Identifier
-
Mp00114:
Permutations
—connectivity set⟶
Binary words
Mp00105: Binary words —complement⟶ Binary words
St000390: Binary words ⟶ ℤ
Values
=>
[1,2]=>1=>0=>0
[2,1]=>0=>1=>1
[1,2,3]=>11=>00=>0
[1,3,2]=>10=>01=>1
[2,1,3]=>01=>10=>1
[2,3,1]=>00=>11=>1
[3,1,2]=>00=>11=>1
[3,2,1]=>00=>11=>1
[1,2,3,4]=>111=>000=>0
[1,2,4,3]=>110=>001=>1
[1,3,2,4]=>101=>010=>1
[1,3,4,2]=>100=>011=>1
[1,4,2,3]=>100=>011=>1
[1,4,3,2]=>100=>011=>1
[2,1,3,4]=>011=>100=>1
[2,1,4,3]=>010=>101=>2
[2,3,1,4]=>001=>110=>1
[2,3,4,1]=>000=>111=>1
[2,4,1,3]=>000=>111=>1
[2,4,3,1]=>000=>111=>1
[3,1,2,4]=>001=>110=>1
[3,1,4,2]=>000=>111=>1
[3,2,1,4]=>001=>110=>1
[3,2,4,1]=>000=>111=>1
[3,4,1,2]=>000=>111=>1
[3,4,2,1]=>000=>111=>1
[4,1,2,3]=>000=>111=>1
[4,1,3,2]=>000=>111=>1
[4,2,1,3]=>000=>111=>1
[4,2,3,1]=>000=>111=>1
[4,3,1,2]=>000=>111=>1
[4,3,2,1]=>000=>111=>1
[1,2,3,4,5]=>1111=>0000=>0
[1,2,3,5,4]=>1110=>0001=>1
[1,2,4,3,5]=>1101=>0010=>1
[1,2,4,5,3]=>1100=>0011=>1
[1,2,5,3,4]=>1100=>0011=>1
[1,2,5,4,3]=>1100=>0011=>1
[1,3,2,4,5]=>1011=>0100=>1
[1,3,2,5,4]=>1010=>0101=>2
[1,3,4,2,5]=>1001=>0110=>1
[1,3,4,5,2]=>1000=>0111=>1
[1,3,5,2,4]=>1000=>0111=>1
[1,3,5,4,2]=>1000=>0111=>1
[1,4,2,3,5]=>1001=>0110=>1
[1,4,2,5,3]=>1000=>0111=>1
[1,4,3,2,5]=>1001=>0110=>1
[1,4,3,5,2]=>1000=>0111=>1
[1,4,5,2,3]=>1000=>0111=>1
[1,4,5,3,2]=>1000=>0111=>1
[1,5,2,3,4]=>1000=>0111=>1
[1,5,2,4,3]=>1000=>0111=>1
[1,5,3,2,4]=>1000=>0111=>1
[1,5,3,4,2]=>1000=>0111=>1
[1,5,4,2,3]=>1000=>0111=>1
[1,5,4,3,2]=>1000=>0111=>1
[2,1,3,4,5]=>0111=>1000=>1
[2,1,3,5,4]=>0110=>1001=>2
[2,1,4,3,5]=>0101=>1010=>2
[2,1,4,5,3]=>0100=>1011=>2
[2,1,5,3,4]=>0100=>1011=>2
[2,1,5,4,3]=>0100=>1011=>2
[2,3,1,4,5]=>0011=>1100=>1
[2,3,1,5,4]=>0010=>1101=>2
[2,3,4,1,5]=>0001=>1110=>1
[2,3,4,5,1]=>0000=>1111=>1
[2,3,5,1,4]=>0000=>1111=>1
[2,3,5,4,1]=>0000=>1111=>1
[2,4,1,3,5]=>0001=>1110=>1
[2,4,1,5,3]=>0000=>1111=>1
[2,4,3,1,5]=>0001=>1110=>1
[2,4,3,5,1]=>0000=>1111=>1
[2,4,5,1,3]=>0000=>1111=>1
[2,4,5,3,1]=>0000=>1111=>1
[2,5,1,3,4]=>0000=>1111=>1
[2,5,1,4,3]=>0000=>1111=>1
[2,5,3,1,4]=>0000=>1111=>1
[2,5,3,4,1]=>0000=>1111=>1
[2,5,4,1,3]=>0000=>1111=>1
[2,5,4,3,1]=>0000=>1111=>1
[3,1,2,4,5]=>0011=>1100=>1
[3,1,2,5,4]=>0010=>1101=>2
[3,1,4,2,5]=>0001=>1110=>1
[3,1,4,5,2]=>0000=>1111=>1
[3,1,5,2,4]=>0000=>1111=>1
[3,1,5,4,2]=>0000=>1111=>1
[3,2,1,4,5]=>0011=>1100=>1
[3,2,1,5,4]=>0010=>1101=>2
[3,2,4,1,5]=>0001=>1110=>1
[3,2,4,5,1]=>0000=>1111=>1
[3,2,5,1,4]=>0000=>1111=>1
[3,2,5,4,1]=>0000=>1111=>1
[3,4,1,2,5]=>0001=>1110=>1
[3,4,1,5,2]=>0000=>1111=>1
[3,4,2,1,5]=>0001=>1110=>1
[3,4,2,5,1]=>0000=>1111=>1
[3,4,5,1,2]=>0000=>1111=>1
[3,4,5,2,1]=>0000=>1111=>1
[3,5,1,2,4]=>0000=>1111=>1
[3,5,1,4,2]=>0000=>1111=>1
[3,5,2,1,4]=>0000=>1111=>1
[3,5,2,4,1]=>0000=>1111=>1
[3,5,4,1,2]=>0000=>1111=>1
