9,4,5,6,8,12]=>11010010010
[3,1,11,10,9,8,2,4,5,6,7,12]=>11000001110
[5,4,1,2,3,8,7,10,9,12,11,6]=>10010110101
[5,4,1,2,3,8,7,12,11,9,10,6]=>10010110101
[5,4,1,2,3,10,9,7,8,12,11,6]=>10010110101
[5,4,1,2,3,12,9,7,11,8,10,6]=>10010111100
[5,4,1,2,3,12,11,10,7,8,9,6]=>10010110011
[5,4,1,2,7,3,6,10,9,12,11,8]=>10110001101
[5,4,1,2,7,3,6,12,11,9,10,8]=>10110001101
[5,4,1,2,7,3,9,6,8,12,11,10]=>10110100011
[5,4,1,2,7,3,9,6,11,8,10,12]=>10110101000
[5,4,1,2,7,3,11,10,6,8,9,12]=>10110100010
[5,4,1,2,9,8,3,6,7,12,11,10]=>10110001011
[5,4,1,2,9,8,3,6,11,7,10,12]=>10110011000
[5,4,1,2,11,8,3,10,6,7,9,12]=>10110101000
[5,4,1,2,11,10,9,3,6,7,8,12]=>10110000110
[7,4,1,6,2,3,5,10,9,12,11,8]=>11010001101
[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]=>11011000011
[7,4,1,6,2,3,9,5,11,8,10,12]=>11011001000
[7,4,1,6,2,3,11,10,5,8,9,12]=>11011000010
[9,4,1,6,2,8,3,5,7,12,11,10]=>11110000011
[9,4,1,6,2,8,3,5,11,7,10,12]=>11110010000
[11,4,1,6,2,8,3,10,5,7,9,12]=>11111000000
[11,4,1,6,2,10,9,3,5,7,8,12]=>11110000100
[9,4,1,8,7,2,3,5,6,12,11,10]=>11010010011
[9,4,1,8,7,2,3,5,11,6,10,12]=>11010110000
[11,4,1,8,7,2,3,10,5,6,9,12]=>11011010000
[11,4,1,10,7,2,9,3,5,6,8,12]=>11110010000
[11,4,1,10,9,8,2,3,5,6,7,12]=>11010001100
[7,6,5,1,2,3,4,10,9,12,11,8]=>10001101101
[7,6,5,1,2,3,4,12,11,9,10,8]=>10001101101
[7,6,5,1,2,3,9,4,8,12,11,10]=>10011100011
[7,6,5,1,2,3,9,4,11,8,10,12]=>10011101000
[7,6,5,1,2,3,11,10,4,8,9,12]=>10011100010
[9,6,5,1,2,8,3,4,7,12,11,10]=>10101100011
[9,6,5,1,2,8,3,4,11,7,10,12]=>10101110000
[11,6,5,1,2,8,3,10,4,7,9,12]=>10111100000
[11,6,5,1,2,10,9,3,4,7,8,12]=>10101100100
[9,8,5,1,7,2,3,4,6,12,11,10]=>11001001011
[9,8,5,1,7,2,3,4,11,6,10,12]=>11001101000
[11,8,5,1,7,2,3,10,4,6,9,12]=>11011001000
[11,10,5,1,7,2,9,3,4,6,8,12]=>11101000010
[11,10,5,1,9,8,2,3,4,6,7,12]=>11001001010
[9,8,7,6,1,2,3,4,5,12,11,10]=>10000111011
[9,8,7,6,1,2,3,4,11,5,10,12]=>10001111000
[11,8,7,6,1,2,3,10,4,5,9,12]=>10010111000
[11,10,7,6,1,2,9,3,4,5,8,12]=>10100110010
[11,10,9,6,1,8,2,3,4,5,7,12]=>11000100110
[11,10,9,8,7,1,2,3,4,5,6,12]=>10000011110
[11,12,8,6,4,2,1,3,5,7,10,9]=>11010101100
[12,9,10,6,4,2,1,3,5,8,7,11]=>11010110100
[11,9,12,6,4,2,1,3,5,8,10,7]=>11010110100
[10,11,12,6,4,2,1,3,5,9,8,7]=>11010111000
[12,10,7,8,4,2,1,3,6,5,9,11]=>11011010010
[11,12,7,8,4,2,1,3,6,5,10,9]=>11011010100
[12,9,7,10,4,2,1,3,6,8,5,11]=>11011010100
[11,9,7,12,4,2,1,3,6,8,10,5]=>11011010100
