Identifier
Images
=>
[1]=>
[1,2]=>1
[2,1]=>0
[1,2,3]=>11
[1,3,2]=>10
[2,1,3]=>01
[2,3,1]=>00
[3,1,2]=>00
[3,2,1]=>00
[1,2,3,4]=>111
[1,2,4,3]=>110
[1,3,2,4]=>101
[1,3,4,2]=>100
[1,4,2,3]=>100
[1,4,3,2]=>100
[2,1,3,4]=>011
[2,1,4,3]=>010
[2,3,1,4]=>001
[2,3,4,1]=>000
[2,4,1,3]=>000
[2,4,3,1]=>000
[3,1,2,4]=>001
[3,1,4,2]=>000
[3,2,1,4]=>001
[3,2,4,1]=>000
[3,4,1,2]=>000
[3,4,2,1]=>000
[4,1,2,3]=>000
[4,1,3,2]=>000
[4,2,1,3]=>000
[4,2,3,1]=>000
[4,3,1,2]=>000
[4,3,2,1]=>000
[1,2,3,4,5]=>1111
[1,2,3,5,4]=>1110
[1,2,4,3,5]=>1101
[1,2,4,5,3]=>1100
[1,2,5,3,4]=>1100
[1,2,5,4,3]=>1100
[1,3,2,4,5]=>1011
[1,3,2,5,4]=>1010
[1,3,4,2,5]=>1001
[1,3,4,5,2]=>1000
[1,3,5,2,4]=>1000
[1,3,5,4,2]=>1000
[1,4,2,3,5]=>1001
[1,4,2,5,3]=>1000
[1,4,3,2,5]=>1001
[1,4,3,5,2]=>1000
[1,4,5,2,3]=>1000
[1,4,5,3,2]=>1000
[1,5,2,3,4]=>1000
[1,5,2,4,3]=>1000
[1,5,3,2,4]=>1000
[1,5,3,4,2]=>1000
[1,5,4,2,3]=>1000
[1,5,4,3,2]=>1000
[2,1,3,4,5]=>0111
[2,1,3,5,4]=>0110
[2,1,4,3,5]=>0101
[2,1,4,5,3]=>0100
[2,1,5,3,4]=>0100
[2,1,5,4,3]=>0100
[2,3,1,4,5]=>0011
[2,3,1,5,4]=>0010
[2,3,4,1,5]=>0001
[2,3,4,5,1]=>0000
[2,3,5,1,4]=>0000
[2,3,5,4,1]=>0000
[2,4,1,3,5]=>0001
[2,4,1,5,3]=>0000
[2,4,3,1,5]=>0001
[2,4,3,5,1]=>0000
[2,4,5,1,3]=>0000
[2,4,5,3,1]=>0000
[2,5,1,3,4]=>0000
[2,5,1,4,3]=>0000
[2,5,3,1,4]=>0000
[2,5,3,4,1]=>0000
[2,5,4,1,3]=>0000
[2,5,4,3,1]=>0000
[3,1,2,4,5]=>0011
[3,1,2,5,4]=>0010
[3,1,4,2,5]=>0001
[3,1,4,5,2]=>0000
[3,1,5,2,4]=>0000
[3,1,5,4,2]=>0000
[3,2,1,4,5]=>0011
[3,2,1,5,4]=>0010
[3,2,4,1,5]=>0001
[3,2,4,5,1]=>0000
[3,2,5,1,4]=>0000
[3,2,5,4,1]=>0000
[3,4,1,2,5]=>0001
[3,4,1,5,2]=>0000
[3,4,2,1,5]=>0001
[3,4,2,5,1]=>0000
[3,4,5,1,2]=>0000
[3,4,5,2,1]=>0000
[3,5,1,2,4]=>0000
[3,5,1,4,2]=>0000
[3,5,2,1,4]=>0000
[3,5,2,4,1]=>0000
[3,5,4,1,2]=>0000
[3,5,4,2,1]=>0000
[4,1,2,3,5]=>0001
[4,1,2,5,3]=>0000
[4,1,3,2,5]=>0001
[4,1,3,5,2]=>0000
[4,1,5,2,3]=>0000
[4,1,5,3,2]=>0000
[4,2,1,3,5]=>0001
[4,2,1,5,3]=>0000
[4,2,3,1,5]=>0001
[4,2,3,5,1]=>0000
[4,2,5,1,3]=>0000
[4,2,5,3,1]=>0000
[4,3,1,2,5]=>0001
[4,3,1,5,2]=>0000
[4,3,2,1,5]=>0001
[4,3,2,5,1]=>0000
[4,3,5,1,2]=>0000
[4,3,5,2,1]=>0000
[4,5,1,2,3]=>0000
[4,5,1,3,2]=>0000
[4,5,2,1,3]=>0000
[4,5,2,3,1]=>0000
[4,5,3,1,2]=>0000
[4,5,3,2,1]=>0000
[5,1,2,3,4]=>0000
[5,1,2,4,3]=>0000
[5,1,3,2,4]=>0000
[5,1,3,4,2]=>0000
[5,1,4,2,3]=>0000
[5,1,4,3,2]=>0000
[5,2,1,3,4]=>0000
[5,2,1,4,3]=>0000
[5,2,3,1,4]=>0000
[5,2,3,4,1]=>0000
[5,2,4,1,3]=>0000
[5,2,4,3,1]=>0000
[5,3,1,2,4]=>0000
[5,3,1,4,2]=>0000
[5,3,2,1,4]=>0000
[5,3,2,4,1]=>0000
[5,3,4,1,2]=>0000
[5,3,4,2,1]=>0000
[5,4,1,2,3]=>0000
[5,4,1,3,2]=>0000
[5,4,2,1,3]=>0000
[5,4,2,3,1]=>0000
[5,4,3,1,2]=>0000
[5,4,3,2,1]=>0000
[1,2,3,4,5,6]=>11111
[1,2,3,4,6,5]=>11110
[1,2,3,5,4,6]=>11101
[1,2,3,5,6,4]=>11100
[1,2,3,6,4,5]=>11100
[1,2,3,6,5,4]=>11100
[1,2,4,3,5,6]=>11011
[1,2,4,3,6,5]=>11010
[1,2,4,5,3,6]=>11001
[1,2,4,5,6,3]=>11000
[1,2,4,6,3,5]=>11000
[1,2,4,6,5,3]=>11000
[1,2,5,3,4,6]=>11001
[1,2,5,3,6,4]=>11000
[1,2,5,4,3,6]=>11001
[1,2,5,4,6,3]=>11000
[1,2,5,6,3,4]=>11000
[1,2,5,6,4,3]=>11000
[1,2,6,3,4,5]=>11000
[1,2,6,3,5,4]=>11000
[1,2,6,4,3,5]=>11000
[1,2,6,4,5,3]=>11000
[1,2,6,5,3,4]=>11000
[1,2,6,5,4,3]=>11000
[1,3,2,4,5,6]=>10111
[1,3,2,4,6,5]=>10110
[1,3,2,5,4,6]=>10101
[1,3,2,5,6,4]=>10100
[1,3,2,6,4,5]=>10100
[1,3,2,6,5,4]=>10100
[1,3,4,2,5,6]=>10011
[1,3,4,2,6,5]=>10010
[1,3,4,5,2,6]=>10001
[1,3,4,5,6,2]=>10000
[1,3,4,6,2,5]=>10000
[1,3,4,6,5,2]=>10000
[1,3,5,2,4,6]=>10001
[1,3,5,2,6,4]=>10000
[1,3,5,4,2,6]=>10001
[1,3,5,4,6,2]=>10000
[1,3,5,6,2,4]=>10000
[1,3,5,6,4,2]=>10000
[1,3,6,2,4,5]=>10000
[1,3,6,2,5,4]=>10000
[1,3,6,4,2,5]=>10000
[1,3,6,4,5,2]=>10000
[1,3,6,5,2,4]=>10000
[1,3,6,5,4,2]=>10000
[1,4,2,3,5,6]=>10011
[1,4,2,3,6,5]=>10010
[1,4,2,5,3,6]=>10001
[1,4,2,5,6,3]=>10000
[1,4,2,6,3,5]=>10000
[1,4,2,6,5,3]=>10000
[1,4,3,2,5,6]=>10011
[1,4,3,2,6,5]=>10010
[1,4,3,5,2,6]=>10001
[1,4,3,5,6,2]=>10000
[1,4,3,6,2,5]=>10000
[1,4,3,6,5,2]=>10000
[1,4,5,2,3,6]=>10001
[1,4,5,2,6,3]=>10000
[1,4,5,3,2,6]=>10001
[1,4,5,3,6,2]=>10000
[1,4,5,6,2,3]=>10000
[1,4,5,6,3,2]=>10000
[1,4,6,2,3,5]=>10000
[1,4,6,2,5,3]=>10000
[1,4,6,3,2,5]=>10000
[1,4,6,3,5,2]=>10000
[1,4,6,5,2,3]=>10000
[1,4,6,5,3,2]=>10000
[1,5,2,3,4,6]=>10001
[1,5,2,3,6,4]=>10000
[1,5,2,4,3,6]=>10001
[1,5,2,4,6,3]=>10000
[1,5,2,6,3,4]=>10000
[1,5,2,6,4,3]=>10000
[1,5,3,2,4,6]=>10001
[1,5,3,2,6,4]=>10000
[1,5,3,4,2,6]=>10001
[1,5,3,4,6,2]=>10000
[1,5,3,6,2,4]=>10000
[1,5,3,6,4,2]=>10000
[1,5,4,2,3,6]=>10001
[1,5,4,2,6,3]=>10000
[1,5,4,3,2,6]=>10001
[1,5,4,3,6,2]=>10000
[1,5,4,6,2,3]=>10000
[1,5,4,6,3,2]=>10000
[1,5,6,2,3,4]=>10000
[1,5,6,2,4,3]=>10000
[1,5,6,3,2,4]=>10000
[1,5,6,3,4,2]=>10000
[1,5,6,4,2,3]=>10000
[1,5,6,4,3,2]=>10000
[1,6,2,3,4,5]=>10000
[1,6,2,3,5,4]=>10000
[1,6,2,4,3,5]=>10000
[1,6,2,4,5,3]=>10000
[1,6,2,5,3,4]=>10000
[1,6,2,5,4,3]=>10000
[1,6,3,2,4,5]=>10000
[1,6,3,2,5,4]=>10000
[1,6,3,4,2,5]=>10000
[1,6,3,4,5,2]=>10000
[1,6,3,5,2,4]=>10000
[1,6,3,5,4,2]=>10000
[1,6,4,2,3,5]=>10000
[1,6,4,2,5,3]=>10000
[1,6,4,3,2,5]=>10000
[1,6,4,3,5,2]=>10000
[1,6,4,5,2,3]=>10000
[1,6,4,5,3,2]=>10000
[1,6,5,2,3,4]=>10000
[1,6,5,2,4,3]=>10000
[1,6,5,3,2,4]=>10000
[1,6,5,3,4,2]=>10000
[1,6,5,4,2,3]=>10000
[1,6,5,4,3,2]=>10000
[2,1,3,4,5,6]=>01111
[2,1,3,4,6,5]=>01110
[2,1,3,5,4,6]=>01101
[2,1,3,5,6,4]=>01100
[2,1,3,6,4,5]=>01100
[2,1,3,6,5,4]=>01100
[2,1,4,3,5,6]=>01011
[2,1,4,3,6,5]=>01010
[2,1,4,5,3,6]=>01001
[2,1,4,5,6,3]=>01000
[2,1,4,6,3,5]=>01000
[2,1,4,6,5,3]=>01000
[2,1,5,3,4,6]=>01001
[2,1,5,3,6,4]=>01000
[2,1,5,4,3,6]=>01001
[2,1,5,4,6,3]=>01000
[2,1,5,6,3,4]=>01000
[2,1,5,6,4,3]=>01000
[2,1,6,3,4,5]=>01000
[2,1,6,3,5,4]=>01000
[2,1,6,4,3,5]=>01000
[2,1,6,4,5,3]=>01000
[2,1,6,5,3,4]=>01000
[2,1,6,5,4,3]=>01000
[2,3,1,4,5,6]=>00111
[2,3,1,4,6,5]=>00110
[2,3,1,5,4,6]=>00101
[2,3,1,5,6,4]=>00100
[2,3,1,6,4,5]=>00100
[2,3,1,6,5,4]=>00100
[2,3,4,1,5,6]=>00011
[2,3,4,1,6,5]=>00010
[2,3,4,5,1,6]=>00001
[2,3,4,5,6,1]=>00000
[2,3,4,6,1,5]=>00000
[2,3,4,6,5,1]=>00000
[2,3,5,1,4,6]=>00001
[2,3,5,1,6,4]=>00000
[2,3,5,4,1,6]=>00001
[2,3,5,4,6,1]=>00000
[2,3,5,6,1,4]=>00000
[2,3,5,6,4,1]=>00000
[2,3,6,1,4,5]=>00000
[2,3,6,1,5,4]=>00000
[2,3,6,4,1,5]=>00000
[2,3,6,4,5,1]=>00000
[2,3,6,5,1,4]=>00000
[2,3,6,5,4,1]=>00000
[2,4,1,3,5,6]=>00011
[2,4,1,3,6,5]=>00010
[2,4,1,5,3,6]=>00001
[2,4,1,5,6,3]=>00000
[2,4,1,6,3,5]=>00000
[2,4,1,6,5,3]=>00000
[2,4,3,1,5,6]=>00011
[2,4,3,1,6,5]=>00010
[2,4,3,5,1,6]=>00001
[2,4,3,5,6,1]=>00000
[2,4,3,6,1,5]=>00000
[2,4,3,6,5,1]=>00000
[2,4,5,1,3,6]=>00001
[2,4,5,1,6,3]=>00000
[2,4,5,3,1,6]=>00001
[2,4,5,3,6,1]=>00000
[2,4,5,6,1,3]=>00000
[2,4,5,6,3,1]=>00000
[2,4,6,1,3,5]=>00000
[2,4,6,1,5,3]=>00000
[2,4,6,3,1,5]=>00000
[2,4,6,3,5,1]=>00000
[2,4,6,5,1,3]=>00000
[2,4,6,5,3,1]=>00000
[2,5,1,3,4,6]=>00001
[2,5,1,3,6,4]=>00000
[2,5,1,4,3,6]=>00001
[2,5,1,4,6,3]=>00000
[2,5,1,6,3,4]=>00000
[2,5,1,6,4,3]=>00000
[2,5,3,1,4,6]=>00001
[2,5,3,1,6,4]=>00000
[2,5,3,4,1,6]=>00001
[2,5,3,4,6,1]=>00000
[2,5,3,6,1,4]=>00000
[2,5,3,6,4,1]=>00000
[2,5,4,1,3,6]=>00001
[2,5,4,1,6,3]=>00000
[2,5,4,3,1,6]=>00001
[2,5,4,3,6,1]=>00000
[2,5,4,6,1,3]=>00000
[2,5,4,6,3,1]=>00000
[2,5,6,1,3,4]=>00000
[2,5,6,1,4,3]=>00000
[2,5,6,3,1,4]=>00000
[2,5,6,3,4,1]=>00000
[2,5,6,4,1,3]=>00000
[2,5,6,4,3,1]=>00000
[2,6,1,3,4,5]=>00000
[2,6,1,3,5,4]=>00000
[2,6,1,4,3,5]=>00000
[2,6,1,4,5,3]=>00000
[2,6,1,5,3,4]=>00000
[2,6,1,5,4,3]=>00000
[2,6,3,1,4,5]=>00000
[2,6,3,1,5,4]=>00000
[2,6,3,4,1,5]=>00000
[2,6,3,4,5,1]=>00000
[2,6,3,5,1,4]=>00000
[2,6,3,5,4,1]=>00000
[2,6,4,1,3,5]=>00000
[2,6,4,1,5,3]=>00000
[2,6,4,3,1,5]=>00000
[2,6,4,3,5,1]=>00000
[2,6,4,5,1,3]=>00000
[2,6,4,5,3,1]=>00000
[2,6,5,1,3,4]=>00000
[2,6,5,1,4,3]=>00000
[2,6,5,3,1,4]=>00000
[2,6,5,3,4,1]=>00000
[2,6,5,4,1,3]=>00000
[2,6,5,4,3,1]=>00000
[3,1,2,4,5,6]=>00111
[3,1,2,4,6,5]=>00110
[3,1,2,5,4,6]=>00101
[3,1,2,5,6,4]=>00100
[3,1,2,6,4,5]=>00100
[3,1,2,6,5,4]=>00100
[3,1,4,2,5,6]=>00011
[3,1,4,2,6,5]=>00010
[3,1,4,5,2,6]=>00001
[3,1,4,5,6,2]=>00000
[3,1,4,6,2,5]=>00000
[3,1,4,6,5,2]=>00000
[3,1,5,2,4,6]=>00001
[3,1,5,2,6,4]=>00000
[3,1,5,4,2,6]=>00001
[3,1,5,4,6,2]=>00000
[3,1,5,6,2,4]=>00000
[3,1,5,6,4,2]=>00000
[3,1,6,2,4,5]=>00000
[3,1,6,2,5,4]=>00000
[3,1,6,4,2,5]=>00000
[3,1,6,4,5,2]=>00000
[3,1,6,5,2,4]=>00000
[3,1,6,5,4,2]=>00000
[3,2,1,4,5,6]=>00111
[3,2,1,4,6,5]=>00110
[3,2,1,5,4,6]=>00101
[3,2,1,5,6,4]=>00100
[3,2,1,6,4,5]=>00100
[3,2,1,6,5,4]=>00100
[3,2,4,1,5,6]=>00011
[3,2,4,1,6,5]=>00010
[3,2,4,5,1,6]=>00001
[3,2,4,5,6,1]=>00000
[3,2,4,6,1,5]=>00000
[3,2,4,6,5,1]=>00000
[3,2,5,1,4,6]=>00001
[3,2,5,1,6,4]=>00000
[3,2,5,4,1,6]=>00001
[3,2,5,4,6,1]=>00000
[3,2,5,6,1,4]=>00000
[3,2,5,6,4,1]=>00000
[3,2,6,1,4,5]=>00000
[3,2,6,1,5,4]=>00000
[3,2,6,4,1,5]=>00000
[3,2,6,4,5,1]=>00000
[3,2,6,5,1,4]=>00000
[3,2,6,5,4,1]=>00000
[3,4,1,2,5,6]=>00011
[3,4,1,2,6,5]=>00010
[3,4,1,5,2,6]=>00001
[3,4,1,5,6,2]=>00000
[3,4,1,6,2,5]=>00000
[3,4,1,6,5,2]=>00000
[3,4,2,1,5,6]=>00011
[3,4,2,1,6,5]=>00010
[3,4,2,5,1,6]=>00001
[3,4,2,5,6,1]=>00000
[3,4,2,6,1,5]=>00000
[3,4,2,6,5,1]=>00000
[3,4,5,1,2,6]=>00001
[3,4,5,1,6,2]=>00000
[3,4,5,2,1,6]=>00001
[3,4,5,2,6,1]=>00000
[3,4,5,6,1,2]=>00000
[3,4,5,6,2,1]=>00000
[3,4,6,1,2,5]=>00000
[3,4,6,1,5,2]=>00000
[3,4,6,2,1,5]=>00000
[3,4,6,2,5,1]=>00000
[3,4,6,5,1,2]=>00000
[3,4,6,5,2,1]=>00000
[3,5,1,2,4,6]=>00001
[3,5,1,2,6,4]=>00000
[3,5,1,4,2,6]=>00001
[3,5,1,4,6,2]=>00000
[3,5,1,6,2,4]=>00000
[3,5,1,6,4,2]=>00000
[3,5,2,1,4,6]=>00001
[3,5,2,1,6,4]=>00000
[3,5,2,4,1,6]=>00001
[3,5,2,4,6,1]=>00000
[3,5,2,6,1,4]=>00000
[3,5,2,6,4,1]=>00000
[3,5,4,1,2,6]=>00001
[3,5,4,1,6,2]=>00000
[3,5,4,2,1,6]=>00001
[3,5,4,2,6,1]=>00000
[3,5,4,6,1,2]=>00000
[3,5,4,6,2,1]=>00000
[3,5,6,1,2,4]=>00000
[3,5,6,1,4,2]=>00000
[3,5,6,2,1,4]=>00000
[3,5,6,2,4,1]=>00000
[3,5,6,4,1,2]=>00000
[3,5,6,4,2,1]=>00000
[3,6,1,2,4,5]=>00000
[3,6,1,2,5,4]=>00000
[3,6,1,4,2,5]=>00000
[3,6,1,4,5,2]=>00000
[3,6,1,5,2,4]=>00000
[3,6,1,5,4,2]=>00000
[3,6,2,1,4,5]=>00000
[3,6,2,1,5,4]=>00000
[3,6,2,4,1,5]=>00000
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[4,5,2,1,3,6]=>00001
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[4,5,3,1,2,6]=>00001
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[4,6,2,1,5,3]=>00000
[4,6,2,3,1,5]=>00000
[4,6,2,3,5,1]=>00000
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[4,6,3,1,2,5]=>00000
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[4,6,3,5,1,2]=>00000
[4,6,3,5,2,1]=>00000
[4,6,5,1,2,3]=>00000
[4,6,5,1,3,2]=>00000
[4,6,5,2,1,3]=>00000
[4,6,5,2,3,1]=>00000
[4,6,5,3,1,2]=>00000
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[5,1,2,3,4,6]=>00001
[5,1,2,3,6,4]=>00000
[5,1,2,4,3,6]=>00001
[5,1,2,4,6,3]=>00000
[5,1,2,6,3,4]=>00000
[5,1,2,6,4,3]=>00000
[5,1,3,2,4,6]=>00001
[5,1,3,2,6,4]=>00000
[5,1,3,4,2,6]=>00001
[5,1,3,4,6,2]=>00000
[5,1,3,6,2,4]=>00000
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[5,1,4,2,3,6]=>00001
[5,1,4,2,6,3]=>00000
[5,1,4,3,2,6]=>00001
[5,1,4,3,6,2]=>00000
[5,1,4,6,2,3]=>00000
[5,1,4,6,3,2]=>00000
[5,1,6,2,3,4]=>00000
[5,1,6,2,4,3]=>00000
[5,1,6,3,2,4]=>00000
[5,1,6,3,4,2]=>00000
[5,1,6,4,2,3]=>00000
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[5,2,1,3,4,6]=>00001
[5,2,1,3,6,4]=>00000
[5,2,1,4,3,6]=>00001
[5,2,1,4,6,3]=>00000
[5,2,1,6,3,4]=>00000
[5,2,1,6,4,3]=>00000
[5,2,3,1,4,6]=>00001
[5,2,3,1,6,4]=>00000
[5,2,3,4,1,6]=>00001
[5,2,3,4,6,1]=>00000
[5,2,3,6,1,4]=>00000
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[5,2,4,1,3,6]=>00001
[5,2,4,1,6,3]=>00000
[5,2,4,3,1,6]=>00001
[5,2,4,3,6,1]=>00000
[5,2,4,6,1,3]=>00000
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[5,2,6,1,3,4]=>00000
[5,2,6,1,4,3]=>00000
[5,2,6,3,1,4]=>00000
[5,2,6,3,4,1]=>00000
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[5,3,1,2,4,6]=>00001
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[5,3,1,4,2,6]=>00001
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[5,3,2,1,4,6]=>00001
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[5,3,2,6,1,4]=>00000
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[5,3,4,1,2,6]=>00001
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[5,3,6,1,2,4]=>00000
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[5,3,6,4,1,2]=>00000
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[5,4,1,2,3,6]=>00001
[5,4,1,2,6,3]=>00000
[5,4,1,3,2,6]=>00001
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[5,4,2,1,3,6]=>00001
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[5,4,2,3,1,6]=>00001
[5,4,2,3,6,1]=>00000
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[5,4,3,1,2,6]=>00001
[5,4,3,1,6,2]=>00000
[5,4,3,2,1,6]=>00001
[5,4,3,2,6,1]=>00000
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[5,4,6,1,2,3]=>00000
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[5,6,1,2,3,4]=>00000
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[5,6,1,4,3,2]=>00000
[5,6,2,1,3,4]=>00000
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[5,6,2,3,1,4]=>00000
[5,6,2,3,4,1]=>00000
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[5,6,3,1,2,4]=>00000
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[5,6,4,1,2,3]=>00000
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[5,6,4,2,3,1]=>00000
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[6,1,2,3,4,5]=>00000
[6,1,2,3,5,4]=>00000
[6,1,2,4,3,5]=>00000
[6,1,2,4,5,3]=>00000
[6,1,2,5,3,4]=>00000
[6,1,2,5,4,3]=>00000
[6,1,3,2,4,5]=>00000
[6,1,3,2,5,4]=>00000
[6,1,3,4,2,5]=>00000
[6,1,3,4,5,2]=>00000
[6,1,3,5,2,4]=>00000
[6,1,3,5,4,2]=>00000
[6,1,4,2,3,5]=>00000
[6,1,4,2,5,3]=>00000
[6,1,4,3,2,5]=>00000
[6,1,4,3,5,2]=>00000
[6,1,4,5,2,3]=>00000
[6,1,4,5,3,2]=>00000
[6,1,5,2,3,4]=>00000
[6,1,5,2,4,3]=>00000
[6,1,5,3,2,4]=>00000
[6,1,5,3,4,2]=>00000
[6,1,5,4,2,3]=>00000
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[6,2,1,3,4,5]=>00000
[6,2,1,3,5,4]=>00000
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[6,2,1,4,5,3]=>00000
[6,2,1,5,3,4]=>00000
[6,2,1,5,4,3]=>00000
[6,2,3,1,4,5]=>00000
[6,2,3,1,5,4]=>00000
[6,2,3,4,1,5]=>00000
[6,2,3,4,5,1]=>00000
[6,2,3,5,1,4]=>00000
[6,2,3,5,4,1]=>00000
[6,2,4,1,3,5]=>00000
[6,2,4,1,5,3]=>00000
[6,2,4,3,1,5]=>00000
[6,2,4,3,5,1]=>00000
[6,2,4,5,1,3]=>00000
[6,2,4,5,3,1]=>00000
[6,2,5,1,3,4]=>00000
[6,2,5,1,4,3]=>00000
[6,2,5,3,1,4]=>00000
[6,2,5,3,4,1]=>00000
[6,2,5,4,1,3]=>00000
[6,2,5,4,3,1]=>00000
[6,3,1,2,4,5]=>00000
[6,3,1,2,5,4]=>00000
[6,3,1,4,2,5]=>00000
[6,3,1,4,5,2]=>00000
[6,3,1,5,2,4]=>00000
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[6,3,2,1,4,5]=>00000
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[6,3,2,4,5,1]=>00000
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[6,3,2,5,4,1]=>00000
[6,3,4,1,2,5]=>00000
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[6,3,4,2,1,5]=>00000
[6,3,4,2,5,1]=>00000
[6,3,4,5,1,2]=>00000
[6,3,4,5,2,1]=>00000
[6,3,5,1,2,4]=>00000
[6,3,5,1,4,2]=>00000
[6,3,5,2,1,4]=>00000
[6,3,5,2,4,1]=>00000
[6,3,5,4,1,2]=>00000
[6,3,5,4,2,1]=>00000
[6,4,1,2,3,5]=>00000
[6,4,1,2,5,3]=>00000
[6,4,1,3,2,5]=>00000
[6,4,1,3,5,2]=>00000
[6,4,1,5,2,3]=>00000
[6,4,1,5,3,2]=>00000
[6,4,2,1,3,5]=>00000
[6,4,2,1,5,3]=>00000
[6,4,2,3,1,5]=>00000
[6,4,2,3,5,1]=>00000
[6,4,2,5,1,3]=>00000
[6,4,2,5,3,1]=>00000
[6,4,3,1,2,5]=>00000
[6,4,3,1,5,2]=>00000
[6,4,3,2,1,5]=>00000
[6,4,3,2,5,1]=>00000
[6,4,3,5,1,2]=>00000
[6,4,3,5,2,1]=>00000
[6,4,5,1,2,3]=>00000
[6,4,5,1,3,2]=>00000
[6,4,5,2,1,3]=>00000
[6,4,5,2,3,1]=>00000
[6,4,5,3,1,2]=>00000
[6,4,5,3,2,1]=>00000
[6,5,1,2,3,4]=>00000
[6,5,1,2,4,3]=>00000
[6,5,1,3,2,4]=>00000
[6,5,1,3,4,2]=>00000
[6,5,1,4,2,3]=>00000
[6,5,1,4,3,2]=>00000
[6,5,2,1,3,4]=>00000
[6,5,2,1,4,3]=>00000
[6,5,2,3,1,4]=>00000
[6,5,2,3,4,1]=>00000
[6,5,2,4,1,3]=>00000
[6,5,2,4,3,1]=>00000
[6,5,3,1,2,4]=>00000
[6,5,3,1,4,2]=>00000
[6,5,3,2,1,4]=>00000
[6,5,3,2,4,1]=>00000
[6,5,3,4,1,2]=>00000
[6,5,3,4,2,1]=>00000
[6,5,4,1,2,3]=>00000
[6,5,4,1,3,2]=>00000
[6,5,4,2,1,3]=>00000
[6,5,4,2,3,1]=>00000
[6,5,4,3,1,2]=>00000
[6,5,4,3,2,1]=>00000
[1,2,3,4,5,6,7]=>111111
[1,2,3,4,5,7,6]=>111110
[1,2,3,4,6,5,7]=>111101
[1,2,3,4,6,7,5]=>111100
[1,2,3,4,7,5,6]=>111100
[1,2,3,4,7,6,5]=>111100
[1,2,3,5,4,6,7]=>111011
[1,2,3,5,4,7,6]=>111010
[1,2,3,5,6,4,7]=>111001
[1,2,3,5,6,7,4]=>111000
[1,2,3,5,7,4,6]=>111000
[1,2,3,5,7,6,4]=>111000
[1,2,3,6,4,5,7]=>111001
[1,2,3,6,4,7,5]=>111000
[1,2,3,6,5,4,7]=>111001
[1,2,3,6,5,7,4]=>111000
[1,2,3,6,7,4,5]=>111000
[1,2,3,6,7,5,4]=>111000
[1,2,3,7,4,5,6]=>111000
[1,2,3,7,4,6,5]=>111000
[1,2,3,7,5,4,6]=>111000
[1,2,3,7,5,6,4]=>111000
[1,2,3,7,6,4,5]=>111000
[1,2,3,7,6,5,4]=>111000
[1,2,4,3,5,6,7]=>110111
[1,2,4,3,5,7,6]=>110110
[1,2,4,3,6,5,7]=>110101
[1,2,4,3,6,7,5]=>110100
[1,2,4,3,7,5,6]=>110100
[1,2,4,3,7,6,5]=>110100
[1,2,4,5,3,6,7]=>110011
[1,2,4,5,3,7,6]=>110010
[1,2,4,5,6,3,7]=>110001
[1,2,4,5,6,7,3]=>110000
[1,2,4,5,7,3,6]=>110000
[1,2,4,5,7,6,3]=>110000
[1,2,4,6,3,5,7]=>110001
[1,2,4,6,3,7,5]=>110000
[1,2,4,6,5,3,7]=>110001
[1,2,4,6,5,7,3]=>110000
[1,2,4,6,7,3,5]=>110000
[1,2,4,6,7,5,3]=>110000
[1,2,4,7,3,5,6]=>110000
[1,2,4,7,3,6,5]=>110000
[1,2,4,7,5,3,6]=>110000
[1,2,4,7,5,6,3]=>110000
[1,2,4,7,6,3,5]=>110000
[1,2,4,7,6,5,3]=>110000
[1,2,5,3,4,6,7]=>110011
[1,2,5,3,4,7,6]=>110010
[1,2,5,3,6,4,7]=>110001
[1,2,5,3,6,7,4]=>110000
[1,2,5,3,7,4,6]=>110000
[1,2,5,3,7,6,4]=>110000
[1,2,5,4,3,6,7]=>110011
[1,2,5,4,3,7,6]=>110010
[1,2,5,4,6,3,7]=>110001
[1,2,5,4,6,7,3]=>110000
[1,2,5,4,7,3,6]=>110000
[1,2,5,4,7,6,3]=>110000
[1,2,5,6,3,4,7]=>110001
[1,2,5,6,3,7,4]=>110000
[1,2,5,6,4,3,7]=>110001
[1,2,5,6,4,7,3]=>110000
[1,2,5,6,7,3,4]=>110000
[1,2,5,6,7,4,3]=>110000
[1,2,5,7,3,4,6]=>110000
[1,2,5,7,3,6,4]=>110000
[1,2,5,7,4,3,6]=>110000
[1,2,5,7,4,6,3]=>110000
[1,2,5,7,6,3,4]=>110000
[1,2,5,7,6,4,3]=>110000
[1,2,6,3,4,5,7]=>110001
[1,2,6,3,4,7,5]=>110000
[1,2,6,3,5,4,7]=>110001
[1,2,6,3,5,7,4]=>110000
[1,2,6,3,7,4,5]=>110000
[1,2,6,3,7,5,4]=>110000
[1,2,6,4,3,5,7]=>110001
[1,2,6,4,3,7,5]=>110000
[1,2,6,4,5,3,7]=>110001
[1,2,6,4,5,7,3]=>110000
[1,2,6,4,7,3,5]=>110000
[1,2,6,4,7,5,3]=>110000
[1,2,6,5,3,4,7]=>110001
[1,2,6,5,3,7,4]=>110000
[1,2,6,5,4,3,7]=>110001
[1,2,6,5,4,7,3]=>110000
[1,2,6,5,7,3,4]=>110000
[1,2,6,5,7,4,3]=>110000
[1,2,6,7,3,4,5]=>110000
[1,2,6,7,3,5,4]=>110000
[1,2,6,7,4,3,5]=>110000
[1,2,6,7,4,5,3]=>110000
[1,2,6,7,5,3,4]=>110000
[1,2,6,7,5,4,3]=>110000
[1,2,7,3,4,5,6]=>110000
[1,2,7,3,4,6,5]=>110000
[1,2,7,3,5,4,6]=>110000
[1,2,7,3,5,6,4]=>110000
[1,2,7,3,6,4,5]=>110000
[1,2,7,3,6,5,4]=>110000
[1,2,7,4,3,5,6]=>110000
[1,2,7,4,3,6,5]=>110000
[1,2,7,4,5,3,6]=>110000
[1,2,7,4,5,6,3]=>110000
[1,2,7,4,6,3,5]=>110000
[1,2,7,4,6,5,3]=>110000
[1,2,7,5,3,4,6]=>110000
[1,2,7,5,3,6,4]=>110000
[1,2,7,5,4,3,6]=>110000
[1,2,7,5,4,6,3]=>110000
[1,2,7,5,6,3,4]=>110000
[1,2,7,5,6,4,3]=>110000
[1,2,7,6,3,4,5]=>110000
[1,2,7,6,3,5,4]=>110000
[1,2,7,6,4,3,5]=>110000
[1,2,7,6,4,5,3]=>110000
[1,2,7,6,5,3,4]=>110000
[1,2,7,6,5,4,3]=>110000
[1,3,2,4,5,6,7]=>101111
[1,3,2,4,5,7,6]=>101110
[1,3,2,4,6,5,7]=>101101
[1,3,2,4,6,7,5]=>101100
[1,3,2,4,7,5,6]=>101100
[1,3,2,4,7,6,5]=>101100
[1,3,2,5,4,6,7]=>101011
[1,3,2,5,4,7,6]=>101010
[1,3,2,5,6,4,7]=>101001
[1,3,2,5,6,7,4]=>101000
[1,3,2,5,7,4,6]=>101000
[1,3,2,5,7,6,4]=>101000
[1,3,2,6,4,5,7]=>101001
[1,3,2,6,4,7,5]=>101000
[1,3,2,6,5,4,7]=>101001
[1,3,2,6,5,7,4]=>101000
[1,3,2,6,7,4,5]=>101000
[1,3,2,6,7,5,4]=>101000
[1,3,2,7,4,5,6]=>101000
[1,3,2,7,4,6,5]=>101000
[1,3,2,7,5,4,6]=>101000
[1,3,2,7,5,6,4]=>101000
[1,3,2,7,6,4,5]=>101000
[1,3,2,7,6,5,4]=>101000
[1,3,4,2,5,6,7]=>100111
[1,3,4,2,5,7,6]=>100110
[1,3,4,2,6,5,7]=>100101
[1,3,4,2,6,7,5]=>100100
[1,3,4,2,7,5,6]=>100100
[1,3,4,2,7,6,5]=>100100
[1,3,4,5,2,6,7]=>100011
[1,3,4,5,2,7,6]=>100010
[1,3,4,5,6,2,7]=>100001
[1,3,4,5,6,7,2]=>100000
[1,3,4,5,7,2,6]=>100000
[1,3,4,5,7,6,2]=>100000
[1,3,4,6,2,5,7]=>100001
[1,3,4,6,2,7,5]=>100000
[1,3,4,6,5,2,7]=>100001
[1,3,4,6,5,7,2]=>100000
[1,3,4,6,7,2,5]=>100000
[1,3,4,6,7,5,2]=>100000
[1,3,4,7,2,5,6]=>100000
[1,3,4,7,2,6,5]=>100000
[1,3,4,7,5,2,6]=>100000
[1,3,4,7,5,6,2]=>100000
[1,3,4,7,6,2,5]=>100000
[1,3,4,7,6,5,2]=>100000
[1,3,5,2,4,6,7]=>100011
[1,3,5,2,4,7,6]=>100010
[1,3,5,2,6,4,7]=>100001
[1,3,5,2,6,7,4]=>100000
[1,3,5,2,7,4,6]=>100000
[1,3,5,2,7,6,4]=>100000
[1,3,5,4,2,6,7]=>100011
[1,3,5,4,2,7,6]=>100010
[1,3,5,4,6,2,7]=>100001
[1,3,5,4,6,7,2]=>100000
[1,3,5,4,7,2,6]=>100000
[1,3,5,4,7,6,2]=>100000
[1,3,5,6,2,4,7]=>100001
[1,3,5,6,2,7,4]=>100000
[1,3,5,6,4,2,7]=>100001
[1,3,5,6,4,7,2]=>100000
[1,3,5,6,7,2,4]=>100000
[1,3,5,6,7,4,2]=>100000
[1,3,5,7,2,4,6]=>100000
[1,3,5,7,2,6,4]=>100000
[1,3,5,7,4,2,6]=>100000
[1,3,5,7,4,6,2]=>100000
[1,3,5,7,6,2,4]=>100000
[1,3,5,7,6,4,2]=>100000
[1,3,6,2,4,5,7]=>100001
[1,3,6,2,4,7,5]=>100000
[1,3,6,2,5,4,7]=>100001
[1,3,6,2,5,7,4]=>100000
[1,3,6,2,7,4,5]=>100000
[1,3,6,2,7,5,4]=>100000
[1,3,6,4,2,5,7]=>100001
[1,3,6,4,2,7,5]=>100000
[1,3,6,4,5,2,7]=>100001
[1,3,6,4,5,7,2]=>100000
[1,3,6,4,7,2,5]=>100000
[1,3,6,4,7,5,2]=>100000
[1,3,6,5,2,4,7]=>100001
[1,3,6,5,2,7,4]=>100000
[1,3,6,5,4,2,7]=>100001
[1,3,6,5,4,7,2]=>100000
[1,3,6,5,7,2,4]=>100000
[1,3,6,5,7,4,2]=>100000
[1,3,6,7,2,4,5]=>100000
[1,3,6,7,2,5,4]=>100000
[1,3,6,7,4,2,5]=>100000
[1,3,6,7,4,5,2]=>100000
[1,3,6,7,5,2,4]=>100000
[1,3,6,7,5,4,2]=>100000
[1,3,7,2,4,5,6]=>100000
[1,3,7,2,4,6,5]=>100000
[1,3,7,2,5,4,6]=>100000
[1,3,7,2,5,6,4]=>100000
[1,3,7,2,6,4,5]=>100000
[1,3,7,2,6,5,4]=>100000
[1,3,7,4,2,5,6]=>100000
[1,3,7,4,2,6,5]=>100000
[1,3,7,4,5,2,6]=>100000
[1,3,7,4,5,6,2]=>100000
[1,3,7,4,6,2,5]=>100000
[1,3,7,4,6,5,2]=>100000
[1,3,7,5,2,4,6]=>100000
[1,3,7,5,2,6,4]=>100000
[1,3,7,5,4,2,6]=>100000
[1,3,7,5,4,6,2]=>100000
[1,3,7,5,6,2,4]=>100000
[1,3,7,5,6,4,2]=>100000
[1,3,7,6,2,4,5]=>100000
[1,3,7,6,2,5,4]=>100000
[1,3,7,6,4,2,5]=>100000
[1,3,7,6,4,5,2]=>100000
[1,3,7,6,5,2,4]=>100000
[1,3,7,6,5,4,2]=>100000
[1,4,2,3,5,6,7]=>100111
[1,4,2,3,5,7,6]=>100110
[1,4,2,3,6,5,7]=>100101
[1,4,2,3,6,7,5]=>100100
[1,4,2,3,7,5,6]=>100100
[1,4,2,3,7,6,5]=>100100
[1,4,2,5,3,6,7]=>100011
[1,4,2,5,3,7,6]=>100010
[1,4,2,5,6,3,7]=>100001
[1,4,2,5,6,7,3]=>100000
[1,4,2,5,7,3,6]=>100000
[1,4,2,5,7,6,3]=>100000
[1,4,2,6,3,5,7]=>100001
[1,4,2,6,3,7,5]=>100000
[1,4,2,6,5,3,7]=>100001
[1,4,2,6,5,7,3]=>100000
[1,4,2,6,7,3,5]=>100000
[1,4,2,6,7,5,3]=>100000
[1,4,2,7,3,5,6]=>100000
[1,4,2,7,3,6,5]=>100000
[1,4,2,7,5,3,6]=>100000
[1,4,2,7,5,6,3]=>100000
[1,4,2,7,6,3,5]=>100000
[1,4,2,7,6,5,3]=>100000
[1,4,3,2,5,6,7]=>100111
[1,4,3,2,5,7,6]=>100110
[1,4,3,2,6,5,7]=>100101
[1,4,3,2,6,7,5]=>100100
[1,4,3,2,7,5,6]=>100100
[1,4,3,2,7,6,5]=>100100
[1,4,3,5,2,6,7]=>100011
[1,4,3,5,2,7,6]=>100010
[1,4,3,5,6,2,7]=>100001
[1,4,3,5,6,7,2]=>100000
[1,4,3,5,7,2,6]=>100000
[1,4,3,5,7,6,2]=>100000
[1,4,3,6,2,5,7]=>100001
[1,4,3,6,2,7,5]=>100000
[1,4,3,6,5,2,7]=>100001
[1,4,3,6,5,7,2]=>100000
[1,4,3,6,7,2,5]=>100000
[1,4,3,6,7,5,2]=>100000
[1,4,3,7,2,5,6]=>100000
[1,4,3,7,2,6,5]=>100000
[1,4,3,7,5,2,6]=>100000
[1,4,3,7,5,6,2]=>100000
[1,4,3,7,6,2,5]=>100000
[1,4,3,7,6,5,2]=>100000
[1,4,5,2,3,6,7]=>100011
[1,4,5,2,3,7,6]=>100010
[1,4,5,2,6,3,7]=>100001
[1,4,5,2,6,7,3]=>100000
[1,4,5,2,7,3,6]=>100000
[1,4,5,2,7,6,3]=>100000
[1,4,5,3,2,6,7]=>100011
[1,4,5,3,2,7,6]=>100010
[1,4,5,3,6,2,7]=>100001
[1,4,5,3,6,7,2]=>100000
[1,4,5,3,7,2,6]=>100000
[1,4,5,3,7,6,2]=>100000
[1,4,5,6,2,3,7]=>100001
[1,4,5,6,2,7,3]=>100000
[1,4,5,6,3,2,7]=>100001
[1,4,5,6,3,7,2]=>100000
[1,4,5,6,7,2,3]=>100000
[1,4,5,6,7,3,2]=>100000
[1,4,5,7,2,3,6]=>100000
[1,4,5,7,2,6,3]=>100000
[1,4,5,7,3,2,6]=>100000
[1,4,5,7,3,6,2]=>100000
[1,4,5,7,6,2,3]=>100000
[1,4,5,7,6,3,2]=>100000
[1,4,6,2,3,5,7]=>100001
[1,4,6,2,3,7,5]=>100000
[1,4,6,2,5,3,7]=>100001
[1,4,6,2,5,7,3]=>100000
[1,4,6,2,7,3,5]=>100000
[1,4,6,2,7,5,3]=>100000
[1,4,6,3,2,5,7]=>100001
[1,4,6,3,2,7,5]=>100000
[1,4,6,3,5,2,7]=>100001
[1,4,6,3,5,7,2]=>100000
[1,4,6,3,7,2,5]=>100000
[1,4,6,3,7,5,2]=>100000
[1,4,6,5,2,3,7]=>100001
[1,4,6,5,2,7,3]=>100000
[1,4,6,5,3,2,7]=>100001
[1,4,6,5,3,7,2]=>100000
[1,4,6,5,7,2,3]=>100000
[1,4,6,5,7,3,2]=>100000
[1,4,6,7,2,3,5]=>100000
[1,4,6,7,2,5,3]=>100000
[1,4,6,7,3,2,5]=>100000
[1,4,6,7,3,5,2]=>100000
[1,4,6,7,5,2,3]=>100000
[1,4,6,7,5,3,2]=>100000
[1,4,7,2,3,5,6]=>100000
[1,4,7,2,3,6,5]=>100000
[1,4,7,2,5,3,6]=>100000
[1,4,7,2,5,6,3]=>100000
[1,4,7,2,6,3,5]=>100000
[1,4,7,2,6,5,3]=>100000
[1,4,7,3,2,5,6]=>100000
[1,4,7,3,2,6,5]=>100000
[1,4,7,3,5,2,6]=>100000
[1,4,7,3,5,6,2]=>100000
[1,4,7,3,6,2,5]=>100000
[1,4,7,3,6,5,2]=>100000
[1,4,7,5,2,3,6]=>100000
[1,4,7,5,2,6,3]=>100000
[1,4,7,5,3,2,6]=>100000
[1,4,7,5,3,6,2]=>100000
[1,4,7,5,6,2,3]=>100000
[1,4,7,5,6,3,2]=>100000
[1,4,7,6,2,3,5]=>100000
[1,4,7,6,2,5,3]=>100000
[1,4,7,6,3,2,5]=>100000
[1,4,7,6,3,5,2]=>100000
[1,4,7,6,5,2,3]=>100000
[1,4,7,6,5,3,2]=>100000
[1,5,2,3,4,6,7]=>100011
[1,5,2,3,4,7,6]=>100010
[1,5,2,3,6,4,7]=>100001
[1,5,2,3,6,7,4]=>100000
[1,5,2,3,7,4,6]=>100000
[1,5,2,3,7,6,4]=>100000
[1,5,2,4,3,6,7]=>100011
[1,5,2,4,3,7,6]=>100010
[1,5,2,4,6,3,7]=>100001
[1,5,2,4,6,7,3]=>100000
[1,5,2,4,7,3,6]=>100000
[1,5,2,4,7,6,3]=>100000
[1,5,2,6,3,4,7]=>100001
[1,5,2,6,3,7,4]=>100000
[1,5,2,6,4,3,7]=>100001
[1,5,2,6,4,7,3]=>100000
[1,5,2,6,7,3,4]=>100000
[1,5,2,6,7,4,3]=>100000
[1,5,2,7,3,4,6]=>100000
[1,5,2,7,3,6,4]=>100000
[1,5,2,7,4,3,6]=>100000
[1,5,2,7,4,6,3]=>100000
[1,5,2,7,6,3,4]=>100000
[1,5,2,7,6,4,3]=>100000
[1,5,3,2,4,6,7]=>100011
[1,5,3,2,4,7,6]=>100010
[1,5,3,2,6,4,7]=>100001
[1,5,3,2,6,7,4]=>100000
[1,5,3,2,7,4,6]=>100000
[1,5,3,2,7,6,4]=>100000
[1,5,3,4,2,6,7]=>100011
[1,5,3,4,2,7,6]=>100010
[1,5,3,4,6,2,7]=>100001
[1,5,3,4,6,7,2]=>100000
[1,5,3,4,7,2,6]=>100000
[1,5,3,4,7,6,2]=>100000
[1,5,3,6,2,4,7]=>100001
[1,5,3,6,2,7,4]=>100000
[1,5,3,6,4,2,7]=>100001
[1,5,3,6,4,7,2]=>100000
[1,5,3,6,7,2,4]=>100000
[1,5,3,6,7,4,2]=>100000
[1,5,3,7,2,4,6]=>100000
[1,5,3,7,2,6,4]=>100000
[1,5,3,7,4,2,6]=>100000
[1,5,3,7,4,6,2]=>100000
[1,5,3,7,6,2,4]=>100000
[1,5,3,7,6,4,2]=>100000
[1,5,4,2,3,6,7]=>100011
[1,5,4,2,3,7,6]=>100010
[1,5,4,2,6,3,7]=>100001
[1,5,4,2,6,7,3]=>100000
[1,5,4,2,7,3,6]=>100000
[1,5,4,2,7,6,3]=>100000
[1,5,4,3,2,6,7]=>100011
[1,5,4,3,2,7,6]=>100010
[1,5,4,3,6,2,7]=>100001
[1,5,4,3,6,7,2]=>100000
[1,5,4,3,7,2,6]=>100000
[1,5,4,3,7,6,2]=>100000
[1,5,4,6,2,3,7]=>100001
[1,5,4,6,2,7,3]=>100000
[1,5,4,6,3,2,7]=>100001
[1,5,4,6,3,7,2]=>100000
[1,5,4,6,7,2,3]=>100000
[1,5,4,6,7,3,2]=>100000
[1,5,4,7,2,3,6]=>100000
[1,5,4,7,2,6,3]=>100000
[1,5,4,7,3,2,6]=>100000
[1,5,4,7,3,6,2]=>100000
[1,5,4,7,6,2,3]=>100000
[1,5,4,7,6,3,2]=>100000
[1,5,6,2,3,4,7]=>100001
[1,5,6,2,3,7,4]=>100000
[1,5,6,2,4,3,7]=>100001
[1,5,6,2,4,7,3]=>100000
[1,5,6,2,7,3,4]=>100000
[1,5,6,2,7,4,3]=>100000
[1,5,6,3,2,4,7]=>100001
[1,5,6,3,2,7,4]=>100000
[1,5,6,3,4,2,7]=>100001
[1,5,6,3,4,7,2]=>100000
[1,5,6,3,7,2,4]=>100000
[1,5,6,3,7,4,2]=>100000
[1,5,6,4,2,3,7]=>100001
[1,5,6,4,2,7,3]=>100000
[1,5,6,4,3,2,7]=>100001
[1,5,6,4,3,7,2]=>100000
[1,5,6,4,7,2,3]=>100000
[1,5,6,4,7,3,2]=>100000
[1,5,6,7,2,3,4]=>100000
[1,5,6,7,2,4,3]=>100000
[1,5,6,7,3,2,4]=>100000
[1,5,6,7,3,4,2]=>100000
[1,5,6,7,4,2,3]=>100000
[1,5,6,7,4,3,2]=>100000
[1,5,7,2,3,4,6]=>100000
[1,5,7,2,3,6,4]=>100000
[1,5,7,2,4,3,6]=>100000
[1,5,7,2,4,6,3]=>100000
[1,5,7,2,6,3,4]=>100000
[1,5,7,2,6,4,3]=>100000
[1,5,7,3,2,4,6]=>100000
[1,5,7,3,2,6,4]=>100000
[1,5,7,3,4,2,6]=>100000
[1,5,7,3,4,6,2]=>100000
[1,5,7,3,6,2,4]=>100000
[1,5,7,3,6,4,2]=>100000
[1,5,7,4,2,3,6]=>100000
[1,5,7,4,2,6,3]=>100000
[1,5,7,4,3,2,6]=>100000
[1,5,7,4,3,6,2]=>100000
[1,5,7,4,6,2,3]=>100000
[1,5,7,4,6,3,2]=>100000
[1,5,7,6,2,3,4]=>100000
[1,5,7,6,2,4,3]=>100000
[1,5,7,6,3,2,4]=>100000
[1,5,7,6,3,4,2]=>100000
[1,5,7,6,4,2,3]=>100000
[1,5,7,6,4,3,2]=>100000
[1,6,2,3,4,5,7]=>100001
[1,6,2,3,4,7,5]=>100000
[1,6,2,3,5,4,7]=>100001
[1,6,2,3,5,7,4]=>100000
[1,6,2,3,7,4,5]=>100000
[1,6,2,3,7,5,4]=>100000
[1,6,2,4,3,5,7]=>100001
[1,6,2,4,3,7,5]=>100000
[1,6,2,4,5,3,7]=>100001
[1,6,2,4,5,7,3]=>100000
[1,6,2,4,7,3,5]=>100000
[1,6,2,4,7,5,3]=>100000
[1,6,2,5,3,4,7]=>100001
[1,6,2,5,3,7,4]=>100000
[1,6,2,5,4,3,7]=>100001
[1,6,2,5,4,7,3]=>100000
[1,6,2,5,7,3,4]=>100000
[1,6,2,5,7,4,3]=>100000
[1,6,2,7,3,4,5]=>100000
[1,6,2,7,3,5,4]=>100000
[1,6,2,7,4,3,5]=>100000
[1,6,2,7,4,5,3]=>100000
[1,6,2,7,5,3,4]=>100000
[1,6,2,7,5,4,3]=>100000
[1,6,3,2,4,5,7]=>100001
[1,6,3,2,4,7,5]=>100000
[1,6,3,2,5,4,7]=>100001
[1,6,3,2,5,7,4]=>100000
[1,6,3,2,7,4,5]=>100000
[1,6,3,2,7,5,4]=>100000
[1,6,3,4,2,5,7]=>100001
[1,6,3,4,2,7,5]=>100000
[1,6,3,4,5,2,7]=>100001
[1,6,3,4,5,7,2]=>100000
[1,6,3,4,7,2,5]=>100000
[1,6,3,4,7,5,2]=>100000
[1,6,3,5,2,4,7]=>100001
[1,6,3,5,2,7,4]=>100000
[1,6,3,5,4,2,7]=>100001
[1,6,3,5,4,7,2]=>100000
[1,6,3,5,7,2,4]=>100000
[1,6,3,5,7,4,2]=>100000
[1,6,3,7,2,4,5]=>100000
[1,6,3,7,2,5,4]=>100000
[1,6,3,7,4,2,5]=>100000
[1,6,3,7,4,5,2]=>100000
[1,6,3,7,5,2,4]=>100000
[1,6,3,7,5,4,2]=>100000
[1,6,4,2,3,5,7]=>100001
[1,6,4,2,3,7,5]=>100000
[1,6,4,2,5,3,7]=>100001
[1,6,4,2,5,7,3]=>100000
[1,6,4,2,7,3,5]=>100000
[1,6,4,2,7,5,3]=>100000
[1,6,4,3,2,5,7]=>100001
[1,6,4,3,2,7,5]=>100000
[1,6,4,3,5,2,7]=>100001
[1,6,4,3,5,7,2]=>100000
[1,6,4,3,7,2,5]=>100000
[1,6,4,3,7,5,2]=>100000
[1,6,4,5,2,3,7]=>100001
[1,6,4,5,2,7,3]=>100000
[1,6,4,5,3,2,7]=>100001
[1,6,4,5,3,7,2]=>100000
[1,6,4,5,7,2,3]=>100000
[1,6,4,5,7,3,2]=>100000
[1,6,4,7,2,3,5]=>100000
[1,6,4,7,2,5,3]=>100000
[1,6,4,7,3,2,5]=>100000
[1,6,4,7,3,5,2]=>100000
[1,6,4,7,5,2,3]=>100000
[1,6,4,7,5,3,2]=>100000
[1,6,5,2,3,4,7]=>100001
[1,6,5,2,3,7,4]=>100000
[1,6,5,2,4,3,7]=>100001
[1,6,5,2,4,7,3]=>100000
[1,6,5,2,7,3,4]=>100000
[1,6,5,2,7,4,3]=>100000
[1,6,5,3,2,4,7]=>100001
[1,6,5,3,2,7,4]=>100000
[1,6,5,3,4,2,7]=>100001
[1,6,5,3,4,7,2]=>100000
[1,6,5,3,7,2,4]=>100000
[1,6,5,3,7,4,2]=>100000
[1,6,5,4,2,3,7]=>100001
[1,6,5,4,2,7,3]=>100000
[1,6,5,4,3,2,7]=>100001
[1,6,5,4,3,7,2]=>100000
[1,6,5,4,7,2,3]=>100000
[1,6,5,4,7,3,2]=>100000
[1,6,5,7,2,3,4]=>100000
[1,6,5,7,2,4,3]=>100000
[1,6,5,7,3,2,4]=>100000
[1,6,5,7,3,4,2]=>100000
[1,6,5,7,4,2,3]=>100000
[1,6,5,7,4,3,2]=>100000
[1,6,7,2,3,4,5]=>100000
[1,6,7,2,3,5,4]=>100000
[1,6,7,2,4,3,5]=>100000
[1,6,7,2,4,5,3]=>100000
[1,6,7,2,5,3,4]=>100000
[1,6,7,2,5,4,3]=>100000
[1,6,7,3,2,4,5]=>100000
[1,6,7,3,2,5,4]=>100000
[1,6,7,3,4,2,5]=>100000
[1,6,7,3,4,5,2]=>100000
[1,6,7,3,5,2,4]=>100000
[1,6,7,3,5,4,2]=>100000
[1,6,7,4,2,3,5]=>100000
[1,6,7,4,2,5,3]=>100000
[1,6,7,4,3,2,5]=>100000
[1,6,7,4,3,5,2]=>100000
[1,6,7,4,5,2,3]=>100000
[1,6,7,4,5,3,2]=>100000
[1,6,7,5,2,3,4]=>100000
[1,6,7,5,2,4,3]=>100000
[1,6,7,5,3,2,4]=>100000
[1,6,7,5,3,4,2]=>100000
[1,6,7,5,4,2,3]=>100000
[1,6,7,5,4,3,2]=>100000
[1,7,2,3,4,5,6]=>100000
[1,7,2,3,4,6,5]=>100000
[1,7,2,3,5,4,6]=>100000
[1,7,2,3,5,6,4]=>100000
[1,7,2,3,6,4,5]=>100000
[1,7,2,3,6,5,4]=>100000
[1,7,2,4,3,5,6]=>100000
[1,7,2,4,3,6,5]=>100000
[1,7,2,4,5,3,6]=>100000
[1,7,2,4,5,6,3]=>100000
[1,7,2,4,6,3,5]=>100000
[1,7,2,4,6,5,3]=>100000
[1,7,2,5,3,4,6]=>100000
[1,7,2,5,3,6,4]=>100000
[1,7,2,5,4,3,6]=>100000
[1,7,2,5,4,6,3]=>100000
[1,7,2,5,6,3,4]=>100000
[1,7,2,5,6,4,3]=>100000
[1,7,2,6,3,4,5]=>100000
[1,7,2,6,3,5,4]=>100000
[1,7,2,6,4,3,5]=>100000
[1,7,2,6,4,5,3]=>100000
[1,7,2,6,5,3,4]=>100000
[1,7,2,6,5,4,3]=>100000
[1,7,3,2,4,5,6]=>100000
[1,7,3,2,4,6,5]=>100000
[1,7,3,2,5,4,6]=>100000
[1,7,3,2,5,6,4]=>100000
[1,7,3,2,6,4,5]=>100000
[1,7,3,2,6,5,4]=>100000
[1,7,3,4,2,5,6]=>100000
[1,7,3,4,2,6,5]=>100000
[1,7,3,4,5,2,6]=>100000
[1,7,3,4,5,6,2]=>100000
[1,7,3,4,6,2,5]=>100000
[1,7,3,4,6,5,2]=>100000
[1,7,3,5,2,4,6]=>100000
[1,7,3,5,2,6,4]=>100000
[1,7,3,5,4,2,6]=>100000
[1,7,3,5,4,6,2]=>100000
[1,7,3,5,6,2,4]=>100000
[1,7,3,5,6,4,2]=>100000
[1,7,3,6,2,4,5]=>100000
[1,7,3,6,2,5,4]=>100000
[1,7,3,6,4,2,5]=>100000
[1,7,3,6,4,5,2]=>100000
[1,7,3,6,5,2,4]=>100000
[1,7,3,6,5,4,2]=>100000
[1,7,4,2,3,5,6]=>100000
[1,7,4,2,3,6,5]=>100000
[1,7,4,2,5,3,6]=>100000
[1,7,4,2,5,6,3]=>100000
[1,7,4,2,6,3,5]=>100000
[1,7,4,2,6,5,3]=>100000
[1,7,4,3,2,5,6]=>100000
[1,7,4,3,2,6,5]=>100000
[1,7,4,3,5,2,6]=>100000
[1,7,4,3,5,6,2]=>100000
[1,7,4,3,6,2,5]=>100000
[1,7,4,3,6,5,2]=>100000
[1,7,4,5,2,3,6]=>100000
[1,7,4,5,2,6,3]=>100000
[1,7,4,5,3,2,6]=>100000
[1,7,4,5,3,6,2]=>100000
[1,7,4,5,6,2,3]=>100000
[1,7,4,5,6,3,2]=>100000
[1,7,4,6,2,3,5]=>100000
[1,7,4,6,2,5,3]=>100000
[1,7,4,6,3,2,5]=>100000
[1,7,4,6,3,5,2]=>100000
[1,7,4,6,5,2,3]=>100000
[1,7,4,6,5,3,2]=>100000
[1,7,5,2,3,4,6]=>100000
[1,7,5,2,3,6,4]=>100000
[1,7,5,2,4,3,6]=>100000
[1,7,5,2,4,6,3]=>100000
[1,7,5,2,6,3,4]=>100000
[1,7,5,2,6,4,3]=>100000
[1,7,5,3,2,4,6]=>100000
[1,7,5,3,2,6,4]=>100000
[1,7,5,3,4,2,6]=>100000
[1,7,5,3,4,6,2]=>100000
[1,7,5,3,6,2,4]=>100000
[1,7,5,3,6,4,2]=>100000
[1,7,5,4,2,3,6]=>100000
[1,7,5,4,2,6,3]=>100000
[1,7,5,4,3,2,6]=>100000
[1,7,5,4,3,6,2]=>100000
[1,7,5,4,6,2,3]=>100000
[1,7,5,4,6,3,2]=>100000
[1,7,5,6,2,3,4]=>100000
[1,7,5,6,2,4,3]=>100000
[1,7,5,6,3,2,4]=>100000
[1,7,5,6,3,4,2]=>100000
[1,7,5,6,4,2,3]=>100000
[1,7,5,6,4,3,2]=>100000
[1,7,6,2,3,4,5]=>100000
[1,7,6,2,3,5,4]=>100000
[1,7,6,2,4,3,5]=>100000
[1,7,6,2,4,5,3]=>100000
[1,7,6,2,5,3,4]=>100000
[1,7,6,2,5,4,3]=>100000
[1,7,6,3,2,4,5]=>100000
[1,7,6,3,2,5,4]=>100000
[1,7,6,3,4,2,5]=>100000
[1,7,6,3,4,5,2]=>100000
[1,7,6,3,5,2,4]=>100000
[1,7,6,3,5,4,2]=>100000
[1,7,6,4,2,3,5]=>100000
[1,7,6,4,2,5,3]=>100000
[1,7,6,4,3,2,5]=>100000
[1,7,6,4,3,5,2]=>100000
[1,7,6,4,5,2,3]=>100000
[1,7,6,4,5,3,2]=>100000
[1,7,6,5,2,3,4]=>100000
[1,7,6,5,2,4,3]=>100000
[1,7,6,5,3,2,4]=>100000
[1,7,6,5,3,4,2]=>100000
[1,7,6,5,4,2,3]=>100000
[1,7,6,5,4,3,2]=>100000
[2,1,3,4,5,6,7]=>011111
[2,1,3,4,5,7,6]=>011110
[2,1,3,4,6,5,7]=>011101
[2,1,3,4,6,7,5]=>011100
[2,1,3,4,7,5,6]=>011100
[2,1,3,4,7,6,5]=>011100
[2,1,3,5,4,6,7]=>011011
[2,1,3,5,4,7,6]=>011010
[2,1,3,5,6,4,7]=>011001
[2,1,3,5,6,7,4]=>011000
[2,1,3,5,7,4,6]=>011000
[2,1,3,5,7,6,4]=>011000
[2,1,3,6,4,5,7]=>011001
[2,1,3,6,4,7,5]=>011000
[2,1,3,6,5,4,7]=>011001
[2,1,3,6,5,7,4]=>011000
[2,1,3,6,7,4,5]=>011000
[2,1,3,6,7,5,4]=>011000
[2,1,3,7,4,5,6]=>011000
[2,1,3,7,4,6,5]=>011000
[2,1,3,7,5,4,6]=>011000
[2,1,3,7,5,6,4]=>011000
[2,1,3,7,6,4,5]=>011000
[2,1,3,7,6,5,4]=>011000
[2,1,4,3,5,6,7]=>010111
[2,1,4,3,5,7,6]=>010110
[2,1,4,3,6,5,7]=>010101
[2,1,4,3,6,7,5]=>010100
[2,1,4,3,7,5,6]=>010100
[2,1,4,3,7,6,5]=>010100
[2,1,4,5,3,6,7]=>010011
[2,1,4,5,3,7,6]=>010010
[2,1,4,5,6,3,7]=>010001
[2,1,4,5,6,7,3]=>010000
[2,1,4,5,7,3,6]=>010000
[2,1,4,5,7,6,3]=>010000
[2,1,4,6,3,5,7]=>010001
[2,1,4,6,3,7,5]=>010000
[2,1,4,6,5,3,7]=>010001
[2,1,4,6,5,7,3]=>010000
[2,1,4,6,7,3,5]=>010000
[2,1,4,6,7,5,3]=>010000
[2,1,4,7,3,5,6]=>010000
[2,1,4,7,3,6,5]=>010000
[2,1,4,7,5,3,6]=>010000
[2,1,4,7,5,6,3]=>010000
[2,1,4,7,6,3,5]=>010000
[2,1,4,7,6,5,3]=>010000
[2,1,5,3,4,6,7]=>010011
[2,1,5,3,4,7,6]=>010010
[2,1,5,3,6,4,7]=>010001
[2,1,5,3,6,7,4]=>010000
[2,1,5,3,7,4,6]=>010000
[2,1,5,3,7,6,4]=>010000
[2,1,5,4,3,6,7]=>010011
[2,1,5,4,3,7,6]=>010010
[2,1,5,4,6,3,7]=>010001
[2,1,5,4,6,7,3]=>010000
[2,1,5,4,7,3,6]=>010000
[2,1,5,4,7,6,3]=>010000
[2,1,5,6,3,4,7]=>010001
[2,1,5,6,3,7,4]=>010000
[2,1,5,6,4,3,7]=>010001
[2,1,5,6,4,7,3]=>010000
[2,1,5,6,7,3,4]=>010000
[2,1,5,6,7,4,3]=>010000
[2,1,5,7,3,4,6]=>010000
[2,1,5,7,3,6,4]=>010000
[2,1,5,7,4,3,6]=>010000
[2,1,5,7,4,6,3]=>010000
[2,1,5,7,6,3,4]=>010000
[2,1,5,7,6,4,3]=>010000
[2,1,6,3,4,5,7]=>010001
[2,1,6,3,4,7,5]=>010000
[2,1,6,3,5,4,7]=>010001
[2,1,6,3,5,7,4]=>010000
[2,1,6,3,7,4,5]=>010000
[2,1,6,3,7,5,4]=>010000
[2,1,6,4,3,5,7]=>010001
[2,1,6,4,3,7,5]=>010000
[2,1,6,4,5,3,7]=>010001
[2,1,6,4,5,7,3]=>010000
[2,1,6,4,7,3,5]=>010000
[2,1,6,4,7,5,3]=>010000
[2,1,6,5,3,4,7]=>010001
[2,1,6,5,3,7,4]=>010000
[2,1,6,5,4,3,7]=>010001
[2,1,6,5,4,7,3]=>010000
[2,1,6,5,7,3,4]=>010000
[2,1,6,5,7,4,3]=>010000
[2,1,6,7,3,4,5]=>010000
[2,1,6,7,3,5,4]=>010000
[2,1,6,7,4,3,5]=>010000
[2,1,6,7,4,5,3]=>010000
[2,1,6,7,5,3,4]=>010000
[2,1,6,7,5,4,3]=>010000
[2,1,7,3,4,5,6]=>010000
[2,1,7,3,4,6,5]=>010000
[2,1,7,3,5,4,6]=>010000
[2,1,7,3,5,6,4]=>010000
[2,1,7,3,6,4,5]=>010000
[2,1,7,3,6,5,4]=>010000
[2,1,7,4,3,5,6]=>010000
[2,1,7,4,3,6,5]=>010000
[2,1,7,4,5,3,6]=>010000
[2,1,7,4,5,6,3]=>010000
[2,1,7,4,6,3,5]=>010000
[2,1,7,4,6,5,3]=>010000
[2,1,7,5,3,4,6]=>010000
[2,1,7,5,3,6,4]=>010000
[2,1,7,5,4,3,6]=>010000
[2,1,7,5,4,6,3]=>010000
[2,1,7,5,6,3,4]=>010000
[2,1,7,5,6,4,3]=>010000
[2,1,7,6,3,4,5]=>010000
[2,1,7,6,3,5,4]=>010000
[2,1,7,6,4,3,5]=>010000
[2,1,7,6,4,5,3]=>010000
[2,1,7,6,5,3,4]=>010000
[2,1,7,6,5,4,3]=>010000
[2,3,1,4,5,6,7]=>001111
[2,3,1,4,5,7,6]=>001110
[2,3,1,4,6,5,7]=>001101
[2,3,1,4,6,7,5]=>001100
[2,3,1,4,7,5,6]=>001100
[2,3,1,4,7,6,5]=>001100
[2,3,1,5,4,6,7]=>001011
[2,3,1,5,4,7,6]=>001010
[2,3,1,5,6,4,7]=>001001
[2,3,1,5,6,7,4]=>001000
[2,3,1,5,7,4,6]=>001000
[2,3,1,5,7,6,4]=>001000
[2,3,1,6,4,5,7]=>001001
[2,3,1,6,4,7,5]=>001000
[2,3,1,6,5,4,7]=>001001
[2,3,1,6,5,7,4]=>001000
[2,3,1,6,7,4,5]=>001000
[2,3,1,6,7,5,4]=>001000
[2,3,1,7,4,5,6]=>001000
[2,3,1,7,4,6,5]=>001000
[2,3,1,7,5,4,6]=>001000
[2,3,1,7,5,6,4]=>001000
[2,3,1,7,6,4,5]=>001000
[2,3,1,7,6,5,4]=>001000
[2,3,4,1,5,6,7]=>000111
[2,3,4,1,5,7,6]=>000110
[2,3,4,1,6,5,7]=>000101
[2,3,4,1,6,7,5]=>000100
[2,3,4,1,7,5,6]=>000100
[2,3,4,1,7,6,5]=>000100
[2,3,4,5,1,6,7]=>000011
[2,3,4,5,1,7,6]=>000010
[2,3,4,5,6,1,7]=>000001
[2,3,4,5,6,7,1]=>000000
[2,3,4,5,7,1,6]=>000000
[2,3,4,5,7,6,1]=>000000
[2,3,4,6,1,5,7]=>000001
[2,3,4,6,1,7,5]=>000000
[2,3,4,6,5,1,7]=>000001
[2,3,4,6,5,7,1]=>000000
[2,3,4,6,7,1,5]=>000000
[2,3,4,6,7,5,1]=>000000
[2,3,4,7,1,5,6]=>000000
[2,3,4,7,1,6,5]=>000000
[2,3,4,7,5,1,6]=>000000
[2,3,4,7,5,6,1]=>000000
[2,3,4,7,6,1,5]=>000000
[2,3,4,7,6,5,1]=>000000
[2,3,5,1,4,6,7]=>000011
[2,3,5,1,4,7,6]=>000010
[2,3,5,1,6,4,7]=>000001
[2,3,5,1,6,7,4]=>000000
[2,3,5,1,7,4,6]=>000000
[2,3,5,1,7,6,4]=>000000
[2,3,5,4,1,6,7]=>000011
[2,3,5,4,1,7,6]=>000010
[2,3,5,4,6,1,7]=>000001
[2,3,5,4,6,7,1]=>000000
[2,3,5,4,7,1,6]=>000000
[2,3,5,4,7,6,1]=>000000
[2,3,5,6,1,4,7]=>000001
[2,3,5,6,1,7,4]=>000000
[2,3,5,6,4,1,7]=>000001
[2,3,5,6,4,7,1]=>000000
[2,3,5,6,7,1,4]=>000000
[2,3,5,6,7,4,1]=>000000
[2,3,5,7,1,4,6]=>000000
[2,3,5,7,1,6,4]=>000000
[2,3,5,7,4,1,6]=>000000
[2,3,5,7,4,6,1]=>000000
[2,3,5,7,6,1,4]=>000000
[2,3,5,7,6,4,1]=>000000
[2,3,6,1,4,5,7]=>000001
[2,3,6,1,4,7,5]=>000000
[2,3,6,1,5,4,7]=>000001
[2,3,6,1,5,7,4]=>000000
[2,3,6,1,7,4,5]=>000000
[2,3,6,1,7,5,4]=>000000
[2,3,6,4,1,5,7]=>000001
[2,3,6,4,1,7,5]=>000000
[2,3,6,4,5,1,7]=>000001
[2,3,6,4,5,7,1]=>000000
[2,3,6,4,7,1,5]=>000000
[2,3,6,4,7,5,1]=>000000
[2,3,6,5,1,4,7]=>000001
[2,3,6,5,1,7,4]=>000000
[2,3,6,5,4,1,7]=>000001
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[5,3,4,6,7,8,1,2]=>0000000
[4,3,5,6,7,8,1,2]=>0000000
[3,4,5,6,7,8,1,2]=>0000000
[8,7,6,5,4,2,1,3]=>0000000
[7,6,8,5,4,2,1,3]=>0000000
[7,8,5,6,4,2,1,3]=>0000000
[7,6,5,8,4,2,1,3]=>0000000
[6,7,5,8,4,2,1,3]=>0000000
[7,5,6,8,4,2,1,3]=>0000000
[5,6,7,8,4,2,1,3]=>0000000
[7,6,4,5,8,2,1,3]=>0000000
[4,5,6,7,8,2,1,3]=>0000000
[6,7,8,5,4,1,2,3]=>0000000
[8,5,6,7,4,1,2,3]=>0000000
[7,6,5,8,4,1,2,3]=>0000000
[6,7,5,8,4,1,2,3]=>0000000
[6,5,7,8,4,1,2,3]=>0000000
[5,6,7,8,4,1,2,3]=>0000000
[8,6,7,4,5,1,2,3]=>0000000
[8,7,5,4,6,1,2,3]=>0000000
[8,6,5,4,7,1,2,3]=>0000000
[8,6,4,5,7,1,2,3]=>0000000
[7,6,5,4,8,1,2,3]=>0000000
[6,7,4,5,8,1,2,3]=>0000000
[6,5,4,7,8,1,2,3]=>0000000
[5,4,6,7,8,1,2,3]=>0000000
[8,7,6,5,3,2,1,4]=>0000000
[7,8,6,5,3,2,1,4]=>0000000
[8,6,7,5,3,2,1,4]=>0000000
[7,6,8,5,3,2,1,4]=>0000000
[6,7,8,5,3,2,1,4]=>0000000
[8,7,5,6,3,2,1,4]=>0000000
[7,8,5,6,3,2,1,4]=>0000000
[8,6,5,7,3,2,1,4]=>0000000
[8,5,6,7,3,2,1,4]=>0000000
[7,6,5,8,3,2,1,4]=>0000000
[6,7,5,8,3,2,1,4]=>0000000
[7,5,6,8,3,2,1,4]=>0000000
[6,5,7,8,3,2,1,4]=>0000000
[5,6,7,8,3,2,1,4]=>0000000
[8,7,6,5,2,3,1,4]=>0000000
[7,8,6,5,2,3,1,4]=>0000000
[8,6,7,5,2,3,1,4]=>0000000
[7,6,8,5,2,3,1,4]=>0000000
[6,7,8,5,2,3,1,4]=>0000000
[8,7,5,6,2,3,1,4]=>0000000
[7,8,5,6,2,3,1,4]=>0000000
[8,6,5,7,2,3,1,4]=>0000000
[8,5,6,7,2,3,1,4]=>0000000
[7,6,5,8,2,3,1,4]=>0000000
[6,7,5,8,2,3,1,4]=>0000000
[7,5,6,8,2,3,1,4]=>0000000
[6,5,7,8,2,3,1,4]=>0000000
[5,6,7,8,2,3,1,4]=>0000000
[7,8,5,6,3,1,2,4]=>0000000
[7,6,5,8,3,1,2,4]=>0000000
[6,7,5,8,3,1,2,4]=>0000000
[7,5,6,8,3,1,2,4]=>0000000
[6,5,7,8,3,1,2,4]=>0000000
[5,6,7,8,3,1,2,4]=>0000000
[8,7,6,5,2,1,3,4]=>0000000
[6,7,8,5,2,1,3,4]=>0000000
[7,8,5,6,2,1,3,4]=>0000000
[8,6,5,7,2,1,3,4]=>0000000
[7,6,5,8,2,1,3,4]=>0000000
[6,7,5,8,2,1,3,4]=>0000000
[7,5,6,8,2,1,3,4]=>0000000
[6,5,7,8,2,1,3,4]=>0000000
[5,6,7,8,2,1,3,4]=>0000000
[8,7,6,5,1,2,3,4]=>0000000
[7,8,6,5,1,2,3,4]=>0000000
[8,6,7,5,1,2,3,4]=>0000000
[7,6,8,5,1,2,3,4]=>0000000
[6,7,8,5,1,2,3,4]=>0000000
[8,7,5,6,1,2,3,4]=>0000000
[7,8,5,6,1,2,3,4]=>0000000
[8,6,5,7,1,2,3,4]=>0000000
[8,5,6,7,1,2,3,4]=>0000000
[7,6,5,8,1,2,3,4]=>0000000
[6,7,5,8,1,2,3,4]=>0000000
[7,5,6,8,1,2,3,4]=>0000000
[6,5,7,8,1,2,3,4]=>0000000
[5,6,7,8,1,2,3,4]=>0000000
[8,7,6,4,3,2,1,5]=>0000000
[7,8,6,4,3,2,1,5]=>0000000
[8,6,7,4,3,2,1,5]=>0000000
[7,6,8,4,3,2,1,5]=>0000000
[6,7,8,4,3,2,1,5]=>0000000
[8,7,6,3,4,2,1,5]=>0000000
[6,7,8,3,4,2,1,5]=>0000000
[8,7,6,4,2,3,1,5]=>0000000
[7,6,8,4,2,3,1,5]=>0000000
[6,7,8,4,2,3,1,5]=>0000000
[8,7,6,3,2,4,1,5]=>0000000
[8,6,7,3,2,4,1,5]=>0000000
[6,7,8,3,2,4,1,5]=>0000000
[8,7,6,2,3,4,1,5]=>0000000
[6,7,8,2,3,4,1,5]=>0000000
[8,7,6,4,3,1,2,5]=>0000000
[6,7,8,4,3,1,2,5]=>0000000
[8,7,6,3,4,1,2,5]=>0000000
[6,7,8,3,4,1,2,5]=>0000000
[8,7,6,4,2,1,3,5]=>0000000
[6,7,8,4,2,1,3,5]=>0000000
[8,7,6,4,1,2,3,5]=>0000000
[6,7,8,4,1,2,3,5]=>0000000
[8,7,6,3,2,1,4,5]=>0000000
[7,6,8,3,2,1,4,5]=>0000000
[6,7,8,3,2,1,4,5]=>0000000
[8,7,6,2,3,1,4,5]=>0000000
[7,6,8,2,3,1,4,5]=>0000000
[6,7,8,2,3,1,4,5]=>0000000
[8,7,6,3,1,2,4,5]=>0000000
[7,8,6,3,1,2,4,5]=>0000000
[6,7,8,3,1,2,4,5]=>0000000
[8,7,6,2,1,3,4,5]=>0000000
[7,8,6,2,1,3,4,5]=>0000000
[6,7,8,2,1,3,4,5]=>0000000
[8,7,6,1,2,3,4,5]=>0000000
[7,8,6,1,2,3,4,5]=>0000000
[8,6,7,1,2,3,4,5]=>0000000
[7,6,8,1,2,3,4,5]=>0000000
[6,7,8,1,2,3,4,5]=>0000000
[8,7,5,4,3,2,1,6]=>0000000
[7,8,5,4,3,2,1,6]=>0000000
[7,8,3,4,5,2,1,6]=>0000000
[8,7,4,5,2,3,1,6]=>0000000
[7,8,4,5,2,3,1,6]=>0000000
[7,8,4,3,2,5,1,6]=>0000000
[7,8,3,4,2,5,1,6]=>0000000
[8,7,5,3,4,1,2,6]=>0000000
[7,8,5,4,1,2,3,6]=>0000000
[8,7,5,2,1,3,4,6]=>0000000
[7,8,5,2,1,3,4,6]=>0000000
[8,7,5,1,2,3,4,6]=>0000000
[7,8,5,1,2,3,4,6]=>0000000
[8,7,4,3,2,1,5,6]=>0000000
[7,8,4,3,2,1,5,6]=>0000000
[8,7,3,4,2,1,5,6]=>0000000
[7,8,3,4,2,1,5,6]=>0000000
[7,8,4,2,3,1,5,6]=>0000000
[8,7,3,2,4,1,5,6]=>0000000
[7,8,3,2,4,1,5,6]=>0000000
[7,8,2,3,4,1,5,6]=>0000000
[7,8,4,3,1,2,5,6]=>0000000
[7,8,3,4,1,2,5,6]=>0000000
[7,8,4,2,1,3,5,6]=>0000000
[7,8,4,1,2,3,5,6]=>0000000
[8,7,3,2,1,4,5,6]=>0000000
[7,8,3,2,1,4,5,6]=>0000000
[7,8,2,3,1,4,5,6]=>0000000
[7,8,3,1,2,4,5,6]=>0000000
[8,7,2,1,3,4,5,6]=>0000000
[7,8,2,1,3,4,5,6]=>0000000
[7,8,1,2,3,4,5,6]=>0000000
[8,6,5,4,3,2,1,7]=>0000000
[8,5,6,4,3,2,1,7]=>0000000
[8,4,5,6,3,2,1,7]=>0000000
[8,4,5,3,6,2,1,7]=>0000000
[8,3,4,5,6,2,1,7]=>0000000
[8,6,5,2,3,4,1,7]=>0000000
[8,6,4,2,3,5,1,7]=>0000000
[8,6,4,5,3,1,2,7]=>0000000
[8,5,6,3,4,1,2,7]=>0000000
[8,4,3,5,6,1,2,7]=>0000000
[8,3,4,5,6,1,2,7]=>0000000
[8,6,5,4,2,1,3,7]=>0000000
[8,4,5,6,1,2,3,7]=>0000000
[8,6,5,2,3,1,4,7]=>0000000
[8,5,6,2,3,1,4,7]=>0000000
[8,5,6,2,1,3,4,7]=>0000000
[8,6,5,1,2,3,4,7]=>0000000
[8,5,6,1,2,3,4,7]=>0000000
[8,6,4,3,2,1,5,7]=>0000000
[8,6,3,4,2,1,5,7]=>0000000
[8,6,4,2,3,1,5,7]=>0000000
[8,6,3,2,4,1,5,7]=>0000000
[8,6,3,4,1,2,5,7]=>0000000
[8,6,4,2,1,3,5,7]=>0000000
[8,6,3,2,1,4,5,7]=>0000000
[8,4,5,3,2,1,6,7]=>0000000
[8,4,3,5,2,1,6,7]=>0000000
[8,5,4,2,1,3,6,7]=>0000000
[8,4,3,2,1,5,6,7]=>0000000
[8,2,3,4,1,5,6,7]=>0000000
[8,3,2,1,4,5,6,7]=>0000000
[8,2,3,1,4,5,6,7]=>0000000
[7,6,5,4,3,2,1,8]=>0000001
[6,7,5,4,3,2,1,8]=>0000001
[7,5,6,4,3,2,1,8]=>0000001
[6,5,7,4,3,2,1,8]=>0000001
[5,6,7,4,3,2,1,8]=>0000001
[7,6,4,5,3,2,1,8]=>0000001
[6,5,4,7,3,2,1,8]=>0000001
[5,6,4,7,3,2,1,8]=>0000001
[4,5,6,7,3,2,1,8]=>0000001
[7,5,6,3,4,2,1,8]=>0000001
[5,6,7,3,4,2,1,8]=>0000001
[7,6,3,4,5,2,1,8]=>0000001
[7,3,4,5,6,2,1,8]=>0000001
[6,5,4,3,7,2,1,8]=>0000001
[5,4,6,3,7,2,1,8]=>0000001
[5,4,3,6,7,2,1,8]=>0000001
[5,6,7,4,2,3,1,8]=>0000001
[7,6,4,5,2,3,1,8]=>0000001
[6,7,4,5,2,3,1,8]=>0000001
[6,5,4,7,2,3,1,8]=>0000001
[5,6,4,7,2,3,1,8]=>0000001
[5,6,7,3,2,4,1,8]=>0000001
[7,6,5,2,3,4,1,8]=>0000001
[6,7,5,2,3,4,1,8]=>0000001
[7,5,6,2,3,4,1,8]=>0000001
[6,5,7,2,3,4,1,8]=>0000001
[5,6,7,2,3,4,1,8]=>0000001
[6,7,4,3,2,5,1,8]=>0000001
[6,7,3,4,2,5,1,8]=>0000001
[7,6,4,2,3,5,1,8]=>0000001
[7,6,3,2,4,5,1,8]=>0000001
[6,7,3,2,4,5,1,8]=>0000001
[7,6,2,3,4,5,1,8]=>0000001
[7,4,5,3,2,6,1,8]=>0000001
[7,4,3,5,2,6,1,8]=>0000001
[7,5,3,2,4,6,1,8]=>0000001
[5,4,6,3,2,7,1,8]=>0000001
[5,6,3,4,2,7,1,8]=>0000001
[6,3,4,5,2,7,1,8]=>0000001
[5,4,3,6,2,7,1,8]=>0000001
[4,5,3,6,2,7,1,8]=>0000001
[3,4,5,6,2,7,1,8]=>0000001
[6,3,2,4,5,7,1,8]=>0000001
[6,2,3,4,5,7,1,8]=>0000001
[5,4,3,2,6,7,1,8]=>0000001
[6,5,7,3,4,1,2,8]=>0000001
[6,7,3,4,5,1,2,8]=>0000001
[6,4,5,3,7,1,2,8]=>0000001
[3,4,5,6,7,1,2,8]=>0000001
[5,6,7,4,1,2,3,8]=>0000001
[5,6,4,7,1,2,3,8]=>0000001
[5,4,6,7,1,2,3,8]=>0000001
[5,6,7,3,1,2,4,8]=>0000001
[5,6,7,2,1,3,4,8]=>0000001
[7,6,5,1,2,3,4,8]=>0000001
[6,7,5,1,2,3,4,8]=>0000001
[7,5,6,1,2,3,4,8]=>0000001
[6,5,7,1,2,3,4,8]=>0000001
[5,6,7,1,2,3,4,8]=>0000001
[7,6,4,3,2,1,5,8]=>0000001
[6,7,3,4,2,1,5,8]=>0000001
[7,6,4,2,3,1,5,8]=>0000001
[7,6,3,2,4,1,5,8]=>0000001
[7,6,2,3,4,1,5,8]=>0000001
[6,7,2,3,4,1,5,8]=>0000001
[7,6,3,2,1,4,5,8]=>0000001
[6,7,3,2,1,4,5,8]=>0000001
[6,7,3,1,2,4,5,8]=>0000001
[6,7,1,2,3,4,5,8]=>0000001
[7,5,2,3,4,1,6,8]=>0000001
[7,2,3,4,5,1,6,8]=>0000001
[7,4,5,1,2,3,6,8]=>0000001
[7,5,3,2,1,4,6,8]=>0000001
[7,5,3,1,2,4,6,8]=>0000001
[7,5,1,2,3,4,6,8]=>0000001
[7,4,3,2,1,5,6,8]=>0000001
[7,4,3,1,2,5,6,8]=>0000001
[7,3,1,2,4,5,6,8]=>0000001
[7,1,2,3,4,5,6,8]=>0000001
[5,4,6,3,2,1,7,8]=>0000011
[4,5,6,3,2,1,7,8]=>0000011
[5,4,3,6,2,1,7,8]=>0000011
[3,4,5,6,2,1,7,8]=>0000011
[6,5,2,3,4,1,7,8]=>0000011
[5,6,2,3,4,1,7,8]=>0000011
[6,4,3,2,5,1,7,8]=>0000011
[5,4,3,2,6,1,7,8]=>0000011
[4,5,3,2,6,1,7,8]=>0000011
[5,3,2,4,6,1,7,8]=>0000011
[5,6,4,3,1,2,7,8]=>0000011
[5,4,6,3,1,2,7,8]=>0000011
[5,6,3,4,1,2,7,8]=>0000011
[6,4,3,5,1,2,7,8]=>0000011
[5,4,3,6,1,2,7,8]=>0000011
[5,6,4,2,1,3,7,8]=>0000011
[5,4,6,2,1,3,7,8]=>0000011
[5,6,3,2,1,4,7,8]=>0000011
[6,4,3,2,1,5,7,8]=>0000011
[6,3,4,2,1,5,7,8]=>0000011
[6,4,3,1,2,5,7,8]=>0000011
[6,4,2,1,3,5,7,8]=>0000011
[5,4,3,2,1,6,7,8]=>0000111
[4,5,3,2,1,6,7,8]=>0000111
[5,3,4,2,1,6,7,8]=>0000111
[4,3,5,2,1,6,7,8]=>0000111
[3,4,5,2,1,6,7,8]=>0000111
[5,4,2,3,1,6,7,8]=>0000111
[4,5,2,3,1,6,7,8]=>0000111
[5,3,2,4,1,6,7,8]=>0000111
[5,2,3,4,1,6,7,8]=>0000111
[4,3,2,5,1,6,7,8]=>0000111
[3,4,2,5,1,6,7,8]=>0000111
[4,2,3,5,1,6,7,8]=>0000111
[3,2,4,5,1,6,7,8]=>0000111
[2,3,4,5,1,6,7,8]=>0000111
[5,4,3,1,2,6,7,8]=>0000111
[5,3,4,1,2,6,7,8]=>0000111
[5,4,2,1,3,6,7,8]=>0000111
[5,4,1,2,3,6,7,8]=>0000111
[4,5,1,2,3,6,7,8]=>0000111
[5,3,2,1,4,6,7,8]=>0000111
[5,2,3,1,4,6,7,8]=>0000111
[5,3,1,2,4,6,7,8]=>0000111
[5,2,1,3,4,6,7,8]=>0000111
[5,1,2,3,4,6,7,8]=>0000111
[4,3,2,1,5,6,7,8]=>0001111
[3,4,2,1,5,6,7,8]=>0001111
[4,2,3,1,5,6,7,8]=>0001111
[3,2,4,1,5,6,7,8]=>0001111
[2,3,4,1,5,6,7,8]=>0001111
[4,3,1,2,5,6,7,8]=>0001111
[3,4,1,2,5,6,7,8]=>0001111
[4,2,1,3,5,6,7,8]=>0001111
[4,1,2,3,5,6,7,8]=>0001111
[3,2,1,4,5,6,7,8]=>0011111
[2,3,1,4,5,6,7,8]=>0011111
[3,1,2,4,5,6,7,8]=>0011111
[2,1,3,4,5,6,7,8]=>0111111
[1,2,3,4,5,6,7,8]=>1111111
[5,8,7,6,4,3,2,1]=>0000000
[6,5,8,7,4,3,2,1]=>0000000
[4,8,7,6,5,3,2,1]=>0000000
[4,7,8,6,5,3,2,1]=>0000000
[4,6,8,7,5,3,2,1]=>0000000
[4,7,6,8,5,3,2,1]=>0000000
[4,6,7,8,5,3,2,1]=>0000000
[4,5,8,7,6,3,2,1]=>0000000
[4,5,7,8,6,3,2,1]=>0000000
[4,6,5,8,7,3,2,1]=>0000000
[4,5,6,8,7,3,2,1]=>0000000
[5,7,6,4,8,3,2,1]=>0000000
[4,7,6,5,8,3,2,1]=>0000000
[4,6,7,5,8,3,2,1]=>0000000
[5,4,7,6,8,3,2,1]=>0000000
[4,5,7,6,8,3,2,1]=>0000000
[4,6,5,7,8,3,2,1]=>0000000
[3,8,7,6,5,4,2,1]=>0000000
[3,5,6,7,8,4,2,1]=>0000000
[4,3,6,7,8,5,2,1]=>0000000
[3,4,8,7,6,5,2,1]=>0000000
[4,5,3,7,8,6,2,1]=>0000000
[4,3,5,7,8,6,2,1]=>0000000
[4,5,6,3,8,7,2,1]=>0000000
[4,3,6,5,8,7,2,1]=>0000000
[5,4,3,6,8,7,2,1]=>0000000
[4,5,3,6,8,7,2,1]=>0000000
[4,3,5,6,8,7,2,1]=>0000000
[3,4,7,6,5,8,2,1]=>0000000
[4,5,3,7,6,8,2,1]=>0000000
[4,3,5,7,6,8,2,1]=>0000000
[3,4,6,5,7,8,2,1]=>0000000
[2,8,7,6,5,4,3,1]=>0000000
[2,5,6,7,8,4,3,1]=>0000000
[2,4,8,7,6,5,3,1]=>0000000
[2,4,6,8,7,5,3,1]=>0000000
[2,5,4,8,7,6,3,1]=>0000000
[2,5,6,4,8,7,3,1]=>0000000
[2,4,7,6,5,8,3,1]=>0000000
[2,6,5,4,7,8,3,1]=>0000000
[3,2,8,7,6,5,4,1]=>0000000
[3,2,6,8,7,5,4,1]=>0000000
[3,2,5,6,7,8,4,1]=>0000000
[2,3,8,7,6,5,4,1]=>0000000
[2,3,5,8,7,6,4,1]=>0000000
[2,3,5,6,7,8,4,1]=>0000000
[4,3,2,8,7,6,5,1]=>0000000
[4,3,2,7,8,6,5,1]=>0000000
[4,3,2,6,8,7,5,1]=>0000000
[3,4,2,8,7,6,5,1]=>0000000
[3,4,2,7,8,6,5,1]=>0000000
[2,4,3,8,7,6,5,1]=>0000000
[3,2,4,8,7,6,5,1]=>0000000
[2,3,4,8,7,6,5,1]=>0000000
[5,4,3,2,8,7,6,1]=>0000000
[5,4,3,2,7,8,6,1]=>0000000
[4,5,3,2,8,7,6,1]=>0000000
[4,3,5,2,8,7,6,1]=>0000000
[2,5,4,3,8,7,6,1]=>0000000
[2,5,4,3,7,8,6,1]=>0000000
[2,4,5,3,8,7,6,1]=>0000000
[2,3,5,4,8,7,6,1]=>0000000
[4,3,2,5,8,7,6,1]=>0000000
[6,5,4,3,2,8,7,1]=>0000000
[4,6,5,3,2,8,7,1]=>0000000
[5,4,6,3,2,8,7,1]=>0000000
[4,5,6,3,2,8,7,1]=>0000000
[4,3,6,5,2,8,7,1]=>0000000
[2,4,6,5,3,8,7,1]=>0000000
[4,3,2,6,5,8,7,1]=>0000000
[3,4,2,6,5,8,7,1]=>0000000
[2,4,3,6,5,8,7,1]=>0000000
[2,3,4,6,5,8,7,1]=>0000000
[5,4,3,2,6,8,7,1]=>0000000
[2,5,4,3,6,8,7,1]=>0000000
[4,3,2,5,6,8,7,1]=>0000000
[3,4,2,5,6,8,7,1]=>0000000
[2,4,3,5,6,8,7,1]=>0000000
[2,3,4,5,6,8,7,1]=>0000000
[4,6,5,7,3,2,8,1]=>0000000
[3,5,7,6,4,2,8,1]=>0000000
[4,3,6,7,5,2,8,1]=>0000000
[5,4,3,7,6,2,8,1]=>0000000
[4,6,5,3,7,2,8,1]=>0000000
[3,6,5,4,7,2,8,1]=>0000000
[2,5,4,7,6,3,8,1]=>0000000
[2,4,6,5,7,3,8,1]=>0000000
[3,2,6,7,5,4,8,1]=>0000000
[2,3,7,6,5,4,8,1]=>0000000
[4,3,2,7,6,5,8,1]=>0000000
[3,4,2,7,6,5,8,1]=>0000000
[2,4,3,7,6,5,8,1]=>0000000
[3,2,4,7,6,5,8,1]=>0000000
[2,3,4,7,6,5,8,1]=>0000000
[5,4,3,2,7,6,8,1]=>0000000
[2,5,4,3,7,6,8,1]=>0000000
[2,4,3,5,7,6,8,1]=>0000000
[2,6,5,4,3,7,8,1]=>0000000
[2,3,6,5,4,7,8,1]=>0000000
[4,3,2,6,5,7,8,1]=>0000000
[2,4,3,6,5,7,8,1]=>0000000
[2,3,4,6,5,7,8,1]=>0000000
[2,5,4,3,6,7,8,1]=>0000000
[2,4,3,5,6,7,8,1]=>0000000
[1,8,7,6,5,4,3,2]=>1000000
[1,7,8,6,5,4,3,2]=>1000000
[1,6,8,7,5,4,3,2]=>1000000
[1,7,6,8,5,4,3,2]=>1000000
[1,6,7,8,5,4,3,2]=>1000000
[1,7,6,5,8,4,3,2]=>1000000
[1,6,7,5,8,4,3,2]=>1000000
[1,5,7,6,8,4,3,2]=>1000000
[1,6,5,7,8,4,3,2]=>1000000
[1,5,6,7,8,4,3,2]=>1000000
[1,4,8,7,6,5,3,2]=>1000000
[1,4,7,8,6,5,3,2]=>1000000
[1,4,6,8,7,5,3,2]=>1000000
[1,4,6,7,8,5,3,2]=>1000000
[1,4,6,5,8,7,3,2]=>1000000
[1,4,7,6,5,8,3,2]=>1000000
[1,6,5,4,7,8,3,2]=>1000000
[1,5,4,6,7,8,3,2]=>1000000
[1,3,8,7,6,5,4,2]=>1000000
[1,3,6,8,7,5,4,2]=>1000000
[1,3,6,7,8,5,4,2]=>1000000
[1,3,5,8,7,6,4,2]=>1000000
[1,3,5,7,8,6,4,2]=>1000000
[1,3,6,5,7,8,4,2]=>1000000
[1,3,5,6,7,8,4,2]=>1000000
[1,4,3,8,7,6,5,2]=>1000000
[1,4,3,7,8,6,5,2]=>1000000
[1,4,3,6,8,7,5,2]=>1000000
[1,4,3,7,6,8,5,2]=>1000000
[1,3,4,8,7,6,5,2]=>1000000
[1,3,4,7,6,8,5,2]=>1000000
[1,3,4,6,7,8,5,2]=>1000000
[1,4,3,5,8,7,6,2]=>1000000
[1,4,3,5,7,8,6,2]=>1000000
[1,6,5,4,3,8,7,2]=>1000000
[1,5,6,4,3,8,7,2]=>1000000
[1,4,6,5,3,8,7,2]=>1000000
[1,3,6,5,4,8,7,2]=>1000000
[1,4,3,6,5,8,7,2]=>1000000
[1,5,4,3,6,8,7,2]=>1000000
[1,3,4,7,6,5,8,2]=>1000000
[1,5,4,3,6,7,8,2]=>1000000
[2,1,8,7,6,5,4,3]=>0100000
[2,1,6,7,8,5,4,3]=>0100000
[2,1,5,6,7,8,4,3]=>0100000
[2,1,4,8,7,6,5,3]=>0100000
[2,1,4,7,8,6,5,3]=>0100000
[2,1,4,6,7,8,5,3]=>0100000
[2,1,4,6,5,8,7,3]=>0100000
[2,1,4,5,6,8,7,3]=>0100000
[2,1,5,6,7,4,8,3]=>0100000
[2,1,4,7,6,5,8,3]=>0100000
[2,1,5,4,7,6,8,3]=>0100000
[1,2,8,7,6,5,4,3]=>1100000
[1,2,6,7,8,5,4,3]=>1100000
[1,2,5,6,7,8,4,3]=>1100000
[1,2,4,8,7,6,5,3]=>1100000
[1,2,4,7,8,6,5,3]=>1100000
[1,2,4,6,8,7,5,3]=>1100000
[1,2,5,4,8,7,6,3]=>1100000
[1,2,5,4,7,8,6,3]=>1100000
[1,2,6,5,4,8,7,3]=>1100000
[1,2,4,6,5,8,7,3]=>1100000
[1,2,5,4,6,8,7,3]=>1100000
[1,2,4,7,6,5,8,3]=>1100000
[3,2,1,8,7,6,5,4]=>0010000
[3,2,1,7,8,6,5,4]=>0010000
[3,2,1,6,8,7,5,4]=>0010000
[3,2,1,7,6,8,5,4]=>0010000
[3,2,1,6,7,8,5,4]=>0010000
[3,2,1,5,8,7,6,4]=>0010000
[3,2,1,5,7,8,6,4]=>0010000
[3,2,1,6,5,8,7,4]=>0010000
[3,2,1,5,6,8,7,4]=>0010000
[3,2,1,7,6,5,8,4]=>0010000
[3,2,1,6,7,5,8,4]=>0010000
[3,2,1,5,7,6,8,4]=>0010000
[3,2,1,6,5,7,8,4]=>0010000
[3,2,1,5,6,7,8,4]=>0010000
[2,3,1,8,7,6,5,4]=>0010000
[2,3,1,6,8,7,5,4]=>0010000
[2,3,1,7,6,8,5,4]=>0010000
[2,3,1,6,7,8,5,4]=>0010000
[2,3,1,6,5,8,7,4]=>0010000
[2,3,1,5,6,7,8,4]=>0010000
[1,3,2,8,7,6,5,4]=>1010000
[1,3,2,6,8,7,5,4]=>1010000