[3,5,4,2,1]=>0000=>1111=>1
[4,1,2,3,5]=>0001=>1110=>1
[4,1,2,5,3]=>0000=>1111=>1
[4,1,3,2,5]=>0001=>1110=>1
[4,1,3,5,2]=>0000=>1111=>1
[4,1,5,2,3]=>0000=>1111=>1
[4,1,5,3,2]=>0000=>1111=>1
[4,2,1,3,5]=>0001=>1110=>1
[4,2,1,5,3]=>0000=>1111=>1
[4,2,3,1,5]=>0001=>1110=>1
[4,2,3,5,1]=>0000=>1111=>1
[4,2,5,1,3]=>0000=>1111=>1
[4,2,5,3,1]=>0000=>1111=>1
[4,3,1,2,5]=>0001=>1110=>1
[4,3,1,5,2]=>0000=>1111=>1
[4,3,2,1,5]=>0001=>1110=>1
[4,3,2,5,1]=>0000=>1111=>1
[4,3,5,1,2]=>0000=>1111=>1
[4,3,5,2,1]=>0000=>1111=>1
[4,5,1,2,3]=>0000=>1111=>1
[4,5,1,3,2]=>0000=>1111=>1
[4,5,2,1,3]=>0000=>1111=>1
[4,5,2,3,1]=>0000=>1111=>1
[4,5,3,1,2]=>0000=>1111=>1
[4,5,3,2,1]=>0000=>1111=>1
[5,1,2,3,4]=>0000=>1111=>1
[5,1,2,4,3]=>0000=>1111=>1
[5,1,3,2,4]=>0000=>1111=>1
[5,1,3,4,2]=>0000=>1111=>1
[5,1,4,2,3]=>0000=>1111=>1
[5,1,4,3,2]=>0000=>1111=>1
[5,2,1,3,4]=>0000=>1111=>1
[5,2,1,4,3]=>0000=>1111=>1
[5,2,3,1,4]=>0000=>1111=>1
[5,2,3,4,1]=>0000=>1111=>1
[5,2,4,1,3]=>0000=>1111=>1
[5,2,4,3,1]=>0000=>1111=>1
[5,3,1,2,4]=>0000=>1111=>1
[5,3,1,4,2]=>0000=>1111=>1
[5,3,2,1,4]=>0000=>1111=>1
[5,3,2,4,1]=>0000=>1111=>1
[5,3,4,1,2]=>0000=>1111=>1
[5,3,4,2,1]=>0000=>1111=>1
[5,4,1,2,3]=>0000=>1111=>1
[5,4,1,3,2]=>0000=>1111=>1
[5,4,2,1,3]=>0000=>1111=>1
[5,4,2,3,1]=>0000=>1111=>1
[5,4,3,1,2]=>0000=>1111=>1
[5,4,3,2,1]=>0000=>1111=>1
[1,2,3,4,5,6]=>11111=>00000=>0
[1,2,3,4,6,5]=>11110=>00001=>1
[1,2,3,5,4,6]=>11101=>00010=>1
[1,2,3,5,6,4]=>11100=>00011=>1
[1,2,3,6,4,5]=>11100=>00011=>1
[1,2,3,6,5,4]=>11100=>00011=>1
[1,2,4,3,5,6]=>11011=>00100=>1
[1,2,4,3,6,5]=>11010=>00101=>2
[1,2,4,5,3,6]=>11001=>00110=>1
[1,2,4,5,6,3]=>11000=>00111=>1
[1,2,4,6,3,5]=>11000=>00111=>1
[1,2,4,6,5,3]=>11000=>00111=>1
[1,2,5,3,4,6]=>11001=>00110=>1
[1,2,5,3,6,4]=>11000=>00111=>1
[1,2,5,4,3,6]=>11001=>00110=>1
[1,2,5,4,6,3]=>11000=>00111=>1
[1,2,5,6,3,4]=>11000=>00111=>1
[1,2,5,6,4,3]=>11000=>00111=>1
[1,2,6,3,4,5]=>11000=>00111=>1
[1,2,6,3,5,4]=>11000=>00111=>1
[1,2,6,4,3,5]=>11000=>00111=>1
[1,2,6,4,5,3]=>11000=>00111=>1
[1,2,6,5,3,4]=>11000=>00111=>1
[1,2,6,5,4,3]=>11000=>00111=>1
[1,3,2,4,5,6]=>10111=>01000=>1
[1,3,2,4,6,5]=>10110=>01001=>2
[1,3,2,5,4,6]=>10101=>01010=>2
[1,3,2,5,6,4]=>10100=>01011=>2
[1,3,2,6,4,5]=>10100=>01011=>2
[1,3,2,6,5,4]=>10100=>01011=>2
[1,3,4,2,5,6]=>10011=>01100=>1
[1,3,4,2,6,5]=>10010=>01101=>2
[1,3,4,5,2,6]=>10001=>01110=>1
[1,3,4,5,6,2]=>10000=>01111=>1
[1,3,4,6,2,5]=>10000=>01111=>1
[1,3,4,6,5,2]=>10000=>01111=>1
[1,3,5,2,4,6]=>10001=>01110=>1
[1,3,5,2,6,4]=>10000=>01111=>1
[1,3,5,4,2,6]=>10001=>01110=>1
[1,3,5,4,6,2]=>10000=>01111=>1
[1,3,5,6,2,4]=>10000=>01111=>1
[1,3,5,6,4,2]=>10000=>01111=>1
[1,3,6,2,4,5]=>10000=>01111=>1
[1,3,6,2,5,4]=>10000=>01111=>1
[1,3,6,4,2,5]=>10000=>01111=>1
[1,3,6,4,5,2]=>10000=>01111=>1
[1,3,6,5,2,4]=>10000=>01111=>1