[10,11,7,12,4,2,1,3,6,9,8,5]=>11011011000
[12,8,9,10,4,2,1,3,7,6,5,11]=>11011101000
[11,8,9,12,4,2,1,3,7,6,10,5]=>11011101000
[10,8,11,12,4,2,1,3,7,9,6,5]=>11011101000
[9,10,11,12,4,2,1,3,8,7,6,5]=>11011110000
[12,10,8,5,6,2,1,4,3,7,9,11]=>11101001010
[11,12,8,5,6,2,1,4,3,7,10,9]=>11101001100
[12,9,10,5,6,2,1,4,3,8,7,11]=>11101010100
[11,9,12,5,6,2,1,4,3,8,10,7]=>11101010100
[10,11,12,5,6,2,1,4,3,9,8,7]=>11101011000
[12,10,7,5,8,2,1,4,6,3,9,11]=>11101010010
[11,12,7,5,8,2,1,4,6,3,10,9]=>11101010100
[12,9,7,5,10,2,1,4,6,8,3,11]=>11101010100
[11,9,7,5,12,2,1,4,6,8,10,3]=>11101010100
[10,11,7,5,12,2,1,4,6,9,8,3]=>11101011000
[12,8,9,5,10,2,1,4,7,6,3,11]=>11101101000
[11,8,9,5,12,2,1,4,7,6,10,3]=>11101101000
[10,8,11,5,12,2,1,4,7,9,6,3]=>11101101000
[9,10,11,5,12,2,1,4,8,7,6,3]=>11101110000
[12,10,6,7,8,2,1,5,4,3,9,11]=>11110100010
[11,12,6,7,8,2,1,5,4,3,10,9]=>11110100100
[12,9,6,7,10,2,1,5,4,8,3,11]=>11110100100
[11,9,6,7,12,2,1,5,4,8,10,3]=>11110100100
[10,11,6,7,12,2,1,5,4,9,8,3]=>11110101000
[12,8,6,9,10,2,1,5,7,4,3,11]=>11110101000
[11,8,6,9,12,2,1,5,7,4,10,3]=>11110101000
[10,8,6,11,12,2,1,5,7,9,4,3]=>11110101000
[9,10,6,11,12,2,1,5,8,7,4,3]=>11110110000
[12,7,8,9,10,2,1,6,5,4,3,11]=>11111010000
[11,7,8,9,12,2,1,6,5,4,10,3]=>11111010000
[10,7,8,11,12,2,1,6,5,9,4,3]=>11111010000
[9,7,10,11,12,2,1,6,8,5,4,3]=>11111010000
[8,9,10,11,12,2,1,7,6,5,4,3]=>11111100000
[12,10,8,6,3,4,2,1,5,7,9,11]=>11100101010
[11,12,8,6,3,4,2,1,5,7,10,9]=>11100101100
[12,9,10,6,3,4,2,1,5,8,7,11]=>11100110100
[11,9,12,6,3,4,2,1,5,8,10,7]=>11100110100
[10,11,12,6,3,4,2,1,5,9,8,7]=>11100111000
[12,10,7,8,3,4,2,1,6,5,9,11]=>11101010010
[11,12,7,8,3,4,2,1,6,5,10,9]=>11101010100
[12,9,7,10,3,4,2,1,6,8,5,11]=>11101010100
[11,9,7,12,3,4,2,1,6,8,10,5]=>11101010100
[10,11,7,12,3,4,2,1,6,9,8,5]=>11101011000
[12,8,9,10,3,4,2,1,7,6,5,11]=>11101101000
[11,8,9,12,3,4,2,1,7,6,10,5]=>11101101000
[10,8,11,12,3,4,2,1,7,9,6,5]=>11101101000
[9,10,11,12,3,4,2,1,8,7,6,5]=>11101110000
[12,10,8,5,3,6,2,4,1,7,9,11]=>11101001010
[11,12,8,5,3,6,2,4,1,7,10,9]=>11101001100
[12,9,10,5,3,6,2,4,1,8,7,11]=>11101010100
[11,9,12,5,3,6,2,4,1,8,10,7]=>11101010100
[10,11,12,5,3,6,2,4,1,9,8,7]=>11101011000
[12,10,7,5,3,8,2,4,6,1,9,11]=>11101010010
[11,12,7,5,3,8,2,4,6,1,10,9]=>11101010100
[12,9,7,5,3,10,2,4,6,8,1,11]=>11101010100
[11,9,7,5,3,12,2,4,6,8,10,1]=>11101010100