[1,3,2,6,5,8,7,4]=>1010000
[2,1,3,8,7,6,5,4]=>0110000
[2,1,3,7,8,6,5,4]=>0110000
[2,1,3,6,8,7,5,4]=>0110000
[1,2,3,8,7,6,5,4]=>1110000
[1,2,3,7,8,6,5,4]=>1110000
[1,2,3,6,8,7,5,4]=>1110000
[1,2,3,7,6,8,5,4]=>1110000
[1,2,3,6,7,8,5,4]=>1110000
[1,2,3,5,8,7,6,4]=>1110000
[1,2,3,5,7,8,6,4]=>1110000
[1,2,3,6,5,8,7,4]=>1110000
[1,2,3,5,6,8,7,4]=>1110000
[1,2,3,7,6,5,8,4]=>1110000
[1,2,3,6,7,5,8,4]=>1110000
[1,2,3,5,7,6,8,4]=>1110000
[1,2,3,6,5,7,8,4]=>1110000
[1,2,3,5,6,7,8,4]=>1110000
[4,3,2,1,8,7,6,5]=>0001000
[4,3,2,1,7,8,6,5]=>0001000
[4,3,2,1,6,8,7,5]=>0001000
[4,3,2,1,7,6,8,5]=>0001000
[4,3,2,1,6,7,8,5]=>0001000
[3,4,2,1,8,7,6,5]=>0001000
[3,4,2,1,7,8,6,5]=>0001000
[3,4,2,1,6,7,8,5]=>0001000
[2,4,3,1,8,7,6,5]=>0001000
[2,4,3,1,7,6,8,5]=>0001000
[3,2,4,1,8,7,6,5]=>0001000
[3,2,4,1,7,8,6,5]=>0001000
[3,2,4,1,6,8,7,5]=>0001000
[2,3,4,1,8,7,6,5]=>0001000
[2,3,4,1,6,7,8,5]=>0001000
[1,4,3,2,8,7,6,5]=>1001000
[1,4,3,2,6,7,8,5]=>1001000
[1,3,4,2,8,7,6,5]=>1001000
[1,3,4,2,7,8,6,5]=>1001000
[1,3,4,2,6,8,7,5]=>1001000
[2,1,4,3,8,7,6,5]=>0101000
[2,1,4,3,7,8,6,5]=>0101000
[2,1,4,3,6,8,7,5]=>0101000
[1,2,4,3,8,7,6,5]=>1101000
[1,2,4,3,7,8,6,5]=>1101000
[1,2,4,3,6,8,7,5]=>1101000
[1,2,4,3,6,7,8,5]=>1101000
[3,2,1,4,8,7,6,5]=>0011000
[3,2,1,4,7,8,6,5]=>0011000
[3,2,1,4,6,8,7,5]=>0011000
[2,3,1,4,8,7,6,5]=>0011000
[2,3,1,4,7,8,6,5]=>0011000
[1,3,2,4,8,7,6,5]=>1011000
[1,3,2,4,6,8,7,5]=>1011000
[1,3,2,4,6,7,8,5]=>1011000
[2,1,3,4,8,7,6,5]=>0111000
[2,1,3,4,6,7,8,5]=>0111000
[1,2,3,4,8,7,6,5]=>1111000
[1,2,3,4,7,8,6,5]=>1111000
[1,2,3,4,6,8,7,5]=>1111000
[1,2,3,4,7,6,8,5]=>1111000
[1,2,3,4,6,7,8,5]=>1111000
[5,4,3,2,1,8,7,6]=>0000100
[5,4,3,2,1,7,8,6]=>0000100
[4,5,3,2,1,8,7,6]=>0000100
[3,5,4,2,1,8,7,6]=>0000100
[3,5,4,2,1,7,8,6]=>0000100
[4,3,5,2,1,8,7,6]=>0000100
[3,4,5,2,1,8,7,6]=>0000100
[2,5,4,3,1,8,7,6]=>0000100
[2,4,5,3,1,8,7,6]=>0000100
[3,2,5,4,1,8,7,6]=>0000100
[3,2,5,4,1,7,8,6]=>0000100
[2,3,5,4,1,8,7,6]=>0000100
[4,3,2,5,1,8,7,6]=>0000100
[3,4,2,5,1,8,7,6]=>0000100
[2,4,3,5,1,8,7,6]=>0000100
[3,2,4,5,1,8,7,6]=>0000100
[2,3,4,5,1,8,7,6]=>0000100
[1,2,5,4,3,7,8,6]=>1100100
[1,2,4,5,3,8,7,6]=>1100100
[1,3,2,5,4,8,7,6]=>1010100
[1,3,2,5,4,7,8,6]=>1010100
[2,1,3,5,4,8,7,6]=>0110100
[1,2,3,5,4,8,7,6]=>1110100
[1,2,3,5,4,7,8,6]=>1110100
[4,3,2,1,5,8,7,6]=>0001100
[4,3,2,1,5,7,8,6]=>0001100
[3,2,4,1,5,8,7,6]=>0001100
[1,4,3,2,5,8,7,6]=>1001100
[1,3,4,2,5,7,8,6]=>1001100
[1,2,4,3,5,7,8,6]=>1101100
[3,2,1,4,5,8,7,6]=>0011100
[3,2,1,4,5,7,8,6]=>0011100
[2,3,1,4,5,7,8,6]=>0011100
[1,2,3,4,5,8,7,6]=>1111100
[1,2,3,4,5,7,8,6]=>1111100
[6,5,4,3,2,1,8,7]=>0000010
[4,5,6,3,2,1,8,7]=>0000010
[4,3,6,5,2,1,8,7]=>0000010
[3,4,5,6,2,1,8,7]=>0000010
[5,4,3,2,6,1,8,7]=>0000010
[4,5,3,2,6,1,8,7]=>0000010
[3,5,4,2,6,1,8,7]=>0000010
[1,5,4,6,3,2,8,7]=>1000010
[1,3,6,5,4,2,8,7]=>1000010
[2,1,6,5,4,3,8,7]=>0100010
[2,1,5,6,4,3,8,7]=>0100010
[2,1,4,5,6,3,8,7]=>0100010
[2,3,1,6,5,4,8,7]=>0010010
[2,1,3,6,5,4,8,7]=>0110010
[1,2,3,6,5,4,8,7]=>1110010
[1,2,3,5,6,4,8,7]=>1110010
[4,3,2,1,6,5,8,7]=>0001010
[3,4,2,1,6,5,8,7]=>0001010
[3,2,4,1,6,5,8,7]=>0001010
[2,1,4,3,6,5,8,7]=>0101010
[1,2,4,3,6,5,8,7]=>1101010
[1,3,2,4,6,5,8,7]=>1011010
[2,1,3,4,6,5,8,7]=>0111010
[1,2,3,4,6,5,8,7]=>1111010
[5,4,3,2,1,6,8,7]=>0000110
[4,5,3,2,1,6,8,7]=>0000110
[3,5,4,2,1,6,8,7]=>0000110
[2,5,4,3,1,6,8,7]=>0000110
[2,4,5,3,1,6,8,7]=>0000110
[3,2,5,4,1,6,8,7]=>0000110
[1,3,5,4,2,6,8,7]=>1000110
[2,1,5,4,3,6,8,7]=>0100110
[1,2,5,4,3,6,8,7]=>1100110
[2,1,3,5,4,6,8,7]=>0110110
[4,3,2,1,5,6,8,7]=>0001110
[1,4,3,2,5,6,8,7]=>1001110
[2,1,4,3,5,6,8,7]=>0101110
[1,2,4,3,5,6,8,7]=>1101110
[2,1,3,4,5,6,8,7]=>0111110
[1,2,3,4,5,6,8,7]=>1111110
[5,7,6,4,3,2,1,8]=>0000001
[4,7,6,5,3,2,1,8]=>0000001
[4,6,7,5,3,2,1,8]=>0000001
[4,5,7,6,3,2,1,8]=>0000001
[4,6,5,7,3,2,1,8]=>0000001
[3,5,7,6,4,2,1,8]=>0000001
[3,5,6,7,4,2,1,8]=>0000001
[3,4,7,6,5,2,1,8]=>0000001
[4,5,3,7,6,2,1,8]=>0000001
[3,5,4,7,6,2,1,8]=>0000001
[4,3,5,7,6,2,1,8]=>0000001
[2,5,6,7,4,3,1,8]=>0000001
[2,4,6,7,5,3,1,8]=>0000001
[3,2,7,6,5,4,1,8]=>0000001
[3,2,6,7,5,4,1,8]=>0000001
[3,2,5,7,6,4,1,8]=>0000001
[2,3,7,6,5,4,1,8]=>0000001
[2,3,6,7,5,4,1,8]=>0000001
[2,3,5,7,6,4,1,8]=>0000001
[2,3,6,5,7,4,1,8]=>0000001
[2,3,5,6,7,4,1,8]=>0000001
[3,2,4,6,7,5,1,8]=>0000001
[2,3,4,7,6,5,1,8]=>0000001
[5,4,3,2,7,6,1,8]=>0000001
[4,5,3,2,7,6,1,8]=>0000001
[3,5,4,2,7,6,1,8]=>0000001
[3,2,5,4,7,6,1,8]=>0000001
[3,4,6,5,2,7,1,8]=>0000001
[3,5,4,6,2,7,1,8]=>0000001
[2,5,4,6,3,7,1,8]=>0000001
[3,2,6,5,4,7,1,8]=>0000001
[3,4,2,6,5,7,1,8]=>0000001
[2,4,3,6,5,7,1,8]=>0000001
[3,5,4,2,6,7,1,8]=>0000001
[2,5,4,3,6,7,1,8]=>0000001
[1,5,6,7,4,3,2,8]=>1000001
[1,4,6,5,7,3,2,8]=>1000001
[1,3,5,7,6,4,2,8]=>1000001
[1,3,5,6,7,4,2,8]=>1000001
[1,3,5,4,7,6,2,8]=>1000001
[1,4,3,5,7,6,2,8]=>1000001
[1,5,4,6,3,7,2,8]=>1000001
[1,3,6,5,4,7,2,8]=>1000001
[1,4,3,6,5,7,2,8]=>1000001
[1,3,4,5,6,7,2,8]=>1000001
[2,1,5,6,7,4,3,8]=>0100001
[1,2,5,7,6,4,3,8]=>1100001
[1,2,5,6,7,4,3,8]=>1100001
[1,2,5,6,4,7,3,8]=>1100001
[1,2,5,4,6,7,3,8]=>1100001
[3,2,1,5,7,6,4,8]=>0010001
[3,2,1,6,5,7,4,8]=>0010001
[2,3,1,6,5,7,4,8]=>0010001
[1,3,2,6,5,7,4,8]=>1010001
[2,1,3,6,7,5,4,8]=>0110001
[1,2,3,7,6,5,4,8]=>1110001
[1,2,3,6,7,5,4,8]=>1110001
[1,2,3,5,7,6,4,8]=>1110001
[1,2,3,6,5,7,4,8]=>1110001
[1,2,3,5,6,7,4,8]=>1110001
[4,3,2,1,7,6,5,8]=>0001001
[4,3,2,1,6,7,5,8]=>0001001
[1,4,3,2,7,6,5,8]=>1001001
[1,4,3,2,6,7,5,8]=>1001001
[1,3,4,2,6,7,5,8]=>1001001
[2,1,4,3,6,7,5,8]=>0101001
[1,2,4,3,6,7,5,8]=>1101001
[3,2,1,4,7,6,5,8]=>0011001
[1,3,2,4,7,6,5,8]=>1011001
[1,2,3,4,7,6,5,8]=>1111001
[1,2,3,4,6,7,5,8]=>1111001
[5,4,3,2,1,7,6,8]=>0000101
[3,5,4,2,1,7,6,8]=>0000101
[2,4,5,3,1,7,6,8]=>0000101
[3,2,5,4,1,7,6,8]=>0000101
[3,4,2,5,1,7,6,8]=>0000101
[2,4,3,5,1,7,6,8]=>0000101
[1,4,3,5,2,7,6,8]=>1000101
[3,2,1,5,4,7,6,8]=>0010101
[2,3,1,5,4,7,6,8]=>0010101
[1,3,2,5,4,7,6,8]=>1010101
[1,2,3,5,4,7,6,8]=>1110101
[4,3,2,1,5,7,6,8]=>0001101
[1,4,3,2,5,7,6,8]=>1001101
[1,3,2,4,5,7,6,8]=>1011101
[1,2,3,4,5,7,6,8]=>1111101
[4,3,6,5,2,1,7,8]=>0000011
[2,4,6,5,3,1,7,8]=>0000011
[2,4,5,6,3,1,7,8]=>0000011
[4,3,2,6,5,1,7,8]=>0000011
[3,5,4,2,6,1,7,8]=>0000011
[1,5,6,4,3,2,7,8]=>1000011
[1,4,6,5,3,2,7,8]=>1000011
[1,5,4,6,3,2,7,8]=>1000011
[1,4,5,6,3,2,7,8]=>1000011
[1,3,5,6,4,2,7,8]=>1000011
[1,4,3,6,5,2,7,8]=>1000011
[1,5,4,3,6,2,7,8]=>1000011
[2,1,5,6,4,3,7,8]=>0100011
[2,1,4,6,5,3,7,8]=>0100011
[1,2,6,5,4,3,7,8]=>1100011
[1,2,4,5,6,3,7,8]=>1100011
[3,2,1,5,6,4,7,8]=>0010011
[1,2,3,5,6,4,7,8]=>1110011
[4,3,2,1,6,5,7,8]=>0001011
[3,2,4,1,6,5,7,8]=>0001011
[2,1,4,3,6,5,7,8]=>0101011
[1,2,4,3,6,5,7,8]=>1101011
[1,3,2,4,6,5,7,8]=>1011011
[2,1,3,4,6,5,7,8]=>0111011
[1,2,3,4,6,5,7,8]=>1111011
[3,5,4,2,1,6,7,8]=>0000111
[2,5,4,3,1,6,7,8]=>0000111
[2,4,5,3,1,6,7,8]=>0000111
[3,2,5,4,1,6,7,8]=>0000111
[2,3,5,4,1,6,7,8]=>0000111
[2,4,3,5,1,6,7,8]=>0000111
[1,3,2,5,4,6,7,8]=>1010111
[1,2,3,5,4,6,7,8]=>1110111
[2,4,3,1,5,6,7,8]=>0001111
[1,4,3,2,5,6,7,8]=>1001111
[1,3,4,2,5,6,7,8]=>1001111
[2,1,4,3,5,6,7,8]=>0101111
[1,2,4,3,5,6,7,8]=>1101111
[1,3,2,4,5,6,7,8]=>1011111
[1,2,3,4,8,6,7,5]=>1111000
[1,2,3,5,8,6,7,4]=>1110000
[1,2,3,7,5,6,4,8]=>1110001
[1,2,3,7,5,6,8,4]=>1110000
[1,2,3,8,5,6,7,4]=>1110000
[1,2,3,8,5,7,6,4]=>1110000
[1,2,3,8,6,5,7,4]=>1110000
[1,2,3,8,6,7,5,4]=>1110000
[1,2,4,5,8,6,7,3]=>1100000
[1,2,4,8,6,5,7,3]=>1100000
[1,2,5,4,8,6,7,3]=>1100000
[1,2,6,4,5,3,7,8]=>1100011
[1,2,8,4,5,6,7,3]=>1100000
[1,2,7,5,4,6,8,3]=>1100000
[1,2,8,5,4,6,7,3]=>1100000
[1,2,8,5,4,7,6,3]=>1100000
[1,3,2,7,5,6,8,4]=>1010000
[1,3,2,8,5,7,6,4]=>1010000
[1,3,6,4,5,2,8,7]=>1000010
[1,3,6,4,5,7,2,8]=>1000001
[1,3,6,4,5,8,7,2]=>1000000
[1,3,8,4,5,6,7,2]=>1000000
[1,3,8,4,6,7,5,2]=>1000000
[1,3,8,5,4,6,7,2]=>1000000
[1,3,8,5,6,7,4,2]=>1000000
[1,3,8,5,7,6,4,2]=>1000000
[1,3,8,6,5,7,4,2]=>1000000
[1,3,8,7,5,6,4,2]=>1000000
[1,4,3,8,5,6,7,2]=>1000000
[1,4,3,8,5,7,6,2]=>1000000
[1,4,3,8,6,7,5,2]=>1000000
[1,5,3,4,2,7,8,6]=>1000100
[1,5,3,4,2,8,7,6]=>1000100
[1,5,3,4,8,6,7,2]=>1000000
[1,8,3,4,6,7,5,2]=>1000000
[1,6,3,5,4,2,7,8]=>1000011
[1,6,3,5,4,8,7,2]=>1000000
[1,8,3,5,6,4,7,2]=>1000000
[1,8,3,5,7,6,4,2]=>1000000
[1,8,3,6,5,4,7,2]=>1000000
[1,8,3,7,6,5,4,2]=>1000000
[1,6,4,3,5,2,7,8]=>1000011
[1,8,4,3,5,6,7,2]=>1000000
[1,8,4,3,5,7,6,2]=>1000000
[1,6,4,5,3,8,7,2]=>1000000
[1,8,4,5,6,7,3,2]=>1000000
[1,8,4,6,5,7,3,2]=>1000000
[1,8,4,7,6,5,3,2]=>1000000
[1,7,5,4,3,6,8,2]=>1000000
[1,8,5,4,3,6,7,2]=>1000000
[1,8,5,4,6,3,7,2]=>1000000
[1,8,5,4,6,7,3,2]=>1000000
[1,8,5,4,7,6,3,2]=>1000000
[1,8,6,4,5,7,3,2]=>1000000
[1,8,6,5,4,7,3,2]=>1000000
[1,8,7,5,6,4,3,2]=>1000000
[2,1,3,4,8,6,7,5]=>0111000
[2,1,4,8,6,5,7,3]=>0100000
[2,1,6,4,5,8,7,3]=>0100000
[2,1,8,5,4,6,7,3]=>0100000
[2,1,8,5,4,7,6,3]=>0100000
[2,1,7,5,6,4,8,3]=>0100000
[2,1,8,7,5,6,4,3]=>0100000
[2,3,1,8,6,7,5,4]=>0010000
[2,3,6,4,5,7,8,1]=>0000000
[2,3,7,4,5,6,8,1]=>0000000
[2,3,8,4,5,6,7,1]=>0000000
[2,3,7,4,6,5,8,1]=>0000000
[2,3,7,5,4,6,8,1]=>0000000
[2,3,7,5,6,4,1,8]=>0000001
[2,3,7,5,6,4,8,1]=>0000000
[2,4,3,5,8,6,7,1]=>0000000
[2,5,3,4,1,6,7,8]=>0000111
[2,5,3,4,1,8,7,6]=>0000100
[2,5,3,4,6,7,1,8]=>0000001
[2,5,3,4,8,7,6,1]=>0000000
[2,6,3,4,5,7,8,1]=>0000000
[2,6,3,5,4,1,8,7]=>0000010
[2,6,3,5,4,7,8,1]=>0000000
[2,7,3,5,4,6,8,1]=>0000000
[2,7,3,5,6,4,8,1]=>0000000
[2,8,3,5,7,6,4,1]=>0000000
[2,7,3,6,5,4,1,8]=>0000001
[2,5,4,3,8,6,7,1]=>0000000
[2,6,4,3,5,7,8,1]=>0000000
[2,8,4,3,5,6,7,1]=>0000000
[2,8,4,3,7,6,5,1]=>0000000
[2,6,4,5,3,1,7,8]=>0000011
[2,6,4,5,3,7,8,1]=>0000000
[2,7,5,4,3,6,8,1]=>0000000
[2,7,5,4,6,3,8,1]=>0000000
[2,8,5,4,7,6,3,1]=>0000000
[2,8,7,5,4,6,3,1]=>0000000
[2,8,7,5,6,4,3,1]=>0000000
[3,2,1,4,8,6,7,5]=>0011000
[3,2,1,5,8,6,7,4]=>0010000
[3,2,1,7,5,6,4,8]=>0010001
[3,2,1,7,5,6,8,4]=>0010000
[3,2,1,8,5,6,7,4]=>0010000
[3,2,1,8,5,7,6,4]=>0010000
[3,2,1,8,6,5,7,4]=>0010000
[3,2,1,8,6,7,5,4]=>0010000
[3,2,4,1,8,6,7,5]=>0001000
[3,2,7,4,6,5,1,8]=>0000001
[3,2,7,4,6,5,8,1]=>0000000
[3,2,8,5,4,6,7,1]=>0000000
[3,2,7,5,6,4,1,8]=>0000001
[3,2,8,5,7,6,4,1]=>0000000
[4,2,3,1,8,6,7,5]=>0001000
[4,2,3,1,8,7,6,5]=>0001000
[4,2,3,5,1,7,8,6]=>0000100
[4,2,3,5,1,8,7,6]=>0000100
[4,2,3,5,6,8,7,1]=>0000000
[4,2,3,7,5,6,1,8]=>0000001
[4,2,3,8,5,6,7,1]=>0000000
[4,2,3,7,6,5,8,1]=>0000000
[4,2,3,8,7,6,5,1]=>0000000
[5,2,3,4,1,8,7,6]=>0000100
[5,2,3,4,8,7,6,1]=>0000000
[6,2,3,5,4,1,7,8]=>0000011
[6,2,3,5,4,1,8,7]=>0000010
[6,2,3,5,4,7,1,8]=>0000001
[7,2,3,5,6,4,1,8]=>0000001
[7,2,3,6,5,4,1,8]=>0000001
[5,2,4,3,1,6,7,8]=>0000111
[5,2,4,3,1,6,8,7]=>0000110
[5,2,4,3,1,7,6,8]=>0000101
[5,2,4,3,1,8,7,6]=>0000100
[5,2,4,3,6,1,7,8]=>0000011
[5,2,4,3,6,1,8,7]=>0000010
[5,2,4,3,7,6,1,8]=>0000001
[5,2,4,3,7,6,8,1]=>0000000
[7,2,4,3,6,5,1,8]=>0000001
[7,2,4,3,6,5,8,1]=>0000000
[6,2,4,5,3,1,7,8]=>0000011
[7,2,4,5,3,6,1,8]=>0000001
[7,2,4,5,3,6,8,1]=>0000000
[8,2,4,7,6,5,3,1]=>0000000
[6,2,5,4,3,1,8,7]=>0000010
[7,2,5,4,3,6,1,8]=>0000001
[8,2,6,4,5,7,3,1]=>0000000
[8,2,7,5,6,4,3,1]=>0000000
[8,2,7,6,5,4,3,1]=>0000000
[4,3,2,1,8,6,7,5]=>0001000
[4,3,2,7,5,6,8,1]=>0000000
[4,3,2,8,5,6,7,1]=>0000000
[4,3,2,8,6,7,5,1]=>0000000
[5,3,2,4,1,6,8,7]=>0000110
[5,3,2,4,1,8,7,6]=>0000100
[5,3,2,4,6,1,8,7]=>0000010
[6,3,2,5,4,1,7,8]=>0000011
[6,3,2,5,4,1,8,7]=>0000010
[6,3,2,5,4,7,1,8]=>0000001
[8,3,2,5,4,7,6,1]=>0000000
[8,3,2,5,6,4,7,1]=>0000000
[8,3,2,7,6,5,4,1]=>0000000
[5,3,4,2,1,7,8,6]=>0000100
[5,3,4,2,1,8,7,6]=>0000100
[5,3,4,2,7,6,1,8]=>0000001
[7,3,4,2,6,5,1,8]=>0000001
[7,3,4,2,6,5,8,1]=>0000000
[7,3,4,6,5,2,1,8]=>0000001
[6,3,5,4,2,7,1,8]=>0000001
[7,3,5,4,6,2,1,8]=>0000001
[7,3,6,4,5,2,1,8]=>0000001
[7,3,6,5,4,2,1,8]=>0000001
[5,4,3,2,8,6,7,1]=>0000000
[6,4,3,5,2,1,8,7]=>0000010
[7,4,3,6,5,2,1,8]=>0000001
[7,4,3,6,5,2,8,1]=>0000000
[6,5,3,4,2,1,8,7]=>0000010
[8,5,3,4,7,6,2,1]=>0000000
[8,7,3,6,5,4,2,1]=>0000000
[8,5,4,3,2,7,6,1]=>0000000
[8,7,4,3,6,5,2,1]=>0000000
[2,4,6,1,3,5,8,7]=>0000010
[2,1,4,6,3,8,5,7]=>0100000
[2,4,1,6,3,8,5,7]=>0000000
[2,4,6,1,3,8,5,7]=>0000000
[2,4,6,1,8,3,5,7]=>0000000
[2,4,6,8,1,3,5,7]=>0000000
[2,4,1,3,6,5,7,8]=>0001011
[2,4,1,6,3,7,5,8]=>0000001
[2,4,6,1,3,7,5,8]=>0000001
[2,4,1,6,3,7,8,5]=>0000000
[2,4,1,6,7,3,8,5]=>0000000
[2,4,6,1,7,3,8,5]=>0000000
[2,4,6,7,1,3,8,5]=>0000000
[2,4,1,6,7,8,3,5]=>0000000
[2,4,6,7,8,1,3,5]=>0000000
[2,1,4,3,7,5,8,6]=>0101000
[2,4,1,3,7,5,8,6]=>0001000
[2,4,1,7,3,5,8,6]=>0000000
[2,4,7,1,3,5,8,6]=>0000000
[2,1,4,3,7,8,5,6]=>0101000
[2,4,1,3,7,8,5,6]=>0001000
[2,4,1,7,3,8,5,6]=>0000000
[2,4,1,7,8,3,5,6]=>0000000
[2,4,1,5,3,7,6,8]=>0000101
[2,4,1,3,5,7,8,6]=>0001100
[2,4,1,5,3,7,8,6]=>0000100
[2,4,5,1,3,7,8,6]=>0000100
[2,1,4,5,7,3,8,6]=>0100000
[2,4,1,5,7,3,8,6]=>0000000
[2,4,5,1,7,3,8,6]=>0000000
[2,4,1,3,8,5,6,7]=>0001000
[2,1,4,8,3,5,6,7]=>0100000
[2,4,1,8,3,5,6,7]=>0000000
[2,4,1,5,3,8,6,7]=>0000100
[2,1,4,5,8,3,6,7]=>0100000
[2,4,1,5,6,3,8,7]=>0000010
[2,1,4,5,6,8,3,7]=>0100000
[2,4,1,3,5,6,7,8]=>0001111
[2,4,1,5,6,3,7,8]=>0000011
[2,4,5,6,1,3,7,8]=>0000011
[2,4,5,6,7,1,3,8]=>0000001
[2,4,5,6,7,1,8,3]=>0000000
[2,1,5,3,6,4,8,7]=>0100010
[2,1,5,6,3,4,8,7]=>0100010
[2,1,5,3,6,8,4,7]=>0100000
[2,5,1,3,6,8,4,7]=>0000000
[2,1,5,6,3,4,7,8]=>0100011
[2,5,1,6,3,4,7,8]=>0000011
[2,1,5,3,6,7,4,8]=>0100001
[2,1,5,6,3,7,4,8]=>0100001
[2,5,1,6,3,7,4,8]=>0000001
[2,5,6,1,3,7,4,8]=>0000001
[2,1,5,6,7,3,4,8]=>0100001
[2,5,1,3,6,7,8,4]=>0000000
[2,1,5,6,3,7,8,4]=>0100000
[2,5,6,1,3,7,8,4]=>0000000
[2,1,5,6,7,8,3,4]=>0100000
[2,1,5,3,7,4,8,6]=>0100000
[2,1,5,7,3,4,8,6]=>0100000
[2,5,1,7,3,4,8,6]=>0000000
[2,5,7,1,3,4,8,6]=>0000000
[2,1,5,3,7,8,4,6]=>0100000
[2,5,1,3,7,8,4,6]=>0000000
[2,1,5,7,3,8,4,6]=>0100000
[2,1,5,7,8,3,4,6]=>0100000
[2,5,1,7,8,3,4,6]=>0000000
[2,5,1,3,7,4,6,8]=>0000001
[2,1,5,7,3,4,6,8]=>0100001
[2,3,5,7,1,4,8,6]=>0000000
[2,3,5,6,1,8,4,7]=>0000000
[2,3,5,6,8,1,4,7]=>0000000
[2,5,1,3,4,6,7,8]=>0000111
[2,3,5,6,1,4,7,8]=>0000011
[2,3,5,6,1,7,8,4]=>0000000
[2,3,5,6,7,8,1,4]=>0000000
[2,1,6,3,7,4,8,5]=>0100000
[2,6,1,3,7,4,8,5]=>0000000
[2,6,7,1,3,4,8,5]=>0000000
[2,1,6,3,7,8,4,5]=>0100000
[2,6,1,7,3,8,4,5]=>0000000
[2,1,6,7,8,3,4,5]=>0100000
[2,6,1,7,8,3,4,5]=>0000000
[2,6,7,8,1,3,4,5]=>0000000
[2,6,1,7,3,4,5,8]=>0000001
[2,6,7,1,3,4,5,8]=>0000001
[2,3,1,6,4,7,5,8]=>0010001
[2,3,6,1,4,7,5,8]=>0000001
[2,1,6,3,4,7,8,5]=>0100000
[2,3,6,1,4,7,8,5]=>0000000
[2,1,3,6,7,4,8,5]=>0110000
[2,3,1,6,7,8,4,5]=>0010000
[2,3,6,7,8,1,4,5]=>0000000
[2,6,1,8,3,4,5,7]=>0000000
[2,1,6,3,4,8,5,7]=>0100000
[2,3,6,1,4,5,8,7]=>0000010
[2,3,4,1,6,8,5,7]=>0001000
[2,3,4,6,7,8,1,5]=>0000000
[2,1,7,8,3,4,5,6]=>0100000
[2,7,1,8,3,4,5,6]=>0000000
[2,7,8,1,3,4,5,6]=>0000000
[2,1,7,3,4,8,5,6]=>0100000
[2,1,3,7,4,8,5,6]=>0110000
[2,3,7,1,4,5,8,6]=>0000000
[2,1,3,4,7,8,5,6]=>0111000
[2,1,3,8,4,5,6,7]=>0110000
[2,3,1,8,4,5,6,7]=>0010000
[2,1,3,4,8,5,6,7]=>0111000
[2,3,4,8,1,5,6,7]=>0000000
[3,1,4,2,6,5,8,7]=>0001010
[3,4,1,2,6,5,8,7]=>0001010
[3,4,6,1,2,5,8,7]=>0000010
[3,1,4,2,6,8,5,7]=>0001000
[3,1,4,6,8,2,5,7]=>0000000
[3,1,4,2,6,5,7,8]=>0001011
[3,4,1,2,6,5,7,8]=>0001011
[3,1,4,2,6,7,5,8]=>0001001
[3,4,1,6,2,7,5,8]=>0000001
[3,1,4,2,6,7,8,5]=>0001000
[3,4,1,2,6,7,8,5]=>0001000
[3,4,6,1,7,2,8,5]=>0000000
[3,1,4,6,7,8,2,5]=>0000000
[3,4,6,1,7,8,2,5]=>0000000
[3,4,6,7,1,8,2,5]=>0000000
[3,4,6,7,8,1,2,5]=>0000000
[3,1,4,2,7,5,8,6]=>0001000
[3,4,1,2,7,5,8,6]=>0001000
[3,4,7,1,2,5,8,6]=>0000000
[3,1,4,2,7,8,5,6]=>0001000
[3,4,1,2,7,8,5,6]=>0001000
[3,4,7,1,8,2,5,6]=>0000000
[3,1,4,2,7,5,6,8]=>0001001
[3,4,1,5,2,7,6,8]=>0000101
[3,1,4,2,5,7,8,6]=>0001100
[3,1,4,5,2,7,8,6]=>0000100
[3,1,4,5,7,8,2,6]=>0000000
[3,4,1,5,7,8,2,6]=>0000000
[3,4,5,1,7,8,2,6]=>0000000
[3,4,1,8,2,5,6,7]=>0000000
[3,1,4,2,5,8,6,7]=>0001100
[3,4,1,5,2,8,6,7]=>0000100
[3,4,1,5,8,2,6,7]=>0000000
[3,4,1,2,5,6,8,7]=>0001110
[3,4,5,6,1,2,8,7]=>0000010
[3,4,5,6,1,8,2,7]=>0000000
[3,4,5,6,8,1,2,7]=>0000000
[3,1,4,2,5,6,7,8]=>0001111
[3,4,1,5,6,7,2,8]=>0000001
[3,4,5,6,1,7,2,8]=>0000001
[3,4,5,1,6,7,8,2]=>0000000
[3,4,5,6,1,7,8,2]=>0000000
[3,1,5,2,6,4,8,7]=>0000010
[3,1,5,6,2,4,8,7]=>0000010
[3,5,1,6,2,4,8,7]=>0000010
[3,5,1,2,6,8,4,7]=>0000000
[3,1,5,6,2,8,4,7]=>0000000
[3,5,6,1,2,8,4,7]=>0000000
[3,1,5,6,8,2,4,7]=>0000000
[3,5,6,1,8,2,4,7]=>0000000
[3,1,5,6,2,4,7,8]=>0000011
[3,5,1,6,2,4,7,8]=>0000011
[3,5,1,6,2,7,4,8]=>0000001
[3,5,6,1,2,7,4,8]=>0000001
[3,1,5,2,6,7,8,4]=>0000000
[3,5,1,2,6,7,8,4]=>0000000
[3,5,1,6,2,7,8,4]=>0000000
[3,1,5,6,7,2,8,4]=>0000000
[3,5,1,6,7,8,2,4]=>0000000
[3,5,6,1,7,8,2,4]=>0000000
[3,1,5,2,7,4,8,6]=>0000000
[3,5,1,2,7,4,8,6]=>0000000
[3,1,5,7,2,4,8,6]=>0000000
[3,5,1,7,2,4,8,6]=>0000000
[3,5,7,1,2,4,8,6]=>0000000
[3,1,5,2,7,8,4,6]=>0000000
[3,5,1,2,7,8,4,6]=>0000000
[3,1,5,7,2,8,4,6]=>0000000
[3,5,1,7,2,8,4,6]=>0000000
[3,1,5,7,8,2,4,6]=>0000000
[3,5,1,7,8,2,4,6]=>0000000
[3,1,5,2,7,4,6,8]=>0000001
[3,1,5,7,2,4,6,8]=>0000001
[3,5,1,7,2,4,6,8]=>0000001
[3,5,7,1,2,4,6,8]=>0000001
[1,3,5,7,2,4,6,8]=>1000001
[3,5,1,2,4,7,8,6]=>0000100
[3,1,2,5,7,4,8,6]=>0010000
[1,3,5,2,7,4,8,6]=>1000000
[1,3,5,7,2,4,8,6]=>1000000
[1,3,5,2,7,8,4,6]=>1000000
[3,1,5,2,8,4,6,7]=>0000000
[3,5,1,2,8,4,6,7]=>0000000
[3,1,5,8,2,4,6,7]=>0000000
[3,5,1,8,2,4,6,7]=>0000000
[3,1,5,2,4,8,6,7]=>0000100
[3,5,1,2,4,8,6,7]=>0000100
[1,3,2,5,4,8,6,7]=>1010100
[1,3,5,2,4,8,6,7]=>1000100
[3,1,2,5,8,4,6,7]=>0010000
[1,3,2,5,8,4,6,7]=>1010000
[1,3,5,2,8,4,6,7]=>1000000
[1,3,5,8,2,4,6,7]=>1000000
[3,5,1,2,4,6,8,7]=>0000110
[3,1,2,5,4,6,8,7]=>0010110
[1,3,5,2,4,6,8,7]=>1000110
[1,3,5,2,6,4,8,7]=>1000010
[1,3,5,6,2,4,8,7]=>1000010
[3,1,2,5,6,8,4,7]=>0010000
[1,3,5,2,6,8,4,7]=>1000000
[3,5,1,2,4,6,7,8]=>0000111
[1,3,5,6,2,4,7,8]=>1000011
[3,1,2,5,6,7,4,8]=>0010001
[1,3,5,2,6,7,4,8]=>1000001
[1,3,5,6,2,7,4,8]=>1000001
[1,3,5,6,7,2,4,8]=>1000001
[3,1,2,5,6,7,8,4]=>0010000
[1,3,5,6,7,8,2,4]=>1000000
[3,1,6,2,7,4,8,5]=>0000000
[3,6,1,2,7,4,8,5]=>0000000
[3,6,1,7,2,4,8,5]=>0000000
[3,6,7,1,2,4,8,5]=>0000000
[3,1,6,7,2,8,4,5]=>0000000
[3,6,1,7,2,8,4,5]=>0000000
[3,6,7,1,2,8,4,5]=>0000000
[3,6,1,7,8,2,4,5]=>0000000
[3,6,7,8,1,2,4,5]=>0000000
[3,1,6,7,2,4,5,8]=>0000001
[3,6,7,1,2,4,5,8]=>0000001
[3,1,6,2,4,7,5,8]=>0000001
[3,1,2,6,4,7,5,8]=>0010001
[1,3,2,6,4,7,5,8]=>1010001
[1,3,6,2,4,7,5,8]=>1000001
[3,1,6,2,4,7,8,5]=>0000000
[3,6,1,2,4,7,8,5]=>0000000
[3,1,2,6,4,7,8,5]=>0010000
[1,3,6,2,4,7,8,5]=>1000000
[3,1,2,6,7,4,8,5]=>0010000
[1,3,6,2,7,4,8,5]=>1000000
[1,3,6,7,2,4,8,5]=>1000000
[1,3,6,2,7,8,4,5]=>1000000
[3,1,6,2,8,4,5,7]=>0000000
[3,1,6,8,2,4,5,7]=>0000000
[3,6,1,8,2,4,5,7]=>0000000
[3,1,6,2,4,8,5,7]=>0000000
[1,3,2,6,4,8,5,7]=>1010000
[1,3,6,2,4,8,5,7]=>1000000
[3,1,6,2,4,5,8,7]=>0000010
[3,1,2,6,4,5,8,7]=>0010010
[1,3,4,6,2,5,8,7]=>1000010
[3,1,2,4,6,8,5,7]=>0011000
[1,3,2,4,6,8,5,7]=>1011000
[1,3,4,6,8,2,5,7]=>1000000
[3,1,6,2,4,5,7,8]=>0000011
[1,3,2,6,4,5,7,8]=>1010011
[1,3,6,2,4,5,7,8]=>1000011
[3,1,2,4,6,7,5,8]=>0011001
[3,1,2,4,6,7,8,5]=>0011000
[3,7,1,2,8,4,5,6]=>0000000
[3,1,7,8,2,4,5,6]=>0000000
[3,7,1,2,4,8,5,6]=>0000000
[3,1,2,7,4,8,5,6]=>0010000
[1,3,2,7,4,8,5,6]=>1010000
[1,3,7,2,4,8,5,6]=>1000000
[1,3,7,2,8,4,5,6]=>1000000
[1,3,7,2,4,5,8,6]=>1000000
[3,1,2,4,7,5,8,6]=>0011000
[1,3,2,4,7,5,8,6]=>1011000
[1,3,4,7,2,5,8,6]=>1000000
[3,7,1,2,4,5,6,8]=>0000001
[1,3,2,7,4,5,6,8]=>1010001
[1,3,4,5,7,8,2,6]=>1000000
[3,1,2,8,4,5,6,7]=>0010000
[1,3,2,8,4,5,6,7]=>1010000
[1,3,8,2,4,5,6,7]=>1000000
[3,1,2,4,8,5,6,7]=>0011000
[1,3,2,4,8,5,6,7]=>1011000
[1,3,4,2,8,5,6,7]=>1001000
[1,3,4,8,2,5,6,7]=>1000000
[3,1,2,4,5,8,6,7]=>0011100
[1,3,2,4,5,8,6,7]=>1011100
[1,3,4,2,5,8,6,7]=>1001100
[1,3,4,5,2,8,6,7]=>1000100
[4,1,5,2,6,3,8,7]=>0000010
[4,5,1,2,6,3,8,7]=>0000010
[4,1,5,6,2,3,8,7]=>0000010
[4,5,6,1,2,3,8,7]=>0000010
[4,1,5,2,6,8,3,7]=>0000000
[4,5,1,2,6,8,3,7]=>0000000
[4,5,1,6,2,8,3,7]=>0000000
[4,1,5,6,8,2,3,7]=>0000000
[4,5,6,8,1,2,3,7]=>0000000
[4,5,1,6,2,7,3,8]=>0000001
[4,1,5,6,7,2,3,8]=>0000001
[4,5,1,6,7,2,3,8]=>0000001
[4,1,5,2,6,7,8,3]=>0000000
[4,5,1,2,6,7,8,3]=>0000000
[4,5,1,6,2,7,8,3]=>0000000
[4,5,1,6,7,2,8,3]=>0000000
[4,5,6,1,7,2,8,3]=>0000000
[4,5,1,6,7,8,2,3]=>0000000
[4,1,5,2,7,3,8,6]=>0000000
[4,5,1,2,7,3,8,6]=>0000000
[4,5,1,7,2,3,8,6]=>0000000
[4,1,5,2,7,8,3,6]=>0000000
[4,5,1,2,7,8,3,6]=>0000000
[4,1,5,7,2,8,3,6]=>0000000
[4,5,1,7,2,8,3,6]=>0000000
[4,5,7,1,2,8,3,6]=>0000000
[4,5,1,7,8,2,3,6]=>0000000
[4,1,5,2,7,3,6,8]=>0000001
[4,5,1,2,7,3,6,8]=>0000001
[1,4,2,5,3,7,6,8]=>1000101
[4,1,2,5,7,3,6,8]=>0000001
[1,4,2,5,7,3,6,8]=>1000001
[1,4,5,2,7,3,6,8]=>1000001
[1,4,5,7,2,3,6,8]=>1000001
[4,1,5,2,3,7,8,6]=>0000100
[4,1,2,5,3,7,8,6]=>0000100
[1,4,5,2,3,7,8,6]=>1000100
[4,1,2,5,7,3,8,6]=>0000000
[1,4,2,5,7,3,8,6]=>1000000
[1,4,5,2,7,3,8,6]=>1000000
[1,4,2,5,7,8,3,6]=>1000000
[1,4,5,2,7,8,3,6]=>1000000
[1,4,5,7,8,2,3,6]=>1000000
[4,1,5,2,8,3,6,7]=>0000000
[4,5,1,2,8,3,6,7]=>0000000
[4,5,1,8,2,3,6,7]=>0000000
[4,5,8,1,2,3,6,7]=>0000000
[4,1,5,2,3,8,6,7]=>0000100
[4,5,1,2,3,8,6,7]=>0000100
[4,1,2,5,3,8,6,7]=>0000100
[1,4,2,5,3,8,6,7]=>1000100
[1,4,5,2,3,8,6,7]=>1000100
[4,1,2,5,8,3,6,7]=>0000000
[1,4,2,5,8,3,6,7]=>1000000
[1,4,2,5,3,6,8,7]=>1000110
[4,1,2,5,6,3,8,7]=>0000010
[1,4,5,2,6,3,8,7]=>1000010
[4,1,2,5,6,8,3,7]=>0000000
[1,4,5,2,6,8,3,7]=>1000000
[1,4,5,6,8,2,3,7]=>1000000
[1,4,2,5,3,6,7,8]=>1000111
[1,4,5,2,3,6,7,8]=>1000111
[4,1,2,5,6,3,7,8]=>0000011
[1,4,5,2,6,3,7,8]=>1000011
[4,1,2,5,6,7,3,8]=>0000001
[1,4,2,5,6,7,3,8]=>1000001
[1,4,5,6,7,2,3,8]=>1000001
[1,4,5,2,6,7,8,3]=>1000000
[1,4,5,6,7,2,8,3]=>1000000
[4,1,6,2,7,3,8,5]=>0000000
[4,6,7,1,2,3,8,5]=>0000000
[4,6,7,1,8,2,3,5]=>0000000
[4,6,7,8,1,2,3,5]=>0000000
[4,1,6,2,7,3,5,8]=>0000001
[4,6,1,2,7,3,5,8]=>0000001
[4,1,6,7,2,3,5,8]=>0000001
[4,6,1,7,2,3,5,8]=>0000001
[4,6,1,2,3,7,5,8]=>0000001
[4,1,2,6,3,7,5,8]=>0000001
[1,4,2,6,3,7,5,8]=>1000001
[4,1,2,6,7,3,5,8]=>0000001
[1,4,2,6,7,3,5,8]=>1000001
[1,4,6,2,7,3,5,8]=>1000001
[4,1,6,2,3,7,8,5]=>0000000
[4,1,2,6,3,7,8,5]=>0000000
[1,4,6,2,3,7,8,5]=>1000000
[1,4,6,2,7,3,8,5]=>1000000
[1,4,2,6,7,8,3,5]=>1000000
[1,4,6,2,7,8,3,5]=>1000000
[1,4,6,7,2,8,3,5]=>1000000
[4,1,6,2,8,3,5,7]=>0000000
[4,6,1,2,8,3,5,7]=>0000000
[4,1,6,8,2,3,5,7]=>0000000
[4,6,1,8,2,3,5,7]=>0000000
[4,6,1,2,3,8,5,7]=>0000000
[4,1,2,6,3,8,5,7]=>0000000
[1,4,2,6,3,8,5,7]=>1000000
[1,4,6,2,3,8,5,7]=>1000000
[1,4,2,6,8,3,5,7]=>1000000
[1,4,6,8,2,3,5,7]=>1000000
[1,4,2,6,3,5,8,7]=>1000010
[1,4,2,3,6,5,8,7]=>1001010
[1,2,4,3,6,8,5,7]=>1101000
[1,2,4,6,3,8,5,7]=>1100000
[1,2,4,6,8,3,5,7]=>1100000
[1,4,2,6,3,5,7,8]=>1000011
[1,4,2,3,6,5,7,8]=>1001011
[1,2,4,6,3,5,7,8]=>1100011
[4,1,2,3,6,7,8,5]=>0001000
[1,4,2,3,6,7,8,5]=>1001000
[4,1,7,2,8,3,5,6]=>0000000
[4,7,1,8,2,3,5,6]=>0000000
[4,1,7,2,3,8,5,6]=>0000000
[1,4,2,7,3,8,5,6]=>1000000
[1,4,7,2,3,8,5,6]=>1000000
[4,1,2,7,8,3,5,6]=>0000000
[1,4,2,7,8,3,5,6]=>1000000
[4,1,7,2,3,5,8,6]=>0000000
[4,1,2,7,3,5,8,6]=>0000000
[1,4,2,7,3,5,8,6]=>1000000
[1,4,7,2,3,5,8,6]=>1000000
[4,1,2,3,7,5,8,6]=>0001000
[1,2,4,3,7,5,8,6]=>1101000
[1,4,2,3,7,8,5,6]=>1001000
[1,2,4,3,7,8,5,6]=>1101000
[1,2,4,7,3,8,5,6]=>1100000
[1,4,2,7,3,5,6,8]=>1000001
[1,4,2,3,7,5,6,8]=>1001001
[1,4,2,3,5,7,6,8]=>1001101
[4,1,2,3,5,7,8,6]=>0001100
[1,4,2,3,5,7,8,6]=>1001100
[1,2,4,5,7,3,8,6]=>1100000
[4,8,1,2,3,5,6,7]=>0000000
[1,4,2,8,3,5,6,7]=>1000000
[1,4,8,2,3,5,6,7]=>1000000
[4,1,2,3,8,5,6,7]=>0001000
[1,4,2,3,8,5,6,7]=>1001000
[1,2,4,3,8,5,6,7]=>1101000
[1,2,4,8,3,5,6,7]=>1100000
[1,4,2,3,5,8,6,7]=>1001100
[1,2,4,3,5,8,6,7]=>1101100
[1,4,2,3,5,6,8,7]=>1001110
[1,4,2,3,5,6,7,8]=>1001111
[5,1,6,2,7,3,8,4]=>0000000
[5,6,7,1,2,3,8,4]=>0000000
[5,1,6,7,2,8,3,4]=>0000000
[5,6,7,1,2,8,3,4]=>0000000
[5,1,6,7,8,2,3,4]=>0000000
[5,6,1,7,8,2,3,4]=>0000000
[5,6,7,1,8,2,3,4]=>0000000
[1,5,2,6,3,7,4,8]=>1000001
[5,1,2,6,7,3,4,8]=>0000001
[1,5,2,6,7,3,4,8]=>1000001
[1,5,2,6,3,7,8,4]=>1000000
[1,5,6,2,3,7,8,4]=>1000000
[1,5,6,7,2,3,8,4]=>1000000
[1,5,6,7,8,2,3,4]=>1000000
[5,1,6,2,8,3,4,7]=>0000000
[5,6,8,1,2,3,4,7]=>0000000
[5,1,6,2,3,8,4,7]=>0000000
[5,6,1,2,3,8,4,7]=>0000000
[5,1,2,6,3,8,4,7]=>0000000
[1,5,2,6,3,8,4,7]=>1000000
[1,5,6,2,3,8,4,7]=>1000000
[5,1,2,6,8,3,4,7]=>0000000
[1,5,2,6,8,3,4,7]=>1000000
[1,5,6,2,8,3,4,7]=>1000000
[1,5,2,6,3,4,8,7]=>1000010
[1,5,6,2,3,4,8,7]=>1000010
[1,5,2,3,6,4,8,7]=>1000010
[1,2,5,3,6,4,8,7]=>1100010
[1,2,5,6,3,4,8,7]=>1100010
[5,1,2,3,6,8,4,7]=>0000000
[1,5,2,3,6,8,4,7]=>1000000
[1,2,5,6,3,8,4,7]=>1100000
[1,2,5,6,8,3,4,7]=>1100000
[5,1,2,6,3,4,7,8]=>0000011
[1,5,2,6,3,4,7,8]=>1000011
[1,2,5,6,3,4,7,8]=>1100011
[1,2,5,6,3,7,4,8]=>1100001
[5,1,2,3,6,7,8,4]=>0000000
[1,5,2,3,6,7,8,4]=>1000000
[1,2,5,3,6,7,8,4]=>1100000
[1,2,5,6,3,7,8,4]=>1100000
[5,1,7,2,8,3,4,6]=>0000000
[5,7,1,2,8,3,4,6]=>0000000
[5,7,8,1,2,3,4,6]=>0000000
[5,1,2,7,3,8,4,6]=>0000000
[1,5,2,7,3,8,4,6]=>1000000
[1,5,7,2,3,8,4,6]=>1000000
[5,1,2,7,8,3,4,6]=>0000000
[1,5,2,7,8,3,4,6]=>1000000
[1,5,7,2,8,3,4,6]=>1000000
[5,1,2,7,3,4,8,6]=>0000000
[1,5,2,7,3,4,8,6]=>1000000
[1,5,7,2,3,4,8,6]=>1000000
[5,1,2,3,7,4,8,6]=>0000000
[1,5,2,3,7,4,8,6]=>1000000
[1,2,5,3,7,4,8,6]=>1100000
[1,2,5,7,3,4,8,6]=>1100000
[5,1,2,3,7,8,4,6]=>0000000
[1,5,2,3,7,8,4,6]=>1000000
[1,2,5,3,7,8,4,6]=>1100000
[1,2,5,7,3,8,4,6]=>1100000
[1,2,5,7,8,3,4,6]=>1100000
[5,7,1,2,3,4,6,8]=>0000001
[1,5,2,7,3,4,6,8]=>1000001
[1,2,5,7,3,4,6,8]=>1100001
[1,5,2,3,4,7,6,8]=>1000101
[1,2,3,5,7,4,6,8]=>1110001
[1,5,2,3,4,7,8,6]=>1000100
[1,2,3,5,7,4,8,6]=>1110000
[1,2,3,5,7,8,4,6]=>1110000
[5,1,2,8,3,4,6,7]=>0000000
[1,5,2,8,3,4,6,7]=>1000000
[1,5,2,3,8,4,6,7]=>1000000
[1,2,5,3,8,4,6,7]=>1100000
[1,2,5,8,3,4,6,7]=>1100000
[1,5,2,3,4,8,6,7]=>1000100
[1,2,5,3,4,8,6,7]=>1100100
[1,2,3,5,4,8,6,7]=>1110100
[1,2,3,5,8,4,6,7]=>1110000
[1,5,2,3,4,6,8,7]=>1000110
[1,2,3,5,6,8,4,7]=>1110000
[1,5,2,3,4,6,7,8]=>1000111
[6,1,7,2,8,3,4,5]=>0000000
[6,1,7,8,2,3,4,5]=>0000000
[6,7,1,8,2,3,4,5]=>0000000
[6,7,1,2,3,8,4,5]=>0000000
[1,6,2,7,3,8,4,5]=>1000000
[1,6,7,2,3,8,4,5]=>1000000
[1,6,7,2,8,3,4,5]=>1000000
[1,6,7,8,2,3,4,5]=>1000000
[6,1,2,7,3,4,8,5]=>0000000
[1,6,2,7,3,4,8,5]=>1000000
[1,6,7,2,3,4,8,5]=>1000000
[1,6,2,3,7,4,8,5]=>1000000
[1,2,6,3,7,4,8,5]=>1100000
[1,2,6,7,3,4,8,5]=>1100000
[1,2,6,7,3,8,4,5]=>1100000
[1,2,6,7,8,3,4,5]=>1100000
[6,1,7,2,3,4,5,8]=>0000001
[1,6,2,7,3,4,5,8]=>1000001
[1,6,7,2,3,4,5,8]=>1000001
[1,6,2,3,4,7,5,8]=>1000001
[1,2,6,3,4,7,5,8]=>1100001
[1,2,3,6,4,7,5,8]=>1110001
[1,2,6,3,4,7,8,5]=>1100000
[1,2,3,6,4,7,8,5]=>1110000
[1,2,3,6,7,4,8,5]=>1110000
[1,2,3,6,7,8,4,5]=>1110000
[6,1,8,2,3,4,5,7]=>0000000
[6,1,2,8,3,4,5,7]=>0000000
[1,6,2,8,3,4,5,7]=>1000000
[1,6,8,2,3,4,5,7]=>1000000
[1,6,2,3,8,4,5,7]=>1000000
[1,2,6,3,8,4,5,7]=>1100000
[1,6,2,3,4,8,5,7]=>1000000
[1,2,6,3,4,8,5,7]=>1100000
[1,2,3,6,4,8,5,7]=>1110000
[1,6,2,3,4,5,8,7]=>1000010
[1,2,6,3,4,5,8,7]=>1100010
[1,2,3,6,4,5,8,7]=>1110010
[1,2,3,4,6,8,5,7]=>1111000
[1,6,2,3,4,5,7,8]=>1000011
[1,2,6,3,4,5,7,8]=>1100011
[1,2,3,6,4,5,7,8]=>1110011
[7,1,2,8,3,4,5,6]=>0000000
[1,7,2,8,3,4,5,6]=>1000000
[1,7,8,2,3,4,5,6]=>1000000
[1,2,7,8,3,4,5,6]=>1100000
[1,2,7,3,4,8,5,6]=>1100000
[1,2,3,7,4,8,5,6]=>1110000
[1,2,3,7,8,4,5,6]=>1110000
[1,2,7,3,4,5,8,6]=>1100000
[1,2,3,7,4,5,8,6]=>1110000
[1,2,3,4,7,5,8,6]=>1111000
[1,2,3,4,7,8,5,6]=>1111000
[1,2,7,3,4,5,6,8]=>1100001
[1,2,3,7,4,5,6,8]=>1110001
[1,2,3,4,7,5,6,8]=>1111001
[1,8,2,3,4,5,6,7]=>1000000
[1,2,8,3,4,5,6,7]=>1100000
[1,2,3,8,4,5,6,7]=>1110000
[1,2,3,4,8,5,6,7]=>1111000
[1,2,3,4,5,8,6,7]=>1111100
[5,3,2,6,1,4,8,7]=>0000010
[7,3,2,5,4,8,1,6]=>0000000
[8,4,5,2,3,7,6,1]=>0000000
[7,4,5,2,3,8,1,6]=>0000000
[6,4,5,2,3,1,8,7]=>0000010
[5,4,6,2,1,3,8,7]=>0000010
[3,6,1,5,4,2,8,7]=>0000010
[4,6,5,1,3,2,8,7]=>0000010
[5,6,4,3,1,2,8,7]=>0000010
[7,5,4,3,2,8,1,6]=>0000000
[8,6,4,3,7,2,5,1]=>0000000
[7,6,4,3,8,2,1,5]=>0000000
[6,7,4,3,8,1,2,5]=>0000000
[5,7,4,3,1,8,2,6]=>0000000
[4,7,5,1,3,8,2,6]=>0000000
[3,7,1,5,4,8,2,6]=>0000000
[2,1,7,5,4,8,3,6]=>0100000
[3,8,1,5,4,7,6,2]=>0000000
[4,8,5,1,3,7,6,2]=>0000000
[5,8,4,3,1,7,6,2]=>0000000
[6,8,4,3,7,1,5,2]=>0000000
[7,8,4,3,6,5,1,2]=>0000000
[6,8,5,7,3,1,4,2]=>0000000
[5,8,6,7,1,3,4,2]=>0000000
[4,8,6,1,7,3,5,2]=>0000000
[3,8,1,6,7,4,5,2]=>0000000
[2,1,8,6,7,4,5,3]=>0100000
[2,1,7,6,8,4,3,5]=>0100000
[3,7,1,6,8,4,2,5]=>0000000
[4,7,6,1,8,3,2,5]=>0000000
[5,7,6,8,1,3,2,4]=>0000000
[5,4,7,2,1,8,3,6]=>0000000
[6,4,7,2,8,1,3,5]=>0000000
[7,4,6,2,8,3,1,5]=>0000000
[8,4,6,2,7,3,5,1]=>0000000
[8,3,2,6,7,4,5,1]=>0000000
[7,3,2,6,8,4,1,5]=>0000000
[6,3,2,7,8,1,4,5]=>0000000
[5,3,2,7,1,8,4,6]=>0000000
[4,3,2,1,7,8,5,6]=>0001000
[3,4,1,2,8,7,6,5]=>0001000
[5,3,2,8,1,7,6,4]=>0000000
[6,3,2,8,7,1,5,4]=>0000000
[7,3,2,8,6,5,1,4]=>0000000
[8,4,7,2,6,5,3,1]=>0000000
[7,4,8,2,6,5,1,3]=>0000000
[6,4,8,2,7,1,5,3]=>0000000
[5,4,8,2,1,7,6,3]=>0000000
[4,5,8,1,2,7,6,3]=>0000000
[3,5,1,8,2,7,6,4]=>0000000
[2,1,5,8,3,7,6,4]=>0100000
[2,1,6,8,7,3,5,4]=>0100000
[3,6,1,8,7,2,5,4]=>0000000
[4,6,8,1,7,2,5,3]=>0000000
[5,6,8,7,1,2,4,3]=>0000000
[6,5,8,7,2,1,4,3]=>0000000
[7,5,8,6,2,4,1,3]=>0000000
[8,5,7,6,2,4,3,1]=>0000000
[5,7,8,6,1,4,2,3]=>0000000
[4,7,8,1,6,5,2,3]=>0000000
[3,7,1,8,6,5,2,4]=>0000000
[2,1,7,8,6,5,3,4]=>0100000
[3,8,1,7,6,5,4,2]=>0000000
[4,8,7,1,6,5,3,2]=>0000000
[5,8,7,6,1,4,3,2]=>0000000
[6,8,7,5,4,1,3,2]=>0000000
[3,2,5,1,4,6,7,8]=>0000111
[5,2,4,1,3,6,7,8]=>0000111
[3,2,6,1,4,5,7,8]=>0000011
[5,4,7,1,2,3,6,8]=>0000001
[6,2,7,1,3,4,5,8]=>0000001
[6,3,7,1,2,4,5,8]=>0000001
[6,4,7,1,2,3,5,8]=>0000001
[7,4,6,1,2,3,5,8]=>0000001
[3,2,8,1,4,5,6,7]=>0000000
[5,4,8,1,2,3,6,7]=>0000000
[6,5,8,1,2,3,4,7]=>0000000
[7,5,8,1,2,3,4,6]=>0000000
[8,5,7,1,2,3,4,6]=>0000000
[3,2,5,7,1,4,6,8]=>0000001
[4,2,6,7,1,3,5,8]=>0000001
[5,2,6,7,1,3,4,8]=>0000001
[5,3,6,7,1,2,4,8]=>0000001
[3,2,5,8,1,4,6,7]=>0000000
[4,2,5,8,1,3,6,7]=>0000000
[4,3,5,8,1,2,6,7]=>0000000
[5,2,4,8,1,3,6,7]=>0000000
[3,2,6,8,1,4,5,7]=>0000000
[5,2,6,8,1,3,4,7]=>0000000
[6,2,4,8,1,3,5,7]=>0000000
[6,2,5,8,1,3,4,7]=>0000000
[3,2,7,8,1,4,5,6]=>0000000
[4,3,7,8,1,2,5,6]=>0000000
[5,4,7,8,1,2,3,6]=>0000000
[6,2,7,8,1,3,4,5]=>0000000
[6,3,7,8,1,2,4,5]=>0000000
[6,4,7,8,1,2,3,5]=>0000000
[7,2,4,8,1,3,5,6]=>0000000
[7,4,5,8,1,2,3,6]=>0000000
[8,2,6,7,1,3,4,5]=>0000000
[8,4,6,7,1,2,3,5]=>0000000
[4,6,2,5,1,3,7,8]=>0000011
[4,6,3,5,1,2,7,8]=>0000011
[5,6,2,4,1,3,7,8]=>0000011
[4,7,3,5,1,2,6,8]=>0000001
[5,7,2,4,1,3,6,8]=>0000001
[3,7,2,6,1,4,5,8]=>0000001
[5,7,2,6,1,3,4,8]=>0000001
[6,7,2,5,1,3,4,8]=>0000001
[4,8,2,5,1,3,6,7]=>0000000
[5,8,3,4,1,2,6,7]=>0000000
[5,8,3,6,1,2,4,7]=>0000000
[6,8,3,5,1,2,4,7]=>0000000
[3,8,2,7,1,4,5,6]=>0000000
[4,8,2,7,1,3,5,6]=>0000000
[4,8,3,7,1,2,5,6]=>0000000
[5,8,2,7,1,3,4,6]=>0000000
[6,8,2,7,1,3,4,5]=>0000000
[6,8,3,7,1,2,4,5]=>0000000
[6,8,5,7,1,2,3,4]=>0000000
[7,8,2,4,1,3,5,6]=>0000000
[7,8,2,5,1,3,4,6]=>0000000
[7,8,4,6,1,2,3,5]=>0000000
[4,3,2,6,1,5,7,8]=>0000011
[5,3,2,6,1,4,7,8]=>0000011
[5,4,2,6,1,3,7,8]=>0000011
[4,3,2,7,1,5,6,8]=>0000001
[5,3,2,7,1,4,6,8]=>0000001
[5,4,3,7,1,2,6,8]=>0000001
[6,3,2,7,1,4,5,8]=>0000001
[6,4,2,7,1,3,5,8]=>0000001
[6,4,3,7,1,2,5,8]=>0000001
[6,5,3,7,1,2,4,8]=>0000001
[7,4,2,5,1,3,6,8]=>0000001
[7,4,3,6,1,2,5,8]=>0000001
[7,5,2,6,1,3,4,8]=>0000001
[7,5,3,6,1,2,4,8]=>0000001
[7,6,3,5,1,2,4,8]=>0000001
[4,3,2,8,1,5,6,7]=>0000000
[5,3,2,8,1,4,6,7]=>0000000
[5,4,3,8,1,2,6,7]=>0000000
[6,3,2,8,1,4,5,7]=>0000000
[6,4,3,8,1,2,5,7]=>0000000
[6,5,2,8,1,3,4,7]=>0000000
[6,5,3,8,1,2,4,7]=>0000000
[7,4,2,8,1,3,5,6]=>0000000
[7,5,3,8,1,2,4,6]=>0000000
[7,6,2,8,1,3,4,5]=>0000000
[8,4,2,5,1,3,6,7]=>0000000
[8,4,2,6,1,3,5,7]=>0000000
[8,5,3,6,1,2,4,7]=>0000000
[8,6,2,5,1,3,4,7]=>0000000
[8,4,2,7,1,3,5,6]=>0000000
[8,4,3,7,1,2,5,6]=>0000000
[8,5,2,7,1,3,4,6]=>0000000
[8,5,3,7,1,2,4,6]=>0000000
[8,7,2,4,1,3,5,6]=>0000000
[8,7,2,5,1,3,4,6]=>0000000
[8,7,3,5,1,2,4,6]=>0000000
[8,7,2,6,1,3,4,5]=>0000000
[8,7,3,6,1,2,4,5]=>0000000
[8,7,4,6,1,2,3,5]=>0000000
[5,6,2,4,8,1,3,7]=>0000000
[4,7,3,5,8,1,2,6]=>0000000
[4,7,3,6,8,1,2,5]=>0000000
[4,8,3,5,7,1,2,6]=>0000000
[7,8,2,4,6,1,3,5]=>0000000
[7,8,3,4,6,1,2,5]=>0000000
[7,8,2,5,6,1,3,4]=>0000000
[7,8,3,5,6,1,2,4]=>0000000
[4,3,2,6,8,1,5,7]=>0000000
[5,4,2,6,8,1,3,7]=>0000000
[5,4,3,6,8,1,2,7]=>0000000
[6,3,2,5,8,1,4,7]=>0000000
[6,5,2,4,8,1,3,7]=>0000000
[4,3,2,7,8,1,5,6]=>0000000
[5,3,2,7,8,1,4,6]=>0000000
[5,4,2,7,8,1,3,6]=>0000000
[5,4,3,7,8,1,2,6]=>0000000
[6,4,2,7,8,1,3,5]=>0000000
[6,4,3,7,8,1,2,5]=>0000000
[6,5,2,7,8,1,3,4]=>0000000
[8,4,2,5,7,1,3,6]=>0000000
[8,5,2,6,7,1,3,4]=>0000000
[8,5,3,6,7,1,2,4]=>0000000
[8,6,2,5,7,1,3,4]=>0000000
[8,6,3,5,7,1,2,4]=>0000000
[8,7,2,4,6,1,3,5]=>0000000
[8,7,3,4,6,1,2,5]=>0000000
[8,7,2,5,6,1,3,4]=>0000000
[4,3,7,2,6,1,5,8]=>0000001
[5,3,7,2,6,1,4,8]=>0000001
[5,4,7,2,6,1,3,8]=>0000001
[6,3,7,2,5,1,4,8]=>0000001
[6,4,7,2,5,1,3,8]=>0000001
[7,3,6,2,5,1,4,8]=>0000001
[4,3,8,2,6,1,5,7]=>0000000
[5,3,8,2,6,1,4,7]=>0000000
[5,4,8,2,6,1,3,7]=>0000000
[6,4,8,2,5,1,3,7]=>0000000
[6,4,8,3,5,1,2,7]=>0000000
[4,3,8,2,7,1,5,6]=>0000000
[5,4,8,2,7,1,3,6]=>0000000
[6,4,8,2,7,1,3,5]=>0000000
[7,3,8,2,5,1,4,6]=>0000000
[7,4,8,3,5,1,2,6]=>0000000
[7,5,8,2,4,1,3,6]=>0000000
[7,5,8,2,6,1,3,4]=>0000000
[7,5,8,4,6,1,2,3]=>0000000
[8,3,6,2,5,1,4,7]=>0000000
[8,4,6,2,5,1,3,7]=>0000000
[8,3,7,2,5,1,4,6]=>0000000
[8,4,7,3,5,1,2,6]=>0000000
[8,3,7,2,6,1,4,5]=>0000000
[8,4,7,2,6,1,3,5]=>0000000
[8,4,7,3,6,1,2,5]=>0000000
[8,5,7,2,6,1,3,4]=>0000000
[8,6,7,2,4,1,3,5]=>0000000
[8,6,7,2,5,1,3,4]=>0000000
[5,4,3,2,7,1,6,8]=>0000001
[6,5,3,2,7,1,4,8]=>0000001
[7,5,3,2,6,1,4,8]=>0000001
[5,4,3,2,8,1,6,7]=>0000000
[6,5,3,2,8,1,4,7]=>0000000
[7,5,3,2,8,1,4,6]=>0000000
[7,6,4,3,8,1,2,5]=>0000000
[8,5,3,2,6,1,4,7]=>0000000
[8,5,4,2,6,1,3,7]=>0000000
[8,5,3,2,7,1,4,6]=>0000000
[8,6,3,2,7,1,4,5]=>0000000
[8,7,5,2,6,1,3,4]=>0000000
[8,7,6,2,4,1,3,5]=>0000000
[4,8,3,7,2,6,1,5]=>0000000
[5,8,3,7,2,6,1,4]=>0000000
[5,8,4,7,2,6,1,3]=>0000000
[5,8,4,7,3,6,1,2]=>0000000
[6,8,3,7,2,5,1,4]=>0000000
[6,8,4,7,2,5,1,3]=>0000000
[6,8,4,7,3,5,1,2]=>0000000
[6,8,5,7,2,4,1,3]=>0000000
[6,8,5,7,3,4,1,2]=>0000000
[7,8,3,6,2,5,1,4]=>0000000
[7,8,4,6,2,5,1,3]=>0000000
[7,8,4,6,3,5,1,2]=>0000000
[7,8,5,6,2,4,1,3]=>0000000
[6,4,3,8,2,7,1,5]=>0000000
[7,5,3,8,2,6,1,4]=>0000000
[7,5,4,8,2,6,1,3]=>0000000
[7,6,3,8,2,5,1,4]=>0000000
[7,6,4,8,2,5,1,3]=>0000000
[7,6,5,8,2,4,1,3]=>0000000
[8,5,3,7,2,6,1,4]=>0000000
[8,6,4,7,2,5,1,3]=>0000000
[8,6,4,7,3,5,1,2]=>0000000
[8,6,5,7,2,4,1,3]=>0000000
[6,5,4,3,2,8,1,7]=>0000000
[8,7,6,3,2,5,1,4]=>0000000
[8,7,6,5,2,4,1,3]=>0000000
[6,1,2,5,3,8,4,7]=>0000000
[4,1,2,8,7,3,5,6]=>0000000
[4,1,2,7,6,3,8,5]=>0000000
[8,1,2,5,6,3,4,7]=>0000000
[8,1,2,7,6,3,4,5]=>0000000
[7,1,2,5,6,3,8,4]=>0000000
[8,1,2,5,6,7,3,4]=>0000000
[3,1,7,2,6,4,8,5]=>0000000
[3,1,8,2,6,7,4,5]=>0000000
[6,1,4,2,3,8,5,7]=>0000000
[7,1,5,2,3,4,8,6]=>0000000
[6,1,5,2,3,8,4,7]=>0000000
[6,1,5,2,3,7,8,4]=>0000000
[5,1,4,2,8,3,6,7]=>0000000
[5,1,4,2,7,3,8,6]=>0000000
[7,1,4,2,6,3,8,5]=>0000000
[8,1,5,2,7,3,4,6]=>0000000
[5,1,4,2,8,7,3,6]=>0000000
[8,1,4,2,6,7,3,5]=>0000000
[8,1,5,2,6,7,3,4]=>0000000
[5,1,4,2,6,7,8,3]=>0000000
[3,1,8,6,2,4,5,7]=>0000000
[3,1,8,5,2,7,4,6]=>0000000
[3,1,8,6,2,7,4,5]=>0000000
[8,1,4,5,2,3,6,7]=>0000000
[7,1,8,6,2,3,4,5]=>0000000
[7,1,6,5,2,3,8,4]=>0000000
[3,1,4,8,6,2,5,7]=>0000000
[3,1,7,5,6,2,8,4]=>0000000
[8,1,4,7,6,2,3,5]=>0000000
[3,1,8,5,6,7,2,4]=>0000000
[8,1,4,5,6,7,2,3]=>0000000
[2,8,1,3,6,7,4,5]=>0000000
[2,4,1,8,3,7,5,6]=>0000000
[2,6,1,5,3,8,4,7]=>0000000
[2,6,1,5,3,7,8,4]=>0000000
[2,8,1,7,6,3,4,5]=>0000000
[5,3,1,2,8,4,6,7]=>0000000
[5,3,1,2,8,7,4,6]=>0000000
[5,4,1,2,8,3,6,7]=>0000000
[7,4,1,2,6,3,8,5]=>0000000
[5,8,1,2,7,3,4,6]=>0000000
[8,7,1,2,6,3,4,5]=>0000000
[5,7,1,2,6,3,8,4]=>0000000
[8,4,1,2,6,7,3,5]=>0000000
[5,8,1,2,6,7,3,4]=>0000000
[5,4,1,2,6,7,8,3]=>0000000
[4,3,1,6,2,8,5,7]=>0000000
[4,3,1,6,2,7,8,5]=>0000000
[8,3,1,5,2,4,6,7]=>0000000
[8,3,1,6,2,4,5,7]=>0000000
[7,3,1,6,2,4,8,5]=>0000000
[8,3,1,6,2,7,4,5]=>0000000
[6,3,1,5,2,7,8,4]=>0000000
[7,4,1,5,2,3,8,6]=>0000000
[8,4,1,6,2,3,5,7]=>0000000
[7,4,1,8,2,3,5,6]=>0000000
[7,4,1,6,2,3,8,5]=>0000000
[8,7,1,6,2,3,4,5]=>0000000
[6,7,1,5,2,3,8,4]=>0000000
[6,8,1,5,2,7,3,4]=>0000000
[6,4,1,5,2,7,8,3]=>0000000
[4,3,1,8,7,2,5,6]=>0000000
[8,3,1,5,6,2,4,7]=>0000000
[8,3,1,5,7,2,4,6]=>0000000
[7,3,1,5,6,2,8,4]=>0000000
[7,8,1,5,6,2,3,4]=>0000000
[8,4,1,5,6,7,2,3]=>0000000
[2,3,7,1,6,4,8,5]=>0000000
[2,3,5,1,8,7,4,6]=>0000000
[2,8,4,1,3,5,6,7]=>0000000
[2,6,4,1,3,7,8,5]=>0000000
[2,6,5,1,3,7,8,4]=>0000000
[2,7,4,1,6,3,8,5]=>0000000
[2,8,5,1,7,3,4,6]=>0000000
[2,7,5,1,6,3,8,4]=>0000000
[6,3,4,1,2,7,8,5]=>0000000
[7,3,5,1,2,4,8,6]=>0000000
[6,3,7,1,2,4,8,5]=>0000000
[6,3,8,1,2,7,4,5]=>0000000
[6,7,4,1,2,3,8,5]=>0000000
[6,8,5,1,2,3,4,7]=>0000000
[8,5,4,1,2,7,3,6]=>0000000
[6,8,4,1,2,7,3,5]=>0000000
[6,8,5,1,2,7,3,4]=>0000000
[8,3,4,1,7,2,5,6]=>0000000
[8,3,5,1,6,2,4,7]=>0000000
[7,3,8,1,6,2,4,5]=>0000000
[8,5,4,1,6,2,3,7]=>0000000
[7,8,4,1,6,2,3,5]=>0000000
[7,8,5,1,6,2,3,4]=>0000000
[5,3,4,1,6,7,8,2]=>0000000
[2,3,7,6,1,4,8,5]=>0000000
[2,3,6,5,1,8,4,7]=>0000000
[2,3,6,5,1,7,8,4]=>0000000
[2,7,4,8,1,3,5,6]=>0000000
[2,7,4,6,1,3,8,5]=>0000000
[2,7,6,5,1,3,8,4]=>0000000
[2,6,4,5,1,8,3,7]=>0000000
[2,8,4,6,1,7,3,5]=>0000000
[7,3,8,5,1,2,4,6]=>0000000
[8,6,4,5,1,7,2,3]=>0000000
[2,3,8,5,7,1,4,6]=>0000000
[2,3,7,5,6,1,8,4]=>0000000
[2,8,4,7,6,1,3,5]=>0000000
[2,8,7,5,6,1,3,4]=>0000000
[8,3,7,5,6,1,2,4]=>0000000
[2,8,4,5,6,7,1,3]=>0000000
[6,5,8,7,3,4,1,2]=>0000000
[4,6,7,3,8,5,1,2]=>0000000
[3,6,7,4,5,8,1,2]=>0000000
[2,6,7,4,5,1,8,3]=>0000000
[1,6,7,4,5,2,3,8]=>1000001
[1,5,4,7,6,2,3,8]=>1000001
[2,5,4,7,6,1,8,3]=>0000000
[3,5,4,7,6,8,1,2]=>0000000
[4,5,3,7,8,6,1,2]=>0000000
[5,4,3,8,7,6,1,2]=>0000000
[6,4,8,3,7,5,1,2]=>0000000
[6,3,8,4,5,7,1,2]=>0000000
[5,3,4,8,6,7,1,2]=>0000000
[4,3,5,6,8,7,1,2]=>0000000
[3,2,5,6,1,8,7,4]=>0000000
[4,2,5,6,8,1,7,3]=>0000000
[5,2,4,8,6,1,7,3]=>0000000
[6,2,8,4,5,1,7,3]=>0000000
[7,8,2,4,5,1,6,3]=>0000000
[7,8,1,4,5,2,3,6]=>0000000
[6,1,8,4,5,2,3,7]=>0000000
[5,1,4,8,6,2,3,7]=>0000000
[4,1,3,2,8,6,5,7]=>0001000
[5,1,3,8,2,6,4,7]=>0000000
[6,1,8,3,2,5,4,7]=>0000000
[7,8,1,3,2,5,4,6]=>0000000
[7,8,2,3,1,5,6,4]=>0000000
[6,2,8,3,1,5,7,4]=>0000000
[5,2,3,8,1,6,7,4]=>0000000
[6,3,8,2,1,7,5,4]=>0000000
[7,8,3,2,1,6,5,4]=>0000000
[7,8,4,2,6,1,5,3]=>0000000
[5,4,2,8,7,1,6,3]=>0000000
[4,5,2,7,8,1,6,3]=>0000000
[3,5,2,7,1,8,6,4]=>0000000
[2,5,3,7,1,6,8,4]=>0000000
[1,5,3,7,2,6,4,8]=>1000001
[1,6,7,3,2,5,4,8]=>1000001
[2,6,7,3,1,5,8,4]=>0000000
[3,6,7,2,1,8,5,4]=>0000000
[4,6,7,2,8,1,5,3]=>0000000
[5,6,7,8,2,1,4,3]=>0000000
[7,8,5,6,2,1,4,3]=>0000000
[6,5,8,7,1,2,3,4]=>0000000
[5,4,1,8,7,2,3,6]=>0000000
[6,4,8,1,7,2,3,5]=>0000000
[7,8,3,1,2,6,4,5]=>0000000
[5,3,1,8,2,7,4,6]=>0000000
[4,3,1,2,8,7,5,6]=>0001000
[4,2,1,3,8,5,7,6]=>0001000
[5,2,1,8,3,4,7,6]=>0000000
[6,2,8,1,3,4,7,5]=>0000000
[7,8,2,1,3,4,6,5]=>0000000
[4,5,2,3,7,6,1,8]=>0000001
[6,4,3,7,2,5,1,8]=>0000001
[8,4,3,6,5,1,2,7]=>0000000
[1,5,6,3,4,8,7,2]=>1000000
[4,6,2,7,3,5,1,8]=>0000001
[3,2,6,7,4,5,1,8]=>0000001
[4,1,2,6,5,8,7,3]=>0000000
[5,1,6,2,4,8,7,3]=>0000000
[8,1,5,4,7,6,2,3]=>0000000
[1,8,6,7,4,5,3,2]=>1000000
[8,1,6,7,4,5,2,3]=>0000000
[6,1,7,8,2,4,5,3]=>0000000
[5,1,7,2,8,4,6,3]=>0000000
[4,1,2,7,8,5,6,3]=>0000000
[3,2,1,7,8,5,6,4]=>0010000
[4,8,2,7,1,5,3,6]=>0000000
[5,8,7,2,1,4,3,6]=>0000000
[6,8,7,1,2,4,3,5]=>0000000
[8,7,6,1,4,3,2,5]=>0000000
[1,6,7,8,3,4,5,2]=>1000000
[7,6,8,1,3,2,4,5]=>0000000
[5,7,8,2,1,3,4,6]=>0000000
[4,7,2,8,1,3,5,6]=>0000000
[3,2,6,8,4,1,5,7]=>0000000
[4,6,2,8,3,1,5,7]=>0000000
[5,6,8,2,3,1,4,7]=>0000000
[7,5,8,3,1,2,4,6]=>0000000
[1,5,7,3,8,4,6,2]=>1000000
[1,4,3,7,8,5,6,2]=>1000000
[6,4,3,8,2,1,5,7]=>0000000
[4,5,2,3,8,1,6,7]=>0000000
[3,2,5,4,8,1,6,7]=>0000000
[4,5,2,3,1,8,7,6]=>0000100
[6,4,3,1,2,8,7,5]=>0000000
[7,4,3,1,8,2,6,5]=>0000000
[8,4,3,1,7,6,2,5]=>0000000
[1,5,8,3,7,6,4,2]=>1000000
[7,5,1,3,8,2,6,4]=>0000000
[5,6,1,2,3,8,7,4]=>0000000
[4,6,2,1,3,8,7,5]=>0000000
[3,2,6,1,4,8,7,5]=>0000000
[3,2,7,1,8,4,6,5]=>0000000
[5,7,1,2,8,3,6,4]=>0000000
[6,7,1,8,2,3,5,4]=>0000000
[7,6,1,8,3,2,5,4]=>0000000
[8,7,1,6,5,3,2,4]=>0000000
[7,8,1,6,5,2,3,4]=>0000000
[6,8,1,7,2,5,3,4]=>0000000
[5,8,1,2,7,6,3,4]=>0000000
[3,2,8,1,7,6,4,5]=>0000000
[4,1,2,8,7,6,5,3]=>0000000
[5,1,8,2,7,6,4,3]=>0000000
[6,1,8,7,2,5,4,3]=>0000000
[8,1,7,6,5,4,2,3]=>0000000
[3,2,5,4,7,1,8,6]=>0000000
[4,2,5,3,6,1,8,7]=>0000010
[4,3,5,2,7,1,8,6]=>0000000
[4,1,5,3,7,2,8,6]=>0000000
[2,1,5,4,7,3,8,6]=>0100000
[4,3,6,5,7,1,8,2]=>0000000
[4,1,6,3,7,5,8,2]=>0000000
[2,1,6,4,7,3,8,5]=>0100000
[3,1,6,4,7,2,8,5]=>0000000
[4,1,6,3,7,2,8,5]=>0000000
[5,2,6,3,7,1,8,4]=>0000000
[4,2,6,1,7,3,8,5]=>0000000
[4,2,6,3,7,1,8,5]=>0000000
[3,2,6,4,7,1,8,5]=>0000000
[3,2,6,1,7,4,8,5]=>0000000
[3,1,4,2,7,6,8,5]=>0001000
[3,2,6,1,7,5,8,4]=>0000000
[4,2,6,1,7,5,8,3]=>0000000
[4,1,6,2,7,5,8,3]=>0000000
[5,4,6,2,7,1,8,3]=>0000000
[3,1,6,5,7,2,8,4]=>0000000
[4,1,6,5,7,3,8,2]=>0000000
[8,6,1,3,4,2,5,7]=>0000000
[8,3,5,2,1,6,4,7]=>0000000
[8,6,3,5,2,4,1,7]=>0000000
[8,3,7,5,2,4,6,1]=>0000000
[2,4,5,7,3,1,8,6]=>0000000
[8,2,4,6,5,3,1,7]=>0000000
[8,1,2,4,5,6,3,7]=>0000000
[8,2,5,1,3,6,4,7]=>0000000
[8,1,5,6,4,3,2,7]=>0000000
[8,5,7,4,3,2,6,1]=>0000000
[8,5,7,4,2,1,6,3]=>0000000
[1,7,4,8,6,3,5,2]=>1000000
[8,4,7,6,3,5,2,1]=>0000000
[4,8,1,6,7,3,5,2]=>0000000
[3,6,4,1,8,7,5,2]=>0000000
[8,2,6,1,4,7,5,3]=>0000000
[3,7,6,5,8,2,1,4]=>0000000
[3,6,8,5,7,2,4,1]=>0000000
[2,1,6,5,7,8,3,4]=>0100000
[5,2,7,1,3,8,4,6]=>0000000
[5,3,1,7,8,2,4,6]=>0000000
[3,7,2,6,4,8,1,5]=>0000000
[3,2,6,1,4,7,8,5]=>0000000
[5,3,7,2,1,8,4,6]=>0000000
[4,7,3,2,1,5,8,6]=>0000000
[1,7,3,4,2,5,8,6]=>1000000
[4,7,2,1,3,5,8,6]=>0000000
[8,7,6,1,3,4,2,5]=>0000000
[8,5,7,3,2,1,6,4]=>0000000
[8,7,6,3,5,2,4,1]=>0000000
[2,7,4,8,1,6,5,3]=>0000000
[4,6,8,2,1,7,5,3]=>0000000
[8,5,3,7,1,6,2,4]=>0000000
[8,5,7,2,1,3,6,4]=>0000000
[4,6,1,8,7,2,5,3]=>0000000
[8,1,2,5,6,7,4,3]=>0000000
[8,2,6,5,7,4,1,3]=>0000000
[1,7,2,5,8,6,4,3]=>1000000
[3,7,8,1,6,5,2,4]=>0000000
[8,7,6,3,5,1,4,2]=>0000000
[8,4,7,6,5,1,3,2]=>0000000
[8,7,1,5,6,4,3,2]=>0000000
[8,1,6,7,5,4,3,2]=>0000000
[3,2,5,1,6,8,4,7]=>0000000
[3,6,2,5,4,8,1,7]=>0000000
[3,5,2,4,7,1,8,6]=>0000000
[3,5,8,2,4,7,6,1]=>0000000
[4,2,6,5,3,8,1,7]=>0000000
[5,3,1,6,8,2,4,7]=>0000000
[5,6,2,8,1,3,4,7]=>0000000
[5,4,3,2,7,1,8,6]=>0000000
[5,4,3,8,2,7,6,1]=>0000000
[4,3,6,2,8,7,5,1]=>0000000
[6,4,3,1,7,2,8,5]=>0000000
[1,4,7,5,8,3,2,6]=>1000000
[2,8,5,7,4,6,1,3]=>0000000
[3,5,8,7,1,4,6,2]=>0000000
[4,3,7,1,8,6,5,2]=>0000000
[4,8,3,7,6,5,2,1]=>0000000
[7,5,3,1,8,6,4,2]=>0000000
[1,5,8,6,3,7,4,2]=>1000000
[6,2,8,7,4,5,1,3]=>0000000
[6,1,7,5,3,2,8,4]=>0000000
[6,5,2,1,7,3,8,4]=>0000000
[6,1,7,4,2,8,3,5]=>0000000
[6,7,2,1,8,3,4,5]=>0000000
[7,5,8,2,1,3,4,6]=>0000000
[5,7,3,1,8,2,4,6]=>0000000
[4,7,1,5,2,8,3,6]=>0000000
[2,4,8,6,3,7,5,1]=>0000000
[3,5,2,7,1,8,4,6]=>0000000
[4,3,7,8,2,1,5,6]=>0000000
[8,3,7,1,4,6,2,5]=>0000000
[3,8,2,5,7,1,6,4]=>0000000
[7,8,3,6,2,1,5,4]=>0000000
[8,7,3,6,2,5,4,1]=>0000000
[4,2,6,8,1,7,5,3]=>0000000
[5,4,8,2,7,1,6,3]=>0000000
[5,8,3,7,1,6,2,4]=>0000000
[5,8,7,2,6,1,3,4]=>0000000
[8,6,2,7,5,1,3,4]=>0000000
[6,4,8,1,7,2,5,3]=>0000000
[5,1,6,8,2,7,4,3]=>0000000
[6,5,2,8,1,7,4,3]=>0000000
[5,2,7,1,8,6,4,3]=>0000000
[5,8,2,7,6,4,3,1]=>0000000
[6,1,7,2,8,5,4,3]=>0000000
[4,7,1,8,6,2,5,3]=>0000000
[8,7,4,6,1,5,3,2]=>0000000
[8,5,7,1,6,4,3,2]=>0000000
[6,8,1,7,5,4,3,2]=>0000000
[7,1,8,6,5,4,3,2]=>0000000
[4,3,5,6,1,2,8,7]=>0000010
[6,5,2,7,1,8,3,4]=>0000000
[3,5,2,6,4,1,8,7]=>0000010
[2,1,6,3,5,4,8,7]=>0100010
[5,3,1,4,6,2,8,7]=>0000010
[3,4,7,8,5,2,1,6]=>0000000
[2,4,6,3,7,5,8,1]=>0000000
[4,1,6,3,8,5,7,2]=>0000000
[3,7,4,2,8,6,5,1]=>0000000
[2,1,5,7,4,8,6,3]=>0100000
[3,1,8,2,7,6,5,4]=>0000000
[4,3,7,2,6,8,5,1]=>0000000
[8,1,2,3,5,6,7,4]=>0000000
[7,8,2,4,3,6,1,5]=>0000000
[2,1,7,8,5,4,3,6]=>0100000
[5,7,3,8,1,4,2,6]=>0000000
[8,3,6,1,4,2,7,5]=>0000000
[4,1,3,2,8,5,7,6]=>0001000
[2,1,4,3,8,5,7,6]=>0101000
[4,1,3,2,6,7,8,5]=>0001000
[5,3,6,1,8,7,2,4]=>0000000
[5,6,2,8,7,4,1,3]=>0000000
[7,8,5,6,1,4,2,3]=>0000000
[8,1,6,4,5,7,2,3]=>0000000
[2,1,8,6,5,7,3,4]=>0100000
[2,1,7,5,3,6,8,4]=>0100000
[4,1,2,5,8,6,7,3]=>0000000
[3,1,4,5,6,8,7,2]=>0000000
[6,3,1,5,2,4,8,7]=>0000010
[3,1,6,5,4,2,8,7]=>0000010
[5,1,7,3,8,4,6,2]=>0000000
[2,5,7,3,8,6,4,1]=>0000000
[5,6,3,7,4,8,1,2]=>0000000
[2,1,6,7,4,8,5,3]=>0100000
[2,8,6,3,1,5,7,4]=>0000000
[8,1,6,3,2,5,4,7]=>0000000
[2,8,4,1,6,3,7,5]=>0000000
[4,8,1,2,7,6,3,5]=>0000000
[6,5,3,2,8,7,1,4]=>0000000
[2,4,1,8,7,6,5,3]=>0000000
[4,1,2,8,7,5,6,3]=>0000000
[8,4,2,1,7,5,3,6]=>0000000
[4,3,1,8,6,7,5,2]=>0000000
[6,4,3,5,8,1,7,2]=>0000000
[5,7,3,6,1,8,2,4]=>0000000
[8,6,2,5,1,7,4,3]=>0000000
[7,5,2,8,3,4,6,1]=>0000000
[4,7,2,8,1,5,3,6]=>0000000
[8,7,2,1,4,5,6,3]=>0000000
[3,6,8,7,1,5,4,2]=>0000000
[5,7,8,6,3,4,1,2]=>0000000
[5,7,3,8,1,4,6,2]=>0000000
[2,1,7,8,5,4,6,3]=>0100000
[8,4,1,3,7,2,6,5]=>0000000
[4,3,8,2,5,1,7,6]=>0000000
[2,1,4,8,3,5,7,6]=>0100000
[7,8,5,6,1,4,3,2]=>0000000
[7,8,4,2,1,5,3,6]=>0000000
[7,8,2,1,6,5,3,4]=>0000000
[6,4,1,2,5,7,3,8]=>0000001
[4,3,8,1,7,2,5,6]=>0000000
[6,3,1,4,7,2,5,8]=>0000001
[7,8,1,4,6,2,5,3]=>0000000
[7,8,3,5,4,2,1,6]=>0000000
[7,8,4,1,2,3,6,5]=>0000000
[7,8,2,6,4,1,3,5]=>0000000
[7,8,1,6,5,4,3,2]=>0000000
[1,3,8,2,6,4,7,5]=>1000000
[5,3,7,1,6,4,8,2]=>0000000
[6,1,2,5,8,7,4,3]=>0000000
[6,3,1,8,4,2,7,5]=>0000000
[6,4,2,1,5,3,8,7]=>0000010
[6,4,3,7,5,8,1,2]=>0000000
[2,4,7,1,5,3,6,8]=>0000001
[3,7,2,8,6,4,1,5]=>0000000
[3,8,1,7,6,4,5,2]=>0000000
[2,7,5,8,3,6,1,4]=>0000000
[1,5,6,8,2,4,7,3]=>1000000
[2,6,1,4,7,3,5,8]=>0000001
[3,6,8,4,7,5,1,2]=>0000000
[5,6,7,3,8,4,1,2]=>0000000
[4,5,7,6,1,8,3,2]=>0000000
[4,7,5,6,3,1,8,2]=>0000000
[5,1,6,3,4,2,8,7]=>0000010
[5,7,1,4,2,3,8,6]=>0000000
[5,7,6,4,3,8,1,2]=>0000000
[6,3,4,5,8,7,1,2]=>0000000
[6,2,4,1,8,3,7,5]=>0000000
[6,2,3,5,4,8,1,7]=>0000000
[5,1,4,2,7,6,8,3]=>0000000
[1,6,2,4,7,8,3,5]=>1000000
[6,1,4,2,8,5,3,7]=>0000000
[6,7,5,8,1,4,3,2]=>0000000
[5,8,7,6,3,4,1,2]=>0000000
[5,8,7,6,2,3,1,4]=>0000000
[4,1,7,2,6,5,3,8]=>0000001
[4,2,7,8,1,6,3,5]=>0000000
[2,1,8,7,6,5,3,4]=>0100000
[4,2,7,1,6,3,8,5]=>0000000
[4,3,7,5,6,8,1,2]=>0000000
[3,8,6,5,2,4,1,7]=>0000000
[3,8,5,6,1,4,7,2]=>0000000
[5,3,7,8,2,1,6,4]=>0000000
[5,2,8,7,1,6,4,3]=>0000000
[3,6,7,8,5,1,4,2]=>0000000
[3,7,8,5,1,2,4,6]=>0000000
[4,1,8,6,2,3,5,7]=>0000000
[3,8,7,6,5,4,1,2]=>0000000
[2,8,6,7,5,1,3,4]=>0000000
[5,3,7,8,2,1,4,6]=>0000000
[7,6,1,2,5,8,3,4]=>0000000
[2,1,7,8,4,3,5,6]=>0100000
[7,8,1,2,5,4,6,3]=>0000000
[8,4,1,3,7,6,2,5]=>0000000
[4,7,2,8,1,3,6,5]=>0000000
[7,3,8,6,1,2,5,4]=>0000000
[3,4,7,1,8,2,6,5]=>0000000
[1,8,2,4,3,5,6,7]=>1000000
[1,7,2,4,3,5,6,8]=>1000001
[1,5,2,4,3,6,7,8]=>1000111
[1,7,2,5,3,4,6,8]=>1000001
[1,8,2,5,3,4,6,7]=>1000000
[1,8,2,6,3,4,5,7]=>1000000
[1,8,2,7,3,4,5,6]=>1000000
[1,8,2,7,3,5,4,6]=>1000000
[1,7,2,8,3,5,4,6]=>1000000
[1,6,2,8,3,5,4,7]=>1000000
[1,5,2,8,3,6,4,7]=>1000000
[1,4,2,8,3,6,5,7]=>1000000
[1,3,2,8,4,6,5,7]=>1010000
[1,2,3,8,4,6,5,7]=>1110000
[1,2,3,7,4,6,5,8]=>1110001
[1,3,2,7,4,6,5,8]=>1010001
[1,4,2,7,3,6,5,8]=>1000001
[1,5,2,7,3,6,4,8]=>1000001
[1,6,2,7,3,5,4,8]=>1000001
[1,7,2,6,3,5,4,8]=>1000001
[1,8,2,6,3,5,4,7]=>1000000
[1,8,2,5,3,6,4,7]=>1000000
[1,7,2,5,3,6,4,8]=>1000001
[1,6,2,5,3,7,4,8]=>1000001
[1,5,2,4,3,7,6,8]=>1000101
[1,6,2,4,3,7,5,8]=>1000001
[1,7,2,4,3,6,5,8]=>1000001
[1,8,2,4,3,6,5,7]=>1000000
[1,8,2,4,3,7,5,6]=>1000000
[1,7,2,4,3,8,5,6]=>1000000
[1,6,2,4,3,8,5,7]=>1000000
[1,5,2,4,3,8,6,7]=>1000100
[1,6,2,5,3,8,4,7]=>1000000
[1,7,2,5,3,8,4,6]=>1000000
[1,8,2,5,3,7,4,6]=>1000000
[1,8,2,6,3,7,4,5]=>1000000
[1,7,2,6,3,8,4,5]=>1000000
[1,2,3,8,4,7,5,6]=>1110000
[1,3,2,8,4,7,5,6]=>1010000
[1,4,2,8,3,7,5,6]=>1000000
[1,5,2,8,3,7,4,6]=>1000000
[1,6,2,8,3,7,4,5]=>1000000
[1,7,2,8,3,6,4,5]=>1000000
[1,8,2,7,3,6,4,5]=>1000000
[2,8,4,1,6,5,3,7]=>0000000
[7,2,8,5,1,6,4,3]=>0000000
[1,3,7,5,2,6,4,8]=>1000001
[1,3,7,5,4,2,6,8]=>1000001
[2,8,5,3,4,1,6,7]=>0000000
[6,2,3,8,5,1,7,4]=>0000000
[6,3,2,8,5,1,4,7]=>0000000
[7,4,8,5,2,1,3,6]=>0000000
[4,3,2,1,8,6,5,7]=>0001000
[4,2,1,3,8,7,6,5]=>0001000
[7,1,6,8,4,3,5,2]=>0000000
[5,6,8,2,3,1,7,4]=>0000000
[7,5,3,8,2,4,1,6]=>0000000
[5,2,1,8,7,6,3,4]=>0000000
[4,1,8,3,6,2,7,5]=>0000000
[2,3,4,8,6,1,7,5]=>0000000
[2,3,4,8,6,5,1,7]=>0000000
[1,5,4,6,2,7,3,8]=>1000001
[6,3,5,1,8,2,7,4]=>0000000
[5,7,1,6,3,8,4,2]=>0000000
[3,2,4,1,7,8,5,6]=>0001000
[2,5,4,6,1,7,8,3]=>0000000
[7,3,4,1,2,6,5,8]=>0000001
[7,4,3,2,1,6,5,8]=>0000001
[6,7,3,2,5,4,8,1]=>0000000
[1,8,5,4,3,2,7,6]=>1000000
[2,6,8,4,3,7,1,5]=>0000000
[2,7,8,4,3,6,5,1]=>0000000
[2,7,8,5,6,3,4,1]=>0000000
[5,3,7,1,6,8,4,2]=>0000000
[5,4,7,6,1,8,3,2]=>0000000
[4,5,7,6,8,1,3,2]=>0000000
[4,6,5,7,8,2,1,3]=>0000000
[5,2,1,6,7,8,3,4]=>0000000
[6,2,1,5,7,3,8,4]=>0000000
[5,6,4,7,2,8,1,3]=>0000000
[1,8,4,6,2,7,3,5]=>1000000
[1,8,3,2,6,7,4,5]=>1000000
[6,5,3,2,7,1,8,4]=>0000000
[6,4,3,2,1,7,8,5]=>0000000
[6,2,1,4,3,7,8,5]=>0000000
[4,5,3,2,8,1,7,6]=>0000000
[4,6,3,2,8,7,1,5]=>0000000
[4,7,3,2,8,6,5,1]=>0000000
[1,8,3,2,7,6,5,4]=>1000000
[1,8,4,7,2,6,5,3]=>1000000
[3,6,4,8,2,7,1,5]=>0000000
[3,4,5,8,1,2,7,6]=>0000000
[4,2,1,5,8,3,7,6]=>0000000
[3,6,5,8,7,2,1,4]=>0000000
[3,6,7,8,5,4,1,2]=>0000000
[3,5,7,8,6,1,4,2]=>0000000
[4,2,1,7,8,6,5,3]=>0000000
[2,3,8,1,7,6,5,4]=>0000000
[2,4,8,7,1,6,5,3]=>0000000
[8,1,6,7,3,2,5,4]=>0000000
[8,1,6,7,2,3,4,5]=>0000000
[8,1,4,3,2,7,6,5]=>0000000
[8,1,5,3,7,2,6,4]=>0000000
[8,1,3,5,6,2,7,4]=>0000000
[4,7,8,5,6,1,2,3]=>0000000
[3,7,8,5,6,2,1,4]=>0000000
[3,7,8,4,2,6,1,5]=>0000000
[3,7,8,2,4,5,1,6]=>0000000
[3,6,2,8,4,5,1,7]=>0000000
[2,3,6,7,4,5,8,1]=>0000000
[3,5,2,4,8,6,1,7]=>0000000
[3,5,4,2,8,7,1,6]=>0000000
[6,4,5,1,7,8,2,3]=>0000000
[5,4,2,3,1,8,6,7]=>0000100
[6,5,3,1,8,2,7,4]=>0000000
[6,5,4,1,8,7,2,3]=>0000000
[7,5,1,4,8,6,2,3]=>0000000
[7,4,1,3,2,8,6,5]=>0000000
[7,4,1,2,3,8,5,6]=>0000000
[6,4,2,1,3,8,5,7]=>0000000
[2,6,4,8,3,7,5,1]=>0000000
[2,6,5,8,7,3,4,1]=>0000000
[6,5,2,1,8,3,4,7]=>0000000
[7,5,1,2,8,3,4,6]=>0000000
[7,6,1,8,2,3,4,5]=>0000000
[7,6,1,8,4,5,2,3]=>0000000
[6,7,8,1,4,5,2,3]=>0000000
[6,7,8,1,3,2,5,4]=>0000000
[4,2,6,7,3,1,5,8]=>0000001
[4,7,8,2,3,1,5,6]=>0000000
[4,7,8,3,2,1,6,5]=>0000000
[5,7,8,3,1,2,6,4]=>0000000
[5,7,8,4,1,6,2,3]=>0000000
[4,6,3,8,2,1,7,5]=>0000000
[4,2,5,3,7,1,6,8]=>0000001
[3,5,6,7,8,2,1,4]=>0000000
[7,3,5,1,8,4,6,2]=>0000000
[4,5,7,3,1,8,6,2]=>0000000
[4,5,6,2,1,8,7,3]=>0000000
[1,6,5,2,7,4,3,8]=>1000001
[7,4,3,1,8,6,5,2]=>0000000
[7,5,6,1,8,3,4,2]=>0000000
[7,6,5,1,8,4,3,2]=>0000000
[6,4,2,1,8,7,5,3]=>0000000
[2,6,5,1,7,8,4,3]=>0000000
[4,5,7,1,3,8,2,6]=>0000000
[4,3,1,2,8,6,5,7]=>0001000
[6,1,2,5,8,3,4,7]=>0000000
[7,1,3,4,8,2,5,6]=>0000000
[2,6,1,5,7,8,3,4]=>0000000
[6,2,5,1,8,4,7,3]=>0000000
[6,1,5,2,8,3,7,4]=>0000000
[7,3,1,4,8,6,2,5]=>0000000
[5,2,1,3,8,7,4,6]=>0000000
[6,1,4,2,8,3,7,5]=>0000000
[7,1,4,3,8,2,6,5]=>0000000
[5,1,3,2,8,4,7,6]=>0000000
[2,6,1,4,7,8,3,5]=>0000000
[7,1,3,5,8,2,4,6]=>0000000
[7,8,5,6,1,3,4,2]=>0000000
[7,8,1,3,6,2,5,4]=>0000000
[4,6,1,2,5,7,3,8]=>0000001
[1,4,8,2,5,7,3,6]=>1000000
[7,8,4,2,5,1,3,6]=>0000000
[7,8,1,5,4,6,3,2]=>0000000
[7,8,2,1,6,3,4,5]=>0000000
[7,8,3,5,6,4,1,2]=>0000000
[7,8,4,5,3,1,6,2]=>0000000
[2,6,4,8,3,7,1,5]=>0000000
[1,4,6,8,3,7,5,2]=>1000000
[2,5,8,1,4,7,6,3]=>0000000
[1,6,2,4,7,3,8,5]=>1000000
[5,6,2,1,4,7,8,3]=>0000000
[4,7,5,1,3,6,8,2]=>0000000
[5,7,3,6,1,4,8,2]=>0000000
[1,4,7,2,5,3,8,6]=>1000000
[6,4,7,3,5,8,1,2]=>0000000
[3,5,6,7,8,1,4,2]=>0000000
[3,6,5,7,8,2,1,4]=>0000000
[2,7,5,6,8,4,1,3]=>0000000
[2,1,6,8,4,5,3,7]=>0100000
[2,7,1,8,5,3,4,6]=>0000000
[3,7,6,8,5,4,1,2]=>0000000
[4,3,8,5,6,7,1,2]=>0000000
[4,2,8,1,6,3,7,5]=>0000000
[3,1,8,5,4,6,7,2]=>0000000
[3,4,2,8,6,1,7,5]=>0000000
[1,7,3,8,5,2,6,4]=>1000000
[4,1,8,3,6,2,5,7]=>0000000
[5,7,8,6,3,2,1,4]=>0000000
[5,7,8,6,1,3,4,2]=>0000000
[7,6,5,8,1,3,4,2]=>0000000
[1,6,4,3,8,2,5,7]=>1000000
[2,6,3,4,5,8,1,7]=>0000000
[2,6,4,1,8,3,7,5]=>0000000
[3,6,4,5,8,7,1,2]=>0000000
[7,2,1,4,8,3,5,6]=>0000000
[7,1,6,5,3,8,4,2]=>0000000
[7,2,5,6,3,8,1,4]=>0000000
[5,6,2,7,3,1,4,8]=>0000001
[6,7,1,5,2,8,3,4]=>0000000
[6,1,5,2,8,3,4,7]=>0000000
[7,5,2,4,3,1,6,8]=>0000001
[6,8,1,3,7,5,4,2]=>0000000
[7,4,2,6,5,1,3,8]=>0000001
[7,4,6,3,1,5,2,8]=>0000001
[7,2,3,5,4,1,6,8]=>0000001
[2,5,1,7,8,3,6,4]=>0000000
[2,5,3,6,8,4,7,1]=>0000000
[3,5,7,4,1,6,2,8]=>0000001
[5,2,8,4,6,1,7,3]=>0000000
[5,2,1,8,6,3,7,4]=>0000000
[1,4,2,7,5,8,6,3]=>1000000
[5,3,8,7,6,2,4,1]=>0000000
[5,8,4,7,6,2,1,3]=>0000000
[5,8,7,4,3,6,1,2]=>0000000
[6,4,8,3,1,7,2,5]=>0000000
[6,4,2,8,7,1,3,5]=>0000000
[6,3,8,7,2,5,1,4]=>0000000
[5,8,3,7,1,6,4,2]=>0000000
[6,8,5,2,4,3,7,1]=>0000000
[6,8,5,3,1,2,7,4]=>0000000
[4,5,1,2,7,6,3,8]=>0000001