[1,3,6,5,4,2]=>10000=>01111=>1
[1,4,2,3,5,6]=>10011=>01100=>1
[1,4,2,3,6,5]=>10010=>01101=>2
[1,4,2,5,3,6]=>10001=>01110=>1
[1,4,2,5,6,3]=>10000=>01111=>1
[1,4,2,6,3,5]=>10000=>01111=>1
[1,4,2,6,5,3]=>10000=>01111=>1
[1,4,3,2,5,6]=>10011=>01100=>1
[1,4,3,2,6,5]=>10010=>01101=>2
[1,4,3,5,2,6]=>10001=>01110=>1
[1,4,3,5,6,2]=>10000=>01111=>1
[1,4,3,6,2,5]=>10000=>01111=>1
[1,4,3,6,5,2]=>10000=>01111=>1
[1,4,5,2,3,6]=>10001=>01110=>1
[1,4,5,2,6,3]=>10000=>01111=>1
[1,4,5,3,2,6]=>10001=>01110=>1
[1,4,5,3,6,2]=>10000=>01111=>1
[1,4,5,6,2,3]=>10000=>01111=>1
[1,4,5,6,3,2]=>10000=>01111=>1
[1,4,6,2,3,5]=>10000=>01111=>1
[1,4,6,2,5,3]=>10000=>01111=>1
[1,4,6,3,2,5]=>10000=>01111=>1
[1,4,6,3,5,2]=>10000=>01111=>1
[1,4,6,5,2,3]=>10000=>01111=>1
[1,4,6,5,3,2]=>10000=>01111=>1
[1,5,2,3,4,6]=>10001=>01110=>1
[1,5,2,3,6,4]=>10000=>01111=>1
[1,5,2,4,3,6]=>10001=>01110=>1
[1,5,2,4,6,3]=>10000=>01111=>1
[1,5,2,6,3,4]=>10000=>01111=>1
[1,5,2,6,4,3]=>10000=>01111=>1
[1,5,3,2,4,6]=>10001=>01110=>1
[1,5,3,2,6,4]=>10000=>01111=>1
[1,5,3,4,2,6]=>10001=>01110=>1
[1,5,3,4,6,2]=>10000=>01111=>1
[1,5,3,6,2,4]=>10000=>01111=>1
[1,5,3,6,4,2]=>10000=>01111=>1
[1,5,4,2,3,6]=>10001=>01110=>1
[1,5,4,2,6,3]=>10000=>01111=>1
[1,5,4,3,2,6]=>10001=>01110=>1
[1,5,4,3,6,2]=>10000=>01111=>1
[1,5,4,6,2,3]=>10000=>01111=>1
[1,5,4,6,3,2]=>10000=>01111=>1
[1,5,6,2,3,4]=>10000=>01111=>1
[1,5,6,2,4,3]=>10000=>01111=>1
[1,5,6,3,2,4]=>10000=>01111=>1
[1,5,6,3,4,2]=>10000=>01111=>1
[1,5,6,4,2,3]=>10000=>01111=>1
[1,5,6,4,3,2]=>10000=>01111=>1
[1,6,2,3,4,5]=>10000=>01111=>1
[1,6,2,3,5,4]=>10000=>01111=>1
[1,6,2,4,3,5]=>10000=>01111=>1
[1,6,2,4,5,3]=>10000=>01111=>1
[1,6,2,5,3,4]=>10000=>01111=>1
[1,6,2,5,4,3]=>10000=>01111=>1
[1,6,3,2,4,5]=>10000=>01111=>1
[1,6,3,2,5,4]=>10000=>01111=>1
[1,6,3,4,2,5]=>10000=>01111=>1
[1,6,3,4,5,2]=>10000=>01111=>1
[1,6,3,5,2,4]=>10000=>01111=>1
[1,6,3,5,4,2]=>10000=>01111=>1
[1,6,4,2,3,5]=>10000=>01111=>1
[1,6,4,2,5,3]=>10000=>01111=>1
[1,6,4,3,2,5]=>10000=>01111=>1
[1,6,4,3,5,2]=>10000=>01111=>1
[1,6,4,5,2,3]=>10000=>01111=>1
[1,6,4,5,3,2]=>10000=>01111=>1
[1,6,5,2,3,4]=>10000=>01111=>1
[1,6,5,2,4,3]=>10000=>01111=>1
[1,6,5,3,2,4]=>10000=>01111=>1
[1,6,5,3,4,2]=>10000=>01111=>1
[1,6,5,4,2,3]=>10000=>01111=>1
[1,6,5,4,3,2]=>10000=>01111=>1
[2,1,3,4,5,6]=>01111=>10000=>1
[2,1,3,4,6,5]=>01110=>10001=>2
[2,1,3,5,4,6]=>01101=>10010=>2
[2,1,3,5,6,4]=>01100=>10011=>2
[2,1,3,6,4,5]=>01100=>10011=>2
[2,1,3,6,5,4]=>01100=>10011=>2
[2,1,4,3,5,6]=>01011=>10100=>2
[2,1,4,3,6,5]=>01010=>10101=>3
[2,1,4,5,3,6]=>01001=>10110=>2
[2,1,4,5,6,3]=>01000=>10111=>2
[2,1,4,6,3,5]=>01000=>10111=>2
[2,1,4,6,5,3]=>01000=>10111=>2
[2,1,5,3,4,6]=>01001=>10110=>2
[2,1,5,3,6,4]=>01000=>10111=>2
[2,1,5,4,3,6]=>01001=>10110=>2
[2,1,5,4,6,3]=>01000=>10111=>2