[10,11,7,5,3,12,2,4,6,9,8,1]=>11101011000
[12,8,9,5,3,10,2,4,7,6,1,11]=>11101101000
[11,8,9,5,3,12,2,4,7,6,10,1]=>11101101000
[10,8,11,5,3,12,2,4,7,9,6,1]=>11101101000
[9,10,11,5,3,12,2,4,8,7,6,1]=>11101110000
[12,10,6,7,3,8,2,5,4,1,9,11]=>11110100010
[11,12,6,7,3,8,2,5,4,1,10,9]=>11110100100
[12,9,6,7,3,10,2,5,4,8,1,11]=>11110100100
[11,9,6,7,3,12,2,5,4,8,10,1]=>11110100100
[10,11,6,7,3,12,2,5,4,9,8,1]=>11110101000
[12,8,6,9,3,10,2,5,7,4,1,11]=>11110101000
[11,8,6,9,3,12,2,5,7,4,10,1]=>11110101000
[10,8,6,11,3,12,2,5,7,9,4,1]=>11110101000
[9,10,6,11,3,12,2,5,8,7,4,1]=>11110110000
[12,7,8,9,3,10,2,6,5,4,1,11]=>11111010000
[11,7,8,9,3,12,2,6,5,4,10,1]=>11111010000
[10,7,8,11,3,12,2,6,5,9,4,1]=>11111010000
[9,7,10,11,3,12,2,6,8,5,4,1]=>11111010000
[8,9,10,11,3,12,2,7,6,5,4,1]=>11111100000
[12,10,8,4,5,6,3,2,1,7,9,11]=>11110001010
[11,12,8,4,5,6,3,2,1,7,10,9]=>11110001100
[12,9,10,4,5,6,3,2,1,8,7,11]=>11110010100
[11,9,12,4,5,6,3,2,1,8,10,7]=>11110010100
[10,11,12,4,5,6,3,2,1,9,8,7]=>11110011000
[12,10,7,4,5,8,3,2,6,1,9,11]=>11110010010
[11,12,7,4,5,8,3,2,6,1,10,9]=>11110010100
[12,9,7,4,5,10,3,2,6,8,1,11]=>11110010100
[11,9,7,4,5,12,3,2,6,8,10,1]=>11110010100
[10,11,7,4,5,12,3,2,6,9,8,1]=>11110011000
[12,8,9,4,5,10,3,2,7,6,1,11]=>11110101000
[11,8,9,4,5,12,3,2,7,6,10,1]=>11110101000
[10,8,11,4,5,12,3,2,7,9,6,1]=>11110101000
[9,10,11,4,5,12,3,2,8,7,6,1]=>11110110000
[12,10,6,4,7,8,3,5,2,1,9,11]=>11110100010
[11,12,6,4,7,8,3,5,2,1,10,9]=>11110100100
[12,9,6,4,7,10,3,5,2,8,1,11]=>11110100100
[11,9,6,4,7,12,3,5,2,8,10,1]=>11110100100
[10,11,6,4,7,12,3,5,2,9,8,1]=>11110101000
[12,8,6,4,9,10,3,5,7,2,1,11]=>11110101000
[11,8,6,4,9,12,3,5,7,2,10,1]=>11110101000
[10,8,6,4,11,12,3,5,7,9,2,1]=>11110101000
[9,10,6,4,11,12,3,5,8,7,2,1]=>11110110000
[12,7,8,4,9,10,3,6,5,2,1,11]=>11111010000
[11,7,8,4,9,12,3,6,5,2,10,1]=>11111010000
[10,7,8,4,11,12,3,6,5,9,2,1]=>11111010000
[9,7,10,4,11,12,3,6,8,5,2,1]=>11111010000
[8,9,10,4,11,12,3,7,6,5,2,1]=>11111100000
[12,10,5,6,7,8,4,3,2,1,9,11]=>11111000010
[11,12,5,6,7,8,4,3,2,1,10,9]=>11111000100
[12,9,5,6,7,10,4,3,2,8,1,11]=>11111000100
[11,9,5,6,7,12,4,3,2,8,10,1]=>11111000100
[10,11,5,6,7,12,4,3,2,9,8,1]=>11111001000
[12,8,5,6,9,10,4,3,7,2,1,11]=>11111001000
[11,8,5,6,9,12,4,3,7,2,10,1]=>11111001000
[10,8,5,6,11,12,4,3,7,9,2,1]=>11111001000
[9,10,5,6,11,12,4,3,8,7,2,1]=>11111010000
[12,7,5,8,9,10,4,6,3,2,1,11]=>11111010000