[4,5,1,2,6,8,7,3]=>0000000
[3,5,6,1,8,4,7,2]=>0000000
[3,5,7,1,2,8,6,4]=>0000000
[4,2,6,1,7,3,5,8]=>0000001
[4,6,3,1,2,7,5,8]=>0000001
[3,5,2,7,8,1,6,4]=>0000000
[3,1,4,7,5,6,2,8]=>0000001
[3,1,4,5,8,6,7,2]=>0000000
[3,4,6,8,5,2,7,1]=>0000000
[2,1,7,5,8,6,4,3]=>0100000
[1,2,7,5,3,8,6,4]=>1100000
[4,1,2,7,3,8,6,5]=>0000000
[7,1,4,2,5,3,8,6]=>0000000
[6,1,3,7,5,2,4,8]=>0000001
[3,1,2,6,8,5,4,7]=>0010000
[3,7,1,2,5,4,8,6]=>0000000
[1,3,7,2,4,8,6,5]=>1000000
[3,2,7,8,1,6,5,4]=>0000000
[2,4,1,7,8,6,5,3]=>0000000
[2,6,8,3,1,5,7,4]=>0000000
[3,6,4,8,5,1,7,2]=>0000000
[6,3,7,4,5,1,8,2]=>0000000
[2,6,3,7,5,8,1,4]=>0000000
[5,2,1,7,8,3,4,6]=>0000000
[5,7,4,6,2,8,1,3]=>0000000
[4,2,8,3,6,7,1,5]=>0000000
[4,8,3,1,7,2,5,6]=>0000000
[5,2,8,4,7,1,6,3]=>0000000
[5,8,4,7,3,1,6,2]=>0000000
[4,6,8,3,1,7,5,2]=>0000000
[6,3,8,2,7,1,5,4]=>0000000
[3,5,1,8,2,7,4,6]=>0000000
[7,5,1,3,6,2,4,8]=>0000001
[5,1,8,4,2,7,3,6]=>0000000
[4,1,6,2,8,3,7,5]=>0000000
[1,6,2,8,5,3,7,4]=>1000000
[6,8,5,3,1,7,4,2]=>0000000
[5,6,7,3,1,8,4,2]=>0000000
[5,6,2,1,7,8,4,3]=>0000000
[8,4,5,1,2,6,3,7]=>0000000
[5,6,3,7,1,2,4,8]=>0000001
[1,6,3,7,2,8,4,5]=>1000000
[6,4,7,2,8,1,5,3]=>0000000
[6,7,4,8,3,1,5,2]=>0000000
[4,5,7,8,3,1,6,2]=>0000000
[4,7,2,5,8,1,6,3]=>0000000
[5,7,3,8,2,6,1,4]=>0000000
[3,4,7,8,2,6,1,5]=>0000000
[8,1,3,4,6,2,5,7]=>0000000
[2,4,5,6,8,1,7,3]=>0000000
[8,4,3,6,5,1,7,2]=>0000000
[8,6,5,4,3,1,7,2]=>0000000
[1,8,6,5,2,7,3,4]=>1000000
[8,7,5,4,1,6,3,2]=>0000000
[7,8,5,4,1,3,6,2]=>0000000
[3,2,8,6,5,1,7,4]=>0000000
[8,1,6,5,2,3,7,4]=>0000000
[8,1,7,2,6,3,5,4]=>0000000
[7,1,8,2,6,4,3,5]=>0000000
[5,1,8,3,2,7,4,6]=>0000000
[3,2,8,7,1,6,5,4]=>0000000
[4,8,2,7,1,6,5,3]=>0000000
[5,8,7,2,1,6,4,3]=>0000000
[8,7,6,1,5,4,3,2]=>0000000
[8,6,7,1,4,5,3,2]=>0000000
[7,6,8,1,4,3,5,2]=>0000000
[6,7,8,1,3,4,5,2]=>0000000
[5,7,8,2,1,4,6,3]=>0000000
[4,7,2,8,1,5,6,3]=>0000000
[3,2,7,8,1,5,6,4]=>0000000
[3,2,6,8,4,1,7,5]=>0000000
[4,6,2,8,3,1,7,5]=>0000000
[6,5,8,3,2,1,7,4]=>0000000
[7,5,8,3,1,4,6,2]=>0000000
[8,4,3,7,1,6,5,2]=>0000000
[6,4,3,8,2,1,7,5]=>0000000
[5,4,3,2,8,1,7,6]=>0000000
[4,5,2,3,8,1,7,6]=>0000000
[3,2,5,4,8,1,7,6]=>0000000
[6,4,3,1,5,2,7,8]=>0000011
[7,4,3,1,2,6,5,8]=>0000001
[1,5,4,2,3,6,7,8]=>1000111
[7,5,1,4,2,6,3,8]=>0000001
[4,6,2,1,5,3,7,8]=>0000011
[3,2,6,1,5,4,7,8]=>0000011
[5,7,1,3,2,6,4,8]=>0000001
[6,7,1,2,4,5,3,8]=>0000001
[7,6,1,2,5,4,3,8]=>0000001
[8,6,1,2,5,3,7,4]=>0000000
[7,8,1,2,3,5,6,4]=>0000000
[3,2,8,1,4,5,7,6]=>0000000
[4,1,3,2,5,6,7,8]=>0001111
[5,1,2,4,3,6,7,8]=>0000111
[5,8,7,3,4,1,2,6]=>0000000
[6,7,3,8,5,1,2,4]=>0000000
[6,7,4,5,1,8,3,2]=>0000000
[5,4,7,6,2,3,8,1]=>0000000
[4,3,8,7,6,1,2,5]=>0000000
[4,8,3,7,5,1,2,6]=>0000000
[4,5,6,7,1,8,3,2]=>0000000
[2,5,6,8,1,7,3,4]=>0000000
[8,2,4,5,1,6,3,7]=>0000000
[1,4,8,6,2,3,7,5]=>1000000
[1,5,6,8,2,3,7,4]=>1000000
[1,5,6,2,8,4,7,3]=>1000000
[1,4,2,6,8,5,7,3]=>1000000
[8,1,3,2,5,4,6,7]=>0000000
[4,3,1,7,6,8,5,2]=>0000000
[3,8,2,1,7,5,4,6]=>0000000
[8,3,2,1,6,5,4,7]=>0000000
[8,4,2,6,1,5,3,7]=>0000000
[4,2,8,7,1,6,3,5]=>0000000
[5,3,7,2,6,4,8,1]=>0000000
[6,7,3,1,5,8,4,2]=>0000000
[6,7,2,1,8,5,4,3]=>0000000
[6,7,2,8,1,5,3,4]=>0000000
[6,7,8,2,1,4,3,5]=>0000000
[8,5,6,2,1,4,3,7]=>0000000
[5,8,7,1,2,3,4,6]=>0000000
[6,7,1,2,8,4,5,3]=>0000000
[6,7,1,3,4,8,5,2]=>0000000
[5,1,7,3,4,8,6,2]=>0000000
[5,1,7,8,2,3,6,4]=>0000000
[4,8,1,7,2,3,5,6]=>0000000
[3,8,1,2,7,4,5,6]=>0000000
[3,1,8,2,7,4,6,5]=>0000000
[3,1,2,8,7,5,6,4]=>0010000
[4,1,3,7,5,8,6,2]=>0000000
[1,8,2,3,4,5,7,6]=>1000000
[1,2,8,3,4,6,7,5]=>1100000
[3,6,4,8,5,7,1,2]=>0000000
[5,1,4,8,6,3,7,2]=>0000000
[3,4,7,1,8,6,5,2]=>0000000
[6,3,8,4,2,7,1,5]=>0000000
[3,6,8,7,1,4,2,5]=>0000000
[4,6,1,2,7,8,5,3]=>0000000
[3,6,4,2,8,7,5,1]=>0000000
[5,8,1,4,6,7,2,3]=>0000000
[3,6,4,5,7,2,8,1]=>0000000
[5,4,2,7,3,6,8,1]=>0000000
[4,2,5,7,3,6,8,1]=>0000000
[1,6,5,3,4,8,2,7]=>1000000
[1,8,6,3,7,5,2,4]=>1000000
[8,7,5,2,6,4,3,1]=>0000000
[8,7,1,6,2,5,4,3]=>0000000
[7,8,1,6,3,2,5,4]=>0000000
[2,8,1,7,3,5,6,4]=>0000000
[4,8,1,3,7,2,6,5]=>0000000
[4,2,8,5,7,3,6,1]=>0000000
[6,7,3,1,8,4,2,5]=>0000000
[1,7,3,8,4,5,2,6]=>1000000
[1,7,2,8,5,3,4,6]=>1000000
[7,6,1,8,4,3,2,5]=>0000000
[7,1,2,8,3,5,4,6]=>0000000
[6,3,7,2,1,8,4,5]=>0000000
[8,2,6,1,7,3,5,4]=>0000000
[5,4,3,1,6,8,2,7]=>0000000
[1,5,3,4,6,8,2,7]=>1000000
[4,3,5,1,6,8,2,7]=>0000000
[4,7,5,6,8,3,2,1]=>0000000
[5,7,3,8,2,6,4,1]=>0000000
[2,3,8,7,4,5,6,1]=>0000000
[7,2,8,6,4,3,5,1]=>0000000
[1,3,8,7,4,6,2,5]=>1000000
[4,7,1,8,6,5,2,3]=>0000000
[6,7,4,8,3,5,1,2]=>0000000
[6,7,4,5,2,8,1,3]=>0000000
[5,7,4,6,2,3,1,8]=>0000001
[5,7,4,6,3,8,1,2]=>0000000
[5,7,4,8,3,6,1,2]=>0000000
[6,8,4,5,3,7,1,2]=>0000000
[5,8,4,6,3,7,1,2]=>0000000
[5,6,4,8,3,7,1,2]=>0000000
[5,6,3,7,2,4,1,8]=>0000001
[5,6,3,7,2,8,1,4]=>0000000
[5,6,3,8,2,7,1,4]=>0000000
[5,6,4,8,2,7,1,3]=>0000000
[5,8,4,6,2,7,1,3]=>0000000
[6,8,4,5,2,7,1,3]=>0000000
[7,8,4,5,2,6,1,3]=>0000000
[6,8,4,5,2,3,1,7]=>0000000
[5,8,4,6,2,3,1,7]=>0000000
[5,6,4,8,2,3,1,7]=>0000000
[5,6,3,8,2,4,1,7]=>0000000
[5,6,3,4,2,8,1,7]=>0000000
[4,6,3,5,2,7,1,8]=>0000001
[4,6,3,5,2,8,1,7]=>0000000
[4,6,3,8,2,5,1,7]=>0000000
[4,8,3,6,2,5,1,7]=>0000000
[5,8,3,6,2,4,1,7]=>0000000
[6,8,3,5,2,4,1,7]=>0000000
[7,8,3,5,2,4,1,6]=>0000000
[7,8,3,5,2,6,1,4]=>0000000
[6,8,3,5,2,7,1,4]=>0000000
[5,8,3,6,2,7,1,4]=>0000000
[4,8,3,6,2,7,1,5]=>0000000
[4,6,3,8,2,7,1,5]=>0000000
[4,6,3,7,2,8,1,5]=>0000000
[4,6,3,7,2,5,1,8]=>0000001
[4,7,3,6,2,5,1,8]=>0000001
[4,7,3,6,2,8,1,5]=>0000000
[4,7,3,8,2,6,1,5]=>0000000
[5,7,4,8,2,6,1,3]=>0000000
[5,7,3,6,2,8,1,4]=>0000000
[5,7,3,6,2,4,1,8]=>0000001
[6,7,3,5,2,4,1,8]=>0000001
[6,7,3,5,2,8,1,4]=>0000000
[6,7,3,8,2,5,1,4]=>0000000
[6,7,4,8,2,5,1,3]=>0000000
[6,7,5,8,2,4,1,3]=>0000000
[6,8,5,7,2,3,1,4]=>0000000
[6,7,4,8,2,3,1,5]=>0000000
[6,7,3,8,2,4,1,5]=>0000000
[6,7,3,4,2,8,1,5]=>0000000
[5,7,3,4,2,6,1,8]=>0000001
[5,7,3,4,2,8,1,6]=>0000000
[5,7,3,8,2,4,1,6]=>0000000
[5,7,4,8,2,3,1,6]=>0000000
[5,8,4,7,2,3,1,6]=>0000000
[6,8,4,7,2,3,1,5]=>0000000
[7,8,4,6,2,3,1,5]=>0000000
[7,8,3,6,2,4,1,5]=>0000000
[6,8,3,7,2,4,1,5]=>0000000
[5,8,3,7,2,4,1,6]=>0000000
[4,8,3,7,2,5,1,6]=>0000000
[4,7,3,8,2,5,1,6]=>0000000
[4,7,3,5,2,8,1,6]=>0000000
[4,7,3,5,2,6,1,8]=>0000001
[4,5,3,7,2,6,1,8]=>0000001
[4,5,3,7,2,8,1,6]=>0000000
[4,5,3,8,2,7,1,6]=>0000000
[4,8,3,5,2,7,1,6]=>0000000
[5,8,3,4,2,7,1,6]=>0000000
[6,8,3,4,2,7,1,5]=>0000000
[7,8,3,4,2,6,1,5]=>0000000
[6,8,3,4,2,5,1,7]=>0000000
[5,8,3,4,2,6,1,7]=>0000000
[4,8,3,5,2,6,1,7]=>0000000
[4,5,3,8,2,6,1,7]=>0000000
[4,5,3,6,2,8,1,7]=>0000000
[4,6,5,2,1,3,8,7]=>0000010
[7,4,8,1,6,5,3,2]=>0000000
[7,4,5,3,1,8,2,6]=>0000000
[6,4,8,1,7,5,2,3]=>0000000
[6,4,7,1,8,2,5,3]=>0000000
[8,4,7,3,6,2,5,1]=>0000000
[5,7,8,6,2,3,1,4]=>0000000
[5,8,7,6,3,2,1,4]=>0000000
[6,7,4,2,8,1,5,3]=>0000000
[6,8,4,2,7,5,1,3]=>0000000
[5,7,4,2,3,8,1,6]=>0000000
[2,1,8,6,7,5,3,4]=>0100000
[5,8,6,7,3,1,2,4]=>0000000
[6,7,5,8,1,3,4,2]=>0000000
[7,6,5,8,1,4,3,2]=>0000000
[2,1,7,6,8,3,5,4]=>0100000
[7,5,6,8,1,4,2,3]=>0000000
[8,1,3,7,4,6,5,2]=>0000000
[6,1,5,4,3,8,7,2]=>0000000
[6,1,8,3,4,5,7,2]=>0000000
[5,6,2,1,4,8,3,7]=>0000000
[8,5,2,7,3,1,6,4]=>0000000
[8,5,6,4,2,1,7,3]=>0000000
[2,6,4,1,8,5,7,3]=>0000000
[1,5,7,3,2,4,6,8]=>1000001
[5,8,2,4,1,3,7,6]=>0000000
[4,8,1,6,3,2,7,5]=>0000000
[3,1,8,6,4,2,7,5]=>0000000
[4,2,1,3,7,8,5,6]=>0001000
[8,6,1,3,7,2,4,5]=>0000000
[5,2,7,8,6,4,1,3]=>0000000
[1,4,2,7,8,6,3,5]=>1000000
[1,6,2,4,8,5,3,7]=>1000000
[1,6,2,4,7,5,3,8]=>1000001
[1,7,3,2,8,6,4,5]=>1000000
[7,8,3,6,5,2,1,4]=>0000000
[4,7,2,8,6,1,5,3]=>0000000
[1,3,6,4,8,5,7,2]=>1000000
[1,3,6,4,7,5,8,2]=>1000000
[6,2,1,3,7,8,4,5]=>0000000
[7,2,5,1,8,3,4,6]=>0000000
[7,8,2,1,4,3,5,6]=>0000000
[7,5,4,2,6,8,1,3]=>0000000
[8,2,5,4,6,7,1,3]=>0000000
[8,2,6,4,3,1,7,5]=>0000000
[8,2,7,4,1,3,5,6]=>0000000
[1,2,8,4,3,5,6,7]=>1100000
[1,8,7,4,3,2,5,6]=>1000000
[5,8,4,7,2,1,6,3]=>0000000
[1,8,7,5,4,3,6,2]=>1000000
[1,6,8,4,3,7,5,2]=>1000000
[6,8,7,3,2,5,1,4]=>0000000
[5,3,8,1,2,7,4,6]=>0000000
[5,1,8,3,2,6,4,7]=>0000000
[5,7,3,1,2,6,4,8]=>0000001
[1,4,6,2,8,3,7,5]=>1000000
[5,2,6,7,8,4,1,3]=>0000000
[5,3,6,1,2,8,4,7]=>0000000
[1,6,3,2,7,8,4,5]=>1000000
[6,7,3,8,5,2,1,4]=>0000000
[4,6,2,7,8,1,5,3]=>0000000
[1,6,4,7,8,3,5,2]=>1000000
[4,5,7,2,1,8,6,3]=>0000000
[7,8,3,4,2,1,6,5]=>0000000
[6,3,4,1,2,5,8,7]=>0000010
[6,3,1,4,2,7,5,8]=>0000001
[1,8,3,2,4,5,6,7]=>1000000
[7,8,3,5,4,6,1,2]=>0000000
[6,8,3,7,5,1,4,2]=>0000000
[5,7,3,8,1,6,2,4]=>0000000
[7,8,4,6,1,5,2,3]=>0000000
[7,8,1,6,4,5,2,3]=>0000000
[6,8,1,7,4,5,2,3]=>0000000
[1,8,6,7,4,5,2,3]=>1000000
[1,8,6,7,3,5,2,4]=>1000000
[6,8,1,7,3,5,2,4]=>0000000
[7,8,1,6,3,5,2,4]=>0000000
[7,8,3,6,1,5,2,4]=>0000000
[7,8,3,6,4,5,1,2]=>0000000
[7,8,2,6,4,5,1,3]=>0000000
[7,8,2,6,3,5,1,4]=>0000000
[7,8,2,6,1,5,3,4]=>0000000
[7,8,1,6,2,5,3,4]=>0000000
[1,8,6,7,2,5,3,4]=>1000000
[1,8,5,7,2,6,3,4]=>1000000
[5,8,1,7,2,6,3,4]=>0000000
[5,8,2,7,1,6,3,4]=>0000000
[6,8,2,7,1,5,3,4]=>0000000
[6,8,2,7,3,5,1,4]=>0000000
[6,8,2,7,4,5,1,3]=>0000000
[6,8,3,7,4,5,1,2]=>0000000
[3,8,6,7,4,5,1,2]=>0000000
[2,8,6,7,4,5,1,3]=>0000000
[2,8,6,7,3,5,1,4]=>0000000
[2,8,6,7,1,5,3,4]=>0000000
[2,8,5,7,1,6,3,4]=>0000000
[2,8,1,7,5,6,3,4]=>0000000
[1,8,2,7,5,6,3,4]=>1000000
[1,8,2,7,4,6,3,5]=>1000000
[2,8,1,7,4,6,3,5]=>0000000
[2,8,4,7,1,6,3,5]=>0000000
[2,8,4,7,3,6,1,5]=>0000000
[2,8,5,7,3,6,1,4]=>0000000
[3,8,5,7,4,6,1,2]=>0000000
[5,8,3,7,4,6,1,2]=>0000000
[5,8,2,7,4,6,1,3]=>0000000
[5,8,2,7,3,6,1,4]=>0000000
[4,8,2,7,3,6,1,5]=>0000000
[4,8,2,7,1,6,3,5]=>0000000
[4,8,1,7,2,6,3,5]=>0000000
[1,8,4,7,2,6,3,5]=>1000000
[1,8,4,7,3,6,2,5]=>1000000
[4,8,1,7,3,6,2,5]=>0000000
[4,8,3,7,1,6,2,5]=>0000000
[6,8,3,7,1,5,2,4]=>0000000
[5,8,1,7,3,6,2,4]=>0000000
[1,8,5,7,3,6,2,4]=>1000000
[1,8,5,7,4,6,2,3]=>1000000
[5,8,1,7,4,6,2,3]=>0000000
[5,8,4,7,1,6,2,3]=>0000000
[6,8,4,7,1,5,2,3]=>0000000
[6,8,5,7,1,4,2,3]=>0000000
[5,8,6,7,3,4,1,2]=>0000000
[5,8,6,7,2,4,1,3]=>0000000
[5,8,6,7,1,4,2,3]=>0000000
[4,8,6,7,1,5,2,3]=>0000000
[4,8,5,7,1,6,2,3]=>0000000
[4,8,1,7,5,6,2,3]=>0000000
[1,8,4,7,5,6,2,3]=>1000000
[1,8,3,7,5,6,2,4]=>1000000
[3,8,1,7,5,6,2,4]=>0000000
[3,8,5,7,1,6,2,4]=>0000000
[3,8,6,7,1,5,2,4]=>0000000
[3,8,6,7,2,5,1,4]=>0000000
[4,8,6,7,2,5,1,3]=>0000000
[4,8,6,7,3,5,1,2]=>0000000
[4,8,5,7,3,6,1,2]=>0000000
[4,8,5,7,2,6,1,3]=>0000000
[3,8,5,7,2,6,1,4]=>0000000
[3,8,4,7,2,6,1,5]=>0000000
[3,8,4,7,1,6,2,5]=>0000000
[3,8,1,7,4,6,2,5]=>0000000
[1,8,3,7,4,6,2,5]=>1000000
[1,8,3,7,2,6,4,5]=>1000000
[3,8,1,7,2,6,4,5]=>0000000
[3,8,2,7,1,6,4,5]=>0000000
[3,8,2,7,4,6,1,5]=>0000000
[3,8,2,7,5,6,1,4]=>0000000
[4,8,2,7,5,6,1,3]=>0000000
[4,8,3,7,5,6,1,2]=>0000000
[3,8,4,7,5,6,1,2]=>0000000
[2,8,4,7,5,6,1,3]=>0000000
[2,8,3,7,5,6,1,4]=>0000000
[2,8,3,7,4,6,1,5]=>0000000
[2,8,3,7,1,6,4,5]=>0000000
[2,8,1,7,3,6,4,5]=>0000000
[7,5,2,8,6,4,1,3]=>0000000
[7,4,8,6,1,5,2,3]=>0000000
[7,1,8,4,5,2,6,3]=>0000000
[1,6,7,4,2,8,5,3]=>1000000
[1,6,7,3,8,5,2,4]=>1000000
[7,1,8,3,5,6,2,4]=>0000000
[7,3,8,6,2,5,1,4]=>0000000
[7,4,2,8,6,1,3,5]=>0000000
[6,8,1,7,2,3,4,5]=>0000000
[1,5,7,8,2,6,3,4]=>1000000
[2,5,3,7,8,1,6,4]=>0000000
[2,5,4,1,3,7,8,6]=>0000100
[3,1,5,4,7,8,2,6]=>0000000
[5,3,1,4,8,2,6,7]=>0000000
[5,2,4,8,6,1,3,7]=>0000000
[4,8,1,3,6,7,2,5]=>0000000
[5,3,8,2,4,7,1,6]=>0000000
[5,4,3,8,1,2,7,6]=>0000000
[6,4,3,1,2,8,5,7]=>0000000
[6,4,2,8,1,3,7,5]=>0000000
[6,3,8,2,5,1,7,4]=>0000000
[6,3,8,1,4,7,2,5]=>0000000
[1,5,7,3,6,8,4,2]=>1000000
[1,5,7,4,2,6,8,3]=>1000000
[5,8,1,4,2,6,3,7]=>0000000
[6,5,3,1,4,2,8,7]=>0000010
[5,3,1,6,4,2,7,8]=>0000011
[5,2,6,4,1,7,3,8]=>0000001
[4,6,1,7,5,2,8,3]=>0000000
[3,5,6,1,2,8,7,4]=>0000000
[3,5,7,1,8,6,2,4]=>0000000
[3,6,2,7,5,1,8,4]=>0000000
[4,3,1,5,7,2,6,8]=>0000001
[3,4,7,2,8,6,1,5]=>0000000
[3,4,5,8,2,7,1,6]=>0000000
[5,3,6,8,4,7,2,1]=>0000000
[5,1,6,8,4,3,2,7]=>0000000
[6,7,8,1,4,3,2,5]=>0000000
[4,7,1,5,8,3,2,6]=>0000000
[8,4,1,5,7,3,2,6]=>0000000
[8,3,6,1,4,7,2,5]=>0000000
[3,7,6,1,4,8,2,5]=>0000000
[6,7,8,2,4,3,5,1]=>0000000
[5,7,3,8,4,6,2,1]=>0000000
[4,7,3,5,8,6,2,1]=>0000000
[8,7,2,1,4,3,6,5]=>0000000
[8,7,3,1,4,6,2,5]=>0000000
[8,7,6,3,2,5,4,1]=>0000000
[8,7,3,5,1,6,2,4]=>0000000
[8,7,2,5,1,3,6,4]=>0000000
[8,4,6,5,7,1,2,3]=>0000000
[8,7,6,5,2,1,4,3]=>0000000
[3,6,4,8,7,5,1,2]=>0000000
[5,6,4,3,8,7,1,2]=>0000000
[1,6,2,4,7,8,5,3]=>1000000
[3,6,2,4,8,1,5,7]=>0000000
[3,4,7,2,8,1,6,5]=>0000000
[7,3,8,4,5,6,1,2]=>0000000
[3,8,7,5,4,6,1,2]=>0000000
[4,3,6,7,8,5,1,2]=>0000000
[3,5,6,4,8,7,1,2]=>0000000
[4,6,8,5,3,7,1,2]=>0000000
[6,5,2,1,4,7,8,3]=>0000000
[4,2,7,5,1,8,6,3]=>0000000
[2,1,6,4,8,7,5,3]=>0100000
[7,8,1,4,2,6,5,3]=>0000000
[6,5,1,3,4,2,8,7]=>0000010
[4,8,5,3,1,7,2,6]=>0000000
[7,4,5,3,2,8,1,6]=>0000000
[5,8,3,6,1,4,2,7]=>0000000
[1,6,8,7,4,2,3,5]=>1000000
[7,6,1,8,3,2,4,5]=>0000000
[7,1,8,6,3,4,2,5]=>0000000
[1,8,7,6,4,3,2,5]=>1000000
[2,1,7,5,6,3,8,4]=>0100000
[3,1,6,7,5,8,2,4]=>0000000
[7,8,1,6,5,3,2,4]=>0000000
[7,8,2,1,4,5,6,3]=>0000000
[4,2,6,1,8,5,7,3]=>0000000
[2,8,1,5,4,6,7,3]=>0000000
[1,2,8,3,6,5,7,4]=>1100000
[2,6,4,1,7,5,8,3]=>0000000
[7,6,5,8,1,4,2,3]=>0000000
[5,8,6,7,3,2,1,4]=>0000000
[1,6,4,3,7,2,8,5]=>1000000
[4,1,6,3,8,2,7,5]=>0000000
[7,8,1,3,4,2,6,5]=>0000000
[2,8,5,7,4,3,1,6]=>0000000
[7,2,5,8,3,4,1,6]=>0000000
[3,5,7,8,4,1,2,6]=>0000000
[5,4,7,3,6,8,1,2]=>0000000
[1,4,7,2,5,8,3,6]=>1000000
[3,6,2,4,7,1,5,8]=>0000001
[7,6,3,5,4,8,1,2]=>0000000
[4,5,6,3,8,7,1,2]=>0000000
[4,8,2,6,1,5,3,7]=>0000000
[7,1,3,6,8,4,2,5]=>0000000
[1,8,3,6,7,4,5,2]=>1000000
[7,1,5,8,3,6,2,4]=>0000000
[3,1,6,4,7,2,5,8]=>0000001
[5,8,7,1,2,4,3,6]=>0000000
[6,8,5,1,3,4,2,7]=>0000000
[7,6,5,1,4,3,2,8]=>0000001
[2,6,4,5,1,3,8,7]=>0000010
[3,5,6,4,1,8,2,7]=>0000000
[7,8,5,4,1,3,2,6]=>0000000
[7,8,2,3,4,1,6,5]=>0000000
[4,2,6,3,8,1,7,5]=>0000000
[7,2,3,5,4,1,8,6]=>0000000
[6,2,4,3,1,5,7,8]=>0000011
[4,2,8,3,1,7,5,6]=>0000000
[5,3,7,4,1,6,2,8]=>0000001
[2,4,7,3,6,1,8,5]=>0000000
[5,8,7,6,3,1,2,4]=>0000000
[7,5,6,8,1,4,3,2]=>0000000
[2,4,7,1,6,5,3,8]=>0000001
[5,2,7,1,8,4,6,3]=>0000000
[4,2,1,3,6,5,8,7]=>0001010
[4,2,6,1,8,5,3,7]=>0000000
[7,8,2,1,4,5,3,6]=>0000000
[7,8,4,1,5,3,6,2]=>0000000
[7,5,1,6,4,3,8,2]=>0000000
[5,8,1,6,3,4,7,2]=>0000000
[6,8,1,7,5,2,3,4]=>0000000
[5,6,1,7,4,8,2,3]=>0000000
[7,8,5,1,6,4,2,3]=>0000000
[2,6,5,7,3,4,8,1]=>0000000
[1,6,4,7,5,8,2,3]=>1000000
[1,3,7,4,6,8,2,5]=>1000000
[5,2,4,7,3,6,8,1]=>0000000
[8,1,6,5,7,2,4,3]=>0000000
[1,2,7,6,8,3,4,5]=>1100000
[7,8,1,6,2,4,5,3]=>0000000
[2,8,1,7,4,3,6,5]=>0000000
[3,7,4,1,8,5,2,6]=>0000000
[6,7,1,4,8,3,2,5]=>0000000
[2,7,1,8,4,5,3,6]=>0000000
[6,1,2,8,4,3,5,7]=>0000000
[5,1,2,4,8,3,6,7]=>0000000
[4,1,3,2,8,5,6,7]=>0001000
[3,2,1,4,8,5,6,7]=>0011000
[4,3,6,1,5,8,2,7]=>0000000
[2,6,1,4,5,8,3,7]=>0000000
[1,6,2,5,8,3,4,7]=>1000000
[8,4,2,1,7,3,6,5]=>0000000
[7,4,2,1,8,5,3,6]=>0000000
[1,5,4,2,8,3,6,7]=>1000000
[6,4,3,1,5,8,2,7]=>0000000
[5,4,3,2,1,8,6,7]=>0000100
[2,5,3,4,1,8,6,7]=>0000100
[4,3,5,2,1,8,6,7]=>0000100
[3,7,6,8,4,5,2,1]=>0000000
[1,7,6,8,5,4,2,3]=>1000000
[2,4,8,6,7,3,5,1]=>0000000
[6,3,5,8,4,7,2,1]=>0000000
[5,4,3,8,6,7,2,1]=>0000000
[3,2,8,5,7,4,6,1]=>0000000
[3,1,8,5,7,6,2,4]=>0000000
[5,8,6,7,4,3,2,1]=>0000000
[4,8,7,5,6,3,2,1]=>0000000
[6,2,1,4,3,8,5,7]=>0000000
[2,1,6,4,3,5,8,7]=>0100010
[8,4,2,1,3,6,5,7]=>0000000
[6,4,2,1,8,3,5,7]=>0000000
[4,6,2,1,3,8,5,7]=>0000000
[2,6,1,4,3,8,5,7]=>0000000
[4,8,2,1,3,6,5,7]=>0000000
[2,6,1,4,8,3,5,7]=>0000000
[2,6,4,1,8,3,5,7]=>0000000
[2,6,4,8,1,3,5,7]=>0000000
[4,6,2,8,1,3,5,7]=>0000000
[6,2,4,1,8,3,5,7]=>0000000
[4,2,1,6,8,3,5,7]=>0000000
[4,2,1,3,8,6,5,7]=>0001000
[4,2,1,8,3,6,5,7]=>0000000
[2,4,8,1,6,3,5,7]=>0000000
[2,8,6,4,1,3,5,7]=>0000000
[4,8,6,2,1,3,5,7]=>0000000
[3,2,6,1,5,4,8,7]=>0000010
[4,3,6,1,5,2,8,7]=>0000010
[4,3,8,2,6,1,7,5]=>0000000
[4,3,8,1,7,2,6,5]=>0000000
[4,3,8,1,5,2,7,6]=>0000000
[2,1,5,4,8,3,7,6]=>0100000
[5,4,7,6,8,1,3,2]=>0000000
[4,3,7,1,8,5,6,2]=>0000000
[4,3,6,5,8,1,7,2]=>0000000
[7,4,6,5,8,1,3,2]=>0000000
[8,4,6,1,3,2,7,5]=>0000000
[8,1,6,3,4,2,7,5]=>0000000
[8,3,5,2,6,1,7,4]=>0000000
[8,2,7,1,5,3,6,4]=>0000000
[2,1,8,3,5,4,7,6]=>0100000
[8,1,3,2,5,4,7,6]=>0000000
[8,1,5,2,4,3,7,6]=>0000000
[8,2,4,1,5,3,7,6]=>0000000
[3,2,8,4,6,1,7,5]=>0000000
[3,2,8,1,7,4,6,5]=>0000000
[3,2,7,1,8,5,6,4]=>0000000
[3,2,6,5,8,1,7,4]=>0000000
[7,6,8,1,5,2,4,3]=>0000000
[7,6,8,1,3,2,5,4]=>0000000
[7,1,8,2,6,4,5,3]=>0000000
[5,4,7,2,6,3,8,1]=>0000000
[6,1,8,4,7,2,5,3]=>0000000
[2,1,6,5,8,3,7,4]=>0100000
[3,2,1,5,8,4,6,7]=>0010000
[2,8,3,1,5,4,6,7]=>0000000
[2,4,8,3,5,7,6,1]=>0000000
[1,8,4,2,5,3,6,7]=>1000000
[8,1,5,3,2,4,6,7]=>0000000
[3,8,1,5,2,4,6,7]=>0000000
[5,4,1,3,8,2,6,7]=>0000000
[1,5,7,3,8,4,2,6]=>1000000
[5,1,4,7,8,3,2,6]=>0000000
[1,4,3,8,7,5,6,2]=>1000000
[1,6,8,5,3,7,4,2]=>1000000
[6,4,8,1,7,3,5,2]=>0000000
[6,4,8,7,1,5,2,3]=>0000000
[7,1,6,8,4,3,2,5]=>0000000
[1,6,7,2,8,4,3,5]=>1000000
[6,7,1,4,2,8,3,5]=>0000000
[6,3,7,1,4,8,2,5]=>0000000
[3,7,8,1,5,2,4,6]=>0000000
[7,1,2,8,5,3,4,6]=>0000000
[1,7,2,8,4,5,3,6]=>1000000
[4,2,1,7,8,5,3,6]=>0000000
[7,2,6,3,4,1,8,5]=>0000000
[2,7,1,8,3,5,4,6]=>0000000
[2,1,7,3,5,8,4,6]=>0100000
[1,2,7,5,8,3,4,6]=>1100000
[8,7,1,3,6,2,4,5]=>0000000
[8,2,1,7,3,5,6,4]=>0000000
[7,8,2,6,3,1,5,4]=>0000000
[2,8,4,1,6,7,5,3]=>0000000
[8,3,7,1,5,6,2,4]=>0000000
[8,1,6,2,7,4,5,3]=>0000000
[1,8,5,2,6,7,4,3]=>1000000
[5,2,1,8,6,7,4,3]=>0000000
[7,8,1,6,4,2,5,3]=>0000000
[8,7,6,5,1,4,2,3]=>0000000
[8,7,6,1,5,3,4,2]=>0000000
[8,1,7,5,6,4,3,2]=>0000000
[1,8,6,7,5,4,3,2]=>1000000
[6,5,3,1,2,4,8,7]=>0000010
[4,5,3,6,1,2,8,7]=>0000010
[8,1,4,7,3,6,2,5]=>0000000
[6,3,4,7,5,8,1,2]=>0000000
[4,7,1,3,5,8,6,2]=>0000000
[4,8,3,7,1,2,6,5]=>0000000
[8,1,7,4,5,2,3,6]=>0000000
[5,3,7,8,2,4,6,1]=>0000000
[5,3,7,6,2,1,8,4]=>0000000
[2,1,6,7,5,8,3,4]=>0100000
[2,1,5,7,3,6,8,4]=>0100000
[2,4,7,1,6,5,8,3]=>0000000
[3,4,6,2,7,8,5,1]=>0000000
[3,5,6,4,7,1,8,2]=>0000000
[3,4,1,5,7,6,8,2]=>0000000
[4,2,1,7,3,5,8,6]=>0000000
[7,3,1,5,4,2,8,6]=>0000000
[6,3,1,4,2,8,5,7]=>0000000
[8,4,1,5,2,7,6,3]=>0000000
[3,6,2,7,1,4,8,5]=>0000000
[2,7,5,4,1,3,8,6]=>0000000
[6,4,3,2,1,8,5,7]=>0000000
[1,7,6,2,4,8,3,5]=>1000000
[7,1,8,5,3,6,4,2]=>0000000
[1,8,5,7,2,4,6,3]=>1000000
[7,2,8,5,6,1,4,3]=>0000000
[3,6,5,8,1,4,2,7]=>0000000
[4,3,6,7,8,1,2,5]=>0000000
[5,4,6,7,2,8,1,3]=>0000000
[3,5,7,1,4,8,2,6]=>0000000
[8,1,5,2,7,4,6,3]=>0000000
[5,4,1,6,8,2,3,7]=>0000000
[5,3,6,4,7,8,1,2]=>0000000
[6,4,7,8,1,5,3,2]=>0000000
[6,3,7,8,5,2,4,1]=>0000000
[4,6,8,2,7,1,5,3]=>0000000
[2,5,8,7,1,3,6,4]=>0000000
[8,2,7,6,5,1,4,3]=>0000000
[4,3,8,7,6,2,1,5]=>0000000
[4,7,3,8,6,5,1,2]=>0000000
[5,8,7,3,6,4,2,1]=>0000000
[2,8,7,6,5,4,1,3]=>0000000
[7,8,5,6,3,1,4,2]=>0000000
[7,5,8,3,1,4,2,6]=>0000000
[7,8,5,3,1,6,2,4]=>0000000
[7,8,5,3,1,6,4,2]=>0000000
[7,8,5,3,6,4,1,2]=>0000000
[7,5,8,3,1,2,6,4]=>0000000
[7,5,6,3,4,1,8,2]=>0000000
[7,5,3,1,6,4,8,2]=>0000000
[7,5,3,6,4,1,8,2]=>0000000
[7,5,3,8,4,6,1,2]=>0000000
[7,5,3,8,4,1,6,2]=>0000000
[7,5,3,8,1,4,6,2]=>0000000
[7,5,3,1,8,4,6,2]=>0000000
[7,5,3,1,8,2,6,4]=>0000000
[7,5,3,1,8,6,2,4]=>0000000
[7,5,3,8,6,1,4,2]=>0000000
[7,5,3,8,1,4,2,6]=>0000000
[7,5,3,8,6,1,2,4]=>0000000
[7,5,8,6,3,1,2,4]=>0000000
[7,5,8,6,3,1,4,2]=>0000000
[7,5,8,6,3,4,1,2]=>0000000
[7,5,6,8,3,1,4,2]=>0000000
[7,5,6,3,8,1,2,4]=>0000000
[7,5,6,3,1,8,4,2]=>0000000
[7,5,3,6,1,8,4,2]=>0000000
[7,5,3,4,1,6,8,2]=>0000000
[4,6,8,3,5,7,1,2]=>0000000
[6,8,1,2,4,5,7,3]=>0000000
[8,3,5,2,4,1,6,7]=>0000000
[3,5,7,2,4,6,1,8]=>0000001
[4,2,5,7,3,6,1,8]=>0000001
[4,5,2,8,3,1,6,7]=>0000000
[2,1,6,8,4,7,3,5]=>0100000
[1,2,5,8,3,6,7,4]=>1100000
[5,3,6,8,4,7,1,2]=>0000000
[4,3,6,2,7,5,1,8]=>0000001
[4,3,1,7,8,2,6,5]=>0000000
[5,4,7,3,8,6,1,2]=>0000000
[5,8,4,7,6,3,1,2]=>0000000
[5,8,7,1,4,2,6,3]=>0000000
[8,3,5,1,2,7,6,4]=>0000000
[4,7,3,6,5,2,1,8]=>0000001
[5,3,7,6,4,2,1,8]=>0000001
[5,3,1,6,4,2,8,7]=>0000010
[1,3,8,5,4,2,7,6]=>1000000
[1,8,3,6,2,7,5,4]=>1000000
[1,6,8,7,4,2,5,3]=>1000000
[6,4,8,7,5,3,1,2]=>0000000
[3,1,2,7,6,4,8,5]=>0010000
[5,2,6,3,7,4,1,8]=>0000001
[2,8,5,3,1,6,4,7]=>0000000
[2,1,7,3,8,5,4,6]=>0100000
[1,6,2,3,7,8,5,4]=>1000000
[1,6,7,2,8,4,5,3]=>1000000
[6,3,7,4,8,5,1,2]=>0000000
[5,7,1,8,2,4,6,3]=>0000000
[5,1,2,7,8,3,6,4]=>0000000
[4,2,1,7,3,8,5,6]=>0000000
[6,2,8,4,3,1,5,7]=>0000000
[6,4,2,7,3,5,1,8]=>0000001
[7,3,2,1,8,4,5,6]=>0000000
[3,7,2,8,6,1,4,5]=>0000000
[7,1,8,2,4,5,6,3]=>0000000
[8,7,6,1,2,4,5,3]=>0000000
[8,3,6,5,2,1,4,7]=>0000000
[8,2,4,1,6,5,3,7]=>0000000
[8,5,1,2,7,3,6,4]=>0000000
[6,1,8,2,3,7,5,4]=>0000000
[8,1,2,6,4,3,7,5]=>0000000
[1,7,2,8,3,6,5,4]=>1000000
[7,3,8,6,5,4,1,2]=>0000000
[8,1,7,3,2,6,5,4]=>0000000
[4,3,1,2,8,7,6,5]=>0001000
[8,6,4,3,1,5,7,2]=>0000000
[8,6,4,1,5,2,7,3]=>0000000
[8,7,2,4,5,3,1,6]=>0000000
[8,5,1,2,6,7,3,4]=>0000000
[8,5,1,6,4,2,7,3]=>0000000
[8,5,1,3,6,4,7,2]=>0000000
[7,4,8,3,1,6,2,5]=>0000000
[7,1,5,8,3,2,6,4]=>0000000
[5,7,4,1,8,2,6,3]=>0000000
[5,7,4,3,1,8,6,2]=>0000000
[8,5,7,4,6,1,3,2]=>0000000
[1,8,7,2,5,4,6,3]=>1000000
[4,3,1,8,7,5,2,6]=>0000000
[3,1,4,6,8,7,2,5]=>0000000
[1,6,2,4,8,7,5,3]=>1000000
[7,1,6,4,8,5,2,3]=>0000000
[1,3,7,2,6,8,4,5]=>1000000
[6,1,2,7,8,5,3,4]=>0000000
[6,1,2,7,4,8,5,3]=>0000000
[3,1,6,4,7,8,5,2]=>0000000
[5,7,1,3,8,4,6,2]=>0000000
[5,7,1,8,4,2,6,3]=>0000000
[5,7,1,2,8,6,3,4]=>0000000
[4,2,6,3,8,1,5,7]=>0000000
[4,2,6,7,3,5,1,8]=>0000001
[3,6,2,4,7,5,1,8]=>0000001
[3,6,2,4,1,8,5,7]=>0000000
[7,1,4,5,2,8,6,3]=>0000000
[4,7,3,1,5,8,6,2]=>0000000
[4,2,8,1,5,7,3,6]=>0000000
[8,5,7,6,1,4,2,3]=>0000000
[1,8,2,4,6,7,3,5]=>1000000
[1,2,7,4,8,6,3,5]=>1100000
[1,2,7,8,3,6,5,4]=>1100000
[1,8,5,7,4,3,2,6]=>1000000
[7,1,5,8,3,4,6,2]=>0000000
[7,1,5,8,4,3,2,6]=>0000000
[7,1,2,5,8,3,6,4]=>0000000
[2,7,1,4,8,3,5,6]=>0000000
[7,1,4,6,5,8,3,2]=>0000000
[7,1,2,3,8,5,4,6]=>0000000
[7,1,3,4,2,6,8,5]=>0000000
[3,6,7,1,4,8,5,2]=>0000000
[3,5,1,4,8,6,2,7]=>0000000
[3,6,2,4,7,8,1,5]=>0000000
[6,5,8,7,2,3,1,4]=>0000000
[3,4,7,2,5,8,1,6]=>0000000
[4,3,8,1,2,7,5,6]=>0000000
[5,6,7,8,1,3,4,2]=>0000000
[5,7,8,6,1,2,3,4]=>0000000
[2,8,3,1,5,6,4,7]=>0000000
[3,8,7,1,5,4,2,6]=>0000000
[4,3,1,7,6,8,2,5]=>0000000
[3,4,1,7,5,6,8,2]=>0000000
[2,4,6,1,7,5,8,3]=>0000000
[4,2,1,5,6,3,7,8]=>0000011
[5,8,1,6,4,3,2,7]=>0000000
[5,8,1,6,3,7,2,4]=>0000000
[7,6,5,1,3,8,2,4]=>0000000
[7,6,5,1,3,4,8,2]=>0000000
[7,2,6,4,1,3,8,5]=>0000000
[4,6,3,8,5,1,7,2]=>0000000
[2,6,4,3,1,5,7,8]=>0000011
[3,6,4,8,1,7,2,5]=>0000000
[7,3,8,4,1,5,2,6]=>0000000
[4,2,8,3,6,1,5,7]=>0000000
[6,7,5,8,2,1,4,3]=>0000000
[6,8,5,7,2,1,3,4]=>0000000
[6,3,5,2,1,7,4,8]=>0000001
[3,6,5,4,2,8,1,7]=>0000000
[7,4,5,3,8,2,1,6]=>0000000
[1,6,4,7,2,5,3,8]=>1000001
[1,4,3,7,2,6,5,8]=>1000001
[1,5,7,2,4,8,3,6]=>1000000
[1,6,5,7,2,4,3,8]=>1000001
[1,7,6,2,8,3,4,5]=>1000000
[1,4,2,3,5,8,7,6]=>1001100
[1,5,2,3,4,8,7,6]=>1000100
[1,6,5,2,3,8,7,4]=>1000000
[1,7,6,5,2,8,4,3]=>1000000
[1,6,5,2,3,8,4,7]=>1000000
[1,6,7,5,2,3,8,4]=>1000000
[1,7,5,2,8,4,3,6]=>1000000
[1,7,5,6,2,8,3,4]=>1000000
[1,5,7,6,2,4,8,3]=>1000000
[1,4,7,6,2,5,8,3]=>1000000
[1,2,6,5,3,7,4,8]=>1100001
[1,3,7,5,2,6,8,4]=>1000000
[1,7,4,6,2,8,3,5]=>1000000
[1,7,3,5,2,8,4,6]=>1000000
[1,3,7,4,2,6,8,5]=>1000000
[1,4,7,3,2,5,8,6]=>1000000
[1,5,7,3,2,4,8,6]=>1000000
[1,7,3,4,2,8,5,6]=>1000000
[1,7,4,2,8,5,3,6]=>1000000
[1,6,7,4,2,3,8,5]=>1000000
[1,4,3,2,5,8,6,7]=>1001100
[1,5,3,2,4,8,6,7]=>1000100
[1,6,4,2,3,8,5,7]=>1000000
[1,7,6,4,2,8,5,3]=>1000000
[1,6,4,2,3,8,7,5]=>1000000
[1,5,3,2,4,8,7,6]=>1000100
[6,8,5,4,3,2,1,7]=>0000000
[7,6,5,1,3,8,4,2]=>0000000
[5,6,8,4,3,1,7,2]=>0000000
[7,5,8,4,3,2,1,6]=>0000000
[4,8,5,7,3,2,1,6]=>0000000
[7,8,1,2,4,3,5,6]=>0000000
[7,8,2,1,4,3,6,5]=>0000000
[3,4,6,5,7,8,1,2]=>0000000
[4,3,6,5,8,7,1,2]=>0000000
[4,2,6,1,8,3,7,5]=>0000000
[6,7,3,8,4,5,1,2]=>0000000
[6,7,4,5,1,8,2,3]=>0000000
[4,7,5,6,1,8,2,3]=>0000000
[4,5,3,8,6,7,1,2]=>0000000
[5,6,3,8,4,7,1,2]=>0000000
[5,6,2,7,3,4,1,8]=>0000001
[4,5,1,8,6,7,2,3]=>0000000
[7,8,4,5,1,6,2,3]=>0000000
[4,5,2,3,1,8,6,7]=>0000100
[5,6,2,3,1,8,4,7]=>0000000
[5,6,3,4,1,8,2,7]=>0000000
[3,6,4,5,1,8,2,7]=>0000000
[2,6,4,8,1,5,3,7]=>0000000
[2,8,3,4,1,6,5,7]=>0000000
[7,8,1,5,3,6,2,4]=>0000000
[1,6,4,7,3,8,2,5]=>1000000
[1,7,2,8,4,6,3,5]=>1000000
[1,7,5,8,2,6,3,4]=>1000000
[6,7,1,8,2,5,3,4]=>0000000
[6,7,1,8,4,5,2,3]=>0000000
[6,7,5,8,1,4,2,3]=>0000000
[5,8,6,7,2,3,1,4]=>0000000
[6,7,2,3,1,8,4,5]=>0000000
[6,7,2,8,1,4,3,5]=>0000000
[6,7,3,4,1,8,2,5]=>0000000
[2,7,5,8,1,4,3,6]=>0000000
[2,3,1,8,6,7,4,5]=>0010000
[7,8,2,3,1,6,4,5]=>0000000
[2,8,1,4,3,7,5,6]=>0000000
[2,8,1,7,3,5,4,6]=>0000000
[4,5,1,7,3,8,2,6]=>0000000
[3,8,1,5,2,7,4,6]=>0000000
[3,4,1,8,6,7,2,5]=>0000000
[7,8,3,4,1,6,2,5]=>0000000
[2,5,4,1,6,3,8,7]=>0000010
[3,6,5,1,2,4,8,7]=>0000010
[5,6,7,8,1,4,3,2]=>0000000
[2,1,4,7,6,3,8,5]=>0100000
[7,4,3,8,2,1,5,6]=>0000000
[2,4,1,5,8,3,7,6]=>0000000
[2,1,5,8,7,3,4,6]=>0100000
[8,5,7,3,6,1,4,2]=>0000000
[4,2,5,1,6,7,8,3]=>0000000
[6,1,8,5,2,7,4,3]=>0000000
[6,8,7,2,5,3,1,4]=>0000000
[7,8,2,5,6,1,4,3]=>0000000
[7,8,4,2,5,1,6,3]=>0000000
[6,1,2,3,7,5,8,4]=>0000000
[4,1,6,3,5,8,7,2]=>0000000
[8,6,7,1,5,4,3,2]=>0000000
[2,1,6,5,8,4,7,3]=>0100000
[2,6,4,8,7,3,5,1]=>0000000
[7,4,8,6,3,2,5,1]=>0000000
[2,1,8,4,3,7,5,6]=>0100000
[6,3,8,2,4,5,7,1]=>0000000
[5,8,2,4,3,1,6,7]=>0000000
[7,3,5,8,1,4,2,6]=>0000000
[3,8,7,6,1,4,2,5]=>0000000
[5,1,8,3,6,7,2,4]=>0000000
[3,6,1,4,7,8,5,2]=>0000000
[1,6,8,4,7,5,2,3]=>1000000
[6,8,1,3,5,7,2,4]=>0000000
[7,6,1,4,3,8,2,5]=>0000000
[8,4,2,6,7,5,3,1]=>0000000
[7,4,1,6,8,2,5,3]=>0000000
[1,8,6,2,5,3,4,7]=>1000000
[4,7,1,2,5,3,8,6]=>0000000
[5,7,8,6,2,1,4,3]=>0000000
[1,8,6,4,5,2,3,7]=>1000000
[1,4,7,2,6,8,3,5]=>1000000
[2,5,4,3,6,8,1,7]=>0000000
[3,8,5,4,6,2,1,7]=>0000000
[4,8,2,1,3,7,5,6]=>0000000
[1,8,3,2,5,6,7,4]=>1000000
[6,4,1,2,7,5,8,3]=>0000000
[4,3,7,8,5,1,6,2]=>0000000
[1,2,7,3,6,5,8,4]=>1100000
[2,8,7,6,3,4,1,5]=>0000000
[5,8,2,6,3,4,1,7]=>0000000
[1,2,4,5,8,3,7,6]=>1100000
[4,8,1,5,2,3,7,6]=>0000000
[2,4,6,3,7,1,8,5]=>0000000
[6,5,8,7,1,3,4,2]=>0000000
[1,5,2,7,4,3,8,6]=>1000000
[7,6,1,2,8,3,5,4]=>0000000
[6,7,8,1,5,2,4,3]=>0000000
[5,7,8,4,1,2,6,3]=>0000000
[4,7,8,5,6,1,3,2]=>0000000
[6,5,4,1,2,3,8,7]=>0000010
[7,5,1,6,2,3,8,4]=>0000000
[4,5,6,7,8,1,3,2]=>0000000
[8,1,3,6,7,4,5,2]=>0000000
[4,5,3,2,8,1,6,7]=>0000000
[7,4,1,5,3,2,6,8]=>0000001
[8,1,5,4,3,2,6,7]=>0000000
[8,1,6,4,2,5,3,7]=>0000000
[6,5,3,1,2,7,4,8]=>0000001
[5,6,3,8,1,4,2,7]=>0000000
[4,6,3,8,2,1,5,7]=>0000000
[4,7,8,3,2,1,5,6]=>0000000
[5,7,8,3,1,4,2,6]=>0000000
[8,1,7,2,5,4,3,6]=>0000000
[8,1,7,2,4,5,6,3]=>0000000
[7,6,1,2,4,5,8,3]=>0000000
[7,5,1,3,2,6,8,4]=>0000000
[8,1,6,3,2,5,7,4]=>0000000
[5,4,2,3,1,6,8,7]=>0000110
[6,3,2,1,5,7,4,8]=>0000001
[3,6,5,8,2,4,1,7]=>0000000
[6,2,4,5,8,3,1,7]=>0000000
[4,8,1,2,5,6,3,7]=>0000000
[8,1,3,5,2,6,4,7]=>0000000
[5,2,1,6,3,8,4,7]=>0000000
[6,1,4,5,8,3,2,7]=>0000000
[6,5,4,3,8,2,1,7]=>0000000
[4,6,8,3,7,2,5,1]=>0000000
[4,7,8,5,3,1,2,6]=>0000000
[8,5,4,7,6,2,1,3]=>0000000
[5,8,7,3,1,4,6,2]=>0000000
[8,5,7,4,3,6,1,2]=>0000000
[1,3,8,6,4,7,5,2]=>1000000
[7,6,8,1,4,3,2,5]=>0000000
[3,2,6,8,5,7,4,1]=>0000000
[1,6,4,7,2,3,8,5]=>1000000
[3,1,7,5,2,8,4,6]=>0000000
[1,7,4,5,2,8,3,6]=>1000000
[6,3,2,1,7,8,4,5]=>0000000
[5,7,3,8,2,1,4,6]=>0000000
[3,7,1,8,4,2,5,6]=>0000000
[4,2,1,3,7,5,8,6]=>0001000
[8,4,2,1,3,7,6,5]=>0000000
[3,6,2,8,7,1,5,4]=>0000000
[7,3,2,8,1,6,5,4]=>0000000
[3,8,7,2,6,5,4,1]=>0000000
[4,2,7,8,6,1,5,3]=>0000000
[5,8,4,2,7,1,6,3]=>0000000
[8,5,3,1,7,2,6,4]=>0000000
[8,2,1,6,3,7,5,4]=>0000000
[1,4,6,8,2,7,5,3]=>1000000
[8,2,1,7,6,5,4,3]=>0000000
[8,6,7,5,1,4,3,2]=>0000000
[6,4,7,3,2,1,8,5]=>0000000
[4,8,7,3,2,1,6,5]=>0000000
[6,4,3,7,2,1,8,5]=>0000000
[5,3,7,6,2,1,4,8]=>0000001
[3,8,7,6,2,1,4,5]=>0000000
[5,8,4,2,6,1,3,7]=>0000000
[4,8,7,2,5,1,3,6]=>0000000
[4,3,7,2,5,1,8,6]=>0000000
[5,4,2,6,7,1,3,8]=>0000001
[2,8,7,6,5,1,3,4]=>0000000
[6,4,7,3,1,5,8,2]=>0000000
[4,8,7,3,1,5,6,2]=>0000000
[6,5,3,7,1,4,8,2]=>0000000
[6,4,3,7,1,5,8,2]=>0000000
[5,3,7,6,1,4,8,2]=>0000000
[3,8,7,6,1,4,5,2]=>0000000
[5,8,4,2,1,7,3,6]=>0000000
[6,4,7,2,1,5,3,8]=>0000001
[5,8,3,2,1,4,7,6]=>0000000
[6,3,7,2,1,4,5,8]=>0000001
[6,5,2,7,1,4,3,8]=>0000001
[5,8,2,6,1,4,3,7]=>0000000
[2,8,7,6,1,4,3,5]=>0000000
[5,8,4,1,6,7,3,2]=>0000000
[6,5,3,1,8,4,7,2]=>0000000
[6,4,3,1,5,8,7,2]=>0000000
[5,8,2,1,6,4,3,7]=>0000000
[6,4,2,1,5,8,3,7]=>0000000
[4,2,7,1,5,6,3,8]=>0000001
[6,5,1,7,8,4,3,2]=>0000000
[5,4,1,6,7,8,3,2]=>0000000
[4,3,1,6,5,7,8,2]=>0000000
[5,2,1,6,7,4,3,8]=>0000001
[4,2,1,6,5,7,3,8]=>0000001
[6,1,7,8,5,4,3,2]=>0000000
[5,1,7,6,8,4,3,2]=>0000000
[4,5,8,1,7,2,3,6]=>0000000
[8,1,3,5,7,2,4,6]=>0000000
[3,6,8,1,7,2,4,5]=>0000000
[8,2,3,5,6,7,1,4]=>0000000
[8,7,2,1,6,3,4,5]=>0000000
[8,6,4,1,7,5,3,2]=>0000000
[2,3,6,7,8,1,5,4]=>0000000
[3,1,7,2,5,4,8,6]=>0000000
[7,1,8,2,5,3,6,4]=>0000000
[7,3,8,4,5,1,6,2]=>0000000
[8,1,2,6,5,4,3,7]=>0000000
[8,2,7,5,6,1,4,3]=>0000000
[3,6,8,1,7,5,4,2]=>0000000
[8,2,6,7,5,4,1,3]=>0000000
[8,6,7,2,3,1,5,4]=>0000000
[8,1,7,6,5,4,3,2]=>0000000
[8,6,1,5,2,7,4,3]=>0000000
[8,5,1,7,4,2,6,3]=>0000000
[2,1,7,8,3,6,5,4]=>0100000
[7,8,1,5,2,6,3,4]=>0000000
[6,4,1,5,2,3,8,7]=>0000010
[5,3,7,4,6,8,1,2]=>0000000
[4,2,6,3,8,5,1,7]=>0000000
[5,8,2,1,7,6,4,3]=>0000000
[8,3,2,4,1,7,5,6]=>0000000
[7,8,3,1,5,4,6,2]=>0000000
[7,2,8,1,4,6,5,3]=>0000000
[5,7,1,8,3,6,2,4]=>0000000
[4,2,1,3,6,7,8,5]=>0001000
[6,3,5,4,1,2,8,7]=>0000010
[3,4,7,2,8,1,5,6]=>0000000
[4,2,3,5,8,1,6,7]=>0000000
[3,2,4,6,1,5,8,7]=>0000010
[6,5,4,3,1,8,7,2]=>0000000
[8,7,5,4,3,1,6,2]=>0000000
[3,4,6,2,8,5,1,7]=>0000000
[3,4,7,2,8,5,6,1]=>0000000
[3,5,2,6,8,4,1,7]=>0000000
[3,5,2,7,4,8,6,1]=>0000000
[3,5,6,2,8,4,1,7]=>0000000
[3,5,7,2,4,8,6,1]=>0000000
[3,5,7,8,4,1,6,2]=>0000000
[3,5,8,2,4,1,6,7]=>0000000
[3,6,2,7,4,8,5,1]=>0000000
[3,6,2,7,8,5,4,1]=>0000000
[3,6,8,2,4,5,1,7]=>0000000
[3,7,2,1,4,8,6,5]=>0000000
[3,7,2,8,4,5,6,1]=>0000000
[4,1,5,7,3,8,6,2]=>0000000
[4,1,5,7,8,2,6,3]=>0000000
[4,1,5,8,3,2,6,7]=>0000000
[4,1,6,3,7,8,5,2]=>0000000
[4,1,6,3,8,5,2,7]=>0000000
[4,1,6,8,3,5,2,7]=>0000000
[4,1,7,3,8,5,6,2]=>0000000
[4,1,8,3,2,5,6,7]=>0000000
[4,5,2,7,3,8,6,1]=>0000000
[4,5,7,3,2,8,6,1]=>0000000
[4,5,8,3,2,1,6,7]=>0000000
[4,6,2,8,3,5,1,7]=>0000000
[5,1,2,6,8,4,3,7]=>0000000
[5,1,6,3,7,8,2,4]=>0000000
[5,1,6,3,8,4,2,7]=>0000000
[5,1,6,7,4,8,2,3]=>0000000
[5,6,2,7,4,8,1,3]=>0000000
[5,6,2,7,8,4,1,3]=>0000000
[5,7,8,3,4,2,6,1]=>0000000
[6,1,2,3,7,8,5,4]=>0000000
[6,1,2,7,8,5,4,3]=>0000000
[6,7,2,8,4,5,3,1]=>0000000
[7,1,2,3,8,5,6,4]=>0000000
[7,1,8,3,4,5,6,2]=>0000000
[2,4,6,1,8,5,7,3]=>0000000
[3,5,8,6,1,2,4,7]=>0000000
[3,5,1,8,2,4,7,6]=>0000000
[3,1,6,8,2,4,7,5]=>0000000
[5,6,4,8,2,1,7,3]=>0000000
[2,5,7,8,6,3,1,4]=>0000000
[2,4,8,1,5,6,7,3]=>0000000
[8,4,1,2,5,6,3,7]=>0000000
[8,3,1,6,5,2,4,7]=>0000000
[2,5,3,8,7,6,1,4]=>0000000
[5,1,8,4,7,6,3,2]=>0000000
[8,2,3,6,5,1,7,4]=>0000000
[4,8,6,5,7,3,2,1]=>0000000
[4,8,5,6,7,3,2,1]=>0000000
[7,2,8,6,5,4,1,3]=>0000000
[6,3,2,8,5,1,7,4]=>0000000
[6,8,5,4,3,1,7,2]=>0000000
[7,6,3,8,5,2,1,4]=>0000000
[5,8,7,4,1,6,3,2]=>0000000
[6,8,3,4,5,1,7,2]=>0000000
[5,2,8,4,1,6,7,3]=>0000000
[4,1,3,6,8,2,5,7]=>0000000
[8,3,2,1,5,4,7,6]=>0000000
[2,5,1,8,4,3,7,6]=>0000000
[5,3,6,2,4,8,1,7]=>0000000
[1,6,2,4,5,8,3,7]=>1000000
[5,3,2,1,6,8,4,7]=>0000000
[2,6,5,8,1,3,4,7]=>0000000
[8,3,4,1,5,2,7,6]=>0000000
[8,2,6,4,1,7,3,5]=>0000000
[5,4,6,8,1,2,7,3]=>0000000
[3,4,7,8,6,2,5,1]=>0000000
[7,5,8,2,4,6,1,3]=>0000000
[8,2,7,4,6,1,3,5]=>0000000
[4,7,3,2,8,1,6,5]=>0000000
[1,2,8,3,5,6,7,4]=>1100000
[4,2,3,7,1,8,6,5]=>0000000
[3,2,6,4,8,1,7,5]=>0000000
[8,2,1,6,7,3,4,5]=>0000000
[2,7,8,5,4,1,3,6]=>0000000
[1,7,5,3,8,4,2,6]=>1000000
[4,7,5,3,1,2,8,6]=>0000000
[5,6,7,3,8,4,2,1]=>0000000
[5,7,3,2,4,1,8,6]=>0000000
[8,4,1,3,7,2,5,6]=>0000000
[2,8,4,7,1,3,5,6]=>0000000
[3,5,2,8,6,1,7,4]=>0000000
[1,7,6,3,2,5,8,4]=>1000000
[3,8,1,5,6,2,7,4]=>0000000
[7,1,5,2,8,6,4,3]=>0000000
[1,8,5,3,6,2,7,4]=>1000000
[6,5,8,7,2,1,3,4]=>0000000
[3,6,2,1,7,5,8,4]=>0000000
[4,7,2,6,5,8,1,3]=>0000000
[6,8,1,4,2,7,3,5]=>0000000
[6,3,4,7,1,8,2,5]=>0000000
[3,4,7,8,2,5,6,1]=>0000000
[1,8,2,4,5,6,7,3]=>1000000
[3,2,5,7,6,1,8,4]=>0000000
[4,3,5,6,1,8,7,2]=>0000000
[1,2,3,4,8,6,5,7]=>1111000
[1,2,3,8,5,4,6,7]=>1110000
[1,2,3,8,5,6,4,7]=>1110000
[1,2,3,8,6,5,4,7]=>1110000
[1,8,3,4,2,5,6,7]=>1000000
[1,2,8,5,4,3,6,7]=>1100000
[1,8,4,3,2,5,6,7]=>1000000
[8,4,7,3,6,5,2,1]=>0000000
[8,1,7,4,6,5,3,2]=>0000000
[8,4,7,1,6,5,3,2]=>0000000
[8,3,7,1,6,5,4,2]=>0000000
[8,2,7,1,6,5,4,3]=>0000000
[8,1,7,2,6,5,4,3]=>0000000
[8,3,7,1,6,4,5,2]=>0000000
[8,4,7,2,6,3,5,1]=>0000000
[8,4,7,6,5,2,3,1]=>0000000
[8,3,7,6,5,1,4,2]=>0000000
[8,4,7,5,6,1,3,2]=>0000000
[8,1,7,3,6,2,5,4]=>0000000
[8,3,7,2,6,1,5,4]=>0000000
[8,5,7,2,6,1,4,3]=>0000000
[8,7,6,1,5,2,4,3]=>0000000
[4,6,7,3,8,5,2,1]=>0000000
[1,4,8,2,6,3,5,7]=>1000000
[1,6,2,4,8,3,5,7]=>1000000
[1,5,2,3,8,4,7,6]=>1000000
[1,7,2,3,5,4,8,6]=>1000000
[1,8,2,3,5,4,6,7]=>1000000
[1,7,8,2,4,5,3,6]=>1000000
[1,2,8,3,6,4,5,7]=>1100000
[1,5,8,2,3,7,4,6]=>1000000
[1,6,8,2,3,5,4,7]=>1000000
[5,7,2,6,3,8,1,4]=>0000000
[5,7,1,6,8,4,3,2]=>0000000
[4,8,1,2,5,7,3,6]=>0000000
[3,7,5,4,8,2,1,6]=>0000000
[4,7,1,3,2,8,6,5]=>0000000
[2,7,3,1,5,8,4,6]=>0000000
[3,8,7,1,6,4,5,2]=>0000000
[4,3,2,1,5,8,6,7]=>0001100
[4,1,3,7,5,6,8,2]=>0000000
[3,4,6,1,5,8,2,7]=>0000000
[6,5,8,7,1,4,2,3]=>0000000
[4,1,7,3,8,5,2,6]=>0000000
[5,6,8,7,2,4,1,3]=>0000000
[7,1,3,4,2,8,5,6]=>0000000
[7,6,1,4,3,5,8,2]=>0000000
[3,5,4,1,6,7,8,2]=>0000000
[2,5,3,4,8,6,1,7]=>0000000
[2,4,8,3,6,1,7,5]=>0000000
[6,8,2,1,5,7,3,4]=>0000000
[1,2,4,8,6,5,3,7]=>1100000
[7,1,5,6,8,4,3,2]=>0000000
[7,3,5,6,1,4,8,2]=>0000000
[3,7,6,5,1,4,8,2]=>0000000
[2,7,6,5,3,8,1,4]=>0000000
[2,7,8,1,4,6,3,5]=>0000000
[4,1,6,8,5,3,7,2]=>0000000
[5,2,6,4,8,3,1,7]=>0000000
[1,2,6,3,4,8,7,5]=>1100000
[5,3,6,1,4,7,8,2]=>0000000
[6,7,1,3,4,5,8,2]=>0000000
[1,7,3,2,4,8,5,6]=>1000000
[6,1,4,2,8,3,5,7]=>0000000
[5,8,6,7,2,1,4,3]=>0000000
[8,6,1,3,5,4,2,7]=>0000000
[2,7,6,3,4,5,8,1]=>0000000
[5,3,8,6,1,2,4,7]=>0000000
[3,8,7,2,6,4,5,1]=>0000000
[4,5,8,7,2,6,3,1]=>0000000
[8,5,2,7,1,4,3,6]=>0000000
[3,7,5,8,2,6,1,4]=>0000000
[1,6,7,4,8,2,3,5]=>1000000
[8,2,1,3,5,6,7,4]=>0000000
[4,1,3,8,2,6,7,5]=>0000000
[3,6,1,4,7,2,8,5]=>0000000
[6,2,7,4,5,8,1,3]=>0000000
[1,8,5,7,3,2,4,6]=>1000000
[3,2,1,6,4,8,5,7]=>0010000
[2,7,4,1,5,3,8,6]=>0000000
[7,4,8,6,2,3,1,5]=>0000000
[7,3,2,4,8,6,1,5]=>0000000
[5,1,7,4,2,3,8,6]=>0000000
[4,8,5,3,6,2,7,1]=>0000000
[5,7,4,3,6,2,8,1]=>0000000
[6,7,5,1,2,8,3,4]=>0000000
[7,5,1,4,2,6,8,3]=>0000000
[5,2,6,8,3,4,7,1]=>0000000
[6,2,7,5,8,3,1,4]=>0000000
[2,1,5,6,8,3,7,4]=>0100000
[1,2,7,4,8,3,6,5]=>1100000
[1,6,8,3,2,7,4,5]=>1000000
[5,7,3,8,2,4,6,1]=>0000000
[5,7,3,6,4,8,2,1]=>0000000
[3,6,2,4,7,1,8,5]=>0000000
[4,2,8,5,1,6,7,3]=>0000000
[1,2,8,3,7,5,4,6]=>1100000
[1,6,3,8,7,4,2,5]=>1000000
[3,8,5,7,1,4,2,6]=>0000000
[4,7,2,5,1,3,8,6]=>0000000
[5,1,7,4,8,6,3,2]=>0000000
[3,6,5,2,1,8,7,4]=>0000000
[5,2,7,4,1,3,6,8]=>0000001
[5,2,6,4,1,8,7,3]=>0000000
[6,3,2,1,4,8,7,5]=>0000000
[5,4,7,6,3,8,1,2]=>0000000
[4,6,3,7,5,8,1,2]=>0000000
[5,7,4,3,8,1,2,6]=>0000000
[1,5,7,4,8,6,3,2]=>1000000
[1,8,2,7,6,5,4,3]=>1000000
[3,8,1,6,7,5,4,2]=>0000000
[3,7,2,6,8,5,1,4]=>0000000
[8,2,4,3,6,1,5,7]=>0000000
[1,7,8,5,4,3,6,2]=>1000000
[7,3,8,1,4,2,6,5]=>0000000
[1,8,4,5,3,2,6,7]=>1000000
[3,7,8,1,2,6,5,4]=>0000000
[1,6,4,5,7,2,3,8]=>1000001
[8,3,6,1,7,2,4,5]=>0000000
[7,3,5,2,1,8,4,6]=>0000000
[6,4,2,8,7,5,1,3]=>0000000
[1,5,3,6,8,7,4,2]=>1000000
[3,5,4,6,1,8,2,7]=>0000000
[3,1,5,7,6,8,2,4]=>0000000
[6,4,5,7,2,8,1,3]=>0000000
[2,6,3,5,4,8,1,7]=>0000000
[3,7,4,5,6,8,1,2]=>0000000
[2,5,7,3,6,8,1,4]=>0000000
[5,4,3,1,8,2,7,6]=>0000000
[1,2,8,3,5,4,6,7]=>1100000
[1,7,8,4,3,5,6,2]=>1000000
[3,1,6,8,4,5,7,2]=>0000000
[1,4,5,8,3,6,7,2]=>1000000
[2,5,7,1,8,3,6,4]=>0000000
[6,2,7,1,8,4,5,3]=>0000000
[4,7,1,3,8,5,6,2]=>0000000
[3,7,2,1,8,4,5,6]=>0000000
[4,2,7,1,8,3,6,5]=>0000000
[4,3,1,6,8,2,7,5]=>0000000
[5,3,4,6,8,2,7,1]=>0000000
[3,5,1,6,8,2,7,4]=>0000000
[5,8,3,2,6,4,1,7]=>0000000
[7,3,8,2,6,4,1,5]=>0000000
[3,8,7,4,5,6,1,2]=>0000000
[2,7,6,3,5,4,1,8]=>0000001
[3,8,7,4,6,2,5,1]=>0000000
[5,8,3,7,6,2,4,1]=>0000000
[5,8,7,4,3,6,2,1]=>0000000
[5,8,6,4,3,7,1,2]=>0000000
[6,5,8,4,3,1,7,2]=>0000000
[2,6,4,7,1,5,3,8]=>0000001
[2,5,6,8,4,3,7,1]=>0000000
[5,3,8,1,7,6,4,2]=>0000000
[5,4,8,7,1,6,3,2]=>0000000
[4,8,6,7,5,3,1,2]=>0000000
[4,8,6,5,7,2,1,3]=>0000000
[6,2,1,5,8,3,7,4]=>0000000
[5,8,3,2,7,6,4,1]=>0000000
[5,8,3,2,6,7,1,4]=>0000000
[6,5,3,2,8,1,7,4]=>0000000
[6,4,3,2,1,8,7,5]=>0000000
[6,3,4,1,2,8,7,5]=>0000000
[5,2,1,4,3,6,7,8]=>0000111
[4,6,3,2,5,1,7,8]=>0000011
[3,5,7,4,2,6,1,8]=>0000001
[4,3,6,1,5,2,7,8]=>0000011
[4,2,1,5,7,6,3,8]=>0000001
[3,5,4,7,1,6,2,8]=>0000001
[3,4,5,8,6,7,1,2]=>0000000
[4,3,5,1,6,8,7,2]=>0000000
[2,1,5,3,8,4,7,6]=>0100000
[3,1,8,2,5,4,7,6]=>0000000
[8,1,3,2,6,4,7,5]=>0000000
[3,1,8,2,6,4,7,5]=>0000000
[2,1,8,3,6,4,7,5]=>0100000
[2,1,7,3,5,4,8,6]=>0100000
[2,1,7,3,6,4,8,5]=>0100000
[2,1,7,3,8,4,6,5]=>0100000
[8,1,4,2,7,3,6,5]=>0000000
[4,1,7,2,8,3,6,5]=>0000000
[3,1,7,2,8,4,6,5]=>0000000
[3,1,6,2,5,4,8,7]=>0000010
[7,1,3,2,6,4,8,5]=>0000000
[7,1,8,2,4,3,6,5]=>0000000
[7,1,5,2,8,3,6,4]=>0000000
[4,1,6,2,5,3,8,7]=>0000010
[4,1,7,2,5,3,8,6]=>0000000
[4,1,7,2,6,3,8,5]=>0000000
[5,1,7,2,6,3,8,4]=>0000000
[5,1,7,2,8,3,6,4]=>0000000
[8,1,5,2,7,3,6,4]=>0000000
[8,1,5,2,6,3,7,4]=>0000000
[5,1,8,2,6,3,7,4]=>0000000
[5,1,6,2,8,3,7,4]=>0000000
[3,1,6,2,8,4,7,5]=>0000000
[4,1,8,2,6,3,7,5]=>0000000
[8,1,4,2,6,3,7,5]=>0000000
[8,1,4,2,5,3,7,6]=>0000000
[4,1,8,2,5,3,7,6]=>0000000
[4,1,5,2,8,3,7,6]=>0000000
[3,1,5,2,8,4,7,6]=>0000000
[5,1,4,2,8,3,7,6]=>0000000
[6,1,3,2,8,4,7,5]=>0000000
[6,1,3,2,7,4,8,5]=>0000000
[6,1,4,2,7,3,8,5]=>0000000
[6,1,7,2,8,3,5,4]=>0000000
[7,8,3,1,2,5,6,4]=>0000000
[7,8,1,3,2,4,6,5]=>0000000
[6,2,8,1,3,5,4,7]=>0000000
[6,2,8,3,1,7,4,5]=>0000000
[3,2,5,7,1,8,4,6]=>0000000
[3,5,2,8,1,7,4,6]=>0000000
[5,1,3,7,2,6,8,4]=>0000000
[2,5,4,6,8,1,7,3]=>0000000
[4,3,5,7,6,8,1,2]=>0000000
[7,6,4,3,2,1,8,5]=>0000000
[7,6,5,8,2,1,4,3]=>0000000
[7,8,4,3,2,1,6,5]=>0000000
[7,6,3,8,2,1,5,4]=>0000000
[7,6,5,8,4,1,3,2]=>0000000
[7,4,8,3,2,1,6,5]=>0000000
[7,6,8,5,2,1,4,3]=>0000000
[4,8,6,1,7,5,2,3]=>0000000
[4,8,7,2,6,5,1,3]=>0000000
[8,4,7,3,6,5,1,2]=>0000000
[6,8,4,3,7,2,1,5]=>0000000
[6,7,4,2,8,3,1,5]=>0000000
[2,8,7,6,5,1,4,3]=>0000000
[7,3,2,5,4,1,6,8]=>0000001
[7,1,4,2,6,3,5,8]=>0000001
[7,3,2,5,1,6,4,8]=>0000001
[7,4,1,3,5,2,6,8]=>0000001
[2,3,6,1,4,8,7,5]=>0000000
[5,6,8,2,4,1,3,7]=>0000000
[5,6,8,7,4,3,1,2]=>0000000
[2,4,8,1,6,3,7,5]=>0000000
[1,8,4,5,2,6,7,3]=>1000000
[5,6,7,3,2,8,1,4]=>0000000
[5,3,2,1,4,8,6,7]=>0000100
[3,4,7,8,1,2,6,5]=>0000000
[3,6,7,8,1,4,5,2]=>0000000
[2,3,6,8,5,1,4,7]=>0000000
[3,1,6,4,8,2,5,7]=>0000000
[7,3,2,6,8,5,1,4]=>0000000
[5,7,8,3,1,4,6,2]=>0000000
[7,4,8,3,2,5,1,6]=>0000000
[7,3,8,2,4,5,6,1]=>0000000
[4,2,7,1,5,3,8,6]=>0000000
[1,2,7,3,4,8,6,5]=>1100000
[4,7,2,1,5,8,6,3]=>0000000
[4,8,3,6,5,1,7,2]=>0000000
[6,4,7,3,5,1,8,2]=>0000000
[3,1,6,4,7,8,2,5]=>0000000
[1,2,5,8,3,7,4,6]=>1100000
[8,2,4,1,7,5,6,3]=>0000000
[3,8,4,7,5,1,6,2]=>0000000
[8,4,3,6,1,7,5,2]=>0000000
[2,1,8,6,7,3,5,4]=>0100000
[1,2,8,6,3,4,7,5]=>1100000
[7,3,2,5,6,1,4,8]=>0000001
[8,4,1,2,7,5,3,6]=>0000000
[1,5,2,8,6,3,7,4]=>1000000
[5,8,6,3,1,7,4,2]=>0000000
[7,8,1,4,2,5,3,6]=>0000000
[5,6,2,7,1,3,4,8]=>0000001
[1,6,2,7,4,8,3,5]=>1000000
[6,2,1,7,8,5,3,4]=>0000000
[6,7,3,8,4,1,5,2]=>0000000
[2,7,1,8,5,6,3,4]=>0000000
[2,1,7,8,6,3,4,5]=>0100000
[7,8,6,2,1,3,5,4]=>0000000
[6,1,3,4,2,8,7,5]=>0000000
[7,1,3,8,6,4,5,2]=>0000000
[7,4,2,1,8,6,5,3]=>0000000
[2,1,6,3,4,8,7,5]=>0100000
[8,1,4,2,5,6,7,3]=>0000000
[8,1,3,2,5,6,7,4]=>0000000
[2,1,4,8,7,5,3,6]=>0100000
[7,1,5,8,2,6,3,4]=>0000000
[3,6,8,2,4,1,5,7]=>0000000
[6,2,8,1,7,5,4,3]=>0000000
[7,8,5,6,4,1,3,2]=>0000000
[3,8,1,4,5,6,2,7]=>0000000
[5,8,7,3,6,1,4,2]=>0000000
[5,8,3,7,6,1,4,2]=>0000000
[7,5,8,4,6,1,3,2]=>0000000
[2,4,8,1,3,7,6,5]=>0000000
[2,5,1,3,8,4,7,6]=>0000000
[2,8,1,5,4,7,3,6]=>0000000
[8,3,2,6,1,4,7,5]=>0000000
[2,5,7,1,3,8,6,4]=>0000000
[2,7,1,6,5,3,8,4]=>0000000
[2,8,1,7,6,5,4,3]=>0000000
[8,3,2,7,1,6,5,4]=>0000000
[7,4,2,8,1,6,5,3]=>0000000
[8,7,5,3,2,1,6,4]=>0000000
[7,4,5,8,6,2,1,3]=>0000000
[4,6,8,5,1,7,3,2]=>0000000
[4,7,5,1,3,8,6,2]=>0000000
[5,1,7,6,4,2,8,3]=>0000000
[5,1,8,7,6,4,3,2]=>0000000
[5,1,6,2,8,7,4,3]=>0000000
[4,5,6,1,8,7,2,3]=>0000000
[3,5,6,8,7,1,4,2]=>0000000
[3,6,1,7,4,8,2,5]=>0000000
[8,4,2,6,3,1,5,7]=>0000000
[3,4,8,7,1,2,6,5]=>0000000
[3,4,6,8,5,7,1,2]=>0000000
[4,6,8,3,5,7,2,1]=>0000000
[4,7,3,5,8,2,6,1]=>0000000
[5,6,8,3,7,2,1,4]=>0000000
[5,6,8,4,2,7,3,1]=>0000000
[6,5,2,7,1,3,8,4]=>0000000
[6,5,4,1,7,2,8,3]=>0000000
[6,4,7,3,1,8,2,5]=>0000000
[5,6,3,7,4,2,1,8]=>0000001
[6,1,3,8,5,2,4,7]=>0000000
[7,4,2,6,3,5,1,8]=>0000001
[3,4,7,5,6,2,1,8]=>0000001
[8,1,3,4,5,2,6,7]=>0000000
[1,6,8,4,2,5,3,7]=>1000000
[8,7,2,3,6,1,4,5]=>0000000
[1,4,8,5,2,6,7,3]=>1000000
[6,1,8,4,3,7,2,5]=>0000000
[1,5,2,4,8,7,3,6]=>1000000
[3,2,6,4,1,8,7,5]=>0000000
[7,6,4,3,1,8,2,5]=>0000000
[8,4,6,5,1,7,2,3]=>0000000
[7,5,4,6,1,2,8,3]=>0000000
[3,2,5,6,1,7,8,4]=>0000000
[3,2,8,7,6,1,4,5]=>0000000
[6,8,4,7,2,1,3,5]=>0000000
[3,8,7,5,6,1,2,4]=>0000000
[8,2,7,6,5,1,3,4]=>0000000
[4,8,6,7,1,5,3,2]=>0000000
[1,8,6,7,2,3,4,5]=>1000000
[3,5,4,2,7,1,8,6]=>0000000
[3,2,6,1,5,7,4,8]=>0000001
[5,2,1,4,7,6,3,8]=>0000001
[4,2,1,3,5,8,7,6]=>0001100
[7,4,1,5,3,6,8,2]=>0000000
[6,8,3,4,1,5,2,7]=>0000000
[5,8,4,1,7,2,6,3]=>0000000
[4,1,8,3,5,7,2,6]=>0000000
[2,4,6,3,5,8,1,7]=>0000000
[4,5,7,2,3,6,8,1]=>0000000
[2,6,3,4,7,5,8,1]=>0000000
[4,5,2,7,1,6,8,3]=>0000000
[2,3,1,7,6,4,8,5]=>0010000
[3,4,1,6,5,8,2,7]=>0000000
[6,4,2,8,7,1,5,3]=>0000000
[3,1,8,2,7,6,4,5]=>0000000
[6,2,8,4,1,7,5,3]=>0000000
[3,6,4,7,2,5,1,8]=>0000001
[7,3,2,8,6,1,4,5]=>0000000
[4,3,8,7,1,2,5,6]=>0000000
[1,2,5,8,4,7,3,6]=>1100000
[1,3,6,8,5,2,7,4]=>1000000
[2,5,7,4,1,8,6,3]=>0000000
[1,4,2,5,8,7,3,6]=>1000000
[3,5,1,7,2,8,6,4]=>0000000
[4,6,3,1,7,8,5,2]=>0000000
[5,3,1,6,7,8,4,2]=>0000000
[2,1,3,4,8,7,5,6]=>0111000
[4,8,7,3,6,5,1,2]=>0000000
[4,3,8,7,6,5,1,2]=>0000000
[2,8,7,6,1,5,4,3]=>0000000
[5,2,8,7,6,1,4,3]=>0000000
[6,2,8,7,5,1,4,3]=>0000000
[7,8,2,6,5,1,4,3]=>0000000
[6,1,8,7,5,4,3,2]=>0000000
[4,1,8,7,6,5,3,2]=>0000000
[3,1,8,7,6,5,4,2]=>0000000
[7,8,2,6,1,5,4,3]=>0000000
[4,2,8,1,7,6,5,3]=>0000000
[3,2,8,1,7,6,5,4]=>0000000
[2,8,7,1,6,5,4,3]=>0000000
[3,8,2,1,7,6,5,4]=>0000000
[4,8,2,7,6,1,5,3]=>0000000
[3,8,2,7,1,6,5,4]=>0000000
[3,8,7,2,1,6,5,4]=>0000000
[4,8,7,2,6,1,5,3]=>0000000
[5,8,7,6,2,1,4,3]=>0000000
[6,5,8,7,1,4,3,2]=>0000000
[3,8,7,1,6,5,4,2]=>0000000
[4,8,1,7,6,5,3,2]=>0000000
[5,4,1,8,7,6,3,2]=>0000000
[6,4,8,1,7,5,3,2]=>0000000
[7,8,4,1,6,5,3,2]=>0000000
[7,8,3,1,6,5,4,2]=>0000000
[5,3,1,8,7,6,4,2]=>0000000
[4,3,1,8,7,6,5,2]=>0000000
[4,2,1,8,7,6,5,3]=>0000000
[6,5,3,1,8,7,4,2]=>0000000
[5,4,2,1,8,7,6,3]=>0000000
[8,6,1,4,2,3,5,7]=>0000000
[6,8,1,4,2,3,5,7]=>0000000
[4,6,2,3,8,1,5,7]=>0000000
[6,4,2,3,8,1,5,7]=>0000000
[2,8,4,3,6,1,5,7]=>0000000
[2,4,8,3,6,1,5,7]=>0000000
[8,3,6,2,4,1,5,7]=>0000000
[8,3,6,2,1,4,5,7]=>0000000
[2,1,8,3,6,4,5,7]=>0100000
[6,3,8,2,1,4,5,7]=>0000000
[3,6,4,7,8,5,1,2]=>0000000
[1,6,4,2,7,5,8,3]=>1000000
[3,4,6,8,7,5,1,2]=>0000000
[5,4,6,3,8,7,1,2]=>0000000
[6,4,8,5,3,7,1,2]=>0000000
[1,8,5,2,6,3,7,4]=>1000000
[1,4,6,2,8,5,7,3]=>1000000
[7,8,1,4,2,5,6,3]=>0000000
[4,8,5,3,1,6,2,7]=>0000000
[5,2,8,6,4,1,3,7]=>0000000
[5,1,6,2,8,7,3,4]=>0000000
[6,1,8,7,4,2,3,5]=>0000000
[1,2,8,5,7,3,6,4]=>1100000
[1,3,6,8,7,5,2,4]=>1000000
[7,8,1,2,4,6,5,3]=>0000000
[1,2,6,4,8,7,5,3]=>1100000
[1,8,2,5,4,7,6,3]=>1000000
[1,2,7,3,5,8,6,4]=>1100000
[4,6,2,1,7,5,3,8]=>0000001
[4,6,2,3,7,8,1,5]=>0000000
[4,2,1,3,5,7,8,6]=>0001100
[7,8,3,2,4,1,6,5]=>0000000
[7,8,4,2,6,3,1,5]=>0000000
[5,8,2,7,4,3,1,6]=>0000000
[7,5,2,8,3,4,1,6]=>0000000
[6,4,3,5,2,8,1,7]=>0000000
[4,1,3,6,5,8,7,2]=>0000000
[2,4,1,3,8,5,7,6]=>0001000
[2,4,1,3,5,8,7,6]=>0001100
[4,6,1,3,5,8,7,2]=>0000000
[1,4,6,3,5,8,7,2]=>1000000
[4,2,1,3,6,5,7,8]=>0001011
[4,2,1,8,3,5,7,6]=>0000000
[6,2,1,8,3,5,7,4]=>0000000
[6,4,1,3,8,5,7,2]=>0000000
[8,2,1,3,6,5,7,4]=>0000000
[8,2,1,4,3,5,7,6]=>0000000
[8,1,4,6,3,5,7,2]=>0000000
[2,4,8,1,3,5,7,6]=>0000000
[4,6,8,1,3,5,7,2]=>0000000
[4,6,1,8,3,5,7,2]=>0000000
[4,1,6,8,3,5,7,2]=>0000000
[1,4,6,8,3,5,7,2]=>1000000
[1,4,6,3,8,5,7,2]=>1000000
[4,6,1,3,8,5,7,2]=>0000000
[2,6,1,3,8,5,7,4]=>0000000
[2,6,1,8,3,5,7,4]=>0000000
[2,1,3,6,8,5,7,4]=>0110000
[4,1,3,6,8,5,7,2]=>0000000
[1,4,3,6,8,5,7,2]=>1000000
[2,1,8,3,6,5,7,4]=>0100000
[2,1,8,6,3,5,7,4]=>0100000
[2,1,8,4,3,5,7,6]=>0100000
[2,8,4,1,3,5,7,6]=>0000000
[6,8,1,4,3,5,7,2]=>0000000
[1,8,6,4,3,5,7,2]=>1000000
[8,6,1,4,3,5,7,2]=>0000000
[8,6,4,1,3,5,7,2]=>0000000
[8,4,2,1,3,5,7,6]=>0000000
[8,5,7,4,3,2,1,6]=>0000000
[8,7,6,5,1,4,3,2]=>0000000
[8,7,3,6,5,2,1,4]=>0000000
[6,5,8,4,3,2,1,7]=>0000000
[8,4,7,6,3,2,1,5]=>0000000
[5,8,7,4,3,2,1,6]=>0000000
[4,5,2,7,3,1,8,6]=>0000000
[4,8,2,6,3,5,7,1]=>0000000
[8,6,1,2,7,4,3,5]=>0000000
[4,6,2,1,7,8,5,3]=>0000000
[2,3,8,7,4,1,6,5]=>0000000
[7,8,2,1,5,6,4,3]=>0000000
[1,6,2,5,8,4,3,7]=>1000000
[5,2,7,1,8,6,3,4]=>0000000
[1,2,8,3,7,6,5,4]=>1100000
[6,5,2,8,1,7,3,4]=>0000000
[2,8,3,5,1,7,4,6]=>0000000
[2,8,5,6,1,7,3,4]=>0000000
[5,4,2,8,6,1,7,3]=>0000000
[8,3,7,4,2,6,5,1]=>0000000
[6,3,2,8,4,1,7,5]=>0000000
[2,8,3,4,1,7,5,6]=>0000000
[5,4,2,8,3,1,7,6]=>0000000
[2,8,6,4,1,7,5,3]=>0000000
[8,4,7,6,2,5,3,1]=>0000000
[4,8,7,6,1,5,3,2]=>0000000
[7,3,8,5,2,1,6,4]=>0000000
[7,3,8,4,2,1,6,5]=>0000000
[7,5,4,3,8,2,1,6]=>0000000
[5,4,2,3,8,1,6,7]=>0000000
[3,7,8,4,1,2,6,5]=>0000000
[7,3,4,8,2,1,5,6]=>0000000
[7,5,8,6,2,1,4,3]=>0000000
[6,5,8,7,3,1,4,2]=>0000000
[2,4,8,3,1,5,7,6]=>0000000
[6,3,2,4,8,1,5,7]=>0000000
[2,4,3,8,1,6,5,7]=>0000000
[2,3,8,4,1,6,7,5]=>0000000
[3,4,8,7,1,5,6,2]=>0000000
[2,5,3,8,1,6,4,7]=>0000000
[3,7,4,8,1,5,2,6]=>0000000
[2,6,8,5,1,3,7,4]=>0000000
[2,6,8,4,1,3,7,5]=>0000000
[3,7,5,8,1,4,2,6]=>0000000
[2,6,5,8,1,4,3,7]=>0000000
[2,5,8,3,1,4,7,6]=>0000000
[4,7,6,8,1,3,2,5]=>0000000
[5,6,8,7,1,3,4,2]=>0000000
[8,7,4,1,6,2,5,3]=>0000000
[6,4,7,2,8,5,1,3]=>0000000
[1,7,6,2,4,3,5,8]=>1000001
[8,7,3,2,4,6,5,1]=>0000000
[6,4,7,3,8,5,2,1]=>0000000
[2,7,1,5,6,3,4,8]=>0000001
[3,6,4,1,2,8,7,5]=>0000000
[3,6,5,1,8,2,7,4]=>0000000
[4,6,5,1,8,7,2,3]=>0000000
[5,7,1,4,8,6,2,3]=>0000000
[5,7,1,3,8,2,6,4]=>0000000
[6,3,7,2,8,4,5,1]=>0000000
[6,7,1,8,3,2,5,4]=>0000000
[8,7,6,1,4,5,2,3]=>0000000
[8,7,6,1,3,2,5,4]=>0000000
[8,7,3,5,1,2,6,4]=>0000000
[8,7,4,5,1,6,2,3]=>0000000
[8,5,6,4,1,7,2,3]=>0000000
[8,4,6,2,3,1,7,5]=>0000000
[4,7,3,5,2,1,6,8]=>0000001
[6,7,8,4,1,5,3,2]=>0000000
[7,1,6,8,4,5,3,2]=>0000000
[7,5,1,6,4,2,3,8]=>0000001
[8,1,5,7,4,6,3,2]=>0000000
[1,8,4,6,7,5,3,2]=>1000000
[6,1,8,4,7,5,3,2]=>0000000
[4,8,5,1,6,7,3,2]=>0000000
[8,4,1,5,6,7,3,2]=>0000000
[8,1,4,5,6,7,3,2]=>0000000
[1,8,4,6,2,5,3,7]=>1000000
[8,5,6,1,2,4,3,7]=>0000000
[2,8,3,1,5,6,7,4]=>0000000
[8,3,2,7,1,5,6,4]=>0000000
[3,2,8,5,7,1,6,4]=>0000000
[3,6,2,8,5,1,7,4]=>0000000
[6,2,1,8,4,7,5,3]=>0000000
[2,8,7,1,4,6,5,3]=>0000000
[8,2,7,1,5,4,6,3]=>0000000
[7,3,1,5,6,2,4,8]=>0000001
[7,2,8,1,6,4,5,3]=>0000000
[7,8,2,6,4,1,5,3]=>0000000
[8,7,2,4,1,6,5,3]=>0000000
[1,2,8,6,3,7,5,4]=>1100000
[1,8,7,2,3,6,5,4]=>1000000
[1,7,8,2,6,4,3,5]=>1000000
[2,1,7,3,6,8,4,5]=>0100000
[7,1,5,8,3,2,4,6]=>0000000
[7,8,1,5,2,4,3,6]=>0000000
[8,7,1,2,5,4,3,6]=>0000000
[1,6,2,8,4,3,7,5]=>1000000
[1,8,3,7,2,5,4,6]=>1000000
[8,1,4,7,3,2,5,6]=>0000000
[4,7,8,1,3,2,5,6]=>0000000
[2,1,8,3,5,7,4,6]=>0100000
[1,2,3,4,8,5,7,6]=>1111000
[3,7,2,5,6,4,1,8]=>0000001
[7,6,2,5,4,3,1,8]=>0000001
[4,7,5,2,6,3,1,8]=>0000001
[5,6,7,2,4,3,1,8]=>0000001
[2,8,3,4,1,6,7,5]=>0000000
[6,1,3,5,7,2,4,8]=>0000001
[8,1,3,6,2,4,7,5]=>0000000
[2,1,8,3,7,5,4,6]=>0100000
[7,1,8,2,5,6,3,4]=>0000000
[6,1,5,8,2,7,3,4]=>0000000
[6,2,5,8,1,4,7,3]=>0000000
[3,2,8,5,1,6,7,4]=>0000000
[1,3,8,2,5,7,4,6]=>1000000
[2,8,7,1,6,4,5,3]=>0000000
[3,8,7,1,5,6,4,2]=>0000000
[4,8,7,5,1,6,3,2]=>0000000
[5,8,6,7,1,4,3,2]=>0000000
[6,7,8,5,1,4,3,2]=>0000000
[5,6,3,8,4,1,7,2]=>0000000
[7,3,8,5,4,1,6,2]=>0000000
[8,3,7,4,1,6,5,2]=>0000000
[3,5,6,8,4,1,7,2]=>0000000
[5,6,4,7,8,1,3,2]=>0000000
[6,2,3,1,5,4,7,8]=>0000011
[8,5,1,3,2,4,7,6]=>0000000
[7,5,1,3,2,6,4,8]=>0000001
[3,6,4,1,5,2,7,8]=>0000011
[4,5,6,1,3,2,7,8]=>0000011
[6,7,1,4,2,5,3,8]=>0000001
[2,7,1,3,5,6,4,8]=>0000001
[8,6,1,2,4,3,7,5]=>0000000
[7,8,1,2,5,3,6,4]=>0000000
[1,8,2,7,5,4,6,3]=>1000000
[1,8,6,3,7,2,4,5]=>1000000
[1,8,2,5,4,6,7,3]=>1000000
[7,2,8,4,3,5,6,1]=>0000000
[1,4,7,5,2,6,8,3]=>1000000
[4,6,5,3,7,1,8,2]=>0000000
[5,6,2,7,3,1,8,4]=>0000000
[1,6,3,7,5,8,2,4]=>1000000
[5,2,4,8,1,3,7,6]=>0000000
[3,5,2,4,7,1,6,8]=>0000001
[6,4,5,3,8,2,1,7]=>0000000
[6,5,3,4,8,7,1,2]=>0000000
[7,6,3,8,5,4,1,2]=>0000000
[5,4,8,1,2,7,3,6]=>0000000
[6,3,8,1,7,2,4,5]=>0000000
[7,2,8,6,1,3,4,5]=>0000000
[7,2,8,6,1,5,3,4]=>0000000
[3,2,4,7,8,1,5,6]=>0000000
[1,5,7,4,2,8,6,3]=>1000000
[1,3,7,2,8,6,4,5]=>1000000
[1,5,3,6,8,2,7,4]=>1000000
[4,3,6,5,7,8,1,2]=>0000000
[4,2,3,5,6,8,1,7]=>0000000
[5,2,6,4,7,8,3,1]=>0000000
[3,2,5,6,8,1,7,4]=>0000000
[4,2,3,6,8,1,5,7]=>0000000
[2,6,1,5,4,8,3,7]=>0000000
[3,2,1,8,7,5,6,4]=>0010000
[3,1,6,2,5,8,4,7]=>0000000
[6,5,1,3,4,8,2,7]=>0000000
[6,2,4,5,8,1,3,7]=>0000000
[2,3,4,8,1,7,6,5]=>0000000
[6,2,7,8,4,5,1,3]=>0000000
[3,1,4,8,7,6,2,5]=>0000000
[2,3,6,5,8,7,1,4]=>0000000
[8,4,1,2,7,6,3,5]=>0000000
[6,3,2,8,5,7,4,1]=>0000000
[3,2,6,8,5,1,7,4]=>0000000
[5,2,4,1,7,8,6,3]=>0000000
[1,8,7,2,4,5,6,3]=>1000000
[5,3,4,7,1,8,6,2]=>0000000
[5,3,7,1,6,2,8,4]=>0000000
[4,7,6,5,8,2,1,3]=>0000000
[1,2,5,3,8,7,6,4]=>1100000
[4,8,2,3,6,7,1,5]=>0000000
[8,2,4,6,7,1,3,5]=>0000000
[3,7,5,1,8,4,6,2]=>0000000
[6,5,3,1,8,4,2,7]=>0000000
[4,2,3,8,5,6,1,7]=>0000000
[2,4,8,7,1,3,5,6]=>0000000
[8,2,6,3,4,5,1,7]=>0000000
[8,1,5,4,3,6,2,7]=>0000000
[8,6,4,2,1,5,3,7]=>0000000
[8,3,2,4,6,1,5,7]=>0000000
[8,2,3,4,7,6,1,5]=>0000000
[8,1,3,7,6,4,2,5]=>0000000
[4,8,1,2,7,3,6,5]=>0000000
[2,5,7,8,4,1,3,6]=>0000000
[6,3,5,8,7,2,4,1]=>0000000
[5,2,8,7,1,3,4,6]=>0000000
[5,2,7,4,8,1,6,3]=>0000000
[8,1,7,4,5,2,6,3]=>0000000
[1,7,8,3,5,4,6,2]=>1000000
[4,6,3,5,8,1,7,2]=>0000000
[8,2,4,1,5,6,7,3]=>0000000
[3,5,1,7,6,8,2,4]=>0000000
[2,1,7,6,4,5,8,3]=>0100000
[1,7,6,5,2,4,8,3]=>1000000
[4,6,2,5,3,8,7,1]=>0000000
[8,6,4,2,3,1,7,5]=>0000000
[8,6,4,2,1,3,7,5]=>0000000
[2,5,7,3,8,4,6,1]=>0000000
[4,2,7,1,8,5,3,6]=>0000000
[1,3,7,5,8,6,4,2]=>1000000
[3,5,7,1,4,8,6,2]=>0000000
[3,4,1,2,8,5,7,6]=>0001000
[8,7,3,1,2,6,4,5]=>0000000
[6,2,3,1,4,8,7,5]=>0000000
[8,4,3,2,5,7,1,6]=>0000000
[5,3,6,8,2,1,4,7]=>0000000
[3,2,6,8,5,4,1,7]=>0000000
[7,3,8,2,5,4,1,6]=>0000000
[7,4,2,5,8,3,1,6]=>0000000
[3,1,2,8,5,6,4,7]=>0010000
[5,2,1,6,8,3,4,7]=>0000000
[3,1,8,6,5,4,2,7]=>0000000
[5,6,8,1,4,3,2,7]=>0000000
[7,8,4,1,5,3,2,6]=>0000000
[7,3,8,5,1,4,2,6]=>0000000
[1,5,4,8,3,7,6,2]=>1000000
[4,7,8,3,1,6,5,2]=>0000000
[8,7,5,3,6,4,2,1]=>0000000
[4,6,1,3,8,7,5,2]=>0000000
[3,6,1,2,7,5,8,4]=>0000000
[3,6,2,5,8,7,4,1]=>0000000
[2,7,3,1,5,6,8,4]=>0000000
[6,7,1,3,2,8,4,5]=>0000000
[6,2,7,1,3,4,8,5]=>0000000
[5,2,1,7,3,8,4,6]=>0000000
[3,7,2,4,6,1,8,5]=>0000000
[5,3,7,2,8,1,4,6]=>0000000
[7,1,8,3,4,2,5,6]=>0000000
[7,2,4,1,8,3,5,6]=>0000000
[4,8,7,6,3,2,1,5]=>0000000
[7,8,2,4,6,1,5,3]=>0000000
[3,5,1,8,7,2,6,4]=>0000000
[5,2,8,1,7,6,3,4]=>0000000
[6,2,1,3,8,7,5,4]=>0000000
[6,7,8,1,2,5,4,3]=>0000000
[5,8,7,1,6,4,3,2]=>0000000
[6,8,7,5,1,4,3,2]=>0000000
[8,6,4,3,2,1,7,5]=>0000000
[6,5,4,3,8,2,7,1]=>0000000
[8,4,3,2,1,7,6,5]=>0000000
[3,7,5,8,1,4,6,2]=>0000000
[4,7,5,8,3,2,1,6]=>0000000
[5,7,2,3,6,1,8,4]=>0000000
[7,3,1,4,8,2,5,6]=>0000000
[7,4,1,2,5,8,3,6]=>0000000
[4,7,1,6,5,8,3,2]=>0000000
[8,6,4,2,3,7,5,1]=>0000000
[7,6,4,2,3,8,1,5]=>0000000
[3,1,2,4,8,7,6,5]=>0011000
[6,5,8,7,3,1,2,4]=>0000000
[5,6,7,8,1,4,2,3]=>0000000
[2,6,7,4,5,3,1,8]=>0000001
[1,3,7,4,2,8,5,6]=>1000000
[4,6,1,3,7,2,5,8]=>0000001
[6,5,7,8,3,1,4,2]=>0000000
[7,5,8,6,2,1,3,4]=>0000000
[2,8,1,3,6,5,4,7]=>0000000
[2,8,7,3,5,4,1,6]=>0000000
[3,4,2,6,8,7,1,5]=>0000000
[6,1,4,2,7,8,5,3]=>0000000
[7,3,8,4,1,2,6,5]=>0000000
[6,8,3,2,7,1,5,4]=>0000000
[5,1,4,3,6,2,7,8]=>0000011
[4,8,5,6,3,2,1,7]=>0000000
[2,8,5,6,3,7,1,4]=>0000000
[3,2,6,7,4,8,1,5]=>0000000
[4,1,8,2,6,3,5,7]=>0000000
[7,5,6,8,2,1,4,3]=>0000000
[5,8,6,7,1,2,3,4]=>0000000
[4,8,1,5,7,2,3,6]=>0000000
[3,5,1,4,7,6,8,2]=>0000000
[5,3,2,7,1,6,8,4]=>0000000
[5,4,1,7,3,6,8,2]=>0000000
[3,4,7,6,2,5,8,1]=>0000000
[4,8,3,6,5,2,1,7]=>0000000
[8,1,7,4,2,5,6,3]=>0000000
[1,8,7,2,5,3,4,6]=>1000000
[4,8,1,5,2,6,3,7]=>0000000
[3,6,8,5,1,2,4,7]=>0000000
[1,5,2,7,8,4,6,3]=>1000000