[2,1,5,6,3,4]=>01000=>10111=>2
[2,1,5,6,4,3]=>01000=>10111=>2
[2,1,6,3,4,5]=>01000=>10111=>2
[2,1,6,3,5,4]=>01000=>10111=>2
[2,1,6,4,3,5]=>01000=>10111=>2
[2,1,6,4,5,3]=>01000=>10111=>2
[2,1,6,5,3,4]=>01000=>10111=>2
[2,1,6,5,4,3]=>01000=>10111=>2
[2,3,1,4,5,6]=>00111=>11000=>1
[2,3,1,4,6,5]=>00110=>11001=>2
[2,3,1,5,4,6]=>00101=>11010=>2
[2,3,1,5,6,4]=>00100=>11011=>2
[2,3,1,6,4,5]=>00100=>11011=>2
[2,3,1,6,5,4]=>00100=>11011=>2
[2,3,4,1,5,6]=>00011=>11100=>1
[2,3,4,1,6,5]=>00010=>11101=>2
[2,3,4,5,1,6]=>00001=>11110=>1
[2,3,4,5,6,1]=>00000=>11111=>1
[2,3,4,6,1,5]=>00000=>11111=>1
[2,3,4,6,5,1]=>00000=>11111=>1
[2,3,5,1,4,6]=>00001=>11110=>1
[2,3,5,1,6,4]=>00000=>11111=>1
[2,3,5,4,1,6]=>00001=>11110=>1
[2,3,5,4,6,1]=>00000=>11111=>1
[2,3,5,6,1,4]=>00000=>11111=>1
[2,3,5,6,4,1]=>00000=>11111=>1
[2,3,6,1,4,5]=>00000=>11111=>1
[2,3,6,1,5,4]=>00000=>11111=>1
[2,3,6,4,1,5]=>00000=>11111=>1
[2,3,6,4,5,1]=>00000=>11111=>1
[2,3,6,5,1,4]=>00000=>11111=>1
[2,3,6,5,4,1]=>00000=>11111=>1
[2,4,1,3,5,6]=>00011=>11100=>1
[2,4,1,3,6,5]=>00010=>11101=>2
[2,4,1,5,3,6]=>00001=>11110=>1
[2,4,1,5,6,3]=>00000=>11111=>1
[2,4,1,6,3,5]=>00000=>11111=>1
[2,4,1,6,5,3]=>00000=>11111=>1
[2,4,3,1,5,6]=>00011=>11100=>1
[2,4,3,1,6,5]=>00010=>11101=>2
[2,4,3,5,1,6]=>00001=>11110=>1
[2,4,3,5,6,1]=>00000=>11111=>1
[2,4,3,6,1,5]=>00000=>11111=>1
[2,4,3,6,5,1]=>00000=>11111=>1
[2,4,5,1,3,6]=>00001=>11110=>1
[2,4,5,1,6,3]=>00000=>11111=>1
[2,4,5,3,1,6]=>00001=>11110=>1
[2,4,5,3,6,1]=>00000=>11111=>1
[2,4,5,6,1,3]=>00000=>11111=>1
[2,4,5,6,3,1]=>00000=>11111=>1
[2,4,6,1,3,5]=>00000=>11111=>1
[2,4,6,1,5,3]=>00000=>11111=>1
[2,4,6,3,1,5]=>00000=>11111=>1
[2,4,6,3,5,1]=>00000=>11111=>1
[2,4,6,5,1,3]=>00000=>11111=>1
[2,4,6,5,3,1]=>00000=>11111=>1
[2,5,1,3,4,6]=>00001=>11110=>1
[2,5,1,3,6,4]=>00000=>11111=>1
[2,5,1,4,3,6]=>00001=>11110=>1
[2,5,1,4,6,3]=>00000=>11111=>1
[2,5,1,6,3,4]=>00000=>11111=>1
[2,5,1,6,4,3]=>00000=>11111=>1
[2,5,3,1,4,6]=>00001=>11110=>1
[2,5,3,1,6,4]=>00000=>11111=>1
[2,5,3,4,1,6]=>00001=>11110=>1
[2,5,3,4,6,1]=>00000=>11111=>1
[2,5,3,6,1,4]=>00000=>11111=>1
[2,5,3,6,4,1]=>00000=>11111=>1
[2,5,4,1,3,6]=>00001=>11110=>1
[2,5,4,1,6,3]=>00000=>11111=>1
[2,5,4,3,1,6]=>00001=>11110=>1
[2,5,4,3,6,1]=>00000=>11111=>1
[2,5,4,6,1,3]=>00000=>11111=>1
[2,5,4,6,3,1]=>00000=>11111=>1
[2,5,6,1,3,4]=>00000=>11111=>1
[2,5,6,1,4,3]=>00000=>11111=>1
[2,5,6,3,1,4]=>00000=>11111=>1
[2,5,6,3,4,1]=>00000=>11111=>1
[2,5,6,4,1,3]=>00000=>11111=>1
[2,5,6,4,3,1]=>00000=>11111=>1
[2,6,1,3,4,5]=>00000=>11111=>1
[2,6,1,3,5,4]=>00000=>11111=>1
[2,6,1,4,3,5]=>00000=>11111=>1
[2,6,1,4,5,3]=>00000=>11111=>1
[2,6,1,5,3,4]=>00000=>11111=>1
[2,6,1,5,4,3]=>00000=>11111=>1
[2,6,3,1,4,5]=>00000=>11111=>1
[2,6,3,1,5,4]=>00000=>11111=>1
[2,6,3,4,1,5]=>00000=>11111=>1