[11,7,5,8,9,12,4,6,3,2,10,1]=>11111010000
[10,7,5,8,11,12,4,6,3,9,2,1]=>11111010000
[9,7,5,10,11,12,4,6,8,3,2,1]=>11111010000
[8,9,5,10,11,12,4,7,6,3,2,1]=>11111100000
[12,6,7,8,9,10,5,4,3,2,1,11]=>11111100000
[11,6,7,8,9,12,5,4,3,2,10,1]=>11111100000
[10,6,7,8,11,12,5,4,3,9,2,1]=>11111100000
[9,6,7,10,11,12,5,4,8,3,2,1]=>11111100000
[8,6,9,10,11,12,5,7,4,3,2,1]=>11111100000
[11,12,2,4,6,8,10,1,3,5,7,9]=>11000000000
[9,10,2,4,6,8,12,1,3,5,7,11]=>11000000000
[11,9,12,2,4,6,8,10,1,3,5,7]=>11000000100
[10,11,12,9,2,4,6,8,1,3,5,7]=>11000000100
[7,8,2,4,6,10,12,1,3,5,9,11]=>11000000000
[7,8,11,12,2,4,6,10,1,3,5,9]=>11000000000
[9,7,10,2,4,6,8,12,1,3,5,11]=>11000010000
[9,11,7,12,2,4,6,8,10,1,3,5]=>11000010000
[7,10,11,12,9,2,4,6,8,1,3,5]=>11000000100
[8,9,10,7,2,4,6,12,1,3,5,11]=>11000010000
[11,8,9,7,12,2,4,6,10,1,3,5]=>11000011000
[10,11,8,12,7,9,2,4,6,1,3,5]=>11000011000
[9,10,11,12,8,7,2,4,6,1,3,5]=>11000011000
[5,6,2,4,8,10,12,1,3,7,9,11]=>11000000000
[5,6,11,12,2,4,8,10,1,3,7,9]=>11000000000
[5,6,9,10,2,4,8,12,1,3,7,11]=>11000000000
[11,5,6,9,12,2,4,8,10,1,3,7]=>11001000000
[10,11,12,5,6,9,2,4,8,1,3,7]=>11001000000
[7,5,8,2,4,6,10,12,1,3,9,11]=>11001000000
[7,5,8,11,12,2,4,6,10,1,3,9]=>11001000000
[7,9,5,10,2,4,6,8,12,1,3,11]=>11001000000
[7,9,11,5,12,2,4,6,8,10,1,3]=>11001000000
[10,7,11,12,5,9,2,4,6,8,1,3]=>11001010000
[5,8,9,10,7,2,4,6,12,1,3,11]=>11000010000
[11,5,8,9,7,12,2,4,6,10,1,3]=>11001010000
[8,10,5,11,12,7,9,2,4,6,1,3]=>11001010000
[9,10,11,12,5,8,7,2,4,6,1,3]=>11001010000
[6,7,8,5,2,4,10,12,1,3,9,11]=>11001000000
[6,7,8,5,11,12,2,4,10,1,3,9]=>11001000000
[9,6,7,5,10,2,4,8,12,1,3,11]=>11001100000
[9,6,7,11,5,12,2,4,8,10,1,3]=>11001100000
[6,10,7,11,12,5,9,2,4,8,1,3]=>11001010000
[8,9,6,10,5,7,2,4,12,1,3,11]=>11001100000
[8,9,11,6,5,7,12,2,4,10,1,3]=>11001100000
[10,8,11,6,12,5,7,9,2,4,1,3]=>11001101000
[9,6,10,11,12,8,5,7,2,4,1,3]=>11001101000
[7,8,9,10,6,5,2,4,12,1,3,11]=>11001100000
[11,7,8,9,6,5,12,2,4,10,1,3]=>11001110000
[10,11,7,8,6,12,5,9,2,4,1,3]=>11001110000
[9,10,11,7,12,6,8,5,2,4,1,3]=>11001110000
[8,9,10,11,12,7,6,5,2,4,1,3]=>11001110000
[3,4,2,6,8,10,12,1,5,7,9,11]=>11000000000
[3,4,11,12,2,6,8,10,1,5,7,9]=>11000000000
[3,4,9,10,2,6,8,12,1,5,7,11]=>11000000000
[11,3,4,9,12,2,6,8,10,1,5,7]=>11100000000
[10,11,12,3,4,9,2,6,8,1,5,7]=>11100000000
[3,4,7,8,2,6,10,12,1,5,9,11]=>11000000000
[3,4,7,8,11,12,2,6,10,1,5,9]=>11000000000