[6,7,2,8,5,3,1,4]=>0000000
[6,7,2,8,3,1,5,4]=>0000000
[3,1,4,6,7,8,5,2]=>0000000
[7,4,6,1,8,2,3,5]=>0000000
[3,4,5,1,6,8,7,2]=>0000000
[5,7,8,3,1,6,4,2]=>0000000
[7,5,8,3,2,4,1,6]=>0000000
[5,8,2,6,3,1,4,7]=>0000000
[8,2,7,5,4,1,3,6]=>0000000
[6,2,7,3,8,4,1,5]=>0000000
[3,7,2,4,8,5,1,6]=>0000000
[1,5,2,6,3,8,7,4]=>1000000
[1,3,6,2,4,8,7,5]=>1000000
[8,3,6,2,5,4,1,7]=>0000000
[3,5,8,2,4,6,1,7]=>0000000
[6,4,7,8,2,3,1,5]=>0000000
[1,5,3,2,8,4,7,6]=>1000000
[3,8,4,7,5,1,2,6]=>0000000
[6,1,2,7,3,8,5,4]=>0000000
[2,1,7,3,4,8,6,5]=>0100000
[8,3,1,6,7,2,5,4]=>0000000
[4,8,3,7,1,5,2,6]=>0000000
[5,7,4,8,2,1,3,6]=>0000000
[4,6,8,2,5,1,3,7]=>0000000
[5,3,7,2,1,4,6,8]=>0000001
[6,4,2,8,3,1,5,7]=>0000000
[5,7,2,3,8,1,4,6]=>0000000
[6,4,7,5,8,1,2,3]=>0000000
[8,6,4,2,1,7,5,3]=>0000000
[7,6,4,1,8,5,2,3]=>0000000
[1,6,4,8,7,5,3,2]=>1000000
[6,3,1,2,8,4,7,5]=>0000000
[7,4,8,1,6,3,5,2]=>0000000
[1,4,8,7,2,6,5,3]=>1000000
[5,4,1,8,7,3,2,6]=>0000000
[8,6,1,7,5,4,3,2]=>0000000
[3,1,8,7,6,5,2,4]=>0000000
[2,6,8,1,3,7,5,4]=>0000000
[2,4,8,1,5,7,6,3]=>0000000
[3,2,8,6,1,7,5,4]=>0000000
[6,2,8,3,1,7,5,4]=>0000000
[7,4,3,8,5,2,1,6]=>0000000
[4,3,8,7,5,1,6,2]=>0000000
[4,2,3,8,5,1,6,7]=>0000000
[4,2,8,5,1,7,6,3]=>0000000
[3,4,2,8,5,6,1,7]=>0000000
[3,2,4,8,6,1,5,7]=>0000000
[3,2,5,8,6,1,4,7]=>0000000
[4,3,7,8,5,1,2,6]=>0000000
[4,2,6,8,5,1,3,7]=>0000000
[3,5,2,8,4,6,1,7]=>0000000
[5,2,6,8,4,1,3,7]=>0000000
[5,3,7,8,4,1,2,6]=>0000000
[5,6,2,8,3,4,1,7]=>0000000
[5,3,8,7,4,1,6,2]=>0000000
[6,4,2,8,5,3,1,7]=>0000000
[7,6,4,3,8,2,5,1]=>0000000
[6,4,5,3,8,2,7,1]=>0000000
[7,4,5,3,8,2,6,1]=>0000000
[8,4,6,3,7,2,5,1]=>0000000
[7,6,8,3,5,2,4,1]=>0000000
[7,5,8,4,6,2,3,1]=>0000000
[7,5,8,3,6,2,4,1]=>0000000
[7,4,8,3,6,2,5,1]=>0000000
[7,4,8,3,5,2,6,1]=>0000000
[6,4,8,3,5,2,7,1]=>0000000
[5,4,7,3,6,2,8,1]=>0000000
[6,5,7,3,8,2,4,1]=>0000000
[5,4,6,3,8,2,7,1]=>0000000
[6,5,3,7,8,2,1,4]=>0000000
[6,5,4,2,8,7,1,3]=>0000000
[6,4,3,7,5,2,1,8]=>0000001
[6,3,7,8,5,2,1,4]=>0000000
[6,3,7,2,5,4,1,8]=>0000001
[6,3,2,7,5,4,1,8]=>0000001
[4,8,2,6,3,7,1,5]=>0000000
[5,4,8,1,2,3,7,6]=>0000000
[1,4,7,6,3,2,5,8]=>1000001
[4,8,3,2,7,6,1,5]=>0000000
[4,8,6,7,2,3,1,5]=>0000000
[4,8,7,3,6,2,1,5]=>0000000
[4,3,8,2,7,1,6,5]=>0000000
[4,1,8,7,3,2,5,6]=>0000000
[4,7,8,1,2,5,3,6]=>0000000
[2,3,6,7,4,1,8,5]=>0000000
[2,6,3,4,7,8,1,5]=>0000000
[3,1,7,8,4,2,5,6]=>0000000
[4,3,1,2,8,5,7,6]=>0001000
[3,7,6,8,4,2,1,5]=>0000000
[3,7,8,2,6,4,1,5]=>0000000
[3,7,2,8,4,6,1,5]=>0000000
[4,2,8,3,6,1,7,5]=>0000000
[3,7,2,4,8,6,1,5]=>0000000
[1,3,6,4,7,2,5,8]=>1000001
[2,4,3,6,1,8,7,5]=>0000000
[2,6,7,3,8,4,1,5]=>0000000
[2,6,3,7,4,8,1,5]=>0000000
[1,3,5,7,4,6,8,2]=>1000000
[1,3,5,4,7,2,6,8]=>1000001
[1,3,5,4,7,2,8,6]=>1000000
[2,3,7,1,4,8,6,5]=>0000000
[2,5,7,3,4,8,6,1]=>0000000
[2,5,4,6,7,1,3,8]=>0000001
[2,4,6,3,7,5,1,8]=>0000001
[5,3,2,7,4,6,1,8]=>0000001
[4,1,2,5,8,3,7,6]=>0000000
[4,6,1,2,5,8,3,7]=>0000000
[5,7,6,8,1,4,2,3]=>0000000
[4,1,6,2,8,5,7,3]=>0000000
[7,1,4,2,3,6,8,5]=>0000000
[6,4,2,1,3,8,7,5]=>0000000
[3,8,6,4,2,1,5,7]=>0000000
[6,1,2,7,5,3,8,4]=>0000000
[2,6,1,4,7,3,8,5]=>0000000
[7,3,2,8,6,4,1,5]=>0000000
[2,7,8,4,6,3,1,5]=>0000000
[7,8,2,5,3,6,1,4]=>0000000
[8,1,6,3,5,7,2,4]=>0000000
[8,3,2,6,4,7,1,5]=>0000000
[8,4,2,5,6,7,1,3]=>0000000
[2,3,8,7,6,5,1,4]=>0000000
[4,1,8,7,2,6,5,3]=>0000000
[1,2,8,7,3,6,5,4]=>1100000
[1,5,8,7,3,2,6,4]=>1000000
[4,5,8,7,3,2,1,6]=>0000000
[2,6,8,3,7,5,1,4]=>0000000
[1,6,8,4,7,2,5,3]=>1000000
[1,6,8,3,7,2,5,4]=>1000000
[2,5,8,1,7,6,4,3]=>0000000
[3,2,8,4,7,6,1,5]=>0000000
[1,5,8,4,7,2,6,3]=>1000000
[1,5,8,3,7,2,6,4]=>1000000
[3,1,8,4,7,2,6,5]=>0000000
[5,6,8,1,2,7,4,3]=>0000000
[1,6,8,2,3,7,5,4]=>1000000
[1,5,8,4,2,7,6,3]=>1000000
[5,6,8,4,3,2,1,7]=>0000000
[7,1,4,8,6,2,5,3]=>0000000
[7,3,4,8,6,2,1,5]=>0000000
[7,1,4,8,2,6,5,3]=>0000000
[7,4,5,8,1,2,6,3]=>0000000
[3,6,2,8,7,5,1,4]=>0000000
[1,6,4,8,7,2,5,3]=>1000000
[3,2,4,8,7,6,1,5]=>0000000
[1,4,5,8,7,2,6,3]=>1000000
[3,1,4,8,7,2,6,5]=>0000000
[1,6,5,8,2,7,4,3]=>1000000
[2,6,5,8,3,7,1,4]=>0000000
[2,4,5,8,3,7,1,6]=>0000000
[4,6,5,8,3,2,1,7]=>0000000
[7,6,2,3,8,5,1,4]=>0000000
[7,6,1,4,8,2,5,3]=>0000000
[7,2,5,3,8,6,1,4]=>0000000
[7,2,1,3,8,6,5,4]=>0000000
[2,6,5,3,8,7,1,4]=>0000000
[2,6,1,4,8,7,5,3]=>0000000
[7,6,5,1,2,8,4,3]=>0000000
[7,1,5,2,3,8,6,4]=>0000000
[7,1,2,4,3,8,6,5]=>0000000
[1,6,2,4,3,8,7,5]=>1000000
[2,6,5,4,3,8,1,7]=>0000000
[7,6,5,1,3,2,8,4]=>0000000
[8,2,7,6,5,4,1,3]=>0000000
[7,2,8,6,5,4,3,1]=>0000000
[3,2,8,7,6,5,1,4]=>0000000
[7,8,6,1,5,4,3,2]=>0000000
[4,8,5,7,6,3,2,1]=>0000000
[3,2,4,6,8,1,5,7]=>0000000
[3,5,7,2,4,8,1,6]=>0000000
[4,5,1,3,6,8,2,7]=>0000000
[4,3,5,7,2,6,8,1]=>0000000
[4,3,5,1,7,8,2,6]=>0000000
[4,6,3,5,7,2,8,1]=>0000000
[5,1,6,7,3,4,8,2]=>0000000
[1,6,7,3,4,5,8,2]=>1000000
[2,6,7,4,8,1,3,5]=>0000000
[6,3,1,7,8,2,4,5]=>0000000
[5,7,2,8,1,3,4,6]=>0000000
[6,3,7,2,8,1,4,5]=>0000000
[2,4,6,7,1,5,8,3]=>0000000
[2,4,7,1,5,6,8,3]=>0000000
[3,7,1,5,6,8,2,4]=>0000000
[1,5,6,7,2,4,8,3]=>1000000
[5,6,2,4,1,7,8,3]=>0000000
[5,6,4,7,1,3,8,2]=>0000000
[6,4,3,7,2,5,8,1]=>0000000
[6,4,3,7,2,8,1,5]=>0000000
[7,4,5,3,1,6,8,2]=>0000000
[6,4,3,7,5,1,8,2]=>0000000
[5,6,3,7,4,1,8,2]=>0000000
[6,7,4,2,1,5,8,3]=>0000000
[6,7,4,2,1,8,3,5]=>0000000
[5,6,7,3,1,8,2,4]=>0000000
[5,6,3,7,8,1,2,4]=>0000000
[5,6,3,7,2,4,8,1]=>0000000
[5,6,7,2,3,8,1,4]=>0000000
[5,6,7,2,8,1,3,4]=>0000000
[6,7,3,8,1,2,4,5]=>0000000
[6,7,3,2,8,1,4,5]=>0000000
[7,6,4,2,1,3,8,5]=>0000000
[7,5,3,2,6,1,8,4]=>0000000
[6,5,3,2,7,8,1,4]=>0000000
[6,4,7,2,5,1,8,3]=>0000000
[5,4,6,7,3,1,8,2]=>0000000
[3,7,8,5,6,1,4,2]=>0000000
[1,7,8,5,6,3,4,2]=>1000000
[1,7,5,8,6,3,4,2]=>1000000
[5,7,3,8,6,4,1,2]=>0000000
[1,5,7,8,6,3,4,2]=>1000000
[1,5,7,8,3,6,4,2]=>1000000
[5,3,7,8,1,6,4,2]=>0000000
[5,3,7,8,6,1,4,2]=>0000000
[7,8,3,5,6,1,4,2]=>0000000
[7,1,8,5,6,3,4,2]=>0000000
[7,1,5,8,6,3,4,2]=>0000000
[5,1,7,8,6,3,4,2]=>0000000
[5,1,7,8,3,6,4,2]=>0000000
[3,1,7,8,5,6,4,2]=>0000000
[1,3,7,8,5,6,4,2]=>1000000
[3,1,7,5,8,6,4,2]=>0000000
[5,1,7,3,8,6,4,2]=>0000000
[7,1,5,3,8,6,4,2]=>0000000
[7,1,5,8,3,6,4,2]=>0000000
[7,3,8,5,1,6,4,2]=>0000000
[7,3,5,8,1,6,4,2]=>0000000
[7,3,5,1,8,6,4,2]=>0000000
[5,3,7,1,8,6,4,2]=>0000000
[3,5,7,1,8,6,4,2]=>0000000
[1,5,7,3,8,6,4,2]=>1000000
[1,7,5,3,8,6,4,2]=>1000000
[3,7,5,1,8,6,4,2]=>0000000
[5,7,3,1,8,6,4,2]=>0000000
[5,7,3,8,6,1,4,2]=>0000000
[3,7,5,8,1,6,4,2]=>0000000
[1,7,5,8,3,6,4,2]=>1000000
[1,7,8,5,3,6,4,2]=>1000000
[5,7,8,6,3,1,4,2]=>0000000
[7,5,8,6,1,3,4,2]=>0000000
[5,7,8,1,6,3,4,2]=>0000000
[1,7,8,3,5,6,4,2]=>1000000
[1,7,3,8,5,6,4,2]=>1000000
[3,7,1,8,5,6,4,2]=>0000000
[5,7,1,8,3,6,4,2]=>0000000
[5,7,1,8,6,3,4,2]=>0000000
[7,5,1,8,6,3,4,2]=>0000000
[7,5,8,1,6,3,4,2]=>0000000
[7,5,1,8,3,6,4,2]=>0000000
[7,5,1,3,8,6,4,2]=>0000000
[5,7,1,3,8,6,4,2]=>0000000
[3,7,1,5,8,6,4,2]=>0000000
[1,7,3,5,8,6,4,2]=>1000000
[1,5,3,7,8,6,4,2]=>1000000
[3,5,1,7,8,6,4,2]=>0000000
[5,3,1,7,8,6,4,2]=>0000000
[7,3,1,5,8,6,4,2]=>0000000
[7,3,1,8,5,6,4,2]=>0000000
[7,1,8,3,5,6,4,2]=>0000000
[7,1,3,8,5,6,4,2]=>0000000
[7,1,3,5,8,6,4,2]=>0000000
[5,1,3,7,8,6,4,2]=>0000000
[3,1,5,7,8,6,4,2]=>0000000
[2,3,6,1,5,4,8,7]=>0000010
[3,5,6,2,4,1,8,7]=>0000010
[8,7,6,1,3,2,4,5]=>0000000
[2,5,3,4,8,1,7,6]=>0000000
[5,1,8,2,3,4,7,6]=>0000000
[5,4,7,6,2,8,1,3]=>0000000
[3,1,8,6,2,7,5,4]=>0000000
[3,8,1,5,6,7,2,4]=>0000000
[8,2,3,5,7,1,6,4]=>0000000
[2,8,3,6,7,5,1,4]=>0000000
[4,3,8,2,7,6,1,5]=>0000000
[2,1,4,5,8,3,7,6]=>0100000
[6,4,7,5,2,3,8,1]=>0000000
[4,2,3,1,8,7,5,6]=>0001000
[4,3,1,2,8,6,7,5]=>0001000
[5,1,6,7,8,4,3,2]=>0000000
[8,7,2,6,4,1,5,3]=>0000000
[6,1,7,4,3,2,8,5]=>0000000
[4,2,6,1,5,7,8,3]=>0000000
[7,1,4,8,3,5,6,2]=>0000000
[3,4,8,2,5,7,6,1]=>0000000
[3,7,1,4,5,6,8,2]=>0000000
[4,7,5,6,8,3,1,2]=>0000000
[6,5,3,8,4,7,1,2]=>0000000
[8,6,4,7,5,3,1,2]=>0000000
[1,6,3,7,5,8,4,2]=>1000000
[1,3,7,4,5,8,6,2]=>1000000
[7,3,8,5,4,6,1,2]=>0000000
[3,4,8,5,6,7,1,2]=>0000000
[4,7,3,8,5,6,1,2]=>0000000
[6,8,4,7,5,3,1,2]=>0000000
[1,7,6,5,3,8,4,2]=>1000000
[2,7,6,4,5,1,3,8]=>0000001
[1,8,2,7,3,6,5,4]=>1000000
[2,1,3,8,4,7,5,6]=>0110000
[3,1,2,8,4,6,7,5]=>0010000
[4,1,7,2,8,5,6,3]=>0000000
[5,1,2,4,8,3,7,6]=>0000000
[1,7,2,8,5,3,6,4]=>1000000
[1,2,3,8,4,5,7,6]=>1110000
[2,4,8,3,1,5,6,7]=>0000000
[3,4,2,7,1,5,6,8]=>0000001
[3,2,5,6,1,4,7,8]=>0000011
[4,7,3,8,2,1,5,6]=>0000000
[7,4,8,3,2,1,5,6]=>0000000
[2,6,4,5,7,1,3,8]=>0000001
[5,4,6,2,7,1,3,8]=>0000001
[7,6,8,5,1,4,3,2]=>0000000
[6,5,1,2,8,3,7,4]=>0000000
[6,8,4,1,3,7,5,2]=>0000000
[6,3,7,1,8,4,5,2]=>0000000
[4,7,1,2,8,3,6,5]=>0000000
[1,2,8,7,6,3,5,4]=>1100000
[2,3,1,8,7,4,5,6]=>0010000
[8,7,1,6,5,4,3,2]=>0000000
[3,1,8,7,6,4,5,2]=>0000000
[1,2,3,4,8,7,5,6]=>1111000
[1,2,3,8,6,4,5,7]=>1110000
[1,2,8,5,3,4,6,7]=>1100000
[1,8,4,2,3,5,6,7]=>1000000
[2,4,7,5,6,8,3,1]=>0000000
[2,5,3,8,7,4,6,1]=>0000000
[3,1,8,5,7,4,2,6]=>0000000
[8,3,6,2,4,5,7,1]=>0000000
[4,8,1,7,6,3,2,5]=>0000000
[4,7,8,1,3,6,2,5]=>0000000
[5,8,7,1,4,3,2,6]=>0000000
[5,6,1,2,4,3,8,7]=>0000010
[3,6,8,1,2,7,5,4]=>0000000
[8,4,6,2,1,3,7,5]=>0000000
[4,8,1,5,3,7,2,6]=>0000000
[5,4,8,7,3,1,2,6]=>0000000
[6,4,3,8,1,5,2,7]=>0000000
[6,8,3,7,2,5,4,1]=>0000000
[5,3,6,8,7,2,4,1]=>0000000
[5,7,4,2,8,3,6,1]=>0000000
[6,4,7,2,1,8,3,5]=>0000000
[6,5,3,1,4,7,2,8]=>0000001
[5,7,8,2,6,4,1,3]=>0000000
[3,6,8,5,7,1,4,2]=>0000000
[1,7,4,8,6,2,3,5]=>1000000
[2,7,4,8,5,6,1,3]=>0000000
[6,3,7,2,8,5,1,4]=>0000000
[8,1,3,6,7,2,4,5]=>0000000
[6,1,3,8,2,7,4,5]=>0000000
[4,1,5,3,2,8,6,7]=>0000100
[2,7,1,4,3,8,5,6]=>0000000
[1,7,5,2,8,6,3,4]=>1000000
[7,4,2,5,1,8,6,3]=>0000000
[5,6,3,2,1,8,7,4]=>0000000
[4,5,3,2,7,1,8,6]=>0000000
[6,4,2,8,5,1,7,3]=>0000000
[1,8,4,7,2,5,3,6]=>1000000
[1,5,8,4,2,6,3,7]=>1000000
[3,5,7,4,1,6,8,2]=>0000000
[4,5,8,3,1,7,6,2]=>0000000
[3,4,7,8,2,1,6,5]=>0000000
[3,5,7,1,2,6,4,8]=>0000001
[3,6,2,1,4,7,5,8]=>0000001
[7,4,1,2,8,6,3,5]=>0000000
[5,2,6,1,3,4,8,7]=>0000010
[7,5,1,6,8,4,3,2]=>0000000
[6,2,7,8,5,4,1,3]=>0000000
[3,8,7,6,2,4,1,5]=>0000000
[3,5,8,7,2,4,6,1]=>0000000
[2,7,1,3,6,5,4,8]=>0000001
[6,3,7,1,5,4,2,8]=>0000001
[5,7,8,3,2,1,4,6]=>0000000
[5,4,2,1,7,8,3,6]=>0000000
[4,7,8,3,5,2,1,6]=>0000000
[8,3,2,1,4,7,6,5]=>0000000
[6,4,1,7,3,8,5,2]=>0000000
[1,7,5,3,8,2,6,4]=>1000000
[5,1,7,4,2,8,6,3]=>0000000
[5,1,4,3,2,7,8,6]=>0000100
[3,7,6,2,4,1,8,5]=>0000000
[6,3,1,7,5,2,8,4]=>0000000
[4,1,6,8,5,7,3,2]=>0000000
[1,8,6,7,3,4,2,5]=>1000000
[6,7,1,8,3,4,2,5]=>0000000
[7,8,2,5,1,6,3,4]=>0000000
[1,8,5,6,2,7,3,4]=>1000000
[5,6,2,7,1,8,3,4]=>0000000
[6,7,2,5,1,8,3,4]=>0000000
[2,5,1,8,6,7,3,4]=>0000000
[2,6,5,8,1,7,3,4]=>0000000
[2,4,3,8,5,6,1,7]=>0000000
[2,3,1,8,5,6,4,7]=>0010000
[4,7,1,6,2,5,3,8]=>0000001
[4,6,3,5,1,7,2,8]=>0000001
[5,6,3,7,1,4,2,8]=>0000001
[1,8,5,6,3,4,2,7]=>1000000
[4,7,1,8,5,6,2,3]=>0000000
[3,4,2,6,5,8,1,7]=>0000000
[3,5,4,6,2,8,1,7]=>0000000
[3,7,1,6,2,8,4,5]=>0000000
[3,5,2,7,4,8,1,6]=>0000000
[4,7,2,3,1,8,5,6]=>0000000
[2,5,8,3,4,1,6,7]=>0000000
[5,1,7,3,4,2,8,6]=>0000000
[4,6,7,3,2,5,8,1]=>0000000
[3,7,2,1,4,5,8,6]=>0000000
[2,7,1,3,4,8,6,5]=>0000000
[2,6,7,3,8,5,4,1]=>0000000
[2,6,1,8,4,5,3,7]=>0000000
[4,2,1,6,5,3,8,7]=>0000010
[6,2,4,3,1,5,8,7]=>0000010
[4,6,2,1,5,3,8,7]=>0000010
[8,4,2,1,6,5,3,7]=>0000000
[2,6,4,5,1,8,7,3]=>0000000
[6,8,7,2,1,4,3,5]=>0000000
[6,8,2,1,7,4,3,5]=>0000000
[8,6,2,4,3,1,5,7]=>0000000
[4,6,5,2,8,3,7,1]=>0000000
[2,6,4,5,8,3,7,1]=>0000000
[8,2,4,3,6,5,1,7]=>0000000
[4,2,1,6,8,7,5,3]=>0000000
[4,2,1,6,5,8,7,3]=>0000000
[6,2,1,8,4,3,7,5]=>0000000
[4,6,5,8,7,2,1,3]=>0000000
[6,4,8,2,1,5,7,3]=>0000000
[2,6,8,4,7,1,5,3]=>0000000
[4,8,6,7,2,1,3,5]=>0000000
[7,4,5,2,3,8,6,1]=>0000000
[3,5,1,6,4,2,8,7]=>0000010
[7,2,3,4,5,8,6,1]=>0000000
[8,2,3,4,5,7,1,6]=>0000000
[5,7,1,3,8,6,2,4]=>0000000
[4,7,3,2,8,6,1,5]=>0000000
[4,8,1,5,6,7,3,2]=>0000000
[6,8,2,5,1,7,3,4]=>0000000
[7,8,3,4,6,2,1,5]=>0000000
[3,8,2,5,4,7,6,1]=>0000000
[3,7,6,1,8,5,2,4]=>0000000
[4,6,7,1,8,5,3,2]=>0000000
[3,6,1,7,8,5,4,2]=>0000000
[2,1,5,7,3,8,6,4]=>0100000
[7,6,1,4,8,5,2,3]=>0000000
[4,1,2,3,7,8,6,5]=>0001000
[3,4,2,1,8,5,6,7]=>0001000
[5,4,8,3,6,7,1,2]=>0000000
[4,5,8,3,6,7,2,1]=>0000000
[2,1,5,8,4,6,7,3]=>0100000
[4,6,8,3,5,2,7,1]=>0000000
[5,7,8,3,2,4,1,6]=>0000000
[3,8,2,4,5,6,7,1]=>0000000
[4,3,1,6,5,8,7,2]=>0000000
[8,2,7,4,1,3,6,5]=>0000000
[3,1,5,2,4,8,7,6]=>0000100
[3,6,4,5,1,8,7,2]=>0000000
[4,3,6,1,2,8,7,5]=>0000000
[6,1,3,5,4,8,7,2]=>0000000
[1,7,3,8,4,6,2,5]=>1000000
[1,6,7,4,8,5,3,2]=>1000000
[8,1,2,5,4,6,3,7]=>0000000
[8,4,2,5,7,1,6,3]=>0000000
[1,8,5,3,7,4,6,2]=>1000000
[4,2,1,7,5,3,6,8]=>0000001
[1,4,8,6,5,7,2,3]=>1000000
[3,5,4,8,6,1,2,7]=>0000000
[4,3,5,8,1,7,2,6]=>0000000
[1,4,5,8,6,7,3,2]=>1000000
[1,7,6,5,8,3,4,2]=>1000000
[7,3,6,1,8,2,4,5]=>0000000
[7,6,4,5,8,1,3,2]=>0000000
[4,3,1,6,8,7,5,2]=>0000000
[4,3,1,8,5,6,7,2]=>0000000
[6,2,8,4,3,1,7,5]=>0000000
[7,1,6,2,3,4,5,8]=>0000001
[1,8,5,4,3,6,2,7]=>1000000
[1,8,3,6,5,2,7,4]=>1000000
[4,7,1,8,2,6,5,3]=>0000000
[1,4,8,3,5,7,6,2]=>1000000
[6,1,5,2,4,7,8,3]=>0000000
[4,1,8,5,2,7,6,3]=>0000000
[4,3,8,5,1,2,6,7]=>0000000
[4,1,8,2,3,7,5,6]=>0000000
[1,8,7,6,2,5,4,3]=>1000000
[4,6,3,1,5,2,7,8]=>0000011
[6,2,7,4,5,1,3,8]=>0000001
[5,7,3,4,1,6,2,8]=>0000001
[4,2,8,1,5,6,7,3]=>0000000
[1,7,8,4,5,6,2,3]=>1000000
[1,6,8,4,5,2,7,3]=>1000000
[1,5,8,4,2,6,7,3]=>1000000
[1,5,3,8,2,6,7,4]=>1000000
[1,6,3,8,5,2,7,4]=>1000000
[1,7,3,8,5,6,2,4]=>1000000
[6,2,3,7,5,1,4,8]=>0000001
[4,2,6,1,5,3,7,8]=>0000011
[5,2,6,4,1,3,7,8]=>0000011
[1,2,7,8,5,6,3,4]=>1100000
[1,2,6,8,5,3,7,4]=>1100000
[1,2,6,4,8,3,7,5]=>1100000
[8,7,3,2,1,6,5,4]=>0000000
[8,7,4,1,6,2,3,5]=>0000000
[1,8,3,2,6,4,5,7]=>1000000
[7,3,8,1,5,2,4,6]=>0000000
[3,1,7,2,6,4,5,8]=>0000001
[1,8,4,2,3,6,7,5]=>1000000
[4,1,7,2,3,6,8,5]=>0000000
[3,1,7,5,4,2,8,6]=>0000000
[3,2,6,7,4,1,8,5]=>0000000
[5,6,2,7,1,4,8,3]=>0000000
[6,4,2,8,1,5,7,3]=>0000000
[7,3,6,8,5,2,4,1]=>0000000
[2,7,8,3,6,5,1,4]=>0000000
[2,7,8,5,4,6,3,1]=>0000000
[2,6,8,3,4,7,1,5]=>0000000
[2,5,6,8,3,4,1,7]=>0000000
[2,7,8,3,6,1,4,5]=>0000000
[2,1,3,7,8,5,6,4]=>0110000
[5,1,2,4,8,7,3,6]=>0000000
[2,3,6,1,8,5,7,4]=>0000000
[5,2,6,1,7,8,4,3]=>0000000
[3,6,5,4,1,8,7,2]=>0000000
[4,1,8,2,5,7,3,6]=>0000000
[1,5,8,2,4,7,3,6]=>1000000
[6,2,1,4,7,8,3,5]=>0000000
[3,8,1,4,2,6,5,7]=>0000000
[8,3,4,2,1,6,5,7]=>0000000
[5,3,2,8,1,6,4,7]=>0000000
[2,4,5,8,3,6,1,7]=>0000000
[2,6,4,3,7,8,5,1]=>0000000
[7,4,1,8,3,2,5,6]=>0000000
[5,6,1,7,4,2,8,3]=>0000000
[1,3,8,6,2,7,4,5]=>1000000
[4,3,7,5,6,1,8,2]=>0000000
[6,7,3,8,4,1,2,5]=>0000000
[4,7,5,8,3,1,2,6]=>0000000
[5,7,3,1,6,8,4,2]=>0000000
[4,6,7,2,8,3,1,5]=>0000000
[4,5,6,7,3,1,8,2]=>0000000
[8,5,3,2,7,6,1,4]=>0000000
[7,5,4,6,2,8,1,3]=>0000000
[2,5,1,3,6,8,7,4]=>0000000
[7,3,8,5,2,1,4,6]=>0000000
[5,8,3,6,4,7,1,2]=>0000000
[4,1,6,3,2,5,8,7]=>0000010
[8,6,1,7,2,5,4,3]=>0000000
[8,7,6,1,2,3,5,4]=>0000000
[5,4,1,6,2,3,8,7]=>0000010
[5,8,7,6,1,2,3,4]=>0000000
[8,2,7,1,5,4,3,6]=>0000000
[2,1,6,3,8,5,4,7]=>0100000
[2,6,3,1,8,5,4,7]=>0000000
[4,6,2,8,5,1,3,7]=>0000000
[4,6,5,2,7,3,8,1]=>0000000
[3,1,6,2,4,8,7,5]=>0000000
[2,8,5,7,4,1,3,6]=>0000000
[6,4,8,3,5,7,1,2]=>0000000
[8,5,7,4,6,2,1,3]=>0000000
[4,1,8,5,6,3,2,7]=>0000000
[5,8,3,2,4,6,1,7]=>0000000
[2,8,4,1,5,3,7,6]=>0000000
[2,1,8,6,4,3,7,5]=>0100000
[3,6,7,1,8,5,2,4]=>0000000
[6,5,7,3,1,8,4,2]=>0000000
[6,1,5,7,2,4,8,3]=>0000000
[7,4,5,1,2,3,8,6]=>0000000
[8,4,7,6,2,1,5,3]=>0000000
[3,5,7,6,4,1,8,2]=>0000000
[5,4,1,7,6,2,8,3]=>0000000
[5,7,2,3,6,4,8,1]=>0000000
[6,1,8,2,7,3,4,5]=>0000000
[1,8,5,7,2,3,4,6]=>1000000
[8,1,5,7,2,3,6,4]=>0000000
[2,3,1,7,8,6,4,5]=>0010000
[5,4,1,6,3,8,7,2]=>0000000
[5,4,1,2,8,7,6,3]=>0000000
[5,6,3,7,8,4,2,1]=>0000000
[4,3,2,6,8,1,7,5]=>0000000
[1,5,4,2,7,8,3,6]=>1000000
[6,1,2,8,7,4,3,5]=>0000000
[3,6,5,8,4,7,1,2]=>0000000
[3,2,8,1,4,7,6,5]=>0000000
[6,4,3,8,2,5,7,1]=>0000000
[2,1,7,8,3,4,6,5]=>0100000
[5,6,1,8,2,7,4,3]=>0000000
[3,6,8,5,2,7,4,1]=>0000000
[2,1,6,5,4,8,3,7]=>0100000
[2,1,7,3,5,8,6,4]=>0100000
[7,8,1,2,4,5,6,3]=>0000000
[3,8,7,4,1,2,5,6]=>0000000
[4,3,8,7,1,6,5,2]=>0000000
[3,7,5,8,1,6,2,4]=>0000000
[4,2,7,5,8,3,6,1]=>0000000
[5,8,2,7,3,4,6,1]=>0000000
[5,7,2,1,8,3,6,4]=>0000000
[7,8,1,2,3,4,6,5]=>0000000
[5,6,2,4,3,1,8,7]=>0000010
[6,3,2,1,4,8,5,7]=>0000000
[8,7,6,2,4,3,1,5]=>0000000
[7,6,8,1,5,4,3,2]=>0000000
[7,6,1,8,5,4,3,2]=>0000000
[6,5,8,1,7,4,3,2]=>0000000
[4,3,8,7,6,1,5,2]=>0000000
[6,5,8,7,4,1,3,2]=>0000000
[5,4,8,7,6,3,1,2]=>0000000
[1,4,8,6,3,2,5,7]=>1000000
[1,6,3,8,5,2,4,7]=>1000000
[4,6,3,7,5,2,1,8]=>0000001
[3,7,2,6,5,4,1,8]=>0000001
[3,2,1,6,8,4,5,7]=>0010000
[3,5,7,4,8,6,1,2]=>0000000
[5,2,7,4,1,6,8,3]=>0000000
[4,5,8,2,1,7,6,3]=>0000000
[1,6,4,8,5,2,7,3]=>1000000
[7,4,1,5,3,8,2,6]=>0000000
[3,4,1,2,7,8,6,5]=>0001000
[3,1,2,4,7,6,8,5]=>0011000
[8,1,3,5,4,7,2,6]=>0000000
[7,1,4,3,5,2,8,6]=>0000000
[3,2,8,1,6,5,4,7]=>0000000
[6,8,4,1,2,5,3,7]=>0000000
[8,2,1,5,6,4,3,7]=>0000000
[4,7,1,8,2,5,3,6]=>0000000
[6,7,8,1,4,5,3,2]=>0000000
[3,2,5,4,7,8,1,6]=>0000000
[8,4,7,6,2,3,1,5]=>0000000
[6,1,2,8,7,3,5,4]=>0000000
[5,7,2,3,8,1,6,4]=>0000000
[3,5,2,6,1,8,7,4]=>0000000
[3,2,5,6,7,8,1,4]=>0000000
[6,4,1,2,8,7,3,5]=>0000000
[4,3,8,5,2,1,6,7]=>0000000
[7,5,4,2,3,8,1,6]=>0000000
[5,6,3,1,8,2,7,4]=>0000000
[4,5,2,1,6,8,3,7]=>0000000
[5,6,2,8,1,7,4,3]=>0000000
[1,5,6,3,4,8,2,7]=>1000000
[2,1,4,5,8,6,3,7]=>0100000
[1,8,3,4,7,6,2,5]=>1000000
[3,1,2,8,6,4,5,7]=>0010000
[2,5,6,1,8,4,3,7]=>0000000
[5,4,7,6,1,8,2,3]=>0000000
[3,5,6,8,4,7,2,1]=>0000000
[2,4,8,5,7,3,6,1]=>0000000
[5,3,7,8,4,6,2,1]=>0000000
[6,7,3,8,4,5,2,1]=>0000000
[2,5,3,7,6,8,1,4]=>0000000
[4,2,1,8,7,3,5,6]=>0000000
[8,7,4,6,2,3,1,5]=>0000000
[6,8,3,5,4,7,1,2]=>0000000
[1,4,6,3,7,2,8,5]=>1000000
[6,2,1,8,4,5,3,7]=>0000000
[4,7,3,8,5,2,1,6]=>0000000
[4,7,5,1,8,6,3,2]=>0000000
[6,2,4,1,7,5,8,3]=>0000000
[3,6,5,8,4,1,7,2]=>0000000
[5,7,3,1,6,4,8,2]=>0000000
[6,1,3,7,4,8,5,2]=>0000000
[3,1,5,4,2,8,6,7]=>0000100
[4,1,5,2,7,6,3,8]=>0000001
[6,2,7,1,4,8,5,3]=>0000000
[4,3,2,1,8,5,7,6]=>0001000
[7,4,3,2,8,1,6,5]=>0000000
[1,8,5,3,6,4,2,7]=>1000000
[8,1,6,2,7,4,3,5]=>0000000
[7,3,1,6,5,4,2,8]=>0000001
[2,8,5,6,1,4,3,7]=>0000000
[3,7,5,8,2,1,4,6]=>0000000
[6,5,8,4,1,3,7,2]=>0000000
[5,4,8,3,2,1,7,6]=>0000000
[2,4,7,1,3,6,5,8]=>0000001
[5,7,4,8,1,3,6,2]=>0000000
[5,1,7,8,2,4,6,3]=>0000000
[3,6,7,8,1,2,5,4]=>0000000
[4,6,7,2,8,1,3,5]=>0000000
[6,3,7,1,8,2,5,4]=>0000000
[5,7,1,4,8,2,6,3]=>0000000
[6,1,2,7,8,3,5,4]=>0000000
[3,6,4,7,8,1,2,5]=>0000000
[3,7,4,8,5,2,1,6]=>0000000
[4,8,2,1,7,5,3,6]=>0000000
[7,3,8,1,6,4,2,5]=>0000000
[2,8,7,1,6,3,5,4]=>0000000
[2,7,6,5,1,4,3,8]=>0000001
[3,8,7,6,2,1,5,4]=>0000000
[5,8,7,2,6,1,4,3]=>0000000
[7,3,8,6,5,1,2,4]=>0000000
[5,8,6,4,3,2,1,7]=>0000000
[8,1,2,3,4,7,6,5]=>0000000
[3,8,2,7,6,5,4,1]=>0000000
[4,2,8,7,6,5,3,1]=>0000000
[8,3,1,7,6,5,4,2]=>0000000
[5,2,8,7,6,4,3,1]=>0000000
[8,3,2,1,7,6,5,4]=>0000000
[8,4,1,7,6,5,3,2]=>0000000
[4,5,6,2,3,8,1,7]=>0000000
[3,2,7,4,5,8,1,6]=>0000000
[5,4,6,1,3,8,2,7]=>0000000
[2,4,1,7,5,8,3,6]=>0000000
[8,1,7,4,2,3,6,5]=>0000000
[3,5,8,1,2,4,7,6]=>0000000
[3,8,4,1,2,7,6,5]=>0000000
[6,4,1,3,2,7,8,5]=>0000000
[2,7,1,6,8,3,5,4]=>0000000
[8,5,3,2,6,1,7,4]=>0000000
[7,8,4,1,2,5,3,6]=>0000000
[6,1,4,2,7,5,3,8]=>0000001
[7,8,2,1,6,3,5,4]=>0000000
[1,2,8,3,6,4,7,5]=>1100000
[6,2,3,7,4,1,5,8]=>0000001
[6,2,4,1,7,3,5,8]=>0000001
[2,7,3,8,6,4,1,5]=>0000000
[1,8,3,7,6,4,5,2]=>1000000
[2,6,8,5,3,1,7,4]=>0000000
[5,6,2,1,7,3,8,4]=>0000000
[5,3,6,2,4,1,7,8]=>0000011
[5,7,4,2,1,3,6,8]=>0000001
[6,4,2,1,5,3,7,8]=>0000011
[5,3,1,4,6,2,7,8]=>0000011
[1,6,4,2,8,7,3,5]=>1000000
[4,8,1,2,6,7,3,5]=>0000000
[3,1,2,4,6,8,7,5]=>0011000
[4,2,8,1,5,3,7,6]=>0000000
[4,3,8,5,7,6,1,2]=>0000000
[4,8,6,3,7,5,1,2]=>0000000
[3,8,6,5,2,7,1,4]=>0000000
[3,8,5,6,1,7,4,2]=>0000000
[4,2,7,8,1,3,6,5]=>0000000
[6,8,1,5,4,7,3,2]=>0000000
[2,6,4,3,1,5,8,7]=>0000010
[5,1,7,2,8,6,4,3]=>0000000
[6,8,2,5,4,7,1,3]=>0000000
[5,8,3,2,7,6,1,4]=>0000000
[4,8,3,2,1,7,6,5]=>0000000
[2,6,8,3,7,1,4,5]=>0000000
[6,8,3,7,2,1,5,4]=>0000000
[4,5,8,1,6,3,2,7]=>0000000
[6,8,4,7,1,5,3,2]=>0000000
[4,3,2,1,6,8,5,7]=>0001000
[2,4,1,3,8,7,6,5]=>0001000
[4,8,6,5,1,7,3,2]=>0000000
[6,5,3,1,7,2,8,4]=>0000000
[2,1,5,4,8,7,3,6]=>0100000
[2,3,8,5,4,1,6,7]=>0000000
[2,1,4,8,6,5,3,7]=>0100000
[4,3,2,8,7,6,1,5]=>0000000
[3,2,8,7,5,4,1,6]=>0000000
[5,4,2,6,3,1,8,7]=>0000010
[5,6,3,1,2,4,8,7]=>0000010
[3,8,4,1,5,7,2,6]=>0000000
[5,6,3,7,4,8,2,1]=>0000000
[8,5,2,6,1,7,3,4]=>0000000
[5,4,2,6,8,3,7,1]=>0000000
[7,6,8,5,1,4,2,3]=>0000000
[2,1,7,8,5,3,4,6]=>0100000
[4,1,8,2,6,5,3,7]=>0000000
[4,7,3,8,1,2,6,5]=>0000000
[3,8,1,2,4,6,5,7]=>0000000
[4,8,7,6,3,5,2,1]=>0000000
[3,8,7,6,5,2,4,1]=>0000000
[4,8,7,3,6,5,2,1]=>0000000
[4,8,7,6,3,2,5,1]=>0000000
[3,8,7,6,5,2,1,4]=>0000000
[7,5,8,3,6,2,1,4]=>0000000
[7,5,8,3,2,6,1,4]=>0000000
[7,5,8,3,2,1,6,4]=>0000000
[2,3,7,8,4,1,6,5]=>0000000
[2,1,7,5,8,4,6,3]=>0100000
[2,5,6,8,1,7,4,3]=>0000000
[4,2,8,6,1,7,3,5]=>0000000
[8,6,4,1,3,2,5,7]=>0000000
[8,1,3,2,6,5,4,7]=>0000000
[8,5,3,6,2,4,1,7]=>0000000
[8,4,1,2,6,5,3,7]=>0000000
[8,3,5,6,2,1,4,7]=>0000000
[4,1,8,2,3,7,6,5]=>0000000
[3,7,4,5,8,2,1,6]=>0000000
[5,3,8,7,4,6,1,2]=>0000000
[7,5,8,2,1,4,6,3]=>0000000
[7,4,8,3,2,6,1,5]=>0000000
[6,8,2,3,1,7,5,4]=>0000000
[7,4,3,2,6,8,5,1]=>0000000
[5,1,2,3,6,8,7,4]=>0000000
[2,4,7,3,8,1,6,5]=>0000000
[6,3,8,2,7,4,1,5]=>0000000
[8,2,1,3,6,4,7,5]=>0000000
[5,7,8,2,1,4,3,6]=>0000000
[3,5,1,7,8,4,2,6]=>0000000
[1,7,8,4,5,3,2,6]=>1000000
[3,2,4,8,6,7,1,5]=>0000000
[3,2,5,7,4,8,1,6]=>0000000
[8,4,7,1,3,2,5,6]=>0000000
[8,4,7,2,1,3,5,6]=>0000000
[6,4,2,1,3,7,8,5]=>0000000
[7,1,6,3,5,8,2,4]=>0000000
[5,3,6,7,8,4,2,1]=>0000000
[1,5,2,7,8,6,4,3]=>1000000
[4,1,7,5,2,6,8,3]=>0000000
[7,6,2,4,5,1,8,3]=>0000000
[8,1,4,5,2,6,7,3]=>0000000
[3,5,7,2,1,6,8,4]=>0000000
[3,5,2,4,7,6,1,8]=>0000001
[3,5,2,7,4,6,1,8]=>0000001
[3,2,5,7,4,6,1,8]=>0000001
[5,7,3,2,4,6,1,8]=>0000001
[3,7,5,2,4,1,6,8]=>0000001
[3,2,7,5,4,1,6,8]=>0000001
[1,7,3,5,2,4,6,8]=>1000001
[3,2,1,5,7,4,6,8]=>0010001
[3,5,7,2,1,4,6,8]=>0000001
[3,5,2,7,1,4,6,8]=>0000001
[3,2,5,7,4,1,6,8]=>0000001
[3,5,2,7,4,1,6,8]=>0000001
[3,5,7,2,4,1,6,8]=>0000001
[5,3,7,2,4,1,6,8]=>0000001
[5,3,2,4,7,1,6,8]=>0000001
[3,2,5,4,7,1,6,8]=>0000001
[3,5,2,4,1,7,6,8]=>0000101
[3,5,2,1,4,7,6,8]=>0000101
[3,5,2,1,7,4,6,8]=>0000001
[5,3,1,7,2,4,6,8]=>0000001
[1,3,7,5,2,4,6,8]=>1000001
[3,7,2,1,5,4,6,8]=>0000001
[3,1,7,2,5,4,6,8]=>0000001
[1,7,5,3,2,4,6,8]=>1000001
[5,8,7,1,2,6,4,3]=>0000000
[6,8,2,1,7,5,4,3]=>0000000
[5,8,7,4,1,2,6,3]=>0000000
[1,8,5,4,2,7,6,3]=>1000000
[7,6,4,2,8,5,3,1]=>0000000
[7,6,4,8,5,1,2,3]=>0000000
[7,6,4,5,1,3,8,2]=>0000000
[1,6,7,5,3,8,4,2]=>1000000
[7,6,3,5,2,4,8,1]=>0000000
[7,6,4,2,5,1,8,3]=>0000000
[2,6,5,7,8,3,4,1]=>0000000
[5,2,3,4,8,6,1,7]=>0000000
[5,3,4,8,2,7,6,1]=>0000000
[5,3,8,2,4,1,7,6]=>0000000
[5,2,8,4,1,7,3,6]=>0000000
[6,4,2,5,1,8,7,3]=>0000000
[6,4,3,5,8,2,1,7]=>0000000
[6,3,5,4,8,2,7,1]=>0000000
[1,5,7,3,4,8,6,2]=>1000000
[5,8,4,1,3,7,6,2]=>0000000
[6,4,5,3,8,1,7,2]=>0000000
[6,4,3,8,5,7,2,1]=>0000000
[5,4,2,6,3,1,7,8]=>0000011
[4,6,5,3,7,1,2,8]=>0000001
[3,5,7,6,1,4,8,2]=>0000000
[3,6,5,7,4,8,1,2]=>0000000
[4,2,6,5,1,7,3,8]=>0000001
[4,3,5,7,2,1,6,8]=>0000001
[3,5,4,7,2,6,1,8]=>0000001
[3,4,7,6,8,1,2,5]=>0000000
[1,8,4,3,7,5,6,2]=>1000000
[5,2,8,6,4,7,3,1]=>0000000
[1,8,6,3,7,4,2,5]=>1000000
[1,8,6,5,7,2,3,4]=>1000000
[4,2,8,3,5,7,1,6]=>0000000
[1,3,7,2,6,5,8,4]=>1000000
[1,5,7,2,4,6,8,3]=>1000000
[1,3,6,4,2,5,8,7]=>1000010
[5,6,3,4,7,1,8,2]=>0000000
[3,5,2,7,4,1,8,6]=>0000000
[5,2,3,8,4,1,7,6]=>0000000
[7,5,3,4,8,2,1,6]=>0000000
[7,6,3,8,4,2,1,5]=>0000000
[7,2,8,5,1,6,3,4]=>0000000
[7,4,3,8,5,2,6,1]=>0000000
[7,2,8,5,1,3,4,6]=>0000000
[7,6,8,1,2,5,3,4]=>0000000
[1,5,3,7,6,8,4,2]=>1000000
[1,2,6,4,5,8,3,7]=>1100000
[1,2,7,4,8,5,3,6]=>1100000
[1,6,3,7,8,2,4,5]=>1000000
[3,2,6,7,8,1,4,5]=>0000000
[1,4,7,3,5,2,6,8]=>1000001
[3,8,4,7,6,1,5,2]=>0000000
[5,7,4,2,6,3,1,8]=>0000001
[6,1,3,7,4,2,5,8]=>0000001
[2,1,8,3,6,7,4,5]=>0100000
[5,7,1,4,2,6,3,8]=>0000001
[3,2,6,8,1,5,7,4]=>0000000
[7,8,5,4,1,6,3,2]=>0000000
[3,6,2,7,8,1,5,4]=>0000000
[5,7,8,4,1,6,3,2]=>0000000
[3,4,8,1,2,5,7,6]=>0000000
[6,3,1,8,2,7,4,5]=>0000000
[5,2,8,1,3,4,7,6]=>0000000
[3,2,1,6,4,7,8,5]=>0010000
[6,1,3,4,2,8,5,7]=>0000000
[3,2,6,1,5,7,8,4]=>0000000
[3,6,4,2,1,7,8,5]=>0000000
[1,8,3,2,6,7,5,4]=>1000000
[4,7,5,3,8,2,1,6]=>0000000
[1,4,7,6,8,2,3,5]=>1000000
[1,3,7,5,6,8,2,4]=>1000000
[3,2,7,1,6,8,4,5]=>0000000
[3,6,4,7,8,5,2,1]=>0000000
[6,3,5,8,7,4,1,2]=>0000000
[4,1,8,3,7,5,6,2]=>0000000
[4,7,2,8,5,6,3,1]=>0000000
[1,4,8,7,3,5,6,2]=>1000000
[3,2,8,7,1,5,6,4]=>0000000
[1,5,8,7,4,6,2,3]=>1000000
[4,8,6,7,5,3,2,1]=>0000000
[3,8,7,5,6,4,2,1]=>0000000
[8,3,2,1,5,6,4,7]=>0000000
[1,7,8,5,4,3,2,6]=>1000000
[1,2,6,7,8,4,3,5]=>1100000
[8,5,7,1,3,4,6,2]=>0000000
[4,7,2,1,5,3,8,6]=>0000000
[4,3,7,2,6,8,1,5]=>0000000
[1,7,8,2,6,4,5,3]=>1000000
[8,7,2,5,4,6,1,3]=>0000000
[8,7,1,2,4,5,6,3]=>0000000
[8,7,6,1,4,5,3,2]=>0000000
[8,7,5,6,1,4,3,2]=>0000000
[6,8,7,1,5,4,3,2]=>0000000
[8,5,7,6,1,4,3,2]=>0000000
[6,7,8,1,5,4,3,2]=>0000000
[8,5,6,7,1,4,3,2]=>0000000
[8,7,6,3,5,4,1,2]=>0000000
[8,7,4,5,6,1,3,2]=>0000000
[4,2,8,7,6,5,1,3]=>0000000
[7,5,8,1,6,4,3,2]=>0000000
[1,5,8,7,6,2,4,3]=>1000000
[7,5,8,4,1,6,3,2]=>0000000
[6,8,5,1,7,4,3,2]=>0000000
[1,6,8,7,2,5,4,3]=>1000000
[4,8,5,7,1,6,3,2]=>0000000
[5,4,3,6,7,1,8,2]=>0000000
[5,4,7,3,6,1,8,2]=>0000000
[4,8,7,6,3,1,5,2]=>0000000
[6,8,5,7,3,2,1,4]=>0000000
[6,8,5,3,7,2,1,4]=>0000000
[6,8,5,7,4,2,1,3]=>0000000
[2,1,8,7,6,3,4,5]=>0100000
[5,8,7,6,2,4,1,3]=>0000000
[6,8,2,7,5,1,4,3]=>0000000
[5,8,7,2,6,4,1,3]=>0000000
[6,8,7,5,2,4,1,3]=>0000000
[5,8,7,6,4,2,3,1]=>0000000
[2,3,6,1,7,5,8,4]=>0000000
[2,3,6,1,8,5,4,7]=>0000000
[2,4,1,6,7,5,8,3]=>0000000
[2,4,1,7,3,8,6,5]=>0000000
[2,4,5,3,7,1,8,6]=>0000000
[2,4,5,7,3,8,6,1]=>0000000
[2,4,6,3,1,8,5,7]=>0000000
[2,4,6,3,8,5,1,7]=>0000000
[2,4,7,3,1,5,8,6]=>0000000
[2,5,1,6,4,8,3,7]=>0000000
[2,5,1,7,4,3,8,6]=>0000000
[2,5,6,7,8,4,1,3]=>0000000
[2,5,6,8,4,3,1,7]=>0000000
[2,6,1,7,4,8,5,3]=>0000000
[7,6,4,8,2,1,3,5]=>0000000
[7,6,5,2,8,4,1,3]=>0000000
[7,6,3,8,2,4,1,5]=>0000000
[7,6,5,8,2,4,3,1]=>0000000
[6,8,4,7,2,5,3,1]=>0000000
[6,4,8,7,5,2,3,1]=>0000000
[6,8,4,2,7,5,3,1]=>0000000
[6,8,4,7,2,1,5,3]=>0000000
[6,8,4,7,3,5,2,1]=>0000000
[6,8,4,2,7,1,5,3]=>0000000
[6,4,2,8,7,5,3,1]=>0000000
[6,8,4,7,3,2,5,1]=>0000000
[6,8,4,2,1,7,5,3]=>0000000
[6,8,4,7,3,2,1,5]=>0000000
[6,8,5,7,1,4,3,2]=>0000000
[1,8,7,3,6,2,5,4]=>1000000
[5,8,7,2,3,6,1,4]=>0000000
[6,8,2,7,5,4,1,3]=>0000000
[6,8,3,7,5,2,1,4]=>0000000
[6,8,1,7,3,5,4,2]=>0000000
[6,8,4,7,3,1,5,2]=>0000000
[6,8,1,7,3,2,5,4]=>0000000
[3,8,2,7,6,5,1,4]=>0000000
[1,8,4,7,6,2,5,3]=>1000000
[3,8,1,7,6,2,5,4]=>0000000
[1,8,4,7,3,6,5,2]=>1000000
[4,8,5,7,1,2,6,3]=>0000000
[1,8,4,7,3,2,6,5]=>1000000
[6,8,5,2,7,4,1,3]=>0000000
[6,8,1,3,7,2,5,4]=>0000000
[2,8,1,3,7,6,5,4]=>0000000
[2,8,3,4,7,6,1,5]=>0000000
[6,8,1,4,2,7,5,3]=>0000000
[6,5,4,3,8,7,1,2]=>0000000
[3,1,7,2,8,5,6,4]=>0000000
[3,1,6,7,4,8,5,2]=>0000000
[3,1,5,7,8,4,6,2]=>0000000
[8,6,5,7,1,4,3,2]=>0000000
[6,4,8,2,7,5,1,3]=>0000000
[8,4,7,6,2,5,1,3]=>0000000
[3,4,5,6,8,7,1,2]=>0000000
[3,4,5,7,8,6,1,2]=>0000000
[3,4,5,8,7,6,1,2]=>0000000
[3,4,6,7,8,5,1,2]=>0000000
[6,4,7,3,5,2,1,8]=>0000001
[5,4,7,3,6,2,1,8]=>0000001
[5,8,3,6,7,2,1,4]=>0000000
[6,4,7,3,2,5,1,8]=>0000001
[6,3,7,8,2,4,1,5]=>0000000
[5,3,7,6,2,4,1,8]=>0000001
[7,5,8,2,6,4,1,3]=>0000000
[5,4,7,2,6,8,1,3]=>0000000
[5,4,3,2,6,8,1,7]=>0000000
[4,8,3,2,5,6,1,7]=>0000000
[5,3,7,2,6,4,1,8]=>0000001
[6,4,2,7,5,8,1,3]=>0000000
[7,5,8,4,1,2,6,3]=>0000000
[7,1,8,2,3,6,5,4]=>0000000
[7,3,8,4,6,2,1,5]=>0000000
[7,1,8,4,2,6,5,3]=>0000000
[7,1,8,3,6,2,5,4]=>0000000
[7,2,3,4,5,1,8,6]=>0000000
[2,7,3,4,1,5,6,8]=>0000001
[5,3,6,1,2,7,4,8]=>0000001
[3,8,1,4,5,6,7,2]=>0000000
[4,5,3,1,2,8,7,6]=>0000100
[4,5,3,1,2,6,8,7]=>0000110
[6,5,3,2,1,8,7,4]=>0000000
[4,5,2,1,8,7,6,3]=>0000000
[3,4,1,8,7,6,5,2]=>0000000
[8,1,2,4,5,6,7,3]=>0000000
[5,1,2,4,8,6,7,3]=>0000000
[4,1,3,8,5,6,7,2]=>0000000
[6,1,2,3,5,7,8,4]=>0000000
[5,1,3,8,4,6,7,2]=>0000000
[4,1,3,5,8,6,7,2]=>0000000
[7,5,2,8,6,3,4,1]=>0000000
[5,3,8,4,1,2,6,7]=>0000000
[6,3,5,8,4,1,2,7]=>0000000
[6,3,8,4,5,1,2,7]=>0000000
[8,5,1,7,4,6,2,3]=>0000000
[7,4,5,1,8,6,2,3]=>0000000
[4,2,7,5,8,6,3,1]=>0000000
[4,2,8,5,6,3,1,7]=>0000000
[4,2,8,5,6,7,3,1]=>0000000
[7,4,8,5,6,1,2,3]=>0000000
[7,5,8,6,1,2,3,4]=>0000000
[7,2,8,3,4,5,6,1]=>0000000
[5,2,4,8,6,7,3,1]=>0000000
[7,5,8,6,2,3,1,4]=>0000000
[7,4,8,5,6,2,3,1]=>0000000
[3,4,5,7,6,8,1,2]=>0000000
[4,8,2,5,1,3,7,6]=>0000000
[4,1,2,8,7,5,3,6]=>0000000
[3,1,7,6,8,2,4,5]=>0000000
[7,3,5,1,8,2,4,6]=>0000000
[7,8,3,1,5,2,4,6]=>0000000
[1,4,6,7,8,3,5,2]=>1000000
[1,5,6,3,7,8,4,2]=>1000000
[5,1,2,3,8,6,7,4]=>0000000
[2,8,5,3,1,4,6,7]=>0000000
[2,4,3,5,7,8,1,6]=>0000000
[2,6,3,7,8,1,4,5]=>0000000
[3,4,8,1,5,6,7,2]=>0000000
[3,5,1,7,4,8,6,2]=>0000000
[3,5,8,4,1,6,7,2]=>0000000
[3,6,1,8,5,4,7,2]=>0000000
[3,6,7,4,8,5,1,2]=>0000000
[3,6,8,4,5,1,7,2]=>0000000
[4,1,7,3,5,8,6,2]=>0000000
[4,6,3,1,8,5,7,2]=>0000000
[4,6,7,3,5,8,1,2]=>0000000
[4,6,8,3,5,1,7,2]=>0000000
[4,7,3,1,8,6,5,2]=>0000000
[5,1,6,7,4,8,3,2]=>0000000
[5,1,6,7,8,3,4,2]=>0000000
[5,6,7,8,4,1,3,2]=>0000000
[5,7,3,8,4,6,1,2]=>0000000
[5,7,8,4,3,6,1,2]=>0000000
[6,1,3,7,8,5,4,2]=>0000000
[6,1,8,4,5,3,7,2]=>0000000
[6,7,3,8,5,4,1,2]=>0000000
[7,1,3,4,8,6,5,2]=>0000000
[8,5,1,2,4,3,6,7]=>0000000
[8,5,1,4,2,3,6,7]=>0000000
[8,7,1,2,3,6,4,5]=>0000000
[5,6,8,7,2,3,1,4]=>0000000
[5,2,3,6,7,8,1,4]=>0000000
[4,2,8,7,5,3,1,6]=>0000000
[1,3,2,4,8,5,7,6]=>1011000
[1,6,3,2,5,7,8,4]=>1000000
[7,6,2,1,4,8,3,5]=>0000000
[2,6,5,1,8,7,3,4]=>0000000
[1,4,2,7,3,8,6,5]=>1000000
[1,2,7,3,8,6,5,4]=>1100000
[3,1,8,4,6,2,7,5]=>0000000
[1,5,2,3,8,7,4,6]=>1000000
[2,8,7,6,3,1,4,5]=>0000000
[8,7,6,2,1,4,3,5]=>0000000
[8,2,7,4,1,5,3,6]=>0000000
[8,7,3,1,4,2,6,5]=>0000000
[1,2,5,3,4,8,7,6]=>1100100
[1,2,3,8,4,7,6,5]=>1110000
[1,6,2,3,7,5,8,4]=>1000000
[1,4,8,2,6,3,7,5]=>1000000
[8,4,1,7,3,2,5,6]=>0000000
[1,8,7,3,2,4,6,5]=>1000000
[3,4,1,6,5,7,2,8]=>0000001
[3,5,1,6,2,8,7,4]=>0000000
[5,4,3,6,1,7,2,8]=>0000001
[4,8,7,2,1,6,5,3]=>0000000
[6,2,1,8,7,5,4,3]=>0000000
[5,8,7,6,3,2,4,1]=>0000000
[5,4,7,2,8,1,6,3]=>0000000
[2,1,5,8,3,7,4,6]=>0100000
[1,2,3,5,8,7,4,6]=>1110000
[6,1,2,7,8,4,3,5]=>0000000
[5,1,4,8,2,7,3,6]=>0000000
[1,2,5,7,8,6,3,4]=>1100000
[2,1,3,4,8,5,7,6]=>0111000
[6,2,5,1,7,3,8,4]=>0000000
[2,4,8,1,3,7,5,6]=>0000000
[2,5,1,8,6,3,7,4]=>0000000
[2,1,3,7,4,8,6,5]=>0110000
[2,6,8,5,1,7,3,4]=>0000000
[1,3,2,7,8,5,4,6]=>1010000
[7,1,2,3,6,8,4,5]=>0000000
[5,1,2,3,8,4,7,6]=>0000000
[4,1,2,3,8,7,5,6]=>0001000
[2,3,1,8,5,4,7,6]=>0010000
[2,3,8,4,1,5,7,6]=>0000000
[5,3,1,8,7,2,4,6]=>0000000
[1,3,8,4,2,7,6,5]=>1000000
[1,2,3,8,5,7,4,6]=>1110000
[6,1,7,2,5,8,3,4]=>0000000
[4,5,1,8,7,2,3,6]=>0000000
[1,4,2,8,5,3,7,6]=>1000000
[7,8,6,5,2,1,4,3]=>0000000
[8,6,7,5,2,1,4,3]=>0000000
[6,7,8,2,1,5,4,3]=>0000000
[8,7,5,6,2,1,4,3]=>0000000
[4,2,5,1,8,7,3,6]=>0000000
[7,2,4,5,8,3,6,1]=>0000000
[2,4,7,8,6,1,5,3]=>0000000
[4,2,7,1,5,6,8,3]=>0000000
[3,2,5,8,1,6,7,4]=>0000000
[8,1,4,3,2,5,6,7]=>0000000
[1,7,3,2,4,5,6,8]=>1000001
[1,6,3,2,4,5,7,8]=>1000011
[1,3,8,4,2,5,6,7]=>1000000
[5,1,8,2,4,3,6,7]=>0000000
[1,7,2,4,5,8,6,3]=>1000000
[1,3,8,2,6,4,5,7]=>1000000
[6,1,2,7,4,3,8,5]=>0000000
[7,6,1,3,8,2,4,5]=>0000000
[5,4,1,2,3,8,6,7]=>0000100
[6,7,8,5,2,4,1,3]=>0000000
[3,4,5,8,2,1,7,6]=>0000000
[3,4,6,2,7,1,5,8]=>0000001
[3,4,6,1,5,2,7,8]=>0000011
[3,4,7,2,1,6,5,8]=>0000001
[3,5,2,6,1,4,7,8]=>0000011
[3,5,2,7,1,6,4,8]=>0000001
[3,5,2,1,4,6,7,8]=>0000111
[3,5,6,4,8,2,1,7]=>0000000
[3,5,6,4,1,2,7,8]=>0000011
[3,5,6,8,4,2,1,7]=>0000000
[3,5,6,1,4,2,7,8]=>0000011
[3,5,7,4,2,8,1,6]=>0000000
[3,5,7,4,2,1,6,8]=>0000001
[3,5,7,4,8,1,6,2]=>0000000
[3,5,7,1,4,6,2,8]=>0000001
[3,5,8,1,4,6,7,2]=>0000000
[3,6,2,4,8,1,7,5]=>0000000
[3,6,2,7,8,5,1,4]=>0000000
[3,6,2,7,8,1,4,5]=>0000000
[3,6,2,1,5,4,7,8]=>0000011
[3,6,7,8,5,1,2,4]=>0000000
[3,6,7,8,1,5,2,4]=>0000000
[3,7,2,4,5,8,1,6]=>0000000
[3,7,2,4,8,1,6,5]=>0000000
[3,7,2,8,5,6,1,4]=>0000000
[3,7,2,1,5,6,4,8]=>0000001
[3,7,8,4,5,1,6,2]=>0000000
[3,8,2,4,1,6,7,5]=>0000000
[8,1,5,4,3,6,7,2]=>0000000
[4,1,7,3,5,6,8,2]=>0000000
[6,1,7,3,8,4,5,2]=>0000000
[4,1,3,6,7,8,5,2]=>0000000
[3,5,2,4,1,6,7,8]=>0000111
[2,3,7,8,1,6,5,4]=>0000000
[2,6,5,8,1,3,7,4]=>0000000
[6,4,7,5,8,2,3,1]=>0000000
[6,7,4,1,8,2,3,5]=>0000000
[6,7,8,1,4,2,5,3]=>0000000
[5,2,6,1,4,8,3,7]=>0000000
[7,2,3,5,8,1,4,6]=>0000000
[2,4,7,5,8,1,3,6]=>0000000
[2,3,6,5,1,8,7,4]=>0000000
[2,3,4,8,1,5,7,6]=>0000000
[2,7,8,5,1,4,6,3]=>0000000
[2,3,7,5,8,1,4,6]=>0000000
[2,3,6,8,5,1,7,4]=>0000000
[7,6,4,5,1,8,2,3]=>0000000
[7,4,6,8,1,5,2,3]=>0000000
[2,6,7,8,5,3,1,4]=>0000000
[2,5,6,1,4,8,3,7]=>0000000
[2,6,4,8,5,7,3,1]=>0000000
[2,5,8,1,4,6,7,3]=>0000000
[7,2,3,4,8,1,6,5]=>0000000
[3,2,5,7,8,1,6,4]=>0000000
[6,4,1,7,8,2,3,5]=>0000000
[5,7,6,1,2,8,3,4]=>0000000
[5,6,8,1,2,4,7,3]=>0000000
[6,2,3,4,5,8,1,7]=>0000000
[4,7,1,3,8,2,6,5]=>0000000
[5,4,1,6,7,8,2,3]=>0000000
[5,7,1,8,6,2,3,4]=>0000000
[7,3,5,1,8,2,6,4]=>0000000
[5,6,7,3,8,2,1,4]=>0000000
[5,7,3,2,8,6,1,4]=>0000000
[5,7,8,3,1,6,2,4]=>0000000
[5,8,3,2,1,6,7,4]=>0000000
[6,2,7,3,8,5,1,4]=>0000000
[6,2,3,7,8,5,1,4]=>0000000
[1,5,8,3,2,6,7,4]=>1000000
[1,6,7,8,5,2,3,4]=>1000000
[1,6,7,8,4,2,3,5]=>1000000
[1,2,6,8,4,3,7,5]=>1100000
[1,8,3,4,2,6,7,5]=>1000000
[6,2,7,8,4,1,3,5]=>0000000
[6,2,3,7,8,1,4,5]=>0000000
[4,5,7,1,8,6,2,3]=>0000000
[4,5,7,8,2,6,1,3]=>0000000
[4,6,2,8,5,1,7,3]=>0000000
[4,6,7,1,8,5,2,3]=>0000000
[4,7,2,8,5,6,1,3]=>0000000
[4,8,2,1,5,6,7,3]=>0000000
[1,2,8,4,5,3,7,6]=>1100000
[1,2,3,7,8,5,4,6]=>1110000
[1,2,3,8,5,4,7,6]=>1110000
[1,7,3,8,5,4,2,6]=>1000000
[5,2,7,4,8,6,1,3]=>0000000
[5,6,2,7,8,1,4,3]=>0000000
[5,8,2,4,1,6,7,3]=>0000000
[6,2,1,7,8,5,4,3]=>0000000
[6,7,2,8,5,4,1,3]=>0000000
[6,8,2,4,5,1,7,3]=>0000000
[3,2,5,6,8,1,4,7]=>0000000
[7,1,3,2,8,4,5,6]=>0000000
[7,1,6,3,8,2,4,5]=>0000000
[6,1,5,8,2,3,4,7]=>0000000
[8,1,6,7,4,2,3,5]=>0000000
[6,1,5,8,2,3,7,4]=>0000000
[4,1,7,2,5,8,3,6]=>0000000
[8,1,6,3,4,7,2,5]=>0000000
[8,1,7,3,2,5,6,4]=>0000000
[4,1,8,2,5,6,7,3]=>0000000
[3,8,1,2,7,5,4,6]=>0000000
[8,4,7,1,3,2,6,5]=>0000000
[8,5,7,3,1,2,6,4]=>0000000
[3,8,1,2,4,5,7,6]=>0000000
[7,6,2,1,8,4,3,5]=>0000000
[8,5,2,3,6,1,4,7]=>0000000
[8,5,7,1,4,3,2,6]=>0000000
[3,6,1,4,2,8,5,7]=>0000000
[7,6,8,1,4,5,2,3]=>0000000
[3,7,1,4,2,8,6,5]=>0000000
[5,4,3,8,2,1,7,6]=>0000000
[5,8,7,3,2,1,6,4]=>0000000
[2,3,7,1,6,8,5,4]=>0000000
[2,6,1,5,7,4,8,3]=>0000000
[2,3,6,1,8,4,7,5]=>0000000
[3,5,1,4,6,7,8,2]=>0000000
[4,5,6,2,1,7,8,3]=>0000000
[5,2,4,7,6,3,8,1]=>0000000
[8,7,6,1,4,3,5,2]=>0000000
[8,7,6,1,3,4,5,2]=>0000000
[8,7,1,4,5,6,3,2]=>0000000
[8,1,5,6,7,4,3,2]=>0000000
[5,8,3,4,1,6,2,7]=>0000000
[4,2,6,1,7,8,5,3]=>0000000
[1,5,2,6,7,8,4,3]=>1000000
[1,5,6,7,4,8,2,3]=>1000000
[4,2,7,8,5,6,1,3]=>0000000
[5,6,2,7,3,8,4,1]=>0000000
[3,7,2,8,4,1,5,6]=>0000000
[3,5,2,4,7,8,6,1]=>0000000
[5,1,3,8,2,4,6,7]=>0000000
[1,8,7,6,3,4,5,2]=>1000000
[8,5,7,6,3,2,1,4]=>0000000
[8,7,5,3,1,6,4,2]=>0000000
[7,8,1,4,5,6,3,2]=>0000000
[4,2,8,3,5,1,7,6]=>0000000
[4,2,7,8,1,6,5,3]=>0000000
[5,1,3,4,2,6,7,8]=>0000111
[4,2,7,3,1,6,5,8]=>0000001
[2,3,4,5,8,1,7,6]=>0000000
[4,1,5,3,6,7,8,2]=>0000000
[5,1,6,3,4,7,8,2]=>0000000
[2,1,7,5,3,8,6,4]=>0100000
[3,2,1,6,4,5,7,8]=>0010011
[3,8,1,2,5,4,7,6]=>0000000
[7,5,8,6,3,2,1,4]=>0000000
[6,4,2,1,8,5,3,7]=>0000000
[5,3,8,4,2,1,6,7]=>0000000
[7,4,5,2,1,8,6,3]=>0000000
[6,3,8,4,5,2,1,7]=>0000000
[7,4,8,5,6,2,1,3]=>0000000
[7,3,8,4,5,6,2,1]=>0000000
[1,8,7,2,6,5,4,3]=>1000000
[1,8,7,6,2,3,4,5]=>1000000
[1,8,2,5,6,7,4,3]=>1000000
[1,2,8,3,4,5,7,6]=>1100000
[7,4,1,2,8,3,5,6]=>0000000
[6,4,1,2,8,3,5,7]=>0000000
[4,8,1,2,3,7,5,6]=>0000000
[6,5,1,2,3,8,4,7]=>0000000
[1,8,5,2,3,7,4,6]=>1000000
[6,5,1,2,7,3,8,4]=>0000000
[7,6,4,1,8,2,3,5]=>0000000
[7,6,3,1,8,2,4,5]=>0000000
[7,5,4,1,8,2,3,6]=>0000000
[7,6,1,4,8,2,3,5]=>0000000
[1,2,8,5,3,7,4,6]=>1100000
[1,2,7,3,8,6,4,5]=>1100000
[7,5,1,6,8,2,3,4]=>0000000
[4,1,2,8,6,3,7,5]=>0000000
[5,4,1,6,2,7,8,3]=>0000000
[6,5,3,1,8,2,4,7]=>0000000
[3,8,1,6,7,2,4,5]=>0000000
[6,5,3,7,1,2,8,4]=>0000000
[7,1,4,2,6,8,3,5]=>0000000
[1,2,6,8,3,5,4,7]=>1100000
[1,2,3,7,8,6,4,5]=>1110000
[1,6,8,5,2,7,3,4]=>1000000
[1,4,8,2,3,7,6,5]=>1000000
[1,2,8,3,5,7,6,4]=>1100000
[4,5,1,7,6,8,2,3]=>0000000
[1,4,2,5,6,8,7,3]=>1000000
[8,2,7,3,1,5,6,4]=>0000000
[7,2,1,8,4,5,6,3]=>0000000
[4,2,7,1,3,8,6,5]=>0000000
[8,2,6,3,4,7,1,5]=>0000000
[7,2,3,4,1,8,6,5]=>0000000
[4,2,8,1,5,6,3,7]=>0000000
[8,2,7,3,1,4,5,6]=>0000000
[5,3,1,6,2,7,8,4]=>0000000
[5,2,1,3,6,7,8,4]=>0000000
[6,5,3,8,7,2,1,4]=>0000000
[5,4,8,7,3,2,1,6]=>0000000
[6,4,3,8,7,2,1,5]=>0000000
[5,6,3,1,4,2,7,8]=>0000011
[5,2,6,1,4,3,7,8]=>0000011
[5,8,3,1,4,6,7,2]=>0000000
[6,2,7,4,1,5,3,8]=>0000001
[6,7,3,8,1,5,2,4]=>0000000
[6,7,3,4,1,5,2,8]=>0000001
[6,7,8,1,5,4,2,3]=>0000000
[4,5,7,8,2,1,6,3]=>0000000
[7,2,3,8,1,6,5,4]=>0000000
[7,2,3,8,5,1,6,4]=>0000000
[7,2,3,1,5,6,4,8]=>0000001
[7,2,8,4,1,6,5,3]=>0000000
[7,2,8,4,5,1,6,3]=>0000000
[4,6,3,8,1,5,7,2]=>0000000
[4,6,7,3,8,1,2,5]=>0000000
[4,6,7,8,1,5,3,2]=>0000000
[4,6,7,1,5,2,3,8]=>0000001
[4,6,8,3,1,5,7,2]=>0000000
[4,7,3,8,5,1,6,2]=>0000000
[4,7,3,8,1,6,5,2]=>0000000
[4,1,8,2,7,3,5,6]=>0000000
[1,8,4,2,7,3,5,6]=>1000000
[7,4,1,2,6,8,3,5]=>0000000
[8,7,1,2,4,5,3,6]=>0000000
[5,4,1,2,7,8,3,6]=>0000000
[1,5,2,8,3,4,7,6]=>1000000
[7,1,2,5,3,6,8,4]=>0000000
[1,8,2,5,6,3,7,4]=>1000000
[1,5,2,4,6,7,8,3]=>1000000
[3,1,8,2,5,4,6,7]=>0000000
[3,1,7,5,8,2,4,6]=>0000000
[1,7,3,2,8,4,5,6]=>1000000
[1,6,4,2,3,5,8,7]=>1000010
[1,7,4,2,3,5,8,6]=>1000000
[1,7,4,2,3,6,8,5]=>1000000
[1,2,7,3,8,4,6,5]=>1100000
[7,1,3,4,5,8,2,6]=>0000000
[1,8,7,6,3,2,4,5]=>1000000
[1,7,4,5,2,6,8,3]=>1000000
[1,4,8,5,6,2,7,3]=>1000000
[3,2,1,8,7,4,5,6]=>0010000
[3,2,8,7,6,1,5,4]=>0000000
[6,5,8,7,3,2,1,4]=>0000000
[4,6,2,8,5,3,7,1]=>0000000
[5,3,8,4,6,2,7,1]=>0000000
[4,6,2,7,1,8,5,3]=>0000000
[6,2,5,3,8,4,7,1]=>0000000
[4,6,5,3,8,2,7,1]=>0000000
[5,7,8,4,3,2,1,6]=>0000000
[4,6,8,7,3,2,1,5]=>0000000
[2,4,8,7,6,5,1,3]=>0000000
[4,7,6,8,3,2,1,5]=>0000000
[4,6,7,8,3,2,1,5]=>0000000
[3,5,6,8,7,2,1,4]=>0000000
[1,4,8,7,6,3,5,2]=>1000000
[2,5,4,7,3,8,1,6]=>0000000
[2,4,6,1,5,8,3,7]=>0000000
[2,5,4,8,6,7,3,1]=>0000000
[3,4,1,7,6,8,5,2]=>0000000
[3,6,1,7,8,4,2,5]=>0000000
[4,3,6,2,8,1,7,5]=>0000000
[5,3,4,7,2,8,1,6]=>0000000
[4,5,7,2,1,8,3,6]=>0000000
[4,5,8,2,1,6,7,3]=>0000000
[3,6,1,7,2,5,8,4]=>0000000
[6,3,7,8,2,5,1,4]=>0000000
[6,7,4,8,2,5,3,1]=>0000000
[3,5,1,4,7,2,8,6]=>0000000
[4,7,8,5,6,2,1,3]=>0000000
[3,5,1,4,8,7,2,6]=>0000000
[4,5,6,3,8,2,1,7]=>0000000
[4,2,6,3,7,8,1,5]=>0000000
[4,2,7,3,5,8,1,6]=>0000000
[5,1,2,7,8,6,4,3]=>0000000
[4,1,2,7,8,6,3,5]=>0000000
[4,1,8,7,2,6,3,5]=>0000000
[5,1,8,2,7,6,3,4]=>0000000
[7,1,6,2,8,3,4,5]=>0000000
[4,5,2,8,7,3,1,6]=>0000000
[8,2,1,7,4,6,3,5]=>0000000
[4,5,2,8,7,1,6,3]=>0000000
[4,2,5,7,3,1,8,6]=>0000000
[4,2,8,7,1,3,6,5]=>0000000
[8,2,1,7,3,5,4,6]=>0000000
[5,2,6,3,8,7,1,4]=>0000000
[5,2,3,8,7,1,4,6]=>0000000
[6,1,2,8,3,7,4,5]=>0000000
[5,6,7,3,8,1,2,4]=>0000000
[8,1,7,3,5,4,2,6]=>0000000
[7,1,6,8,5,2,3,4]=>0000000
[8,1,7,3,5,2,6,4]=>0000000
[6,2,3,8,7,5,1,4]=>0000000
[3,8,5,7,2,4,1,6]=>0000000
[3,6,5,8,2,1,7,4]=>0000000
[7,6,2,3,4,1,8,5]=>0000000
[4,8,6,7,1,2,3,5]=>0000000
[8,5,7,3,1,6,2,4]=>0000000
[3,8,6,1,4,7,2,5]=>0000000
[3,7,6,8,2,5,1,4]=>0000000
[8,6,2,3,1,5,7,4]=>0000000
[3,8,7,1,2,5,6,4]=>0000000
[3,4,8,2,5,6,7,1]=>0000000
[6,3,4,8,7,5,1,2]=>0000000
[2,1,8,5,6,7,3,4]=>0100000
[8,3,2,5,6,7,1,4]=>0000000
[4,8,6,7,3,5,2,1]=>0000000
[4,3,1,2,6,7,8,5]=>0001000
[7,4,6,5,8,3,2,1]=>0000000
[2,5,8,6,7,3,1,4]=>0000000
[1,4,6,5,2,7,3,8]=>1000001
[2,3,4,1,8,7,5,6]=>0001000
[4,2,6,5,1,8,7,3]=>0000000
[7,8,4,2,1,5,6,3]=>0000000
[7,8,2,3,6,1,5,4]=>0000000
[2,1,7,8,4,5,6,3]=>0100000
[8,6,2,7,1,3,5,4]=>0000000
[5,8,2,3,4,7,6,1]=>0000000
[2,5,1,4,3,7,6,8]=>0000101
[1,4,5,3,7,2,8,6]=>1000000
[5,1,4,3,7,2,8,6]=>0000000
[1,6,7,4,3,2,8,5]=>1000000
[2,6,7,3,1,4,5,8]=>0000001
[5,1,4,6,7,2,3,8]=>0000001
[2,6,4,3,1,8,5,7]=>0000000
[1,6,5,2,3,4,8,7]=>1000010
[7,8,2,1,5,4,3,6]=>0000000
[7,8,1,2,3,6,4,5]=>0000000
[1,4,7,8,5,2,3,6]=>1000000
[1,3,2,6,5,8,4,7]=>1010000
[2,1,5,7,8,4,3,6]=>0100000
[3,1,7,2,6,5,8,4]=>0000000
[1,3,2,7,5,4,8,6]=>1010000
[1,4,5,8,6,2,3,7]=>1000000
[1,6,7,2,3,5,8,4]=>1000000
[2,4,1,8,6,5,3,7]=>0000000
[2,3,4,6,8,5,7,1]=>0000000
[3,6,2,4,7,5,8,1]=>0000000
[4,3,5,8,7,2,6,1]=>0000000
[5,1,6,3,7,8,4,2]=>0000000
[4,2,6,7,5,1,8,3]=>0000000
[6,4,7,5,8,3,2,1]=>0000000
[3,6,7,5,8,1,4,2]=>0000000
[3,2,7,4,6,1,8,5]=>0000000
[8,2,4,1,6,7,5,3]=>0000000
[3,4,8,7,6,1,5,2]=>0000000
[4,3,8,7,6,2,5,1]=>0000000
[4,3,7,5,8,6,2,1]=>0000000
[3,4,7,5,8,6,1,2]=>0000000
[2,7,5,6,8,3,4,1]=>0000000
[7,8,3,4,6,5,1,2]=>0000000
[2,1,7,6,8,4,5,3]=>0100000
[3,5,4,7,6,1,8,2]=>0000000
[6,5,4,2,7,8,3,1]=>0000000
[2,6,8,5,7,4,3,1]=>0000000
[2,1,8,6,7,5,4,3]=>0100000
[2,5,3,1,6,4,7,8]=>0000011
[7,5,4,2,3,1,8,6]=>0000000
[6,3,2,4,5,8,1,7]=>0000000
[3,5,4,2,8,6,1,7]=>0000000
[5,6,8,7,3,2,1,4]=>0000000
[6,4,5,3,2,8,1,7]=>0000000
[4,2,5,7,3,1,6,8]=>0000001
[7,4,1,3,2,6,8,5]=>0000000
[1,6,4,2,3,7,8,5]=>1000000
[1,4,5,3,8,2,6,7]=>1000000
[6,2,5,1,3,7,4,8]=>0000001
[7,6,5,8,1,2,4,3]=>0000000
[5,7,4,1,3,6,2,8]=>0000001
[4,3,8,1,6,5,7,2]=>0000000
[3,2,8,1,6,7,4,5]=>0000000
[7,2,6,3,8,1,5,4]=>0000000
[7,2,8,1,6,3,5,4]=>0000000
[7,4,8,2,3,5,6,1]=>0000000
[7,4,8,1,5,6,2,3]=>0000000
[7,2,8,1,6,5,4,3]=>0000000
[8,6,5,7,2,1,4,3]=>0000000
[2,4,7,8,5,6,3,1]=>0000000
[2,8,1,3,5,6,7,4]=>0000000
[3,8,7,5,2,6,4,1]=>0000000
[1,8,7,3,4,6,5,2]=>1000000
[2,8,1,4,5,7,6,3]=>0000000
[1,2,6,7,8,3,5,4]=>1100000
[1,2,6,8,7,3,4,5]=>1100000
[3,7,8,1,5,6,2,4]=>0000000
[4,1,3,7,6,8,5,2]=>0000000
[6,5,7,8,1,4,3,2]=>0000000
[3,1,8,6,7,5,4,2]=>0000000
[2,8,3,1,7,5,4,6]=>0000000
[4,1,2,6,7,5,3,8]=>0000001
[1,2,5,3,8,6,4,7]=>1100000
[5,8,7,6,2,1,3,4]=>0000000
[3,6,8,2,5,7,4,1]=>0000000
[3,2,8,5,6,1,7,4]=>0000000
[3,4,8,1,5,7,6,2]=>0000000
[4,5,6,2,7,3,8,1]=>0000000
[3,5,8,7,4,6,2,1]=>0000000
[3,5,7,6,2,4,8,1]=>0000000
[1,6,8,7,4,5,3,2]=>1000000
[1,3,5,6,8,7,2,4]=>1000000
[3,5,6,7,8,2,4,1]=>0000000
[8,5,6,7,2,4,3,1]=>0000000
[7,8,4,5,1,6,3,2]=>0000000
[4,5,6,8,3,7,2,1]=>0000000
[8,1,4,3,6,5,2,7]=>0000000
[8,1,2,3,6,5,4,7]=>0000000
[8,1,2,3,7,6,5,4]=>0000000
[2,8,1,6,7,5,3,4]=>0000000
[4,8,5,2,7,1,6,3]=>0000000
[3,7,8,4,6,2,1,5]=>0000000
[8,3,1,5,7,6,2,4]=>0000000
[4,5,2,8,6,7,1,3]=>0000000
[8,4,5,1,3,2,6,7]=>0000000
[8,1,6,7,2,5,4,3]=>0000000
[5,4,1,3,2,8,7,6]=>0000100
[3,2,7,4,1,6,5,8]=>0000001
[5,7,3,2,1,6,4,8]=>0000001
[7,6,5,1,3,4,2,8]=>0000001
[7,6,5,1,4,2,3,8]=>0000001
[1,7,6,3,2,4,5,8]=>1000001
[1,5,7,2,4,3,6,8]=>1000001
[7,1,6,8,2,4,5,3]=>0000000
[5,8,1,3,4,7,2,6]=>0000000
[5,8,6,2,3,1,4,7]=>0000000
[3,8,2,7,6,4,1,5]=>0000000
[1,6,8,4,7,5,3,2]=>1000000
[6,5,8,3,7,4,2,1]=>0000000
[2,6,8,5,4,7,3,1]=>0000000
[2,7,4,6,8,5,3,1]=>0000000
[6,4,7,8,3,5,2,1]=>0000000
[7,3,4,2,6,1,8,5]=>0000000
[2,3,7,4,6,1,8,5]=>0000000
[7,5,4,2,6,3,8,1]=>0000000
[5,4,7,2,6,1,8,3]=>0000000
[5,2,7,4,6,1,8,3]=>0000000
[5,2,4,1,7,6,8,3]=>0000000
[4,2,7,5,6,1,8,3]=>0000000
[4,2,7,5,6,3,8,1]=>0000000
[2,6,4,3,7,5,8,1]=>0000000
[4,3,7,5,8,6,1,2]=>0000000
[6,7,4,8,3,5,2,1]=>0000000
[3,6,8,5,4,7,1,2]=>0000000
[6,7,5,8,2,4,3,1]=>0000000
[2,5,4,1,7,8,6,3]=>0000000
[1,6,3,2,5,8,7,4]=>1000000
[1,6,8,3,2,4,7,5]=>1000000
[1,8,7,6,4,2,3,5]=>1000000
[8,6,1,2,4,5,7,3]=>0000000
[1,8,6,7,3,4,5,2]=>1000000
[1,7,3,8,2,4,6,5]=>1000000
[8,4,3,1,5,6,7,2]=>0000000
[1,8,7,6,3,4,2,5]=>1000000
[7,1,3,8,4,5,2,6]=>0000000
[1,8,5,3,7,6,2,4]=>1000000
[3,5,2,6,1,4,8,7]=>0000010
[4,5,7,2,3,8,6,1]=>0000000
[4,5,7,2,3,8,1,6]=>0000000
[4,5,6,2,3,1,8,7]=>0000010
[4,5,6,2,1,3,8,7]=>0000010
[4,5,6,1,3,2,8,7]=>0000010
[4,5,6,3,1,2,8,7]=>0000010
[4,5,7,3,2,8,1,6]=>0000000
[4,6,7,3,8,2,5,1]=>0000000
[4,6,7,3,8,2,1,5]=>0000000
[4,5,7,3,1,8,2,6]=>0000000
[3,5,1,7,4,8,2,6]=>0000000
[2,1,5,7,4,8,3,6]=>0100000
[4,5,7,1,3,8,6,2]=>0000000
[4,6,7,3,8,1,5,2]=>0000000
[5,6,7,8,3,1,4,2]=>0000000
[4,6,7,1,8,3,5,2]=>0000000
[3,6,1,7,8,4,5,2]=>0000000
[2,1,6,7,8,4,5,3]=>0100000
[2,1,6,7,8,4,3,5]=>0100000
[4,6,7,1,8,3,2,5]=>0000000
[5,6,7,8,1,3,2,4]=>0000000
[4,6,7,2,8,3,5,1]=>0000000
[3,6,2,7,8,4,5,1]=>0000000
[3,6,2,7,8,4,1,5]=>0000000
[3,4,2,1,7,8,5,6]=>0001000
[4,6,7,2,8,5,3,1]=>0000000
[4,6,7,2,8,5,1,3]=>0000000
[4,5,7,1,2,8,6,3]=>0000000
[2,1,6,7,8,3,5,4]=>0100000
[3,6,1,7,8,2,5,4]=>0000000
[4,6,7,1,8,2,5,3]=>0000000
[5,6,7,8,1,2,4,3]=>0000000
[5,6,7,8,2,4,1,3]=>0000000
[5,6,7,8,2,4,3,1]=>0000000
[3,6,1,7,8,5,2,4]=>0000000
[2,1,6,7,8,5,3,4]=>0100000
[7,4,5,1,2,8,3,6]=>0000000
[6,4,5,1,2,3,8,7]=>0000010
[5,4,6,1,2,3,8,7]=>0000010
[4,6,5,1,2,3,8,7]=>0000010
[5,6,4,1,2,3,8,7]=>0000010
[7,5,4,1,2,8,3,6]=>0000000
[8,6,4,1,7,2,3,5]=>0000000
[2,1,7,5,3,8,4,6]=>0100000
[2,1,8,6,7,3,4,5]=>0100000
[5,7,6,8,1,2,3,4]=>0000000
[6,4,7,1,8,2,3,5]=>0000000
[8,4,6,1,7,2,3,5]=>0000000
[8,3,1,6,7,2,4,5]=>0000000
[4,3,1,2,7,8,5,6]=>0001000
[7,4,8,1,6,2,3,5]=>0000000
[4,5,8,1,2,7,3,6]=>0000000
[5,6,8,7,1,2,3,4]=>0000000
[8,5,7,6,1,2,3,4]=>0000000
[3,8,1,7,6,2,4,5]=>0000000
[6,8,7,5,1,2,3,4]=>0000000
[6,4,7,3,8,5,1,2]=>0000000
[5,4,2,7,6,1,3,8]=>0000001
[5,4,2,7,6,1,8,3]=>0000000
[5,4,3,7,6,8,1,2]=>0000000
[5,4,3,7,8,6,1,2]=>0000000
[5,4,3,8,6,7,1,2]=>0000000
[5,4,3,6,8,7,1,2]=>0000000
[5,4,2,6,7,1,8,3]=>0000000
[5,3,2,6,1,7,4,8]=>0000001
[5,3,2,6,1,7,8,4]=>0000000
[5,3,2,6,1,8,7,4]=>0000000
[5,4,2,6,8,1,7,3]=>0000000
[6,4,8,2,5,1,7,3]=>0000000
[5,4,2,8,6,1,3,7]=>0000000
[5,3,2,6,1,8,4,7]=>0000000
[6,3,8,2,1,5,4,7]=>0000000
[7,8,3,2,1,5,4,6]=>0000000
[7,8,3,2,1,5,6,4]=>0000000
[6,3,8,2,1,5,7,4]=>0000000
[5,3,2,8,1,6,7,4]=>0000000
[5,4,2,7,8,1,6,3]=>0000000
[5,3,2,7,1,8,6,4]=>0000000
[5,3,2,7,1,6,4,8]=>0000001
[6,3,7,2,1,5,4,8]=>0000001
[6,3,7,2,1,5,8,4]=>0000000
[6,3,7,2,1,8,5,4]=>0000000
[6,5,7,8,2,1,4,3]=>0000000
[6,3,7,2,1,4,8,5]=>0000000
[5,3,2,7,1,4,8,6]=>0000000
[5,4,2,8,7,1,3,6]=>0000000
[7,8,4,2,6,1,3,5]=>0000000
[7,8,3,2,1,6,4,5]=>0000000
[6,3,8,2,1,7,4,5]=>0000000
[5,3,2,8,1,7,4,6]=>0000000
[4,3,2,1,8,7,5,6]=>0001000
[4,3,2,1,7,5,8,6]=>0001000
[4,3,2,1,7,5,6,8]=>0001001
[5,3,2,8,1,4,7,6]=>0000000
[6,3,8,2,1,4,7,5]=>0000000
[7,8,3,2,1,4,6,5]=>0000000
[4,3,2,1,8,5,6,7]=>0001000
[7,8,5,6,1,2,4,3]=>0000000
[7,8,4,1,6,2,5,3]=>0000000
[1,6,8,3,2,7,5,4]=>1000000
[6,1,8,3,2,7,5,4]=>0000000
[7,8,1,3,2,6,5,4]=>0000000
[7,8,3,1,2,6,5,4]=>0000000
[7,8,2,3,1,6,5,4]=>0000000
[7,8,2,1,3,6,5,4]=>0000000
[7,8,1,2,3,6,5,4]=>0000000
[1,5,2,8,3,7,6,4]=>1000000
[5,1,2,8,3,7,6,4]=>0000000
[5,2,1,8,3,7,6,4]=>0000000
[6,2,8,1,3,7,5,4]=>0000000
[6,2,8,4,7,1,5,3]=>0000000
[6,3,8,4,7,5,1,2]=>0000000
[2,6,8,3,1,7,5,4]=>0000000
[2,5,1,8,3,7,6,4]=>0000000
[1,2,5,8,3,7,6,4]=>1100000
[2,5,3,8,1,7,6,4]=>0000000
[2,5,4,8,7,1,6,3]=>0000000
[3,5,4,8,7,6,1,2]=>0000000
[5,3,4,8,7,6,1,2]=>0000000
[5,2,4,8,7,1,6,3]=>0000000
[5,2,3,8,1,7,6,4]=>0000000
[4,1,2,3,8,7,6,5]=>0001000
[1,4,2,3,8,7,6,5]=>1001000
[4,1,3,2,8,7,6,5]=>0001000
[6,3,8,1,2,7,5,4]=>0000000
[5,3,1,8,2,7,6,4]=>0000000
[5,1,3,8,2,7,6,4]=>0000000
[1,5,3,8,2,7,6,4]=>1000000
[1,5,4,8,7,2,6,3]=>1000000
[5,1,4,8,7,2,6,3]=>0000000
[5,4,1,8,7,2,6,3]=>0000000
[6,5,8,7,1,2,4,3]=>0000000
[5,6,8,7,3,4,1,2]=>0000000
[5,6,8,7,2,1,4,3]=>0000000
[4,5,1,8,7,2,6,3]=>0000000
[4,1,5,8,7,2,6,3]=>0000000
[1,3,5,8,2,7,6,4]=>1000000
[3,1,5,8,2,7,6,4]=>0000000
[3,6,8,2,1,7,5,4]=>0000000
[4,6,8,3,7,5,1,2]=>0000000
[4,5,3,8,7,6,1,2]=>0000000
[3,5,2,8,1,7,6,4]=>0000000
[3,1,4,2,8,7,6,5]=>0001000
[3,2,5,8,1,7,6,4]=>0000000
[4,2,5,8,7,1,6,3]=>0000000
[4,3,5,8,7,6,1,2]=>0000000
[2,4,5,8,7,1,6,3]=>0000000
[2,3,5,8,1,7,6,4]=>0000000
[5,2,7,1,4,3,8,6]=>0000000
[6,2,8,1,4,3,7,5]=>0000000
[6,2,7,1,4,3,8,5]=>0000000
[6,2,7,1,5,3,8,4]=>0000000
[7,4,8,1,3,2,6,5]=>0000000
[8,3,7,1,4,2,6,5]=>0000000
[6,2,7,3,8,1,5,4]=>0000000
[6,2,8,3,7,1,5,4]=>0000000
[5,1,8,3,7,2,6,4]=>0000000
[4,1,8,3,7,2,6,5]=>0000000
[3,1,7,4,8,2,6,5]=>0000000
[5,1,7,3,8,2,6,4]=>0000000
[7,3,8,2,6,1,5,4]=>0000000
[3,4,2,6,8,1,5,7]=>0000000
[5,3,6,2,8,1,4,7]=>0000000
[7,4,2,5,8,3,6,1]=>0000000
[4,5,2,6,3,8,1,7]=>0000000
[3,5,6,1,4,8,2,7]=>0000000
[4,1,5,6,3,8,2,7]=>0000000
[4,5,1,6,3,8,2,7]=>0000000
[4,5,6,3,2,8,1,7]=>0000000
[6,7,4,8,3,2,5,1]=>0000000
[6,7,4,8,3,2,1,5]=>0000000
[6,7,4,1,8,3,2,5]=>0000000
[5,3,7,8,1,4,2,6]=>0000000
[7,3,5,8,1,4,6,2]=>0000000
[4,5,1,7,8,3,6,2]=>0000000
[7,4,1,5,8,3,6,2]=>0000000
[6,7,4,3,8,1,5,2]=>0000000
[5,6,1,7,3,8,4,2]=>0000000
[5,1,6,7,3,8,4,2]=>0000000
[6,4,7,1,8,3,5,2]=>0000000
[6,7,8,3,1,4,5,2]=>0000000
[6,7,2,8,4,5,1,3]=>0000000
[6,7,2,8,4,1,3,5]=>0000000
[6,1,7,4,8,3,2,5]=>0000000
[5,1,6,7,3,2,8,4]=>0000000
[5,6,1,7,3,2,8,4]=>0000000
[5,6,7,3,2,1,8,4]=>0000000
[5,6,7,3,2,8,4,1]=>0000000
[7,4,2,5,1,8,3,6]=>0000000
[6,7,4,2,8,3,5,1]=>0000000
[3,6,7,2,8,4,5,1]=>0000000
[3,6,7,2,8,4,1,5]=>0000000
[3,6,7,2,1,8,4,5]=>0000000
[3,4,7,8,2,1,5,6]=>0000000
[3,7,8,1,4,6,2,5]=>0000000
[3,6,7,2,8,5,1,4]=>0000000
[3,6,7,8,5,2,1,4]=>0000000
[3,6,7,8,5,2,4,1]=>0000000
[6,4,7,8,2,5,3,1]=>0000000
[6,4,7,8,2,1,5,3]=>0000000
[5,3,7,8,1,6,2,4]=>0000000
[6,7,2,8,5,1,3,4]=>0000000
[6,4,1,7,8,2,5,3]=>0000000
[5,1,6,2,7,8,4,3]=>0000000
[5,6,2,7,1,8,4,3]=>0000000
[5,6,2,7,8,4,3,1]=>0000000
[5,6,7,2,8,4,3,1]=>0000000
[5,6,7,2,1,8,4,3]=>0000000
[5,6,1,7,2,8,4,3]=>0000000
[5,1,6,7,2,8,4,3]=>0000000
[6,7,8,3,5,1,4,2]=>0000000
[5,6,1,7,8,4,3,2]=>0000000
[5,6,7,1,8,4,3,2]=>0000000
[8,3,2,5,1,6,4,7]=>0000000
[5,3,2,7,4,1,8,6]=>0000000
[7,5,3,8,2,4,6,1]=>0000000
[8,2,4,5,6,3,1,7]=>0000000
[8,2,4,5,6,1,3,7]=>0000000
[8,5,3,6,4,1,2,7]=>0000000
[8,4,1,5,6,3,2,7]=>0000000
[8,1,4,5,6,3,2,7]=>0000000
[4,5,3,7,2,1,8,6]=>0000000
[7,4,5,8,3,2,6,1]=>0000000
[4,3,6,7,2,8,5,1]=>0000000
[4,3,6,7,2,8,1,5]=>0000000
[1,4,3,6,7,2,8,5]=>1000000
[4,5,3,7,1,8,2,6]=>0000000
[5,3,4,7,1,2,8,6]=>0000000
[7,4,5,8,3,6,1,2]=>0000000
[4,3,6,7,8,1,5,2]=>0000000
[3,5,6,7,8,4,1,2]=>0000000
[3,1,5,6,7,8,4,2]=>0000000
[4,6,1,7,8,3,5,2]=>0000000
[6,2,4,1,7,8,5,3]=>0000000
[2,6,7,1,4,8,3,5]=>0000000
[1,5,3,6,7,8,2,4]=>1000000
[4,5,2,7,8,1,3,6]=>0000000
[4,2,6,7,8,3,1,5]=>0000000
[4,2,6,7,8,3,5,1]=>0000000
[3,6,2,7,4,8,1,5]=>0000000
[3,7,4,2,1,5,8,6]=>0000000
[7,8,4,2,1,3,6,5]=>0000000
[6,3,2,7,1,8,5,4]=>0000000
[3,6,2,7,1,8,5,4]=>0000000
[6,7,3,8,2,5,4,1]=>0000000
[6,4,7,8,5,2,3,1]=>0000000
[2,6,4,7,8,1,5,3]=>0000000
[7,4,1,5,8,6,2,3]=>0000000
[7,5,8,2,1,6,3,4]=>0000000
[6,2,7,1,3,8,5,4]=>0000000
[6,3,1,7,8,2,5,4]=>0000000
[4,6,1,7,8,5,2,3]=>0000000
[5,1,2,6,7,8,4,3]=>0000000
[5,2,6,7,8,4,3,1]=>0000000
[1,6,4,7,8,5,2,3]=>1000000
[2,6,7,1,3,8,5,4]=>0000000
[6,7,3,8,5,1,4,2]=>0000000
[6,4,7,8,5,3,1,2]=>0000000
[3,1,2,6,5,8,7,4]=>0010000
[4,5,1,2,3,8,7,6]=>0000100
[4,6,1,2,3,8,7,5]=>0000000
[1,6,5,3,4,8,7,2]=>1000000
[6,1,5,2,4,8,7,3]=>0000000
[6,5,1,2,3,8,7,4]=>0000000
[6,4,1,2,3,8,7,5]=>0000000
[5,4,1,2,3,8,7,6]=>0000100
[5,4,1,2,7,3,6,8]=>0000001
[6,4,1,7,2,3,5,8]=>0000001
[6,4,1,8,2,3,5,7]=>0000000
[7,4,1,2,8,3,6,5]=>0000000
[7,5,1,2,8,3,6,4]=>0000000
[7,1,5,2,8,4,6,3]=>0000000
[1,7,5,3,8,4,6,2]=>1000000
[8,4,1,2,7,3,6,5]=>0000000
[8,4,1,7,2,3,5,6]=>0000000
[7,4,1,6,2,3,5,8]=>0000001
[8,6,1,7,2,3,5,4]=>0000000
[8,1,6,7,2,4,5,3]=>0000000
[1,7,6,8,3,4,5,2]=>1000000
[7,6,1,8,2,3,5,4]=>0000000
[3,1,2,7,8,5,6,4]=>0010000
[3,1,8,7,2,4,5,6]=>0000000
[3,1,7,6,2,4,5,8]=>0000001
[4,7,1,6,2,3,5,8]=>0000001
[4,8,1,6,2,3,5,7]=>0000000
[5,8,1,2,7,3,6,4]=>0000000
[5,1,8,2,7,4,6,3]=>0000000
[1,5,8,3,7,4,6,2]=>1000000
[1,6,8,7,3,4,5,2]=>1000000
[6,1,8,7,2,4,5,3]=>0000000
[6,8,1,7,2,3,5,4]=>0000000
[6,8,7,1,2,3,4,5]=>0000000
[5,8,6,1,2,3,4,7]=>0000000
[5,7,6,1,2,3,4,8]=>0000001
[7,8,1,6,2,3,5,4]=>0000000
[7,1,8,6,2,4,5,3]=>0000000
[1,7,8,6,3,4,5,2]=>1000000
[8,1,7,6,2,4,5,3]=>0000000
[8,7,1,6,2,3,5,4]=>0000000
[8,5,3,7,2,1,4,6]=>0000000
[3,1,6,4,5,2,8,7]=>0000010
[5,8,7,4,2,6,3,1]=>0000000
[3,7,8,4,5,1,2,6]=>0000000
[5,6,3,8,1,7,2,4]=>0000000
[7,6,1,4,5,8,3,2]=>0000000
[3,7,6,4,5,8,2,1]=>0000000
[8,5,7,4,1,6,3,2]=>0000000
[2,5,8,4,7,6,1,3]=>0000000
[3,8,4,2,5,6,7,1]=>0000000
[7,5,8,4,3,6,1,2]=>0000000
[7,3,8,4,2,6,1,5]=>0000000
[5,6,3,8,4,2,7,1]=>0000000
[8,6,3,5,1,2,7,4]=>0000000
[7,8,5,4,2,6,1,3]=>0000000
[4,8,1,2,5,6,7,3]=>0000000
[3,4,2,8,5,6,7,1]=>0000000
[8,4,2,1,5,6,7,3]=>0000000
[3,8,7,4,5,2,1,6]=>0000000
[4,6,3,5,8,2,7,1]=>0000000
[5,4,2,3,7,6,1,8]=>0000001
[3,2,7,6,4,5,1,8]=>0000001
[4,7,2,6,3,5,1,8]=>0000001
[5,7,6,2,3,4,1,8]=>0000001
[1,7,5,2,8,3,4,6]=>1000000
[6,8,5,2,3,1,4,7]=>0000000
[4,8,2,6,3,1,5,7]=>0000000
[3,2,8,6,4,1,5,7]=>0000000
[7,1,5,2,8,3,4,6]=>0000000
[1,8,5,2,7,3,4,6]=>1000000
[7,1,6,8,2,3,4,5]=>0000000