[2,6,3,4,5,1]=>00000=>11111=>1
[2,6,3,5,1,4]=>00000=>11111=>1
[2,6,3,5,4,1]=>00000=>11111=>1
[2,6,4,1,3,5]=>00000=>11111=>1
[2,6,4,1,5,3]=>00000=>11111=>1
[2,6,4,3,1,5]=>00000=>11111=>1
[2,6,4,3,5,1]=>00000=>11111=>1
[2,6,4,5,1,3]=>00000=>11111=>1
[2,6,4,5,3,1]=>00000=>11111=>1
[2,6,5,1,3,4]=>00000=>11111=>1
[2,6,5,1,4,3]=>00000=>11111=>1
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[6,1,2,5,3,4]=>00000=>11111=>1
[6,1,2,5,4,3]=>00000=>11111=>1
[6,1,3,2,4,5]=>00000=>11111=>1
[6,1,3,2,5,4]=>00000=>11111=>1
[6,1,3,4,2,5]=>00000=>11111=>1
[6,1,3,4,5,2]=>00000=>11111=>1
[6,1,3,5,2,4]=>00000=>11111=>1
[6,1,3,5,4,2]=>00000=>11111=>1
[6,1,4,2,3,5]=>00000=>11111=>1
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[6,1,4,3,2,5]=>00000=>11111=>1
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[6,1,4,5,2,3]=>00000=>11111=>1
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[6,1,5,2,3,4]=>00000=>11111=>1
[6,1,5,2,4,3]=>00000=>11111=>1
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[6,2,1,3,4,5]=>00000=>11111=>1
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[6,2,1,5,3,4]=>00000=>11111=>1
[6,2,1,5,4,3]=>00000=>11111=>1
[6,2,3,1,4,5]=>00000=>11111=>1
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[6,2,3,4,1,5]=>00000=>11111=>1
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[6,2,5,4,1,3]=>00000=>11111=>1
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[6,3,1,4,5,2]=>00000=>11111=>1
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[6,3,4,1,2,5]=>00000=>11111=>1
[6,3,4,1,5,2]=>00000=>11111=>1
[6,3,4,2,1,5]=>00000=>11111=>1
[6,3,4,2,5,1]=>00000=>11111=>1
[6,3,4,5,1,2]=>00000=>11111=>1
[6,3,4,5,2,1]=>00000=>11111=>1
[6,3,5,1,2,4]=>00000=>11111=>1
[6,3,5,1,4,2]=>00000=>11111=>1
[6,3,5,2,1,4]=>00000=>11111=>1
[6,3,5,2,4,1]=>00000=>11111=>1
[6,3,5,4,1,2]=>00000=>11111=>1
[6,3,5,4,2,1]=>00000=>11111=>1
[6,4,1,2,3,5]=>00000=>11111=>1
[6,4,1,2,5,3]=>00000=>11111=>1
[6,4,1,3,2,5]=>00000=>11111=>1
[6,4,1,3,5,2]=>00000=>11111=>1
[6,4,1,5,2,3]=>00000=>11111=>1
[6,4,1,5,3,2]=>00000=>11111=>1
[6,4,2,1,3,5]=>00000=>11111=>1
[6,4,2,1,5,3]=>00000=>11111=>1
[6,4,2,3,1,5]=>00000=>11111=>1
[6,4,2,3,5,1]=>00000=>11111=>1
[6,4,2,5,1,3]=>00000=>11111=>1
[6,4,2,5,3,1]=>00000=>11111=>1
[6,4,3,1,2,5]=>00000=>11111=>1
[6,4,3,1,5,2]=>00000=>11111=>1
[6,4,3,2,1,5]=>00000=>11111=>1
[6,4,3,2,5,1]=>00000=>11111=>1
[6,4,3,5,1,2]=>00000=>11111=>1
[6,4,3,5,2,1]=>00000=>11111=>1
[6,4,5,1,2,3]=>00000=>11111=>1
[6,4,5,1,3,2]=>00000=>11111=>1
[6,4,5,2,1,3]=>00000=>11111=>1
[6,4,5,2,3,1]=>00000=>11111=>1
[6,4,5,3,1,2]=>00000=>11111=>1
[6,4,5,3,2,1]=>00000=>11111=>1
[6,5,1,2,3,4]=>00000=>11111=>1
[6,5,1,2,4,3]=>00000=>11111=>1
[6,5,1,3,2,4]=>00000=>11111=>1
[6,5,1,3,4,2]=>00000=>11111=>1
[6,5,1,4,2,3]=>00000=>11111=>1