[9,3,4,7,10,2,6,8,12,1,5,11]=>11100000000
[9,11,3,4,7,12,2,6,8,10,1,5]=>11100000000
[3,10,11,12,4,7,9,2,6,8,1,5]=>11010000000
[8,9,10,3,4,7,2,6,12,1,5,11]=>11100000000
[11,8,9,3,4,7,12,2,6,10,1,5]=>11100001000
[10,11,8,12,3,4,7,9,2,6,1,5]=>11100001000
[9,10,11,12,8,3,4,7,2,6,1,5]=>11100001000
[5,3,6,2,4,8,10,12,1,7,9,11]=>11100000000
[5,3,6,11,12,2,4,8,10,1,7,9]=>11100000000
[5,3,6,9,10,2,4,8,12,1,7,11]=>11100000000
[5,11,3,6,9,12,2,4,8,10,1,7]=>11100000000
[5,10,11,12,3,6,9,2,4,8,1,7]=>11100000000
[5,7,3,8,2,4,6,10,12,1,9,11]=>11100000000
[5,7,3,8,11,12,2,4,6,10,1,9]=>11100000000
[5,7,9,3,10,2,4,6,8,12,1,11]=>11100000000
[5,7,9,11,3,12,2,4,6,8,10,1]=>11100000000
[10,5,7,11,12,3,9,2,4,6,8,1]=>11101000000
[8,5,9,10,3,7,2,4,6,12,1,11]=>11101000000
[8,11,5,9,3,7,12,2,4,6,10,1]=>11101000000
[8,10,11,5,12,3,7,9,2,4,6,1]=>11101000000
[5,9,10,11,12,8,3,7,2,4,6,1]=>11100001000
[3,6,7,8,5,2,4,10,12,1,9,11]=>11001000000
[3,6,7,8,5,11,12,2,4,10,1,9]=>11001000000
[9,3,6,7,5,10,2,4,8,12,1,11]=>11101000000
[9,3,6,7,11,5,12,2,4,8,10,1]=>11101000000
[6,10,3,7,11,12,5,9,2,4,8,1]=>11101000000
[6,8,3,9,10,5,7,2,4,12,1,11]=>11101000000
[6,8,9,3,11,5,7,12,2,4,10,1]=>11101000000
[10,6,8,3,11,12,5,7,9,2,4,1]=>11101100000
[9,6,10,11,12,3,8,5,7,2,4,1]=>11101100000
[7,8,9,10,3,6,5,2,4,12,1,11]=>11101000000
[11,7,8,9,3,6,5,12,2,4,10,1]=>11101010000
[10,11,7,8,3,6,12,5,9,2,4,1]=>11101010000
[9,10,11,7,12,3,6,8,5,2,4,1]=>11101010000
[8,9,10,11,12,7,3,6,5,2,4,1]=>11101010000
[4,5,6,3,2,8,10,12,1,7,9,11]=>11100000000
[4,5,6,3,11,12,2,8,10,1,7,9]=>11100000000
[4,5,6,3,9,10,2,8,12,1,7,11]=>11100000000
[4,5,6,11,3,9,12,2,8,10,1,7]=>11100000000
[4,5,6,10,11,12,3,9,2,8,1,7]=>11100000000
[7,4,5,3,8,2,6,10,12,1,9,11]=>11110000000
[7,4,5,3,8,11,12,2,6,10,1,9]=>11110000000
[7,4,5,9,3,10,2,6,8,12,1,11]=>11110000000
[7,4,5,9,11,3,12,2,6,8,10,1]=>11110000000
[7,10,4,5,11,12,3,9,2,6,8,1]=>11110000000
[4,8,5,9,10,3,7,2,6,12,1,11]=>11101000000
[4,8,11,5,9,3,7,12,2,6,10,1]=>11101000000
[4,8,10,11,5,12,3,7,9,2,6,1]=>11101000000
[4,5,9,10,11,12,8,3,7,2,6,1]=>11100001000
[6,7,4,8,3,5,2,10,12,1,9,11]=>11110000000
[6,7,4,8,3,5,11,12,2,10,1,9]=>11110000000
[6,7,9,4,3,5,10,2,8,12,1,11]=>11110000000
[6,7,9,4,11,3,5,12,2,8,10,1]=>11110000000
[10,6,7,4,11,12,3,5,9,2,8,1]=>11110100000
[8,6,9,4,10,3,5,7,2,12,1,11]=>11110100000
[8,6,9,11,4,3,5,7,12,2,10,1]=>11110100000
[8,10,6,11,4,12,3,5,7,9,2,1]=>11110100000