[3,2,1,7,8,4,5,6]=>0010000
[3,2,8,7,1,4,5,6]=>0000000
[5,8,7,2,1,3,4,6]=>0000000
[1,7,6,8,2,3,4,5]=>1000000
[6,5,8,2,3,1,4,7]=>0000000
[8,5,7,2,1,3,4,6]=>0000000
[3,2,5,4,1,8,6,7]=>0000100
[7,4,2,1,8,3,5,6]=>0000000
[8,4,2,1,7,3,5,6]=>0000000
[1,4,2,8,7,3,5,6]=>1000000
[1,5,8,2,7,3,4,6]=>1000000
[8,5,1,2,7,3,4,6]=>0000000
[3,2,6,1,4,8,5,7]=>0000000
[3,2,7,1,8,4,5,6]=>0000000
[4,7,2,1,8,3,5,6]=>0000000
[8,6,1,7,2,3,4,5]=>0000000
[1,6,8,7,2,3,4,5]=>1000000
[1,7,8,6,2,3,4,5]=>1000000
[7,8,1,6,2,3,4,5]=>0000000
[4,8,2,1,7,3,5,6]=>0000000
[3,2,8,1,7,4,5,6]=>0000000
[5,1,8,2,7,3,4,6]=>0000000
[6,1,8,7,2,3,4,5]=>0000000
[8,1,7,6,2,3,4,5]=>0000000
[2,8,4,1,6,5,7,3]=>0000000
[7,5,8,6,1,4,2,3]=>0000000
[7,5,8,2,4,6,3,1]=>0000000
[7,5,8,6,1,4,3,2]=>0000000
[3,5,7,2,4,1,8,6]=>0000000
[6,5,2,7,3,4,8,1]=>0000000
[5,1,6,7,4,3,8,2]=>0000000
[4,1,2,3,8,6,5,7]=>0001000
[4,1,2,3,8,6,7,5]=>0001000
[4,1,2,3,8,5,7,6]=>0001000
[4,5,2,6,3,7,1,8]=>0000001
[4,1,2,6,8,5,7,3]=>0000000
[6,4,2,7,1,3,8,5]=>0000000
[8,5,3,6,1,7,2,4]=>0000000
[7,3,6,2,4,8,1,5]=>0000000
[3,7,5,1,2,4,8,6]=>0000000
[7,4,8,5,2,6,1,3]=>0000000
[5,8,2,6,3,7,1,4]=>0000000
[3,8,6,2,4,7,1,5]=>0000000
[4,8,6,2,7,1,3,5]=>0000000
[5,4,7,3,8,1,2,6]=>0000000
[8,4,1,6,7,2,3,5]=>0000000
[4,7,1,5,8,6,2,3]=>0000000
[8,6,1,7,5,2,3,4]=>0000000
[5,7,2,8,1,6,3,4]=>0000000
[8,3,7,6,1,2,4,5]=>0000000
[8,4,7,6,1,2,3,5]=>0000000
[3,5,8,7,1,2,4,6]=>0000000
[2,5,8,7,1,3,4,6]=>0000000
[6,8,4,7,5,1,2,3]=>0000000
[5,8,7,1,6,2,3,4]=>0000000
[2,8,7,6,1,3,4,5]=>0000000
[3,8,7,6,1,2,4,5]=>0000000
[4,8,7,6,1,2,3,5]=>0000000
[3,8,7,4,5,1,6,2]=>0000000
[5,7,3,8,1,2,6,4]=>0000000
[7,5,1,4,8,6,3,2]=>0000000
[5,3,2,7,4,6,8,1]=>0000000
[7,5,3,6,2,4,8,1]=>0000000
[6,3,2,5,1,8,4,7]=>0000000
[8,5,3,6,2,7,1,4]=>0000000
[7,2,6,3,4,5,8,1]=>0000000
[6,2,7,3,4,5,8,1]=>0000000
[6,7,3,5,2,4,8,1]=>0000000
[3,7,6,2,4,5,8,1]=>0000000
[6,5,3,1,2,8,4,7]=>0000000
[8,6,5,2,3,7,1,4]=>0000000
[8,5,2,1,7,3,4,6]=>0000000
[7,5,2,1,8,3,4,6]=>0000000
[1,6,3,2,8,4,5,7]=>1000000
[5,4,8,6,2,7,1,3]=>0000000
[7,8,5,2,3,6,1,4]=>0000000
[2,8,1,7,3,4,5,6]=>0000000
[3,8,6,1,7,2,4,5]=>0000000
[4,2,8,3,7,1,5,6]=>0000000
[8,1,2,7,3,4,5,6]=>0000000
[7,2,6,1,8,3,4,5]=>0000000
[7,3,1,5,8,2,4,6]=>0000000
[5,4,1,3,6,8,2,7]=>0000000
[8,5,3,7,6,1,2,4]=>0000000
[6,1,8,3,7,2,4,5]=>0000000
[7,6,8,2,3,5,1,4]=>0000000
[3,7,8,2,4,6,1,5]=>0000000
[5,4,7,8,2,6,1,3]=>0000000
[4,2,5,8,7,1,3,6]=>0000000
[2,3,8,7,1,4,5,6]=>0000000
[2,1,8,7,3,4,5,6]=>0100000
[8,2,7,6,1,3,4,5]=>0000000
[1,2,8,7,3,4,5,6]=>1100000
[1,3,8,7,2,4,5,6]=>1000000
[1,7,8,3,6,2,4,5]=>1000000
[5,4,8,7,6,1,2,3]=>0000000
[6,8,3,7,5,1,2,4]=>0000000
[7,8,6,2,5,1,3,4]=>0000000
[8,1,6,7,3,2,4,5]=>0000000
[8,1,5,3,7,2,4,6]=>0000000
[8,1,5,3,6,2,4,7]=>0000000
[7,4,8,3,2,6,5,1]=>0000000
[7,4,1,3,2,6,5,8]=>0000001
[8,1,4,3,2,6,5,7]=>0000000
[8,1,4,3,2,7,5,6]=>0000000
[8,1,5,4,6,7,2,3]=>0000000
[8,1,5,3,6,2,7,4]=>0000000
[8,1,4,3,2,6,7,5]=>0000000
[8,1,4,3,2,5,7,6]=>0000000
[7,4,1,3,2,5,6,8]=>0000001
[7,4,8,3,2,5,6,1]=>0000000
[6,4,3,1,2,5,8,7]=>0000010
[7,4,1,3,2,5,8,6]=>0000000
[7,5,1,3,6,2,8,4]=>0000000
[7,5,1,4,6,8,2,3]=>0000000
[6,4,3,8,2,5,1,7]=>0000000
[5,4,3,2,8,6,1,7]=>0000000
[5,4,3,2,8,7,1,6]=>0000000
[6,5,4,8,7,1,2,3]=>0000000
[6,5,4,1,7,8,2,3]=>0000000
[6,4,3,1,2,7,8,5]=>0000000
[7,4,1,3,2,8,5,6]=>0000000
[6,4,3,1,2,7,5,8]=>0000001
[6,4,3,8,2,7,5,1]=>0000000
[6,5,3,8,7,2,4,1]=>0000000
[6,5,3,1,7,2,4,8]=>0000001
[7,5,1,3,8,2,4,6]=>0000000
[6,5,3,7,8,2,4,1]=>0000000
[6,4,3,7,2,8,5,1]=>0000000
[6,4,3,7,2,1,5,8]=>0000001
[7,5,8,4,1,6,2,3]=>0000000
[6,5,4,8,1,7,2,3]=>0000000
[6,5,3,8,1,2,7,4]=>0000000
[6,5,4,7,1,8,2,3]=>0000000
[5,4,3,2,7,8,1,6]=>0000000
[4,6,3,8,5,1,2,7]=>0000000
[5,6,8,3,4,1,2,7]=>0000000
[5,6,8,3,4,1,7,2]=>0000000
[4,6,2,7,5,3,1,8]=>0000001
[5,6,8,4,3,1,2,7]=>0000000
[5,7,8,4,1,3,6,2]=>0000000
[5,6,8,4,2,1,7,3]=>0000000
[5,6,8,2,4,1,7,3]=>0000000
[3,2,6,8,5,1,4,7]=>0000000
[5,6,8,4,2,1,3,7]=>0000000
[5,7,8,4,1,3,2,6]=>0000000
[5,7,8,4,1,2,3,6]=>0000000
[6,7,8,1,5,2,3,4]=>0000000
[6,7,8,1,5,3,2,4]=>0000000
[6,7,8,1,3,5,2,4]=>0000000
[5,7,8,2,1,6,3,4]=>0000000
[4,7,2,8,1,6,3,5]=>0000000
[3,2,7,8,1,6,4,5]=>0000000
[4,7,2,8,1,6,5,3]=>0000000
[5,7,8,2,1,6,4,3]=>0000000
[6,7,8,1,3,5,4,2]=>0000000
[6,7,8,1,5,3,4,2]=>0000000
[6,7,8,1,4,3,5,2]=>0000000
[5,6,8,3,2,1,7,4]=>0000000
[4,7,3,8,1,6,2,5]=>0000000
[4,7,3,8,1,5,6,2]=>0000000
[4,7,3,8,1,5,2,6]=>0000000
[4,7,3,8,1,2,5,6]=>0000000
[5,7,8,3,1,2,4,6]=>0000000
[5,6,8,3,2,1,4,7]=>0000000
[3,2,7,8,1,5,4,6]=>0000000
[6,7,8,1,3,4,2,5]=>0000000
[6,7,8,1,4,2,3,5]=>0000000
[6,7,8,1,2,5,3,4]=>0000000
[6,7,8,1,2,4,5,3]=>0000000
[5,7,8,2,1,3,6,4]=>0000000
[3,2,7,8,1,4,6,5]=>0000000
[6,7,8,1,3,2,4,5]=>0000000
[6,7,8,1,2,4,3,5]=>0000000
[6,7,8,1,2,3,5,4]=>0000000
[4,6,2,1,7,5,8,3]=>0000000
[6,7,5,1,8,4,3,2]=>0000000
[6,8,4,1,7,5,3,2]=>0000000
[4,6,1,2,7,5,8,3]=>0000000
[6,7,1,5,8,2,3,4]=>0000000
[8,4,1,6,7,5,2,3]=>0000000
[7,6,2,1,5,8,3,4]=>0000000
[6,1,4,2,7,5,8,3]=>0000000
[2,5,1,3,7,6,8,4]=>0000000
[4,7,1,2,8,6,5,3]=>0000000
[4,6,8,1,2,7,5,3]=>0000000
[6,8,7,1,5,3,2,4]=>0000000
[6,8,7,3,5,1,2,4]=>0000000
[7,8,1,3,6,5,2,4]=>0000000
[1,7,3,4,8,6,5,2]=>1000000
[4,2,7,1,8,6,5,3]=>0000000
[7,8,2,3,6,5,1,4]=>0000000
[8,5,7,1,6,2,3,4]=>0000000
[8,5,7,1,2,6,3,4]=>0000000
[6,8,2,7,1,3,5,4]=>0000000
[6,2,4,8,7,1,5,3]=>0000000
[1,6,8,3,7,4,5,2]=>1000000
[1,6,8,3,4,7,5,2]=>1000000
[6,2,4,8,1,7,5,3]=>0000000
[6,8,7,2,3,5,1,4]=>0000000
[6,8,2,1,7,3,5,4]=>0000000
[8,5,7,2,1,6,3,4]=>0000000
[8,5,7,1,2,3,6,4]=>0000000
[8,5,7,2,3,1,6,4]=>0000000
[1,8,7,5,3,4,6,2]=>1000000
[1,8,7,3,5,4,6,2]=>1000000
[8,2,5,4,7,1,6,3]=>0000000
[8,7,6,1,2,4,3,5]=>0000000
[8,7,6,1,4,2,3,5]=>0000000
[8,7,6,4,1,3,2,5]=>0000000
[8,5,7,1,3,2,6,4]=>0000000
[5,8,4,7,1,2,6,3]=>0000000
[8,1,2,6,5,7,4,3]=>0000000
[8,2,5,6,7,4,1,3]=>0000000
[4,8,5,1,7,2,6,3]=>0000000
[8,5,3,7,1,2,6,4]=>0000000
[4,6,2,8,1,7,5,3]=>0000000
[1,6,4,8,3,7,5,2]=>1000000
[1,8,7,4,5,3,6,2]=>1000000
[4,8,5,7,2,1,6,3]=>0000000
[8,5,3,7,2,1,6,4]=>0000000
[8,7,6,3,1,4,2,5]=>0000000
[8,5,3,2,7,1,6,4]=>0000000
[1,8,7,4,3,5,6,2]=>1000000
[1,8,7,3,4,5,6,2]=>1000000
[8,2,4,5,7,1,6,3]=>0000000
[8,5,2,3,7,1,6,4]=>0000000
[8,3,1,5,2,7,6,4]=>0000000
[8,7,4,1,6,3,2,5]=>0000000
[8,7,4,1,6,3,5,2]=>0000000
[8,7,4,1,6,5,3,2]=>0000000
[8,7,4,1,6,5,2,3]=>0000000
[8,3,2,7,6,4,5,1]=>0000000
[8,5,4,2,3,7,6,1]=>0000000
[8,7,4,2,6,3,5,1]=>0000000
[8,7,4,2,6,3,1,5]=>0000000
[8,3,2,5,4,7,1,6]=>0000000
[8,3,2,7,6,1,5,4]=>0000000
[7,4,5,2,3,1,8,6]=>0000000
[5,2,7,3,4,1,8,6]=>0000000
[6,2,7,3,4,1,8,5]=>0000000
[3,1,8,6,7,4,5,2]=>0000000
[8,5,7,3,4,1,6,2]=>0000000
[8,4,7,3,5,1,6,2]=>0000000
[2,1,8,5,7,4,6,3]=>0100000
[6,2,4,1,7,3,8,5]=>0000000
[8,5,6,2,3,1,7,4]=>0000000
[7,3,8,5,6,2,4,1]=>0000000
[3,1,6,2,8,5,7,4]=>0000000
[5,1,6,2,8,4,7,3]=>0000000
[7,3,8,4,6,2,5,1]=>0000000
[4,1,8,5,6,2,7,3]=>0000000
[3,1,8,5,6,2,7,4]=>0000000
[6,8,7,3,4,1,2,5]=>0000000
[5,4,8,7,2,6,3,1]=>0000000
[5,3,8,7,6,1,2,4]=>0000000
[8,3,4,6,5,1,2,7]=>0000000
[3,4,8,7,6,1,2,5]=>0000000
[3,5,8,7,6,1,2,4]=>0000000
[4,5,8,7,6,1,2,3]=>0000000
[4,5,8,7,1,6,3,2]=>0000000
[3,5,8,2,7,6,4,1]=>0000000
[3,5,8,1,7,6,4,2]=>0000000
[2,5,8,7,1,6,3,4]=>0000000
[2,4,8,7,1,6,3,5]=>0000000
[2,8,4,7,1,5,3,6]=>0000000
[8,2,4,6,1,5,3,7]=>0000000
[8,1,4,6,2,5,3,7]=>0000000
[1,4,8,7,2,6,3,5]=>1000000
[1,5,8,7,2,6,3,4]=>1000000
[1,5,8,2,7,6,4,3]=>1000000
[2,5,8,3,7,6,4,1]=>0000000
[1,4,2,8,7,6,5,3]=>1000000
[1,3,8,2,7,6,4,5]=>1000000
[1,8,3,2,7,5,4,6]=>1000000
[8,2,3,1,6,5,4,7]=>0000000
[2,3,8,1,7,6,4,5]=>0000000
[5,2,8,7,1,6,3,4]=>0000000
[5,2,8,1,7,6,4,3]=>0000000
[5,3,8,2,7,6,4,1]=>0000000
[6,8,3,2,7,5,4,1]=>0000000
[6,8,3,1,7,5,4,2]=>0000000
[6,8,1,2,7,5,4,3]=>0000000
[6,8,2,3,7,5,4,1]=>0000000
[5,2,8,3,7,6,4,1]=>0000000
[5,1,8,3,7,6,4,2]=>0000000
[5,1,8,7,2,6,3,4]=>0000000
[4,8,1,7,2,5,3,6]=>0000000
[8,4,1,6,2,5,3,7]=>0000000
[8,3,1,2,6,5,4,7]=>0000000
[3,1,2,8,7,6,5,4]=>0010000
[4,1,3,8,7,6,5,2]=>0000000
[3,1,4,8,7,6,5,2]=>0000000
[2,1,8,3,7,6,4,5]=>0100000
[2,8,1,3,7,5,4,6]=>0000000
[8,2,1,3,6,5,4,7]=>0000000
[1,8,2,3,7,5,4,6]=>1000000
[1,2,8,3,7,6,4,5]=>1100000
[1,4,3,6,8,2,5,7]=>1000000
[1,4,5,2,8,3,7,6]=>1000000
[1,4,2,6,5,8,3,7]=>1000000
[1,5,4,2,6,8,3,7]=>1000000
[3,1,6,5,8,2,4,7]=>0000000
[1,6,4,2,5,8,3,7]=>1000000
[1,5,2,6,4,8,3,7]=>1000000
[1,2,6,5,4,8,3,7]=>1100000
[1,2,5,4,7,3,8,6]=>1100000
[4,1,2,6,3,8,7,5]=>0000000
[7,1,5,4,2,8,3,6]=>0000000
[1,4,7,5,2,8,3,6]=>1000000
[7,1,3,5,2,8,4,6]=>0000000
[1,4,5,2,8,7,3,6]=>1000000
[1,6,4,2,8,3,7,5]=>1000000
[1,4,2,8,3,7,6,5]=>1000000
[1,2,8,6,5,3,7,4]=>1100000
[6,2,1,8,7,3,4,5]=>0000000
[7,6,2,1,8,3,4,5]=>0000000
[7,3,1,6,2,8,4,5]=>0000000
[1,7,6,4,2,8,3,5]=>1000000
[1,7,5,2,6,3,8,4]=>1000000
[1,6,2,7,5,3,8,4]=>1000000
[1,2,7,6,5,3,8,4]=>1100000
[1,2,6,5,3,8,7,4]=>1100000
[1,5,2,7,6,3,8,4]=>1000000
[1,6,5,2,7,3,8,4]=>1000000
[1,5,7,4,2,8,3,6]=>1000000
[3,1,8,6,2,4,7,5]=>0000000
[4,3,7,1,8,2,5,6]=>0000000
[8,3,1,6,2,4,7,5]=>0000000
[7,1,8,3,2,4,6,5]=>0000000
[1,4,2,8,7,3,6,5]=>1000000
[1,7,4,2,8,3,6,5]=>1000000
[8,1,5,4,2,7,3,6]=>0000000
[1,4,8,5,2,7,3,6]=>1000000
[8,5,3,1,7,2,4,6]=>0000000
[8,6,2,1,7,3,4,5]=>0000000
[1,8,6,4,2,7,3,5]=>1000000
[1,5,2,7,3,8,6,4]=>1000000
[1,2,8,5,3,7,6,4]=>1100000
[1,2,6,3,8,7,5,4]=>1100000
[1,2,7,6,3,8,5,4]=>1100000
[1,6,2,7,3,8,5,4]=>1000000
[1,7,4,2,8,6,3,5]=>1000000
[7,1,8,3,2,6,4,5]=>0000000
[7,2,1,8,6,3,4,5]=>0000000
[1,8,7,3,2,6,4,5]=>1000000
[1,4,2,8,7,6,3,5]=>1000000
[1,2,8,7,5,3,6,4]=>1100000
[5,7,1,6,2,4,3,8]=>0000001
[6,1,4,5,3,8,7,2]=>0000000
[6,3,5,8,2,1,7,4]=>0000000
[8,4,5,7,3,6,1,2]=>0000000
[8,4,1,5,2,6,3,7]=>0000000
[8,7,5,6,1,4,2,3]=>0000000
[2,3,8,1,6,4,7,5]=>0000000
[5,2,6,1,4,8,7,3]=>0000000
[5,7,2,3,8,6,1,4]=>0000000
[5,6,2,3,1,8,7,4]=>0000000
[5,6,2,1,3,8,7,4]=>0000000
[5,1,6,4,2,8,7,3]=>0000000
[5,6,1,3,2,8,7,4]=>0000000
[5,6,3,1,2,8,7,4]=>0000000
[5,7,3,2,8,1,6,4]=>0000000
[6,7,3,8,2,1,5,4]=>0000000
[6,7,3,8,1,2,5,4]=>0000000
[5,7,3,1,8,2,6,4]=>0000000
[5,1,7,4,8,2,6,3]=>0000000
[1,5,7,4,8,3,6,2]=>1000000
[5,1,7,4,8,6,2,3]=>0000000
[5,7,3,1,8,6,2,4]=>0000000
[6,7,8,3,1,4,2,5]=>0000000
[6,7,1,8,3,5,2,4]=>0000000
[6,1,7,8,4,5,2,3]=>0000000
[1,6,7,8,4,5,3,2]=>1000000
[1,6,7,8,4,3,5,2]=>1000000
[6,1,7,8,4,2,5,3]=>0000000
[6,7,2,8,1,3,5,4]=>0000000
[6,7,2,8,3,5,1,4]=>0000000
[6,2,7,8,4,1,5,3]=>0000000
[6,2,7,8,1,4,5,3]=>0000000
[4,2,1,7,8,5,6,3]=>0000000
[4,1,2,7,8,6,5,3]=>0000000
[6,2,7,8,1,5,4,3]=>0000000
[6,2,7,8,5,1,4,3]=>0000000
[5,7,2,1,8,6,3,4]=>0000000
[1,6,7,8,3,5,4,2]=>1000000
[6,1,7,8,2,5,4,3]=>0000000
[6,7,8,2,4,1,3,5]=>0000000
[6,7,8,2,4,3,1,5]=>0000000
[6,7,1,8,5,2,3,4]=>0000000
[6,1,7,8,5,2,4,3]=>0000000
[1,6,7,8,5,3,4,2]=>1000000
[6,1,7,8,5,4,2,3]=>0000000
[6,7,1,8,5,3,2,4]=>0000000
[6,7,8,4,1,3,2,5]=>0000000
[3,7,4,8,5,6,1,2]=>0000000
[3,7,1,8,5,6,2,4]=>0000000
[2,7,3,8,5,6,1,4]=>0000000
[1,7,4,8,5,6,2,3]=>1000000
[2,7,3,8,4,6,1,5]=>0000000
[3,7,1,8,4,6,2,5]=>0000000
[1,5,2,8,6,7,3,4]=>1000000
[2,6,1,8,5,7,3,4]=>0000000
[1,6,2,8,5,7,3,4]=>1000000
[1,6,2,8,4,7,3,5]=>1000000
[2,6,1,8,4,7,3,5]=>0000000
[3,7,2,6,1,8,4,5]=>0000000
[4,8,1,6,2,7,3,5]=>0000000
[5,8,1,6,2,7,3,4]=>0000000
[5,8,2,6,1,7,3,4]=>0000000
[4,8,2,6,1,7,3,5]=>0000000
[1,7,3,6,2,8,4,5]=>1000000
[2,7,3,6,1,8,4,5]=>0000000
[8,6,1,4,3,2,5,7]=>0000000
[3,7,5,1,8,2,4,6]=>0000000
[4,1,5,2,8,7,3,6]=>0000000
[8,1,2,4,6,5,3,7]=>0000000
[8,2,6,5,1,3,4,7]=>0000000
[8,3,1,6,2,5,4,7]=>0000000
[8,1,2,6,4,5,3,7]=>0000000
[8,1,2,5,6,4,3,7]=>0000000
[1,7,5,4,2,8,3,6]=>1000000
[1,4,6,8,2,7,3,5]=>1000000
[1,4,7,6,2,8,3,5]=>1000000
[5,1,4,7,2,8,3,6]=>0000000
[3,7,5,1,2,8,4,6]=>0000000
[4,1,5,8,2,7,3,6]=>0000000
[1,4,6,2,8,7,3,5]=>1000000
[1,4,2,8,6,7,3,5]=>1000000
[3,1,2,6,4,8,7,5]=>0010000
[2,1,7,6,3,4,8,5]=>0100000
[3,1,2,7,4,6,8,5]=>0010000
[1,2,3,6,8,5,7,4]=>1110000
[5,1,4,2,7,8,3,6]=>0000000
[1,4,2,7,6,8,3,5]=>1000000
[1,4,2,6,8,7,3,5]=>1000000
[5,3,7,1,8,2,4,6]=>0000000
[1,7,4,3,2,5,8,6]=>1000000
[4,8,7,2,1,3,5,6]=>0000000
[1,8,7,3,4,2,5,6]=>1000000
[3,1,7,8,2,6,4,5]=>0000000
[1,4,2,7,8,3,6,5]=>1000000
[2,1,8,6,3,4,7,5]=>0100000
[1,4,2,6,8,3,7,5]=>1000000
[1,2,3,7,8,5,6,4]=>1110000
[1,2,3,7,5,8,6,4]=>1110000
[3,1,7,2,8,6,4,5]=>0000000
[1,2,3,8,7,5,6,4]=>1110000
[5,7,8,4,2,6,1,3]=>0000000
[6,7,8,4,2,5,1,3]=>0000000
[8,6,3,7,2,1,5,4]=>0000000
[6,7,8,3,2,1,5,4]=>0000000
[5,7,8,3,2,1,6,4]=>0000000
[2,7,8,4,3,5,6,1]=>0000000
[3,7,8,4,2,5,1,6]=>0000000
[7,6,3,8,2,1,4,5]=>0000000
[8,6,3,7,2,1,4,5]=>0000000
[5,6,3,8,2,1,4,7]=>0000000
[3,6,4,8,2,5,1,7]=>0000000
[2,6,4,8,3,5,7,1]=>0000000
[2,6,4,7,3,5,8,1]=>0000000
[4,6,3,7,2,1,5,8]=>0000001
[5,6,3,7,2,1,4,8]=>0000001
[8,4,3,2,1,6,5,7]=>0000000
[6,4,3,2,1,7,5,8]=>0000001
[4,5,3,2,7,1,6,8]=>0000001
[7,4,3,2,1,8,5,6]=>0000000
[8,4,3,2,1,7,5,6]=>0000000
[7,4,3,2,1,8,6,5]=>0000000
[5,6,3,8,2,1,7,4]=>0000000
[7,5,3,2,8,1,6,4]=>0000000
[8,5,4,2,7,6,1,3]=>0000000
[7,5,4,2,8,6,1,3]=>0000000
[6,5,4,2,7,8,1,3]=>0000000
[8,5,4,2,6,7,1,3]=>0000000
[5,6,3,7,2,1,8,4]=>0000000
[4,6,3,7,2,1,8,5]=>0000000
[3,6,4,7,2,8,1,5]=>0000000
[2,6,4,7,3,8,5,1]=>0000000
[3,5,4,2,7,8,1,6]=>0000000
[7,4,3,2,1,6,8,5]=>0000000
[8,4,3,2,1,6,7,5]=>0000000
[8,4,3,2,1,5,7,6]=>0000000
[7,4,3,2,1,5,8,6]=>0000000
[6,4,3,2,1,5,8,7]=>0000010
[3,5,4,2,6,8,1,7]=>0000000
[3,2,6,4,8,5,1,7]=>0000000
[3,2,5,8,4,6,1,7]=>0000000
[4,2,1,5,7,3,6,8]=>0000001
[4,5,2,3,7,1,6,8]=>0000001
[4,2,5,3,8,1,6,7]=>0000000
[4,2,5,8,3,1,6,7]=>0000000
[4,1,5,3,8,2,6,7]=>0000000
[4,3,2,7,5,1,6,8]=>0000001
[4,3,6,2,5,1,7,8]=>0000011
[4,6,7,1,3,2,5,8]=>0000001
[4,5,1,7,3,2,6,8]=>0000001
[4,5,1,3,7,2,6,8]=>0000001
[3,5,1,4,2,7,6,8]=>0000101
[2,5,1,4,3,7,8,6]=>0000100
[5,2,1,4,3,7,8,6]=>0000100
[5,3,1,4,2,7,6,8]=>0000101
[4,3,1,7,5,2,6,8]=>0000001
[5,3,6,4,1,2,7,8]=>0000011
[4,3,6,1,7,2,5,8]=>0000001
[6,3,4,1,2,7,5,8]=>0000001
[6,2,4,1,3,7,8,5]=>0000000
[3,6,4,1,2,7,5,8]=>0000001
[4,6,3,1,7,2,5,8]=>0000001
[5,3,6,2,1,4,7,8]=>0000011
[4,5,2,7,3,1,6,8]=>0000001
[4,6,7,2,3,1,5,8]=>0000001
[4,6,2,1,7,3,5,8]=>0000001
[3,2,6,1,4,7,5,8]=>0000001
[3,6,7,2,4,5,1,8]=>0000001
[7,2,1,4,6,3,8,5]=>0000000
[7,3,1,4,6,8,2,5]=>0000000
[3,6,2,1,5,7,4,8]=>0000001
[7,4,1,5,6,2,3,8]=>0000001
[7,3,1,5,2,6,4,8]=>0000001
[7,2,1,5,3,6,8,4]=>0000000
[6,2,5,1,3,7,8,4]=>0000000
[6,3,5,1,2,7,4,8]=>0000001
[6,4,5,1,7,2,3,8]=>0000001
[4,6,5,1,7,2,3,8]=>0000001
[3,6,5,1,2,7,4,8]=>0000001
[2,4,1,5,3,8,7,6]=>0000100
[3,4,5,1,2,8,7,6]=>0000100
[3,4,5,2,8,1,7,6]=>0000000
[2,4,8,6,3,7,1,5]=>0000000
[1,8,4,6,3,7,2,5]=>1000000
[3,5,6,2,7,8,4,1]=>0000000
[4,5,6,7,2,8,3,1]=>0000000
[2,5,8,6,7,3,4,1]=>0000000
[4,5,6,7,2,1,8,3]=>0000000
[2,5,1,6,7,8,4,3]=>0000000
[3,4,6,8,1,7,5,2]=>0000000
[2,4,8,6,1,7,5,3]=>0000000
[8,2,4,3,7,1,6,5]=>0000000
[6,1,5,7,3,2,4,8]=>0000001
[6,1,5,8,3,2,4,7]=>0000000
[7,3,2,4,6,1,5,8]=>0000001
[5,7,6,1,8,3,4,2]=>0000000
[3,2,5,1,6,4,7,8]=>0000011
[3,8,6,5,1,7,4,2]=>0000000
[3,7,6,5,1,8,4,2]=>0000000
[3,2,5,1,6,7,8,4]=>0000000
[3,2,4,1,6,8,5,7]=>0001000
[8,3,2,4,7,6,1,5]=>0000000
[3,2,5,1,8,4,7,6]=>0000000
[3,2,5,1,6,7,4,8]=>0000001
[8,4,2,3,7,5,1,6]=>0000000
[5,2,6,1,8,3,7,4]=>0000000
[5,2,6,1,8,4,7,3]=>0000000
[7,4,2,3,8,5,1,6]=>0000000
[8,5,1,6,4,2,3,7]=>0000000
[8,5,6,1,7,3,4,2]=>0000000
[3,6,8,5,1,7,4,2]=>0000000
[3,2,5,1,8,6,7,4]=>0000000
[3,2,5,1,7,8,6,4]=>0000000
[4,6,3,7,1,8,5,2]=>0000000
[4,6,3,7,5,1,8,2]=>0000000
[4,2,6,1,7,5,3,8]=>0000001
[2,5,7,4,1,6,3,8]=>0000001
[2,5,7,4,1,6,8,3]=>0000000
[5,4,7,8,3,1,6,2]=>0000000
[4,3,7,5,1,8,6,2]=>0000000
[6,4,3,8,5,1,7,2]=>0000000
[5,8,4,3,6,1,7,2]=>0000000
[5,4,8,3,6,1,7,2]=>0000000
[2,5,4,6,1,7,3,8]=>0000001
[4,6,2,1,8,5,7,3]=>0000000
[2,4,1,7,5,8,6,3]=>0000000
[2,4,1,7,5,3,8,6]=>0000000
[2,6,4,1,8,5,3,7]=>0000000
[5,4,8,2,1,6,3,7]=>0000000
[2,5,8,4,1,6,3,7]=>0000000
[3,2,5,6,1,8,4,7]=>0000000
[4,8,3,2,6,1,5,7]=>0000000
[3,5,2,8,1,6,4,7]=>0000000
[3,2,1,6,8,5,4,7]=>0010000
[3,2,7,1,5,4,8,6]=>0000000
[3,2,7,1,5,8,6,4]=>0000000
[3,8,2,5,1,6,7,4]=>0000000
[4,8,3,2,6,7,1,5]=>0000000
[4,3,8,2,6,7,1,5]=>0000000
[4,3,2,6,7,8,1,5]=>0000000
[4,3,2,6,7,1,5,8]=>0000001
[4,3,7,8,2,6,1,5]=>0000000
[2,5,7,4,8,1,6,3]=>0000000
[3,2,5,7,1,6,8,4]=>0000000
[3,2,5,7,1,6,4,8]=>0000001
[6,3,2,7,1,5,4,8]=>0000001
[6,3,2,7,1,5,8,4]=>0000000
[6,3,2,7,8,1,5,4]=>0000000
[6,5,2,1,7,8,4,3]=>0000000
[6,2,1,8,5,3,7,4]=>0000000
[6,3,2,7,1,4,8,5]=>0000000
[6,3,2,1,4,7,8,5]=>0000000
[6,3,2,1,4,7,5,8]=>0000001
[3,5,2,1,7,8,4,6]=>0000000
[4,6,2,1,8,3,7,5]=>0000000
[3,2,7,1,4,8,6,5]=>0000000
[3,5,8,2,1,7,4,6]=>0000000
[4,8,3,7,2,1,5,6]=>0000000
[4,3,7,2,8,1,5,6]=>0000000
[4,3,7,2,1,5,6,8]=>0000001
[4,8,3,2,7,1,5,6]=>0000000
[6,3,2,8,1,4,7,5]=>0000000
[3,2,1,4,7,5,8,6]=>0011000
[5,3,2,1,8,4,6,7]=>0000000
[4,8,3,2,1,5,6,7]=>0000000
[4,3,8,2,1,5,6,7]=>0000000
[6,2,5,3,4,1,8,7]=>0000010
[8,1,7,3,4,2,6,5]=>0000000
[8,2,7,1,4,3,6,5]=>0000000
[8,2,3,1,5,4,7,6]=>0000000
[2,1,8,5,7,3,6,4]=>0100000
[3,6,7,8,4,2,5,1]=>0000000
[5,2,7,8,1,4,6,3]=>0000000
[2,8,4,5,3,1,6,7]=>0000000
[2,7,6,8,4,3,5,1]=>0000000
[4,6,8,5,1,3,2,7]=>0000000
[2,4,8,3,6,5,1,7]=>0000000
[1,7,3,8,5,4,6,2]=>1000000
[2,8,5,4,3,1,6,7]=>0000000
[1,4,3,2,8,5,6,7]=>1001000
[6,4,8,2,5,3,1,7]=>0000000
[6,2,8,4,5,3,1,7]=>0000000
[5,1,3,2,4,8,6,7]=>0000100
[2,8,1,5,3,4,7,6]=>0000000
[1,4,2,8,5,3,6,7]=>1000000
[3,5,1,4,8,2,6,7]=>0000000
[1,5,2,8,4,3,6,7]=>1000000
[1,2,5,4,3,8,6,7]=>1100100
[1,2,4,8,5,3,7,6]=>1100000
[1,5,2,7,8,4,3,6]=>1000000
[5,1,2,7,4,8,3,6]=>0000000
[8,3,5,1,4,7,2,6]=>0000000
[1,2,8,5,7,4,3,6]=>1100000
[1,2,4,8,7,5,3,6]=>1100000
[2,8,1,4,3,7,6,5]=>0000000
[7,6,1,4,2,8,3,5]=>0000000
[7,1,6,2,8,4,3,5]=>0000000
[1,4,2,7,8,5,3,6]=>1000000
[6,1,2,8,4,3,7,5]=>0000000
[6,4,1,2,8,3,7,5]=>0000000
[7,6,1,3,2,4,8,5]=>0000000
[6,7,1,3,2,4,8,5]=>0000000
[1,2,7,3,5,8,4,6]=>1100000
[5,8,1,3,7,2,4,6]=>0000000
[1,2,5,8,7,3,4,6]=>1100000
[8,6,1,3,2,4,7,5]=>0000000
[4,2,8,1,7,3,6,5]=>0000000
[7,1,2,8,4,3,6,5]=>0000000
[1,2,8,4,7,5,3,6]=>1100000
[1,2,8,7,4,5,3,6]=>1100000
[2,8,1,7,5,3,4,6]=>0000000
[8,3,7,1,5,2,4,6]=>0000000
[8,6,1,4,2,7,3,5]=>0000000
[7,1,2,8,6,4,3,5]=>0000000
[3,7,4,8,1,6,2,5]=>0000000
[3,4,8,7,1,6,2,5]=>0000000
[4,2,8,1,7,6,3,5]=>0000000
[2,8,1,7,6,4,3,5]=>0000000
[7,8,3,4,1,5,2,6]=>0000000
[6,8,3,4,1,7,2,5]=>0000000
[5,7,3,4,1,8,2,6]=>0000000
[5,8,3,4,1,7,2,6]=>0000000
[4,7,3,5,1,6,2,8]=>0000001
[4,8,3,5,1,6,2,7]=>0000000
[4,8,3,5,1,7,2,6]=>0000000
[4,7,3,5,1,8,2,6]=>0000000
[5,6,2,3,1,7,4,8]=>0000001
[5,6,2,4,1,8,3,7]=>0000000
[5,6,2,4,1,7,3,8]=>0000001
[4,6,2,5,1,7,3,8]=>0000001
[4,6,2,5,1,8,3,7]=>0000000
[4,5,1,8,3,7,2,6]=>0000000
[4,6,2,7,3,8,1,5]=>0000000
[5,6,2,7,3,8,1,4]=>0000000
[5,6,2,8,4,7,1,3]=>0000000
[5,6,2,8,3,7,1,4]=>0000000
[4,6,2,8,3,7,1,5]=>0000000
[4,5,1,7,3,6,2,8]=>0000001
[4,5,1,8,3,6,2,7]=>0000000
[6,3,8,4,5,7,2,1]=>0000000
[2,5,8,4,7,6,3,1]=>0000000
[4,3,8,1,5,6,7,2]=>0000000
[3,8,7,4,1,6,2,5]=>0000000
[6,1,8,4,5,7,2,3]=>0000000
[4,5,7,6,2,3,8,1]=>0000000
[3,5,7,2,6,4,8,1]=>0000000
[2,5,7,3,6,4,8,1]=>0000000
[8,4,3,7,6,1,5,2]=>0000000
[6,7,2,3,5,4,8,1]=>0000000
[5,2,7,3,6,4,8,1]=>0000000
[8,3,4,7,6,1,5,2]=>0000000
[8,2,4,7,1,6,5,3]=>0000000
[3,1,4,7,6,8,5,2]=>0000000
[5,1,7,3,6,8,4,2]=>0000000
[6,7,1,3,5,8,4,2]=>0000000
[4,8,3,7,6,1,5,2]=>0000000
[2,8,4,7,1,6,5,3]=>0000000
[8,1,4,7,2,6,5,3]=>0000000
[8,1,3,2,7,6,5,4]=>0000000
[2,8,3,1,7,6,5,4]=>0000000
[6,7,1,2,8,5,4,3]=>0000000
[8,2,3,1,7,6,5,4]=>0000000
[1,4,2,7,8,6,5,3]=>1000000
[8,4,2,7,1,6,5,3]=>0000000
[8,5,7,2,1,6,4,3]=>0000000
[1,5,7,2,8,6,4,3]=>1000000
[2,5,7,1,8,6,4,3]=>0000000
[3,5,7,1,6,8,4,2]=>0000000
[6,7,4,5,8,1,3,2]=>0000000
[2,5,7,8,1,6,4,3]=>0000000
[1,5,7,8,2,6,4,3]=>1000000
[8,5,7,1,2,6,4,3]=>0000000
[8,4,1,7,2,6,5,3]=>0000000
[6,7,2,8,1,5,4,3]=>0000000
[5,2,7,8,1,6,4,3]=>0000000
[4,2,8,7,1,6,5,3]=>0000000
[1,3,8,2,7,6,5,4]=>1000000
[8,3,1,2,7,6,5,4]=>0000000
[8,2,1,3,7,6,5,4]=>0000000
[2,1,8,3,7,6,5,4]=>0100000
[5,1,7,8,2,6,4,3]=>0000000
[6,7,1,8,2,5,4,3]=>0000000
[4,8,1,7,2,6,5,3]=>0000000
[3,8,1,2,7,6,5,4]=>0000000
[1,8,2,3,7,6,5,4]=>1000000
[3,7,1,5,8,2,6,4]=>0000000
[2,7,1,5,8,3,6,4]=>0000000
[2,6,5,1,8,3,7,4]=>0000000
[5,6,4,1,8,7,2,3]=>0000000
[8,1,4,5,7,6,2,3]=>0000000
[6,4,5,1,8,7,2,3]=>0000000
[5,4,6,1,8,7,2,3]=>0000000
[3,5,6,1,8,2,7,4]=>0000000
[2,5,6,1,8,3,7,4]=>0000000
[2,4,6,1,3,8,7,5]=>0000000
[3,4,6,1,2,8,7,5]=>0000000
[5,3,6,1,8,2,7,4]=>0000000
[7,3,1,5,8,2,6,4]=>0000000
[8,1,3,5,7,2,6,4]=>0000000
[8,1,2,5,7,3,6,4]=>0000000
[7,2,1,5,8,3,6,4]=>0000000
[6,2,5,1,8,3,7,4]=>0000000
[4,2,6,1,3,8,7,5]=>0000000
[4,2,5,3,1,8,7,6]=>0000100
[6,2,4,1,3,8,7,5]=>0000000
[7,2,1,4,3,8,6,5]=>0000000
[8,1,2,4,3,7,6,5]=>0000000
[8,1,3,4,2,7,6,5]=>0000000
[7,3,1,4,2,8,6,5]=>0000000
[4,6,3,1,2,8,7,5]=>0000000
[2,6,4,1,3,8,7,5]=>0000000
[2,7,1,4,3,8,6,5]=>0000000
[8,1,6,7,2,3,5,4]=>0000000
[4,7,1,2,3,8,6,5]=>0000000
[3,7,1,2,4,8,6,5]=>0000000
[2,6,3,1,4,8,7,5]=>0000000
[3,6,2,1,4,8,7,5]=>0000000
[5,6,2,1,8,3,7,4]=>0000000
[6,5,2,1,8,3,7,4]=>0000000
[8,1,4,2,3,7,6,5]=>0000000
[7,4,1,2,3,8,6,5]=>0000000
[5,4,2,3,1,8,7,6]=>0000100
[3,5,2,4,1,8,7,6]=>0000100
[7,3,1,2,4,8,6,5]=>0000000
[8,1,3,2,4,7,6,5]=>0000000
[7,2,1,3,4,8,6,5]=>0000000
[2,4,6,3,5,8,7,1]=>0000000
[4,2,6,5,8,1,3,7]=>0000000
[2,4,1,6,5,8,3,7]=>0000000
[2,6,4,3,8,7,5,1]=>0000000
[4,2,6,8,5,3,7,1]=>0000000
[2,4,6,8,1,5,7,3]=>0000000
[2,1,4,6,8,5,3,7]=>0100000
[2,4,6,1,8,5,3,7]=>0000000
[2,4,6,8,1,5,3,7]=>0000000
[2,4,6,8,3,5,7,1]=>0000000
[2,4,6,3,8,5,7,1]=>0000000
[2,4,3,6,8,5,7,1]=>0000000
[2,4,3,6,8,5,1,7]=>0000000
[2,4,3,6,8,1,5,7]=>0000000
[4,6,5,2,8,7,1,3]=>0000000
[2,6,4,1,8,7,5,3]=>0000000
[1,3,7,4,5,8,2,6]=>1000000
[1,7,6,3,4,8,2,5]=>1000000
[8,1,6,3,7,2,4,5]=>0000000
[1,2,7,4,8,3,5,6]=>1100000
[6,1,7,3,4,8,2,5]=>0000000
[2,1,7,4,5,8,3,6]=>0100000
[5,1,4,7,3,8,2,6]=>0000000
[4,3,1,7,5,8,2,6]=>0000000
[2,8,6,3,7,1,4,5]=>0000000
[6,8,1,3,7,2,4,5]=>0000000
[5,8,2,1,7,3,4,6]=>0000000
[5,7,2,1,8,3,4,6]=>0000000
[6,7,1,3,8,2,4,5]=>0000000
[8,5,1,3,7,2,4,6]=>0000000
[1,5,3,2,8,4,6,7]=>1000000
[2,6,4,8,7,1,3,5]=>0000000
[1,6,4,8,7,2,3,5]=>1000000
[4,3,2,8,7,1,5,6]=>0000000
[5,2,4,8,7,1,3,6]=>0000000
[6,2,8,3,7,1,4,5]=>0000000
[5,1,4,8,7,2,3,6]=>0000000
[3,7,2,1,5,4,8,6]=>0000000
[3,8,2,1,5,4,7,6]=>0000000
[8,3,2,1,5,4,6,7]=>0000000
[8,3,2,1,6,4,5,7]=>0000000
[8,4,2,5,1,6,3,7]=>0000000
[8,3,2,1,4,6,5,7]=>0000000
[3,8,2,1,4,5,7,6]=>0000000
[3,2,7,1,4,6,8,5]=>0000000
[3,2,8,1,4,6,7,5]=>0000000
[3,8,2,1,4,7,5,6]=>0000000
[3,8,2,1,5,7,4,6]=>0000000
[4,8,2,5,1,7,3,6]=>0000000
[4,7,2,5,1,8,3,6]=>0000000
[3,7,2,1,5,8,4,6]=>0000000
[3,7,2,1,4,8,5,6]=>0000000
[3,2,1,7,5,8,6,4]=>0010000
[4,2,7,6,1,8,3,5]=>0000000
[4,3,7,6,8,1,2,5]=>0000000
[4,3,8,6,7,1,2,5]=>0000000
[3,8,2,1,7,4,5,6]=>0000000
[3,2,8,1,6,4,7,5]=>0000000
[3,2,7,1,6,4,8,5]=>0000000
[4,2,7,6,1,3,8,5]=>0000000
[4,2,8,6,1,3,7,5]=>0000000
[5,7,8,3,4,1,2,6]=>0000000
[4,2,6,8,1,3,7,5]=>0000000
[4,2,6,7,1,3,8,5]=>0000000
[3,2,6,1,8,4,7,5]=>0000000
[3,7,2,1,8,5,4,6]=>0000000
[4,7,3,8,5,1,2,6]=>0000000
[4,3,7,8,6,1,2,5]=>0000000
[3,2,7,1,8,6,4,5]=>0000000
[3,2,1,6,8,5,7,4]=>0010000
[3,2,6,1,8,7,4,5]=>0000000
[4,2,6,8,1,7,3,5]=>0000000
[4,3,6,8,7,1,2,5]=>0000000
[4,2,6,7,1,8,3,5]=>0000000
[3,2,6,1,7,8,4,5]=>0000000
[5,3,6,4,8,7,1,2]=>0000000
[1,4,6,2,7,8,5,3]=>1000000
[3,1,8,5,4,2,6,7]=>0000000
[1,2,7,5,4,8,6,3]=>1100000
[6,3,7,5,4,8,1,2]=>0000000
[1,6,2,5,4,8,7,3]=>1000000
[1,8,2,5,7,3,6,4]=>1000000
[6,2,1,5,4,8,7,3]=>0000000
[4,1,6,2,8,7,5,3]=>0000000
[7,8,3,1,4,2,6,5]=>0000000
[4,3,6,1,8,2,7,5]=>0000000
[7,5,1,6,4,3,2,8]=>0000001
[6,1,5,7,4,3,2,8]=>0000001
[1,5,8,6,4,3,2,7]=>1000000
[7,8,5,1,6,3,2,4]=>0000000
[2,6,1,5,7,3,8,4]=>0000000
[1,6,8,7,4,3,2,5]=>1000000
[6,8,1,7,4,3,2,5]=>0000000
[5,6,1,7,4,3,2,8]=>0000001
[5,1,7,6,4,3,2,8]=>0000001
[6,1,7,8,4,3,2,5]=>0000000
[7,1,8,6,4,3,2,5]=>0000000
[7,2,1,5,4,6,8,3]=>0000000
[1,2,8,5,6,3,7,4]=>1100000
[6,1,2,5,7,3,8,4]=>0000000
[4,3,6,1,5,7,2,8]=>0000001
[1,3,6,8,5,7,2,4]=>1000000
[1,3,6,4,8,7,2,5]=>1000000
[4,1,6,7,3,8,2,5]=>0000000
[5,4,6,1,3,7,2,8]=>0000001
[6,4,1,5,2,3,7,8]=>0000011
[4,1,7,5,2,3,8,6]=>0000000
[2,8,3,5,4,1,7,6]=>0000000
[7,8,1,4,6,3,2,5]=>0000000
[5,1,8,7,4,3,2,6]=>0000000
[6,5,1,8,4,3,2,7]=>0000000
[6,5,7,1,4,3,2,8]=>0000001
[7,5,8,1,4,3,2,6]=>0000000
[1,5,7,8,4,3,2,6]=>1000000
[2,4,7,5,1,3,8,6]=>0000000
[7,8,4,6,1,3,2,5]=>0000000
[1,6,5,8,4,3,2,7]=>1000000
[6,8,5,1,4,3,2,7]=>0000000
[3,6,2,5,4,1,7,8]=>0000011
[4,3,6,2,8,1,5,7]=>0000000
[6,1,2,5,4,7,8,3]=>0000000
[6,2,4,5,1,3,7,8]=>0000011
[4,2,8,5,1,3,7,6]=>0000000
[4,3,6,8,1,7,2,5]=>0000000
[5,3,6,4,1,7,2,8]=>0000001
[1,6,7,4,8,3,5,2]=>1000000
[1,4,6,3,7,5,8,2]=>1000000
[4,6,7,2,5,8,1,3]=>0000000
[2,4,6,1,7,5,3,8]=>0000001
[2,7,5,4,1,6,3,8]=>0000001
[1,7,5,4,3,8,6,2]=>1000000
[1,5,8,4,3,6,7,2]=>1000000
[5,4,6,2,7,8,1,3]=>0000000
[2,5,4,1,6,7,3,8]=>0000001
[5,6,3,2,7,1,4,8]=>0000001
[5,6,3,2,7,1,8,4]=>0000000
[8,5,6,3,2,7,1,4]=>0000000
[5,4,6,2,8,1,7,3]=>0000000
[2,4,1,7,8,5,3,6]=>0000000
[5,6,3,2,1,8,4,7]=>0000000
[3,5,2,1,6,4,7,8]=>0000011
[6,8,4,3,2,1,5,7]=>0000000
[5,3,8,2,1,6,4,7]=>0000000
[7,3,2,8,5,1,6,4]=>0000000
[8,4,6,3,2,1,7,5]=>0000000
[5,4,7,2,1,8,6,3]=>0000000
[5,7,3,2,1,6,8,4]=>0000000
[6,3,7,2,5,1,8,4]=>0000000
[6,7,8,3,5,2,1,4]=>0000000
[6,2,5,7,8,4,1,3]=>0000000
[2,1,5,7,8,6,3,4]=>0100000
[3,6,7,2,8,1,4,5]=>0000000
[3,2,6,1,7,4,5,8]=>0000001
[2,5,8,4,1,3,7,6]=>0000000
[2,4,1,7,8,3,6,5]=>0000000
[3,6,8,2,1,7,4,5]=>0000000
[5,3,8,2,1,4,7,6]=>0000000
[4,8,7,3,2,1,5,6]=>0000000
[4,7,3,2,1,5,6,8]=>0000001
[8,4,7,3,2,1,5,6]=>0000000
[8,3,5,2,1,4,7,6]=>0000000
[3,5,2,1,4,6,8,7]=>0000110
[2,7,6,5,1,8,3,4]=>0000000
[2,7,6,5,1,8,4,3]=>0000000
[7,3,5,1,8,4,2,6]=>0000000
[2,3,4,8,7,6,1,5]=>0000000
[2,1,4,5,8,7,3,6]=>0100000
[6,4,3,5,8,7,1,2]=>0000000
[5,7,3,6,1,8,4,2]=>0000000
[2,3,4,8,7,1,6,5]=>0000000
[6,1,4,2,8,5,7,3]=>0000000
[1,3,8,5,7,6,2,4]=>1000000
[8,6,1,5,7,2,3,4]=>0000000
[3,2,8,5,7,6,1,4]=>0000000
[7,8,5,4,1,6,2,3]=>0000000
[7,2,6,4,5,1,8,3]=>0000000
[3,8,2,7,6,1,5,4]=>0000000
[4,8,7,2,6,5,3,1]=>0000000
[4,8,7,3,1,6,5,2]=>0000000
[4,8,7,3,2,6,1,5]=>0000000
[4,8,7,3,2,6,5,1]=>0000000
[4,8,7,3,6,2,5,1]=>0000000
[4,8,7,3,6,1,5,2]=>0000000
[5,8,7,6,3,4,2,1]=>0000000
[5,8,7,6,3,1,4,2]=>0000000
[5,8,7,6,2,4,3,1]=>0000000
[5,8,7,6,4,2,1,3]=>0000000
[5,8,7,6,4,1,3,2]=>0000000
[5,8,7,6,4,3,1,2]=>0000000
[7,3,5,2,6,4,1,8]=>0000001
[7,2,1,5,6,4,3,8]=>0000001
[6,2,1,5,7,4,8,3]=>0000000
[3,2,1,5,7,4,8,6]=>0010000
[2,4,6,7,3,8,1,5]=>0000000
[1,4,6,7,3,8,5,2]=>1000000
[3,2,1,6,7,8,4,5]=>0010000
[5,2,1,6,7,8,4,3]=>0000000
[5,3,6,1,7,8,4,2]=>0000000
[4,3,6,2,7,8,5,1]=>0000000
[4,2,1,5,7,3,8,6]=>0000000
[1,5,6,7,8,2,4,3]=>1000000
[1,5,6,7,8,4,2,3]=>1000000
[4,3,6,1,7,8,5,2]=>0000000
[1,4,3,6,2,5,7,8]=>1000011
[1,4,3,7,2,5,6,8]=>1000001
[1,4,3,7,6,8,2,5]=>1000000
[1,4,3,7,5,8,2,6]=>1000000
[1,5,3,7,4,8,2,6]=>1000000
[1,5,4,8,2,6,3,7]=>1000000
[1,5,4,8,3,7,2,6]=>1000000
[1,2,3,6,5,8,4,7]=>1110000
[7,8,1,4,5,3,6,2]=>0000000
[5,8,1,4,7,6,3,2]=>0000000
[7,5,1,8,6,2,4,3]=>0000000
[7,4,1,8,2,6,3,5]=>0000000
[7,1,8,4,2,6,3,5]=>0000000
[7,3,1,8,4,2,6,5]=>0000000
[7,2,8,3,6,5,1,4]=>0000000
[7,2,8,3,6,1,5,4]=>0000000
[6,1,2,8,3,5,4,7]=>0000000
[5,2,3,8,1,4,7,6]=>0000000
[6,2,4,1,8,7,3,5]=>0000000
[3,1,6,4,2,8,5,7]=>0000000
[2,6,3,8,7,1,5,4]=>0000000
[2,6,3,8,5,1,4,7]=>0000000
[2,5,1,8,3,4,7,6]=>0000000
[1,2,5,3,8,4,7,6]=>1100000
[1,2,4,8,3,7,6,5]=>1100000
[2,4,8,3,7,1,6,5]=>0000000
[2,4,8,3,7,6,1,5]=>0000000
[2,5,3,8,1,7,4,6]=>0000000
[2,5,4,1,3,8,7,6]=>0000100
[3,1,5,4,8,2,7,6]=>0000000
[5,3,1,4,8,2,7,6]=>0000000
[5,2,3,8,4,7,1,6]=>0000000
[4,8,2,3,7,6,1,5]=>0000000
[4,8,2,3,7,1,6,5]=>0000000
[4,8,1,2,3,7,6,5]=>0000000
[1,4,8,3,7,2,6,5]=>1000000
[6,3,8,1,5,2,4,7]=>0000000
[5,3,8,1,2,4,7,6]=>0000000
[5,1,3,8,2,4,7,6]=>0000000
[1,5,3,8,2,4,7,6]=>1000000
[1,5,4,8,2,7,6,3]=>1000000
[5,1,4,8,2,7,6,3]=>0000000
[5,4,8,1,2,7,6,3]=>0000000
[6,5,1,2,8,7,4,3]=>0000000
[4,1,5,8,2,7,6,3]=>0000000
[4,1,2,5,8,7,6,3]=>0000000
[1,4,2,5,8,7,6,3]=>1000000
[1,3,5,2,8,7,4,6]=>1000000
[3,5,1,2,8,7,4,6]=>0000000
[4,2,6,1,8,7,3,5]=>0000000
[4,3,1,5,8,2,7,6]=>0000000
[3,5,2,8,7,1,4,6]=>0000000
[3,4,8,7,2,6,1,5]=>0000000
[3,4,8,1,7,2,6,5]=>0000000
[1,3,4,8,7,2,6,5]=>1000000
[1,3,4,8,2,7,6,5]=>1000000
[3,4,8,1,2,7,6,5]=>0000000
[3,4,8,2,7,1,6,5]=>0000000
[3,4,8,2,7,6,1,5]=>0000000
[4,2,5,8,1,7,6,3]=>0000000
[4,3,1,2,5,8,7,6]=>0001100
[3,1,4,2,5,8,7,6]=>0001100
[2,3,5,1,8,7,6,4]=>0000000
[7,8,2,1,5,3,6,4]=>0000000
[6,4,1,2,7,3,5,8]=>0000001
[2,3,7,5,4,1,8,6]=>0000000
[6,3,1,5,4,2,7,8]=>0000011
[7,8,1,5,4,2,6,3]=>0000000
[7,8,3,5,4,1,6,2]=>0000000
[7,8,2,5,4,1,3,6]=>0000000
[7,8,2,5,4,6,1,3]=>0000000
[6,2,1,5,4,7,3,8]=>0000001
[5,3,6,2,4,7,1,8]=>0000001
[6,4,2,1,7,3,8,5]=>0000000
[2,7,6,5,3,1,4,8]=>0000001
[3,7,6,4,8,5,1,2]=>0000000
[5,7,6,3,8,4,1,2]=>0000000
[5,1,6,2,4,8,3,7]=>0000000
[4,7,6,5,2,1,3,8]=>0000001
[4,7,6,5,2,8,1,3]=>0000000
[4,7,6,5,1,8,3,2]=>0000000
[1,7,6,5,2,8,3,4]=>1000000
[1,7,6,5,3,2,8,4]=>1000000
[4,7,6,5,1,2,8,3]=>0000000
[4,7,6,5,3,1,8,2]=>0000000
[5,2,6,3,4,1,7,8]=>0000011
[5,1,6,2,4,7,8,3]=>0000000
[1,7,2,4,8,3,6,5]=>1000000
[4,7,2,1,5,3,6,8]=>0000001
[4,7,1,6,2,3,8,5]=>0000000
[1,7,2,6,8,3,5,4]=>1000000
[1,2,6,7,4,8,5,3]=>1100000
[3,1,6,7,4,2,8,5]=>0000000
[3,2,8,5,4,6,1,7]=>0000000
[4,7,6,3,5,8,1,2]=>0000000
[3,7,6,5,2,4,1,8]=>0000001
[3,7,6,5,2,1,8,4]=>0000000
[1,7,6,5,8,2,4,3]=>1000000
[3,7,6,5,8,1,4,2]=>0000000
[3,7,6,5,1,2,4,8]=>0000001
[3,1,6,8,4,2,5,7]=>0000000
[4,7,6,8,3,5,1,2]=>0000000
[2,7,6,5,8,1,3,4]=>0000000
[2,7,6,5,8,4,1,3]=>0000000
[3,7,5,8,2,4,1,6]=>0000000
[5,1,7,8,4,3,2,6]=>0000000
[4,7,1,8,3,6,2,5]=>0000000
[7,1,2,3,8,6,5,4]=>0000000
[6,8,1,4,3,7,2,5]=>0000000
[8,7,3,2,4,1,6,5]=>0000000
[7,1,2,3,6,8,5,4]=>0000000
[3,8,7,1,4,2,6,5]=>0000000
[5,8,3,7,1,4,2,6]=>0000000
[7,1,2,3,5,6,8,4]=>0000000
[5,1,2,3,7,8,6,4]=>0000000
[8,6,3,2,4,7,1,5]=>0000000
[7,8,1,2,6,3,5,4]=>0000000
[1,4,8,2,7,3,5,6]=>1000000
[1,2,8,5,4,7,3,6]=>1100000
[2,3,6,8,4,7,1,5]=>0000000
[1,3,6,8,4,7,5,2]=>1000000
[2,4,8,1,7,3,6,5]=>0000000
[3,4,8,5,7,6,1,2]=>0000000
[1,2,6,8,4,5,7,3]=>1100000
[7,5,1,2,4,3,6,8]=>0000001
[7,4,6,1,5,2,3,8]=>0000001
[6,8,1,4,7,2,3,5]=>0000000
[1,6,4,2,8,3,5,7]=>1000000
[1,6,3,8,5,4,2,7]=>1000000
[7,1,3,6,5,4,2,8]=>0000001
[7,2,1,4,6,3,5,8]=>0000001
[7,2,3,6,5,1,4,8]=>0000001
[7,1,2,3,6,5,4,8]=>0000001
[6,8,1,2,7,3,5,4]=>0000000
[1,6,2,3,8,5,4,7]=>1000000
[1,5,8,2,7,6,3,4]=>1000000
[5,8,2,7,6,3,4,1]=>0000000
[6,2,8,1,7,3,5,4]=>0000000
[3,6,4,1,2,8,5,7]=>0000000
[2,5,1,8,7,6,3,4]=>0000000
[1,2,5,3,8,7,4,6]=>1100000
[2,5,3,8,7,1,6,4]=>0000000
[2,5,8,4,1,7,6,3]=>0000000
[3,5,8,7,1,4,2,6]=>0000000
[5,3,8,4,1,7,6,2]=>0000000
[4,2,8,7,6,3,5,1]=>0000000
[6,3,1,8,7,2,5,4]=>0000000
[5,1,3,8,7,6,2,4]=>0000000
[1,5,3,8,7,6,2,4]=>1000000
[5,1,8,4,7,2,6,3]=>0000000
[5,8,7,4,6,1,2,3]=>0000000
[6,8,5,1,2,4,7,3]=>0000000
[4,5,8,1,7,2,6,3]=>0000000
[1,3,2,5,8,7,4,6]=>1010000
[3,5,1,8,7,4,6,2]=>0000000
[4,3,6,1,2,8,5,7]=>0000000
[4,5,8,3,1,7,2,6]=>0000000
[4,5,2,8,7,1,3,6]=>0000000
[3,2,5,8,7,1,6,4]=>0000000
[3,4,8,7,6,2,1,5]=>0000000
[3,4,8,7,6,5,1,2]=>0000000
[1,3,4,8,7,6,2,5]=>1000000
[3,4,8,7,6,2,5,1]=>0000000
[3,2,5,8,7,4,6,1]=>0000000
[2,1,3,5,8,7,4,6]=>0110000
[1,2,7,5,8,6,4,3]=>1100000
[6,8,1,3,7,5,2,4]=>0000000
[1,3,7,8,2,6,5,4]=>1000000
[2,7,8,1,3,6,5,4]=>0000000
[8,1,2,6,7,3,5,4]=>0000000
[8,1,2,6,7,5,3,4]=>0000000
[8,2,5,7,1,3,6,4]=>0000000
[2,8,1,6,7,3,5,4]=>0000000
[2,6,8,3,7,1,5,4]=>0000000
[2,8,6,4,7,1,5,3]=>0000000
[6,8,3,4,1,7,5,2]=>0000000
[6,8,3,7,4,1,5,2]=>0000000
[8,2,5,7,1,6,3,4]=>0000000
[8,4,7,2,3,6,1,5]=>0000000
[8,5,7,4,2,6,1,3]=>0000000
[8,3,5,7,4,1,6,2]=>0000000
[8,5,2,4,7,1,6,3]=>0000000
[8,2,4,7,3,6,1,5]=>0000000
[8,2,7,1,4,6,3,5]=>0000000
[8,7,1,2,4,6,3,5]=>0000000
[8,7,1,4,6,2,3,5]=>0000000
[8,4,7,1,3,6,2,5]=>0000000
[8,3,5,7,1,2,6,4]=>0000000
[5,8,7,1,3,6,2,4]=>0000000
[8,5,4,7,1,6,2,3]=>0000000
[8,5,4,7,1,2,6,3]=>0000000
[8,5,1,4,7,2,6,3]=>0000000
[8,5,6,3,1,7,4,2]=>0000000
[1,8,4,5,7,2,6,3]=>1000000
[5,8,7,3,6,1,2,4]=>0000000
[8,3,5,7,1,6,2,4]=>0000000
[1,6,8,3,7,5,2,4]=>1000000
[6,3,8,2,7,5,1,4]=>0000000
[8,6,4,7,3,1,5,2]=>0000000
[8,4,5,7,3,1,6,2]=>0000000
[8,3,4,7,2,6,1,5]=>0000000
[8,7,1,3,4,6,2,5]=>0000000
[8,3,7,2,4,6,1,5]=>0000000
[2,8,4,5,7,1,6,3]=>0000000
[8,7,3,4,5,1,6,2]=>0000000
[8,7,4,5,2,6,1,3]=>0000000
[8,7,2,3,4,6,1,5]=>0000000
[8,6,5,1,3,2,7,4]=>0000000
[8,6,3,1,7,2,4,5]=>0000000
[8,7,3,1,5,2,4,6]=>0000000
[8,6,1,2,4,7,3,5]=>0000000
[8,6,1,5,3,4,7,2]=>0000000
[8,6,1,5,2,4,7,3]=>0000000
[8,6,1,2,5,7,3,4]=>0000000
[5,1,4,2,3,8,6,7]=>0000100
[5,1,4,2,7,3,6,8]=>0000001
[5,7,8,1,2,4,6,3]=>0000000
[5,7,8,1,3,4,6,2]=>0000000
[5,8,1,7,3,4,6,2]=>0000000
[8,1,5,7,2,4,6,3]=>0000000
[1,4,2,3,8,7,5,6]=>1001000
[1,4,2,7,6,3,5,8]=>1000001
[6,1,2,8,7,5,3,4]=>0000000
[6,1,2,4,8,7,5,3]=>0000000
[3,1,8,4,6,7,5,2]=>0000000
[3,1,7,6,4,8,5,2]=>0000000
[7,1,2,4,6,8,5,3]=>0000000
[7,1,2,6,8,5,3,4]=>0000000
[7,1,5,3,2,8,6,4]=>0000000
[8,1,7,5,3,2,6,4]=>0000000
[8,3,7,1,2,6,4,5]=>0000000
[3,1,2,8,4,7,5,6]=>0010000
[1,4,2,3,8,6,5,7]=>1001000
[1,4,2,3,8,5,7,6]=>1001000
[5,8,1,7,2,4,6,3]=>0000000
[5,8,1,3,4,7,6,2]=>0000000
[3,1,8,6,4,7,5,2]=>0000000
[8,1,2,6,7,4,5,3]=>0000000
[1,2,3,5,8,4,7,6]=>1110000
[1,2,3,5,8,6,4,7]=>1110000
[7,1,2,8,3,6,5,4]=>0000000
[7,1,2,8,6,4,5,3]=>0000000
[3,1,7,8,4,6,5,2]=>0000000
[8,1,2,7,4,6,5,3]=>0000000
[8,1,2,7,3,6,5,4]=>0000000
[1,2,3,6,8,5,4,7]=>1110000
[5,4,8,3,2,7,6,1]=>0000000
[2,1,5,8,4,7,6,3]=>0100000
[8,3,2,6,7,5,4,1]=>0000000
[8,4,5,3,2,7,6,1]=>0000000
[8,4,6,3,7,5,2,1]=>0000000
[3,6,2,8,7,5,4,1]=>0000000
[1,6,4,8,2,5,3,7]=>1000000
[1,6,5,8,2,4,3,7]=>1000000
[1,6,8,2,4,3,7,5]=>1000000
[1,6,2,4,3,7,8,5]=>1000000
[1,5,6,2,4,7,3,8]=>1000001
[1,5,6,2,4,7,8,3]=>1000000
[1,6,7,2,4,3,8,5]=>1000000
[1,5,8,2,4,6,7,3]=>1000000
[1,5,7,8,3,2,4,6]=>1000000
[1,5,8,3,2,4,6,7]=>1000000
[1,5,6,2,4,8,3,7]=>1000000
[1,7,3,4,2,8,6,5]=>1000000
[1,5,6,2,4,8,7,3]=>1000000
[1,5,8,7,3,2,4,6]=>1000000
[1,7,4,2,8,6,5,3]=>1000000
[1,5,8,3,2,4,7,6]=>1000000
[1,6,5,2,3,7,4,8]=>1000001
[1,6,5,2,3,7,8,4]=>1000000
[1,6,8,4,2,3,7,5]=>1000000
[1,6,8,5,2,3,7,4]=>1000000
[1,6,4,2,3,7,5,8]=>1000001
[1,5,8,6,2,4,7,3]=>1000000
[1,7,5,2,8,6,4,3]=>1000000
[3,7,5,6,1,4,8,2]=>0000000
[8,6,1,4,2,7,5,3]=>0000000
[1,6,7,4,3,5,8,2]=>1000000
[6,7,1,4,3,5,8,2]=>0000000
[4,7,1,6,3,5,8,2]=>0000000
[3,1,4,7,6,5,8,2]=>0000000
[6,1,7,4,3,5,8,2]=>0000000
[7,1,6,4,3,5,8,2]=>0000000
[1,7,6,4,3,5,8,2]=>1000000
[8,1,6,4,2,7,5,3]=>0000000
[4,7,1,3,8,2,5,6]=>0000000
[7,4,1,3,8,2,5,6]=>0000000
[1,3,6,4,2,8,5,7]=>1000000
[4,7,3,1,2,8,5,6]=>0000000
[4,7,8,1,2,6,5,3]=>0000000
[1,8,6,4,2,7,5,3]=>1000000
[4,8,1,3,7,2,5,6]=>0000000
[8,7,1,3,6,2,5,4]=>0000000
[1,8,4,3,7,2,5,6]=>1000000
[3,7,4,6,8,2,1,5]=>0000000
[2,4,3,7,8,6,1,5]=>0000000
[1,4,7,3,8,2,5,6]=>1000000
[5,7,6,8,3,2,1,4]=>0000000
[6,1,4,3,8,2,5,7]=>0000000
[4,1,7,3,8,2,5,6]=>0000000
[8,1,4,3,7,2,5,6]=>0000000
[4,2,3,7,8,6,1,5]=>0000000
[2,7,5,6,3,8,1,4]=>0000000
[5,7,2,6,8,4,1,3]=>0000000
[7,2,5,6,8,4,1,3]=>0000000
[5,2,3,8,7,6,1,4]=>0000000
[8,2,3,7,5,6,1,4]=>0000000
[6,1,8,3,7,2,5,4]=>0000000
[1,7,8,4,2,6,5,3]=>1000000
[4,7,1,8,2,5,6,3]=>0000000
[1,4,8,3,6,2,5,7]=>1000000
[3,7,5,8,6,2,1,4]=>0000000
[3,7,8,6,5,2,1,4]=>0000000
[6,8,7,5,3,2,1,4]=>0000000
[5,7,6,8,3,4,1,2]=>0000000
[3,7,6,8,4,5,1,2]=>0000000
[1,5,4,7,6,8,2,3]=>1000000
[1,7,4,6,5,8,2,3]=>1000000
[3,7,4,6,5,8,1,2]=>0000000
[3,5,4,8,6,7,1,2]=>0000000
[3,8,4,6,5,7,1,2]=>0000000
[3,6,4,7,5,8,1,2]=>0000000
[1,6,2,7,5,8,3,4]=>1000000
[1,6,4,8,5,7,2,3]=>1000000
[1,8,4,6,5,7,2,3]=>1000000
[1,5,4,8,6,7,2,3]=>1000000
[7,8,1,5,4,6,2,3]=>0000000
[1,8,2,6,5,7,3,4]=>1000000
[1,7,2,8,5,6,3,4]=>1000000
[1,7,2,6,5,8,3,4]=>1000000
[1,5,2,7,6,8,3,4]=>1000000
[1,7,6,8,2,5,3,4]=>1000000
[1,7,6,8,4,5,2,3]=>1000000
[7,8,5,6,1,3,2,4]=>0000000
[5,8,6,7,1,3,2,4]=>0000000
[1,3,2,7,6,8,4,5]=>1010000
[1,7,6,8,2,4,3,5]=>1000000
[1,3,2,8,6,7,4,5]=>1010000
[7,8,1,3,2,6,4,5]=>0000000
[7,8,1,6,2,4,3,5]=>0000000
[1,8,6,7,2,4,3,5]=>1000000
[7,8,1,4,2,6,3,5]=>0000000
[8,4,7,5,2,6,1,3]=>0000000
[5,4,6,8,2,1,7,3]=>0000000
[4,8,7,5,6,1,3,2]=>0000000
[3,2,6,8,5,7,1,4]=>0000000
[7,4,8,6,5,2,1,3]=>0000000
[2,5,3,7,4,1,8,6]=>0000000
[4,2,8,7,3,5,6,1]=>0000000
[2,6,3,5,8,7,1,4]=>0000000
[8,1,6,4,7,3,2,5]=>0000000
[4,8,7,5,6,1,2,3]=>0000000
[6,1,4,8,7,3,5,2]=>0000000
[2,8,3,7,1,5,6,4]=>0000000
[4,1,6,5,8,2,3,7]=>0000000
[8,3,6,1,4,5,2,7]=>0000000
[2,8,6,1,7,4,5,3]=>0000000
[1,8,5,2,3,6,7,4]=>1000000
[4,8,3,2,5,6,7,1]=>0000000
[2,1,8,3,5,6,7,4]=>0100000
[4,2,7,1,8,6,3,5]=>0000000
[3,8,4,1,2,6,7,5]=>0000000
[7,6,1,5,8,2,3,4]=>0000000
[4,2,1,8,5,6,7,3]=>0000000
[6,5,4,8,7,1,3,2]=>0000000
[6,5,4,8,1,2,7,3]=>0000000
[7,5,1,6,8,2,4,3]=>0000000
[6,5,4,1,8,2,7,3]=>0000000
[6,5,4,7,1,2,8,3]=>0000000
[6,5,4,7,8,1,3,2]=>0000000
[6,5,3,7,1,4,2,8]=>0000001
[7,5,1,4,8,3,2,6]=>0000000
[8,1,6,4,7,3,5,2]=>0000000
[7,5,1,4,8,3,6,2]=>0000000
[7,4,1,5,3,8,6,2]=>0000000
[8,1,5,4,3,7,6,2]=>0000000
[8,1,5,4,3,7,2,6]=>0000000
[6,5,3,8,1,4,2,7]=>0000000
[8,1,7,2,5,4,6,3]=>0000000
[7,6,1,2,5,4,8,3]=>0000000
[6,5,3,8,1,4,7,2]=>0000000
[6,5,3,1,2,7,8,4]=>0000000
[8,1,6,4,2,5,7,3]=>0000000
[8,1,5,4,3,2,7,6]=>0000000
[7,4,1,5,3,2,8,6]=>0000000
[6,4,3,1,5,2,8,7]=>0000010
[6,4,3,1,5,7,2,8]=>0000001
[7,4,1,5,3,6,2,8]=>0000001
[6,4,3,1,5,7,8,2]=>0000000
[7,1,5,8,4,6,2,3]=>0000000
[8,6,7,1,4,2,5,3]=>0000000
[8,6,3,7,5,1,2,4]=>0000000
[8,6,1,7,3,2,5,4]=>0000000
[7,6,1,8,3,5,2,4]=>0000000
[7,6,1,3,8,5,2,4]=>0000000
[7,6,8,2,4,5,1,3]=>0000000
[7,6,2,8,3,5,1,4]=>0000000
[8,7,1,5,2,6,3,4]=>0000000
[8,7,1,5,2,3,6,4]=>0000000
[8,5,2,3,1,7,6,4]=>0000000
[8,6,2,3,7,1,5,4]=>0000000
[8,6,2,7,3,1,5,4]=>0000000
[8,6,7,2,4,1,5,3]=>0000000
[6,8,7,3,4,1,5,2]=>0000000
[8,7,2,5,1,6,3,4]=>0000000
[8,7,2,1,4,6,3,5]=>0000000
[8,4,2,1,7,6,3,5]=>0000000
[8,5,2,7,1,6,3,4]=>0000000
[8,5,7,2,1,4,3,6]=>0000000
[5,8,7,3,1,4,2,6]=>0000000
[8,5,7,2,1,4,6,3]=>0000000
[8,5,2,7,1,3,6,4]=>0000000
[8,7,4,1,2,3,6,5]=>0000000
[8,7,4,1,2,6,3,5]=>0000000
[8,4,3,1,7,2,6,5]=>0000000
[8,4,3,1,2,7,6,5]=>0000000
[8,6,1,3,7,2,5,4]=>0000000
[8,5,1,3,2,7,6,4]=>0000000
[8,5,7,4,1,6,2,3]=>0000000
[8,5,7,4,1,2,6,3]=>0000000
[8,1,5,4,2,7,6,3]=>0000000
[8,1,6,4,7,2,5,3]=>0000000
[6,1,5,8,4,2,7,3]=>0000000
[5,8,3,6,4,1,2,7]=>0000000
[8,4,7,5,1,6,2,3]=>0000000
[8,4,7,5,1,2,6,3]=>0000000
[8,4,7,5,1,2,3,6]=>0000000
[8,3,2,6,5,1,4,7]=>0000000
[4,8,6,3,5,1,2,7]=>0000000
[4,8,7,3,1,5,2,6]=>0000000
[8,4,7,2,1,5,3,6]=>0000000
[8,3,2,7,1,5,4,6]=>0000000
[8,3,2,1,7,6,4,5]=>0000000
[8,7,3,1,6,2,4,5]=>0000000
[8,7,3,1,2,4,6,5]=>0000000
[8,3,2,1,7,4,6,5]=>0000000
[8,4,7,2,1,5,6,3]=>0000000
[8,7,2,1,3,6,4,5]=>0000000
[8,7,2,1,3,4,6,5]=>0000000
[1,2,7,3,5,4,8,6]=>1100000
[1,5,7,2,3,6,4,8]=>1000001
[1,3,8,2,4,5,7,6]=>1000000
[1,2,3,8,4,6,7,5]=>1110000
[1,7,8,2,3,6,4,5]=>1000000
[1,6,7,8,2,3,5,4]=>1000000
[1,7,8,2,5,3,6,4]=>1000000
[1,8,2,3,6,4,5,7]=>1000000
[1,2,7,8,3,6,4,5]=>1100000
[1,5,2,7,8,3,6,4]=>1000000
[1,3,2,8,4,6,7,5]=>1010000
[1,8,2,3,4,6,7,5]=>1000000
[1,7,8,2,4,3,6,5]=>1000000
[6,7,3,1,5,2,8,4]=>0000000
[7,3,6,1,5,2,4,8]=>0000001
[6,2,1,7,5,3,8,4]=>0000000
[4,6,5,7,8,1,2,3]=>0000000
[5,7,4,6,1,8,2,3]=>0000000
[5,7,3,1,6,8,2,4]=>0000000
[2,5,4,7,3,6,1,8]=>0000001
[4,2,7,3,6,5,1,8]=>0000001
[4,2,6,3,1,5,8,7]=>0000010
[2,5,3,1,6,4,8,7]=>0000010
[2,5,3,7,6,4,1,8]=>0000001
[2,6,5,3,7,4,1,8]=>0000001
[4,2,7,6,3,5,1,8]=>0000001
[2,7,5,3,6,4,1,8]=>0000001
[2,6,3,7,5,4,1,8]=>0000001
[1,7,5,2,3,8,4,6]=>1000000
[2,1,3,7,5,4,8,6]=>0110000
[2,3,1,8,6,5,4,7]=>0010000
[2,5,3,1,8,6,4,7]=>0000000
[4,2,8,3,1,6,5,7]=>0000000
[8,3,2,6,4,1,5,7]=>0000000
[3,6,8,2,1,4,5,7]=>0000000
[1,2,6,3,8,7,4,5]=>1100000
[1,2,7,6,3,4,8,5]=>1100000
[2,1,3,8,7,5,4,6]=>0110000
[1,2,3,8,6,4,7,5]=>1110000
[1,2,3,7,4,8,6,5]=>1110000
[1,2,7,6,3,8,4,5]=>1100000
[1,2,3,6,4,8,7,5]=>1110000
[1,2,3,7,6,4,8,5]=>1110000
[2,1,3,8,5,4,7,6]=>0110000
[7,1,8,4,2,3,5,6]=>0000000
[4,2,6,3,1,8,5,7]=>0000000
[5,4,2,8,3,1,6,7]=>0000000
[2,5,4,8,3,1,6,7]=>0000000
[1,8,7,4,2,3,5,6]=>1000000
[1,5,2,8,7,3,4,6]=>1000000
[1,2,7,3,6,4,8,5]=>1100000
[1,2,8,6,3,7,4,5]=>1100000
[1,2,6,3,8,4,7,5]=>1100000
[4,2,1,8,3,7,5,6]=>0000000
[8,3,2,1,7,4,5,6]=>0000000
[1,2,3,8,7,4,6,5]=>1110000
[1,2,3,8,7,6,4,5]=>1110000
[2,6,5,7,1,4,3,8]=>0000001
[2,6,5,7,1,3,8,4]=>0000000
[3,8,5,7,1,2,6,4]=>0000000
[3,8,5,7,2,6,4,1]=>0000000
[3,4,8,6,2,5,7,1]=>0000000
[3,4,8,6,1,2,5,7]=>0000000
[2,5,7,1,4,8,6,3]=>0000000
[2,8,1,7,5,6,4,3]=>0000000
[2,3,8,1,6,5,7,4]=>0000000
[3,5,7,6,1,2,4,8]=>0000001
[4,8,6,7,2,3,5,1]=>0000000
[4,8,6,7,1,3,5,2]=>0000000
[3,4,8,6,1,5,7,2]=>0000000
[3,8,5,7,1,6,4,2]=>0000000
[3,8,5,7,2,1,6,4]=>0000000
[3,4,8,6,2,1,5,7]=>0000000
[3,5,7,6,2,1,4,8]=>0000001
[5,8,6,7,3,4,2,1]=>0000000
[5,8,6,7,2,1,3,4]=>0000000
[4,8,6,7,2,1,5,3]=>0000000
[4,3,1,7,5,2,8,6]=>0000000
[4,3,2,8,5,1,7,6]=>0000000
[4,3,8,5,1,6,7,2]=>0000000
[5,8,6,7,2,3,4,1]=>0000000
[5,8,6,7,2,4,3,1]=>0000000
[5,8,6,7,1,2,4,3]=>0000000
[3,2,5,7,6,1,4,8]=>0000001
[4,8,6,7,1,3,2,5]=>0000000
[4,8,6,7,1,2,5,3]=>0000000
[4,8,6,7,2,5,3,1]=>0000000
[4,3,8,5,2,6,7,1]=>0000000
[4,2,6,7,5,1,3,8]=>0000001
[3,8,4,7,1,5,2,6]=>0000000
[3,5,1,7,4,6,2,8]=>0000001
[3,8,4,7,2,5,1,6]=>0000000
[4,1,3,8,5,2,6,7]=>0000000
[4,2,6,7,5,3,8,1]=>0000000
[4,8,6,7,3,2,5,1]=>0000000
[4,8,6,7,3,1,2,5]=>0000000
[3,1,5,7,6,2,4,8]=>0000001
[3,4,1,7,5,6,2,8]=>0000001
[4,1,7,5,2,8,6,3]=>0000000
[4,1,6,7,5,2,3,8]=>0000001
[5,8,6,7,3,2,4,1]=>0000000
[5,8,6,7,4,2,3,1]=>0000000
[5,8,6,7,4,1,2,3]=>0000000
[5,8,6,7,4,1,3,2]=>0000000
[5,8,6,7,3,1,4,2]=>0000000
[4,8,6,7,3,1,5,2]=>0000000
[4,1,6,7,5,3,8,2]=>0000000
[4,1,7,5,3,2,8,6]=>0000000
[4,2,8,5,3,1,7,6]=>0000000
[4,2,1,6,7,5,3,8]=>0000001
[4,8,6,7,3,2,1,5]=>0000000
[5,8,6,7,4,2,1,3]=>0000000
[5,8,6,7,4,3,1,2]=>0000000
[2,7,1,5,8,6,3,4]=>0000000
[2,4,7,1,8,5,6,3]=>0000000
[4,7,5,8,3,1,6,2]=>0000000
[7,3,5,8,6,2,1,4]=>0000000
[1,2,7,6,8,3,5,4]=>1100000
[6,7,4,1,8,5,3,2]=>0000000
[7,2,6,8,5,4,1,3]=>0000000
[6,7,3,1,8,5,4,2]=>0000000
[6,7,1,8,5,4,3,2]=>0000000
[7,8,4,2,1,6,5,3]=>0000000
[6,2,3,4,8,7,1,5]=>0000000
[6,2,3,4,7,8,1,5]=>0000000
[7,8,3,6,4,2,1,5]=>0000000
[7,8,3,5,6,2,1,4]=>0000000
[5,2,6,3,8,1,7,4]=>0000000
[6,3,2,5,8,7,1,4]=>0000000
[6,3,2,8,4,7,1,5]=>0000000
[6,4,3,8,7,5,1,2]=>0000000
[6,4,3,7,8,5,1,2]=>0000000
[6,3,2,7,4,8,1,5]=>0000000
[6,3,2,5,7,8,1,4]=>0000000
[5,8,2,3,6,1,7,4]=>0000000
[4,5,6,8,3,2,1,7]=>0000000
[4,6,8,5,3,2,1,7]=>0000000
[5,6,1,4,2,3,7,8]=>0000011
[5,6,8,4,3,7,1,2]=>0000000
[5,6,1,4,2,3,8,7]=>0000010
[5,2,8,3,4,1,7,6]=>0000000
[4,5,8,6,3,2,1,7]=>0000000
[4,7,5,6,3,2,1,8]=>0000001
[5,1,4,3,6,2,8,7]=>0000010
[5,1,4,3,8,2,7,6]=>0000000
[5,6,2,4,1,8,7,3]=>0000000
[5,7,2,4,1,8,6,3]=>0000000
[6,1,4,2,8,7,5,3]=>0000000
[5,8,2,4,1,7,6,3]=>0000000
[5,4,1,3,7,2,6,8]=>0000001
[5,8,1,4,2,3,7,6]=>0000000
[5,1,6,3,4,2,7,8]=>0000011
[4,8,6,5,3,2,1,7]=>0000000
[5,4,7,8,3,2,1,6]=>0000000
[4,7,8,5,3,2,1,6]=>0000000
[5,7,1,3,4,2,6,8]=>0000001
[5,1,8,4,2,3,6,7]=>0000000
[5,1,7,4,2,3,6,8]=>0000001
[5,8,1,3,4,2,6,7]=>0000000
[4,8,7,5,3,2,1,6]=>0000000
[4,7,8,6,3,2,1,5]=>0000000
[4,8,7,6,3,1,2,5]=>0000000
[1,4,3,8,2,6,5,7]=>1000000
[4,1,3,8,2,6,5,7]=>0000000
[3,6,7,8,4,1,2,5]=>0000000
[3,7,8,2,6,4,5,1]=>0000000
[4,2,3,8,1,6,5,7]=>0000000
[7,3,6,8,4,2,1,5]=>0000000
[1,3,2,4,8,6,5,7]=>1011000
[3,1,2,4,8,6,5,7]=>0011000
[3,7,4,8,5,1,2,6]=>0000000
[2,1,3,4,8,6,5,7]=>0111000
[3,5,7,8,6,1,2,4]=>0000000
[5,1,6,3,8,4,7,2]=>0000000
[2,5,1,6,8,3,7,4]=>0000000
[5,1,2,6,8,3,7,4]=>0000000
[6,1,7,5,2,8,3,4]=>0000000
[5,7,2,8,6,1,3,4]=>0000000
[1,2,6,7,5,8,3,4]=>1100000
[1,6,7,4,5,2,8,3]=>1000000
[6,2,7,4,5,1,8,3]=>0000000
[7,5,1,6,3,8,2,4]=>0000000
[2,7,6,1,3,8,5,4]=>0000000
[2,6,7,4,1,8,3,5]=>0000000
[2,1,6,7,3,8,5,4]=>0100000
[3,7,5,4,8,1,6,2]=>0000000
[4,6,1,5,8,7,3,2]=>0000000
[8,3,4,6,2,1,5,7]=>0000000
[3,5,6,2,1,8,4,7]=>0000000
[7,5,3,2,8,4,1,6]=>0000000
[7,5,3,2,8,4,6,1]=>0000000
[4,2,5,6,8,3,1,7]=>0000000
[5,3,6,8,1,4,2,7]=>0000000
[4,5,6,8,1,3,2,7]=>0000000
[1,4,5,6,8,3,2,7]=>1000000
[4,5,3,7,2,8,6,1]=>0000000
[6,4,7,3,2,8,5,1]=>0000000
[6,1,4,7,3,2,8,5]=>0000000
[5,1,7,3,8,4,2,6]=>0000000
[5,3,7,1,4,8,6,2]=>0000000
[6,4,3,1,7,8,5,2]=>0000000
[5,6,1,3,7,8,4,2]=>0000000
[5,6,1,7,8,3,4,2]=>0000000
[1,6,3,7,4,8,5,2]=>1000000
[6,7,2,4,1,8,5,3]=>0000000
[6,7,2,1,4,3,8,5]=>0000000
[6,4,7,3,1,2,8,5]=>0000000
[5,6,3,1,2,7,8,4]=>0000000
[5,6,1,3,2,7,8,4]=>0000000
[5,6,3,2,1,7,8,4]=>0000000
[5,6,3,2,7,8,4,1]=>0000000
[2,5,6,3,7,8,4,1]=>0000000
[2,5,6,3,1,7,8,4]=>0000000
[2,6,4,7,3,1,8,5]=>0000000
[6,3,7,2,8,4,1,5]=>0000000
[6,3,2,7,1,8,4,5]=>0000000
[7,5,3,2,1,8,4,6]=>0000000
[7,3,8,4,2,1,5,6]=>0000000
[4,7,2,1,3,8,6,5]=>0000000
[1,3,7,8,6,4,2,5]=>1000000
[5,7,3,8,2,1,6,4]=>0000000
[4,6,2,7,8,5,3,1]=>0000000
[2,5,1,7,3,8,6,4]=>0000000
[6,7,2,1,3,8,5,4]=>0000000
[5,1,6,7,8,2,4,3]=>0000000
[6,3,7,1,8,5,2,4]=>0000000
[6,2,1,7,3,8,5,4]=>0000000
[6,2,7,1,8,5,4,3]=>0000000
[6,3,1,7,8,5,4,2]=>0000000
[5,3,2,1,8,4,7,6]=>0000000
[4,5,2,1,3,8,7,6]=>0000100
[3,2,6,4,5,8,1,7]=>0000000
[2,4,6,5,8,1,3,7]=>0000000
[1,3,4,6,5,8,2,7]=>1000000
[1,6,3,4,5,8,2,7]=>1000000
[3,4,1,8,5,2,7,6]=>0000000
[2,8,4,1,7,6,3,5]=>0000000
[1,5,3,2,8,7,4,6]=>1000000
[8,2,1,7,5,3,4,6]=>0000000
[1,7,6,4,5,8,3,2]=>1000000
[5,8,7,4,6,2,1,3]=>0000000
[3,4,2,5,8,6,7,1]=>0000000
[4,1,3,5,6,8,7,2]=>0000000
[2,4,8,6,7,1,3,5]=>0000000
[3,7,4,8,2,1,6,5]=>0000000
[2,3,5,8,6,7,1,4]=>0000000
[3,2,5,6,8,7,1,4]=>0000000
[7,2,4,8,5,3,1,6]=>0000000
[4,8,3,1,2,7,6,5]=>0000000
[8,4,2,3,7,1,5,6]=>0000000
[3,5,2,7,6,1,8,4]=>0000000
[5,8,7,3,4,6,2,1]=>0000000
[5,8,2,7,4,1,6,3]=>0000000
[5,1,4,2,8,7,6,3]=>0000000
[5,2,6,8,7,1,3,4]=>0000000
[6,3,2,1,8,5,7,4]=>0000000
[2,7,5,4,1,8,6,3]=>0000000
[4,2,5,6,8,7,1,3]=>0000000
[1,8,4,2,5,6,7,3]=>1000000
[3,8,4,1,5,6,7,2]=>0000000
[4,2,8,5,6,7,1,3]=>0000000
[5,2,4,7,1,8,6,3]=>0000000
[8,1,3,6,5,2,4,7]=>0000000
[8,3,2,4,6,5,1,7]=>0000000
[8,3,6,4,1,5,2,7]=>0000000
[1,3,4,8,5,7,2,6]=>1000000
[5,8,4,7,6,2,3,1]=>0000000
[1,3,4,7,5,8,2,6]=>1000000
[1,3,5,2,4,8,7,6]=>1000100
[2,6,5,1,3,8,7,4]=>0000000
[2,8,5,1,4,7,6,3]=>0000000
[4,3,1,5,8,6,7,2]=>0000000
[5,4,2,1,6,8,7,3]=>0000000
[6,8,4,3,2,7,1,5]=>0000000
[5,1,3,2,8,6,7,4]=>0000000
[5,3,1,2,8,6,7,4]=>0000000
[5,2,3,1,6,8,7,4]=>0000000
[5,3,2,1,8,6,7,4]=>0000000
[5,2,1,3,6,8,7,4]=>0000000
[2,7,4,5,8,3,1,6]=>0000000
[1,8,4,3,7,2,6,5]=>1000000
[3,4,8,7,2,1,6,5]=>0000000
[5,4,7,8,3,6,2,1]=>0000000
[6,3,8,7,4,1,2,5]=>0000000
[8,4,7,2,3,1,5,6]=>0000000
[8,6,4,1,3,2,7,5]=>0000000
[3,5,7,2,6,1,8,4]=>0000000
[6,1,3,8,5,7,2,4]=>0000000
[2,8,1,5,4,7,6,3]=>0000000
[1,7,2,4,6,5,8,3]=>1000000
[5,8,2,6,1,3,7,4]=>0000000
[6,3,5,8,7,2,1,4]=>0000000
[2,5,7,8,4,1,6,3]=>0000000
[4,1,5,2,6,8,7,3]=>0000000
[4,1,8,5,2,6,7,3]=>0000000
[2,7,1,8,5,4,6,3]=>0000000
[5,8,6,2,1,3,7,4]=>0000000
[3,4,5,1,8,6,7,2]=>0000000
[5,1,3,6,4,8,7,2]=>0000000
[1,3,2,7,5,8,6,4]=>1010000
[1,4,2,5,8,3,7,6]=>1000000
[1,4,2,7,8,5,6,3]=>1000000
[5,1,2,6,8,4,7,3]=>0000000
[3,1,2,6,5,8,4,7]=>0010000
[4,1,2,6,8,5,3,7]=>0000000
[1,5,2,4,8,7,6,3]=>1000000
[1,2,7,4,8,6,5,3]=>1100000
[1,3,2,7,5,8,4,6]=>1010000
[2,3,1,7,5,4,8,6]=>0010000
[1,3,2,8,5,7,4,6]=>1010000
[1,2,6,4,8,7,3,5]=>1100000
[1,2,6,8,5,7,3,4]=>1100000
[1,5,6,8,2,7,3,4]=>1000000
[1,3,8,2,6,7,4,5]=>1000000
[1,4,7,2,8,6,3,5]=>1000000
[1,6,7,8,2,5,3,4]=>1000000
[1,2,6,8,3,7,5,4]=>1100000
[1,5,7,8,2,3,6,4]=>1000000
[1,4,7,2,8,3,6,5]=>1000000
[1,6,7,3,4,8,5,2]=>1000000
[1,5,3,7,4,8,6,2]=>1000000
[1,3,6,4,2,8,7,5]=>1000000
[1,3,7,4,2,8,6,5]=>1000000
[1,2,8,4,7,3,6,5]=>1100000
[1,5,2,4,8,3,7,6]=>1000000
[1,8,4,5,7,2,3,6]=>1000000
[1,8,3,5,2,7,4,6]=>1000000
[2,8,3,5,1,4,7,6]=>0000000
[2,3,8,6,1,4,7,5]=>0000000
[1,4,8,6,7,2,3,5]=>1000000
[1,5,6,8,7,2,3,4]=>1000000
[1,2,7,8,5,3,6,4]=>1100000
[1,2,5,8,7,3,6,4]=>1100000
[1,2,6,8,7,3,5,4]=>1100000
[1,2,7,8,6,3,5,4]=>1100000
[1,5,7,8,6,2,3,4]=>1000000
[1,3,7,6,2,8,4,5]=>1000000
[1,2,8,4,7,6,3,5]=>1100000
[1,2,5,8,7,6,3,4]=>1100000
[1,2,6,8,7,5,3,4]=>1100000
[1,2,7,8,6,5,3,4]=>1100000
[5,2,6,7,3,4,8,1]=>0000000
[5,6,2,1,7,8,3,4]=>0000000
[5,6,2,1,4,8,7,3]=>0000000
[2,6,1,4,5,8,7,3]=>0000000
[5,4,2,7,6,3,8,1]=>0000000
[2,3,7,6,4,5,8,1]=>0000000
[2,6,1,7,5,8,3,4]=>0000000
[5,1,2,7,8,4,3,6]=>0000000
[2,6,1,7,4,8,3,5]=>0000000
[3,6,4,1,7,8,2,5]=>0000000
[5,4,6,1,7,8,2,3]=>0000000
[5,4,6,1,3,8,7,2]=>0000000
[3,6,4,1,5,8,7,2]=>0000000
[2,6,1,5,4,8,7,3]=>0000000
[2,6,1,4,7,8,5,3]=>0000000
[5,1,2,4,8,7,6,3]=>0000000
[2,1,5,3,8,6,4,7]=>0100000
[5,1,2,4,8,6,3,7]=>0000000
[5,6,3,1,4,8,2,7]=>0000000
[2,5,4,3,1,8,6,7]=>0000100
[5,4,6,3,1,8,7,2]=>0000000
[2,1,3,7,8,6,4,5]=>0110000
[5,1,4,2,8,6,7,3]=>0000000
[1,2,3,8,6,7,4,5]=>1110000
[1,2,3,8,7,5,4,6]=>1110000
[1,2,3,8,7,4,5,6]=>1110000
[2,1,3,6,8,7,4,5]=>0110000
[3,1,6,2,8,7,5,4]=>0000000
[6,8,1,3,2,5,4,7]=>0000000
[6,8,1,4,2,5,3,7]=>0000000
[7,8,3,6,1,4,2,5]=>0000000
[7,8,2,5,1,4,3,6]=>0000000
[7,8,1,4,3,6,2,5]=>0000000
[5,8,1,4,3,7,2,6]=>0000000
[6,8,2,5,1,4,3,7]=>0000000
[6,8,2,5,3,7,1,4]=>0000000
[2,5,4,7,6,8,1,3]=>0000000
[2,6,1,4,3,7,5,8]=>0000001
[2,6,1,5,3,7,4,8]=>0000001
[2,6,4,7,5,8,1,3]=>0000000
[5,8,2,6,4,7,1,3]=>0000000
[6,8,3,7,1,4,2,5]=>0000000
[5,8,1,3,2,6,4,7]=>0000000
[5,8,4,7,1,3,2,6]=>0000000
[6,8,4,7,1,3,2,5]=>0000000
[6,8,5,7,1,3,2,4]=>0000000
[5,7,6,8,2,4,1,3]=>0000000
[4,7,5,8,1,3,2,6]=>0000000
[4,7,1,3,2,6,5,8]=>0000001
[3,7,1,4,2,6,5,8]=>0000001
[3,7,6,8,1,4,2,5]=>0000000
[4,7,6,8,2,5,1,3]=>0000000
[4,7,5,8,3,6,1,2]=>0000000
[4,7,5,8,2,6,1,3]=>0000000
[3,7,4,8,2,6,1,5]=>0000000
[3,7,1,5,2,6,4,8]=>0000001
[3,7,2,6,1,5,4,8]=>0000001
[3,7,2,6,5,8,1,4]=>0000000
[4,7,3,6,5,8,1,2]=>0000000
[2,6,5,8,4,7,1,3]=>0000000
[2,6,3,7,1,5,4,8]=>0000001
[7,6,4,8,5,2,3,1]=>0000000
[6,7,4,3,5,1,8,2]=>0000000
[6,7,3,5,4,8,2,1]=>0000000
[6,8,3,7,5,2,4,1]=>0000000
[7,6,3,5,8,2,4,1]=>0000000
[7,6,2,8,4,1,5,3]=>0000000
[7,6,3,4,8,2,5,1]=>0000000
[6,8,3,7,4,5,2,1]=>0000000
[6,7,3,5,8,4,2,1]=>0000000
[5,7,8,3,6,2,1,4]=>0000000
[6,3,4,8,7,2,5,1]=>0000000
[6,3,8,4,7,2,1,5]=>0000000
[6,3,4,7,5,8,2,1]=>0000000
[6,3,5,7,8,4,2,1]=>0000000
[5,7,3,6,8,2,1,4]=>0000000
[5,6,7,3,4,1,8,2]=>0000000
[4,6,7,8,3,5,2,1]=>0000000
[4,7,3,5,6,8,2,1]=>0000000
[5,3,4,7,8,2,1,6]=>0000000
[5,3,8,2,4,1,6,7]=>0000000
[5,3,4,8,2,6,1,7]=>0000000
[4,8,3,6,2,5,7,1]=>0000000
[4,8,3,5,7,2,6,1]=>0000000
[4,8,3,5,6,7,2,1]=>0000000
[4,7,8,3,5,6,2,1]=>0000000
[4,7,8,3,6,2,5,1]=>0000000
[4,8,3,6,7,2,5,1]=>0000000
[4,8,3,7,2,5,6,1]=>0000000
[5,8,3,7,2,6,4,1]=>0000000
[5,7,3,4,8,2,1,6]=>0000000
[5,8,4,2,3,1,6,7]=>0000000
[5,8,4,2,3,1,7,6]=>0000000
[6,4,8,5,3,7,2,1]=>0000000
[6,4,2,7,3,1,8,5]=>0000000
[6,4,3,7,8,5,2,1]=>0000000
[6,4,5,3,7,1,8,2]=>0000000
[5,7,4,2,3,1,6,8]=>0000001
[5,6,3,7,1,8,2,4]=>0000000
[5,6,3,4,8,2,1,7]=>0000000
[6,3,5,7,4,8,2,1]=>0000000
[6,3,5,4,7,8,2,1]=>0000000
[6,4,3,5,7,1,8,2]=>0000000
[6,4,2,5,1,7,3,8]=>0000001
[5,3,4,7,2,6,1,8]=>0000001
[4,7,3,6,2,5,8,1]=>0000000
[4,7,3,6,8,2,5,1]=>0000000
[4,6,7,3,5,8,2,1]=>0000000
[4,5,7,8,3,6,2,1]=>0000000
[4,5,8,3,7,2,6,1]=>0000000
[5,3,4,6,8,2,1,7]=>0000000
[5,3,6,7,1,8,2,4]=>0000000
[5,3,4,6,7,1,8,2]=>0000000
[4,6,3,5,7,8,2,1]=>0000000
[4,5,7,3,6,8,2,1]=>0000000
[7,1,4,5,8,2,3,6]=>0000000
[2,1,7,5,8,3,4,6]=>0100000
[7,1,5,4,8,2,3,6]=>0000000
[8,3,7,1,2,4,6,5]=>0000000
[8,3,7,5,1,2,4,6]=>0000000
[6,7,1,8,4,2,3,5]=>0000000
[6,8,1,7,4,2,3,5]=>0000000
[7,1,8,4,5,2,3,6]=>0000000
[6,1,2,3,8,7,5,4]=>0000000
[6,8,3,1,2,7,4,5]=>0000000
[6,7,3,1,2,8,4,5]=>0000000
[6,7,1,4,2,3,8,5]=>0000000
[4,3,6,8,5,7,1,2]=>0000000
[6,1,2,5,4,8,3,7]=>0000000
[1,3,6,8,7,4,2,5]=>1000000
[1,2,8,5,7,3,4,6]=>1100000
[3,6,1,4,2,7,8,5]=>0000000
[1,2,6,3,5,8,7,4]=>1100000
[2,3,5,1,8,4,7,6]=>0000000
[3,1,7,5,4,8,6,2]=>0000000
[1,2,7,6,4,8,5,3]=>1100000
[1,2,7,3,6,8,5,4]=>1100000
[1,2,6,8,5,4,3,7]=>1100000
[1,4,6,8,3,2,5,7]=>1000000
[1,2,6,7,3,8,5,4]=>1100000
[1,2,5,7,3,8,6,4]=>1100000
[4,6,2,7,5,8,3,1]=>0000000
[3,5,7,4,8,2,6,1]=>0000000
[1,3,5,8,2,7,4,6]=>1000000
[1,2,5,8,4,7,6,3]=>1100000
[1,2,5,8,7,4,3,6]=>1100000
[1,3,5,8,7,2,4,6]=>1000000
[3,2,7,4,6,8,1,5]=>0000000
[5,3,6,2,7,1,4,8]=>0000001
[2,6,3,4,7,1,5,8]=>0000001
[2,7,3,4,5,8,1,6]=>0000000
[4,7,6,2,3,8,1,5]=>0000000
[7,3,5,2,4,8,1,6]=>0000000
[7,6,2,4,5,8,1,3]=>0000000
[6,5,2,3,4,8,1,7]=>0000000
[5,3,1,2,8,4,7,6]=>0000000
[6,5,2,3,7,1,4,8]=>0000001
[5,2,1,7,3,4,6,8]=>0000001
[5,2,1,8,3,4,6,7]=>0000000
[6,3,2,8,4,5,7,1]=>0000000
[7,3,1,2,8,4,6,5]=>0000000
[6,2,3,1,8,4,7,5]=>0000000
[8,3,5,2,7,1,4,6]=>0000000
[8,6,2,4,7,1,5,3]=>0000000
[8,2,1,7,3,4,5,6]=>0000000
[8,6,3,7,2,4,5,1]=>0000000
[8,2,7,3,4,5,6,1]=>0000000
[8,1,6,2,3,4,5,7]=>0000000
[8,1,7,3,4,5,6,2]=>0000000
[8,6,1,7,2,4,5,3]=>0000000
[1,7,5,8,2,3,6,4]=>1000000
[7,2,1,8,3,4,5,6]=>0000000
[1,7,8,3,4,5,6,2]=>1000000