[6,5,1,4,3,2]=>00000=>11111=>1
[6,5,2,1,3,4]=>00000=>11111=>1
[6,5,2,1,4,3]=>00000=>11111=>1
[6,5,2,3,1,4]=>00000=>11111=>1
[6,5,2,3,4,1]=>00000=>11111=>1
[6,5,2,4,1,3]=>00000=>11111=>1
[6,5,2,4,3,1]=>00000=>11111=>1
[6,5,3,1,2,4]=>00000=>11111=>1
[6,5,3,1,4,2]=>00000=>11111=>1
[6,5,3,2,1,4]=>00000=>11111=>1
[6,5,3,2,4,1]=>00000=>11111=>1
[6,5,3,4,1,2]=>00000=>11111=>1
[6,5,3,4,2,1]=>00000=>11111=>1
[6,5,4,1,2,3]=>00000=>11111=>1
[6,5,4,1,3,2]=>00000=>11111=>1
[6,5,4,2,1,3]=>00000=>11111=>1
[6,5,4,2,3,1]=>00000=>11111=>1
[6,5,4,3,1,2]=>00000=>11111=>1
[6,5,4,3,2,1]=>00000=>11111=>1
[1,2,3,4,5,6,7]=>111111=>000000=>0
[1,2,3,4,5,7,6]=>111110=>000001=>1
[1,2,3,4,6,5,7]=>111101=>000010=>1
[1,2,3,4,6,7,5]=>111100=>000011=>1
[1,2,3,4,7,5,6]=>111100=>000011=>1
[1,2,3,4,7,6,5]=>111100=>000011=>1
[1,2,3,5,4,6,7]=>111011=>000100=>1
[1,2,3,5,4,7,6]=>111010=>000101=>2
[1,2,3,5,6,4,7]=>111001=>000110=>1
[1,2,3,5,6,7,4]=>111000=>000111=>1
[1,2,3,5,7,4,6]=>111000=>000111=>1
[1,2,3,5,7,6,4]=>111000=>000111=>1
[1,2,3,6,4,5,7]=>111001=>000110=>1
[1,2,3,6,4,7,5]=>111000=>000111=>1
[1,2,3,6,5,4,7]=>111001=>000110=>1
[1,2,3,6,5,7,4]=>111000=>000111=>1
[1,2,3,6,7,4,5]=>111000=>000111=>1
[1,2,3,6,7,5,4]=>111000=>000111=>1
[1,2,3,7,4,5,6]=>111000=>000111=>1
[1,2,3,7,4,6,5]=>111000=>000111=>1
[1,2,3,7,5,4,6]=>111000=>000111=>1
[1,2,3,7,5,6,4]=>111000=>000111=>1
[1,2,3,7,6,4,5]=>111000=>000111=>1
[1,2,3,7,6,5,4]=>111000=>000111=>1
[1,2,4,3,5,6,7]=>110111=>001000=>1
[1,2,4,3,5,7,6]=>110110=>001001=>2
[1,2,4,3,6,5,7]=>110101=>001010=>2
[1,2,4,3,6,7,5]=>110100=>001011=>2
[1,2,4,3,7,5,6]=>110100=>001011=>2
[1,2,4,3,7,6,5]=>110100=>001011=>2
[1,2,4,5,3,6,7]=>110011=>001100=>1
[1,2,4,5,3,7,6]=>110010=>001101=>2
[1,2,4,5,6,3,7]=>110001=>001110=>1
[1,2,4,5,6,7,3]=>110000=>001111=>1
[1,2,4,5,7,3,6]=>110000=>001111=>1
[1,2,4,5,7,6,3]=>110000=>001111=>1
[1,2,4,6,3,5,7]=>110001=>001110=>1
[1,2,4,6,3,7,5]=>110000=>001111=>1
[1,2,4,6,5,3,7]=>110001=>001110=>1
[1,2,4,6,5,7,3]=>110000=>001111=>1
[1,2,4,6,7,3,5]=>110000=>001111=>1
[1,2,4,6,7,5,3]=>110000=>001111=>1
[1,2,4,7,3,5,6]=>110000=>001111=>1
[1,2,4,7,3,6,5]=>110000=>001111=>1
[1,2,4,7,5,3,6]=>110000=>001111=>1
[1,2,4,7,5,6,3]=>110000=>001111=>1
[1,2,4,7,6,3,5]=>110000=>001111=>1
[1,2,4,7,6,5,3]=>110000=>001111=>1
[1,2,5,3,4,6,7]=>110011=>001100=>1
[1,2,5,3,4,7,6]=>110010=>001101=>2
[1,2,5,3,6,4,7]=>110001=>001110=>1
[1,2,5,3,6,7,4]=>110000=>001111=>1
[1,2,5,3,7,4,6]=>110000=>001111=>1
[1,2,5,3,7,6,4]=>110000=>001111=>1
[1,2,5,4,3,6,7]=>110011=>001100=>1
[1,2,5,4,3,7,6]=>110010=>001101=>2
[1,2,5,4,6,3,7]=>110001=>001110=>1
[1,2,5,4,6,7,3]=>110000=>001111=>1
[1,2,5,4,7,3,6]=>110000=>001111=>1
[1,2,5,4,7,6,3]=>110000=>001111=>1
[1,2,5,6,3,4,7]=>110001=>001110=>1
[1,2,5,6,3,7,4]=>110000=>001111=>1