[6,9,4,10,11,12,8,3,5,7,2,1]=>11110001000
[7,4,8,9,10,6,3,5,2,12,1,11]=>11110100000
[7,11,4,8,9,6,3,5,12,2,10,1]=>11110100000
[7,8,10,4,11,6,12,3,5,9,2,1]=>11110100000
[9,7,10,4,11,12,6,8,3,5,2,1]=>11110110000
[4,8,9,10,11,12,7,6,3,5,2,1]=>11100110000
[5,6,7,8,4,3,2,10,12,1,9,11]=>11110000000
[5,6,7,8,4,3,11,12,2,10,1,9]=>11110000000
[9,5,6,7,4,3,10,2,8,12,1,11]=>11111000000
[9,5,6,7,4,11,3,12,2,8,10,1]=>11111000000
[5,10,6,7,4,11,12,3,9,2,8,1]=>11110100000
[8,9,5,6,4,10,3,7,2,12,1,11]=>11111000000
[8,9,5,6,11,4,3,7,12,2,10,1]=>11111000000
[10,8,5,6,11,4,12,3,7,9,2,1]=>11111001000
[9,5,10,6,11,12,4,8,3,7,2,1]=>11111100000
[7,8,9,5,10,4,6,3,2,12,1,11]=>11111000000
[7,8,9,11,5,4,6,3,12,2,10,1]=>11111000000
[10,7,8,11,5,4,6,12,3,9,2,1]=>11111010000
[9,10,7,11,5,12,4,6,8,3,2,1]=>11111010000
[8,9,5,10,11,12,7,4,6,3,2,1]=>11111010000
[6,7,8,9,10,5,4,3,2,12,1,11]=>11111000000
[11,6,7,8,9,5,4,3,12,2,10,1]=>11111100000
[10,11,6,7,8,5,4,12,3,9,2,1]=>11111100000
[9,10,11,6,7,5,12,4,8,3,2,1]=>11111100000
[8,9,10,11,6,12,5,7,4,3,2,1]=>11111100000
[2,1,4,3,6,5,8,7,12,9,11,10]=>10101010110
[2,1,4,3,6,5,10,7,9,8,12,11]=>10101011001
[2,1,4,3,6,5,12,11,9,7,8,10]=>10101010101
[2,1,4,3,6,5,12,7,8,10,11,9]=>10101010100
[2,1,4,3,8,5,7,6,10,9,12,11]=>10101100101
[2,1,4,3,8,5,7,6,12,9,11,10]=>10101100110
[2,1,4,3,10,9,7,5,6,8,12,11]=>10101010101
[2,1,4,3,12,9,7,11,6,5,8,10]=>10101110100
[2,1,4,3,12,10,7,5,8,6,11,9]=>10101110110
[2,1,4,3,10,5,6,8,9,7,12,11]=>10101010001
[2,1,4,3,12,11,6,8,9,5,7,10]=>10101100001
[2,1,4,3,12,5,11,8,6,10,7,9]=>10101111000
[2,1,4,3,12,5,6,7,9,10,11,8]=>10101001000
[2,1,6,3,5,4,8,7,10,9,12,11]=>10110010101
[2,1,6,3,5,4,8,7,12,9,11,10]=>10110010110
[2,1,6,3,5,4,10,7,9,8,12,11]=>10110011001
[2,1,6,3,5,4,12,11,9,7,8,10]=>10110010101
[2,1,6,3,5,4,12,7,8,10,11,9]=>10110010100
[2,1,8,7,5,3,4,6,10,9,12,11]=>10101010101
[2,1,8,7,5,3,4,6,12,9,11,10]=>10101010110
[2,1,10,7,5,9,4,3,6,8,12,11]=>10111010001
[2,1,12,7,5,9,4,11,6,3,8,10]=>10111110000
[2,1,12,7,5,10,4,3,8,6,11,9]=>10111110100
[2,1,10,8,5,3,6,4,9,7,12,11]=>10111011001
[2,1,12,8,5,11,6,4,9,3,7,10]=>10111101000
[2,1,12,8,5,3,11,4,6,10,7,9]=>10111011000
[2,1,12,9,5,3,6,7,4,10,11,8]=>10111001100
[2,1,8,3,4,6,7,5,10,9,12,11]=>10101000101
[2,1,8,3,4,6,7,5,12,9,11,10]=>10101000110
[2,1,10,9,4,6,7,3,5,8,12,11]=>10110000101
[2,1,12,9,4,6,7,11,5,3,8,10]=>10111000100
[2,1,12,10,4,6,7,3,8,5,11,9]=>10111000110