[1,6,2,8,4,5,7,3]=>1000000
[4,1,3,6,8,2,7,5]=>0000000
[4,6,3,8,7,1,2,5]=>0000000
[6,4,5,8,7,1,2,3]=>0000000
[5,3,4,8,7,1,2,6]=>0000000
[3,2,8,7,1,4,6,5]=>0000000
[3,1,8,7,2,4,6,5]=>0000000
[5,3,7,6,1,2,4,8]=>0000001
[1,8,3,7,2,4,5,6]=>1000000
[3,8,1,7,2,4,5,6]=>0000000
[6,8,2,3,5,1,4,7]=>0000000
[4,7,8,2,6,1,3,5]=>0000000
[6,2,8,7,1,4,5,3]=>0000000
[3,8,7,1,4,5,6,2]=>0000000
[2,8,6,1,3,4,5,7]=>0000000
[2,7,6,1,3,4,5,8]=>0000001
[1,7,6,2,3,4,5,8]=>1000001
[1,8,6,2,3,4,5,7]=>1000000
[2,8,7,3,4,5,6,1]=>0000000
[3,8,7,2,4,5,6,1]=>0000000
[7,8,3,6,2,4,5,1]=>0000000
[1,5,8,7,2,3,6,4]=>1000000
[1,7,3,6,5,2,8,4]=>1000000
[8,6,2,5,4,1,7,3]=>0000000
[3,2,6,4,7,5,1,8]=>0000001
[6,2,3,7,5,4,1,8]=>0000001
[1,3,4,7,6,2,8,5]=>1000000
[2,8,3,6,1,7,5,4]=>0000000
[8,7,2,5,1,6,4,3]=>0000000
[3,8,2,6,5,1,7,4]=>0000000
[7,8,2,5,4,1,6,3]=>0000000
[4,8,5,2,6,1,7,3]=>0000000
[4,5,1,3,7,2,8,6]=>0000000
[6,1,3,7,5,2,8,4]=>0000000
[7,1,3,6,2,8,5,4]=>0000000
[8,1,3,6,2,7,5,4]=>0000000
[1,2,4,7,3,8,6,5]=>1100000
[7,1,8,2,6,5,4,3]=>0000000
[4,1,7,8,2,6,5,3]=>0000000
[3,4,8,6,5,1,7,2]=>0000000
[8,3,7,5,1,6,4,2]=>0000000
[1,4,8,6,2,7,5,3]=>1000000
[8,4,6,7,1,5,3,2]=>0000000
[3,4,6,5,1,2,8,7]=>0000010
[7,3,5,1,2,8,6,4]=>0000000
[1,4,6,2,3,8,7,5]=>1000000
[1,3,2,7,4,8,6,5]=>1010000
[7,2,1,6,3,8,5,4]=>0000000
[4,5,2,1,7,3,8,6]=>0000000
[5,6,7,1,2,8,4,3]=>0000000
[4,7,5,1,2,8,6,3]=>0000000
[3,7,1,6,2,8,5,4]=>0000000
[7,6,1,2,8,5,4,3]=>0000000
[2,7,1,3,8,6,5,4]=>0000000
[8,6,1,2,7,5,4,3]=>0000000
[1,7,2,3,8,6,5,4]=>1000000
[8,7,1,2,6,5,4,3]=>0000000
[7,8,1,2,6,5,4,3]=>0000000
[3,8,1,6,2,7,5,4]=>0000000
[4,8,5,1,2,7,6,3]=>0000000
[1,8,2,7,4,3,5,6]=>1000000
[1,8,6,4,7,2,3,5]=>1000000
[1,8,4,2,6,3,5,7]=>1000000
[7,4,8,1,5,2,3,6]=>0000000
[4,1,7,2,6,3,5,8]=>0000001
[5,1,7,4,3,6,2,8]=>0000001
[1,8,5,4,3,7,2,6]=>1000000
[1,8,4,2,5,3,7,6]=>1000000
[1,8,5,4,2,6,7,3]=>1000000
[7,4,8,2,1,3,5,6]=>0000000
[4,1,7,3,2,5,6,8]=>0000001
[7,5,4,8,2,3,6,1]=>0000000
[3,1,7,2,6,8,4,5]=>0000000
[5,1,7,4,2,6,8,3]=>0000000
[4,3,1,6,2,5,7,8]=>0000011
[6,5,4,3,7,1,8,2]=>0000000
[6,5,1,7,3,8,2,4]=>0000000
[6,3,2,8,5,7,1,4]=>0000000
[5,4,8,2,1,7,3,6]=>0000000
[7,2,8,6,3,1,4,5]=>0000000
[2,1,7,8,3,6,4,5]=>0100000
[4,2,1,6,7,3,5,8]=>0000001
[4,3,1,5,2,7,6,8]=>0000101
[5,4,2,7,3,8,1,6]=>0000000
[3,1,6,2,8,7,4,5]=>0000000
[6,5,4,1,7,8,3,2]=>0000000
[5,4,3,1,6,7,2,8]=>0000001
[5,4,2,6,3,8,7,1]=>0000000
[4,3,1,5,2,6,8,7]=>0000110
[5,4,2,1,6,7,8,3]=>0000000
[5,4,3,1,6,7,8,2]=>0000000
[7,8,2,4,5,1,3,6]=>0000000
[4,6,7,2,5,1,3,8]=>0000001
[7,8,1,3,2,4,5,6]=>0000000
[7,8,4,1,5,2,3,6]=>0000000
[3,6,7,2,1,4,5,8]=>0000001
[5,2,3,6,1,4,7,8]=>0000011
[2,5,3,6,1,4,7,8]=>0000011
[6,4,7,1,5,2,3,8]=>0000001
[6,2,7,3,1,4,5,8]=>0000001
[3,5,4,6,7,8,1,2]=>0000000
[1,5,4,6,7,2,3,8]=>1000001
[1,6,7,3,2,4,5,8]=>1000001
[1,5,3,6,2,4,7,8]=>1000011
[5,1,3,6,2,4,7,8]=>0000011
[5,2,4,6,7,1,3,8]=>0000001
[2,6,7,4,5,1,3,8]=>0000001
[4,2,5,6,7,1,3,8]=>0000001
[4,5,2,6,7,1,3,8]=>0000001
[5,3,1,6,2,4,7,8]=>0000011
[6,1,7,3,2,4,5,8]=>0000001
[6,1,7,4,5,2,3,8]=>0000001
[6,3,7,4,5,8,1,2]=>0000000
[5,4,1,6,7,2,3,8]=>0000001
[5,2,1,6,3,4,7,8]=>0000011
[1,3,6,7,5,2,8,4]=>1000000
[1,3,4,5,8,7,2,6]=>1000000
[3,1,2,5,6,8,7,4]=>0010000
[7,1,5,2,6,8,3,4]=>0000000
[2,3,6,7,5,1,8,4]=>0000000
[4,3,2,6,7,1,8,5]=>0000000
[7,1,5,4,6,8,3,2]=>0000000
[5,7,4,6,1,8,3,2]=>0000000
[6,3,4,5,8,1,2,7]=>0000000
[6,2,1,7,3,5,4,8]=>0000001
[2,1,8,6,3,5,4,7]=>0100000
[2,7,3,1,5,4,6,8]=>0000001
[2,6,3,1,4,8,5,7]=>0000000
[4,2,1,8,3,6,7,5]=>0000000
[6,2,1,7,3,5,8,4]=>0000000
[2,7,3,1,4,8,5,6]=>0000000
[3,2,1,5,7,8,4,6]=>0010000
[2,4,7,5,1,6,8,3]=>0000000
[4,3,6,8,5,1,7,2]=>0000000
[2,1,6,8,3,7,4,5]=>0100000
[3,2,1,5,6,8,4,7]=>0010000
[2,1,7,3,6,4,5,8]=>0100001
[2,1,6,3,5,8,4,7]=>0100000
[2,6,1,8,3,5,4,7]=>0000000
[2,7,3,1,5,6,4,8]=>0000001
[2,4,7,5,1,6,3,8]=>0000001
[8,2,4,1,7,5,3,6]=>0000000
[2,4,7,1,8,5,3,6]=>0000000
[2,4,8,5,1,6,3,7]=>0000000
[6,2,1,7,3,4,8,5]=>0000000
[6,2,1,7,8,3,5,4]=>0000000
[2,7,1,8,3,5,6,4]=>0000000
[3,2,1,6,7,4,5,8]=>0010001
[3,2,1,7,4,5,6,8]=>0010001
[2,1,8,3,7,4,5,6]=>0100000
[2,4,8,5,1,6,7,3]=>0000000
[4,3,8,5,6,1,7,2]=>0000000
[3,2,1,8,4,5,6,7]=>0010000
[1,6,8,3,7,2,4,5]=>1000000
[3,8,1,5,7,2,4,6]=>0000000
[1,2,6,8,4,7,3,5]=>1100000
[6,1,5,8,2,4,7,3]=>0000000
[1,2,4,8,3,6,7,5]=>1100000
[4,1,2,7,8,3,6,5]=>0000000
[5,3,8,4,7,6,1,2]=>0000000
[8,7,1,2,5,4,6,3]=>0000000
[5,8,1,2,3,7,6,4]=>0000000
[1,2,8,4,3,5,7,6]=>1100000
[1,2,5,3,7,6,4,8]=>1100001
[6,1,2,8,7,4,5,3]=>0000000
[7,1,6,2,8,4,5,3]=>0000000
[1,2,6,3,8,5,4,7]=>1100000
[1,2,8,5,3,6,4,7]=>1100000
[1,2,7,3,8,5,4,6]=>1100000
[1,6,2,8,4,3,5,7]=>1000000
[1,6,4,2,7,3,5,8]=>1000001
[1,8,6,3,2,4,5,7]=>1000000
[3,1,7,8,6,2,4,5]=>0000000
[1,8,7,3,5,6,2,4]=>1000000
[1,3,2,8,7,4,5,6]=>1010000
[1,2,8,4,3,7,5,6]=>1100000
[8,5,1,7,2,4,6,3]=>0000000
[3,8,6,4,7,5,1,2]=>0000000
[6,1,8,2,7,4,5,3]=>0000000
[1,2,7,5,3,6,4,8]=>1100001
[1,2,6,3,7,5,4,8]=>1100001
[1,2,3,7,5,4,8,6]=>1110000
[3,7,4,8,6,5,1,2]=>0000000
[1,8,2,7,6,4,5,3]=>1000000
[7,4,6,3,8,5,1,2]=>0000000
[8,4,6,2,7,5,3,1]=>0000000
[6,5,7,8,4,1,3,2]=>0000000
[7,5,6,8,2,4,1,3]=>0000000
[7,4,6,2,8,5,1,3]=>0000000
[4,3,2,6,8,5,1,7]=>0000000
[3,5,6,8,2,4,1,7]=>0000000
[2,6,7,8,1,4,5,3]=>0000000
[3,6,7,8,1,4,2,5]=>0000000
[3,5,7,8,2,1,4,6]=>0000000
[2,6,7,8,1,4,3,5]=>0000000
[2,5,7,8,3,1,4,6]=>0000000
[2,4,7,3,8,1,5,6]=>0000000
[6,4,7,3,8,1,5,2]=>0000000
[6,4,7,3,8,1,2,5]=>0000000
[7,4,6,3,8,2,1,5]=>0000000
[6,3,2,5,4,8,1,7]=>0000000
[6,4,5,2,3,8,1,7]=>0000000
[5,4,6,3,8,2,1,7]=>0000000
[5,4,7,3,8,1,6,2]=>0000000
[2,5,7,8,3,1,6,4]=>0000000
[4,5,7,8,3,1,2,6]=>0000000
[4,5,6,8,2,3,1,7]=>0000000
[5,4,6,2,8,3,1,7]=>0000000
[5,3,2,6,8,4,1,7]=>0000000
[5,4,7,2,8,1,3,6]=>0000000
[4,5,7,8,2,1,3,6]=>0000000
[4,6,7,8,1,3,2,5]=>0000000
[4,6,7,8,1,3,5,2]=>0000000
[2,6,7,8,1,3,5,4]=>0000000
[2,6,7,8,1,5,3,4]=>0000000
[4,6,7,8,1,5,2,3]=>0000000
[4,6,7,8,1,2,5,3]=>0000000
[5,3,2,7,8,1,6,4]=>0000000
[4,3,2,7,8,1,6,5]=>0000000
[3,5,7,8,2,1,6,4]=>0000000
[3,6,7,8,1,5,4,2]=>0000000
[2,6,7,8,1,5,4,3]=>0000000
[4,5,8,3,6,7,1,2]=>0000000
[4,5,8,3,7,6,1,2]=>0000000
[4,2,8,3,7,1,6,5]=>0000000
[7,2,3,4,8,1,5,6]=>0000000
[7,6,3,4,8,5,1,2]=>0000000
[7,6,3,5,8,4,1,2]=>0000000
[7,6,3,8,4,5,1,2]=>0000000
[7,2,3,8,5,1,4,6]=>0000000
[2,6,4,8,1,5,7,3]=>0000000
[7,2,3,8,4,1,5,6]=>0000000
[7,8,2,3,6,1,4,5]=>0000000
[4,2,6,3,7,1,5,8]=>0000001
[7,2,3,5,8,1,6,4]=>0000000
[7,2,3,8,4,1,6,5]=>0000000
[2,6,4,8,1,3,7,5]=>0000000
[3,6,4,8,1,7,5,2]=>0000000
[7,6,5,1,2,3,8,4]=>0000000
[7,6,5,1,4,2,8,3]=>0000000
[7,8,5,4,1,2,6,3]=>0000000
[3,5,6,4,1,2,8,7]=>0000010
[7,6,5,1,2,4,3,8]=>0000001
[7,6,5,1,2,4,8,3]=>0000000
[7,6,5,1,3,2,4,8]=>0000001
[2,6,4,3,1,8,7,5]=>0000000
[3,5,8,4,1,2,7,6]=>0000000
[3,5,8,4,1,2,6,7]=>0000000
[3,5,8,4,1,6,2,7]=>0000000
[2,5,8,4,1,7,3,6]=>0000000
[3,6,4,2,1,7,5,8]=>0000001
[3,5,6,4,1,8,7,2]=>0000000
[2,6,4,5,1,3,7,8]=>0000011
[7,6,5,1,4,3,8,2]=>0000000
[7,6,5,1,2,8,3,4]=>0000000
[7,6,5,1,8,2,4,3]=>0000000
[7,6,5,1,8,2,3,4]=>0000000
[7,6,5,1,8,3,2,4]=>0000000
[7,6,5,1,4,8,2,3]=>0000000
[3,6,4,5,1,7,2,8]=>0000001
[2,5,6,4,1,7,8,3]=>0000000
[2,5,6,4,1,7,3,8]=>0000001
[3,6,4,5,1,7,8,2]=>0000000
[7,6,5,1,4,8,3,2]=>0000000
[7,6,5,1,8,3,4,2]=>0000000
[7,6,5,1,8,4,2,3]=>0000000
[6,7,4,2,5,3,1,8]=>0000001
[7,6,4,8,3,1,5,2]=>0000000
[7,4,8,5,6,1,3,2]=>0000000
[7,4,2,5,6,3,1,8]=>0000001
[4,2,7,5,6,3,1,8]=>0000001
[4,7,3,5,6,2,1,8]=>0000001
[1,6,8,5,2,7,4,3]=>1000000
[6,2,8,5,1,7,4,3]=>0000000
[6,7,4,8,2,1,5,3]=>0000000
[3,2,7,8,6,1,5,4]=>0000000
[6,8,4,1,2,3,7,5]=>0000000
[1,8,2,5,6,4,3,7]=>1000000
[6,1,8,5,3,7,4,2]=>0000000
[3,8,1,5,2,7,6,4]=>0000000
[8,2,1,5,3,7,6,4]=>0000000
[8,1,6,5,3,7,2,4]=>0000000
[7,1,4,6,3,2,8,5]=>0000000
[3,2,6,4,1,7,8,5]=>0000000
[7,6,4,3,1,2,8,5]=>0000000
[8,6,3,5,1,7,2,4]=>0000000
[4,5,3,1,6,7,8,2]=>0000000
[3,5,2,1,6,7,8,4]=>0000000
[5,2,3,1,6,7,8,4]=>0000000
[1,5,3,2,6,7,8,4]=>1000000
[8,2,7,5,6,1,3,4]=>0000000
[1,7,4,6,2,3,8,5]=>1000000
[7,6,4,2,1,5,8,3]=>0000000
[5,7,4,6,1,3,8,2]=>0000000
[8,6,4,7,3,1,2,5]=>0000000
[5,2,4,3,7,1,8,6]=>0000000
[8,6,4,1,3,5,2,7]=>0000000
[6,7,4,1,5,3,8,2]=>0000000
[7,5,4,1,2,6,8,3]=>0000000
[1,8,2,5,3,7,6,4]=>1000000
[3,8,1,5,6,4,2,7]=>0000000
[7,6,4,1,5,2,8,3]=>0000000
[8,6,1,5,4,7,2,3]=>0000000
[5,2,1,4,6,7,8,3]=>0000000
[5,4,1,3,6,7,8,2]=>0000000
[8,4,1,5,3,7,2,6]=>0000000
[7,5,4,1,3,2,8,6]=>0000000
[3,2,5,1,4,7,8,6]=>0000100
[5,1,3,4,6,7,8,2]=>0000000
[5,7,4,1,8,6,3,2]=>0000000
[3,6,7,4,5,8,2,1]=>0000000
[5,4,6,1,7,8,3,2]=>0000000
[3,7,1,5,4,6,8,2]=>0000000
[6,7,1,4,5,3,8,2]=>0000000
[5,4,7,2,8,3,6,1]=>0000000
[3,8,1,5,4,6,2,7]=>0000000
[3,6,1,5,4,2,7,8]=>0000011
[3,6,1,5,4,8,2,7]=>0000000
[3,4,1,2,6,8,7,5]=>0001000
[3,8,1,5,4,7,2,6]=>0000000
[7,8,3,1,4,6,2,5]=>0000000
[6,5,8,7,3,4,2,1]=>0000000
[3,7,1,5,4,2,6,8]=>0000001
[3,8,1,5,4,2,7,6]=>0000000
[6,7,3,1,4,5,8,2]=>0000000
[2,5,6,1,4,7,8,3]=>0000000
[1,8,4,5,2,7,3,6]=>1000000
[1,8,4,5,2,7,6,3]=>1000000
[1,8,4,3,6,2,5,7]=>1000000
[2,7,6,4,8,5,3,1]=>0000000
[1,8,4,5,2,6,3,7]=>1000000
[7,3,5,8,4,6,2,1]=>0000000
[8,2,1,3,5,7,4,6]=>0000000
[7,5,4,1,3,8,2,6]=>0000000
[7,3,8,5,4,1,2,6]=>0000000
[1,7,2,3,5,8,4,6]=>1000000
[3,5,2,6,7,1,8,4]=>0000000
[3,2,8,4,7,5,1,6]=>0000000
[6,8,3,1,7,2,4,5]=>0000000
[2,7,5,3,8,4,1,6]=>0000000
[8,3,2,1,5,7,4,6]=>0000000
[1,2,8,3,5,7,4,6]=>1100000
[6,5,1,7,4,2,8,3]=>0000000
[7,3,6,4,8,2,1,5]=>0000000
[4,6,1,7,3,5,2,8]=>0000001
[5,6,1,7,3,4,2,8]=>0000001
[6,1,7,3,4,2,8,5]=>0000000
[7,3,8,1,6,5,2,4]=>0000000
[8,3,7,1,6,5,2,4]=>0000000
[2,8,1,7,6,5,3,4]=>0000000
[4,2,8,6,5,1,7,3]=>0000000
[8,6,4,7,1,5,2,3]=>0000000
[7,6,4,8,1,5,2,3]=>0000000
[5,1,6,4,2,3,8,7]=>0000010
[4,2,3,8,7,5,1,6]=>0000000
[3,8,7,1,6,5,2,4]=>0000000
[2,4,3,8,1,6,7,5]=>0000000
[2,4,3,7,1,6,8,5]=>0000000
[4,2,3,7,8,5,1,6]=>0000000
[5,1,6,4,2,3,7,8]=>0000011
[6,4,7,8,1,5,2,3]=>0000000
[8,7,4,6,1,5,2,3]=>0000000
[6,5,7,8,1,4,2,3]=>0000000
[4,7,8,6,1,5,2,3]=>0000000
[3,2,4,8,7,1,5,6]=>0000000
[4,8,7,6,1,5,2,3]=>0000000
[5,8,7,6,1,4,2,3]=>0000000
[8,6,5,7,1,4,2,3]=>0000000
[5,1,6,7,4,2,3,8]=>0000001
[6,7,4,8,1,5,2,3]=>0000000
[8,4,7,6,1,5,2,3]=>0000000
[8,3,2,4,7,1,5,6]=>0000000
[7,3,2,4,8,1,5,6]=>0000000
[2,5,3,7,1,6,4,8]=>0000001
[8,4,6,7,1,5,2,3]=>0000000
[5,1,6,8,4,2,3,7]=>0000000
[4,2,3,7,5,1,6,8]=>0000001
[2,4,3,7,1,6,5,8]=>0000001
[2,4,7,1,5,8,6,3]=>0000000
[3,2,4,7,6,1,5,8]=>0000001
[4,7,6,8,1,5,2,3]=>0000000
[8,5,6,7,1,4,2,3]=>0000000
[8,6,7,5,1,4,2,3]=>0000000
[6,8,7,5,1,4,2,3]=>0000000
[5,6,8,7,1,4,2,3]=>0000000
[4,6,8,7,1,5,2,3]=>0000000
[3,2,4,6,1,5,7,8]=>0000011
[6,7,8,5,1,4,2,3]=>0000000
[7,8,6,5,1,4,2,3]=>0000000
[2,1,8,5,4,6,3,7]=>0100000
[4,1,8,5,2,3,6,7]=>0000000
[5,4,1,3,6,7,2,8]=>0000001
[8,4,1,2,6,3,7,5]=>0000000
[8,2,7,1,5,3,4,6]=>0000000
[3,2,7,1,5,8,4,6]=>0000000
[7,3,8,1,5,4,2,6]=>0000000
[7,1,5,3,8,4,2,6]=>0000000
[3,6,8,1,5,4,2,7]=>0000000
[6,8,3,1,5,4,2,7]=>0000000
[7,6,3,1,5,4,2,8]=>0000001
[3,6,2,1,5,8,4,7]=>0000000
[8,6,2,1,5,3,4,7]=>0000000
[2,3,8,1,5,7,4,6]=>0000000
[7,1,3,2,8,6,4,5]=>0000000
[4,7,1,2,6,3,8,5]=>0000000
[2,7,8,1,5,3,4,6]=>0000000
[6,7,2,1,5,3,4,8]=>0000001
[4,7,2,1,8,5,3,6]=>0000000
[8,7,2,1,4,5,3,6]=>0000000
[5,7,8,6,1,4,3,2]=>0000000
[2,7,4,1,6,5,3,8]=>0000001
[7,1,6,4,5,8,3,2]=>0000000
[2,6,4,1,7,5,3,8]=>0000001
[5,6,8,7,1,4,3,2]=>0000000
[4,2,8,1,6,5,3,7]=>0000000
[6,2,4,1,8,5,3,7]=>0000000
[8,3,1,4,5,6,7,2]=>0000000
[5,3,1,4,8,6,7,2]=>0000000
[7,5,1,6,3,4,8,2]=>0000000
[7,1,5,8,4,3,6,2]=>0000000
[5,8,1,6,4,3,7,2]=>0000000
[5,3,1,8,4,6,7,2]=>0000000
[8,3,1,5,4,6,7,2]=>0000000
[8,2,6,1,4,5,3,7]=>0000000
[6,2,8,1,4,5,3,7]=>0000000
[7,2,6,1,5,3,4,8]=>0000001
[2,8,6,1,5,3,4,7]=>0000000
[4,2,1,5,6,3,8,7]=>0000010
[7,1,2,5,8,3,4,6]=>0000000
[7,1,4,5,6,8,3,2]=>0000000
[2,6,7,1,4,5,3,8]=>0000001
[3,5,1,7,4,6,8,2]=>0000000
[7,1,5,6,4,8,3,2]=>0000000
[7,1,6,5,4,8,3,2]=>0000000
[2,7,6,1,4,5,3,8]=>0000001
[5,7,6,8,1,4,3,2]=>0000000
[7,8,6,5,1,4,3,2]=>0000000
[5,3,1,2,4,8,7,6]=>0000100
[5,3,6,2,1,8,7,4]=>0000000
[5,3,7,2,8,4,1,6]=>0000000
[7,2,4,5,8,3,1,6]=>0000000
[7,2,4,5,1,3,6,8]=>0000001
[6,2,4,5,1,8,7,3]=>0000000
[3,1,4,5,2,8,7,6]=>0000100
[1,6,4,5,2,8,7,3]=>1000000
[3,7,4,5,1,2,6,8]=>0000001
[1,7,4,2,6,3,5,8]=>1000001
[8,7,4,5,2,1,6,3]=>0000000
[6,3,7,1,8,4,2,5]=>0000000
[5,7,4,1,6,3,2,8]=>0000001
[1,7,4,8,6,3,2,5]=>1000000
[5,7,4,8,6,3,1,2]=>0000000
[4,8,3,5,6,7,1,2]=>0000000
[1,8,3,5,6,7,2,4]=>1000000
[4,8,1,5,6,7,2,3]=>0000000
[4,1,3,5,6,7,2,8]=>0000001
[5,8,4,3,6,1,2,7]=>0000000
[5,3,8,4,1,7,2,6]=>0000000
[1,5,8,4,6,7,3,2]=>1000000
[1,4,8,3,6,7,5,2]=>1000000
[4,3,8,2,1,7,5,6]=>0000000
[3,8,4,2,6,1,5,7]=>0000000
[3,8,1,5,6,7,4,2]=>0000000
[3,8,2,5,6,7,1,4]=>0000000
[8,2,1,5,6,7,4,3]=>0000000
[8,1,3,5,6,7,4,2]=>0000000
[7,1,4,3,6,2,5,8]=>0000001
[7,8,4,3,6,2,1,5]=>0000000
[4,3,1,8,5,7,6,2]=>0000000
[6,3,5,8,2,7,1,4]=>0000000
[7,5,4,8,6,2,1,3]=>0000000
[7,1,4,8,6,2,3,5]=>0000000
[7,5,4,1,6,2,3,8]=>0000001
[1,6,4,5,8,2,3,7]=>1000000
[1,8,5,3,6,7,4,2]=>1000000
[8,3,5,2,1,7,4,6]=>0000000
[4,1,8,5,6,7,3,2]=>0000000
[1,2,8,5,6,7,3,4]=>1100000
[4,2,1,5,6,7,3,8]=>0000001
[1,5,3,8,6,7,4,2]=>1000000
[1,4,8,5,6,7,2,3]=>1000000
[2,6,5,7,3,1,8,4]=>0000000
[6,3,2,4,7,5,1,8]=>0000001
[4,2,1,6,3,7,5,8]=>0000001
[4,2,1,6,3,7,8,5]=>0000000
[4,2,1,3,7,8,6,5]=>0001000
[5,8,1,7,4,3,2,6]=>0000000
[7,3,4,2,6,8,1,5]=>0000000
[3,6,7,5,2,4,8,1]=>0000000
[4,8,1,7,3,6,5,2]=>0000000
[4,2,1,8,3,7,6,5]=>0000000
[2,6,1,5,4,7,8,3]=>0000000
[4,6,3,5,8,7,1,2]=>0000000
[4,7,5,2,1,3,6,8]=>0000001
[3,5,6,2,4,1,7,8]=>0000011
[3,1,8,5,2,7,6,4]=>0000000
[4,8,1,5,2,7,3,6]=>0000000
[4,1,2,5,3,8,7,6]=>0000100
[4,3,6,8,7,5,1,2]=>0000000
[6,4,8,1,2,5,3,7]=>0000000
[6,5,1,2,3,4,8,7]=>0000010
[6,7,4,1,2,5,3,8]=>0000001
[1,2,6,7,5,3,8,4]=>1100000
[1,7,5,3,2,8,4,6]=>1000000
[1,6,5,7,2,3,8,4]=>1000000
[1,3,8,2,6,5,7,4]=>1000000
[1,2,5,7,6,3,4,8]=>1100001
[1,3,4,8,2,5,7,6]=>1000000
[1,5,7,6,2,3,4,8]=>1000001
[1,5,3,8,2,6,4,7]=>1000000
[1,4,8,3,2,5,7,6]=>1000000
[1,2,4,8,3,5,7,6]=>1100000
[1,3,8,4,2,6,7,5]=>1000000
[1,4,8,2,3,5,7,6]=>1000000
[4,2,6,7,5,8,3,1]=>0000000
[6,7,5,2,1,8,4,3]=>0000000
[3,4,8,7,5,2,1,6]=>0000000
[1,7,5,2,8,4,6,3]=>1000000
[5,6,8,3,1,7,2,4]=>0000000
[6,1,4,8,3,2,7,5]=>0000000
[3,4,7,1,8,6,2,5]=>0000000
[3,4,6,8,2,1,5,7]=>0000000
[3,8,2,5,6,1,4,7]=>0000000
[3,5,2,8,6,4,1,7]=>0000000
[4,2,5,7,3,8,6,1]=>0000000
[7,4,2,5,3,8,1,6]=>0000000
[1,5,6,8,3,4,2,7]=>1000000
[4,5,1,6,8,3,2,7]=>0000000
[4,5,7,3,8,2,6,1]=>0000000
[6,4,3,7,8,2,5,1]=>0000000
[6,4,3,1,7,8,2,5]=>0000000
[4,5,3,1,7,8,2,6]=>0000000
[7,1,3,5,4,8,2,6]=>0000000
[7,5,2,8,1,4,3,6]=>0000000
[1,4,5,7,3,8,6,2]=>1000000
[4,6,3,7,8,5,2,1]=>0000000
[1,5,3,6,7,8,4,2]=>1000000
[4,6,1,7,3,8,5,2]=>0000000
[6,7,2,4,8,1,5,3]=>0000000
[5,2,3,6,7,8,4,1]=>0000000
[6,4,2,7,1,8,3,5]=>0000000
[4,2,6,3,7,8,5,1]=>0000000
[6,7,3,8,2,4,5,1]=>0000000
[3,6,2,7,4,1,8,5]=>0000000
[6,7,3,2,1,4,8,5]=>0000000
[7,2,4,8,6,1,3,5]=>0000000
[3,5,7,2,1,8,6,4]=>0000000
[6,7,8,3,2,5,1,4]=>0000000
[6,3,7,8,2,5,4,1]=>0000000
[2,6,7,4,8,5,3,1]=>0000000
[6,2,4,7,1,8,5,3]=>0000000
[1,7,4,8,5,2,6,3]=>1000000
[1,3,7,8,5,2,6,4]=>1000000
[2,5,7,8,1,6,3,4]=>0000000
[1,6,4,7,8,2,5,3]=>1000000
[2,5,6,1,7,8,4,3]=>0000000
[5,6,1,2,7,8,4,3]=>0000000
[6,7,2,1,8,5,3,4]=>0000000
[6,4,2,5,3,8,7,1]=>0000000
[2,6,4,5,8,7,3,1]=>0000000
[2,6,4,8,7,5,3,1]=>0000000
[8,2,4,6,7,5,3,1]=>0000000
[4,2,6,8,7,5,3,1]=>0000000
[4,2,6,5,8,7,3,1]=>0000000
[6,4,8,7,2,5,3,1]=>0000000
[4,6,5,8,7,2,3,1]=>0000000
[4,7,8,3,1,2,6,5]=>0000000
[4,7,8,2,1,3,6,5]=>0000000
[3,6,2,8,4,7,1,5]=>0000000
[3,2,6,8,4,7,1,5]=>0000000
[4,2,6,8,3,1,7,5]=>0000000
[4,2,5,1,8,3,7,6]=>0000000
[4,2,5,3,8,1,7,6]=>0000000
[3,2,5,4,8,7,1,6]=>0000000
[5,4,3,1,2,8,7,6]=>0000100
[5,3,1,4,2,8,7,6]=>0000100
[5,3,2,1,4,8,7,6]=>0000100
[4,3,2,5,8,1,7,6]=>0000000
[3,2,4,5,8,7,1,6]=>0000000
[1,7,2,3,5,6,8,4]=>1000000
[3,7,4,2,1,5,6,8]=>0000001
[3,4,6,2,8,5,7,1]=>0000000
[4,2,1,7,5,8,3,6]=>0000000
[4,7,2,6,5,1,3,8]=>0000001
[3,7,4,1,2,5,8,6]=>0000000
[4,7,1,6,5,2,8,3]=>0000000
[4,7,3,6,5,1,8,2]=>0000000
[4,3,7,1,6,8,5,2]=>0000000
[4,2,1,7,5,6,8,3]=>0000000
[4,2,6,8,7,3,1,5]=>0000000
[3,4,6,1,8,5,2,7]=>0000000
[4,1,6,7,5,8,2,3]=>0000000
[4,3,6,7,5,1,2,8]=>0000001
[4,3,7,1,6,8,2,5]=>0000000
[4,3,7,5,6,8,2,1]=>0000000
[4,1,7,3,6,5,2,8]=>0000001
[2,8,7,4,5,3,1,6]=>0000000
[2,8,7,4,3,5,1,6]=>0000000
[4,1,7,3,6,2,5,8]=>0000001
[5,8,7,6,1,2,4,3]=>0000000
[4,1,7,2,6,8,5,3]=>0000000
[4,2,7,3,6,1,8,5]=>0000000
[4,2,7,3,6,5,8,1]=>0000000
[3,8,5,6,2,4,1,7]=>0000000
[2,8,6,5,3,7,1,4]=>0000000
[3,8,6,5,1,4,7,2]=>0000000
[3,8,2,1,4,6,7,5]=>0000000
[3,8,2,5,4,6,7,1]=>0000000
[4,2,6,7,5,3,1,8]=>0000001
[3,2,6,1,4,5,8,7]=>0000010
[2,8,7,3,4,5,1,6]=>0000000
[5,8,7,6,1,3,4,2]=>0000000
[5,8,7,6,2,3,4,1]=>0000000
[4,1,7,5,6,2,3,8]=>0000001
[3,8,1,5,2,6,4,7]=>0000000
[2,8,7,5,3,4,1,6]=>0000000
[2,8,7,5,4,3,1,6]=>0000000
[4,1,7,5,6,3,2,8]=>0000001
[5,8,7,6,1,3,2,4]=>0000000
[5,8,7,6,4,1,2,3]=>0000000
[8,1,7,2,4,5,3,6]=>0000000
[8,1,3,6,2,5,4,7]=>0000000
[7,2,1,6,3,5,4,8]=>0000001
[2,7,1,6,3,5,4,8]=>0000001
[2,7,1,5,4,3,6,8]=>0000001
[7,2,1,5,4,3,6,8]=>0000001
[8,1,3,5,4,2,6,7]=>0000000
[8,1,5,3,4,2,6,7]=>0000000
[8,1,5,6,2,3,7,4]=>0000000
[8,1,4,5,3,2,6,7]=>0000000
[8,1,4,3,5,2,6,7]=>0000000
[7,2,1,4,5,3,6,8]=>0000001
[2,7,1,4,5,3,6,8]=>0000001
[2,6,3,1,5,4,7,8]=>0000011
[6,3,2,1,5,4,7,8]=>0000011
[7,3,1,4,5,2,6,8]=>0000001
[7,3,1,5,4,2,6,8]=>0000001
[7,3,1,6,2,5,4,8]=>0000001
[3,7,1,6,2,5,4,8]=>0000001
[3,7,1,4,5,2,6,8]=>0000001
[2,3,6,1,5,4,7,8]=>0000011
[6,3,4,1,5,2,7,8]=>0000011
[6,2,4,1,5,3,7,8]=>0000011
[2,6,4,1,5,3,7,8]=>0000011
[2,6,5,1,3,7,4,8]=>0000001
[6,5,2,1,3,7,4,8]=>0000001
[7,6,1,2,4,5,3,8]=>0000001
[6,7,1,2,8,3,5,4]=>0000000
[6,7,1,2,5,4,3,8]=>0000001
[5,6,2,1,3,7,4,8]=>0000001
[5,2,6,1,3,7,4,8]=>0000001
[2,4,6,1,5,3,7,8]=>0000011
[4,7,1,3,5,2,6,8]=>0000001
[4,7,1,5,3,2,6,8]=>0000001
[5,7,1,6,2,3,8,4]=>0000000
[5,6,3,1,2,7,4,8]=>0000001
[4,2,5,3,1,6,7,8]=>0000111
[5,8,7,3,2,6,4,1]=>0000000
[8,1,7,2,5,6,3,4]=>0000000
[4,8,1,5,2,6,7,3]=>0000000
[7,1,2,8,5,6,3,4]=>0000000
[8,7,2,1,5,6,3,4]=>0000000
[8,6,7,1,5,2,3,4]=>0000000
[6,1,7,8,5,2,3,4]=>0000000
[8,7,5,2,1,6,4,3]=>0000000
[4,6,8,1,5,3,7,2]=>0000000
[6,5,8,1,3,4,7,2]=>0000000
[5,8,2,4,3,6,7,1]=>0000000
[8,1,3,7,5,2,6,4]=>0000000
[3,6,8,2,4,1,7,5]=>0000000
[2,5,8,4,6,7,3,1]=>0000000
[5,8,4,1,6,7,2,3]=>0000000
[1,6,4,5,2,3,7,8]=>1000011
[1,7,4,5,2,3,6,8]=>1000001
[1,6,3,5,2,4,7,8]=>1000011
[1,6,3,4,2,5,7,8]=>1000011
[1,7,3,4,2,5,6,8]=>1000001
[1,8,5,7,3,4,2,6]=>1000000
[1,7,3,4,2,6,5,8]=>1000001
[1,5,2,8,4,7,3,6]=>1000000
[1,4,2,8,5,7,3,6]=>1000000
[1,7,3,5,2,6,4,8]=>1000001
[1,8,4,7,3,5,2,6]=>1000000
[1,7,3,6,2,5,4,8]=>1000001
[1,7,3,6,2,4,5,8]=>1000001
[1,7,4,6,2,3,5,8]=>1000001
[1,8,5,6,2,3,4,7]=>1000000
[1,8,5,6,2,4,3,7]=>1000000
[1,3,2,8,5,6,4,7]=>1010000
[1,4,2,8,5,6,3,7]=>1000000
[1,5,2,8,4,6,3,7]=>1000000
[1,6,2,8,4,5,3,7]=>1000000
[8,6,4,7,2,1,3,5]=>0000000
[1,6,4,7,2,8,3,5]=>1000000
[1,4,7,3,5,8,2,6]=>1000000
[8,4,6,2,3,5,1,7]=>0000000
[5,4,8,2,3,6,1,7]=>0000000
[7,4,8,5,2,3,1,6]=>0000000
[3,8,6,2,4,5,1,7]=>0000000
[4,8,6,2,3,5,1,7]=>0000000
[1,7,5,3,4,8,2,6]=>1000000
[1,7,6,4,8,2,3,5]=>1000000
[5,8,7,4,1,2,3,6]=>0000000
[6,8,5,3,4,1,2,7]=>0000000
[6,8,3,7,2,1,4,5]=>0000000
[8,5,1,6,3,7,2,4]=>0000000
[6,1,3,7,4,8,2,5]=>0000000
[4,1,7,3,5,8,2,6]=>0000000
[7,1,6,4,8,2,3,5]=>0000000
[5,1,7,3,8,2,4,6]=>0000000
[6,1,5,7,8,2,3,4]=>0000000
[7,4,8,6,1,2,3,5]=>0000000
[3,8,7,5,1,2,4,6]=>0000000
[3,7,6,1,2,4,5,8]=>0000001
[4,7,6,1,2,3,5,8]=>0000001
[1,6,5,8,2,3,4,7]=>1000000
[6,5,8,4,1,2,3,7]=>0000000
[8,5,7,4,1,2,3,6]=>0000000
[1,5,7,4,8,2,3,6]=>1000000
[7,6,2,3,8,1,4,5]=>0000000
[7,4,8,5,1,6,2,3]=>0000000
[8,6,2,3,1,7,4,5]=>0000000
[8,6,4,1,2,7,3,5]=>0000000
[1,7,2,8,6,3,4,5]=>1000000
[7,5,8,1,3,6,2,4]=>0000000
[5,4,1,8,2,3,6,7]=>0000000
[1,4,8,7,2,3,5,6]=>1000000
[1,5,8,7,2,3,4,6]=>1000000
[6,5,1,8,2,3,4,7]=>0000000
[5,7,1,3,8,2,4,6]=>0000000
[7,6,8,1,5,2,3,4]=>0000000
[7,1,5,8,6,2,3,4]=>0000000
[4,1,8,7,2,3,5,6]=>0000000
[5,1,8,7,2,3,4,6]=>0000000
[7,1,5,8,3,4,2,6]=>0000000
[7,1,4,3,2,5,6,8]=>0000001
[6,4,2,3,8,5,7,1]=>0000000
[6,4,2,7,5,8,3,1]=>0000000
[7,1,4,6,5,2,3,8]=>0000001
[7,1,4,6,5,8,2,3]=>0000000
[7,1,4,6,3,8,2,5]=>0000000
[7,1,4,3,2,5,8,6]=>0000000
[7,1,4,6,5,2,8,3]=>0000000
[7,1,4,6,5,3,8,2]=>0000000
[7,1,4,6,5,3,2,8]=>0000001
[6,4,2,7,5,3,8,1]=>0000000
[3,4,7,2,6,8,5,1]=>0000000
[3,4,7,1,6,8,2,5]=>0000000
[3,4,7,1,6,8,5,2]=>0000000
[2,4,1,7,5,3,6,8]=>0000001
[3,4,1,7,8,6,2,5]=>0000000
[6,4,2,3,8,5,1,7]=>0000000
[6,4,2,7,5,3,1,8]=>0000001
[3,4,7,2,6,8,1,5]=>0000000
[5,4,7,3,6,8,2,1]=>0000000
[3,4,7,2,6,5,1,8]=>0000001
[4,8,7,3,5,1,2,6]=>0000000
[4,8,7,1,3,5,2,6]=>0000000
[4,8,3,1,2,6,5,7]=>0000000
[3,4,7,1,6,2,5,8]=>0000001
[3,4,7,1,6,2,8,5]=>0000000
[3,4,7,2,6,5,8,1]=>0000000
[4,8,3,1,2,6,7,5]=>0000000
[5,8,1,6,3,4,2,7]=>0000000
[6,8,5,1,3,7,2,4]=>0000000
[6,8,5,1,3,4,7,2]=>0000000
[5,8,3,4,2,6,7,1]=>0000000
[6,4,3,7,5,1,2,8]=>0000001
[3,8,7,4,1,5,2,6]=>0000000
[2,4,7,3,6,1,5,8]=>0000001
[5,8,3,2,1,6,4,7]=>0000000
[5,8,7,4,3,1,2,6]=>0000000
[5,3,7,2,4,6,8,1]=>0000000
[4,2,1,5,8,6,3,7]=>0000000
[3,2,1,8,5,4,6,7]=>0010000
[6,7,2,1,8,4,5,3]=>0000000
[4,3,1,6,7,8,5,2]=>0000000
[4,2,1,6,8,5,3,7]=>0000000
[5,2,6,1,8,3,4,7]=>0000000
[4,2,1,7,8,6,3,5]=>0000000
[3,2,1,8,6,4,7,5]=>0010000
[3,2,1,8,6,4,5,7]=>0010000
[3,2,1,8,4,6,5,7]=>0010000
[3,2,1,8,4,6,7,5]=>0010000
[4,2,1,7,8,3,5,6]=>0000000
[3,2,1,8,4,5,7,6]=>0010000
[7,4,8,6,2,5,3,1]=>0000000
[7,3,8,6,2,4,5,1]=>0000000
[7,4,3,1,8,2,5,6]=>0000000
[7,4,2,8,5,6,1,3]=>0000000
[7,3,8,5,2,4,6,1]=>0000000
[6,3,8,2,4,5,1,7]=>0000000
[6,3,8,2,5,7,4,1]=>0000000
[5,6,7,3,8,2,4,1]=>0000000
[5,3,8,2,4,6,7,1]=>0000000
[6,3,8,2,4,7,5,1]=>0000000
[5,7,4,2,6,8,1,3]=>0000000
[6,5,3,1,4,2,7,8]=>0000011
[5,7,4,2,6,1,3,8]=>0000001
[5,6,4,2,3,8,1,7]=>0000000
[5,6,3,7,8,2,4,1]=>0000000
[5,6,3,8,2,4,7,1]=>0000000
[6,3,7,2,4,5,1,8]=>0000001
[6,3,7,2,5,8,4,1]=>0000000
[5,3,6,8,2,4,7,1]=>0000000
[5,4,6,2,3,8,1,7]=>0000000
[5,3,6,7,8,2,4,1]=>0000000
[5,6,3,4,2,1,8,7]=>0000010
[5,6,4,2,1,3,8,7]=>0000010
[2,8,6,3,5,4,1,7]=>0000000
[4,3,8,5,7,6,2,1]=>0000000
[3,8,5,6,4,2,1,7]=>0000000
[6,3,7,8,4,2,1,5]=>0000000
[7,8,4,2,1,6,3,5]=>0000000
[8,5,7,6,2,1,4,3]=>0000000
[4,8,5,7,6,2,1,3]=>0000000
[8,4,2,6,3,1,7,5]=>0000000
[1,5,3,7,4,2,8,6]=>1000000
[1,6,7,3,4,2,8,5]=>1000000
[8,6,5,2,3,1,7,4]=>0000000
[1,7,6,3,4,2,8,5]=>1000000
[1,8,6,3,2,5,7,4]=>1000000
[8,7,5,2,1,4,6,3]=>0000000
[7,8,5,2,1,4,6,3]=>0000000
[6,8,5,2,3,1,7,4]=>0000000
[5,8,6,2,3,1,7,4]=>0000000
[4,8,2,6,3,1,7,5]=>0000000
[3,2,8,6,4,1,7,5]=>0000000
[3,2,1,7,5,4,8,6]=>0010000
[4,1,3,7,5,2,8,6]=>0000000
[7,1,6,3,2,5,8,4]=>0000000
[1,2,7,4,3,6,8,5]=>1100000
[6,1,8,2,4,5,7,3]=>0000000
[5,1,8,3,2,6,7,4]=>0000000
[4,8,2,7,1,5,6,3]=>0000000
[5,8,7,2,1,4,6,3]=>0000000
[6,8,7,1,3,4,5,2]=>0000000
[7,8,6,1,3,4,5,2]=>0000000
[1,7,8,2,4,5,6,3]=>1000000
[8,6,7,1,3,4,5,2]=>0000000
[7,6,8,1,3,4,5,2]=>0000000
[6,5,8,2,3,1,7,4]=>0000000
[1,6,8,3,2,5,7,4]=>1000000
[8,4,2,7,1,5,6,3]=>0000000
[7,4,2,8,1,5,6,3]=>0000000
[6,4,2,8,3,1,7,5]=>0000000
[5,4,2,3,8,1,7,6]=>0000000
[4,5,2,3,1,6,8,7]=>0000110
[7,4,2,1,3,6,8,5]=>0000000
[8,4,2,1,3,6,7,5]=>0000000
[1,5,3,2,4,7,8,6]=>1000100
[8,5,1,3,2,6,7,4]=>0000000
[5,6,1,3,4,2,8,7]=>0000010
[4,7,2,1,3,6,8,5]=>0000000
[5,7,1,3,2,6,8,4]=>0000000
[6,7,1,2,4,5,8,3]=>0000000
[1,8,2,3,5,6,7,4]=>1000000
[5,8,1,3,2,6,7,4]=>0000000
[4,8,2,1,3,6,7,5]=>0000000
[4,1,3,2,5,7,8,6]=>0001100
[5,1,2,4,3,7,8,6]=>0000100
[1,2,6,4,7,5,8,3]=>1100000
[3,1,7,5,4,2,6,8]=>0000001
[6,3,8,5,4,7,1,2]=>0000000
[1,6,2,5,4,7,8,3]=>1000000
[1,2,6,4,8,5,7,3]=>1100000
[7,8,3,1,4,2,5,6]=>0000000
[4,8,1,5,2,3,6,7]=>0000000
[7,4,1,5,2,3,6,8]=>0000001
[5,6,1,8,4,3,2,7]=>0000000
[5,1,8,6,4,3,2,7]=>0000000
[5,1,6,3,8,7,2,4]=>0000000
[6,1,2,5,8,3,7,4]=>0000000
[6,1,8,7,4,3,2,5]=>0000000
[7,1,2,5,4,8,6,3]=>0000000
[1,2,7,5,8,3,6,4]=>1100000
[4,1,6,3,7,5,2,8]=>0000001
[1,3,6,7,8,5,2,4]=>1000000
[1,2,6,4,7,8,5,3]=>1100000
[4,1,6,3,7,8,2,5]=>0000000
[3,1,6,4,8,2,7,5]=>0000000
[7,8,4,1,6,3,2,5]=>0000000
[4,1,6,3,8,7,2,5]=>0000000
[7,5,1,8,4,3,2,6]=>0000000
[6,5,1,7,4,3,2,8]=>0000001
[4,1,8,5,2,3,7,6]=>0000000
[4,1,6,8,3,7,2,5]=>0000000
[6,5,8,1,4,3,2,7]=>0000000
[1,6,3,2,7,4,8,5]=>1000000
[1,3,7,5,2,4,8,6]=>1000000
[2,5,3,7,4,8,1,6]=>0000000
[3,2,6,7,8,1,5,4]=>0000000
[3,5,2,7,8,4,1,6]=>0000000
[3,5,2,6,8,4,7,1]=>0000000
[2,5,7,4,3,8,6,1]=>0000000
[1,5,7,2,4,8,6,3]=>1000000
[4,6,3,7,2,8,5,1]=>0000000
[1,4,7,3,8,6,2,5]=>1000000
[5,1,6,8,2,4,3,7]=>0000000
[5,3,7,8,2,4,1,6]=>0000000
[8,5,3,7,2,4,1,6]=>0000000
[8,2,4,7,3,1,5,6]=>0000000
[2,4,7,8,3,1,5,6]=>0000000
[6,3,1,5,8,2,4,7]=>0000000
[6,5,3,4,2,8,1,7]=>0000000
[5,2,4,3,8,1,6,7]=>0000000
[3,2,4,8,1,5,6,7]=>0000000
[8,1,5,7,3,2,4,6]=>0000000
[8,4,6,7,2,3,1,5]=>0000000
[4,6,7,8,2,3,1,5]=>0000000
[7,4,6,8,2,3,1,5]=>0000000
[7,2,4,8,3,1,5,6]=>0000000
[5,3,8,7,2,4,1,6]=>0000000
[2,4,8,7,3,1,5,6]=>0000000
[4,6,8,7,2,3,1,5]=>0000000
[6,4,8,7,2,3,1,5]=>0000000
[3,1,7,4,2,8,6,5]=>0000000
[3,2,8,4,1,7,6,5]=>0000000
[7,6,4,8,2,3,1,5]=>0000000
[5,7,6,8,2,3,1,4]=>0000000
[4,7,6,8,2,3,1,5]=>0000000
[8,6,4,7,2,3,1,5]=>0000000
[8,2,3,7,4,1,6,5]=>0000000
[3,7,4,8,2,5,1,6]=>0000000
[2,3,7,4,1,6,8,5]=>0000000
[8,1,6,4,2,3,7,5]=>0000000
[4,7,8,6,2,3,1,5]=>0000000
[6,3,1,7,4,2,8,5]=>0000000
[8,5,7,6,2,3,1,4]=>0000000
[7,1,6,4,2,3,8,5]=>0000000
[3,1,7,6,4,2,8,5]=>0000000
[4,8,7,6,2,3,1,5]=>0000000
[6,8,7,5,2,3,1,4]=>0000000
[4,3,6,1,5,8,7,2]=>0000000
[4,3,6,5,1,8,7,2]=>0000000
[4,6,3,5,1,8,7,2]=>0000000
[4,6,3,1,5,8,7,2]=>0000000
[4,1,6,5,3,8,7,2]=>0000000
[4,6,1,5,3,8,7,2]=>0000000
[2,6,5,3,1,8,7,4]=>0000000
[2,6,5,8,3,1,7,4]=>0000000
[2,6,5,3,8,1,7,4]=>0000000
[4,6,1,5,8,3,7,2]=>0000000
[4,1,6,5,8,3,7,2]=>0000000
[1,4,6,5,8,3,7,2]=>1000000
[4,1,6,5,8,7,3,2]=>0000000
[6,4,3,8,7,1,5,2]=>0000000
[6,4,8,3,7,1,5,2]=>0000000
[2,6,8,5,3,7,1,4]=>0000000
[4,6,8,1,5,7,3,2]=>0000000
[4,6,1,8,5,7,3,2]=>0000000
[1,4,6,8,5,7,3,2]=>1000000
[1,4,6,8,5,3,7,2]=>1000000
[4,6,1,8,5,3,7,2]=>0000000
[4,6,3,8,5,7,1,2]=>0000000
[4,3,6,8,1,5,7,2]=>0000000
[4,3,6,1,8,5,7,2]=>0000000
[4,3,1,6,8,5,7,2]=>0000000
[4,1,3,6,8,7,5,2]=>0000000
[4,3,6,1,8,7,5,2]=>0000000
[4,3,6,8,1,7,5,2]=>0000000
[6,5,2,8,7,3,1,4]=>0000000
[6,5,2,8,7,1,3,4]=>0000000
[6,2,5,8,7,1,3,4]=>0000000
[6,2,5,8,7,3,1,4]=>0000000
[4,6,3,8,1,7,5,2]=>0000000
[4,6,3,1,8,7,5,2]=>0000000
[4,1,6,3,8,7,5,2]=>0000000
[1,4,6,3,8,7,5,2]=>1000000
[4,1,6,8,3,7,5,2]=>0000000
[4,6,1,8,3,7,5,2]=>0000000
[4,6,8,1,3,7,5,2]=>0000000
[6,2,8,5,7,3,1,4]=>0000000
[6,2,8,5,7,1,3,4]=>0000000
[2,4,8,7,1,5,3,6]=>0000000
[6,4,1,8,7,5,3,2]=>0000000
[6,1,4,8,7,5,3,2]=>0000000
[1,6,4,8,7,3,5,2]=>1000000
[6,4,1,8,7,3,5,2]=>0000000
[4,2,8,7,5,1,3,6]=>0000000
[2,4,8,7,3,5,1,6]=>0000000
[1,5,3,2,6,4,7,8]=>1000011
[1,7,3,2,8,5,4,6]=>1000000
[1,6,2,8,5,3,4,7]=>1000000
[1,5,7,2,8,4,3,6]=>1000000
[2,3,1,8,4,5,7,6]=>0010000
[7,8,1,4,3,5,2,6]=>0000000
[8,4,2,5,3,1,6,7]=>0000000
[2,4,7,8,1,5,3,6]=>0000000
[6,1,2,8,5,3,4,7]=>0000000
[6,8,1,3,4,7,2,5]=>0000000
[6,7,2,3,4,1,8,5]=>0000000
[4,8,7,3,5,6,1,2]=>0000000
[4,8,7,5,3,6,1,2]=>0000000
[5,8,7,3,4,6,1,2]=>0000000
[5,8,4,2,1,6,7,3]=>0000000
[5,8,4,1,2,6,7,3]=>0000000
[5,3,7,2,6,1,8,4]=>0000000
[5,2,8,1,6,3,7,4]=>0000000
[5,8,2,1,4,7,6,3]=>0000000
[4,8,2,5,1,7,6,3]=>0000000
[7,8,4,1,2,6,5,3]=>0000000
[4,8,1,5,2,7,6,3]=>0000000
[5,8,1,2,4,7,6,3]=>0000000
[5,2,8,3,6,7,1,4]=>0000000
[2,8,7,6,4,1,3,5]=>0000000
[7,8,2,6,5,1,3,4]=>0000000
[1,8,7,6,2,4,3,5]=>1000000
[2,8,1,4,5,6,7,3]=>0000000
[2,1,7,3,6,5,8,4]=>0100000
[3,2,7,1,6,5,8,4]=>0000000
[6,1,2,8,5,7,3,4]=>0000000
[6,2,1,8,5,7,3,4]=>0000000
[6,3,1,8,5,7,2,4]=>0000000
[6,4,2,1,7,5,8,3]=>0000000
[6,1,3,8,5,2,7,4]=>0000000
[1,3,7,2,6,8,5,4]=>1000000
[7,8,2,6,5,3,1,4]=>0000000
[3,2,6,7,5,8,1,4]=>0000000
[1,2,7,5,6,3,8,4]=>1100000
[2,8,7,6,4,3,1,5]=>0000000
[3,8,7,6,1,2,5,4]=>0000000
[4,8,7,6,2,1,3,5]=>0000000
[4,8,7,6,1,3,2,5]=>0000000
[3,8,7,6,4,1,2,5]=>0000000
[7,8,3,6,5,1,2,4]=>0000000
[2,3,7,5,6,8,1,4]=>0000000
[3,8,7,6,4,2,1,5]=>0000000
[3,4,2,6,7,8,1,5]=>0000000
[3,1,4,2,6,8,7,5]=>0001000
[8,3,4,2,6,1,7,5]=>0000000
[2,6,7,3,5,4,1,8]=>0000001
[2,7,8,3,5,4,1,6]=>0000000
[2,6,8,3,5,4,1,7]=>0000000
[4,7,1,2,8,5,3,6]=>0000000
[4,8,1,2,7,5,3,6]=>0000000
[2,1,6,3,7,5,4,8]=>0100001
[2,7,1,3,6,8,4,5]=>0000000
[7,4,1,2,8,5,3,6]=>0000000
[8,7,4,2,1,5,3,6]=>0000000
[7,4,1,2,6,5,3,8]=>0000001
[7,4,3,1,5,6,8,2]=>0000000
[6,7,4,1,5,8,3,2]=>0000000
[4,7,5,1,6,8,3,2]=>0000000
[4,5,3,1,7,6,8,2]=>0000000
[4,6,1,2,7,5,3,8]=>0000001
[4,6,1,2,8,5,3,7]=>0000000
[4,5,3,1,8,6,7,2]=>0000000
[4,8,5,6,3,1,7,2]=>0000000
[5,1,3,4,8,6,7,2]=>0000000
[5,4,3,8,1,6,7,2]=>0000000
[8,5,3,4,1,6,7,2]=>0000000
[6,4,8,2,1,5,3,7]=>0000000
[6,7,3,2,5,1,4,8]=>0000001
[6,8,3,2,5,1,4,7]=>0000000
[5,7,1,4,6,8,3,2]=>0000000
[5,1,3,4,7,6,8,2]=>0000000
[5,4,3,7,1,6,8,2]=>0000000
[6,7,5,4,1,8,3,2]=>0000000
[7,6,4,2,1,5,3,8]=>0000001
[8,5,6,1,3,2,4,7]=>0000000
[8,6,1,5,3,2,4,7]=>0000000
[7,8,1,5,3,2,4,6]=>0000000
[8,1,7,5,3,2,4,6]=>0000000
[8,6,1,4,5,2,3,7]=>0000000
[8,6,3,1,5,2,4,7]=>0000000
[8,4,6,1,5,2,3,7]=>0000000
[8,6,2,1,5,4,3,7]=>0000000
[8,5,2,6,1,4,3,7]=>0000000
[8,5,2,1,7,4,3,6]=>0000000
[8,2,7,5,1,3,4,6]=>0000000
[8,4,1,7,5,2,3,6]=>0000000
[8,2,6,1,7,4,3,5]=>0000000
[8,1,7,4,3,2,6,5]=>0000000
[8,1,5,7,3,2,6,4]=>0000000
[5,7,8,1,3,2,6,4]=>0000000
[8,2,6,1,5,7,3,4]=>0000000
[5,8,1,6,7,2,3,4]=>0000000
[5,7,6,1,8,2,3,4]=>0000000
[8,1,5,6,7,2,3,4]=>0000000
[6,5,7,1,8,2,3,4]=>0000000
[8,1,6,4,7,2,3,5]=>0000000
[7,5,8,1,3,2,4,6]=>0000000
[7,8,4,1,3,2,5,6]=>0000000
[8,3,7,4,1,2,5,6]=>0000000
[8,5,1,7,3,2,4,6]=>0000000
[6,8,1,7,3,2,4,5]=>0000000
[7,1,8,4,3,6,2,5]=>0000000
[7,3,1,8,6,4,2,5]=>0000000
[8,3,1,7,4,6,2,5]=>0000000
[8,4,5,1,7,2,3,6]=>0000000
[5,6,8,1,7,2,3,4]=>0000000
[6,5,8,1,2,7,3,4]=>0000000
[7,3,1,8,5,6,2,4]=>0000000
[6,2,7,8,3,1,5,4]=>0000000
[5,8,1,7,3,2,6,4]=>0000000
[8,4,1,7,3,2,6,5]=>0000000
[8,3,4,7,1,2,6,5]=>0000000
[7,4,8,2,1,3,6,5]=>0000000
[7,4,3,8,1,2,6,5]=>0000000
[8,2,3,6,7,1,5,4]=>0000000
[6,8,5,2,3,4,7,1]=>0000000
[5,3,7,1,4,2,8,6]=>0000000
[3,7,5,1,2,8,6,4]=>0000000
[7,3,5,8,1,2,6,4]=>0000000
[2,5,7,4,8,6,1,3]=>0000000
[3,6,2,5,8,7,1,4]=>0000000
[5,2,8,4,7,6,1,3]=>0000000
[2,5,1,4,7,3,8,6]=>0000000
[3,1,5,6,2,8,7,4]=>0000000
[1,2,4,6,3,8,7,5]=>1100000
[7,2,3,5,1,8,6,4]=>0000000
[1,6,4,2,8,7,5,3]=>1000000
[4,6,2,7,5,1,8,3]=>0000000
[1,5,3,6,2,8,7,4]=>1000000
[3,5,2,1,7,4,8,6]=>0000000
[6,3,1,7,2,8,5,4]=>0000000
[7,5,1,2,8,6,4,3]=>0000000
[4,5,1,2,8,7,6,3]=>0000000
[5,8,2,7,1,6,4,3]=>0000000
[2,1,6,4,5,8,3,7]=>0100000
[8,6,3,7,5,2,1,4]=>0000000
[4,6,3,8,5,2,1,7]=>0000000
[4,6,3,7,5,2,8,1]=>0000000
[4,8,3,7,5,2,1,6]=>0000000
[5,2,8,3,7,6,1,4]=>0000000
[8,2,7,3,1,6,4,5]=>0000000
[8,6,7,4,1,5,3,2]=>0000000
[4,8,6,7,5,1,3,2]=>0000000
[7,1,8,4,6,5,2,3]=>0000000
[8,7,1,5,4,6,2,3]=>0000000
[8,5,7,1,4,6,3,2]=>0000000
[6,4,8,5,1,7,3,2]=>0000000
[8,4,7,1,5,6,3,2]=>0000000
[8,7,5,1,4,6,2,3]=>0000000
[8,7,2,5,1,4,6,3]=>0000000
[4,8,7,2,5,1,6,3]=>0000000
[8,7,1,4,2,5,6,3]=>0000000
[8,7,5,1,2,4,6,3]=>0000000
[7,1,8,5,6,2,3,4]=>0000000
[3,5,8,7,1,2,6,4]=>0000000
[2,3,8,5,7,1,6,4]=>0000000
[3,8,7,1,5,6,2,4]=>0000000
[3,5,8,7,1,6,2,4]=>0000000
[2,3,8,6,7,5,1,4]=>0000000
[3,2,8,6,7,5,1,4]=>0000000
[4,1,8,6,2,7,5,3]=>0000000
[8,7,4,1,2,6,5,3]=>0000000
[1,3,8,6,7,5,2,4]=>1000000
[5,7,1,8,2,6,3,4]=>0000000
[2,8,7,1,5,6,3,4]=>0000000
[8,7,1,5,2,4,6,3]=>0000000
[7,1,8,2,4,6,5,3]=>0000000
[1,6,2,8,4,7,5,3]=>1000000
[1,3,8,5,7,2,6,4]=>1000000
[1,8,3,7,2,5,6,4]=>1000000
[2,8,7,1,3,5,6,4]=>0000000
[5,7,1,8,2,3,6,4]=>0000000
[7,1,8,2,3,5,6,4]=>0000000
[8,6,3,7,4,1,5,2]=>0000000
[4,2,8,6,7,5,1,3]=>0000000
[8,4,2,7,5,6,1,3]=>0000000
[4,8,3,6,1,7,5,2]=>0000000
[8,3,4,7,5,1,6,2]=>0000000
[8,3,7,4,5,1,6,2]=>0000000
[8,7,4,2,5,6,1,3]=>0000000
[8,7,5,1,6,2,3,4]=>0000000
[8,7,2,4,1,5,6,3]=>0000000
[4,8,6,1,7,2,5,3]=>0000000
[4,2,8,6,7,1,5,3]=>0000000
[8,7,4,1,2,5,6,3]=>0000000
[8,2,7,1,6,3,4,5]=>0000000
[8,2,7,1,3,6,4,5]=>0000000
[2,8,3,6,7,1,5,4]=>0000000
[8,7,2,1,3,5,6,4]=>0000000
[1,8,7,2,3,6,4,5]=>1000000
[1,8,7,2,6,3,4,5]=>1000000
[8,2,7,3,6,1,4,5]=>0000000
[1,8,7,3,6,2,4,5]=>1000000
[1,8,2,7,6,3,4,5]=>1000000
[8,2,7,4,1,5,6,3]=>0000000
[8,2,1,7,5,6,3,4]=>0000000
[8,7,3,1,5,6,2,4]=>0000000
[2,8,7,3,5,6,1,4]=>0000000
[8,3,1,6,7,5,2,4]=>0000000
[8,5,2,1,6,7,4,3]=>0000000
[1,5,2,8,6,7,4,3]=>1000000
[1,2,8,6,7,5,3,4]=>1100000
[1,8,3,6,7,5,2,4]=>1000000
[8,2,3,6,7,5,1,4]=>0000000
[8,3,7,2,5,6,1,4]=>0000000
[8,1,3,7,5,6,2,4]=>0000000
[8,4,1,2,7,5,6,3]=>0000000
[8,1,4,2,6,7,5,3]=>0000000
[1,2,8,6,7,3,5,4]=>1100000
[8,1,2,7,3,6,4,5]=>0000000
[8,1,7,3,6,2,4,5]=>0000000
[8,1,7,2,6,3,4,5]=>0000000
[8,1,7,2,3,6,4,5]=>0000000
[8,1,3,7,2,5,6,4]=>0000000
[1,8,3,6,7,2,5,4]=>1000000
[1,7,8,2,3,6,5,4]=>1000000
[8,3,7,1,2,5,6,4]=>0000000
[7,4,2,6,1,5,3,8]=>0000001
[7,4,2,5,6,1,3,8]=>0000001
[7,3,5,6,4,2,1,8]=>0000001
[7,4,3,1,5,6,2,8]=>0000001
[7,4,5,2,6,1,3,8]=>0000001
[5,3,7,2,8,6,4,1]=>0000000
[5,3,8,2,6,7,4,1]=>0000000
[6,3,8,2,5,4,7,1]=>0000000
[6,4,3,1,8,2,7,5]=>0000000
[5,3,7,8,2,6,4,1]=>0000000
[4,7,8,5,6,3,2,1]=>0000000
[5,3,7,6,8,2,4,1]=>0000000
[5,7,8,4,6,2,1,3]=>0000000
[5,8,4,3,6,7,1,2]=>0000000
[5,8,6,4,7,2,1,3]=>0000000
[5,3,8,6,2,7,4,1]=>0000000
[4,7,5,8,6,3,2,1]=>0000000
[6,3,8,7,2,4,1,5]=>0000000
[5,3,8,7,2,6,4,1]=>0000000
[5,3,8,6,7,2,4,1]=>0000000
[5,3,7,8,6,2,4,1]=>0000000
[5,7,6,4,8,2,1,3]=>0000000
[5,8,4,6,7,2,1,3]=>0000000
[6,4,2,8,1,7,3,5]=>0000000
[6,5,2,4,3,7,8,1]=>0000000
[5,4,6,2,8,7,1,3]=>0000000
[5,6,3,8,7,2,4,1]=>0000000
[6,7,4,3,1,8,2,5]=>0000000
[5,7,4,3,6,8,1,2]=>0000000
[5,7,3,8,6,2,4,1]=>0000000
[4,5,8,6,7,3,2,1]=>0000000
[4,6,8,5,7,3,2,1]=>0000000
[5,6,8,3,7,2,4,1]=>0000000
[5,4,6,8,2,7,1,3]=>0000000
[7,8,4,5,1,3,2,6]=>0000000
[6,7,1,3,2,5,4,8]=>0000001
[6,7,1,4,3,5,2,8]=>0000001
[7,8,2,3,1,5,4,6]=>0000000
[7,8,2,4,3,5,1,6]=>0000000
[7,8,2,4,1,5,3,6]=>0000000
[1,4,2,6,5,7,3,8]=>1000001
[5,6,1,4,2,7,3,8]=>0000001
[6,7,2,4,1,5,3,8]=>0000001
[6,7,2,4,3,5,1,8]=>0000001
[6,7,2,3,1,5,4,8]=>0000001
[6,7,3,5,4,8,1,2]=>0000000
[2,4,1,6,5,7,3,8]=>0000001
[1,5,2,6,4,7,3,8]=>1000001
[2,5,1,6,4,7,3,8]=>0000001
[5,6,2,4,3,7,1,8]=>0000001
[4,5,2,6,1,7,3,8]=>0000001
[4,5,1,6,3,7,2,8]=>0000001
[4,5,3,6,1,7,2,8]=>0000001
[5,6,3,4,1,7,2,8]=>0000001
[5,6,1,4,3,7,2,8]=>0000001
[5,6,1,3,2,7,4,8]=>0000001
[5,6,4,7,1,3,2,8]=>0000001
[6,7,4,5,1,3,2,8]=>0000001
[6,7,5,8,1,3,2,4]=>0000000
[4,5,1,3,2,7,6,8]=>0000101
[4,6,5,7,1,3,2,8]=>0000001
[4,6,1,3,2,7,5,8]=>0000001
[1,4,3,6,2,7,5,8]=>1000001
[4,5,2,3,1,7,6,8]=>0000101
[4,5,3,7,6,8,1,2]=>0000000
[4,6,5,7,3,8,1,2]=>0000000
[4,6,5,7,2,3,1,8]=>0000001
[3,5,4,6,1,7,2,8]=>0000001
[3,5,1,6,4,7,2,8]=>0000001
[1,5,3,6,4,7,2,8]=>1000001
[1,5,3,6,2,7,4,8]=>1000001
[3,5,2,6,1,7,4,8]=>0000001
[3,5,2,6,4,7,1,8]=>0000001
[3,4,2,6,1,7,5,8]=>0000001
[4,6,2,3,1,7,5,8]=>0000001
[2,4,3,6,1,7,5,8]=>0000001
[2,5,3,6,4,7,1,8]=>0000001
[2,5,3,6,1,7,4,8]=>0000001
[3,6,2,7,5,4,8,1]=>0000000
[5,2,6,7,4,3,8,1]=>0000000
[3,5,2,7,6,4,8,1]=>0000000
[2,1,5,6,8,4,3,7]=>0100000
[1,3,7,2,8,5,4,6]=>1000000
[4,6,2,7,1,8,3,5]=>0000000
[1,5,4,3,6,8,2,7]=>1000000
[1,6,4,5,7,8,3,2]=>1000000
[2,1,5,6,8,4,7,3]=>0100000
[2,1,5,6,8,7,3,4]=>0100000
[3,6,5,2,7,8,4,1]=>0000000
[6,2,4,7,5,8,3,1]=>0000000
[1,5,7,8,4,2,6,3]=>1000000
[3,7,4,1,8,6,2,5]=>0000000
[3,4,6,8,5,7,2,1]=>0000000
[4,5,6,2,8,7,3,1]=>0000000
[4,5,6,1,8,7,3,2]=>0000000
[4,5,6,3,1,8,7,2]=>0000000
[4,3,6,2,1,7,5,8]=>0000001
[4,6,3,2,1,7,5,8]=>0000001
[4,6,3,1,7,5,2,8]=>0000001
[4,5,3,7,6,1,8,2]=>0000000
[4,5,1,7,3,8,6,2]=>0000000
[2,5,7,1,4,3,8,6]=>0000000
[4,3,5,7,6,1,8,2]=>0000000
[4,3,6,1,7,5,2,8]=>0000001
[4,3,2,6,1,7,5,8]=>0000001
[5,3,2,1,6,4,7,8]=>0000011
[5,3,1,6,2,7,4,8]=>0000001
[5,1,6,3,2,7,4,8]=>0000001
[2,6,1,4,7,5,3,8]=>0000001
[3,6,1,7,4,2,5,8]=>0000001
[4,6,1,7,5,3,2,8]=>0000001
[5,1,6,3,7,4,2,8]=>0000001
[5,3,6,4,2,1,7,8]=>0000011
[5,3,2,6,4,1,7,8]=>0000011
[5,2,1,6,3,7,4,8]=>0000001
[5,2,6,3,1,7,4,8]=>0000001
[4,2,6,3,1,7,8,5]=>0000000
[3,6,2,1,7,4,5,8]=>0000001
[3,6,2,7,4,1,5,8]=>0000001
[3,5,7,2,8,6,4,1]=>0000000
[2,6,1,3,7,5,4,8]=>0000001
[3,6,1,7,5,2,4,8]=>0000001
[5,1,6,2,7,4,3,8]=>0000001
[5,2,6,4,3,1,7,8]=>0000011
[5,2,1,6,4,3,7,8]=>0000011
[5,4,2,1,6,3,7,8]=>0000011
[5,4,1,6,2,7,3,8]=>0000001
[5,1,6,4,2,7,3,8]=>0000001
[3,6,1,7,5,4,8,2]=>0000000
[2,6,1,5,4,3,7,8]=>0000011
[3,1,6,2,5,4,7,8]=>0000011
[4,1,6,3,2,7,8,5]=>0000000
[5,1,6,4,3,2,7,8]=>0000011
[5,4,1,6,3,2,7,8]=>0000011
[5,4,3,1,6,2,7,8]=>0000011
[4,5,1,8,7,6,2,3]=>0000000
[6,8,3,5,7,1,4,2]=>0000000
[1,5,8,2,7,3,6,4]=>1000000
[6,7,4,8,1,5,3,2]=>0000000
[6,8,5,3,7,2,4,1]=>0000000
[7,5,3,8,2,6,4,1]=>0000000
[3,6,8,4,5,7,1,2]=>0000000
[1,6,8,4,7,2,3,5]=>1000000
[1,4,5,7,8,2,6,3]=>1000000
[1,4,5,8,7,2,3,6]=>1000000
[1,2,5,8,3,6,4,7]=>1100000
[7,8,1,4,6,2,3,5]=>0000000
[1,6,7,4,8,2,5,3]=>1000000
[1,4,5,6,8,2,7,3]=>1000000
[1,4,5,8,6,2,7,3]=>1000000
[1,2,5,8,3,4,7,6]=>1100000
[7,8,1,2,3,5,4,6]=>0000000
[1,6,7,2,3,5,4,8]=>1000001
[1,4,5,7,6,2,3,8]=>1000001
[1,2,5,7,3,6,4,8]=>1100001
[1,2,5,7,3,6,8,4]=>1100000
[1,6,8,2,3,5,7,4]=>1000000
[1,6,8,4,5,2,3,7]=>1000000
[1,6,8,2,3,4,7,5]=>1000000
[1,6,8,2,3,7,4,5]=>1000000
[1,4,5,7,6,2,8,3]=>1000000
[7,8,1,4,5,2,6,3]=>0000000
[1,6,7,2,3,8,5,4]=>1000000
[1,2,5,6,3,8,7,4]=>1100000
[2,7,4,8,3,5,1,6]=>0000000
[2,7,4,8,3,5,6,1]=>0000000
[7,2,8,4,3,5,1,6]=>0000000
[8,4,2,1,5,3,6,7]=>0000000
[8,4,1,5,3,2,6,7]=>0000000
[6,7,3,8,4,2,5,1]=>0000000
[6,7,3,8,4,2,1,5]=>0000000
[7,1,8,4,3,5,2,6]=>0000000
[1,7,8,4,3,5,2,6]=>1000000
[7,1,4,8,3,5,2,6]=>0000000
[7,1,8,4,3,5,6,2]=>0000000
[6,7,3,1,8,4,5,2]=>0000000
[6,7,1,4,8,3,5,2]=>0000000
[6,7,4,1,3,8,2,5]=>0000000
[1,6,7,8,4,3,2,5]=>1000000
[7,2,1,8,4,5,3,6]=>0000000
[6,2,7,1,8,4,3,5]=>0000000
[6,2,7,8,4,3,1,5]=>0000000
[6,2,7,8,4,3,5,1]=>0000000
[2,6,7,4,8,3,5,1]=>0000000
[2,6,7,4,8,3,1,5]=>0000000
[7,8,1,3,6,2,4,5]=>0000000
[1,2,7,8,6,3,4,5]=>1100000
[2,6,7,1,8,5,3,4]=>0000000
[2,6,7,8,5,3,4,1]=>0000000
[6,2,7,8,4,5,3,1]=>0000000
[1,7,2,8,4,5,6,3]=>1000000
[6,3,7,8,1,5,2,4]=>0000000
[6,7,1,2,8,5,3,4]=>0000000
[1,6,7,8,4,2,5,3]=>1000000
[4,1,5,7,3,2,6,8]=>0000001
[4,6,1,7,3,2,5,8]=>0000001
[8,1,7,4,6,3,2,5]=>0000000
[6,7,3,5,1,4,8,2]=>0000000
[5,7,8,4,2,6,3,1]=>0000000
[5,4,7,6,2,8,3,1]=>0000000
[5,7,4,1,6,8,3,2]=>0000000
[6,8,4,5,7,1,3,2]=>0000000
[5,8,4,6,1,7,3,2]=>0000000
[5,6,1,4,7,8,3,2]=>0000000
[5,6,7,2,4,8,3,1]=>0000000
[5,3,6,7,4,8,2,1]=>0000000
[5,3,2,8,6,7,4,1]=>0000000
[5,4,8,2,6,7,3,1]=>0000000
[5,4,8,6,2,7,3,1]=>0000000
[6,4,8,5,7,2,3,1]=>0000000
[4,6,8,5,7,2,3,1]=>0000000
[5,6,8,2,4,7,3,1]=>0000000
[5,6,3,8,4,7,2,1]=>0000000
[4,6,3,5,8,7,2,1]=>0000000
[4,6,3,2,8,7,5,1]=>0000000
[5,6,3,8,2,7,4,1]=>0000000
[3,6,5,8,7,2,4,1]=>0000000
[5,3,6,8,2,7,4,1]=>0000000
[4,3,7,2,8,6,5,1]=>0000000
[5,4,7,2,6,8,3,1]=>0000000
[5,3,2,7,6,8,4,1]=>0000000
[6,7,3,8,5,2,4,1]=>0000000
[6,3,2,7,5,4,8,1]=>0000000
[6,4,7,2,5,3,8,1]=>0000000
[6,2,7,5,1,4,8,3]=>0000000
[2,7,8,5,3,6,1,4]=>0000000
[6,3,7,8,4,2,5,1]=>0000000
[3,5,7,8,4,6,2,1]=>0000000
[5,7,8,2,4,6,3,1]=>0000000
[2,5,8,4,3,7,6,1]=>0000000
[2,6,8,4,7,3,5,1]=>0000000
[3,7,4,8,6,2,1,5]=>0000000
[3,6,4,8,7,2,5,1]=>0000000
[3,5,4,8,2,7,6,1]=>0000000
[4,5,7,3,8,6,2,1]=>0000000
[6,3,1,8,7,5,4,2]=>0000000
[8,5,4,1,7,6,3,2]=>0000000
[1,8,2,5,6,3,4,7]=>1000000
[7,2,8,4,5,1,3,6]=>0000000
[1,3,7,5,6,2,4,8]=>1000001
[1,6,7,4,3,5,2,8]=>1000001
[1,8,2,5,3,6,7,4]=>1000000
[2,6,8,4,3,5,7,1]=>0000000
[7,2,8,4,1,5,6,3]=>0000000
[7,5,8,1,2,6,3,4]=>0000000
[1,5,2,6,4,7,8,3]=>1000000
[1,5,4,6,2,3,7,8]=>1000011
[6,2,5,7,1,4,8,3]=>0000000
[6,5,4,3,8,1,7,2]=>0000000
[2,6,5,8,3,4,1,7]=>0000000
[2,6,5,7,3,4,1,8]=>0000001
[6,2,5,7,4,1,3,8]=>0000001
[6,2,5,8,4,1,3,7]=>0000000
[2,7,8,4,6,1,3,5]=>0000000
[6,1,2,8,5,4,7,3]=>0000000
[6,2,5,7,8,1,3,4]=>0000000
[1,5,4,2,6,7,3,8]=>1000001
[2,6,5,7,3,8,1,4]=>0000000
[1,6,2,7,5,8,4,3]=>1000000
[1,3,2,7,8,5,6,4]=>1010000
[1,6,2,4,8,7,3,5]=>1000000
[6,5,2,1,8,7,3,4]=>0000000
[2,6,5,3,7,8,4,1]=>0000000
[6,5,2,3,8,7,1,4]=>0000000
[5,1,4,2,3,7,8,6]=>0000100
[1,5,4,2,6,3,8,7]=>1000010
[6,5,8,7,4,3,1,2]=>0000000
[1,2,7,5,4,8,3,6]=>1100000
[3,2,7,5,4,8,1,6]=>0000000
[6,8,3,2,4,7,1,5]=>0000000
[3,7,2,5,4,8,1,6]=>0000000
[1,3,7,5,4,8,2,6]=>1000000
[2,7,3,5,4,8,1,6]=>0000000
[6,3,5,2,1,4,7,8]=>0000011
[2,3,5,8,1,4,7,6]=>0000000
[6,3,8,5,2,7,1,4]=>0000000
[2,3,6,8,1,4,7,5]=>0000000
[2,5,8,1,7,3,6,4]=>0000000
[2,8,1,5,7,3,6,4]=>0000000
[2,6,8,1,5,7,3,4]=>0000000
[2,7,1,5,8,3,4,6]=>0000000
[3,7,5,8,1,2,6,4]=>0000000
[7,3,6,1,2,8,4,5]=>0000000
[6,8,4,5,1,7,2,3]=>0000000
[5,1,8,7,6,2,3,4]=>0000000
[4,6,1,8,7,5,2,3]=>0000000
[3,4,8,7,1,2,5,6]=>0000000
[5,6,8,3,7,1,4,2]=>0000000
[6,4,7,1,2,8,5,3]=>0000000
[6,5,1,8,2,7,3,4]=>0000000
[6,5,1,8,7,2,3,4]=>0000000
[6,5,1,7,2,8,3,4]=>0000000
[6,5,1,7,2,3,8,4]=>0000000
[5,6,8,7,4,1,2,3]=>0000000
[6,8,5,7,4,1,2,3]=>0000000
[6,8,3,1,5,2,4,7]=>0000000
[6,8,4,3,1,5,7,2]=>0000000
[6,8,4,2,1,5,7,3]=>0000000
[6,3,2,1,7,4,5,8]=>0000001
[6,4,2,1,7,5,3,8]=>0000001
[6,3,2,8,7,1,4,5]=>0000000
[4,2,8,1,7,3,5,6]=>0000000
[4,3,1,6,2,7,5,8]=>0000001
[5,4,1,7,2,8,6,3]=>0000000
[5,4,2,1,6,7,3,8]=>0000001
[8,6,1,4,5,7,2,3]=>0000000
[5,2,8,3,7,4,6,1]=>0000000
[6,2,8,5,4,7,3,1]=>0000000
[5,2,8,4,3,6,7,1]=>0000000
[5,4,2,7,3,6,1,8]=>0000001
[5,4,2,8,3,6,1,7]=>0000000
[6,5,3,8,4,7,2,1]=>0000000
[5,2,8,4,3,7,1,6]=>0000000
[6,2,8,3,7,4,1,5]=>0000000
[5,4,2,7,3,1,8,6]=>0000000
[6,4,3,7,1,2,8,5]=>0000000
[6,4,3,8,1,2,7,5]=>0000000
[7,2,8,4,3,1,5,6]=>0000000
[7,5,3,8,4,2,6,1]=>0000000
[6,4,2,7,3,1,5,8]=>0000001
[7,6,4,8,2,3,5,1]=>0000000
[5,3,1,7,8,4,6,2]=>0000000
[5,3,2,7,8,4,6,1]=>0000000
[6,5,1,7,8,2,3,4]=>0000000
[6,3,1,7,8,4,2,5]=>0000000
[5,4,1,7,3,8,2,6]=>0000000
[6,3,2,7,8,4,1,5]=>0000000
[8,7,6,1,3,5,2,4]=>0000000
[5,7,2,1,6,3,8,4]=>0000000
[6,4,8,1,3,2,7,5]=>0000000
[3,6,7,8,4,2,1,5]=>0000000
[2,5,8,3,1,6,7,4]=>0000000
[4,8,7,2,1,6,3,5]=>0000000
[3,6,1,2,5,8,4,7]=>0000000
[1,4,5,8,2,3,7,6]=>1000000
[1,5,2,4,6,8,3,7]=>1000000
[3,6,1,5,8,2,4,7]=>0000000
[2,6,5,1,4,8,3,7]=>0000000
[2,5,1,8,4,7,3,6]=>0000000
[2,7,1,4,3,6,8,5]=>0000000
[1,3,7,5,8,2,4,6]=>1000000
[8,2,1,5,7,3,4,6]=>0000000
[2,5,4,8,1,3,7,6]=>0000000
[2,4,1,3,8,6,7,5]=>0001000
[8,4,3,7,1,2,6,5]=>0000000
[1,7,3,5,8,2,6,4]=>1000000
[1,8,4,2,6,7,3,5]=>1000000
[3,1,6,8,7,2,4,5]=>0000000
[7,2,1,6,8,3,4,5]=>0000000
[4,1,7,2,6,8,3,5]=>0000000
[5,1,7,2,3,6,8,4]=>0000000
[7,2,1,6,3,5,8,4]=>0000000
[2,6,1,7,3,5,8,4]=>0000000
[8,1,3,2,4,6,7,5]=>0000000
[7,3,1,2,4,6,8,5]=>0000000
[1,8,3,4,7,2,5,6]=>1000000
[3,5,8,1,2,7,4,6]=>0000000
[3,6,8,1,2,4,7,5]=>0000000
[4,1,3,8,7,2,6,5]=>0000000
[1,3,7,4,8,2,6,5]=>1000000
[1,4,6,8,2,3,7,5]=>1000000
[3,5,8,1,7,2,4,6]=>0000000
[2,6,8,1,7,3,4,5]=>0000000
[1,8,3,2,7,5,6,4]=>1000000
[2,6,7,3,8,1,5,4]=>0000000
[8,4,1,7,3,6,2,5]=>0000000
[3,7,2,8,6,1,5,4]=>0000000
[6,2,3,8,7,1,5,4]=>0000000
[3,7,8,2,4,1,5,6]=>0000000
[1,7,2,4,5,8,3,6]=>1000000
[1,7,4,5,8,3,2,6]=>1000000
[2,6,4,7,8,3,5,1]=>0000000
[1,2,6,4,7,8,3,5]=>1100000
[6,1,4,7,8,3,5,2]=>0000000
[3,6,4,7,2,8,5,1]=>0000000
[6,1,4,7,8,5,2,3]=>0000000
[6,8,5,7,4,2,3,1]=>0000000
[2,3,8,7,1,6,4,5]=>0000000
[4,8,1,2,7,3,5,6]=>0000000
[6,4,8,7,5,1,2,3]=>0000000
[6,3,8,7,2,1,4,5]=>0000000
[2,6,7,8,5,1,3,4]=>0000000
[2,8,3,4,1,5,7,6]=>0000000
[4,5,3,2,8,6,7,1]=>0000000
[3,5,8,6,1,4,7,2]=>0000000
[2,6,4,8,5,1,7,3]=>0000000
[7,5,3,2,8,6,1,4]=>0000000
[4,5,1,2,8,6,7,3]=>0000000
[1,6,4,8,3,2,5,7]=>1000000
[1,8,3,5,6,2,4,7]=>1000000
[1,4,8,5,6,2,3,7]=>1000000
[6,1,4,8,2,3,5,7]=>0000000
[8,7,2,5,6,1,4,3]=>0000000
[1,8,2,5,4,7,3,6]=>1000000
[5,7,4,1,2,3,8,6]=>0000000
[1,7,4,2,5,3,8,6]=>1000000
[6,7,4,2,1,3,8,5]=>0000000
[6,4,3,8,5,7,1,2]=>0000000
[7,4,3,6,2,1,5,8]=>0000001
[7,2,5,3,4,1,6,8]=>0000001
[8,3,7,4,5,6,1,2]=>0000000
[2,7,4,3,1,5,6,8]=>0000001
[6,8,4,2,3,1,5,7]=>0000000
[2,1,7,4,8,3,5,6]=>0100000
[5,2,8,6,1,3,4,7]=>0000000
[2,8,3,1,4,5,6,7]=>0000000
[7,4,8,2,3,1,5,6]=>0000000
[4,2,7,3,1,5,6,8]=>0000001
[8,3,7,2,1,4,5,6]=>0000000
[6,5,2,4,7,1,3,8]=>0000001
[6,5,7,4,1,8,2,3]=>0000000
[8,6,4,1,3,7,2,5]=>0000000
[6,4,3,1,8,2,5,7]=>0000000
[4,8,1,3,5,7,2,6]=>0000000
[7,8,4,1,3,6,2,5]=>0000000
[6,5,8,1,3,7,2,4]=>0000000
[5,3,6,1,8,2,4,7]=>0000000
[4,7,3,1,8,2,5,6]=>0000000
[8,3,1,7,2,4,5,6]=>0000000
[2,8,1,4,7,3,5,6]=>0000000
[3,1,8,5,4,7,6,2]=>0000000
[4,1,5,8,3,7,6,2]=>0000000
[4,1,5,3,8,7,6,2]=>0000000
[4,5,1,8,2,7,6,3]=>0000000
[4,8,5,3,1,7,6,2]=>0000000
[4,5,2,8,1,7,6,3]=>0000000
[4,6,2,8,7,1,5,3]=>0000000
[4,8,6,3,7,1,5,2]=>0000000
[4,6,8,2,7,5,1,3]=>0000000
[4,6,2,8,7,5,1,3]=>0000000
[5,6,2,7,4,1,8,3]=>0000000
[5,6,7,2,3,1,8,4]=>0000000
[5,6,7,2,8,3,1,4]=>0000000
[5,6,7,2,1,8,3,4]=>0000000
[5,6,7,2,1,3,8,4]=>0000000
[5,6,1,7,8,2,4,3]=>0000000
[5,6,1,7,2,4,8,3]=>0000000
[4,1,6,8,7,3,5,2]=>0000000
[4,1,6,8,7,5,3,2]=>0000000
[5,6,1,7,8,4,2,3]=>0000000
[4,6,8,1,7,5,2,3]=>0000000
[4,8,6,1,7,5,3,2]=>0000000
[5,6,7,1,8,3,2,4]=>0000000
[5,6,7,1,3,8,2,4]=>0000000
[5,6,7,1,3,2,8,4]=>0000000
[5,6,7,3,1,2,8,4]=>0000000
[5,6,8,7,4,2,1,3]=>0000000
[1,3,7,5,8,2,6,4]=>1000000
[3,1,7,5,8,2,6,4]=>0000000
[3,5,7,1,8,4,6,2]=>0000000
[5,2,8,1,7,3,4,6]=>0000000
[5,8,3,2,7,1,4,6]=>0000000
[5,1,8,3,7,2,4,6]=>0000000
[5,1,8,4,6,2,3,7]=>0000000
[4,8,5,2,6,1,3,7]=>0000000
[4,1,7,5,6,2,8,3]=>0000000
[5,7,4,3,8,1,6,2]=>0000000
[5,7,4,3,8,2,6,1]=>0000000
[3,8,4,2,6,7,5,1]=>0000000
[3,8,4,1,6,7,5,2]=>0000000
[6,1,7,5,2,8,4,3]=>0000000
[5,6,4,3,2,8,1,7]=>0000000
[2,6,7,5,3,8,4,1]=>0000000
[2,1,6,7,5,3,8,4]=>0100000
[3,8,4,2,1,6,7,5]=>0000000
[5,7,4,3,8,2,1,6]=>0000000
[6,7,4,8,1,2,5,3]=>0000000
[6,7,5,8,1,2,4,3]=>0000000
[6,7,4,8,3,1,2,5]=>0000000
[6,1,3,4,8,2,5,7]=>0000000
[6,2,3,4,8,1,5,7]=>0000000
[3,4,8,2,1,5,7,6]=>0000000
[6,7,5,8,3,1,4,2]=>0000000
[2,5,7,6,1,4,8,3]=>0000000
[6,7,4,8,2,3,5,1]=>0000000
[6,7,4,8,1,3,5,2]=>0000000
[2,6,7,5,1,3,8,4]=>0000000
[6,3,1,4,8,2,5,7]=>0000000
[6,7,4,8,1,3,2,5]=>0000000
[6,7,5,8,4,1,3,2]=>0000000
[6,7,4,8,2,1,3,5]=>0000000
[6,7,4,8,1,2,3,5]=>0000000
[7,8,3,2,6,1,4,5]=>0000000
[3,4,8,2,6,1,7,5]=>0000000
[7,8,4,1,5,6,3,2]=>0000000
[7,8,1,2,6,3,4,5]=>0000000
[7,8,5,1,4,6,3,2]=>0000000
[5,3,8,4,1,6,7,2]=>0000000
[6,2,4,8,1,5,3,7]=>0000000
[3,4,8,5,1,6,7,2]=>0000000
[5,3,8,1,4,6,7,2]=>0000000
[4,2,6,8,1,5,3,7]=>0000000
[7,4,2,8,1,5,3,6]=>0000000
[6,1,7,5,8,4,3,2]=>0000000
[1,2,7,8,5,3,4,6]=>1100000
[6,3,7,8,5,4,1,2]=>0000000
[6,1,5,7,8,4,3,2]=>0000000
[1,7,5,6,8,4,3,2]=>1000000
[3,1,8,4,5,6,7,2]=>0000000
[4,2,1,8,6,5,3,7]=>0000000
[3,2,7,8,5,1,4,6]=>0000000
[2,3,7,8,5,1,4,6]=>0000000
[2,7,3,8,5,1,4,6]=>0000000
[3,6,2,8,5,1,4,7]=>0000000
[1,4,2,8,7,5,3,6]=>1000000
[7,3,6,8,5,4,1,2]=>0000000
[7,2,1,8,5,3,4,6]=>0000000
[1,2,6,8,4,5,3,7]=>1100000
[7,1,6,5,8,4,3,2]=>0000000
[6,5,7,1,8,4,3,2]=>0000000
[5,7,6,1,8,4,3,2]=>0000000
[6,7,1,5,8,4,3,2]=>0000000
[7,1,2,8,4,5,3,6]=>0000000
[7,6,1,5,8,4,3,2]=>0000000
[7,5,6,1,8,4,3,2]=>0000000
[1,8,7,5,3,2,4,6]=>1000000
[1,8,7,4,2,5,3,6]=>1000000
[5,3,7,1,6,4,2,8]=>0000001
[1,5,3,8,7,4,2,6]=>1000000
[1,8,6,3,5,7,4,2]=>1000000
[1,8,6,3,2,4,7,5]=>1000000
[1,7,5,8,6,3,2,4]=>1000000
[1,7,4,2,5,8,6,3]=>1000000
[8,7,4,2,5,3,1,6]=>0000000
[1,8,5,2,7,4,6,3]=>1000000
[1,7,4,6,3,8,5,2]=>1000000
[4,1,8,5,7,3,2,6]=>0000000
[4,7,2,8,3,6,1,5]=>0000000
[1,8,5,4,2,3,7,6]=>1000000
[3,5,4,8,1,2,7,6]=>0000000
[5,6,3,8,7,1,2,4]=>0000000
[2,6,8,4,1,7,3,5]=>0000000
[1,8,7,4,2,6,3,5]=>1000000
[5,2,8,6,7,1,3,4]=>0000000
[6,2,8,7,5,1,3,4]=>0000000
[1,8,5,7,6,2,3,4]=>1000000
[1,8,6,7,5,2,3,4]=>1000000
[5,2,8,7,1,4,3,6]=>0000000
[6,1,7,3,2,8,5,4]=>0000000
[4,7,2,1,6,3,8,5]=>0000000
[6,1,8,3,7,5,2,4]=>0000000
[6,1,8,4,5,2,7,3]=>0000000
[3,5,2,7,1,6,8,4]=>0000000
[6,1,4,2,5,3,7,8]=>0000011
[1,3,7,5,4,2,8,6]=>1000000
[6,1,3,5,4,2,7,8]=>0000011
[6,1,2,5,4,7,3,8]=>0000001
[5,2,6,3,4,7,1,8]=>0000001
[2,4,7,1,5,3,8,6]=>0000000
[2,3,6,7,4,8,1,5]=>0000000
[1,3,6,7,4,8,5,2]=>1000000
[2,7,6,5,3,1,8,4]=>0000000
[5,2,6,1,4,7,8,3]=>0000000
[4,7,6,5,2,1,8,3]=>0000000
[6,3,1,5,4,7,8,2]=>0000000
[5,3,6,1,4,2,7,8]=>0000011
[1,7,4,2,6,3,8,5]=>1000000
[5,7,4,1,2,3,6,8]=>0000001
[6,4,1,2,5,3,7,8]=>0000011
[4,7,6,3,8,5,1,2]=>0000000
[3,7,6,5,2,8,1,4]=>0000000
[3,7,6,5,1,2,8,4]=>0000000
[4,7,2,6,1,3,8,5]=>0000000
[2,7,6,5,8,1,4,3]=>0000000
[4,2,6,8,3,1,5,7]=>0000000
[3,7,6,2,4,5,1,8]=>0000001
[2,3,6,5,8,1,4,7]=>0000000
[2,3,5,8,6,1,4,7]=>0000000
[4,2,3,8,6,1,5,7]=>0000000
[1,2,3,7,4,6,8,5]=>1110000
[3,2,7,1,4,5,8,6]=>0000000
[2,1,5,3,8,7,4,6]=>0100000
[5,8,3,2,4,1,6,7]=>0000000
[4,2,7,1,8,3,5,6]=>0000000
[1,2,7,5,3,8,4,6]=>1100000
[3,2,7,1,4,8,5,6]=>0000000
[1,2,3,7,6,8,4,5]=>1110000
[1,2,3,6,8,7,4,5]=>1110000
[1,2,3,7,8,4,6,5]=>1110000
[1,2,3,6,8,4,7,5]=>1110000
[6,2,8,3,7,5,1,4]=>0000000
[4,2,8,3,7,5,6,1]=>0000000
[7,3,4,8,6,5,1,2]=>0000000
[5,3,4,8,7,2,6,1]=>0000000
[4,6,3,8,5,7,2,1]=>0000000
[7,5,3,8,6,2,4,1]=>0000000
[2,6,8,3,7,4,5,1]=>0000000
[2,5,8,3,7,4,6,1]=>0000000
[7,4,3,8,6,2,5,1]=>0000000
[3,5,4,8,7,2,6,1]=>0000000
[4,5,3,8,6,7,2,1]=>0000000
[3,6,7,8,4,5,2,1]=>0000000
[1,8,5,6,4,7,3,2]=>1000000
[2,5,8,6,4,7,3,1]=>0000000
[6,3,7,8,4,5,2,1]=>0000000
[4,3,7,8,5,6,2,1]=>0000000
[4,2,8,6,5,7,3,1]=>0000000
[3,2,8,6,7,4,5,1]=>0000000
[2,3,8,7,5,4,6,1]=>0000000
[1,8,2,7,4,5,6,3]=>1000000
[7,2,8,6,3,4,5,1]=>0000000
[6,2,8,4,5,7,3,1]=>0000000
[5,2,8,4,6,7,3,1]=>0000000
[4,3,6,8,5,7,2,1]=>0000000
[3,4,6,8,7,2,5,1]=>0000000
[7,3,5,8,6,2,4,1]=>0000000
[1,8,3,5,7,4,6,2]=>1000000
[2,7,8,4,5,6,3,1]=>0000000
[3,7,5,8,4,6,2,1]=>0000000
[5,7,4,6,8,3,2,1]=>0000000
[3,6,5,8,4,7,2,1]=>0000000
[2,6,8,4,5,7,3,1]=>0000000
[4,2,7,1,3,8,5,6]=>0000000
[4,2,5,1,3,8,6,7]=>0000100
[5,3,6,1,7,2,4,8]=>0000001
[3,7,1,2,5,8,6,4]=>0000000
[3,7,4,1,2,8,5,6]=>0000000
[7,5,1,3,4,8,6,2]=>0000000
[7,5,1,2,4,8,6,3]=>0000000
[6,4,2,3,7,1,5,8]=>0000001
[7,6,3,8,1,2,5,4]=>0000000
[7,4,2,3,8,1,6,5]=>0000000
[4,7,5,2,8,1,3,6]=>0000000
[8,2,6,3,7,1,4,5]=>0000000
[8,6,1,2,7,4,5,3]=>0000000
[8,4,7,1,2,3,6,5]=>0000000
[8,5,7,1,2,4,6,3]=>0000000
[3,8,5,6,1,2,4,7]=>0000000
[3,7,5,8,1,2,4,6]=>0000000
[7,6,4,8,1,3,5,2]=>0000000
[6,5,8,1,2,4,7,3]=>0000000
[3,6,8,1,2,5,7,4]=>0000000
[4,6,3,8,1,2,5,7]=>0000000
[4,6,3,7,1,2,5,8]=>0000001
[4,1,7,8,2,3,6,5]=>0000000
[5,1,2,8,6,3,4,7]=>0000000
[5,3,8,1,6,2,4,7]=>0000000
[6,1,8,5,2,3,4,7]=>0000000
[6,1,7,5,2,3,4,8]=>0000001
[6,8,1,3,7,4,5,2]=>0000000
[7,2,8,1,6,3,4,5]=>0000000
[4,7,8,2,5,1,3,6]=>0000000
[6,8,2,7,1,4,5,3]=>0000000
[4,8,7,1,3,5,6,2]=>0000000
[3,8,7,1,2,4,6,5]=>0000000
[4,8,7,1,2,3,6,5]=>0000000
[5,8,7,1,2,4,6,3]=>0000000
[5,8,7,1,3,4,6,2]=>0000000
[7,1,8,6,2,3,5,4]=>0000000
[5,8,6,4,1,2,3,7]=>0000000
[5,1,3,4,6,7,2,8]=>0000001
[1,3,4,8,7,5,2,6]=>1000000
[8,2,4,1,7,3,5,6]=>0000000
[8,6,1,4,2,3,7,5]=>0000000
[3,6,1,4,2,8,7,5]=>0000000
[1,6,8,4,3,7,2,5]=>1000000
[3,1,4,7,8,5,2,6]=>0000000
[6,1,7,4,3,8,2,5]=>0000000
[1,8,7,4,3,6,2,5]=>1000000
[7,4,1,3,8,2,6,5]=>0000000
[4,8,2,3,1,5,7,6]=>0000000
[4,8,6,2,1,3,7,5]=>0000000
[2,7,4,1,8,3,5,6]=>0000000
[1,7,8,4,2,3,6,5]=>1000000
[8,7,1,3,4,2,6,5]=>0000000
[1,7,4,3,6,2,8,5]=>1000000
[3,8,6,4,5,2,1,7]=>0000000
[3,8,4,6,5,2,1,7]=>0000000
[2,4,3,7,5,8,1,6]=>0000000
[1,4,7,3,6,2,8,5]=>1000000
[6,4,1,3,7,2,8,5]=>0000000
[8,1,4,3,6,2,7,5]=>0000000
[4,2,3,8,5,7,1,6]=>0000000
[2,8,5,7,3,4,1,6]=>0000000
[5,8,2,6,4,3,1,7]=>0000000
[7,2,5,8,4,3,1,6]=>0000000
[4,2,3,5,8,7,1,6]=>0000000
[8,2,3,5,4,7,1,6]=>0000000
[6,1,8,3,4,2,7,5]=>0000000
[1,8,6,4,2,3,7,5]=>1000000
[3,8,4,5,6,2,1,7]=>0000000
[3,8,6,5,4,2,1,7]=>0000000
[6,3,1,4,2,8,7,5]=>0000000
[7,3,8,1,2,6,4,5]=>0000000
[7,1,4,5,3,2,6,8]=>0000001
[1,8,4,2,6,5,3,7]=>1000000
[5,1,4,8,6,3,2,7]=>0000000
[5,3,1,8,4,7,2,6]=>0000000
[4,3,8,1,5,7,2,6]=>0000000
[6,3,1,2,5,7,4,8]=>0000001
[7,1,4,2,6,5,3,8]=>0000001
[3,8,4,1,6,5,2,7]=>0000000
[8,7,2,4,5,1,6,3]=>0000000
[7,1,5,4,8,6,3,2]=>0000000
[5,7,1,4,8,6,3,2]=>0000000
[6,5,3,7,4,8,2,1]=>0000000
[2,7,8,4,5,1,6,3]=>0000000
[5,6,3,8,1,4,7,2]=>0000000
[8,7,3,1,5,4,2,6]=>0000000
[3,5,4,7,6,1,2,8]=>0000001
[3,5,7,4,6,1,8,2]=>0000000
[3,5,7,4,6,1,2,8]=>0000001
[3,5,7,4,6,2,1,8]=>0000001
[3,5,2,7,6,4,1,8]=>0000001
[3,5,7,2,6,4,1,8]=>0000001
[5,3,7,6,1,2,8,4]=>0000000
[5,3,7,6,1,4,2,8]=>0000001
[5,3,7,6,4,1,2,8]=>0000001
[3,5,7,2,6,1,4,8]=>0000001
[3,5,2,7,6,1,4,8]=>0000001
[5,3,7,6,4,1,8,2]=>0000000
[3,7,5,4,1,8,2,6]=>0000000
[3,7,5,4,1,8,6,2]=>0000000
[3,7,5,1,4,8,6,2]=>0000000
[3,7,5,1,4,8,2,6]=>0000000
[3,5,7,1,2,6,8,4]=>0000000
[3,5,7,2,1,6,4,8]=>0000001
[5,3,7,1,6,2,4,8]=>0000001
[3,5,7,1,4,6,8,2]=>0000000
[3,5,7,1,4,2,6,8]=>0000001
[3,5,7,4,1,2,6,8]=>0000001
[3,5,4,7,1,6,8,2]=>0000000
[3,5,4,7,1,2,6,8]=>0000001
[3,5,4,7,2,1,6,8]=>0000001
[3,5,4,2,7,1,6,8]=>0000001
[3,5,4,7,2,1,8,6]=>0000000