[1,2,5,6,4,3,7]=>110001=>001110=>1
[1,2,5,6,4,7,3]=>110000=>001111=>1
[1,2,5,6,7,3,4]=>110000=>001111=>1
[1,2,5,6,7,4,3]=>110000=>001111=>1
[1,2,5,7,3,4,6]=>110000=>001111=>1
[1,2,5,7,3,6,4]=>110000=>001111=>1
[1,2,5,7,4,3,6]=>110000=>001111=>1
[1,2,5,7,4,6,3]=>110000=>001111=>1
[1,2,5,7,6,3,4]=>110000=>001111=>1
[1,2,5,7,6,4,3]=>110000=>001111=>1
[1,2,6,3,4,5,7]=>110001=>001110=>1
[1,2,6,3,4,7,5]=>110000=>001111=>1
[1,2,6,3,5,4,7]=>110001=>001110=>1
[1,2,6,3,5,7,4]=>110000=>001111=>1
[1,2,6,3,7,4,5]=>110000=>001111=>1
[1,2,6,3,7,5,4]=>110000=>001111=>1
[1,2,6,4,3,5,7]=>110001=>001110=>1
[1,2,6,4,3,7,5]=>110000=>001111=>1
[1,2,6,4,5,3,7]=>110001=>001110=>1
[1,2,6,4,5,7,3]=>110000=>001111=>1
[1,2,6,4,7,3,5]=>110000=>001111=>1
[1,2,6,4,7,5,3]=>110000=>001111=>1
[1,2,6,5,3,4,7]=>110001=>001110=>1
[1,2,6,5,3,7,4]=>110000=>001111=>1
[1,2,6,5,4,3,7]=>110001=>001110=>1
[1,2,6,5,4,7,3]=>110000=>001111=>1
[1,2,6,5,7,3,4]=>110000=>001111=>1
[1,2,6,5,7,4,3]=>110000=>001111=>1
[1,2,6,7,3,4,5]=>110000=>001111=>1
[1,2,6,7,3,5,4]=>110000=>001111=>1
[1,2,6,7,4,3,5]=>110000=>001111=>1
[1,2,6,7,4,5,3]=>110000=>001111=>1
[1,2,6,7,5,3,4]=>110000=>001111=>1
[1,2,6,7,5,4,3]=>110000=>001111=>1
[1,2,7,3,4,5,6]=>110000=>001111=>1
[1,2,7,3,4,6,5]=>110000=>001111=>1
[1,2,7,3,5,4,6]=>110000=>001111=>1
[1,2,7,3,5,6,4]=>110000=>001111=>1
[1,2,7,3,6,4,5]=>110000=>001111=>1
[1,2,7,3,6,5,4]=>110000=>001111=>1
[1,2,7,4,3,5,6]=>110000=>001111=>1
[1,2,7,4,3,6,5]=>110000=>001111=>1
[1,2,7,4,5,3,6]=>110000=>001111=>1
[1,2,7,4,5,6,3]=>110000=>001111=>1
[1,2,7,4,6,3,5]=>110000=>001111=>1
[1,2,7,4,6,5,3]=>110000=>001111=>1
[1,2,7,5,3,4,6]=>110000=>001111=>1
[1,2,7,5,3,6,4]=>110000=>001111=>1
[1,2,7,5,4,3,6]=>110000=>001111=>1
[1,2,7,5,4,6,3]=>110000=>001111=>1
[1,2,7,5,6,3,4]=>110000=>001111=>1
[1,2,7,5,6,4,3]=>110000=>001111=>1
[1,2,7,6,3,4,5]=>110000=>001111=>1
[1,2,7,6,3,5,4]=>110000=>001111=>1
[1,2,7,6,4,3,5]=>110000=>001111=>1
[1,2,7,6,4,5,3]=>110000=>001111=>1
[1,2,7,6,5,3,4]=>110000=>001111=>1
[1,2,7,6,5,4,3]=>110000=>001111=>1
[1,3,2,4,5,6,7]=>101111=>010000=>1
[1,3,2,4,5,7,6]=>101110=>010001=>2
[1,3,2,4,6,5,7]=>101101=>010010=>2
[1,3,2,4,6,7,5]=>101100=>010011=>2
[1,3,2,4,7,5,6]=>101100=>010011=>2
[1,3,2,4,7,6,5]=>101100=>010011=>2
[1,3,2,5,4,6,7]=>101011=>010100=>2
[1,3,2,5,4,7,6]=>101010=>010101=>3
[1,3,2,5,6,4,7]=>101001=>010110=>2
[1,3,2,5,6,7,4]=>101000=>010111=>2
[1,3,2,5,7,4,6]=>101000=>010111=>2
[1,3,2,5,7,6,4]=>101000=>010111=>2
[1,3,2,6,4,5,7]=>101001=>010110=>2
[1,3,2,6,4,7,5]=>101000=>010111=>2
[1,3,2,6,5,4,7]=>101001=>010110=>2
[1,3,2,6,5,7,4]=>101000=>010111=>2
[1,3,2,6,7,4,5]=>101000=>010111=>2
[1,3,2,6,7,5,4]=>101000=>010111=>2
[1,3,2,7,4,5,6]=>101000=>010111=>2
[1,3,2,7,4,6,5]=>101000=>010111=>2
[1,3,2,7,5,4,6]=>101000=>010111=>2