[2,1,10,3,9,6,4,8,5,7,12,11]=>10111100001
[2,1,12,11,9,6,4,8,5,3,7,10]=>10111100101
[2,1,12,3,10,6,11,8,4,5,7,9]=>10110101000
[2,1,12,3,10,6,4,7,9,5,11,8]=>10111101000
[2,1,10,3,4,5,7,8,9,6,12,11]=>10100100001
[2,1,12,11,4,5,7,8,9,3,6,10]=>10110000001
[2,1,12,3,11,5,7,8,4,10,6,9]=>10111100000
[2,1,12,3,4,11,7,5,9,10,6,8]=>10101110000
[2,1,12,3,4,5,6,8,9,10,11,7]=>10100010000
[4,1,3,2,6,5,8,7,10,9,12,11]=>11001010101
[4,1,3,2,6,5,8,7,12,9,11,10]=>11001010110
[4,1,3,2,6,5,10,7,9,8,12,11]=>11001011001
[4,1,3,2,6,5,12,11,9,7,8,10]=>11001010101
[4,1,3,2,6,5,12,7,8,10,11,9]=>11001010100
[4,1,3,2,8,5,7,6,10,9,12,11]=>11001100101
[4,1,3,2,8,5,7,6,12,9,11,10]=>11001100110
[4,1,3,2,10,9,7,5,6,8,12,11]=>11001010101
[4,1,3,2,12,9,7,11,6,5,8,10]=>11001110100
[4,1,3,2,12,10,7,5,8,6,11,9]=>11001110110
[4,1,3,2,10,5,6,8,9,7,12,11]=>11001010001
[4,1,3,2,12,11,6,8,9,5,7,10]=>11001100001
[4,1,3,2,12,5,11,8,6,10,7,9]=>11001111000
[4,1,3,2,12,5,6,7,9,10,11,8]=>11001001000
[6,5,3,1,2,4,8,7,10,9,12,11]=>10101010101
[6,5,3,1,2,4,8,7,12,9,11,10]=>10101010110
[6,5,3,1,2,4,10,7,9,8,12,11]=>10101011001
[6,5,3,1,2,4,12,11,9,7,8,10]=>10101010101
[6,5,3,1,2,4,12,7,8,10,11,9]=>10101010100
[8,5,3,7,2,1,4,6,10,9,12,11]=>11101000101
[8,5,3,7,2,1,4,6,12,9,11,10]=>11101000110
[10,5,3,7,2,9,4,1,6,8,12,11]=>11111000001
[12,5,3,7,2,9,4,11,6,1,8,10]=>11111100000
[12,5,3,7,2,10,4,1,8,6,11,9]=>11111100100
[10,5,3,8,2,1,6,4,9,7,12,11]=>11111010001
[12,5,3,8,2,11,6,4,9,1,7,10]=>11111100000
[12,5,3,8,2,1,11,4,6,10,7,9]=>11111010000
[12,5,3,9,2,1,6,7,4,10,11,8]=>11111001000
[8,6,3,1,4,2,7,5,10,9,12,11]=>11101100101
[8,6,3,1,4,2,7,5,12,9,11,10]=>11101100110
[10,6,3,9,4,2,7,1,5,8,12,11]=>11110100001
[12,6,3,9,4,2,7,11,5,1,8,10]=>11111100000
[12,6,3,10,4,2,7,1,8,5,11,9]=>11111100100
[10,6,3,1,9,2,4,8,5,7,12,11]=>11101100001
[12,6,3,11,9,2,4,8,5,1,7,10]=>11101100100
[12,6,3,1,10,2,11,8,4,5,7,9]=>11110101000
[12,6,3,1,10,2,4,7,9,5,11,8]=>11101101000
[10,7,3,1,4,5,2,8,9,6,12,11]=>11100110001
[12,7,3,11,4,5,2,8,9,1,6,10]=>11110010000
[12,7,3,1,11,5,2,8,4,10,6,9]=>11111110000
[12,7,3,1,4,11,2,5,9,10,6,8]=>11100110000
[12,8,3,1,4,5,6,2,9,10,11,7]=>11100011000
[6,1,2,4,5,3,8,7,10,9,12,11]=>10100010101
[6,1,2,4,5,3,8,7,12,9,11,10]=>10100010110
[6,1,2,4,5,3,10,7,9,8,12,11]=>10100011001
[6,1,2,4,5,3,12,11,9,7,8,10]=>10100010101
[6,1,2,4,5,3,12,7,8,10,11,9]=>10100010100
[8,7,2,4,5,1,3,6,10,9,12,11]=>11000010101