[3,5,4,7,1,2,8,6]=>0000000
[5,7,6,3,1,8,4,2]=>0000000
[5,7,6,3,1,8,2,4]=>0000000
[3,5,7,4,1,2,8,6]=>0000000
[3,5,7,4,2,1,8,6]=>0000000
[3,2,5,7,4,1,8,6]=>0000000
[3,2,5,7,1,4,8,6]=>0000000
[3,5,2,7,1,4,8,6]=>0000000
[3,5,7,2,1,4,8,6]=>0000000
[3,5,7,1,4,2,8,6]=>0000000
[3,7,5,2,1,8,6,4]=>0000000
[3,7,2,5,1,8,6,4]=>0000000
[3,2,7,5,1,8,6,4]=>0000000
[3,2,7,5,1,8,4,6]=>0000000
[3,7,2,5,1,8,4,6]=>0000000
[3,7,5,2,1,8,4,6]=>0000000
[3,8,4,1,7,6,5,2]=>0000000
[5,8,2,4,1,6,3,7]=>0000000
[3,2,6,8,1,5,4,7]=>0000000
[3,2,6,8,7,1,5,4]=>0000000
[8,7,3,2,5,6,1,4]=>0000000
[7,2,4,1,8,3,6,5]=>0000000
[1,7,2,3,6,8,5,4]=>1000000
[3,5,6,4,8,2,7,1]=>0000000
[3,5,1,4,8,2,7,6]=>0000000
[1,7,5,4,8,2,6,3]=>1000000
[3,7,5,1,6,4,8,2]=>0000000
[2,7,5,4,8,1,3,6]=>0000000
[2,7,5,4,8,6,1,3]=>0000000
[1,7,5,4,8,6,3,2]=>1000000
[2,5,1,4,8,7,3,6]=>0000000
[3,6,4,2,8,7,1,5]=>0000000
[3,5,2,4,8,1,6,7]=>0000000
[4,5,6,1,7,3,8,2]=>0000000
[3,5,6,4,8,1,2,7]=>0000000
[1,5,6,4,8,7,2,3]=>1000000
[3,6,4,1,8,7,2,5]=>0000000
[3,6,4,5,8,7,2,1]=>0000000
[1,6,4,3,8,5,2,7]=>1000000
[7,6,1,4,5,3,8,2]=>0000000
[7,6,1,3,5,4,8,2]=>0000000
[7,1,3,2,5,8,4,6]=>0000000
[1,6,4,2,8,5,3,7]=>1000000
[7,6,5,8,3,1,4,2]=>0000000
[2,6,4,3,8,1,7,5]=>0000000
[2,6,4,3,8,5,7,1]=>0000000
[7,2,3,1,5,8,6,4]=>0000000
[7,1,5,6,3,8,4,2]=>0000000
[7,3,6,5,1,4,8,2]=>0000000
[7,2,6,5,3,8,1,4]=>0000000
[7,2,3,1,4,8,6,5]=>0000000
[7,2,3,5,4,8,6,1]=>0000000
[2,6,4,5,8,1,7,3]=>0000000
[1,5,6,4,8,3,7,2]=>1000000
[2,5,6,4,8,3,1,7]=>0000000
[3,5,6,1,4,7,8,2]=>0000000
[7,6,1,3,4,5,8,2]=>0000000
[7,1,3,2,4,8,5,6]=>0000000
[7,6,1,5,3,4,8,2]=>0000000
[7,6,1,5,4,3,8,2]=>0000000
[1,6,4,5,8,3,2,7]=>1000000
[7,6,5,8,1,3,2,4]=>0000000
[3,4,6,8,7,2,1,5]=>0000000
[3,5,6,8,2,1,7,4]=>0000000
[4,2,1,5,3,7,8,6]=>0000100
[4,2,5,6,3,1,8,7]=>0000010
[3,5,6,8,1,7,2,4]=>0000000
[4,1,5,6,3,2,8,7]=>0000010
[4,5,3,1,7,2,8,6]=>0000000
[4,1,3,5,2,7,8,6]=>0000100
[2,5,4,7,3,8,6,1]=>0000000
[3,5,7,1,8,4,2,6]=>0000000
[4,1,5,3,2,7,8,6]=>0000100
[4,5,3,7,1,2,8,6]=>0000000
[4,3,6,1,2,7,5,8]=>0000001
[5,1,3,2,4,6,7,8]=>0000111
[3,6,1,7,4,5,2,8]=>0000001
[5,3,1,4,2,6,7,8]=>0000111
[4,5,2,3,7,1,8,6]=>0000000
[4,2,6,1,3,7,5,8]=>0000001
[4,6,2,1,3,7,5,8]=>0000001
[3,6,2,1,7,4,8,5]=>0000000
[3,1,4,7,6,5,2,8]=>0000001
[3,6,2,7,1,5,8,4]=>0000000
[4,6,2,7,1,3,5,8]=>0000001
[3,5,7,1,8,2,6,4]=>0000000
[5,1,4,2,3,6,7,8]=>0000111
[2,6,5,3,4,7,8,1]=>0000000
[3,6,1,7,5,4,2,8]=>0000001
[5,1,4,3,2,6,7,8]=>0000111
[5,4,1,3,2,6,7,8]=>0000111
[6,7,4,8,5,1,3,2]=>0000000
[3,6,5,8,7,1,4,2]=>0000000
[5,6,8,3,1,7,4,2]=>0000000
[5,3,8,1,7,2,6,4]=>0000000
[6,5,3,8,2,7,4,1]=>0000000
[6,4,8,1,3,7,5,2]=>0000000
[4,2,8,7,6,3,1,5]=>0000000
[7,6,3,1,8,4,2,5]=>0000000
[5,2,7,4,1,8,6,3]=>0000000
[1,3,7,6,5,8,2,4]=>1000000
[6,3,1,4,7,5,2,8]=>0000001
[4,6,7,2,5,3,1,8]=>0000001
[4,2,6,8,7,1,5,3]=>0000000
[6,3,7,1,2,8,5,4]=>0000000
[1,8,2,3,6,5,4,7]=>1000000
[3,5,8,4,7,2,6,1]=>0000000
[1,8,5,4,6,2,3,7]=>1000000
[3,8,5,4,6,1,2,7]=>0000000
[3,8,5,1,6,4,2,7]=>0000000
[2,8,5,4,6,1,3,7]=>0000000
[2,8,5,4,6,3,1,7]=>0000000
[1,8,5,4,6,3,2,7]=>1000000
[2,5,8,4,7,3,6,1]=>0000000
[3,6,4,2,7,8,5,1]=>0000000
[3,6,4,2,7,8,1,5]=>0000000
[3,5,4,1,6,2,7,8]=>0000011
[4,5,8,1,7,6,2,3]=>0000000
[3,5,8,4,7,1,6,2]=>0000000
[1,5,8,4,7,3,6,2]=>1000000
[3,6,4,1,7,8,5,2]=>0000000
[3,6,4,8,7,5,2,1]=>0000000
[1,6,4,3,7,8,5,2]=>1000000
[7,6,1,3,8,4,2,5]=>0000000
[1,6,4,2,7,8,3,5]=>1000000
[2,6,4,3,7,1,8,5]=>0000000
[2,6,4,1,7,8,3,5]=>0000000
[7,2,3,4,8,6,5,1]=>0000000
[7,2,3,1,8,6,4,5]=>0000000
[7,2,3,4,1,6,8,5]=>0000000
[1,2,4,3,8,5,7,6]=>1101000
[7,3,8,6,1,4,2,5]=>0000000
[7,2,8,6,3,4,1,5]=>0000000
[7,2,3,1,5,6,8,4]=>0000000
[7,2,3,8,5,6,4,1]=>0000000
[2,6,4,8,7,1,5,3]=>0000000
[1,5,8,4,7,6,2,3]=>1000000
[3,5,8,1,6,7,2,4]=>0000000
[7,6,1,3,5,8,2,4]=>0000000
[7,1,3,2,5,6,8,4]=>0000000
[7,1,3,8,2,6,5,4]=>0000000
[7,6,1,8,5,4,2,3]=>0000000
[4,3,7,1,6,5,8,2]=>0000000
[5,2,6,4,8,1,7,3]=>0000000
[5,3,7,4,8,1,6,2]=>0000000
[4,3,7,1,6,2,8,5]=>0000000
[4,1,7,8,6,3,2,5]=>0000000
[1,2,6,8,3,7,4,5]=>1100000
[6,8,2,4,1,3,7,5]=>0000000
[6,1,2,7,5,8,4,3]=>0000000
[4,5,2,6,8,3,7,1]=>0000000
[6,8,4,1,5,3,7,2]=>0000000
[8,3,6,1,5,7,4,2]=>0000000
[2,4,6,7,8,1,5,3]=>0000000
[7,4,3,8,6,2,1,5]=>0000000
[4,3,6,2,1,8,5,7]=>0000000
[4,6,2,3,7,5,8,1]=>0000000
[8,4,5,3,2,1,7,6]=>0000000
[6,4,8,3,2,7,1,5]=>0000000
[5,8,3,7,2,1,6,4]=>0000000
[1,2,6,5,8,7,3,4]=>1100000
[5,6,3,4,8,7,2,1]=>0000000
[6,5,3,4,8,7,2,1]=>0000000
[7,5,3,8,4,6,2,1]=>0000000
[8,5,3,7,4,6,2,1]=>0000000
[5,8,1,2,3,4,7,6]=>0000000
[4,3,8,7,5,6,2,1]=>0000000
[5,8,3,7,4,6,2,1]=>0000000
[6,8,7,3,4,5,2,1]=>0000000
[8,6,2,3,5,1,4,7]=>0000000
[8,2,4,5,7,3,1,6]=>0000000
[2,6,3,8,7,5,4,1]=>0000000
[8,2,3,7,5,4,1,6]=>0000000
[8,2,6,3,5,4,1,7]=>0000000
[8,6,1,5,2,4,3,7]=>0000000
[8,6,2,4,1,5,3,7]=>0000000
[8,4,1,6,5,3,2,7]=>0000000
[8,3,6,1,5,4,2,7]=>0000000
[8,3,2,6,5,4,1,7]=>0000000
[8,3,2,5,7,4,1,6]=>0000000
[8,3,1,7,5,4,2,6]=>0000000
[6,1,3,8,7,5,4,2]=>0000000
[3,6,1,8,7,5,4,2]=>0000000
[3,8,1,5,7,6,4,2]=>0000000
[3,5,2,8,7,6,4,1]=>0000000
[3,4,8,2,7,6,5,1]=>0000000
[3,4,8,7,1,6,5,2]=>0000000
[8,1,3,5,7,6,4,2]=>0000000
[4,1,8,5,7,6,3,2]=>0000000
[8,2,7,1,4,5,6,3]=>0000000
[8,1,7,3,4,6,2,5]=>0000000
[8,3,1,7,2,6,5,4]=>0000000
[3,8,2,4,7,6,5,1]=>0000000
[2,8,3,7,4,6,5,1]=>0000000
[8,2,3,7,1,6,5,4]=>0000000
[8,2,7,1,3,6,5,4]=>0000000
[8,1,7,2,6,4,3,5]=>0000000
[8,1,7,5,2,4,3,6]=>0000000
[8,2,3,7,4,6,1,5]=>0000000
[2,4,8,5,7,6,3,1]=>0000000
[8,2,4,3,7,6,1,5]=>0000000
[8,2,7,3,5,1,4,6]=>0000000
[8,2,7,4,3,1,5,6]=>0000000
[8,2,1,5,7,6,4,3]=>0000000
[6,1,8,2,7,5,4,3]=>0000000
[8,1,5,2,7,6,4,3]=>0000000
[8,1,7,2,4,6,5,3]=>0000000
[8,2,4,1,7,6,5,3]=>0000000
[4,2,8,3,7,6,5,1]=>0000000
[4,8,2,1,7,6,5,3]=>0000000
[5,1,8,7,2,6,4,3]=>0000000
[5,8,1,3,7,6,2,4]=>0000000
[8,2,5,4,1,7,6,3]=>0000000
[5,1,4,8,7,6,3,2]=>0000000
[8,1,4,3,7,6,5,2]=>0000000
[4,8,1,3,7,6,5,2]=>0000000
[4,3,8,1,7,6,5,2]=>0000000
[6,2,8,1,5,7,3,4]=>0000000
[7,3,2,8,5,6,1,4]=>0000000
[4,7,6,5,1,3,8,2]=>0000000
[1,7,6,3,2,8,4,5]=>1000000
[5,4,2,1,7,3,6,8]=>0000001
[3,7,6,2,8,4,5,1]=>0000000
[4,3,6,8,5,1,2,7]=>0000000
[2,7,1,5,8,4,3,6]=>0000000
[7,1,2,6,3,5,4,8]=>0000001
[6,7,8,4,2,5,3,1]=>0000000
[4,7,3,1,2,6,8,5]=>0000000
[3,8,5,6,4,2,7,1]=>0000000
[3,2,6,4,7,8,5,1]=>0000000
[5,2,1,4,7,8,3,6]=>0000000
[5,6,2,7,3,4,8,1]=>0000000
[1,5,8,6,4,2,3,7]=>1000000
[1,6,2,3,5,8,7,4]=>1000000
[4,3,8,2,5,7,1,6]=>0000000
[6,7,2,3,1,5,8,4]=>0000000
[4,7,5,8,6,3,1,2]=>0000000
[7,3,2,5,8,1,6,4]=>0000000
[2,4,8,3,7,1,5,6]=>0000000
[5,2,8,4,1,6,3,7]=>0000000
[7,6,5,2,1,8,4,3]=>0000000
[2,7,5,1,8,3,6,4]=>0000000
[5,7,1,3,2,4,8,6]=>0000000
[4,2,7,6,3,5,8,1]=>0000000
[8,1,7,4,2,3,5,6]=>0000000
[8,6,5,1,7,4,3,2]=>0000000
[7,6,4,1,3,5,8,2]=>0000000
[8,2,3,7,1,4,5,6]=>0000000
[5,6,2,7,4,3,1,8]=>0000001
[4,8,6,5,1,2,7,3]=>0000000
[4,8,6,5,1,2,3,7]=>0000000
[5,8,2,6,1,4,7,3]=>0000000
[3,8,7,5,6,1,4,2]=>0000000
[7,4,6,5,1,3,8,2]=>0000000
[4,6,3,8,7,5,1,2]=>0000000
[2,8,4,1,5,7,6,3]=>0000000
[1,8,4,2,5,7,6,3]=>1000000
[2,8,5,4,1,7,6,3]=>0000000
[2,5,8,3,7,1,6,4]=>0000000
[1,8,5,2,4,7,6,3]=>1000000
[1,4,6,2,8,7,5,3]=>1000000
[7,8,2,4,1,6,5,3]=>0000000
[2,4,6,1,8,7,5,3]=>0000000
[2,8,4,5,1,7,6,3]=>0000000
[3,5,8,1,7,6,2,4]=>0000000
[3,5,8,2,7,6,1,4]=>0000000
[2,1,6,8,7,5,3,4]=>0100000
[1,8,2,4,5,7,6,3]=>1000000
[1,3,8,2,5,7,6,4]=>1000000
[2,3,8,1,5,7,6,4]=>0000000
[2,6,1,8,7,5,3,4]=>0000000
[1,6,2,8,7,5,3,4]=>1000000
[1,6,3,8,7,5,2,4]=>1000000
[2,6,3,8,7,5,1,4]=>0000000
[3,2,8,1,5,7,6,4]=>0000000
[3,1,8,2,5,7,6,4]=>0000000
[2,1,8,3,5,7,6,4]=>0100000
[7,8,2,1,4,6,5,3]=>0000000
[2,3,6,8,7,5,1,4]=>0000000
[3,1,6,8,7,2,5,4]=>0000000
[3,8,4,5,1,6,2,7]=>0000000
[6,1,4,5,7,2,3,8]=>0000001
[8,1,4,7,6,3,2,5]=>0000000
[8,3,1,6,4,7,2,5]=>0000000
[5,3,8,6,2,7,1,4]=>0000000
[8,3,6,1,5,7,2,4]=>0000000
[6,8,1,4,5,2,3,7]=>0000000
[1,5,8,4,6,2,3,7]=>1000000
[5,6,8,1,4,2,3,7]=>0000000
[5,7,4,8,1,2,3,6]=>0000000
[4,7,8,1,2,6,3,5]=>0000000
[8,7,1,5,6,2,3,4]=>0000000
[1,6,5,8,7,2,3,4]=>1000000
[3,7,1,6,2,4,8,5]=>0000000
[5,1,2,7,6,8,3,4]=>0000000
[1,7,6,5,8,2,3,4]=>1000000
[1,6,8,5,7,2,3,4]=>1000000
[7,5,1,2,6,8,3,4]=>0000000
[6,1,5,2,7,8,3,4]=>0000000
[5,1,2,6,8,7,3,4]=>0000000
[1,8,6,2,5,7,3,4]=>1000000
[5,7,8,1,2,6,3,4]=>0000000
[8,1,5,7,6,2,3,4]=>0000000
[3,7,1,2,8,4,6,5]=>0000000
[1,5,8,7,6,2,3,4]=>1000000
[7,8,6,1,5,2,3,4]=>0000000
[2,6,4,7,5,3,8,1]=>0000000
[2,6,8,7,5,3,1,4]=>0000000
[6,4,1,7,5,2,8,3]=>0000000
[1,3,8,5,2,7,4,6]=>1000000
[1,3,8,6,7,2,4,5]=>1000000
[2,8,3,7,6,1,4,5]=>0000000
[1,3,8,7,6,2,4,5]=>1000000
[1,4,6,8,7,2,3,5]=>1000000
[7,6,4,8,5,1,3,2]=>0000000
[4,6,5,7,2,8,1,3]=>0000000
[5,3,6,7,8,1,4,2]=>0000000
[6,3,2,8,5,4,1,7]=>0000000
[4,3,5,1,2,7,6,8]=>0000101
[7,3,2,1,6,4,5,8]=>0000001
[2,8,6,1,7,4,3,5]=>0000000
[2,5,4,6,1,3,7,8]=>0000011
[2,5,6,4,1,3,7,8]=>0000011
[8,5,2,6,1,3,7,4]=>0000000
[7,1,2,6,5,4,3,8]=>0000001
[8,2,1,5,6,3,7,4]=>0000000
[2,8,5,1,6,4,7,3]=>0000000
[5,6,3,8,7,4,1,2]=>0000000
[5,2,6,8,7,4,1,3]=>0000000
[5,2,3,1,4,8,6,7]=>0000100
[5,4,1,3,2,8,6,7]=>0000100
[5,1,3,4,2,8,6,7]=>0000100
[4,2,7,3,8,5,1,6]=>0000000
[1,3,2,6,4,8,7,5]=>1010000
[1,6,2,5,3,8,7,4]=>1000000
[1,8,2,6,3,7,5,4]=>1000000
[1,8,3,6,4,7,5,2]=>1000000
[1,7,2,6,3,8,5,4]=>1000000
[1,5,2,7,4,8,6,3]=>1000000
[1,4,2,8,5,7,6,3]=>1000000
[1,5,3,8,4,7,6,2]=>1000000
[6,8,7,3,1,5,4,2]=>0000000
[2,5,8,7,4,6,3,1]=>0000000
[6,8,4,1,5,2,7,3]=>0000000
[4,8,7,5,1,6,2,3]=>0000000
[4,5,2,1,8,6,7,3]=>0000000
[2,6,7,4,1,3,8,5]=>0000000
[2,4,6,3,5,7,8,1]=>0000000
[2,3,6,1,5,7,8,4]=>0000000
[1,4,5,8,6,3,2,7]=>1000000
[5,2,6,3,1,7,8,4]=>0000000
[5,7,6,1,2,3,8,4]=>0000000
[4,3,6,2,1,8,7,5]=>0000000
[5,3,6,4,8,2,1,7]=>0000000
[3,7,4,5,1,6,2,8]=>0000001
[3,6,4,5,8,2,1,7]=>0000000
[6,1,4,5,2,8,7,3]=>0000000
[7,2,4,5,1,6,3,8]=>0000001
[7,5,4,1,6,3,2,8]=>0000001
[1,5,4,8,6,3,2,7]=>1000000
[7,5,4,8,6,3,1,2]=>0000000
[1,8,7,5,3,6,4,2]=>1000000
[8,3,7,4,1,6,2,5]=>0000000
[8,5,4,1,6,3,2,7]=>0000000
[1,7,4,2,6,5,3,8]=>1000001
[8,2,1,5,6,7,3,4]=>0000000
[6,3,1,8,4,7,2,5]=>0000000
[7,1,4,8,6,3,2,5]=>0000000
[4,1,8,5,6,7,2,3]=>0000000
[5,7,4,8,6,2,1,3]=>0000000
[5,3,6,8,2,7,1,4]=>0000000
[6,3,7,4,8,2,1,5]=>0000000
[5,3,6,1,4,7,2,8]=>0000001
[4,3,6,8,2,7,1,5]=>0000000
[5,3,7,4,8,2,1,6]=>0000000
[5,3,8,4,1,6,2,7]=>0000000
[5,3,8,1,4,7,2,6]=>0000000
[5,8,4,1,6,3,2,7]=>0000000
[7,3,8,4,1,6,2,5]=>0000000
[1,5,8,3,6,7,4,2]=>1000000
[1,8,2,5,6,7,3,4]=>1000000
[7,8,4,1,6,5,2,3]=>0000000
[6,3,8,1,5,7,2,4]=>0000000
[8,3,1,2,5,7,4,6]=>0000000
[8,1,4,2,6,5,3,7]=>0000000
[3,8,5,6,2,7,1,4]=>0000000
[2,4,5,8,7,3,1,6]=>0000000
[4,5,1,8,6,7,3,2]=>0000000
[3,4,5,8,7,1,2,6]=>0000000
[6,5,4,7,1,3,8,2]=>0000000
[6,1,4,7,2,3,8,5]=>0000000
[1,6,2,5,4,8,3,7]=>1000000
[4,1,2,7,5,8,3,6]=>0000000
[6,1,3,5,8,2,4,7]=>0000000
[5,6,4,3,1,8,2,7]=>0000000
[6,2,3,5,8,1,4,7]=>0000000
[6,7,2,3,8,4,5,1]=>0000000
[6,7,2,1,3,8,4,5]=>0000000
[5,7,4,1,8,3,2,6]=>0000000
[4,1,7,5,8,3,6,2]=>0000000
[6,7,1,3,8,4,5,2]=>0000000
[1,6,7,4,3,8,5,2]=>1000000
[6,1,7,4,2,8,5,3]=>0000000
[2,1,6,7,4,3,8,5]=>0100000
[6,7,3,2,1,8,4,5]=>0000000
[2,5,7,3,1,4,8,6]=>0000000
[6,7,3,2,8,4,5,1]=>0000000
[2,6,7,4,3,8,5,1]=>0000000
[1,2,6,7,4,3,8,5]=>1100000
[1,7,5,8,2,4,3,6]=>1000000
[2,7,1,8,4,6,3,5]=>0000000
[2,7,5,8,1,6,3,4]=>0000000
[1,6,7,3,8,5,4,2]=>1000000
[6,7,1,8,4,5,3,2]=>0000000
[8,6,1,5,4,3,2,7]=>0000000
[1,5,6,7,3,8,2,4]=>1000000
[1,6,5,4,8,3,2,7]=>1000000
[1,3,7,6,4,8,5,2]=>1000000
[3,1,8,7,6,4,2,5]=>0000000
[3,1,8,7,5,4,2,6]=>0000000
[3,1,7,6,5,4,2,8]=>0000001
[4,7,1,6,5,3,2,8]=>0000001
[4,8,1,6,5,3,2,7]=>0000000
[4,8,1,7,5,3,2,6]=>0000000
[8,4,1,7,6,3,2,5]=>0000000
[5,4,1,8,6,3,2,7]=>0000000
[5,4,1,7,6,3,2,8]=>0000001
[6,4,1,7,5,3,2,8]=>0000001
[6,4,1,8,5,3,2,7]=>0000000
[8,4,1,7,5,3,2,6]=>0000000
[7,4,1,6,5,3,2,8]=>0000001
[7,5,6,1,4,3,2,8]=>0000001
[8,5,6,1,4,3,2,7]=>0000000
[5,7,6,1,4,3,2,8]=>0000001
[5,8,6,1,4,3,2,7]=>0000000
[6,7,5,1,4,3,2,8]=>0000001
[8,7,5,1,4,3,2,6]=>0000000
[8,6,5,1,4,3,2,7]=>0000000
[1,8,6,3,4,2,5,7]=>1000000
[3,1,6,4,5,8,7,2]=>0000000
[8,2,7,6,1,4,3,5]=>0000000
[5,2,7,8,1,4,3,6]=>0000000
[5,2,3,7,1,6,8,4]=>0000000
[1,7,5,2,6,4,8,3]=>1000000
[7,1,3,6,8,2,4,5]=>0000000
[1,2,5,7,8,4,6,3]=>1100000
[3,1,2,7,5,4,8,6]=>0010000
[6,7,4,1,3,2,8,5]=>0000000
[1,7,2,8,4,3,5,6]=>1000000
[4,1,6,5,7,8,2,3]=>0000000
[1,6,3,5,7,8,2,4]=>1000000
[8,6,1,7,5,2,4,3]=>0000000
[7,6,4,1,8,3,2,5]=>0000000
[8,4,1,6,5,2,7,3]=>0000000
[1,5,3,4,7,8,2,6]=>1000000
[4,2,1,5,7,8,3,6]=>0000000
[5,1,4,6,7,8,2,3]=>0000000
[4,1,5,3,7,8,2,6]=>0000000
[8,1,4,6,5,2,7,3]=>0000000
[7,1,5,4,6,3,2,8]=>0000001
[8,2,1,6,7,5,4,3]=>0000000
[1,2,4,7,6,3,8,5]=>1100000
[6,7,4,1,8,5,2,3]=>0000000
[8,6,4,1,5,7,3,2]=>0000000
[5,2,4,3,7,1,6,8]=>0000001
[6,1,5,4,8,3,2,7]=>0000000
[1,2,8,7,4,3,6,5]=>1100000
[3,2,1,7,5,8,4,6]=>0010000
[8,1,7,6,4,2,5,3]=>0000000
[1,3,6,4,7,8,2,5]=>1000000
[5,1,3,4,7,8,2,6]=>0000000
[4,5,1,3,7,8,2,6]=>0000000
[5,2,3,1,7,8,4,6]=>0000000
[1,6,4,3,7,8,2,5]=>1000000
[7,6,4,3,1,5,2,8]=>0000001
[3,2,6,4,1,8,5,7]=>0000000
[7,5,4,6,1,3,2,8]=>0000001
[8,4,6,5,1,2,7,3]=>0000000
[1,5,6,3,7,8,2,4]=>1000000
[4,2,5,1,7,8,3,6]=>0000000
[4,7,8,1,6,5,3,2]=>0000000
[1,8,4,2,7,6,3,5]=>1000000
[3,7,2,8,1,5,4,6]=>0000000
[7,3,8,1,6,5,4,2]=>0000000
[2,4,1,8,7,3,6,5]=>0000000
[7,3,8,6,1,5,4,2]=>0000000
[3,5,1,7,8,2,6,4]=>0000000
[5,4,7,8,2,1,6,3]=>0000000
[6,4,7,1,5,3,2,8]=>0000001
[3,4,6,2,1,8,5,7]=>0000000
[5,6,4,8,3,2,1,7]=>0000000
[5,7,4,8,2,1,6,3]=>0000000
[4,7,5,8,2,1,6,3]=>0000000
[4,7,3,2,8,1,5,6]=>0000000
[7,1,2,6,3,8,5,4]=>0000000
[8,1,2,6,3,7,5,4]=>0000000
[8,1,2,7,6,3,5,4]=>0000000
[4,8,7,3,1,6,2,5]=>0000000
[4,7,8,3,1,6,2,5]=>0000000
[7,4,3,1,6,2,8,5]=>0000000
[3,7,6,2,4,8,1,5]=>0000000
[5,1,2,7,3,8,6,4]=>0000000
[6,1,2,7,3,5,8,4]=>0000000
[6,2,5,4,1,8,7,3]=>0000000
[4,6,3,2,1,8,7,5]=>0000000
[8,4,3,2,7,6,1,5]=>0000000
[1,5,8,4,7,6,3,2]=>1000000
[3,2,7,4,8,6,1,5]=>0000000
[7,4,3,2,8,6,1,5]=>0000000
[6,4,3,8,5,2,1,7]=>0000000
[8,2,5,4,7,6,1,3]=>0000000
[7,2,5,4,8,6,1,3]=>0000000
[6,2,8,7,5,4,1,3]=>0000000
[4,5,3,2,8,6,1,7]=>0000000
[3,2,5,4,8,6,1,7]=>0000000
[3,2,8,6,5,4,1,7]=>0000000
[8,4,3,6,5,2,1,7]=>0000000
[8,4,3,7,5,2,1,6]=>0000000
[3,2,7,8,5,4,1,6]=>0000000
[6,8,7,4,3,2,1,5]=>0000000
[6,3,2,1,8,7,4,5]=>0000000
[6,2,3,1,8,7,4,5]=>0000000
[3,4,8,1,7,5,6,2]=>0000000
[7,2,1,5,8,4,6,3]=>0000000
[3,7,4,1,5,8,6,2]=>0000000
[6,7,1,4,3,8,5,2]=>0000000
[8,5,3,6,1,7,4,2]=>0000000
[8,5,6,1,2,7,4,3]=>0000000
[3,6,1,5,7,8,2,4]=>0000000
[2,1,5,8,6,3,7,4]=>0100000
[3,7,8,5,4,1,6,2]=>0000000
[4,6,5,1,7,3,8,2]=>0000000
[5,7,3,1,2,4,8,6]=>0000000
[6,3,2,5,1,7,4,8]=>0000001
[6,3,1,7,2,5,8,4]=>0000000
[6,8,4,3,1,7,2,5]=>0000000
[4,8,1,3,7,5,6,2]=>0000000
[2,1,6,8,5,3,4,7]=>0100000
[4,5,1,3,8,6,7,2]=>0000000
[6,3,2,4,7,1,8,5]=>0000000
[5,7,6,3,8,1,2,4]=>0000000
[1,2,5,3,6,8,7,4]=>1100000
[7,1,5,6,2,3,8,4]=>0000000
[8,2,1,4,6,7,3,5]=>0000000
[7,2,6,1,3,4,8,5]=>0000000
[4,1,3,7,2,5,8,6]=>0000000
[6,2,7,5,1,3,8,4]=>0000000
[1,7,5,6,2,3,8,4]=>1000000
[3,7,6,1,2,4,8,5]=>0000000
[8,6,1,3,5,7,2,4]=>0000000
[1,7,4,3,8,2,5,6]=>1000000
[6,1,5,3,4,8,2,7]=>0000000
[3,6,7,5,2,8,1,4]=>0000000
[7,8,4,1,5,6,2,3]=>0000000
[5,8,1,3,6,7,2,4]=>0000000
[2,8,4,3,7,1,5,6]=>0000000
[3,8,4,6,7,1,2,5]=>0000000
[6,3,8,4,7,1,2,5]=>0000000
[1,2,5,4,8,3,6,7]=>1100000
[7,1,3,8,2,4,5,6]=>0000000
[8,1,3,7,2,4,5,6]=>0000000
[3,5,4,7,8,1,2,6]=>0000000
[8,3,1,4,7,2,5,6]=>0000000
[1,6,4,7,8,2,3,5]=>1000000
[1,3,7,8,5,6,2,4]=>1000000
[7,5,4,8,6,1,2,3]=>0000000
[8,2,6,7,5,1,3,4]=>0000000
[8,1,7,4,6,2,3,5]=>0000000
[2,5,8,4,7,1,3,6]=>0000000
[4,5,8,7,1,2,3,6]=>0000000
[4,1,8,5,7,2,3,6]=>0000000
[1,8,7,4,6,2,3,5]=>1000000
[2,6,5,4,1,8,3,7]=>0000000
[8,5,4,1,3,6,7,2]=>0000000
[8,4,7,6,5,3,1,2]=>0000000
[1,8,4,2,3,7,6,5]=>1000000
[2,3,1,8,7,6,4,5]=>0010000
[8,2,7,5,6,4,1,3]=>0000000
[1,8,4,7,6,5,2,3]=>1000000
[2,1,7,5,8,3,6,4]=>0100000
[2,6,3,5,8,7,4,1]=>0000000
[5,1,6,3,8,2,4,7]=>0000000
[4,3,5,8,2,1,6,7]=>0000000
[7,8,6,3,1,4,2,5]=>0000000
[6,5,3,7,2,4,8,1]=>0000000
[5,6,2,8,4,3,7,1]=>0000000
[4,6,2,7,8,3,5,1]=>0000000
[3,1,2,4,8,5,7,6]=>0011000
[4,6,3,5,2,8,7,1]=>0000000
[5,3,2,6,8,4,7,1]=>0000000
[5,6,3,4,8,2,7,1]=>0000000
[5,2,6,4,1,7,8,3]=>0000000
[5,8,4,6,3,2,7,1]=>0000000
[5,4,3,8,6,2,7,1]=>0000000
[5,7,8,2,4,3,6,1]=>0000000
[5,6,2,4,8,3,7,1]=>0000000
[5,4,2,8,6,3,7,1]=>0000000
[5,7,4,2,6,3,8,1]=>0000000
[6,4,7,8,2,3,5,1]=>0000000
[3,7,5,2,4,8,1,6]=>0000000
[4,7,5,2,3,8,6,1]=>0000000
[6,4,7,3,2,5,8,1]=>0000000
[6,3,7,8,2,4,5,1]=>0000000
[5,7,3,2,8,4,6,1]=>0000000
[5,3,7,2,8,4,6,1]=>0000000
[4,3,7,2,5,8,6,1]=>0000000
[4,7,3,2,5,8,6,1]=>0000000
[4,7,3,2,6,8,5,1]=>0000000
[7,5,3,2,6,4,8,1]=>0000000
[5,7,3,2,6,4,8,1]=>0000000
[5,3,2,8,6,4,7,1]=>0000000
[8,5,2,6,7,3,4,1]=>0000000
[8,4,2,6,3,7,5,1]=>0000000
[7,4,6,2,3,8,5,1]=>0000000
[7,5,6,2,8,3,4,1]=>0000000
[6,3,7,5,2,4,8,1]=>0000000
[5,7,6,2,8,3,4,1]=>0000000
[4,7,6,2,3,8,5,1]=>0000000
[7,6,3,2,5,8,1,4]=>0000000
[7,6,4,2,5,8,3,1]=>0000000
[4,8,3,7,1,6,5,2]=>0000000
[8,7,2,6,5,1,4,3]=>0000000
[5,8,3,2,1,7,6,4]=>0000000
[5,4,3,8,1,7,6,2]=>0000000
[6,5,3,8,7,1,4,2]=>0000000
[4,3,8,2,7,6,5,1]=>0000000
[4,8,2,7,6,5,3,1]=>0000000
[7,8,2,6,5,4,1,3]=>0000000
[3,8,7,6,2,5,1,4]=>0000000
[4,8,3,7,2,1,6,5]=>0000000
[8,6,3,1,7,5,4,2]=>0000000
[8,6,3,7,1,5,4,2]=>0000000
[4,8,3,7,6,2,5,1]=>0000000
[8,4,2,1,7,6,5,3]=>0000000
[1,6,4,2,5,3,7,8]=>1000011
[1,6,7,2,5,3,4,8]=>1000001
[1,8,6,2,7,3,4,5]=>1000000
[1,5,2,6,4,3,7,8]=>1000011
[1,5,2,4,6,3,7,8]=>1000011
[1,8,6,2,3,7,4,5]=>1000000
[1,5,2,8,6,3,4,7]=>1000000
[1,7,3,2,6,8,4,5]=>1000000
[1,3,6,8,2,7,4,5]=>1000000
[1,4,3,8,2,5,6,7]=>1000000
[1,7,2,3,8,5,4,6]=>1000000
[1,6,2,8,5,4,3,7]=>1000000
[1,7,2,3,8,6,4,5]=>1000000
[1,5,3,8,2,7,4,6]=>1000000
[1,7,2,5,3,4,8,6]=>1000000
[1,4,8,2,5,6,3,7]=>1000000
[1,2,7,3,6,8,4,5]=>1100000
[1,7,2,3,6,8,4,5]=>1000000
[1,4,8,3,2,5,6,7]=>1000000
[1,7,2,5,8,3,4,6]=>1000000
[1,5,6,3,4,2,7,8]=>1000011
[1,5,3,6,4,2,7,8]=>1000011
[2,5,7,4,1,3,8,6]=>0000000
[3,5,6,1,8,7,2,4]=>0000000
[2,4,6,8,7,3,1,5]=>0000000
[7,2,4,8,6,3,1,5]=>0000000
[8,5,3,6,2,1,7,4]=>0000000
[4,5,7,3,1,2,8,6]=>0000000
[4,5,1,8,3,2,7,6]=>0000000
[2,5,3,8,4,1,7,6]=>0000000
[2,6,4,5,8,1,3,7]=>0000000
[6,4,1,3,5,8,2,7]=>0000000
[3,1,6,4,8,7,5,2]=>0000000
[4,2,6,1,3,7,8,5]=>0000000
[8,5,4,2,7,6,3,1]=>0000000
[2,8,4,6,7,1,3,5]=>0000000
[5,8,2,1,4,6,7,3]=>0000000
[3,6,7,1,8,2,5,4]=>0000000
[3,1,5,7,2,8,6,4]=>0000000
[4,1,8,3,2,7,6,5]=>0000000
[3,8,2,4,7,1,6,5]=>0000000
[3,2,4,8,7,1,6,5]=>0000000
[3,2,5,7,1,8,6,4]=>0000000
[4,2,8,3,1,7,6,5]=>0000000
[4,8,2,1,3,7,6,5]=>0000000
[4,2,8,1,3,7,6,5]=>0000000
[2,3,4,6,8,7,1,5]=>0000000
[6,7,2,8,3,1,4,5]=>0000000
[6,3,7,8,4,1,2,5]=>0000000
[7,6,2,3,1,8,4,5]=>0000000
[2,3,7,8,5,4,1,6]=>0000000
[2,8,7,4,5,1,6,3]=>0000000
[1,3,8,5,2,6,7,4]=>1000000
[8,6,2,4,1,5,7,3]=>0000000
[1,6,4,3,2,7,8,5]=>1000000
[8,5,3,2,1,6,7,4]=>0000000
[8,5,3,2,1,6,4,7]=>0000000
[8,7,6,1,5,2,3,4]=>0000000
[8,7,5,1,3,6,2,4]=>0000000
[8,3,2,7,4,6,5,1]=>0000000
[7,4,8,2,6,3,1,5]=>0000000
[8,7,3,1,4,6,5,2]=>0000000
[8,7,3,1,6,2,5,4]=>0000000
[8,7,3,2,6,1,5,4]=>0000000
[1,4,8,6,7,5,3,2]=>1000000
[7,1,3,6,8,5,4,2]=>0000000
[6,7,2,5,8,1,4,3]=>0000000
[6,5,7,3,8,1,4,2]=>0000000
[6,3,7,4,8,1,5,2]=>0000000
[6,2,7,4,8,1,5,3]=>0000000
[7,2,1,5,3,8,6,4]=>0000000
[5,8,2,7,6,1,3,4]=>0000000
[4,2,3,1,5,8,6,7]=>0001100
[1,8,3,6,7,4,2,5]=>1000000
[8,1,7,2,5,6,4,3]=>0000000
[8,1,3,5,2,7,6,4]=>0000000
[8,1,7,4,3,6,5,2]=>0000000
[2,7,1,5,4,8,6,3]=>0000000
[8,6,2,4,3,7,5,1]=>0000000
[8,1,4,5,6,3,7,2]=>0000000
[8,1,4,5,6,2,7,3]=>0000000
[8,1,4,7,6,2,5,3]=>0000000
[2,5,1,7,8,6,4,3]=>0000000
[3,5,6,2,8,7,4,1]=>0000000
[3,5,6,1,8,7,4,2]=>0000000
[2,4,5,1,7,6,3,8]=>0000001
[7,3,1,5,6,4,2,8]=>0000001
[8,6,2,4,7,3,1,5]=>0000000
[8,4,7,3,5,2,1,6]=>0000000
[8,4,5,3,7,6,2,1]=>0000000
[3,4,5,6,2,8,1,7]=>0000000
[3,7,4,2,8,5,1,6]=>0000000
[7,3,4,1,6,8,2,5]=>0000000
[2,6,3,1,4,7,5,8]=>0000001
[7,2,1,6,3,4,8,5]=>0000000
[7,3,4,1,6,5,8,2]=>0000000
[3,7,4,2,5,8,6,1]=>0000000
[2,3,5,1,4,8,7,6]=>0000100
[2,7,1,3,6,8,5,4]=>0000000
[2,7,1,3,8,4,6,5]=>0000000
[3,8,7,1,6,2,5,4]=>0000000
[3,8,7,1,4,5,2,6]=>0000000
[3,7,4,2,1,8,6,5]=>0000000
[4,8,5,7,2,6,3,1]=>0000000
[8,4,5,7,3,2,6,1]=>0000000
[8,3,7,2,4,1,5,6]=>0000000
[8,6,7,2,1,4,3,5]=>0000000
[8,3,7,5,1,2,6,4]=>0000000
[7,3,4,6,2,1,5,8]=>0000001
[3,7,4,6,1,5,2,8]=>0000001
[3,4,7,6,1,2,8,5]=>0000000
[4,5,8,7,6,1,3,2]=>0000000
[8,7,3,5,6,1,4,2]=>0000000
[8,5,2,7,6,1,3,4]=>0000000
[6,4,7,2,1,5,8,3]=>0000000
[8,5,3,1,6,4,7,2]=>0000000
[7,4,8,2,6,1,5,3]=>0000000
[8,5,3,1,6,4,2,7]=>0000000
[8,7,3,1,4,2,5,6]=>0000000
[8,7,4,1,2,5,3,6]=>0000000
[1,6,7,3,2,8,4,5]=>1000000
[1,4,6,2,8,5,3,7]=>1000000
[1,5,6,2,8,4,3,7]=>1000000
[3,4,8,6,5,7,2,1]=>0000000
[2,3,8,6,7,1,5,4]=>0000000
[1,2,5,7,4,6,8,3]=>1100000
[1,2,4,7,6,8,3,5]=>1100000
[1,8,3,5,6,2,7,4]=>1000000
[4,2,5,1,6,8,7,3]=>0000000
[5,4,2,7,8,6,1,3]=>0000000
[6,7,2,8,1,3,4,5]=>0000000
[1,7,8,5,2,6,3,4]=>1000000
[7,6,2,4,8,1,5,3]=>0000000
[4,8,3,1,7,6,5,2]=>0000000
[5,3,8,7,1,6,4,2]=>0000000
[5,8,7,3,1,6,4,2]=>0000000
[5,3,8,2,1,7,6,4]=>0000000
[3,8,7,2,6,5,1,4]=>0000000
[7,4,1,8,6,5,3,2]=>0000000
[5,4,2,8,1,7,6,3]=>0000000
[5,8,4,7,1,6,3,2]=>0000000
[8,5,6,1,4,7,2,3]=>0000000
[6,7,4,1,2,5,8,3]=>0000000
[3,6,7,5,8,1,2,4]=>0000000
[6,5,8,7,4,2,3,1]=>0000000
[6,1,7,3,8,5,2,4]=>0000000
[4,6,5,8,7,3,1,2]=>0000000
[8,4,5,1,7,6,2,3]=>0000000
[8,5,6,1,7,2,4,3]=>0000000
[7,5,6,1,3,8,4,2]=>0000000
[5,7,6,1,3,8,4,2]=>0000000
[6,7,1,4,2,8,5,3]=>0000000
[2,1,6,4,8,3,7,5]=>0100000
[7,4,5,1,3,8,6,2]=>0000000
[5,8,7,4,6,2,3,1]=>0000000
[6,4,8,1,5,7,3,2]=>0000000
[2,4,7,8,5,6,1,3]=>0000000
[3,4,6,8,2,1,7,5]=>0000000
[2,8,7,1,4,3,6,5]=>0000000
[1,2,7,8,4,3,6,5]=>1100000
[2,8,5,4,1,3,7,6]=>0000000
[5,4,6,3,1,7,2,8]=>0000001
[1,4,8,3,6,5,2,7]=>1000000
[1,2,8,6,4,3,7,5]=>1100000
[6,5,1,8,7,4,3,2]=>0000000
[7,5,1,8,6,4,3,2]=>0000000
[8,5,1,7,6,4,3,2]=>0000000
[8,5,3,7,6,1,4,2]=>0000000
[3,8,7,6,1,5,4,2]=>0000000
[8,5,2,6,1,4,7,3]=>0000000
[2,7,5,8,1,4,6,3]=>0000000
[8,5,6,1,7,3,2,4]=>0000000
[3,2,6,7,1,8,5,4]=>0000000
[3,4,6,7,8,2,1,5]=>0000000
[6,7,1,3,8,5,4,2]=>0000000
[1,6,2,7,8,5,3,4]=>1000000
[1,2,6,7,8,5,3,4]=>1100000
[1,6,7,4,8,3,2,5]=>1000000
[3,7,2,1,8,4,6,5]=>0000000
[3,7,2,4,1,8,6,5]=>0000000
[3,2,6,4,8,7,5,1]=>0000000
[4,7,2,8,6,5,1,3]=>0000000
[4,7,1,8,6,5,3,2]=>0000000
[2,7,4,8,3,6,1,5]=>0000000
[4,7,3,8,6,1,5,2]=>0000000
[4,7,3,8,6,2,1,5]=>0000000
[4,3,6,8,7,2,5,1]=>0000000
[4,3,8,2,5,7,6,1]=>0000000
[4,3,8,1,5,7,6,2]=>0000000
[4,1,2,6,8,7,5,3]=>0000000
[2,4,3,6,8,7,1,5]=>0000000
[3,1,6,4,8,7,2,5]=>0000000
[4,1,6,8,7,5,2,3]=>0000000
[3,8,1,4,5,7,2,6]=>0000000
[3,8,1,4,2,5,7,6]=>0000000
[4,1,8,3,5,2,7,6]=>0000000
[4,2,3,6,8,7,1,5]=>0000000
[4,2,8,3,5,7,6,1]=>0000000
[3,8,2,4,5,7,6,1]=>0000000
[3,8,2,4,1,5,7,6]=>0000000
[3,8,2,5,1,4,7,6]=>0000000
[4,2,8,5,7,1,3,6]=>0000000
[3,8,1,5,2,4,7,6]=>0000000
[7,3,2,1,4,6,5,8]=>0000001
[2,7,1,3,5,6,8,4]=>0000000
[2,3,6,1,5,8,7,4]=>0000000
[4,5,2,3,8,6,7,1]=>0000000
[4,8,5,3,2,6,7,1]=>0000000
[6,4,1,8,5,2,7,3]=>0000000
[2,6,1,8,5,4,7,3]=>0000000
[3,1,6,8,5,4,7,2]=>0000000
[7,5,6,1,2,3,8,4]=>0000000
[1,5,7,6,3,2,8,4]=>1000000
[7,5,2,1,4,3,8,6]=>0000000
[3,1,7,8,5,4,2,6]=>0000000
[7,6,4,8,3,1,2,5]=>0000000
[6,2,8,5,1,3,4,7]=>0000000
[3,2,7,8,6,1,4,5]=>0000000
[6,8,2,5,1,3,7,4]=>0000000
[6,7,4,2,1,5,3,8]=>0000001
[5,7,4,1,6,8,2,3]=>0000000
[5,6,8,1,3,7,2,4]=>0000000
[3,7,4,8,6,1,2,5]=>0000000
[1,6,8,5,3,2,4,7]=>1000000
[7,2,8,4,6,1,3,5]=>0000000
[7,1,3,4,6,2,8,5]=>0000000
[5,8,7,4,2,1,3,6]=>0000000
[1,8,7,3,2,5,4,6]=>1000000
[1,2,5,4,8,7,3,6]=>1100000
[1,2,4,8,6,3,5,7]=>1100000
[1,7,3,4,2,6,8,5]=>1000000
[1,6,3,5,8,4,2,7]=>1000000
[1,8,5,7,6,3,2,4]=>1000000
[1,6,3,5,7,8,4,2]=>1000000
[7,6,2,5,3,4,1,8]=>0000001
[7,6,2,4,5,3,1,8]=>0000001
[7,6,2,4,3,5,1,8]=>0000001
[7,6,2,3,5,4,1,8]=>0000001
[8,4,2,7,1,6,3,5]=>0000000
[8,7,6,1,5,3,2,4]=>0000000
[8,7,6,1,3,5,4,2]=>0000000
[8,7,6,1,5,4,2,3]=>0000000
[4,5,3,8,2,1,6,7]=>0000000
[7,5,8,2,1,4,3,6]=>0000000
[8,7,6,1,2,5,3,4]=>0000000
[8,7,6,1,2,5,4,3]=>0000000
[8,7,6,1,4,2,5,3]=>0000000
[6,1,4,8,5,2,7,3]=>0000000
[3,1,6,8,5,2,7,4]=>0000000
[5,8,2,7,3,4,1,6]=>0000000
[5,3,8,1,6,7,4,2]=>0000000
[4,8,2,1,3,5,6,7]=>0000000
[5,1,8,3,6,7,4,2]=>0000000
[8,4,1,6,5,2,3,7]=>0000000
[6,8,7,3,2,4,1,5]=>0000000
[3,2,4,7,5,8,1,6]=>0000000
[1,2,7,4,6,3,8,5]=>1100000
[2,8,7,6,4,5,1,3]=>0000000
[3,5,7,6,1,8,4,2]=>0000000
[3,5,7,6,2,8,4,1]=>0000000
[5,3,6,2,8,7,4,1]=>0000000
[5,8,3,1,7,6,4,2]=>0000000
[6,2,3,8,7,5,4,1]=>0000000
[4,1,3,5,8,7,6,2]=>0000000
[4,2,5,3,7,6,1,8]=>0000001
[6,2,4,3,7,5,1,8]=>0000001
[1,3,6,4,7,5,2,8]=>1000001
[8,2,5,3,6,4,1,7]=>0000000
[7,2,5,3,6,4,1,8]=>0000001
[6,2,5,3,7,4,1,8]=>0000001
[4,2,6,3,7,5,1,8]=>0000001
[5,2,7,3,6,4,1,8]=>0000001
[7,3,6,2,5,4,1,8]=>0000001
[6,3,8,2,5,4,1,7]=>0000000
[7,3,1,4,6,5,2,8]=>0000001
[8,3,7,2,5,4,1,6]=>0000000
[5,2,8,3,6,4,1,7]=>0000000
[4,2,8,3,6,5,1,7]=>0000000
[3,2,8,4,6,5,1,7]=>0000000
[1,4,7,3,6,5,2,8]=>1000001
[8,2,5,4,1,6,3,7]=>0000000
[1,3,6,5,2,7,4,8]=>1000001
[8,2,6,4,1,5,3,7]=>0000000
[1,4,8,3,7,5,2,6]=>1000000
[6,2,1,4,8,5,3,7]=>0000000
[5,2,1,4,8,6,3,7]=>0000000
[3,2,1,5,8,6,4,7]=>0010000
[4,2,8,3,7,5,1,6]=>0000000
[5,2,8,3,7,4,1,6]=>0000000
[8,3,7,2,6,4,1,5]=>0000000
[7,3,1,4,8,5,2,6]=>0000000
[1,3,7,4,8,5,2,6]=>1000000
[8,2,6,3,7,4,1,5]=>0000000
[7,2,6,3,8,4,1,5]=>0000000
[5,2,7,3,8,4,1,6]=>0000000
[3,2,7,4,8,5,1,6]=>0000000
[5,2,6,3,8,4,1,7]=>0000000
[6,2,5,3,8,4,1,7]=>0000000
[7,2,5,3,8,4,1,6]=>0000000
[8,2,5,3,7,4,1,6]=>0000000
[1,3,6,4,8,5,2,7]=>1000000
[1,3,5,4,8,6,2,7]=>1000000
[8,2,4,3,7,5,1,6]=>0000000
[7,2,4,3,8,5,1,6]=>0000000
[6,2,4,3,8,5,1,7]=>0000000
[5,2,4,3,8,6,1,7]=>0000000
[4,2,5,3,8,6,1,7]=>0000000
[4,2,5,3,1,7,6,8]=>0000101
[6,2,4,3,1,7,5,8]=>0000001
[7,2,4,3,1,6,5,8]=>0000001
[8,5,1,3,6,4,2,7]=>0000000
[8,4,1,3,6,5,2,7]=>0000000
[1,5,2,4,7,6,3,8]=>1000001
[7,2,5,3,1,6,4,8]=>0000001
[6,2,5,3,1,7,4,8]=>0000001
[4,2,6,3,1,7,5,8]=>0000001
[3,2,6,4,1,7,5,8]=>0000001
[5,2,7,3,1,6,4,8]=>0000001
[6,2,7,3,1,5,4,8]=>0000001
[7,2,6,3,1,5,4,8]=>0000001
[1,5,2,4,8,6,3,7]=>1000000
[8,4,1,3,7,5,2,6]=>0000000
[6,2,1,5,3,7,4,8]=>0000001
[3,2,1,6,4,7,5,8]=>0010001
[3,2,8,5,1,6,4,7]=>0000000
[4,2,8,5,1,6,3,7]=>0000000
[6,2,8,4,1,5,3,7]=>0000000
[1,4,8,5,2,6,3,7]=>1000000
[8,3,7,4,1,5,2,6]=>0000000
[7,1,3,2,5,6,4,8]=>0000001
[1,5,2,8,7,4,3,6]=>1000000
[5,7,2,8,1,4,3,6]=>0000000
[2,7,1,5,6,4,3,8]=>0000001
[1,7,3,4,5,2,8,6]=>1000000
[3,2,1,7,8,5,4,6]=>0010000
[1,7,6,3,2,4,8,5]=>1000000
[1,8,5,3,2,4,7,6]=>1000000
[2,6,1,5,4,7,3,8]=>0000001
[1,3,8,5,4,2,6,7]=>1000000
[2,3,6,8,4,1,7,5]=>0000000
[1,7,2,8,6,3,5,4]=>1000000
[4,2,7,6,1,8,5,3]=>0000000
[7,3,2,1,6,4,8,5]=>0000000
[6,7,2,4,3,5,8,1]=>0000000
[4,3,8,2,1,5,7,6]=>0000000
[4,3,2,8,1,6,7,5]=>0000000
[4,5,8,3,2,7,1,6]=>0000000
[4,3,8,2,1,6,7,5]=>0000000
[4,6,7,2,5,3,8,1]=>0000000
[6,4,7,8,3,1,5,2]=>0000000
[5,6,7,1,8,3,4,2]=>0000000
[7,1,8,6,2,5,4,3]=>0000000
[1,5,8,2,6,4,7,3]=>1000000
[1,5,7,4,6,8,3,2]=>1000000
[3,1,8,6,5,2,7,4]=>0000000
[2,3,7,6,5,8,1,4]=>0000000
[2,3,7,6,5,1,8,4]=>0000000
[7,3,5,2,1,6,8,4]=>0000000
[1,5,4,7,8,6,2,3]=>1000000
[3,6,2,1,4,7,8,5]=>0000000
[6,3,8,7,5,4,2,1]=>0000000
[6,8,2,7,5,4,3,1]=>0000000
[5,8,1,7,6,4,3,2]=>0000000
[4,2,6,3,8,5,7,1]=>0000000
[8,2,7,4,5,1,6,3]=>0000000
[1,7,5,2,4,8,6,3]=>1000000
[7,2,8,5,3,1,6,4]=>0000000
[4,7,6,1,5,8,3,2]=>0000000
[5,4,7,3,8,2,1,6]=>0000000
[4,3,5,7,2,6,1,8]=>0000001
[1,7,2,8,5,4,3,6]=>1000000
[5,4,8,3,6,2,1,7]=>0000000
[4,7,3,2,5,1,6,8]=>0000001
[4,2,5,3,8,7,1,6]=>0000000
[6,7,3,2,5,4,1,8]=>0000001
[4,5,6,2,7,3,1,8]=>0000001
[7,4,8,6,5,1,2,3]=>0000000
[4,5,8,2,7,3,1,6]=>0000000
[6,5,8,2,7,3,1,4]=>0000000
[6,4,8,2,7,3,1,5]=>0000000
[7,8,1,3,6,4,2,5]=>0000000
[4,5,7,8,3,2,1,6]=>0000000
[5,3,7,2,1,8,6,4]=>0000000
[5,4,3,7,2,1,6,8]=>0000001
[5,4,3,7,8,2,1,6]=>0000000
[6,1,3,5,8,7,4,2]=>0000000
[6,8,5,7,3,4,2,1]=>0000000
[5,3,6,8,4,2,1,7]=>0000000
[5,1,6,8,4,7,3,2]=>0000000
[6,2,8,3,4,1,5,7]=>0000000
[2,4,1,8,7,6,3,5]=>0000000
[1,3,5,8,4,7,2,6]=>1000000
[2,3,8,7,5,1,6,4]=>0000000
[8,5,4,7,6,1,3,2]=>0000000
[5,8,7,2,4,1,3,6]=>0000000
[4,1,3,5,6,2,8,7]=>0000010
[6,3,8,5,1,7,4,2]=>0000000
[5,2,4,6,1,3,8,7]=>0000010
[8,2,4,6,1,3,7,5]=>0000000
[6,4,8,7,3,5,2,1]=>0000000
[8,2,3,5,6,1,4,7]=>0000000
[4,3,5,6,8,2,7,1]=>0000000
[8,2,3,4,6,1,7,5]=>0000000
[1,7,4,3,5,2,8,6]=>1000000
[2,7,4,3,8,1,5,6]=>0000000
[5,3,6,2,1,8,4,7]=>0000000
[4,3,8,6,2,7,1,5]=>0000000
[8,2,1,4,6,3,7,5]=>0000000
[3,1,6,8,2,7,5,4]=>0000000
[5,3,8,6,7,2,1,4]=>0000000
[5,8,7,2,4,6,1,3]=>0000000
[1,5,2,8,7,6,4,3]=>1000000
[2,7,1,4,6,5,3,8]=>0000001
[4,7,1,2,6,5,8,3]=>0000000
[3,2,4,5,1,8,6,7]=>0000100
[4,2,5,6,8,7,3,1]=>0000000
[8,2,5,1,6,3,7,4]=>0000000
[8,3,4,5,1,6,7,2]=>0000000
[3,5,7,6,4,8,1,2]=>0000000
[1,3,7,8,5,4,6,2]=>1000000
[7,2,8,6,5,1,4,3]=>0000000
[4,2,7,5,3,1,8,6]=>0000000
[7,3,2,5,4,1,8,6]=>0000000
[3,6,4,1,8,2,7,5]=>0000000
[4,6,3,8,7,2,1,5]=>0000000
[4,3,5,1,8,7,2,6]=>0000000
[7,5,2,8,4,3,1,6]=>0000000
[1,7,2,4,5,3,6,8]=>1000001
[1,7,4,5,3,2,6,8]=>1000001
[1,6,4,7,3,5,2,8]=>1000001
[8,3,5,6,1,4,7,2]=>0000000
[1,6,4,7,5,2,3,8]=>1000001
[1,5,2,6,7,4,3,8]=>1000001
[8,5,6,1,4,3,7,2]=>0000000
[5,4,7,8,3,1,2,6]=>0000000
[2,5,4,7,8,3,1,6]=>0000000
[6,4,5,8,2,3,1,7]=>0000000
[8,6,1,3,2,5,7,4]=>0000000
[7,5,8,1,4,6,3,2]=>0000000
[4,2,6,7,8,1,5,3]=>0000000
[3,4,6,7,8,1,5,2]=>0000000
[4,3,2,7,5,8,1,6]=>0000000
[4,8,5,3,2,6,1,7]=>0000000
[2,8,4,5,3,6,1,7]=>0000000
[8,1,5,3,2,4,7,6]=>0000000
[8,1,2,4,5,3,7,6]=>0000000
[8,1,4,5,3,2,7,6]=>0000000
[7,8,4,1,3,6,5,2]=>0000000
[8,6,1,3,2,7,4,5]=>0000000
[7,3,8,2,4,1,6,5]=>0000000
[6,2,3,7,8,1,5,4]=>0000000
[6,3,7,8,1,5,4,2]=>0000000
[2,6,3,7,8,1,5,4]=>0000000
[7,5,8,1,6,4,2,3]=>0000000
[1,3,6,4,2,5,7,8]=>1000011
[1,7,6,4,2,3,5,8]=>1000001
[1,2,3,7,6,4,5,8]=>1110001
[1,3,2,5,8,6,4,7]=>1010000
[4,8,2,7,1,3,6,5]=>0000000
[7,1,8,4,6,3,5,2]=>0000000
[4,1,5,2,3,8,7,6]=>0000100
[2,8,7,1,4,6,3,5]=>0000000
[3,1,2,8,5,7,4,6]=>0010000
[2,1,8,6,3,7,5,4]=>0100000
[1,6,5,3,2,4,7,8]=>1000011
[1,7,2,4,6,5,3,8]=>1000001
[1,4,7,2,6,5,3,8]=>1000001
[1,3,7,2,4,6,5,8]=>1000001
[1,7,2,6,4,3,5,8]=>1000001
[1,2,6,8,7,4,3,5]=>1100000
[1,2,7,4,3,5,8,6]=>1100000
[1,8,6,3,5,2,7,4]=>1000000
[1,6,2,8,7,4,3,5]=>1000000
[1,3,8,7,5,4,6,2]=>1000000
[1,2,8,6,3,5,7,4]=>1100000
[1,8,5,2,3,6,4,7]=>1000000
[1,7,4,8,5,2,3,6]=>1000000
[1,4,7,5,8,6,3,2]=>1000000
[1,4,7,5,2,8,6,3]=>1000000
[1,6,3,7,4,2,8,5]=>1000000
[1,8,5,2,7,4,3,6]=>1000000
[1,4,8,6,3,2,7,5]=>1000000
[1,4,8,7,5,3,2,6]=>1000000
[1,2,5,8,6,3,7,4]=>1100000
[1,2,4,7,5,8,6,3]=>1100000
[1,3,5,8,7,6,2,4]=>1000000
[1,5,2,4,3,6,8,7]=>1000110
[1,6,8,7,5,3,2,4]=>1000000
[1,2,5,7,4,3,8,6]=>1100000
[1,5,3,2,6,8,7,4]=>1000000
[1,4,2,6,8,7,5,3]=>1000000
[1,5,8,6,3,2,7,4]=>1000000
[1,8,5,2,6,3,4,7]=>1000000
[1,7,4,6,3,2,8,5]=>1000000
[1,6,3,2,8,5,4,7]=>1000000
[1,4,2,8,6,3,5,7]=>1000000
[1,3,8,6,4,2,5,7]=>1000000
[1,5,7,4,2,3,8,6]=>1000000
[8,2,7,3,1,5,4,6]=>0000000
[8,4,7,2,5,3,1,6]=>0000000
[8,6,1,4,7,3,5,2]=>0000000
[5,3,6,7,2,8,4,1]=>0000000
[1,3,8,2,5,6,7,4]=>1000000
[5,1,7,4,3,6,8,2]=>0000000
[7,1,3,6,5,2,8,4]=>0000000
[6,1,8,5,2,7,3,4]=>0000000
[5,4,1,3,7,2,8,6]=>0000000
[3,1,8,7,5,2,4,6]=>0000000
[6,5,8,7,2,4,3,1]=>0000000
[4,3,6,5,8,2,1,7]=>0000000
[4,7,3,1,8,5,2,6]=>0000000
[5,1,7,8,6,2,3,4]=>0000000
[8,5,1,6,7,2,3,4]=>0000000
[1,8,3,6,4,5,7,2]=>1000000
[8,1,6,4,2,3,5,7]=>0000000
[7,1,8,2,5,3,4,6]=>0000000
[5,1,7,2,6,3,4,8]=>0000001
[1,6,3,8,4,5,7,2]=>1000000
[2,7,4,3,8,5,1,6]=>0000000
[2,4,7,3,5,1,6,8]=>0000001
[2,4,8,6,3,5,1,7]=>0000000
[2,3,7,5,4,1,6,8]=>0000001
[3,4,6,2,1,5,8,7]=>0000010
[2,3,6,1,5,8,4,7]=>0000000
[2,3,7,1,6,5,8,4]=>0000000
[2,4,7,1,3,6,8,5]=>0000000
[5,4,7,8,1,3,2,6]=>0000000
[2,5,7,1,4,6,3,8]=>0000001
[2,4,7,1,6,3,5,8]=>0000001
[2,3,7,1,6,5,4,8]=>0000001
[2,5,7,1,4,3,6,8]=>0000001
[2,5,7,3,1,4,6,8]=>0000001
[3,4,7,2,1,6,8,5]=>0000000
[5,7,3,2,8,1,4,6]=>0000000
[5,4,7,8,1,3,6,2]=>0000000
[2,5,7,1,4,6,8,3]=>0000000
[2,4,7,1,6,3,8,5]=>0000000
[2,4,7,1,6,8,3,5]=>0000000
[8,7,5,1,4,2,3,6]=>0000000
[6,8,3,2,4,5,1,7]=>0000000
[3,8,5,2,4,6,1,7]=>0000000
[8,2,4,5,3,1,6,7]=>0000000
[4,8,2,5,3,1,6,7]=>0000000
[4,3,7,5,2,1,6,8]=>0000001
[1,6,7,4,3,2,5,8]=>1000001
[1,4,5,7,3,2,6,8]=>1000001
[3,5,1,4,7,2,6,8]=>0000001
[2,5,4,7,8,1,3,6]=>0000000
[2,5,1,4,7,8,3,6]=>0000000
[4,3,7,1,5,2,6,8]=>0000001
[3,5,1,6,4,2,7,8]=>0000011
[6,4,3,1,7,2,5,8]=>0000001
[6,2,7,4,3,1,5,8]=>0000001
[2,6,4,1,7,3,5,8]=>0000001
[6,3,2,7,4,5,1,8]=>0000001
[7,2,4,1,3,6,8,5]=>0000000
[6,3,2,5,7,1,4,8]=>0000001
[3,2,6,5,7,1,4,8]=>0000001
[1,7,3,2,5,6,4,8]=>1000001
[2,1,7,3,5,6,8,4]=>0100000
[2,1,6,3,5,7,8,4]=>0100000
[1,6,3,2,5,7,4,8]=>1000001
[5,6,2,1,4,3,7,8]=>0000011
[2,5,1,6,4,3,7,8]=>0000011
[2,5,4,1,6,3,7,8]=>0000011
[4,6,1,5,2,7,3,8]=>0000001
[1,6,5,3,7,2,4,8]=>1000001
[2,6,1,8,5,4,3,7]=>0000000
[4,5,8,6,2,1,3,7]=>0000000
[4,2,8,5,3,6,1,7]=>0000000
[5,6,3,2,8,1,7,4]=>0000000
[8,2,6,3,1,5,7,4]=>0000000
[8,2,5,3,4,7,6,1]=>0000000
[7,5,3,2,4,1,8,6]=>0000000
[6,5,3,2,4,8,1,7]=>0000000
[3,1,8,4,6,5,7,2]=>0000000
[3,4,7,5,8,2,6,1]=>0000000
[8,7,1,4,6,5,2,3]=>0000000
[8,3,7,6,4,5,1,2]=>0000000
[5,3,8,6,4,1,7,2]=>0000000
[6,4,7,1,8,5,2,3]=>0000000
[3,8,2,5,1,7,4,6]=>0000000
[8,6,4,1,7,3,2,5]=>0000000
[3,4,7,8,5,1,2,6]=>0000000
[5,7,2,4,3,6,8,1]=>0000000
[4,7,3,2,5,6,8,1]=>0000000
[3,2,7,6,4,5,8,1]=>0000000
[1,7,3,6,8,4,2,5]=>1000000
[8,3,1,2,6,4,7,5]=>0000000
[1,7,8,2,4,3,5,6]=>1000000
[3,6,4,7,1,2,8,5]=>0000000
[2,4,7,8,5,1,3,6]=>0000000
[5,7,4,8,1,3,2,6]=>0000000
[4,3,7,8,1,5,2,6]=>0000000
[8,5,4,2,6,1,7,3]=>0000000
[3,2,6,8,7,4,1,5]=>0000000
[2,3,7,5,1,8,6,4]=>0000000
[6,3,1,2,8,7,4,5]=>0000000
[5,2,1,3,8,7,6,4]=>0000000
[7,2,1,5,3,8,4,6]=>0000000
[1,5,8,2,4,3,6,7]=>1000000
[4,3,6,8,1,5,2,7]=>0000000
[2,4,6,8,5,1,3,7]=>0000000
[1,6,8,2,4,3,5,7]=>1000000
[5,4,6,8,3,1,7,2]=>0000000
[8,6,1,7,2,4,3,5]=>0000000
[7,3,1,2,8,6,4,5]=>0000000
[2,3,7,6,1,8,5,4]=>0000000
[3,2,7,8,6,4,1,5]=>0000000
[6,2,8,3,1,4,7,5]=>0000000
[3,1,2,8,7,4,5,6]=>0010000
[2,1,3,8,7,4,6,5]=>0110000
[2,1,3,8,7,4,5,6]=>0110000
[8,5,1,7,2,4,3,6]=>0000000
[8,3,1,6,2,7,5,4]=>0000000
[1,3,2,8,7,6,4,5]=>1010000
[2,1,3,8,7,6,4,5]=>0110000
[3,5,8,2,4,1,7,6]=>0000000
[1,3,6,8,5,4,2,7]=>1000000
[1,4,2,5,7,6,3,8]=>1000001
[1,4,2,6,8,5,3,7]=>1000000
[1,5,3,2,6,8,4,7]=>1000000
[1,5,4,2,3,6,8,7]=>1000110
[1,6,8,3,5,4,2,7]=>1000000
[1,5,3,2,4,6,8,7]=>1000110
[1,5,8,7,6,3,2,4]=>1000000
[1,5,7,6,3,2,4,8]=>1000001
[1,6,3,2,4,7,5,8]=>1000001
[1,6,3,2,4,8,7,5]=>1000000
[1,2,7,6,4,3,5,8]=>1100001
[1,8,7,5,2,4,6,3]=>1000000
[1,7,5,2,4,6,3,8]=>1000001
[1,7,4,2,5,3,6,8]=>1000001
[1,8,4,7,5,2,6,3]=>1000000
[1,7,5,2,3,6,4,8]=>1000001
[1,7,5,2,6,3,4,8]=>1000001
[1,6,3,7,4,2,5,8]=>1000001
[1,6,3,2,7,5,4,8]=>1000001
[1,4,8,7,5,2,6,3]=>1000000
[1,4,7,5,2,6,3,8]=>1000001
[1,3,6,4,8,7,5,2]=>1000000
[1,3,7,6,4,2,5,8]=>1000001
[1,3,8,7,5,2,4,6]=>1000000
[1,4,6,3,2,7,5,8]=>1000001
[1,4,6,3,2,8,7,5]=>1000000
[1,5,7,6,4,2,3,8]=>1000001
[1,2,6,4,7,5,3,8]=>1100001
[1,6,3,2,8,4,7,5]=>1000000
[1,5,2,7,4,3,6,8]=>1000001
[1,6,3,5,2,7,4,8]=>1000001
[1,6,3,5,2,8,7,4]=>1000000
[1,8,3,7,5,2,4,6]=>1000000
[1,8,4,6,3,2,7,5]=>1000000
[3,2,1,4,8,5,7,6]=>0011000
[7,4,1,6,2,5,3,8]=>0000001
[5,4,1,8,2,6,3,7]=>0000000
[5,4,1,6,2,8,3,7]=>0000000
[2,8,6,4,5,1,7,3]=>0000000
[2,8,3,1,4,5,7,6]=>0000000
[6,1,7,2,8,4,5,3]=>0000000
[8,3,2,1,5,6,7,4]=>0000000
[7,2,8,1,4,5,6,3]=>0000000
[5,1,7,3,8,6,2,4]=>0000000
[3,2,5,8,7,4,1,6]=>0000000
[4,2,5,8,7,3,1,6]=>0000000
[8,3,4,1,6,5,2,7]=>0000000
[3,4,8,5,7,2,1,6]=>0000000
[3,6,4,8,5,7,2,1]=>0000000
[5,8,4,7,3,6,2,1]=>0000000
[4,2,8,7,3,1,6,5]=>0000000
[6,5,8,2,1,7,4,3]=>0000000
[6,1,4,3,8,7,2,5]=>0000000
[5,1,3,2,6,8,7,4]=>0000000
[6,1,3,8,7,2,4,5]=>0000000
[1,2,8,4,5,7,3,6]=>1100000
[4,2,1,8,7,6,3,5]=>0000000
[3,2,5,8,7,1,4,6]=>0000000
[5,6,3,8,7,2,1,4]=>0000000
[2,5,8,4,7,1,6,3]=>0000000
[1,6,2,4,8,5,7,3]=>1000000
[3,1,6,5,8,7,2,4]=>0000000
[4,8,5,3,6,7,1,2]=>0000000
[1,8,5,3,4,7,6,2]=>1000000
[1,4,6,2,5,3,7,8]=>1000011
[4,3,6,5,1,2,7,8]=>0000011
[1,3,8,7,6,5,2,4]=>1000000
[1,8,7,2,6,3,5,4]=>1000000
[2,8,7,1,6,3,4,5]=>0000000
[1,3,7,5,4,8,6,2]=>1000000
[1,5,6,3,8,4,2,7]=>1000000
[2,6,5,3,8,4,1,7]=>0000000
[2,3,6,5,4,8,1,7]=>0000000
[2,7,5,1,8,4,6,3]=>0000000
[1,7,6,4,8,2,5,3]=>1000000
[6,3,8,7,2,4,5,1]=>0000000
[2,4,3,8,7,1,6,5]=>0000000
[8,3,7,2,1,6,5,4]=>0000000
[8,4,7,3,6,2,1,5]=>0000000
[3,8,7,5,6,4,1,2]=>0000000
[3,8,7,5,6,2,1,4]=>0000000
[3,8,7,5,6,2,4,1]=>0000000
[2,8,7,5,6,4,1,3]=>0000000
[3,6,2,4,8,7,1,5]=>0000000
[1,5,6,3,8,2,7,4]=>1000000
[2,6,3,8,4,7,1,5]=>0000000
[2,6,3,5,7,8,1,4]=>0000000
[1,5,6,3,7,2,8,4]=>1000000
[1,7,5,3,6,2,8,4]=>1000000
[1,5,7,3,4,2,8,6]=>1000000
[1,5,8,3,4,2,7,6]=>1000000
[1,4,5,3,8,2,7,6]=>1000000
[6,5,1,4,2,7,8,3]=>0000000
[6,5,1,4,2,8,7,3]=>0000000
[1,7,5,4,2,8,6,3]=>1000000
[1,4,8,2,6,5,3,7]=>1000000
[7,5,1,8,3,4,2,6]=>0000000
[1,2,5,6,8,7,3,4]=>1100000
[2,6,7,3,4,1,8,5]=>0000000
[1,3,7,2,6,4,8,5]=>1000000
[7,6,1,2,3,5,4,8]=>0000001
[6,1,3,4,2,5,7,8]=>0000011
[5,3,8,2,4,6,1,7]=>0000000
[4,1,5,6,3,2,7,8]=>0000011
[4,5,8,3,2,6,1,7]=>0000000
[5,8,2,1,4,6,3,7]=>0000000
[4,1,5,8,3,6,2,7]=>0000000
[4,5,8,3,6,1,2,7]=>0000000
[1,6,3,4,7,8,5,2]=>1000000
[8,1,3,4,2,6,5,7]=>0000000
[4,7,8,5,2,3,1,6]=>0000000
[4,1,5,8,6,2,3,7]=>0000000
[5,8,2,1,6,3,4,7]=>0000000
[2,6,7,8,4,1,3,5]=>0000000
[2,6,7,8,4,3,1,5]=>0000000
[1,7,8,5,4,2,3,6]=>1000000
[3,6,4,5,2,8,1,7]=>0000000
[8,1,5,4,7,6,3,2]=>0000000
[2,5,1,4,6,7,3,8]=>0000001
[8,6,3,5,4,1,2,7]=>0000000
[8,2,6,5,4,1,3,7]=>0000000
[8,2,6,5,4,3,1,7]=>0000000
[8,3,2,6,1,5,4,7]=>0000000
[8,1,6,5,4,3,2,7]=>0000000
[4,8,1,7,6,3,5,2]=>0000000
[8,5,1,7,4,3,6,2]=>0000000
[8,5,7,6,2,1,3,4]=>0000000
[5,4,8,3,1,7,2,6]=>0000000
[5,1,4,8,3,2,7,6]=>0000000
[4,8,1,7,6,5,2,3]=>0000000
[4,3,8,7,2,6,1,5]=>0000000
[3,8,7,2,6,4,1,5]=>0000000
[8,2,7,6,4,1,5,3]=>0000000
[4,3,8,7,2,6,5,1]=>0000000
[8,2,5,7,4,3,6,1]=>0000000
[3,8,7,4,6,1,2,5]=>0000000
[8,3,7,5,4,1,6,2]=>0000000
[2,8,4,7,6,1,5,3]=>0000000
[2,5,4,8,3,1,7,6]=>0000000
[5,4,8,2,1,3,7,6]=>0000000
[3,8,7,2,6,1,5,4]=>0000000
[1,8,4,7,6,3,5,2]=>1000000
[1,8,3,7,6,5,2,4]=>1000000
[1,4,3,8,7,2,6,5]=>1000000
[8,1,2,7,6,5,4,3]=>0000000
[7,8,1,3,6,4,5,2]=>0000000
[7,2,6,8,4,5,3,1]=>0000000
[7,3,6,8,5,1,4,2]=>0000000
[7,5,8,1,6,2,4,3]=>0000000
[5,7,8,1,6,3,2,4]=>0000000
[7,2,6,8,5,1,4,3]=>0000000
[6,7,8,3,5,4,2,1]=>0000000
[6,7,8,4,2,1,5,3]=>0000000
[7,2,6,8,4,3,1,5]=>0000000
[7,5,2,4,8,3,1,6]=>0000000
[5,6,2,4,3,8,1,7]=>0000000
[7,8,3,1,6,2,5,4]=>0000000
[6,7,8,4,3,1,5,2]=>0000000
[7,8,2,6,3,5,4,1]=>0000000
[7,8,3,6,4,1,5,2]=>0000000
[6,1,5,2,4,8,3,7]=>0000000
[1,5,6,3,8,2,4,7]=>1000000
[7,3,8,1,6,4,5,2]=>0000000
[7,2,6,8,4,3,5,1]=>0000000
[7,5,2,4,8,3,6,1]=>0000000
[1,7,5,8,2,4,6,3]=>1000000
[7,5,2,8,1,4,6,3]=>0000000
[3,7,8,2,6,5,1,4]=>0000000
[3,7,8,2,1,6,4,5]=>0000000
[7,2,8,1,6,4,3,5]=>0000000
[7,8,1,6,3,5,4,2]=>0000000
[6,7,8,3,2,5,4,1]=>0000000
[6,7,8,2,5,4,3,1]=>0000000
[6,7,8,3,1,5,4,2]=>0000000
[7,8,1,6,2,5,4,3]=>0000000
[5,6,1,4,3,8,2,7]=>0000000
[1,6,4,5,2,7,3,8]=>1000001
[6,2,1,5,7,3,4,8]=>0000001
[1,6,7,4,2,8,3,5]=>1000000
[1,4,7,2,3,6,8,5]=>1000000
[3,1,2,6,7,8,5,4]=>0010000
[1,6,3,4,7,8,2,5]=>1000000
[3,1,5,7,6,2,8,4]=>0000000
[6,3,1,4,2,7,8,5]=>0000000
[2,4,3,7,6,1,8,5]=>0000000
[3,1,6,5,2,8,7,4]=>0000000
[3,1,7,6,5,2,8,4]=>0000000
[1,4,7,6,8,3,2,5]=>1000000
[7,2,1,5,6,3,8,4]=>0000000
[4,3,1,8,6,2,7,5]=>0000000
[3,1,5,2,8,7,6,4]=>0000000
[1,2,8,4,3,7,6,5]=>1100000
[1,8,5,4,2,7,3,6]=>1000000
[3,1,8,5,4,7,2,6]=>0000000
[2,6,1,8,7,4,3,5]=>0000000
[7,5,1,8,3,2,6,4]=>0000000
[4,7,6,3,1,8,2,5]=>0000000
[5,3,1,8,6,2,4,7]=>0000000
[5,1,8,6,3,2,4,7]=>0000000
[1,5,4,2,8,6,3,7]=>1000000
[8,3,1,6,4,2,5,7]=>0000000
[3,6,7,1,8,4,2,5]=>0000000
[1,7,4,8,3,5,2,6]=>1000000
[7,3,2,4,8,5,1,6]=>0000000
[6,3,4,7,1,8,5,2]=>0000000
[5,7,8,1,4,2,6,3]=>0000000
[5,7,1,2,3,8,6,4]=>0000000
[7,2,8,1,4,3,6,5]=>0000000
[2,6,3,8,1,7,5,4]=>0000000
[1,8,3,6,4,7,2,5]=>1000000
[2,8,6,4,1,7,3,5]=>0000000
[1,8,4,2,7,5,3,6]=>1000000
[6,5,1,7,2,8,4,3]=>0000000
[2,8,1,7,5,3,6,4]=>0000000
[1,2,8,7,6,4,3,5]=>1100000
[1,6,5,8,7,4,2,3]=>1000000
[4,3,5,7,1,6,2,8]=>0000001
[4,2,8,5,3,6,7,1]=>0000000
[4,1,8,5,3,6,2,7]=>0000000
[6,4,2,5,3,1,7,8]=>0000011
[3,1,5,8,2,7,4,6]=>0000000
[6,4,1,5,3,2,7,8]=>0000011
[6,2,1,5,4,3,7,8]=>0000011
[3,1,8,5,4,6,2,7]=>0000000
[6,2,8,4,5,3,7,1]=>0000000
[6,1,8,4,5,3,2,7]=>0000000
[4,5,2,7,1,6,3,8]=>0000001
[4,3,5,7,1,6,8,2]=>0000000
[4,1,8,5,3,6,7,2]=>0000000
[6,3,8,4,5,1,7,2]=>0000000
[3,1,6,8,5,7,4,2]=>0000000
[2,6,1,8,5,7,4,3]=>0000000
[6,5,8,7,1,3,2,4]=>0000000
[6,5,8,7,2,3,4,1]=>0000000
[6,5,8,7,3,2,4,1]=>0000000
[6,3,8,4,5,2,7,1]=>0000000
[3,1,6,8,5,7,2,4]=>0000000
[2,1,6,8,5,3,7,4]=>0100000
[3,1,6,8,5,4,2,7]=>0000000
[3,2,6,8,5,4,7,1]=>0000000
[4,1,8,5,2,6,3,7]=>0000000
[3,1,6,8,5,2,4,7]=>0000000
[6,2,8,4,5,1,3,7]=>0000000
[6,5,8,7,4,1,2,3]=>0000000
[6,5,8,7,4,2,1,3]=>0000000
[6,5,8,7,2,4,1,3]=>0000000
[6,2,8,4,5,7,1,3]=>0000000
[6,1,8,4,5,7,3,2]=>0000000
[4,2,7,3,5,8,6,1]=>0000000
[3,6,2,4,8,5,7,1]=>0000000
[3,5,1,8,4,7,6,2]=>0000000
[2,4,8,3,7,6,5,1]=>0000000
[3,6,8,5,2,4,7,1]=>0000000
[2,6,8,5,4,3,7,1]=>0000000
[3,6,8,2,5,4,7,1]=>0000000
[4,6,8,3,2,5,7,1]=>0000000
[4,6,2,8,3,5,7,1]=>0000000
[3,6,1,8,5,7,4,2]=>0000000
[3,5,8,2,7,4,6,1]=>0000000
[2,4,8,7,3,6,5,1]=>0000000
[2,5,8,7,4,3,6,1]=>0000000
[2,4,8,7,6,3,5,1]=>0000000
[4,7,2,5,6,3,1,8]=>0000001
[6,1,2,8,7,3,4,5]=>0000000
[3,2,6,1,5,8,4,7]=>0000000
[4,5,2,1,7,8,3,6]=>0000000
[2,3,7,8,5,1,6,4]=>0000000
[8,1,3,2,5,6,4,7]=>0000000
[3,2,5,8,4,7,1,6]=>0000000
[8,6,4,1,5,2,3,7]=>0000000
[2,5,8,1,3,4,7,6]=>0000000
[8,1,5,2,3,7,6,4]=>0000000
[6,4,7,2,8,3,1,5]=>0000000
[4,8,1,2,7,6,5,3]=>0000000
[3,7,4,8,5,2,6,1]=>0000000
[3,4,2,8,6,7,5,1]=>0000000
[3,6,1,5,2,7,8,4]=>0000000
[7,1,6,8,3,4,2,5]=>0000000
[6,2,8,4,7,1,3,5]=>0000000
[1,8,4,3,7,6,2,5]=>1000000
[4,3,8,7,1,2,6,5]=>0000000
[1,8,3,6,7,2,4,5]=>1000000
[1,8,4,5,7,6,2,3]=>1000000
[4,3,8,5,7,1,6,2]=>0000000
[6,3,4,8,7,2,1,5]=>0000000
[5,3,8,4,7,1,6,2]=>0000000
[5,2,8,7,1,4,6,3]=>0000000
[3,2,8,7,1,6,4,5]=>0000000
[2,7,8,3,1,6,4,5]=>0000000
[3,5,8,7,4,1,6,2]=>0000000
[7,4,6,8,3,5,1,2]=>0000000
[7,2,8,4,1,3,6,5]=>0000000
[2,7,8,1,3,6,4,5]=>0000000
[2,7,8,1,5,4,6,3]=>0000000
[2,7,8,1,4,5,6,3]=>0000000
[3,6,7,8,2,4,1,5]=>0000000
[4,5,7,8,6,3,1,2]=>0000000
[5,4,6,8,7,3,1,2]=>0000000
[4,5,8,6,7,1,3,2]=>0000000
[5,7,6,8,2,1,3,4]=>0000000
[3,7,6,8,2,4,1,5]=>0000000
[5,4,7,8,6,3,1,2]=>0000000
[3,6,7,8,2,1,4,5]=>0000000
[4,5,6,8,7,3,1,2]=>0000000
[5,3,6,2,4,1,8,7]=>0000010
[4,5,3,7,1,2,6,8]=>0000001
[6,7,2,8,4,3,1,5]=>0000000
[6,7,3,2,8,4,1,5]=>0000000
[4,5,8,1,3,2,6,7]=>0000000
[5,7,2,8,3,4,6,1]=>0000000
[3,1,5,8,6,4,7,2]=>0000000
[3,6,2,8,4,7,5,1]=>0000000
[2,3,8,6,7,5,4,1]=>0000000
[3,1,5,8,6,2,4,7]=>0000000
[1,5,8,6,3,4,2,7]=>1000000
[5,3,7,8,4,2,6,1]=>0000000
[5,1,6,4,3,8,7,2]=>0000000
[4,7,6,8,3,1,5,2]=>0000000
[3,5,4,7,1,8,6,2]=>0000000
[1,8,5,4,2,3,6,7]=>1000000
[6,1,3,8,4,5,2,7]=>0000000
[4,1,5,7,6,3,2,8]=>0000001
[5,3,8,2,7,1,6,4]=>0000000
[4,5,1,7,6,3,2,8]=>0000001
[1,5,3,7,4,2,6,8]=>1000001
[1,5,4,2,3,8,7,6]=>1000100
[1,5,4,2,3,8,6,7]=>1000100
[1,5,4,2,3,7,8,6]=>1000100
[3,6,5,2,4,1,7,8]=>0000011
[4,6,7,2,5,1,8,3]=>0000000
[3,6,2,5,1,7,8,4]=>0000000
[8,7,3,6,2,1,5,4]=>0000000
[7,3,5,4,1,2,6,8]=>0000001
[7,1,3,8,2,5,4,6]=>0000000
[6,7,1,8,3,4,5,2]=>0000000
[8,6,7,2,5,3,1,4]=>0000000
[1,2,8,6,4,5,3,7]=>1100000
[1,5,7,8,4,2,3,6]=>1000000
[1,2,3,7,5,4,6,8]=>1110001
[1,3,4,8,5,2,7,6]=>1000000
[4,6,5,2,1,7,8,3]=>0000000
[3,5,6,2,1,4,7,8]=>0000011
[4,3,6,5,1,7,8,2]=>0000000
[4,6,5,3,1,7,8,2]=>0000000
[5,1,3,4,8,2,6,7]=>0000000
[5,8,1,4,2,3,6,7]=>0000000
[4,3,1,8,5,2,6,7]=>0000000
[4,5,8,2,3,1,6,7]=>0000000
[3,5,4,8,1,7,2,6]=>0000000
[5,3,6,8,1,4,7,2]=>0000000
[5,1,6,8,3,4,7,2]=>0000000
[3,5,1,8,6,4,7,2]=>0000000
[6,4,8,1,5,7,2,3]=>0000000
[4,7,2,8,3,1,6,5]=>0000000
[1,2,5,6,8,3,7,4]=>1100000
[5,1,6,8,7,2,3,4]=>0000000
[1,5,6,8,3,7,2,4]=>1000000
[5,6,8,1,2,3,7,4]=>0000000
[2,8,1,3,5,7,4,6]=>0000000
[7,4,8,1,5,2,6,3]=>0000000
[8,3,2,1,6,5,7,4]=>0000000
[4,1,5,6,8,7,2,3]=>0000000
[1,2,5,6,8,4,7,3]=>1100000
[1,5,6,8,4,7,2,3]=>1000000
[6,8,1,4,5,7,2,3]=>0000000
[4,3,5,1,8,6,7,2]=>0000000
[1,3,5,6,8,4,7,2]=>1000000
[5,6,8,1,3,4,7,2]=>0000000
[5,6,8,2,3,4,7,1]=>0000000
[2,3,1,7,6,8,4,5]=>0010000
[2,7,4,1,3,6,8,5]=>0000000
[6,3,2,8,1,7,5,4]=>0000000
[4,5,3,1,2,8,6,7]=>0000100
[6,2,1,7,5,8,4,3]=>0000000
[1,5,7,8,6,4,2,3]=>1000000
[1,6,4,8,5,3,7,2]=>1000000
[4,2,6,7,8,1,3,5]=>0000000
[4,5,1,7,6,3,8,2]=>0000000
[8,1,5,4,2,3,6,7]=>0000000
[6,1,4,8,7,2,3,5]=>0000000
[6,1,7,5,8,2,3,4]=>0000000
[6,1,7,4,8,2,3,5]=>0000000
[3,5,8,6,2,1,4,7]=>0000000
[8,7,3,6,5,2,4,1]=>0000000
[7,3,8,6,2,1,4,5]=>0000000
[2,5,1,4,7,3,6,8]=>0000001
[3,1,6,5,7,2,4,8]=>0000001
[2,5,7,1,6,3,4,8]=>0000001
[2,5,7,1,6,3,8,4]=>0000000
[2,6,1,5,7,4,3,8]=>0000001
[3,1,6,5,2,4,7,8]=>0000011
[3,6,5,1,4,2,7,8]=>0000011
[3,5,6,2,8,1,7,4]=>0000000
[3,6,5,1,7,2,4,8]=>0000001
[3,6,5,2,1,4,7,8]=>0000011
[4,5,2,7,6,1,3,8]=>0000001
[4,6,5,3,1,2,7,8]=>0000011
[5,4,1,6,3,7,2,8]=>0000001
[5,4,2,6,3,7,8,1]=>0000000
[3,6,5,7,1,4,2,8]=>0000001
[3,6,5,1,4,7,2,8]=>0000001
[4,3,6,5,7,1,2,8]=>0000001
[4,2,6,5,1,3,7,8]=>0000011
[4,1,6,5,3,7,8,2]=>0000000
[4,1,5,7,6,3,8,2]=>0000000
[4,2,5,7,6,1,3,8]=>0000001
[3,4,7,6,1,2,5,8]=>0000001
[3,4,7,6,8,2,5,1]=>0000000
[4,2,5,7,6,3,8,1]=>0000000
[4,1,6,5,2,7,3,8]=>0000001
[4,2,6,5,7,3,1,8]=>0000001
[3,6,5,7,2,1,4,8]=>0000001
[3,5,7,6,2,4,1,8]=>0000001
[5,4,2,6,3,7,1,8]=>0000001
[4,6,5,2,7,3,1,8]=>0000001
[4,5,2,7,6,3,8,1]=>0000000
[4,6,5,2,1,7,3,8]=>0000001
[3,5,8,2,1,4,6,7]=>0000000
[3,5,8,2,4,6,7,1]=>0000000
[5,3,8,2,1,4,6,7]=>0000000
[5,3,1,8,2,4,6,7]=>0000000
[1,5,3,8,2,4,6,7]=>1000000
[1,5,8,4,2,3,6,7]=>1000000
[5,8,2,1,4,3,6,7]=>0000000
[5,8,2,4,6,3,1,7]=>0000000
[5,8,2,4,3,6,1,7]=>0000000
[5,8,1,4,6,2,3,7]=>0000000
[1,5,8,4,6,7,2,3]=>1000000
[5,1,8,4,6,7,2,3]=>0000000
[5,8,2,4,6,3,7,1]=>0000000
[3,8,4,6,7,2,1,5]=>0000000
[3,8,4,6,7,2,5,1]=>0000000
[8,4,3,6,7,2,5,1]=>0000000
[8,4,3,6,7,2,1,5]=>0000000
[8,6,2,4,5,3,7,1]=>0000000
[8,6,4,1,5,7,2,3]=>0000000
[1,8,6,4,5,7,2,3]=>1000000
[8,1,6,4,5,2,3,7]=>0000000
[8,6,2,4,5,3,1,7]=>0000000
[1,8,6,4,2,3,5,7]=>1000000
[3,8,1,6,2,4,5,7]=>0000000
[1,3,8,6,2,4,5,7]=>1000000
[3,8,6,2,1,4,5,7]=>0000000
[3,8,6,2,4,1,5,7]=>0000000
[3,8,6,2,4,5,7,1]=>0000000
[8,3,6,2,4,5,1,7]=>0000000
[1,8,3,6,2,4,5,7]=>1000000
[8,1,3,6,2,4,5,7]=>0000000
[8,3,6,7,2,1,4,5]=>0000000
[2,5,8,4,6,1,7,3]=>0000000
[3,8,6,7,2,1,4,5]=>0000000
[3,1,8,6,7,2,4,5]=>0000000
[8,2,6,4,5,1,7,3]=>0000000
[8,4,6,1,7,2,5,3]=>0000000
[1,8,4,6,7,5,2,3]=>1000000
[8,1,4,6,7,5,2,3]=>0000000
[8,4,6,1,3,7,2,5]=>0000000
[8,1,4,6,3,7,2,5]=>0000000
[8,4,1,6,3,7,2,5]=>0000000
[8,2,4,6,1,7,5,3]=>0000000
[8,4,6,2,3,7,5,1]=>0000000
[8,4,7,2,1,3,6,5]=>0000000
[8,4,2,1,5,3,7,6]=>0000000
[8,2,1,4,7,3,6,5]=>0000000
[2,8,4,1,7,5,3,6]=>0000000
[4,7,3,1,8,6,2,5]=>0000000
[2,1,5,8,7,3,6,4]=>0100000
[4,3,1,7,8,5,2,6]=>0000000
[5,8,2,6,4,3,7,1]=>0000000
[2,8,5,3,6,4,7,1]=>0000000
[1,2,8,6,4,7,3,5]=>1100000
[4,2,7,8,3,5,6,1]=>0000000
[2,8,3,7,1,4,6,5]=>0000000
[3,2,4,8,7,5,6,1]=>0000000
[1,8,6,4,7,5,3,2]=>1000000
[8,6,4,7,5,1,2,3]=>0000000
[2,7,4,6,3,8,5,1]=>0000000
[1,2,8,6,4,7,5,3]=>1100000
[1,6,5,4,3,8,2,7]=>1000000
[6,4,2,1,5,7,3,8]=>0000001
[3,1,5,8,7,2,4,6]=>0000000
[3,2,5,7,8,4,1,6]=>0000000
[3,2,5,7,8,4,6,1]=>0000000
[5,3,7,4,2,6,8,1]=>0000000
[5,3,7,4,2,6,1,8]=>0000001
[5,2,8,4,3,1,6,7]=>0000000
[5,1,8,4,3,2,6,7]=>0000000
[5,2,7,4,3,6,1,8]=>0000001
[5,2,7,4,3,6,8,1]=>0000000
[5,3,7,4,1,6,8,2]=>0000000
[3,1,5,7,8,4,2,6]=>0000000
[1,2,8,6,4,5,7,3]=>1100000
[6,2,3,7,4,1,8,5]=>0000000
[5,2,7,4,1,3,8,6]=>0000000
[6,2,3,7,4,8,5,1]=>0000000
[6,2,3,7,4,8,1,5]=>0000000
[6,1,3,7,4,2,8,5]=>0000000
[6,2,3,7,4,5,1,8]=>0000001
[6,2,3,7,4,5,8,1]=>0000000
[6,1,3,7,4,5,8,2]=>0000000
[1,2,8,6,4,3,5,7]=>1100000
[6,1,3,7,4,5,2,8]=>0000001
[1,8,6,3,5,4,2,7]=>1000000
[2,5,4,1,8,6,7,3]=>0000000
[1,8,5,3,2,6,7,4]=>1000000
[5,6,8,3,4,2,7,1]=>0000000
[6,3,8,2,4,1,7,5]=>0000000
[5,1,7,8,2,4,3,6]=>0000000
[5,3,2,4,8,1,7,6]=>0000000
[5,3,2,4,8,1,6,7]=>0000000
[5,3,2,4,7,1,8,6]=>0000000
[8,4,5,3,7,1,2,6]=>0000000
[5,3,2,4,6,8,1,7]=>0000000
[7,6,4,2,8,3,1,5]=>0000000
[1,2,6,4,7,3,5,8]=>1100001
[7,5,4,1,3,6,8,2]=>0000000
[6,7,2,4,5,1,8,3]=>0000000
[5,2,7,8,3,6,1,4]=>0000000
[2,7,8,5,6,1,4,3]=>0000000
[5,2,8,3,1,4,7,6]=>0000000
[8,3,5,1,2,4,7,6]=>0000000
[8,3,6,5,4,1,2,7]=>0000000
[8,4,1,7,5,2,6,3]=>0000000
[8,4,2,7,5,3,1,6]=>0000000
[1,5,2,6,8,3,7,4]=>1000000
[7,2,8,4,1,3,5,6]=>0000000
[6,7,8,5,2,1,4,3]=>0000000
[1,6,2,7,8,4,3,5]=>1000000
[4,3,8,6,5,2,7,1]=>0000000
[2,3,8,6,5,1,7,4]=>0000000
[7,3,2,6,1,4,8,5]=>0000000
[8,4,7,1,2,5,3,6]=>0000000
[8,5,6,7,2,1,4,3]=>0000000
[8,5,6,7,3,1,4,2]=>0000000
[5,7,8,1,3,2,4,6]=>0000000
[7,8,6,1,3,5,4,2]=>0000000
[1,2,5,7,8,3,6,4]=>1100000
[3,4,5,8,1,7,2,6]=>0000000
[4,3,8,6,7,5,1,2]=>0000000
[4,5,6,2,7,8,3,1]=>0000000
[4,5,6,2,7,1,8,3]=>0000000
[4,5,6,2,1,7,3,8]=>0000001
[4,5,6,1,7,8,3,2]=>0000000
[4,5,1,6,7,8,3,2]=>0000000
[4,5,1,6,7,3,8,2]=>0000000
[4,5,1,6,7,3,2,8]=>0000001
[4,5,6,1,7,3,2,8]=>0000001
[1,6,4,3,8,2,7,5]=>1000000
[7,8,1,4,3,2,5,6]=>0000000
[1,7,8,4,5,3,6,2]=>1000000
[2,7,6,3,4,1,8,5]=>0000000
[8,1,7,4,3,5,6,2]=>0000000
[7,1,8,4,5,3,6,2]=>0000000
[4,3,1,8,6,5,7,2]=>0000000
[4,3,2,7,5,1,8,6]=>0000000
[5,2,3,7,4,1,8,6]=>0000000
[2,1,7,4,3,6,8,5]=>0100000
[7,1,2,4,5,6,8,3]=>0000000
[2,8,7,1,4,5,6,3]=>0000000
[8,7,1,3,4,5,6,2]=>0000000
[7,8,1,3,4,5,6,2]=>0000000
[1,7,2,5,4,6,8,3]=>1000000
[2,5,3,8,1,6,7,4]=>0000000
[1,6,4,2,5,7,8,3]=>1000000
[8,5,3,1,4,6,7,2]=>0000000
[6,5,3,4,1,7,8,2]=>0000000
[5,6,3,4,1,7,8,2]=>0000000
[2,5,3,1,4,7,8,6]=>0000100
[2,6,1,4,3,7,8,5]=>0000000
[6,8,2,3,1,5,7,4]=>0000000
[6,1,3,4,2,7,8,5]=>0000000
[4,3,1,5,2,7,8,6]=>0000100
[5,2,3,1,4,7,8,6]=>0000100
[7,2,1,3,5,6,8,4]=>0000000
[5,2,4,7,8,6,3,1]=>0000000
[8,4,2,7,6,1,5,3]=>0000000
[5,3,7,6,1,8,4,2]=>0000000
[8,6,4,1,2,5,3,7]=>0000000
[8,6,1,4,2,5,7,3]=>0000000
[8,6,4,1,2,5,7,3]=>0000000
[8,6,1,4,7,2,5,3]=>0000000
[4,2,6,3,5,1,7,8]=>0000011
[3,4,6,8,7,1,2,5]=>0000000
[2,5,4,8,3,7,6,1]=>0000000
[1,3,6,2,5,8,7,4]=>1000000
[1,3,5,8,6,4,7,2]=>1000000
[5,8,7,1,4,6,3,2]=>0000000
[6,2,5,1,3,4,8,7]=>0000010
[2,6,5,1,3,4,8,7]=>0000010
[4,6,5,1,2,7,3,8]=>0000001
[5,6,4,1,2,7,3,8]=>0000001
[8,1,5,6,2,4,3,7]=>0000000
[6,4,5,1,2,7,3,8]=>0000001
[5,4,6,1,3,2,7,8]=>0000011
[5,7,1,4,3,2,6,8]=>0000001
[2,6,4,1,3,7,5,8]=>0000001
[6,3,2,5,7,4,8,1]=>0000000
[4,5,2,7,6,3,1,8]=>0000001
[4,5,2,1,7,6,3,8]=>0000001
[5,4,1,6,7,2,8,3]=>0000000
[4,1,6,5,2,7,8,3]=>0000000
[5,4,6,2,7,8,3,1]=>0000000
[3,5,2,6,7,8,4,1]=>0000000
[6,3,2,5,1,7,8,4]=>0000000
[4,6,3,7,8,2,1,5]=>0000000
[5,6,7,1,8,4,2,3]=>0000000
[5,6,7,2,8,4,1,3]=>0000000
[2,8,4,7,6,3,1,5]=>0000000
[6,4,8,7,2,1,5,3]=>0000000
[2,5,1,8,4,7,6,3]=>0000000
[2,4,5,8,1,7,6,3]=>0000000
[2,6,8,1,4,3,7,5]=>0000000
[2,6,1,5,8,7,3,4]=>0000000
[7,5,8,1,6,2,3,4]=>0000000
[7,6,1,3,5,2,4,8]=>0000001
[6,2,4,5,3,8,1,7]=>0000000
[1,2,5,4,7,8,3,6]=>1100000
[3,6,2,4,7,8,5,1]=>0000000
[1,3,5,4,8,7,2,6]=>1000000
[1,6,2,4,8,3,7,5]=>1000000
[7,1,4,2,3,8,6,5]=>0000000
[1,7,3,2,4,6,5,8]=>1000001
[1,5,7,3,2,6,4,8]=>1000001
[5,1,3,7,2,6,4,8]=>0000001
[1,7,8,5,4,2,6,3]=>1000000
[8,1,7,5,4,2,6,3]=>0000000
[1,6,5,2,7,4,8,3]=>1000000
[1,5,4,2,8,6,7,3]=>1000000
[1,6,3,5,2,7,8,4]=>1000000
[3,1,2,6,8,7,5,4]=>0010000
[6,4,8,2,5,7,1,3]=>0000000
[6,8,4,2,7,1,3,5]=>0000000
[6,8,2,4,1,7,3,5]=>0000000
[2,5,4,7,6,1,3,8]=>0000001
[5,2,3,7,6,1,4,8]=>0000001
[4,2,3,7,6,1,5,8]=>0000001
[4,2,7,3,5,1,6,8]=>0000001
[5,6,2,3,8,4,7,1]=>0000000
[5,6,2,3,1,7,8,4]=>0000000
[5,7,2,3,4,1,6,8]=>0000001
[6,2,7,3,5,1,4,8]=>0000001
[7,2,6,3,5,1,4,8]=>0000001
[6,5,2,3,1,7,8,4]=>0000000
[6,5,2,3,8,4,7,1]=>0000000
[7,5,2,1,4,6,8,3]=>0000000
[8,5,2,1,4,6,7,3]=>0000000
[8,5,2,3,1,6,4,7]=>0000000
[8,6,2,3,1,5,4,7]=>0000000
[8,2,6,3,1,7,4,5]=>0000000
[1,6,3,4,2,7,5,8]=>1000001
[8,5,2,7,3,4,6,1]=>0000000
[1,7,2,4,5,6,8,3]=>1000000
[1,8,3,2,5,6,4,7]=>1000000
[8,6,1,3,4,5,7,2]=>0000000
[6,8,1,3,4,5,7,2]=>0000000
[7,2,8,1,4,6,3,5]=>0000000
[2,7,8,1,5,6,3,4]=>0000000
[6,8,2,3,1,5,4,7]=>0000000
[5,8,2,3,1,6,4,7]=>0000000
[5,7,2,1,4,6,8,3]=>0000000
[4,2,3,8,1,7,5,6]=>0000000
[5,2,3,8,1,7,4,6]=>0000000
[2,5,4,8,1,7,3,6]=>0000000
[2,5,4,1,3,8,6,7]=>0000100
[4,2,1,5,3,7,6,8]=>0000101
[5,1,3,2,6,7,8,4]=>0000000
[5,1,3,4,2,7,6,8]=>0000101
[6,1,3,4,2,7,5,8]=>0000001
[7,2,1,3,5,8,4,6]=>0000000
[6,1,2,4,5,7,8,3]=>0000000
[6,8,7,2,3,4,5,1]=>0000000
[2,8,7,5,1,3,4,6]=>0000000
[8,3,7,5,1,4,2,6]=>0000000
[8,3,7,1,6,4,2,5]=>0000000
[4,2,6,5,3,1,7,8]=>0000011
[4,3,7,5,1,6,2,8]=>0000001