[8,7,2,4,5,1,3,6,12,9,11,10]=>11000010110
[10,7,2,4,5,9,3,1,6,8,12,11]=>11100010001
[12,7,2,4,5,9,3,11,6,1,8,10]=>11100110000
[12,7,2,4,5,10,3,1,8,6,11,9]=>11100110100
[10,8,2,4,5,1,6,3,9,7,12,11]=>11100011001
[12,8,2,4,5,11,6,3,9,1,7,10]=>11100101000
[12,8,2,4,5,1,11,3,6,10,7,9]=>11100011000
[12,9,2,4,5,1,6,7,3,10,11,8]=>11100001100
[8,1,7,4,2,6,3,5,10,9,12,11]=>11110000101
[8,1,7,4,2,6,3,5,12,9,11,10]=>11110000110
[10,9,7,4,2,6,3,1,5,8,12,11]=>11110010101
[12,9,7,4,2,6,3,11,5,1,8,10]=>11111010100
[12,10,7,4,2,6,3,1,8,5,11,9]=>11111010110
[10,1,8,4,9,6,2,3,5,7,12,11]=>11010100001
[12,11,8,4,9,6,2,3,5,1,7,10]=>11010101001
[12,1,8,4,10,6,11,3,2,5,7,9]=>11110100000
[12,1,9,4,10,6,2,7,3,5,11,8]=>11110101000
[10,1,8,4,2,5,7,3,9,6,12,11]=>11110100001
[12,11,8,4,2,5,7,3,9,1,6,10]=>11110001001
[12,1,8,4,11,5,7,3,2,10,6,9]=>11111100000
[12,1,9,4,2,11,7,5,3,10,6,8]=>11111110000
[12,1,9,4,2,5,6,8,3,10,11,7]=>11110010000
[8,1,2,3,5,6,7,4,10,9,12,11]=>10010000101
[8,1,2,3,5,6,7,4,12,9,11,10]=>10010000110
[10,9,2,3,5,6,7,1,4,8,12,11]=>11000000101
[12,9,2,3,5,6,7,11,4,1,8,10]=>11010000100
[12,10,2,3,5,6,7,1,8,4,11,9]=>11010000110
[10,1,9,3,5,6,2,8,4,7,12,11]=>11110000001
[12,11,9,3,5,6,2,8,4,1,7,10]=>11110000101
[12,1,10,3,5,6,11,8,2,4,7,9]=>11100001000
[12,1,10,3,5,6,2,7,9,4,11,8]=>11110001000
[10,1,2,9,5,3,7,8,4,6,12,11]=>10111000001
[12,11,2,9,5,3,7,8,4,1,6,10]=>11111000001
[12,1,11,10,5,3,7,8,2,4,6,9]=>11101000010
[12,1,2,10,5,11,7,3,9,4,6,8]=>10111010000
[12,1,2,10,5,3,6,8,9,4,11,7]=>10111010000
[10,1,2,3,4,6,7,8,9,5,12,11]=>10001000001
[12,11,2,3,4,6,7,8,9,1,5,10]=>11000000001
[12,1,11,3,4,6,7,8,2,10,5,9]=>11101000000
[12,1,2,11,4,6,7,3,9,10,5,8]=>10111000000
[12,1,2,3,11,6,4,8,9,10,5,7]=>10011100000
[12,1,2,3,4,5,7,8,9,10,11,6]=>10000100000
          

click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

The descent bottoms of a permutation as a binary word.

Properties

surjective, graded

Sage code

def mapping(pi):
    """
    Return the elements which are descent bottoms as a binary word.
    Since n is never a descent bottom, it is omitted.

    sage: mapping(Permutation([3,1,2]))
    word: 10
    """
    D = [pi[i+1] for i in pi.descents(from_zero=True)]
    return Words([0,1])([1 if i in D else 0 for i in range(1,len(pi))])

Weight

Created

Jan 29, 2020 at 13:27 by FindStatCrew

Updated

Jan 29, 2020 at 13:27 by Martin Rubey