[3,5,2,8,6,7,4,1]=>0000000
[5,3,7,4,2,8,6,1]=>0000000
[5,6,2,8,7,1,4,3]=>0000000
[4,3,7,5,2,6,1,8]=>0000001
[4,6,3,5,2,7,8,1]=>0000000
[4,1,6,3,5,7,2,8]=>0000001
[3,1,5,7,4,6,8,2]=>0000000
[7,2,5,8,6,1,4,3]=>0000000
[7,8,4,5,1,3,6,2]=>0000000
[4,3,6,1,5,7,8,2]=>0000000
[6,4,7,1,3,5,2,8]=>0000001
[3,5,4,1,2,6,7,8]=>0000111
[5,3,1,4,6,7,8,2]=>0000000
[6,2,1,4,7,5,8,3]=>0000000
[4,6,7,1,3,5,8,2]=>0000000
[5,6,1,3,4,7,2,8]=>0000001
[2,5,3,7,8,4,6,1]=>0000000
[4,5,7,2,3,6,1,8]=>0000001
[4,6,2,1,3,7,8,5]=>0000000
[3,6,2,4,1,7,5,8]=>0000001
[3,2,6,7,4,8,5,1]=>0000000
[7,3,4,8,5,2,1,6]=>0000000
[7,1,8,3,4,6,2,5]=>0000000
[6,3,2,7,5,8,4,1]=>0000000
[6,2,7,1,4,5,3,8]=>0000001
[4,2,6,1,5,7,3,8]=>0000001
[2,7,5,8,6,3,4,1]=>0000000
[2,5,4,1,3,6,7,8]=>0000111
[5,4,1,2,6,7,3,8]=>0000001
[6,5,2,7,4,1,3,8]=>0000001
[6,5,7,3,1,4,2,8]=>0000001
[6,7,4,3,1,5,8,2]=>0000000
[6,4,1,2,7,8,3,5]=>0000000
[5,1,4,7,2,6,8,3]=>0000000
[5,2,6,8,3,7,1,4]=>0000000
[1,7,2,4,3,5,8,6]=>1000000
[8,4,1,5,2,6,7,3]=>0000000
[7,4,1,3,6,5,2,8]=>0000001
[5,7,2,8,1,3,6,4]=>0000000
[5,4,1,2,6,3,8,7]=>0000010
[2,7,8,4,1,3,6,5]=>0000000
[3,6,5,1,4,8,2,7]=>0000000
[3,6,4,1,2,7,8,5]=>0000000
[4,1,7,3,8,6,2,5]=>0000000
[4,8,2,7,6,5,1,3]=>0000000
[5,4,2,8,7,6,1,3]=>0000000
[7,4,2,8,6,5,1,3]=>0000000
[6,5,8,2,7,4,1,3]=>0000000
[8,6,5,2,7,1,4,3]=>0000000
[7,8,5,2,1,6,4,3]=>0000000
[6,8,5,2,7,1,4,3]=>0000000
[6,5,8,2,7,1,4,3]=>0000000
[7,5,8,2,1,6,4,3]=>0000000
[3,2,1,6,5,8,4,7]=>0010000
[6,3,1,4,5,8,2,7]=>0000000
[3,4,8,5,2,1,7,6]=>0000000
[4,8,7,1,3,2,6,5]=>0000000
[3,5,1,4,2,8,7,6]=>0000100
[5,8,7,4,6,1,3,2]=>0000000
[5,1,8,7,4,6,3,2]=>0000000
[3,4,1,8,7,6,2,5]=>0000000
[3,5,2,8,6,4,7,1]=>0000000
[2,8,7,5,4,1,6,3]=>0000000
[4,2,5,8,6,7,1,3]=>0000000
[8,1,5,7,4,2,6,3]=>0000000
[8,4,5,3,1,6,7,2]=>0000000
[5,8,7,3,4,1,6,2]=>0000000
[2,4,5,8,1,3,7,6]=>0000000
[7,1,4,3,8,5,6,2]=>0000000
[6,3,2,5,8,4,1,7]=>0000000
[8,4,1,3,7,6,5,2]=>0000000
[5,1,6,4,7,8,2,3]=>0000000
[2,8,3,5,6,1,4,7]=>0000000
[1,3,6,4,2,7,5,8]=>1000001
[3,2,8,5,6,1,4,7]=>0000000
[7,2,5,8,1,4,6,3]=>0000000
[4,7,5,8,1,2,6,3]=>0000000
[5,4,7,8,2,1,3,6]=>0000000
[4,7,5,8,1,2,3,6]=>0000000
[3,4,7,5,2,8,1,6]=>0000000
[4,3,2,5,7,8,1,6]=>0000000
[5,4,8,6,2,3,1,7]=>0000000
[2,4,7,5,8,3,1,6]=>0000000
[7,2,5,8,1,6,3,4]=>0000000
[3,7,8,4,2,1,6,5]=>0000000
[1,5,4,8,7,6,2,3]=>1000000
[1,3,6,8,2,4,7,5]=>1000000
[4,7,2,8,5,1,6,3]=>0000000
[4,7,5,2,6,3,8,1]=>0000000
[3,5,6,2,8,1,4,7]=>0000000
[1,6,8,2,5,3,4,7]=>1000000
[8,6,3,5,2,1,4,7]=>0000000
[8,7,3,2,6,5,1,4]=>0000000
[5,2,8,7,6,4,1,3]=>0000000
[4,1,3,8,5,6,2,7]=>0000000
[3,2,4,8,5,7,1,6]=>0000000
[4,5,2,8,3,7,1,6]=>0000000
[7,8,5,1,6,4,3,2]=>0000000
[8,7,5,1,6,4,3,2]=>0000000
[4,5,8,3,1,2,7,6]=>0000000
[7,1,6,8,5,4,3,2]=>0000000
[5,8,1,3,4,2,7,6]=>0000000
[1,4,6,3,7,5,2,8]=>1000001
[1,3,2,8,7,4,6,5]=>1010000
[7,5,2,8,3,1,6,4]=>0000000
[6,7,1,3,2,5,8,4]=>0000000
[6,3,5,4,8,1,2,7]=>0000000
[6,2,5,4,1,7,8,3]=>0000000
[4,1,5,6,3,8,7,2]=>0000000
[8,1,5,4,6,7,3,2]=>0000000
[2,4,5,8,3,7,6,1]=>0000000
[6,1,3,5,4,8,2,7]=>0000000
[1,3,8,7,2,5,6,4]=>1000000
[2,5,4,1,8,3,7,6]=>0000000
[6,1,5,4,3,8,2,7]=>0000000
[1,4,8,3,2,7,6,5]=>1000000
[5,1,4,8,3,7,6,2]=>0000000
[3,5,8,2,1,4,7,6]=>0000000
[8,4,1,2,7,6,5,3]=>0000000
[4,8,3,2,7,6,5,1]=>0000000
[2,4,8,1,7,6,5,3]=>0000000
[8,7,3,2,1,4,6,5]=>0000000
[1,4,8,5,2,3,6,7]=>1000000
[6,1,4,2,8,7,3,5]=>0000000
[1,5,8,7,2,4,3,6]=>1000000
[8,7,1,3,2,5,4,6]=>0000000
[6,7,4,2,8,1,3,5]=>0000000
[8,5,1,4,7,6,3,2]=>0000000
[8,1,3,7,2,4,6,5]=>0000000
[5,3,1,6,4,8,2,7]=>0000000
[2,5,6,7,1,4,8,3]=>0000000
[1,4,2,7,5,8,3,6]=>1000000
[5,8,1,2,7,4,3,6]=>0000000
[4,6,3,7,8,1,5,2]=>0000000
[2,4,7,3,6,8,1,5]=>0000000
[2,7,3,1,8,5,4,6]=>0000000
[2,3,1,6,8,7,4,5]=>0010000
[6,4,8,2,1,7,3,5]=>0000000
[8,5,1,2,7,4,3,6]=>0000000
[1,3,7,6,8,4,2,5]=>1000000
[2,1,5,7,4,6,8,3]=>0100000
[2,3,5,7,8,1,6,4]=>0000000
[1,6,4,2,3,5,7,8]=>1000011
[1,5,7,4,2,3,6,8]=>1000001
[8,1,7,2,4,6,3,5]=>0000000
[2,4,7,8,3,5,1,6]=>0000000
[1,3,6,2,5,8,4,7]=>1000000
[1,5,3,6,8,2,4,7]=>1000000
[2,8,5,1,4,3,7,6]=>0000000
[1,8,6,2,4,3,7,5]=>1000000
[4,1,6,5,2,3,7,8]=>0000011
[4,1,3,6,7,2,5,8]=>0000001
[2,7,5,8,1,3,6,4]=>0000000
[5,1,6,7,3,2,4,8]=>0000001
[7,4,1,2,3,6,8,5]=>0000000
[2,7,4,1,5,8,3,6]=>0000000
[6,1,7,3,4,2,5,8]=>0000001
[2,6,4,7,8,5,3,1]=>0000000
[6,8,4,3,1,5,2,7]=>0000000
[3,2,4,8,6,1,7,5]=>0000000
[2,1,3,8,4,5,7,6]=>0110000
[2,1,3,7,8,4,6,5]=>0110000
[2,1,3,8,4,7,6,5]=>0110000
[3,1,2,8,4,5,7,6]=>0010000
[1,2,8,7,5,4,6,3]=>1100000
[1,3,6,8,2,7,5,4]=>1000000
[3,2,6,5,1,8,4,7]=>0000000
[2,8,3,7,6,1,5,4]=>0000000
[5,4,2,6,8,7,3,1]=>0000000
[3,7,2,5,8,6,4,1]=>0000000
[5,4,3,7,2,8,6,1]=>0000000
[4,6,5,3,8,1,7,2]=>0000000
[2,4,8,7,6,1,5,3]=>0000000
[4,8,5,2,7,6,3,1]=>0000000
[2,8,6,5,7,1,3,4]=>0000000
[1,8,7,4,5,2,3,6]=>1000000
[5,8,1,7,6,2,3,4]=>0000000
[1,7,6,2,4,3,8,5]=>1000000
[5,6,8,7,1,3,2,4]=>0000000
[7,1,6,8,2,5,4,3]=>0000000
[6,4,2,7,1,5,8,3]=>0000000
[5,3,6,7,4,2,8,1]=>0000000
[2,6,3,7,5,4,8,1]=>0000000
[1,7,3,2,4,8,6,5]=>1000000
[6,4,1,3,8,7,5,2]=>0000000
[4,3,1,8,2,6,7,5]=>0000000
[4,8,1,3,2,5,7,6]=>0000000
[7,2,6,5,8,3,4,1]=>0000000
[1,7,5,3,8,6,2,4]=>1000000
[2,5,3,8,1,4,7,6]=>0000000
[4,2,5,8,1,3,7,6]=>0000000
[8,1,2,4,3,5,7,6]=>0000000
[2,4,3,8,1,5,7,6]=>0000000
[7,5,2,3,8,4,6,1]=>0000000
[2,7,5,1,4,8,3,6]=>0000000
[3,1,7,4,8,6,5,2]=>0000000
[6,4,5,3,2,8,7,1]=>0000000
[2,7,3,8,5,1,6,4]=>0000000
[8,7,3,2,5,6,4,1]=>0000000
[1,5,8,2,6,4,3,7]=>1000000
[3,1,8,2,6,5,4,7]=>0000000
[7,6,2,8,1,4,5,3]=>0000000
[8,4,2,3,1,5,7,6]=>0000000
[8,2,3,4,1,5,7,6]=>0000000
[2,5,6,3,8,1,4,7]=>0000000
[7,3,5,6,1,8,4,2]=>0000000
[7,4,5,6,8,1,3,2]=>0000000
[7,5,1,8,4,6,3,2]=>0000000
[2,8,1,7,4,5,3,6]=>0000000
[6,1,5,3,8,4,7,2]=>0000000
[1,6,5,3,8,4,7,2]=>1000000
[7,6,2,3,5,4,8,1]=>0000000
[7,6,2,3,5,1,4,8]=>0000001
[6,1,5,2,3,4,8,7]=>0000010
[6,2,5,3,4,8,1,7]=>0000000
[6,2,5,3,4,8,7,1]=>0000000
[2,6,5,3,4,8,7,1]=>0000000
[2,6,5,3,4,8,1,7]=>0000000
[2,5,1,4,8,3,7,6]=>0000000
[1,2,5,4,8,3,7,6]=>1100000
[5,3,4,8,1,7,2,6]=>0000000
[5,1,3,4,8,7,2,6]=>0000000
[1,5,3,4,8,7,2,6]=>1000000
[5,1,3,8,4,7,6,2]=>0000000
[5,3,8,1,4,7,6,2]=>0000000
[4,3,5,8,1,7,6,2]=>0000000
[3,6,5,4,8,1,2,7]=>0000000
[3,6,5,4,8,2,7,1]=>0000000
[4,3,5,8,2,1,7,6]=>0000000
[3,5,2,4,8,7,6,1]=>0000000
[2,3,6,5,8,4,1,7]=>0000000
[5,2,3,8,7,4,1,6]=>0000000
[2,3,1,7,4,8,6,5]=>0010000
[7,4,1,3,6,2,5,8]=>0000001
[7,2,5,8,1,3,6,4]=>0000000
[1,2,6,5,3,4,7,8]=>1100011
[1,4,6,5,7,2,3,8]=>1000001
[2,4,6,5,7,1,8,3]=>0000000
[3,5,2,1,7,8,6,4]=>0000000
[7,1,6,3,2,4,8,5]=>0000000
[6,4,8,1,2,3,7,5]=>0000000
[4,3,5,1,7,8,6,2]=>0000000
[4,6,7,2,3,8,5,1]=>0000000
[2,3,5,8,7,4,1,6]=>0000000
[2,3,5,8,7,4,6,1]=>0000000
[1,7,4,5,8,3,6,2]=>1000000
[7,1,5,2,4,8,3,6]=>0000000
[8,1,5,2,4,7,3,6]=>0000000
[7,5,8,1,4,2,3,6]=>0000000
[1,3,4,8,5,6,2,7]=>1000000
[4,8,3,6,1,7,2,5]=>0000000
[4,6,3,1,2,5,7,8]=>0000011
[7,4,6,8,3,1,2,5]=>0000000
[8,5,4,7,3,1,2,6]=>0000000
[2,5,6,4,8,1,3,7]=>0000000
[5,4,1,6,2,3,7,8]=>0000011
[1,5,6,4,2,3,7,8]=>1000011
[2,5,1,4,6,3,8,7]=>0000010
[8,1,4,3,7,5,6,2]=>0000000
[8,3,7,6,2,4,5,1]=>0000000
[8,1,2,7,6,4,5,3]=>0000000
[1,7,3,8,6,2,5,4]=>1000000
[1,2,4,6,8,3,7,5]=>1100000
[1,3,5,6,4,8,2,7]=>1000000
[6,3,5,7,1,4,2,8]=>0000001
[5,4,8,6,3,7,1,2]=>0000000
[3,4,8,5,6,1,2,7]=>0000000
[1,7,6,2,5,4,8,3]=>1000000
[3,7,2,1,5,6,8,4]=>0000000
[8,1,6,4,3,5,2,7]=>0000000
[4,6,8,5,1,3,7,2]=>0000000
[4,3,1,8,5,7,2,6]=>0000000
[4,8,3,6,1,5,2,7]=>0000000
[8,3,2,4,7,1,6,5]=>0000000
[7,3,2,4,8,1,6,5]=>0000000
[8,3,2,4,6,1,7,5]=>0000000
[8,3,2,4,5,7,1,6]=>0000000
[8,3,6,2,4,1,7,5]=>0000000
[7,4,6,2,1,3,8,5]=>0000000
[3,2,4,5,7,8,1,6]=>0000000
[3,6,7,2,4,1,8,5]=>0000000
[7,3,5,2,8,1,4,6]=>0000000
[2,6,8,4,5,1,7,3]=>0000000
[1,5,8,7,4,2,3,6]=>1000000
[1,5,2,7,6,4,8,3]=>1000000
[1,4,6,8,7,2,5,3]=>1000000
[1,3,6,8,7,2,5,4]=>1000000
[1,4,3,6,8,7,2,5]=>1000000
[1,6,2,7,5,3,4,8]=>1000001
[1,7,2,5,4,3,8,6]=>1000000
[1,6,3,7,2,4,5,8]=>1000001
[1,3,2,6,8,5,4,7]=>1010000
[1,6,3,2,7,4,5,8]=>1000001
[1,5,8,6,2,7,4,3]=>1000000
[1,3,7,2,6,4,5,8]=>1000001
[1,3,7,5,8,6,2,4]=>1000000
[1,7,3,2,8,5,6,4]=>1000000
[1,6,5,2,4,8,3,7]=>1000000
[1,4,7,6,2,3,5,8]=>1000001
[1,7,3,8,4,2,5,6]=>1000000
[1,6,2,4,7,5,8,3]=>1000000
[1,6,2,7,4,3,8,5]=>1000000
[1,5,8,2,3,6,4,7]=>1000000
[5,4,7,8,1,6,3,2]=>0000000
[1,7,8,4,3,6,5,2]=>1000000
[1,7,8,3,6,5,4,2]=>1000000
[1,8,4,2,3,7,5,6]=>1000000
[6,5,1,3,8,4,2,7]=>0000000
[6,1,4,2,7,8,3,5]=>0000000
[6,5,1,3,7,8,4,2]=>0000000
[5,6,8,2,4,7,1,3]=>0000000
[5,1,3,2,6,8,4,7]=>0000000
[1,5,7,3,6,4,2,8]=>1000001
[1,6,3,5,7,4,8,2]=>1000000
[1,7,2,4,8,3,5,6]=>1000000
[1,6,7,2,4,8,3,5]=>1000000
[1,6,7,8,2,4,3,5]=>1000000
[3,1,6,7,8,4,2,5]=>0000000
[3,1,6,7,8,4,5,2]=>0000000
[1,6,7,8,2,4,5,3]=>1000000
[4,2,7,6,8,5,1,3]=>0000000
[5,3,4,1,7,8,6,2]=>0000000
[3,7,5,6,1,8,4,2]=>0000000
[2,4,7,5,8,3,6,1]=>0000000
[6,8,7,4,2,5,1,3]=>0000000
[7,6,3,1,2,8,5,4]=>0000000
[3,1,8,6,4,7,2,5]=>0000000
[6,2,7,8,3,4,5,1]=>0000000
[8,1,3,5,6,4,7,2]=>0000000
[2,3,7,5,8,4,6,1]=>0000000
[8,1,7,4,2,5,3,6]=>0000000
[5,2,6,4,1,3,8,7]=>0000010
[2,1,8,5,4,3,7,6]=>0100000
[5,2,4,7,8,1,3,6]=>0000000
[1,7,6,2,8,5,3,4]=>1000000
[5,6,2,8,1,7,3,4]=>0000000
[3,1,2,4,8,6,7,5]=>0011000
[1,8,7,2,3,4,5,6]=>1000000
[3,7,5,2,8,1,4,6]=>0000000
[1,2,7,4,8,5,6,3]=>1100000
[5,6,3,4,2,8,7,1]=>0000000
[3,2,7,5,8,1,6,4]=>0000000
[3,6,5,8,2,7,4,1]=>0000000
[2,7,1,8,5,6,4,3]=>0000000
[4,3,6,8,5,2,1,7]=>0000000
[4,3,6,8,5,2,7,1]=>0000000
[4,5,3,2,1,8,6,7]=>0000100
[3,6,5,8,1,7,4,2]=>0000000
[3,6,5,8,1,2,7,4]=>0000000
[4,1,6,8,5,2,3,7]=>0000000
[4,5,2,8,6,7,3,1]=>0000000
[3,5,8,6,2,4,7,1]=>0000000
[3,2,4,5,8,6,1,7]=>0000000
[3,4,5,8,6,2,1,7]=>0000000
[3,4,5,8,6,2,7,1]=>0000000
[4,5,2,1,3,8,6,7]=>0000100
[4,2,3,6,8,5,1,7]=>0000000
[4,1,3,6,8,5,2,7]=>0000000
[3,1,4,5,8,6,2,7]=>0000000
[4,5,1,3,2,8,6,7]=>0000100
[3,4,5,8,6,1,7,2]=>0000000
[3,4,5,8,6,1,2,7]=>0000000
[8,2,5,4,1,3,7,6]=>0000000
[8,2,6,4,1,3,7,5]=>0000000
[1,5,8,2,4,3,7,6]=>1000000
[2,4,8,3,5,7,1,6]=>0000000
[1,4,8,5,7,2,3,6]=>1000000
[1,8,7,3,2,4,5,6]=>1000000
[2,8,4,3,5,7,1,6]=>0000000
[5,6,2,7,8,3,1,4]=>0000000
[8,6,2,7,3,4,1,5]=>0000000
[8,6,2,7,3,4,5,1]=>0000000
[5,6,2,7,8,3,4,1]=>0000000
[5,6,3,2,8,7,1,4]=>0000000
[6,8,5,3,1,7,2,4]=>0000000
[8,6,1,7,3,4,2,5]=>0000000
[5,1,6,7,8,3,2,4]=>0000000
[1,5,6,3,7,2,4,8]=>1000001
[6,2,4,8,3,7,1,5]=>0000000
[1,6,8,7,5,2,3,4]=>1000000
[1,5,6,7,4,2,3,8]=>1000001
[5,1,6,7,3,4,2,8]=>0000001
[8,6,1,7,3,4,5,2]=>0000000
[6,1,8,7,4,5,2,3]=>0000000
[2,6,8,4,7,5,1,3]=>0000000
[6,8,5,1,7,4,2,3]=>0000000
[4,6,5,7,2,3,8,1]=>0000000
[5,3,7,4,6,2,8,1]=>0000000
[3,6,7,2,5,8,4,1]=>0000000
[3,5,7,6,8,2,1,4]=>0000000
[5,3,6,7,4,8,1,2]=>0000000
[3,5,7,6,8,1,4,2]=>0000000
[4,2,7,8,3,6,5,1]=>0000000
[5,4,3,7,8,1,6,2]=>0000000
[5,3,6,7,8,2,1,4]=>0000000
[3,5,7,8,4,2,1,6]=>0000000
[4,6,7,8,2,1,3,5]=>0000000
[4,6,7,3,2,8,1,5]=>0000000
[4,6,5,3,7,8,1,2]=>0000000
[4,6,5,2,7,8,3,1]=>0000000
[3,7,5,2,8,6,1,4]=>0000000
[5,6,2,4,7,8,3,1]=>0000000
[5,4,6,2,8,3,7,1]=>0000000
[5,6,3,2,8,4,7,1]=>0000000
[5,6,2,8,3,4,7,1]=>0000000
[3,7,4,8,1,6,5,2]=>0000000
[5,2,6,4,8,7,3,1]=>0000000
[2,4,7,8,6,5,1,3]=>0000000
[2,5,7,8,6,1,4,3]=>0000000
[1,3,6,4,8,2,7,5]=>1000000
[2,4,5,3,8,7,1,6]=>0000000
[8,6,3,7,2,4,1,5]=>0000000
[1,8,5,6,4,2,3,7]=>1000000
[1,7,6,2,3,5,8,4]=>1000000
[8,1,6,5,2,7,4,3]=>0000000
[2,7,1,5,3,8,6,4]=>0000000
[7,3,2,1,4,8,6,5]=>0000000
[8,3,7,2,6,5,1,4]=>0000000
[7,5,8,2,6,1,4,3]=>0000000
[8,5,1,3,2,4,6,7]=>0000000
[3,8,5,1,2,4,6,7]=>0000000
[5,1,3,2,4,6,8,7]=>0000110
[5,3,8,1,4,2,6,7]=>0000000
[5,8,4,1,2,3,6,7]=>0000000
[5,1,7,8,4,2,3,6]=>0000000
[1,5,7,8,2,4,3,6]=>1000000
[3,5,8,1,4,2,7,6]=>0000000
[2,8,5,7,1,4,3,6]=>0000000
[4,8,7,5,1,2,3,6]=>0000000
[8,6,4,1,2,3,7,5]=>0000000
[8,1,2,4,6,3,7,5]=>0000000
[6,3,8,4,1,7,2,5]=>0000000
[7,6,1,4,2,3,8,5]=>0000000
[1,7,5,2,3,4,8,6]=>1000000
[7,8,1,2,5,3,4,6]=>0000000
[1,8,7,5,2,3,4,6]=>1000000
[7,1,4,8,2,3,6,5]=>0000000
[1,8,4,7,5,2,3,6]=>1000000
[7,3,4,1,8,6,2,5]=>0000000
[8,4,7,2,1,6,3,5]=>0000000
[3,4,7,8,6,1,2,5]=>0000000
[7,6,1,8,2,5,4,3]=>0000000
[5,8,4,2,1,6,3,7]=>0000000
[7,6,4,1,2,5,3,8]=>0000001
[4,8,6,5,1,3,7,2]=>0000000
[1,7,5,4,8,6,2,3]=>1000000
[1,6,3,7,2,4,8,5]=>1000000
[8,7,2,4,1,5,3,6]=>0000000
[5,2,4,1,8,3,6,7]=>0000000
[4,3,1,6,7,2,5,8]=>0000001
[6,3,1,5,7,2,4,8]=>0000001
[4,5,2,1,3,7,6,8]=>0000101
[2,7,6,4,5,1,8,3]=>0000000
[2,8,4,6,3,1,5,7]=>0000000
[2,8,3,1,6,7,4,5]=>0000000
[4,8,5,7,1,2,3,6]=>0000000
[7,4,8,3,6,2,1,5]=>0000000
[1,5,7,4,8,6,2,3]=>1000000
[4,8,7,5,2,3,1,6]=>0000000
[1,2,7,8,6,4,3,5]=>1100000
[3,5,1,7,8,6,2,4]=>0000000
[1,8,6,7,4,2,3,5]=>1000000
[1,5,4,7,3,8,6,2]=>1000000
[2,5,6,4,1,3,8,7]=>0000010
[7,2,3,1,6,8,4,5]=>0000000
[5,7,8,1,6,2,3,4]=>0000000
[1,6,3,8,2,7,4,5]=>1000000
[1,4,2,5,8,6,3,7]=>1000000
[4,8,2,1,5,7,3,6]=>0000000
[5,2,7,1,6,3,4,8]=>0000001
[4,8,2,5,1,6,3,7]=>0000000
[5,8,1,2,4,6,3,7]=>0000000
[5,1,7,3,6,4,2,8]=>0000001
[3,1,7,5,6,2,4,8]=>0000001
[3,2,7,5,6,1,4,8]=>0000001
[3,2,7,1,6,4,5,8]=>0000001
[6,3,1,7,5,4,2,8]=>0000001
[5,8,3,2,4,1,7,6]=>0000000
[2,7,5,6,8,3,1,4]=>0000000
[1,7,8,6,3,4,2,5]=>1000000
[7,3,2,1,4,6,8,5]=>0000000
[7,8,5,3,2,1,6,4]=>0000000
[1,4,7,2,5,3,6,8]=>1000001
[4,5,1,3,8,2,6,7]=>0000000
[4,1,5,3,2,7,6,8]=>0000101
[7,3,5,1,4,2,6,8]=>0000001
[7,5,2,4,1,3,8,6]=>0000000
[6,2,1,7,4,3,8,5]=>0000000
[2,4,3,6,7,1,5,8]=>0000001
[3,1,7,4,2,6,8,5]=>0000000
[7,3,5,2,1,6,4,8]=>0000001
[4,6,5,2,1,3,7,8]=>0000011
[1,4,7,2,5,6,3,8]=>1000001
[7,2,5,6,1,3,8,4]=>0000000
[2,5,6,1,4,3,7,8]=>0000011
[6,1,5,3,7,2,4,8]=>0000001
[3,6,5,4,1,7,2,8]=>0000001
[6,8,5,7,2,1,4,3]=>0000000
[1,4,2,6,7,8,5,3]=>1000000
[5,6,4,2,1,8,3,7]=>0000000
[4,1,2,6,7,8,5,3]=>0000000
[5,6,2,7,8,1,3,4]=>0000000
[3,7,8,2,1,4,5,6]=>0000000
[5,1,4,7,8,3,6,2]=>0000000
[5,6,4,1,7,3,8,2]=>0000000
[2,7,1,6,5,8,3,4]=>0000000
[4,6,1,7,3,2,8,5]=>0000000
[1,7,3,6,4,2,8,5]=>1000000
[1,3,7,6,2,4,8,5]=>1000000
[4,7,3,5,1,2,8,6]=>0000000
[2,5,1,8,3,7,4,6]=>0000000
[5,1,2,4,3,6,8,7]=>0000110
[4,8,3,5,2,1,6,7]=>0000000
[3,8,4,1,7,5,2,6]=>0000000
[4,7,3,2,6,5,1,8]=>0000001
[4,7,5,2,3,6,1,8]=>0000001
[4,3,7,8,2,1,6,5]=>0000000
[4,8,7,2,1,5,6,3]=>0000000
[7,3,8,2,5,1,6,4]=>0000000
[4,5,3,8,2,1,7,6]=>0000000
[4,5,3,8,6,1,2,7]=>0000000
[7,3,8,4,5,1,2,6]=>0000000
[4,8,7,5,1,3,2,6]=>0000000
[4,8,7,5,1,2,6,3]=>0000000
[7,8,4,6,1,3,5,2]=>0000000
[4,8,7,5,1,3,6,2]=>0000000
[4,5,3,6,8,1,2,7]=>0000000
[7,8,6,2,1,4,3,5]=>0000000
[4,7,5,8,2,1,3,6]=>0000000
[4,8,5,7,1,3,2,6]=>0000000
[7,8,6,3,1,2,5,4]=>0000000
[5,3,1,2,4,6,8,7]=>0000110
[6,1,5,2,8,7,4,3]=>0000000
[3,2,6,1,5,8,7,4]=>0000000
[4,5,2,1,6,7,8,3]=>0000000
[1,4,7,2,6,5,8,3]=>1000000
[1,7,6,2,8,5,4,3]=>1000000
[1,2,7,8,3,4,6,5]=>1100000
[2,8,4,3,1,6,5,7]=>0000000
[2,4,3,8,6,5,1,7]=>0000000
[2,8,6,4,3,1,7,5]=>0000000
[7,4,5,8,1,3,6,2]=>0000000
[4,2,5,7,1,6,8,3]=>0000000
[4,5,3,7,1,6,8,2]=>0000000
[6,8,4,1,5,7,3,2]=>0000000
[6,8,4,1,5,7,2,3]=>0000000
[5,2,6,7,4,1,8,3]=>0000000
[5,6,7,4,3,1,8,2]=>0000000
[8,5,6,4,1,7,3,2]=>0000000
[5,8,2,6,1,7,4,3]=>0000000
[7,8,3,1,6,4,5,2]=>0000000
[5,8,2,6,3,1,7,4]=>0000000
[4,5,8,1,6,3,7,2]=>0000000
[8,1,4,6,2,5,7,3]=>0000000
[4,8,1,3,6,2,7,5]=>0000000
[4,5,8,1,6,2,7,3]=>0000000
[5,2,6,8,1,4,3,7]=>0000000
[6,2,7,3,8,1,4,5]=>0000000
[6,7,3,8,2,1,4,5]=>0000000
[6,2,7,8,3,1,4,5]=>0000000
[8,7,3,1,2,5,6,4]=>0000000
[2,8,3,6,4,1,7,5]=>0000000
[6,1,3,7,2,8,5,4]=>0000000
[5,4,3,6,1,7,8,2]=>0000000
[4,8,3,2,1,7,5,6]=>0000000
[1,3,7,8,4,6,2,5]=>1000000
[5,8,4,3,7,1,2,6]=>0000000
[5,6,4,8,7,2,1,3]=>0000000
[4,1,7,8,6,5,2,3]=>0000000
[2,1,8,7,3,5,4,6]=>0100000
[1,7,6,2,3,8,5,4]=>1000000
[1,8,5,3,2,7,4,6]=>1000000
[4,5,1,3,7,6,2,8]=>0000001
[7,2,3,8,6,4,5,1]=>0000000
[3,5,8,1,7,4,2,6]=>0000000
[5,8,1,2,7,6,4,3]=>0000000
[8,7,1,3,2,6,4,5]=>0000000
[8,1,6,3,7,5,4,2]=>0000000
[8,5,1,3,7,6,4,2]=>0000000
[1,6,4,7,3,8,5,2]=>1000000
[2,8,1,5,6,4,3,7]=>0000000
[1,2,6,8,3,4,7,5]=>1100000
[1,6,7,5,8,4,2,3]=>1000000
[5,3,8,2,7,6,1,4]=>0000000
[7,4,2,8,6,5,3,1]=>0000000
[5,8,2,7,6,1,4,3]=>0000000
[7,4,8,3,1,6,5,2]=>0000000
[5,8,7,2,6,4,3,1]=>0000000
[6,8,7,5,2,1,4,3]=>0000000
[6,8,7,3,5,1,4,2]=>0000000
[7,2,5,4,1,3,8,6]=>0000000
[1,5,7,2,4,3,8,6]=>1000000
[1,2,7,5,8,4,3,6]=>1100000
[5,1,3,8,2,7,4,6]=>0000000
[5,7,1,3,2,8,4,6]=>0000000
[7,1,6,3,2,8,4,5]=>0000000
[8,1,7,2,3,6,5,4]=>0000000
[1,7,2,5,8,4,3,6]=>1000000
[7,1,2,6,4,3,8,5]=>0000000
[1,4,7,8,3,2,5,6]=>1000000
[8,7,1,3,2,4,6,5]=>0000000
[8,1,6,3,2,4,7,5]=>0000000
[1,8,2,7,6,3,5,4]=>1000000
[1,8,6,2,7,4,3,5]=>1000000
[8,1,6,3,2,7,4,5]=>0000000
[8,2,1,7,6,3,4,5]=>0000000
[6,4,5,3,1,8,7,2]=>0000000
[1,8,2,3,5,6,4,7]=>1000000
[2,8,1,3,5,6,4,7]=>0000000
[2,5,7,4,8,3,6,1]=>0000000
[2,6,3,4,7,8,5,1]=>0000000
[2,3,5,4,7,1,8,6]=>0000000
[7,4,1,3,6,8,5,2]=>0000000
[7,2,1,3,6,8,4,5]=>0000000
[7,4,2,3,6,8,5,1]=>0000000
[7,2,3,6,8,5,4,1]=>0000000
[7,6,3,1,8,5,2,4]=>0000000
[7,2,1,3,6,8,5,4]=>0000000
[7,6,3,8,1,5,2,4]=>0000000
[1,6,4,7,8,5,3,2]=>1000000
[7,2,5,1,6,4,3,8]=>0000001
[1,2,4,6,8,5,7,3]=>1100000
[2,6,3,7,4,1,8,5]=>0000000
[3,8,5,1,2,4,7,6]=>0000000
[1,8,3,7,5,2,6,4]=>1000000
[8,1,3,6,5,2,7,4]=>0000000
[7,1,3,8,5,2,6,4]=>0000000
[4,7,1,5,2,6,8,3]=>0000000
[7,4,1,5,2,6,8,3]=>0000000
[3,1,6,7,5,2,8,4]=>0000000
[8,6,2,4,5,1,7,3]=>0000000
[4,6,2,5,3,1,7,8]=>0000011
[7,1,4,5,2,6,8,3]=>0000000
[5,7,6,8,2,1,4,3]=>0000000
[4,5,1,3,6,7,8,2]=>0000000
[6,4,7,1,5,2,8,3]=>0000000
[3,5,6,2,1,7,8,4]=>0000000
[4,5,1,6,2,8,7,3]=>0000000
[3,2,5,8,6,1,7,4]=>0000000
[5,6,3,2,7,4,1,8]=>0000001
[5,2,6,7,4,3,1,8]=>0000001
[8,5,1,6,4,3,2,7]=>0000000
[8,5,1,6,4,3,7,2]=>0000000
[8,5,2,1,6,4,3,7]=>0000000
[8,6,3,5,2,7,1,4]=>0000000
[8,4,6,2,1,5,7,3]=>0000000
[5,6,2,1,8,4,7,3]=>0000000
[8,5,2,1,6,4,7,3]=>0000000
[1,7,2,8,5,4,6,3]=>1000000
[6,7,1,4,8,5,3,2]=>0000000
[7,4,8,2,1,5,6,3]=>0000000
[7,3,2,8,5,1,4,6]=>0000000
[6,7,1,4,3,2,8,5]=>0000000
[4,1,7,3,2,8,5,6]=>0000000
[8,3,5,2,4,7,1,6]=>0000000
[4,3,7,8,6,1,5,2]=>0000000
[6,2,8,4,3,7,1,5]=>0000000
[1,2,6,3,7,8,5,4]=>1100000
[6,1,3,2,7,8,5,4]=>0000000
[6,7,1,3,2,8,5,4]=>0000000
[2,6,4,7,5,3,1,8]=>0000001
[5,6,1,8,7,2,3,4]=>0000000
[1,4,7,5,2,3,6,8]=>1000001
[1,5,8,6,2,3,4,7]=>1000000
[5,8,4,3,6,2,7,1]=>0000000
[4,6,5,8,3,2,7,1]=>0000000
[3,4,7,5,6,8,2,1]=>0000000
[3,4,7,8,5,2,6,1]=>0000000
[2,3,8,4,7,1,6,5]=>0000000
[1,8,7,5,2,6,3,4]=>1000000
[1,8,7,5,4,3,2,6]=>1000000
[1,7,6,3,4,5,8,2]=>1000000
[1,8,7,4,5,6,2,3]=>1000000
[1,8,7,3,6,4,2,5]=>1000000
[1,8,7,2,4,6,3,5]=>1000000
[1,4,7,8,6,2,5,3]=>1000000
[1,7,6,4,2,5,3,8]=>1000001
[1,4,7,5,8,2,3,6]=>1000000
[1,4,7,5,8,2,6,3]=>1000000
[1,6,8,3,4,2,5,7]=>1000000
[1,4,7,2,3,6,5,8]=>1000001
[1,3,2,6,8,4,7,5]=>1010000
[1,7,2,5,6,3,4,8]=>1000001
[1,5,8,3,6,4,7,2]=>1000000
[1,2,6,5,8,3,4,7]=>1100000
[1,6,8,2,7,3,4,5]=>1000000
[1,4,5,8,2,6,3,7]=>1000000
[3,5,6,7,2,4,1,8]=>0000001
[6,4,7,5,2,3,1,8]=>0000001
[1,5,6,4,8,3,2,7]=>1000000
[5,2,6,4,8,7,1,3]=>0000000
[2,1,5,6,4,8,3,7]=>0100000
[5,1,4,7,8,6,2,3]=>0000000
[2,5,7,1,8,6,3,4]=>0000000
[1,6,7,2,8,5,4,3]=>1000000
[4,6,1,7,8,5,3,2]=>0000000
[5,3,2,1,7,8,6,4]=>0000000
[7,4,3,8,6,1,5,2]=>0000000
[4,3,7,1,5,8,6,2]=>0000000
[8,2,4,5,3,1,7,6]=>0000000
[8,5,3,2,4,1,7,6]=>0000000
[1,4,3,2,7,5,8,6]=>1001000
[7,2,5,3,4,6,1,8]=>0000001
[7,1,2,6,4,3,5,8]=>0000001
[7,1,2,6,3,4,5,8]=>0000001
[7,1,2,6,4,5,3,8]=>0000001
[7,1,2,6,5,3,4,8]=>0000001
[5,3,1,4,7,2,8,6]=>0000000
[7,1,3,8,2,6,4,5]=>0000000
[1,8,3,7,2,4,6,5]=>1000000
[7,4,3,1,6,5,2,8]=>0000001
[3,5,1,2,6,8,7,4]=>0000000
[1,5,2,4,3,8,7,6]=>1000100
[3,1,2,4,8,7,5,6]=>0011000
[5,2,1,6,3,8,7,4]=>0000000
[3,4,6,7,2,1,5,8]=>0000001
[2,5,7,4,6,8,1,3]=>0000000
[4,6,2,7,5,8,1,3]=>0000000
[4,7,2,5,3,8,1,6]=>0000000
[2,4,7,6,3,8,1,5]=>0000000
[5,8,3,6,4,1,7,2]=>0000000
[4,6,8,5,1,2,3,7]=>0000000
[4,6,5,7,1,2,3,8]=>0000001
[4,6,5,7,1,3,8,2]=>0000000
[3,4,7,6,1,8,2,5]=>0000000
[1,6,5,7,3,8,2,4]=>1000000
[8,6,2,7,5,3,1,4]=>0000000
[4,3,7,1,2,8,5,6]=>0000000
[2,6,7,1,4,3,8,5]=>0000000
[4,5,2,1,6,3,8,7]=>0000010
[4,5,2,1,6,7,3,8]=>0000001
[5,3,8,6,2,4,7,1]=>0000000
[2,5,1,6,4,3,8,7]=>0000010
[3,6,2,8,5,7,1,4]=>0000000
[4,6,8,1,5,7,2,3]=>0000000
[4,1,2,5,7,6,3,8]=>0000001
[5,2,3,8,7,1,6,4]=>0000000
[3,2,8,1,7,5,4,6]=>0000000
[4,8,5,1,3,7,2,6]=>0000000
[4,6,5,8,1,7,3,2]=>0000000
[2,1,3,6,4,8,7,5]=>0110000
[4,8,2,1,6,7,5,3]=>0000000
[4,8,1,2,7,5,6,3]=>0000000
[5,2,8,1,7,4,6,3]=>0000000
[5,7,4,8,1,2,6,3]=>0000000
[8,1,6,7,3,4,2,5]=>0000000
[4,5,1,6,8,7,2,3]=>0000000
[3,4,7,2,5,8,6,1]=>0000000
[3,4,7,1,5,8,2,6]=>0000000
[6,2,7,4,5,3,1,8]=>0000001
[8,6,4,7,5,1,3,2]=>0000000
[5,1,4,8,2,3,7,6]=>0000000
[4,5,2,3,8,6,1,7]=>0000000
[4,5,1,3,2,6,8,7]=>0000110
[4,7,1,8,5,3,6,2]=>0000000
[6,4,7,5,1,3,2,8]=>0000001
[6,7,2,4,1,8,3,5]=>0000000
[5,1,6,3,2,7,8,4]=>0000000
[2,3,7,8,5,4,6,1]=>0000000
[7,4,5,1,2,6,8,3]=>0000000
[6,7,8,2,1,5,3,4]=>0000000
[5,2,1,6,4,7,3,8]=>0000001
[6,7,2,5,4,1,3,8]=>0000001
[7,4,8,6,3,5,1,2]=>0000000
[4,6,3,5,1,8,2,7]=>0000000
[8,5,7,6,2,3,4,1]=>0000000
[2,4,7,5,8,6,3,1]=>0000000
[1,4,6,5,3,8,2,7]=>1000000
[2,4,5,8,7,1,3,6]=>0000000
[3,1,6,8,7,5,4,2]=>0000000
[3,1,8,7,5,6,4,2]=>0000000
[5,1,8,7,6,3,4,2]=>0000000
[1,3,8,4,7,2,6,5]=>1000000
[1,8,2,4,7,3,6,5]=>1000000
[8,2,7,5,3,6,4,1]=>0000000
[8,4,1,3,6,7,2,5]=>0000000
[8,7,2,3,1,5,6,4]=>0000000
[1,2,8,6,7,5,4,3]=>1100000
[2,8,5,7,6,1,3,4]=>0000000
[1,8,7,2,6,4,5,3]=>1000000
[8,7,2,1,6,4,5,3]=>0000000
[8,7,2,4,3,6,5,1]=>0000000
[4,2,8,7,3,6,5,1]=>0000000
[8,7,1,6,4,3,5,2]=>0000000
[8,4,1,7,3,6,5,2]=>0000000
[4,5,1,8,7,3,6,2]=>0000000
[4,3,8,5,2,6,1,7]=>0000000
[5,7,4,1,2,6,8,3]=>0000000
[2,8,6,7,5,3,1,4]=>0000000
[5,2,6,3,7,8,4,1]=>0000000
[3,6,2,5,7,8,4,1]=>0000000
[2,7,4,6,8,3,5,1]=>0000000
[2,7,3,6,8,5,4,1]=>0000000
[3,7,6,8,1,5,4,2]=>0000000
[4,7,6,8,2,3,5,1]=>0000000
[3,7,5,6,8,2,4,1]=>0000000
[3,7,2,6,8,4,5,1]=>0000000
[1,5,7,6,8,4,2,3]=>1000000
[2,7,5,6,8,4,3,1]=>0000000
[3,7,6,8,5,1,4,2]=>0000000
[7,1,3,8,6,2,4,5]=>0000000
[2,7,1,8,6,5,3,4]=>0000000
[5,3,4,7,6,2,1,8]=>0000001
[7,1,4,6,8,5,3,2]=>0000000
[7,2,5,1,6,4,8,3]=>0000000
[2,7,1,5,6,4,8,3]=>0000000
[1,5,7,8,4,6,3,2]=>1000000
[1,4,8,5,7,6,3,2]=>1000000
[2,8,1,5,6,4,7,3]=>0000000
[8,2,1,5,6,4,7,3]=>0000000
[2,8,5,1,6,4,3,7]=>0000000
[3,7,2,8,1,5,6,4]=>0000000
[7,3,2,5,1,6,8,4]=>0000000
[8,7,2,1,3,6,5,4]=>0000000
[7,3,2,8,1,4,6,5]=>0000000
[2,7,8,1,5,4,3,6]=>0000000
[3,6,2,1,8,4,7,5]=>0000000
[3,8,6,1,5,7,4,2]=>0000000
[6,4,2,3,7,8,1,5]=>0000000
[5,4,3,1,7,2,8,6]=>0000000
[5,3,1,6,4,7,2,8]=>0000001
[6,5,2,4,1,7,8,3]=>0000000
[4,3,6,2,5,8,1,7]=>0000000
[1,6,2,7,8,4,5,3]=>1000000
[8,5,2,4,1,3,7,6]=>0000000
[6,3,2,8,4,5,1,7]=>0000000
[5,4,7,2,1,3,8,6]=>0000000
[4,1,7,6,5,2,8,3]=>0000000
[6,4,7,1,2,3,8,5]=>0000000
[8,2,3,1,6,4,7,5]=>0000000
[3,1,8,5,7,2,6,4]=>0000000
[5,6,4,2,1,7,3,8]=>0000001
[6,5,7,1,2,8,3,4]=>0000000
[6,4,7,1,2,5,3,8]=>0000001
[1,2,4,8,5,7,3,6]=>1100000
[1,2,7,5,8,6,3,4]=>1100000
[7,4,5,1,6,8,2,3]=>0000000
[1,7,8,4,2,6,3,5]=>1000000
[6,3,2,5,7,4,1,8]=>0000001
[6,4,7,5,3,8,1,2]=>0000000
[6,2,1,5,3,7,8,4]=>0000000
[4,1,7,8,3,6,5,2]=>0000000
[6,3,2,4,8,5,1,7]=>0000000
[6,4,2,1,7,3,5,8]=>0000001
[5,7,4,2,1,6,3,8]=>0000001
[5,8,4,2,1,3,6,7]=>0000000
[8,3,2,6,5,1,7,4]=>0000000
[1,8,5,6,4,3,7,2]=>1000000
[1,7,5,8,4,6,3,2]=>1000000
[8,3,5,6,1,7,2,4]=>0000000
[1,5,3,7,8,4,6,2]=>1000000
[1,4,7,3,5,8,6,2]=>1000000
[1,6,3,7,8,5,4,2]=>1000000
[8,5,6,1,7,4,2,3]=>0000000
[8,6,1,4,3,7,2,5]=>0000000
[3,7,8,2,5,1,6,4]=>0000000
[8,1,3,5,6,4,2,7]=>0000000
[8,6,1,4,3,2,7,5]=>0000000
[7,3,8,2,4,1,5,6]=>0000000
[6,3,7,8,1,2,5,4]=>0000000
[7,5,8,1,2,3,6,4]=>0000000
[8,6,1,5,3,7,2,4]=>0000000
[8,1,7,5,6,4,2,3]=>0000000
[8,1,4,7,6,5,2,3]=>0000000
[6,1,4,8,2,7,5,3]=>0000000
[8,6,4,2,7,3,5,1]=>0000000
[6,8,7,5,2,1,3,4]=>0000000
[7,6,1,5,2,3,8,4]=>0000000
[5,1,8,6,7,2,3,4]=>0000000
[5,7,1,6,8,2,3,4]=>0000000
[5,1,7,6,8,2,3,4]=>0000000
[6,1,5,7,2,8,3,4]=>0000000
[6,8,4,2,1,7,3,5]=>0000000
[5,8,6,1,7,2,3,4]=>0000000
[6,3,2,8,1,7,4,5]=>0000000
[1,4,7,8,3,5,2,6]=>1000000
[2,5,6,8,1,4,7,3]=>0000000
[8,4,5,1,6,7,2,3]=>0000000
[7,3,6,1,4,2,8,5]=>0000000
[7,4,1,6,5,2,3,8]=>0000001
[4,1,6,5,2,3,8,7]=>0000010
[4,5,1,7,8,6,2,3]=>0000000
[8,3,1,4,6,2,7,5]=>0000000
[2,5,3,4,6,8,1,7]=>0000000
[8,3,6,1,5,2,4,7]=>0000000
[4,7,1,2,5,6,3,8]=>0000001
[6,7,3,1,8,2,4,5]=>0000000
[7,3,1,4,6,2,8,5]=>0000000
[7,4,1,2,5,6,3,8]=>0000001
[4,5,1,3,6,8,7,2]=>0000000
[8,4,1,2,5,7,3,6]=>0000000
[8,4,1,3,6,7,5,2]=>0000000
[5,4,1,6,3,7,8,2]=>0000000
[6,7,3,1,5,2,4,8]=>0000001
[5,4,1,3,6,8,7,2]=>0000000
[6,4,1,2,5,8,3,7]=>0000000
[5,7,4,8,1,6,3,2]=>0000000
[7,5,3,6,4,2,1,8]=>0000001
[4,3,1,2,6,5,7,8]=>0001011
[4,3,1,2,5,7,6,8]=>0001101
[4,7,3,1,5,2,8,6]=>0000000
[6,5,1,2,7,4,8,3]=>0000000
[5,3,8,1,4,2,7,6]=>0000000
[6,5,3,4,1,8,2,7]=>0000000
[3,1,8,4,2,7,6,5]=>0000000
[2,8,7,4,1,3,6,5]=>0000000
[8,2,3,1,7,6,4,5]=>0000000
[5,2,4,1,6,8,3,7]=>0000000
[8,7,2,3,1,6,4,5]=>0000000
[6,2,3,1,7,8,4,5]=>0000000
[7,2,5,8,3,1,4,6]=>0000000
[6,8,2,3,1,7,4,5]=>0000000
[8,2,5,7,3,1,4,6]=>0000000
[2,5,8,7,3,1,4,6]=>0000000
[2,8,7,3,1,4,5,6]=>0000000
[8,2,3,1,6,7,4,5]=>0000000
[2,8,4,1,3,6,7,5]=>0000000
[2,7,3,1,4,5,8,6]=>0000000
[7,2,8,3,1,4,5,6]=>0000000
[2,7,8,3,1,4,5,6]=>0000000
[5,3,2,8,7,1,6,4]=>0000000
[6,8,7,2,1,5,4,3]=>0000000
[4,8,5,3,6,1,7,2]=>0000000
[6,3,1,5,4,8,2,7]=>0000000
[8,4,2,6,5,7,3,1]=>0000000
[4,7,6,3,5,2,8,1]=>0000000
[1,7,5,3,4,8,6,2]=>1000000
[4,8,6,2,5,7,3,1]=>0000000
[8,7,3,2,6,4,5,1]=>0000000
[8,3,1,4,7,5,2,6]=>0000000
[5,3,1,6,4,8,7,2]=>0000000
[3,4,8,5,7,2,6,1]=>0000000
[4,1,7,8,3,2,5,6]=>0000000
[8,5,1,2,7,6,4,3]=>0000000
[4,6,5,3,1,8,7,2]=>0000000
[6,4,7,2,5,3,1,8]=>0000001
[4,3,6,1,2,7,8,5]=>0000000
[2,7,4,6,3,8,1,5]=>0000000
[7,3,5,6,4,1,8,2]=>0000000
[5,7,6,3,4,2,1,8]=>0000001
[3,7,5,6,4,2,1,8]=>0000001
[5,7,3,6,4,2,1,8]=>0000001
[5,7,3,6,4,1,8,2]=>0000000
[3,7,5,6,4,1,8,2]=>0000000
[5,7,6,3,4,1,8,2]=>0000000
[3,2,7,5,6,1,8,4]=>0000000
[5,3,4,7,6,1,8,2]=>0000000
[5,3,4,2,7,1,8,6]=>0000000
[3,5,4,1,7,8,6,2]=>0000000
[3,1,2,7,5,8,4,6]=>0010000
[8,4,1,5,6,2,7,3]=>0000000
[1,8,5,3,2,4,6,7]=>1000000
[4,8,5,1,2,3,6,7]=>0000000
[3,5,1,4,2,6,8,7]=>0000110
[4,8,7,1,2,5,3,6]=>0000000
[8,7,2,6,1,4,3,5]=>0000000
[1,7,6,8,4,2,3,5]=>1000000
[1,7,4,8,2,5,3,6]=>1000000
[6,1,7,3,8,2,4,5]=>0000000
[1,5,8,2,3,4,7,6]=>1000000
[8,4,2,7,1,3,6,5]=>0000000
[7,1,8,6,4,2,3,5]=>0000000
[1,7,8,6,4,2,3,5]=>1000000
[5,1,7,3,2,6,8,4]=>0000000
[8,7,5,3,2,6,4,1]=>0000000
[4,5,2,3,8,7,1,6]=>0000000
[4,6,7,5,2,3,1,8]=>0000001
[6,5,2,3,1,8,7,4]=>0000000
[6,2,5,3,1,8,7,4]=>0000000
[6,2,5,3,8,7,1,4]=>0000000
[6,4,5,3,8,7,1,2]=>0000000
[1,6,4,5,8,7,3,2]=>1000000
[8,4,7,5,2,3,1,6]=>0000000
[8,2,7,4,5,3,1,6]=>0000000
[6,2,4,7,5,3,1,8]=>0000001
[8,2,4,7,5,3,1,6]=>0000000
[8,2,6,7,5,3,1,4]=>0000000
[8,4,6,7,5,3,1,2]=>0000000
[6,4,5,8,7,3,1,2]=>0000000
[6,2,8,7,5,3,1,4]=>0000000
[2,4,8,7,5,3,1,6]=>0000000
[4,6,8,7,5,3,1,2]=>0000000
[4,6,5,3,8,7,1,2]=>0000000
[2,6,5,8,7,3,1,4]=>0000000
[6,7,2,4,5,3,1,8]=>0000001
[4,5,8,7,2,3,1,6]=>0000000
[4,8,7,2,5,3,1,6]=>0000000
[6,8,7,4,5,3,1,2]=>0000000
[2,8,4,7,5,3,1,6]=>0000000
[4,8,2,7,5,3,1,6]=>0000000
[6,8,2,7,5,3,1,4]=>0000000
[7,4,3,8,1,6,5,2]=>0000000
[3,7,4,6,2,1,8,5]=>0000000
[2,6,5,7,8,3,1,4]=>0000000
[3,4,8,6,2,1,7,5]=>0000000
[1,6,2,3,8,5,7,4]=>1000000
[1,2,7,3,8,5,6,4]=>1100000
[2,3,6,5,8,4,7,1]=>0000000
[3,4,2,6,8,5,7,1]=>0000000
[2,4,7,3,8,5,1,6]=>0000000
[1,2,8,3,5,4,7,6]=>1100000
[1,3,6,7,4,5,8,2]=>1000000
[7,4,1,3,6,8,2,5]=>0000000
[5,1,7,3,4,6,8,2]=>0000000
[6,1,7,3,5,8,2,4]=>0000000
[6,8,1,2,7,3,4,5]=>0000000
[5,6,2,1,8,3,4,7]=>0000000
[6,4,1,3,7,8,2,5]=>0000000
[1,6,2,8,7,3,4,5]=>1000000
[5,2,8,4,7,1,3,6]=>0000000
[3,8,7,2,6,1,4,5]=>0000000
[2,5,1,8,3,6,4,7]=>0000000
[2,3,8,1,4,6,5,7]=>0000000
[1,3,8,2,5,4,7,6]=>1000000
[3,1,8,4,6,2,5,7]=>0000000
[6,3,2,4,8,7,1,5]=>0000000
[1,4,8,6,2,3,5,7]=>1000000
[3,1,8,4,5,6,2,7]=>0000000
[4,5,8,3,6,1,7,2]=>0000000
[3,5,4,8,6,1,7,2]=>0000000
[4,2,7,8,6,3,1,5]=>0000000
[7,1,4,2,8,6,3,5]=>0000000
[2,3,7,4,8,1,6,5]=>0000000
[8,3,1,2,5,4,7,6]=>0000000
[6,5,1,2,8,4,7,3]=>0000000
[8,1,5,3,7,4,2,6]=>0000000
[1,3,4,8,6,2,7,5]=>1000000
[1,2,4,8,6,7,3,5]=>1100000
[8,1,2,6,5,7,3,4]=>0000000
[7,1,2,6,5,8,3,4]=>0000000
[7,1,6,8,3,2,4,5]=>0000000
[2,6,1,4,7,5,8,3]=>0000000
[5,1,4,3,7,8,6,2]=>0000000
[6,4,1,3,7,8,5,2]=>0000000
[3,1,5,7,2,6,8,4]=>0000000
[7,2,4,8,5,1,6,3]=>0000000
[3,1,7,5,2,6,8,4]=>0000000
[3,2,7,5,1,6,8,4]=>0000000
[5,2,7,3,1,6,8,4]=>0000000
[6,7,2,1,3,4,8,5]=>0000000
[4,6,3,1,2,7,8,5]=>0000000
[6,7,3,1,2,4,8,5]=>0000000
[3,8,5,2,1,6,7,4]=>0000000
[6,4,7,8,3,5,1,2]=>0000000
[6,4,7,8,1,2,5,3]=>0000000
[3,5,6,7,1,8,4,2]=>0000000
[1,7,4,5,2,8,6,3]=>1000000
[1,7,3,8,2,5,4,6]=>1000000
[8,6,4,5,1,3,7,2]=>0000000
[7,5,8,4,1,3,6,2]=>0000000
[4,7,5,3,6,8,1,2]=>0000000
[4,8,5,3,7,1,2,6]=>0000000
[2,8,1,6,5,7,3,4]=>0000000
[4,7,5,3,8,1,6,2]=>0000000
[7,4,8,5,3,6,1,2]=>0000000
[7,4,5,3,8,1,6,2]=>0000000
[8,4,6,5,1,3,7,2]=>0000000
[6,3,5,8,1,7,4,2]=>0000000
[7,3,6,1,5,8,4,2]=>0000000
[4,5,3,8,7,1,2,6]=>0000000
[8,5,4,7,6,1,2,3]=>0000000
[3,7,6,1,5,8,4,2]=>0000000
[8,2,3,6,4,1,7,5]=>0000000
[2,7,3,6,4,1,8,5]=>0000000
[2,3,7,8,1,4,6,5]=>0000000
[2,7,3,5,4,1,8,6]=>0000000
[8,2,3,5,4,1,7,6]=>0000000
[7,1,3,8,2,4,6,5]=>0000000
[7,2,3,6,4,1,8,5]=>0000000
[6,5,2,4,1,8,3,7]=>0000000
[5,7,2,4,1,3,8,6]=>0000000
[6,2,5,4,1,8,3,7]=>0000000
[8,1,2,5,3,7,6,4]=>0000000
[1,8,5,4,2,6,3,7]=>1000000
[8,3,6,5,4,2,1,7]=>0000000
[5,4,8,7,6,2,3,1]=>0000000
[6,8,4,7,5,1,3,2]=>0000000
[1,7,2,5,6,8,3,4]=>1000000
[4,1,7,5,6,8,2,3]=>0000000
[1,5,8,3,2,7,4,6]=>1000000
[7,6,4,2,5,3,1,8]=>0000001
[1,8,6,5,2,7,4,3]=>1000000
[8,2,6,5,1,7,4,3]=>0000000
[6,1,4,7,2,5,8,3]=>0000000
[6,8,2,5,1,7,4,3]=>0000000
[1,6,4,7,2,5,8,3]=>1000000
[7,6,4,1,2,5,8,3]=>0000000
[6,8,1,5,2,7,4,3]=>0000000
[8,6,5,2,1,7,4,3]=>0000000
[1,6,5,2,8,7,4,3]=>1000000
[1,8,5,2,7,6,4,3]=>1000000
[1,8,6,7,2,5,4,3]=>1000000
[1,7,6,8,2,5,4,3]=>1000000
[1,7,8,6,2,5,4,3]=>1000000
[8,1,7,6,2,5,4,3]=>0000000
[1,7,8,6,3,5,4,2]=>1000000
[1,4,2,3,7,8,6,5]=>1001000
[1,8,4,2,3,6,5,7]=>1000000
[1,3,8,5,6,4,2,7]=>1000000
[1,6,3,7,8,4,2,5]=>1000000
[1,6,3,8,4,2,5,7]=>1000000
[1,7,8,4,2,3,5,6]=>1000000
[1,7,8,5,6,4,2,3]=>1000000
[1,6,3,4,2,5,8,7]=>1000010
[1,3,5,8,6,4,2,7]=>1000000
[1,7,6,2,3,8,4,5]=>1000000
[1,5,7,6,2,3,8,4]=>1000000
[1,3,7,6,2,4,5,8]=>1000001
[1,4,3,7,6,2,5,8]=>1000001
[1,5,8,4,3,7,6,2]=>1000000
[1,7,5,8,4,3,6,2]=>1000000
[4,1,5,7,3,8,2,6]=>0000000
[1,3,7,4,6,8,5,2]=>1000000
[1,5,2,6,8,7,4,3]=>1000000
[1,3,7,6,4,8,2,5]=>1000000
[6,5,1,4,3,8,7,2]=>0000000
[5,6,1,4,3,8,7,2]=>0000000
[5,8,6,4,3,1,7,2]=>0000000
[4,1,3,7,8,6,5,2]=>0000000
[8,5,6,4,3,1,7,2]=>0000000
[8,4,3,1,7,6,5,2]=>0000000
[3,2,7,1,8,6,5,4]=>0000000
[9,10,7,8,5,6,3,4,1,2]=>000000000
[5,4,3,2,1,6,7,8,9,10]=>000011111
[6,4,3,2,7,1,5,8,9,10]=>000000111
[7,5,3,8,2,6,1,4,9,10]=>000000011
[8,6,9,4,7,2,5,1,3,10]=>000000001
[6,7,8,9,10,5,4,3,2,1]=>000000000
[1,2,3,4,5,10,9,8,7,6]=>111110000
[10,8,6,4,2,1,3,5,7,9]=>000000000
[6,5,4,3,7,8,9,10,1,2]=>000000000
[7,8,10,9,5,6,3,4,1,2]=>000000000
[9,10,5,6,8,7,3,4,1,2]=>000000000
[5,8,10,6,9,7,3,4,1,2]=>000000000
[5,6,7,10,9,8,3,4,1,2]=>000000000
[9,10,7,8,3,4,6,5,1,2]=>000000000
[7,8,10,9,3,4,6,5,1,2]=>000000000
[9,10,3,6,8,4,7,5,1,2]=>000000000
[3,8,10,6,9,4,7,5,1,2]=>000000000
[3,6,7,10,9,4,8,5,1,2]=>000000000
[9,10,3,4,5,8,7,6,1,2]=>000000000
[3,8,10,4,5,9,7,6,1,2]=>000000000
[3,4,7,10,5,9,8,6,1,2]=>000000000
[3,4,5,6,10,9,8,7,1,2]=>000000000
[9,10,7,8,5,6,1,2,4,3]=>000000000
[7,8,10,9,5,6,1,2,4,3]=>000000000
[9,10,5,6,8,7,1,2,4,3]=>000000000
[5,8,10,6,9,7,1,2,4,3]=>000000000
[5,6,7,10,9,8,1,2,4,3]=>000000000
[9,10,7,8,1,4,6,2,5,3]=>000000000
[7,8,10,9,1,4,6,2,5,3]=>000000000
[9,10,1,6,8,4,7,2,5,3]=>000000000
[1,8,10,6,9,4,7,2,5,3]=>100000000
[1,6,7,10,9,4,8,2,5,3]=>100000000
[9,10,1,4,5,8,7,2,6,3]=>000000000
[1,8,10,4,5,9,7,2,6,3]=>100000000
[1,4,7,10,5,9,8,2,6,3]=>100000000
[1,4,5,6,10,9,8,2,7,3]=>100000000
[9,10,7,8,1,2,3,6,5,4]=>000000000
[7,8,10,9,1,2,3,6,5,4]=>000000000
[9,10,1,6,8,2,3,7,5,4]=>000000000
[1,8,10,6,9,2,3,7,5,4]=>100000000
[1,6,7,10,9,2,3,8,5,4]=>100000000
[9,10,1,2,5,8,3,7,6,4]=>000000000
[1,8,10,2,5,9,3,7,6,4]=>100000000
[1,2,7,10,5,9,3,8,6,4]=>110000000
[1,2,5,6,10,9,3,8,7,4]=>110000000
[9,10,1,2,3,4,8,7,6,5]=>000000000
[1,8,10,2,3,4,9,7,6,5]=>100000000
[1,2,7,10,3,4,9,8,6,5]=>110000000
[1,2,3,6,10,4,9,8,7,5]=>111000000
[9,10,7,8,5,6,2,1,3,4]=>000000000
[9,10,7,8,4,3,5,6,1,2]=>000000000
[9,10,7,8,4,2,5,1,3,6]=>000000000
[9,10,7,8,3,2,1,4,5,6]=>000000000
[9,10,6,5,7,8,3,4,1,2]=>000000000
[9,10,6,5,7,8,2,1,3,4]=>000000000
[9,10,6,4,7,3,5,8,1,2]=>000000000
[9,10,6,4,7,2,5,1,3,8]=>000000000
[9,10,6,3,7,2,1,4,5,8]=>000000000
[9,10,5,4,3,6,7,8,1,2]=>000000000
[9,10,5,4,2,6,7,1,3,8]=>000000000
[9,10,5,3,2,6,1,4,7,8]=>000000000
[9,10,4,3,2,1,5,6,7,8]=>000000000
[8,7,9,10,5,6,3,4,1,2]=>000000000
[8,7,9,10,5,6,2,1,3,4]=>000000000
[8,7,9,10,4,3,5,6,1,2]=>000000000
[8,7,9,10,4,2,5,1,3,6]=>000000000
[8,7,9,10,3,2,1,4,5,6]=>000000000
[8,6,9,5,7,10,3,4,1,2]=>000000000
[8,6,9,5,7,10,2,1,3,4]=>000000000
[8,6,9,4,7,3,5,10,1,2]=>000000000
[8,6,9,3,7,2,1,4,5,10]=>000000001
[8,5,9,4,3,6,7,10,1,2]=>000000000
[8,5,9,4,2,6,7,1,3,10]=>000000001
[8,5,9,3,2,6,1,4,7,10]=>000000001
[8,4,9,3,2,1,5,6,7,10]=>000000001
[7,6,5,8,9,10,3,4,1,2]=>000000000
[7,6,5,8,9,10,2,1,3,4]=>000000000
[7,6,4,8,9,3,5,10,1,2]=>000000000
[7,6,4,8,9,2,5,1,3,10]=>000000001
[7,6,3,8,9,2,1,4,5,10]=>000000001
[7,5,4,8,3,6,9,10,1,2]=>000000000
[7,5,4,8,2,6,9,1,3,10]=>000000001
[7,4,3,8,2,1,5,6,9,10]=>000000011
[6,5,4,2,7,8,9,1,3,10]=>000000001
[6,5,3,2,7,8,1,4,9,10]=>000000011
[9,10,6,4,2,1,3,5,8,7]=>000000000
[10,7,8,4,2,1,3,6,5,9]=>000000000
[9,7,10,4,2,1,3,6,8,5]=>000000000
[8,9,10,4,2,1,3,7,6,5]=>000000000
[10,8,5,6,2,1,4,3,7,9]=>000000000
[9,10,5,6,2,1,4,3,8,7]=>000000000
[10,7,5,8,2,1,4,6,3,9]=>000000000
[9,7,5,10,2,1,4,6,8,3]=>000000000
[8,9,5,10,2,1,4,7,6,3]=>000000000
[10,6,7,8,2,1,5,4,3,9]=>000000000
[9,6,7,10,2,1,5,4,8,3]=>000000000
[8,6,9,10,2,1,5,7,4,3]=>000000000
[7,8,9,10,2,1,6,5,4,3]=>000000000
[10,8,6,3,4,2,1,5,7,9]=>000000000
[9,10,6,3,4,2,1,5,8,7]=>000000000
[10,7,8,3,4,2,1,6,5,9]=>000000000
[9,7,10,3,4,2,1,6,8,5]=>000000000
[8,9,10,3,4,2,1,7,6,5]=>000000000
[10,8,5,3,6,2,4,1,7,9]=>000000000
[9,10,5,3,6,2,4,1,8,7]=>000000000
[10,7,5,3,8,2,4,6,1,9]=>000000000
[9,7,5,3,10,2,4,6,8,1]=>000000000
[8,9,5,3,10,2,4,7,6,1]=>000000000
[10,6,7,3,8,2,5,4,1,9]=>000000000
[9,6,7,3,10,2,5,4,8,1]=>000000000
[8,6,9,3,10,2,5,7,4,1]=>000000000
[7,8,9,3,10,2,6,5,4,1]=>000000000
[10,8,4,5,6,3,2,1,7,9]=>000000000
[9,10,4,5,6,3,2,1,8,7]=>000000000
[10,7,4,5,8,3,2,6,1,9]=>000000000
[9,7,4,5,10,3,2,6,8,1]=>000000000
[8,9,4,5,10,3,2,7,6,1]=>000000000
[10,6,4,7,8,3,5,2,1,9]=>000000000
[9,6,4,7,10,3,5,2,8,1]=>000000000
[8,6,4,9,10,3,5,7,2,1]=>000000000
[7,8,4,9,10,3,6,5,2,1]=>000000000
[10,5,6,7,8,4,3,2,1,9]=>000000000
[9,5,6,7,10,4,3,2,8,1]=>000000000
[8,5,6,9,10,4,3,7,2,1]=>000000000
[7,5,8,9,10,4,6,3,2,1]=>000000000
[11,12,9,10,7,8,5,6,3,4,1,2]=>00000000000
[12,10,8,6,4,2,1,3,5,7,9,11]=>00000000000
[7,8,9,10,11,12,6,5,4,3,2,1]=>00000000000
[9,10,12,11,7,8,5,6,3,4,1,2]=>00000000000
[11,12,7,8,10,9,5,6,3,4,1,2]=>00000000000
[7,10,12,8,11,9,5,6,3,4,1,2]=>00000000000
[7,8,9,12,11,10,5,6,3,4,1,2]=>00000000000
[11,12,9,10,5,6,8,7,3,4,1,2]=>00000000000
[9,10,12,11,5,6,8,7,3,4,1,2]=>00000000000
[11,12,5,8,10,6,9,7,3,4,1,2]=>00000000000
[5,10,12,8,11,6,9,7,3,4,1,2]=>00000000000
[5,8,9,12,11,6,10,7,3,4,1,2]=>00000000000
[11,12,5,6,7,10,9,8,3,4,1,2]=>00000000000
[5,10,12,6,7,11,9,8,3,4,1,2]=>00000000000
[5,6,9,12,7,11,10,8,3,4,1,2]=>00000000000
[5,6,7,8,12,11,10,9,3,4,1,2]=>00000000000
[11,12,9,10,7,8,3,4,6,5,1,2]=>00000000000
[9,10,12,11,7,8,3,4,6,5,1,2]=>00000000000
[11,12,7,8,10,9,3,4,6,5,1,2]=>00000000000
[7,10,12,8,11,9,3,4,6,5,1,2]=>00000000000
[7,8,9,12,11,10,3,4,6,5,1,2]=>00000000000
[11,12,9,10,3,6,8,4,7,5,1,2]=>00000000000
[9,10,12,11,3,6,8,4,7,5,1,2]=>00000000000
[11,12,3,8,10,6,9,4,7,5,1,2]=>00000000000
[3,10,12,8,11,6,9,4,7,5,1,2]=>00000000000
[3,8,9,12,11,6,10,4,7,5,1,2]=>00000000000
[11,12,3,6,7,10,9,4,8,5,1,2]=>00000000000
[3,10,12,6,7,11,9,4,8,5,1,2]=>00000000000
[3,6,9,12,7,11,10,4,8,5,1,2]=>00000000000
[3,6,7,8,12,11,10,4,9,5,1,2]=>00000000000
[11,12,9,10,3,4,5,8,7,6,1,2]=>00000000000
[9,10,12,11,3,4,5,8,7,6,1,2]=>00000000000
[11,12,3,8,10,4,5,9,7,6,1,2]=>00000000000
[3,10,12,8,11,4,5,9,7,6,1,2]=>00000000000
[3,8,9,12,11,4,5,10,7,6,1,2]=>00000000000
[11,12,3,4,7,10,5,9,8,6,1,2]=>00000000000
[3,10,12,4,7,11,5,9,8,6,1,2]=>00000000000
[3,4,9,12,7,11,5,10,8,6,1,2]=>00000000000
[3,4,7,8,12,11,5,10,9,6,1,2]=>00000000000
[11,12,3,4,5,6,10,9,8,7,1,2]=>00000000000
[3,10,12,4,5,6,11,9,8,7,1,2]=>00000000000
[3,4,9,12,5,6,11,10,8,7,1,2]=>00000000000
[3,4,5,8,12,6,11,10,9,7,1,2]=>00000000000
[3,4,5,6,7,12,11,10,9,8,1,2]=>00000000000
[11,12,9,10,7,8,5,6,1,2,4,3]=>00000000000
[9,10,12,11,7,8,5,6,1,2,4,3]=>00000000000
[11,12,7,8,10,9,5,6,1,2,4,3]=>00000000000
[7,10,12,8,11,9,5,6,1,2,4,3]=>00000000000
[7,8,9,12,11,10,5,6,1,2,4,3]=>00000000000
[11,12,9,10,5,6,8,7,1,2,4,3]=>00000000000
[9,10,12,11,5,6,8,7,1,2,4,3]=>00000000000
[11,12,5,8,10,6,9,7,1,2,4,3]=>00000000000
[5,10,12,8,11,6,9,7,1,2,4,3]=>00000000000
[5,8,9,12,11,6,10,7,1,2,4,3]=>00000000000
[11,12,5,6,7,10,9,8,1,2,4,3]=>00000000000
[5,10,12,6,7,11,9,8,1,2,4,3]=>00000000000
[5,6,9,12,7,11,10,8,1,2,4,3]=>00000000000
[5,6,7,8,12,11,10,9,1,2,4,3]=>00000000000
[11,12,9,10,7,8,1,4,6,2,5,3]=>00000000000
[9,10,12,11,7,8,1,4,6,2,5,3]=>00000000000
[11,12,7,8,10,9,1,4,6,2,5,3]=>00000000000
[7,10,12,8,11,9,1,4,6,2,5,3]=>00000000000
[7,8,9,12,11,10,1,4,6,2,5,3]=>00000000000
[11,12,9,10,1,6,8,4,7,2,5,3]=>00000000000
[9,10,12,11,1,6,8,4,7,2,5,3]=>00000000000
[11,12,1,8,10,6,9,4,7,2,5,3]=>00000000000
[1,10,12,8,11,6,9,4,7,2,5,3]=>10000000000
[1,8,9,12,11,6,10,4,7,2,5,3]=>10000000000
[11,12,1,6,7,10,9,4,8,2,5,3]=>00000000000
[1,10,12,6,7,11,9,4,8,2,5,3]=>10000000000
[1,6,9,12,7,11,10,4,8,2,5,3]=>10000000000
[1,6,7,8,12,11,10,4,9,2,5,3]=>10000000000
[11,12,9,10,1,4,5,8,7,2,6,3]=>00000000000
[9,10,12,11,1,4,5,8,7,2,6,3]=>00000000000
[11,12,1,8,10,4,5,9,7,2,6,3]=>00000000000
[1,10,12,8,11,4,5,9,7,2,6,3]=>10000000000
[1,8,9,12,11,4,5,10,7,2,6,3]=>10000000000
[11,12,1,4,7,10,5,9,8,2,6,3]=>00000000000
[1,10,12,4,7,11,5,9,8,2,6,3]=>10000000000
[1,4,9,12,7,11,5,10,8,2,6,3]=>10000000000
[1,4,7,8,12,11,5,10,9,2,6,3]=>10000000000
[11,12,1,4,5,6,10,9,8,2,7,3]=>00000000000
[1,10,12,4,5,6,11,9,8,2,7,3]=>10000000000
[1,4,9,12,5,6,11,10,8,2,7,3]=>10000000000
[1,4,5,8,12,6,11,10,9,2,7,3]=>10000000000
[1,4,5,6,7,12,11,10,9,2,8,3]=>10000000000
[11,12,9,10,7,8,1,2,3,6,5,4]=>00000000000
[9,10,12,11,7,8,1,2,3,6,5,4]=>00000000000
[11,12,7,8,10,9,1,2,3,6,5,4]=>00000000000
[7,10,12,8,11,9,1,2,3,6,5,4]=>00000000000
[7,8,9,12,11,10,1,2,3,6,5,4]=>00000000000
[11,12,9,10,1,6,8,2,3,7,5,4]=>00000000000
[9,10,12,11,1,6,8,2,3,7,5,4]=>00000000000
[11,12,1,8,10,6,9,2,3,7,5,4]=>00000000000
[1,10,12,8,11,6,9,2,3,7,5,4]=>10000000000
[1,8,9,12,11,6,10,2,3,7,5,4]=>10000000000
[11,12,1,6,7,10,9,2,3,8,5,4]=>00000000000
[1,10,12,6,7,11,9,2,3,8,5,4]=>10000000000
[1,6,9,12,7,11,10,2,3,8,5,4]=>10000000000
[1,6,7,8,12,11,10,2,3,9,5,4]=>10000000000
[11,12,9,10,1,2,5,8,3,7,6,4]=>00000000000
[9,10,12,11,1,2,5,8,3,7,6,4]=>00000000000
[11,12,1,8,10,2,5,9,3,7,6,4]=>00000000000
[1,10,12,8,11,2,5,9,3,7,6,4]=>10000000000
[1,8,9,12,11,2,5,10,3,7,6,4]=>10000000000
[11,12,1,2,7,10,5,9,3,8,6,4]=>00000000000
[1,10,12,2,7,11,5,9,3,8,6,4]=>10000000000
[1,2,9,12,7,11,5,10,3,8,6,4]=>11000000000
[1,2,7,8,12,11,5,10,3,9,6,4]=>11000000000
[11,12,1,2,5,6,10,9,3,8,7,4]=>00000000000
[1,10,12,2,5,6,11,9,3,8,7,4]=>10000000000
[1,2,9,12,5,6,11,10,3,8,7,4]=>11000000000
[1,2,5,8,12,6,11,10,3,9,7,4]=>11000000000
[1,2,5,6,7,12,11,10,3,9,8,4]=>11000000000
[11,12,9,10,1,2,3,4,8,7,6,5]=>00000000000
[9,10,12,11,1,2,3,4,8,7,6,5]=>00000000000
[11,12,1,8,10,2,3,4,9,7,6,5]=>00000000000
[1,10,12,8,11,2,3,4,9,7,6,5]=>10000000000
[1,8,9,12,11,2,3,4,10,7,6,5]=>10000000000
[11,12,1,2,7,10,3,4,9,8,6,5]=>00000000000
[1,10,12,2,7,11,3,4,9,8,6,5]=>10000000000
[1,2,9,12,7,11,3,4,10,8,6,5]=>11000000000
[1,2,7,8,12,11,3,4,10,9,6,5]=>11000000000
[11,12,1,2,3,6,10,4,9,8,7,5]=>00000000000
[1,10,12,2,3,6,11,4,9,8,7,5]=>10000000000
[1,2,9,12,3,6,11,4,10,8,7,5]=>11000000000
[1,2,3,8,12,6,11,4,10,9,7,5]=>11100000000
[1,2,3,6,7,12,11,4,10,9,8,5]=>11100000000
[11,12,1,2,3,4,5,10,9,8,7,6]=>00000000000
[1,10,12,2,3,4,5,11,9,8,7,6]=>10000000000
[1,2,9,12,3,4,5,11,10,8,7,6]=>11000000000
[1,2,3,8,12,4,5,11,10,9,7,6]=>11100000000
[1,2,3,4,7,12,5,11,10,9,8,6]=>11110000000
[1,2,3,4,5,6,12,11,10,9,8,7]=>11111100000
[11,12,9,10,7,8,5,6,2,1,3,4]=>00000000000
[11,12,9,10,7,8,4,3,5,6,1,2]=>00000000000
[11,12,9,10,7,8,4,2,5,1,3,6]=>00000000000
[11,12,9,10,7,8,3,2,1,4,5,6]=>00000000000
[11,12,9,10,6,5,7,8,3,4,1,2]=>00000000000
[11,12,9,10,6,5,7,8,2,1,3,4]=>00000000000
[11,12,9,10,6,4,7,3,5,8,1,2]=>00000000000
[11,12,9,10,6,4,7,2,5,1,3,8]=>00000000000
[11,12,9,10,6,3,7,2,1,4,5,8]=>00000000000
[11,12,9,10,5,4,3,6,7,8,1,2]=>00000000000
[11,12,9,10,5,4,2,6,7,1,3,8]=>00000000000
[11,12,9,10,5,3,2,6,1,4,7,8]=>00000000000
[11,12,9,10,4,3,2,1,5,6,7,8]=>00000000000
[11,12,8,7,9,10,5,6,3,4,1,2]=>00000000000
[11,12,8,7,9,10,5,6,2,1,3,4]=>00000000000
[11,12,8,7,9,10,4,3,5,6,1,2]=>00000000000
[11,12,8,7,9,10,4,2,5,1,3,6]=>00000000000
[11,12,8,7,9,10,3,2,1,4,5,6]=>00000000000
[11,12,8,6,9,5,7,10,3,4,1,2]=>00000000000
[11,12,8,6,9,5,7,10,2,1,3,4]=>00000000000
[11,12,8,6,9,4,7,3,5,10,1,2]=>00000000000
[11,12,8,6,9,4,7,2,5,1,3,10]=>00000000000
[11,12,8,6,9,3,7,2,1,4,5,10]=>00000000000
[11,12,8,5,9,4,3,6,7,10,1,2]=>00000000000
[11,12,8,5,9,4,2,6,7,1,3,10]=>00000000000
[11,12,8,5,9,3,2,6,1,4,7,10]=>00000000000
[11,12,8,4,9,3,2,1,5,6,7,10]=>00000000000
[11,12,7,6,5,8,9,10,3,4,1,2]=>00000000000
[11,12,7,6,5,8,9,10,2,1,3,4]=>00000000000
[11,12,7,6,4,8,9,3,5,10,1,2]=>00000000000
[11,12,7,6,4,8,9,2,5,1,3,10]=>00000000000
[11,12,7,6,3,8,9,2,1,4,5,10]=>00000000000
[11,12,7,5,4,8,3,6,9,10,1,2]=>00000000000
[11,12,7,5,4,8,2,6,9,1,3,10]=>00000000000
[11,12,7,5,3,8,2,6,1,4,9,10]=>00000000000
[11,12,7,4,3,8,2,1,5,6,9,10]=>00000000000
[11,12,6,5,4,3,7,8,9,10,1,2]=>00000000000
[11,12,6,5,4,2,7,8,9,1,3,10]=>00000000000
[11,12,6,5,3,2,7,8,1,4,9,10]=>00000000000
[11,12,6,4,3,2,7,1,5,8,9,10]=>00000000000
[11,12,5,4,3,2,1,6,7,8,9,10]=>00000000000
[10,9,11,12,7,8,5,6,3,4,1,2]=>00000000000
[10,9,11,12,7,8,5,6,2,1,3,4]=>00000000000
[10,9,11,12,7,8,4,3,5,6,1,2]=>00000000000
[10,9,11,12,7,8,4,2,5,1,3,6]=>00000000000
[10,9,11,12,7,8,3,2,1,4,5,6]=>00000000000
[10,9,11,12,6,5,7,8,3,4,1,2]=>00000000000
[10,9,11,12,6,5,7,8,2,1,3,4]=>00000000000
[10,9,11,12,6,4,7,3,5,8,1,2]=>00000000000
[10,9,11,12,6,4,7,2,5,1,3,8]=>00000000000
[10,9,11,12,6,3,7,2,1,4,5,8]=>00000000000
[10,9,11,12,5,4,3,6,7,8,1,2]=>00000000000
[10,9,11,12,5,4,2,6,7,1,3,8]=>00000000000
[10,9,11,12,5,3,2,6,1,4,7,8]=>00000000000
[10,9,11,12,4,3,2,1,5,6,7,8]=>00000000000
[10,8,11,7,9,12,5,6,3,4,1,2]=>00000000000
[10,8,11,7,9,12,5,6,2,1,3,4]=>00000000000
[10,8,11,7,9,12,4,3,5,6,1,2]=>00000000000
[10,8,11,7,9,12,4,2,5,1,3,6]=>00000000000
[10,8,11,7,9,12,3,2,1,4,5,6]=>00000000000
[10,8,11,6,9,5,7,12,3,4,1,2]=>00000000000
[10,8,11,6,9,5,7,12,2,1,3,4]=>00000000000
[10,8,11,6,9,4,7,3,5,12,1,2]=>00000000000
[10,8,11,6,9,4,7,2,5,1,3,12]=>00000000001
[10,8,11,6,9,3,7,2,1,4,5,12]=>00000000001
[10,8,11,5,9,4,3,6,7,12,1,2]=>00000000000
[10,8,11,5,9,4,2,6,7,1,3,12]=>00000000001
[10,8,11,5,9,3,2,6,1,4,7,12]=>00000000001
[10,8,11,4,9,3,2,1,5,6,7,12]=>00000000001
[10,7,11,6,5,8,9,12,3,4,1,2]=>00000000000
[10,7,11,6,5,8,9,12,2,1,3,4]=>00000000000
[10,7,11,6,4,8,9,3,5,12,1,2]=>00000000000
[10,7,11,6,4,8,9,2,5,1,3,12]=>00000000001
[10,7,11,6,3,8,9,2,1,4,5,12]=>00000000001
[10,7,11,5,4,8,3,6,9,12,1,2]=>00000000000
[10,7,11,5,4,8,2,6,9,1,3,12]=>00000000001
[10,7,11,5,3,8,2,6,1,4,9,12]=>00000000001
[10,7,11,4,3,8,2,1,5,6,9,12]=>00000000001
[10,6,11,5,4,3,7,8,9,12,1,2]=>00000000000
[10,6,11,5,4,2,7,8,9,1,3,12]=>00000000001
[10,6,11,5,3,2,7,8,1,4,9,12]=>00000000001
[10,6,11,4,3,2,7,1,5,8,9,12]=>00000000001
[10,5,11,4,3,2,1,6,7,8,9,12]=>00000000001
[9,8,7,10,11,12,5,6,3,4,1,2]=>00000000000
[9,8,7,10,11,12,5,6,2,1,3,4]=>00000000000
[9,8,7,10,11,12,4,3,5,6,1,2]=>00000000000
[9,8,7,10,11,12,4,2,5,1,3,6]=>00000000000
[9,8,7,10,11,12,3,2,1,4,5,6]=>00000000000
[9,8,6,10,11,5,7,12,3,4,1,2]=>00000000000
[9,8,6,10,11,5,7,12,2,1,3,4]=>00000000000
[9,8,6,10,11,4,7,3,5,12,1,2]=>00000000000
[9,8,6,10,11,4,7,2,5,1,3,12]=>00000000001
[9,8,6,10,11,3,7,2,1,4,5,12]=>00000000001
[9,8,5,10,11,4,3,6,7,12,1,2]=>00000000000
[9,8,5,10,11,4,2,6,7,1,3,12]=>00000000001
[9,8,5,10,11,3,2,6,1,4,7,12]=>00000000001
[9,8,4,10,11,3,2,1,5,6,7,12]=>00000000001
[9,7,6,10,5,8,11,12,3,4,1,2]=>00000000000
[9,7,6,10,5,8,11,12,2,1,3,4]=>00000000000
[9,7,6,10,4,8,11,3,5,12,1,2]=>00000000000
[9,7,6,10,4,8,11,2,5,1,3,12]=>00000000001
[9,7,6,10,3,8,11,2,1,4,5,12]=>00000000001
[9,7,5,10,4,8,3,6,11,12,1,2]=>00000000000
[9,7,5,10,4,8,2,6,11,1,3,12]=>00000000001
[9,7,5,10,3,8,2,6,1,4,11,12]=>00000000011
[9,7,4,10,3,8,2,1,5,6,11,12]=>00000000011
[9,6,5,10,4,3,7,8,11,12,1,2]=>00000000000
[9,6,5,10,4,2,7,8,11,1,3,12]=>00000000001
[9,6,5,10,3,2,7,8,1,4,11,12]=>00000000011
[9,6,4,10,3,2,7,1,5,8,11,12]=>00000000011
[9,5,4,10,3,2,1,6,7,8,11,12]=>00000000011
[8,7,6,5,9,10,11,12,3,4,1,2]=>00000000000
[8,7,6,5,9,10,11,12,2,1,3,4]=>00000000000
[8,7,6,4,9,10,11,3,5,12,1,2]=>00000000000
[8,7,6,4,9,10,11,2,5,1,3,12]=>00000000001
[8,7,6,3,9,10,11,2,1,4,5,12]=>00000000001
[8,7,5,4,9,10,3,6,11,12,1,2]=>00000000000
[8,7,5,4,9,10,2,6,11,1,3,12]=>00000000001
[8,7,5,3,9,10,2,6,1,4,11,12]=>00000000011
[8,7,4,3,9,10,2,1,5,6,11,12]=>00000000011
[8,6,5,4,9,3,7,10,11,12,1,2]=>00000000000
[8,6,5,4,9,2,7,10,11,1,3,12]=>00000000001
[8,6,5,3,9,2,7,10,1,4,11,12]=>00000000011
[8,6,4,3,9,2,7,1,5,10,11,12]=>00000000111
[8,5,4,3,9,2,1,6,7,10,11,12]=>00000000111
[7,6,5,4,3,8,9,10,11,12,1,2]=>00000000000
[7,6,5,4,2,8,9,10,11,1,3,12]=>00000000001
[7,6,5,3,2,8,9,10,1,4,11,12]=>00000000011
[7,6,4,3,2,8,9,1,5,10,11,12]=>00000000111
[7,5,4,3,2,8,1,6,9,10,11,12]=>00000001111
[6,5,4,3,2,1,7,8,9,10,11,12]=>00000111111
[11,12,8,6,4,2,1,3,5,7,10,9]=>00000000000
[12,9,10,6,4,2,1,3,5,8,7,11]=>00000000000
[11,9,12,6,4,2,1,3,5,8,10,7]=>00000000000
[10,11,12,6,4,2,1,3,5,9,8,7]=>00000000000
[12,10,7,8,4,2,1,3,6,5,9,11]=>00000000000
[11,12,7,8,4,2,1,3,6,5,10,9]=>00000000000
[12,9,7,10,4,2,1,3,6,8,5,11]=>00000000000
[11,9,7,12,4,2,1,3,6,8,10,5]=>00000000000
[10,11,7,12,4,2,1,3,6,9,8,5]=>00000000000
[12,8,9,10,4,2,1,3,7,6,5,11]=>00000000000
[11,8,9,12,4,2,1,3,7,6,10,5]=>00000000000
[10,8,11,12,4,2,1,3,7,9,6,5]=>00000000000
[9,10,11,12,4,2,1,3,8,7,6,5]=>00000000000
[12,10,8,5,6,2,1,4,3,7,9,11]=>00000000000
[11,12,8,5,6,2,1,4,3,7,10,9]=>00000000000
[12,9,10,5,6,2,1,4,3,8,7,11]=>00000000000
[11,9,12,5,6,2,1,4,3,8,10,7]=>00000000000
[10,11,12,5,6,2,1,4,3,9,8,7]=>00000000000
[12,10,7,5,8,2,1,4,6,3,9,11]=>00000000000
[11,12,7,5,8,2,1,4,6,3,10,9]=>00000000000
[12,9,7,5,10,2,1,4,6,8,3,11]=>00000000000
[11,9,7,5,12,2,1,4,6,8,10,3]=>00000000000
[10,11,7,5,12,2,1,4,6,9,8,3]=>00000000000
[12,8,9,5,10,2,1,4,7,6,3,11]=>00000000000
[11,8,9,5,12,2,1,4,7,6,10,3]=>00000000000
[10,8,11,5,12,2,1,4,7,9,6,3]=>00000000000
[9,10,11,5,12,2,1,4,8,7,6,3]=>00000000000
[12,10,6,7,8,2,1,5,4,3,9,11]=>00000000000
[11,12,6,7,8,2,1,5,4,3,10,9]=>00000000000
[12,9,6,7,10,2,1,5,4,8,3,11]=>00000000000
[11,9,6,7,12,2,1,5,4,8,10,3]=>00000000000
[10,11,6,7,12,2,1,5,4,9,8,3]=>00000000000
[12,8,6,9,10,2,1,5,7,4,3,11]=>00000000000
[11,8,6,9,12,2,1,5,7,4,10,3]=>00000000000
[10,8,6,11,12,2,1,5,7,9,4,3]=>00000000000
[9,10,6,11,12,2,1,5,8,7,4,3]=>00000000000
[12,7,8,9,10,2,1,6,5,4,3,11]=>00000000000
[11,7,8,9,12,2,1,6,5,4,10,3]=>00000000000
[10,7,8,11,12,2,1,6,5,9,4,3]=>00000000000
[9,7,10,11,12,2,1,6,8,5,4,3]=>00000000000
[8,9,10,11,12,2,1,7,6,5,4,3]=>00000000000
[12,10,8,6,3,4,2,1,5,7,9,11]=>00000000000
[11,12,8,6,3,4,2,1,5,7,10,9]=>00000000000
[12,9,10,6,3,4,2,1,5,8,7,11]=>00000000000
[11,9,12,6,3,4,2,1,5,8,10,7]=>00000000000
[10,11,12,6,3,4,2,1,5,9,8,7]=>00000000000
[12,10,7,8,3,4,2,1,6,5,9,11]=>00000000000
[11,12,7,8,3,4,2,1,6,5,10,9]=>00000000000
[12,9,7,10,3,4,2,1,6,8,5,11]=>00000000000
[11,9,7,12,3,4,2,1,6,8,10,5]=>00000000000
[10,11,7,12,3,4,2,1,6,9,8,5]=>00000000000
[12,8,9,10,3,4,2,1,7,6,5,11]=>00000000000
[11,8,9,12,3,4,2,1,7,6,10,5]=>00000000000
[10,8,11,12,3,4,2,1,7,9,6,5]=>00000000000
[9,10,11,12,3,4,2,1,8,7,6,5]=>00000000000
[12,10,8,5,3,6,2,4,1,7,9,11]=>00000000000
[11,12,8,5,3,6,2,4,1,7,10,9]=>00000000000
[12,9,10,5,3,6,2,4,1,8,7,11]=>00000000000
[11,9,12,5,3,6,2,4,1,8,10,7]=>00000000000
[10,11,12,5,3,6,2,4,1,9,8,7]=>00000000000
[12,10,7,5,3,8,2,4,6,1,9,11]=>00000000000
[11,12,7,5,3,8,2,4,6,1,10,9]=>00000000000
[12,9,7,5,3,10,2,4,6,8,1,11]=>00000000000
[11,9,7,5,3,12,2,4,6,8,10,1]=>00000000000
[10,11,7,5,3,12,2,4,6,9,8,1]=>00000000000
[12,8,9,5,3,10,2,4,7,6,1,11]=>00000000000
[11,8,9,5,3,12,2,4,7,6,10,1]=>00000000000
[10,8,11,5,3,12,2,4,7,9,6,1]=>00000000000
[9,10,11,5,3,12,2,4,8,7,6,1]=>00000000000
[12,10,6,7,3,8,2,5,4,1,9,11]=>00000000000
[11,12,6,7,3,8,2,5,4,1,10,9]=>00000000000
[12,9,6,7,3,10,2,5,4,8,1,11]=>00000000000
[11,9,6,7,3,12,2,5,4,8,10,1]=>00000000000
[10,11,6,7,3,12,2,5,4,9,8,1]=>00000000000
[12,8,6,9,3,10,2,5,7,4,1,11]=>00000000000
[11,8,6,9,3,12,2,5,7,4,10,1]=>00000000000
[10,8,6,11,3,12,2,5,7,9,4,1]=>00000000000
[9,10,6,11,3,12,2,5,8,7,4,1]=>00000000000
[12,7,8,9,3,10,2,6,5,4,1,11]=>00000000000
[11,7,8,9,3,12,2,6,5,4,10,1]=>00000000000
[10,7,8,11,3,12,2,6,5,9,4,1]=>00000000000
[9,7,10,11,3,12,2,6,8,5,4,1]=>00000000000
[8,9,10,11,3,12,2,7,6,5,4,1]=>00000000000
[12,10,8,4,5,6,3,2,1,7,9,11]=>00000000000
[11,12,8,4,5,6,3,2,1,7,10,9]=>00000000000
[12,9,10,4,5,6,3,2,1,8,7,11]=>00000000000
[11,9,12,4,5,6,3,2,1,8,10,7]=>00000000000
[10,11,12,4,5,6,3,2,1,9,8,7]=>00000000000
[12,10,7,4,5,8,3,2,6,1,9,11]=>00000000000
[11,12,7,4,5,8,3,2,6,1,10,9]=>00000000000
[12,9,7,4,5,10,3,2,6,8,1,11]=>00000000000
[11,9,7,4,5,12,3,2,6,8,10,1]=>00000000000
[10,11,7,4,5,12,3,2,6,9,8,1]=>00000000000
[12,8,9,4,5,10,3,2,7,6,1,11]=>00000000000
[11,8,9,4,5,12,3,2,7,6,10,1]=>00000000000
[10,8,11,4,5,12,3,2,7,9,6,1]=>00000000000
[9,10,11,4,5,12,3,2,8,7,6,1]=>00000000000
[12,10,6,4,7,8,3,5,2,1,9,11]=>00000000000
[11,12,6,4,7,8,3,5,2,1,10,9]=>00000000000
[12,9,6,4,7,10,3,5,2,8,1,11]=>00000000000
[11,9,6,4,7,12,3,5,2,8,10,1]=>00000000000
[10,11,6,4,7,12,3,5,2,9,8,1]=>00000000000
[12,8,6,4,9,10,3,5,7,2,1,11]=>00000000000
[11,8,6,4,9,12,3,5,7,2,10,1]=>00000000000
[10,8,6,4,11,12,3,5,7,9,2,1]=>00000000000
[9,10,6,4,11,12,3,5,8,7,2,1]=>00000000000
[12,7,8,4,9,10,3,6,5,2,1,11]=>00000000000
[11,7,8,4,9,12,3,6,5,2,10,1]=>00000000000
[10,7,8,4,11,12,3,6,5,9,2,1]=>00000000000
[9,7,10,4,11,12,3,6,8,5,2,1]=>00000000000
[8,9,10,4,11,12,3,7,6,5,2,1]=>00000000000
[12,10,5,6,7,8,4,3,2,1,9,11]=>00000000000
[11,12,5,6,7,8,4,3,2,1,10,9]=>00000000000
[12,9,5,6,7,10,4,3,2,8,1,11]=>00000000000
[11,9,5,6,7,12,4,3,2,8,10,1]=>00000000000
[10,11,5,6,7,12,4,3,2,9,8,1]=>00000000000
[12,8,5,6,9,10,4,3,7,2,1,11]=>00000000000
[11,8,5,6,9,12,4,3,7,2,10,1]=>00000000000
[10,8,5,6,11,12,4,3,7,9,2,1]=>00000000000
[9,10,5,6,11,12,4,3,8,7,2,1]=>00000000000
[12,7,5,8,9,10,4,6,3,2,1,11]=>00000000000
[11,7,5,8,9,12,4,6,3,2,10,1]=>00000000000
[10,7,5,8,11,12,4,6,3,9,2,1]=>00000000000
[9,7,5,10,11,12,4,6,8,3,2,1]=>00000000000
[8,9,5,10,11,12,4,7,6,3,2,1]=>00000000000
[12,6,7,8,9,10,5,4,3,2,1,11]=>00000000000
[11,6,7,8,9,12,5,4,3,2,10,1]=>00000000000
[10,6,7,8,11,12,5,4,3,9,2,1]=>00000000000
[9,6,7,10,11,12,5,4,8,3,2,1]=>00000000000
[8,6,9,10,11,12,5,7,4,3,2,1]=>00000000000
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
References
[1] Stanley, R. P. The descent set and connectivity set of a permutation MathSciNet:2167418 arXiv:math/0507224
[2] Bergeron, N., Hohlweg, C., Zabrocki, M. Posets related to the connectivity set of Coxeter groups MathSciNet:2255139 arXiv:math/0509271
[3] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns arXiv:1102.4226
[2] Bergeron, N., Hohlweg, C., Zabrocki, M. Posets related to the connectivity set of Coxeter groups MathSciNet:2255139 arXiv:math/0509271
[3] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns arXiv:1102.4226
Properties
surjective, graded
Sage code
def mapping(pi): C = [1 if all(pi[j] < pi[k] for j in range(i) for k in range(i, len(pi))) else 0 for i in range(1, len(pi))] return Words([0,1])(C)
Weight
26
Created
Jan 29, 2020 at 13:25 by FindStatCrew
Updated
Jan 29, 2020 at 13:25 by Martin Rubey
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