[1,3,2,7,5,6,4]=>101000=>010111=>2
[1,3,2,7,6,4,5]=>101000=>010111=>2
[1,3,2,7,6,5,4]=>101000=>010111=>2
[1,3,4,2,5,6,7]=>100111=>011000=>1
[1,3,4,2,5,7,6]=>100110=>011001=>2
[1,3,4,2,6,5,7]=>100101=>011010=>2
[1,3,4,2,6,7,5]=>100100=>011011=>2
[1,3,4,2,7,5,6]=>100100=>011011=>2
[1,3,4,2,7,6,5]=>100100=>011011=>2
[1,3,4,5,2,6,7]=>100011=>011100=>1
[1,3,4,5,2,7,6]=>100010=>011101=>2
[1,3,4,5,6,2,7]=>100001=>011110=>1
[1,3,4,5,6,7,2]=>100000=>011111=>1
[1,3,4,5,7,2,6]=>100000=>011111=>1
[1,3,4,5,7,6,2]=>100000=>011111=>1
[1,3,4,6,2,5,7]=>100001=>011110=>1
[1,3,4,6,2,7,5]=>100000=>011111=>1
[1,3,4,6,5,2,7]=>100001=>011110=>1
[1,3,4,6,5,7,2]=>100000=>011111=>1
[1,3,4,6,7,2,5]=>100000=>011111=>1
[1,3,4,6,7,5,2]=>100000=>011111=>1
[1,3,4,7,2,5,6]=>100000=>011111=>1
[1,3,4,7,2,6,5]=>100000=>011111=>1
[1,3,4,7,5,2,6]=>100000=>011111=>1
[1,3,4,7,5,6,2]=>100000=>011111=>1
[1,3,4,7,6,2,5]=>100000=>011111=>1
[1,3,4,7,6,5,2]=>100000=>011111=>1
[1,3,5,2,4,6,7]=>100011=>011100=>1
[1,3,5,2,4,7,6]=>100010=>011101=>2
[1,3,5,2,6,4,7]=>100001=>011110=>1
[1,3,5,2,6,7,4]=>100000=>011111=>1
[1,3,5,2,7,4,6]=>100000=>011111=>1
[1,3,5,2,7,6,4]=>100000=>011111=>1
[1,3,5,4,2,6,7]=>100011=>011100=>1
[1,3,5,4,2,7,6]=>100010=>011101=>2
[1,3,5,4,6,2,7]=>100001=>011110=>1
[1,3,5,4,6,7,2]=>100000=>011111=>1
[1,3,5,4,7,2,6]=>100000=>011111=>1
[1,3,5,4,7,6,2]=>100000=>011111=>1
[1,3,5,6,2,4,7]=>100001=>011110=>1
[1,3,5,6,2,7,4]=>100000=>011111=>1
[1,3,5,6,4,2,7]=>100001=>011110=>1
[1,3,5,6,4,7,2]=>100000=>011111=>1
[1,3,5,6,7,2,4]=>100000=>011111=>1
[1,3,5,6,7,4,2]=>100000=>011111=>1
[1,3,5,7,2,4,6]=>100000=>011111=>1
[1,3,5,7,2,6,4]=>100000=>011111=>1
[1,3,5,7,4,2,6]=>100000=>011111=>1
[1,3,5,7,4,6,2]=>100000=>011111=>1
[1,3,5,7,6,2,4]=>100000=>011111=>1
[1,3,5,7,6,4,2]=>100000=>011111=>1
[1,3,6,2,4,5,7]=>100001=>011110=>1
[1,3,6,2,4,7,5]=>100000=>011111=>1
[1,3,6,2,5,4,7]=>100001=>011110=>1
[1,3,6,2,5,7,4]=>100000=>011111=>1
[1,3,6,2,7,4,5]=>100000=>011111=>1
[1,3,6,2,7,5,4]=>100000=>011111=>1
[1,3,6,4,2,5,7]=>100001=>011110=>1
[1,3,6,4,2,7,5]=>100000=>011111=>1
[1,3,6,4,5,2,7]=>100001=>011110=>1
[1,3,6,4,5,7,2]=>100000=>011111=>1
[1,3,6,4,7,2,5]=>100000=>011111=>1
[1,3,6,4,7,5,2]=>100000=>011111=>1
[1,3,6,5,2,4,7]=>100001=>011110=>1
[1,3,6,5,2,7,4]=>100000=>011111=>1
[1,3,6,5,4,2,7]=>100001=>011110=>1
[1,3,6,5,4,7,2]=>100000=>011111=>1
[1,3,6,5,7,2,4]=>100000=>011111=>1
[1,3,6,5,7,4,2]=>100000=>011111=>1
[1,3,6,7,2,4,5]=>100000=>011111=>1
[1,3,6,7,2,5,4]=>100000=>011111=>1
[1,3,6,7,4,2,5]=>100000=>011111=>1
[1,3,6,7,4,5,2]=>100000=>011111=>1
[1,3,6,7,5,2,4]=>100000=>011111=>1
[1,3,6,7,5,4,2]=>100000=>011111=>1
[1,3,7,2,4,5,6]=>100000=>011111=>1
[1,3,7,2,4,6,5]=>100000=>011111=>1
[1,3,7,2,5,4,6]=>100000=>011111=>1
[1,3,7,2,5,6,4]=>100000=>011111=>1
[1,3,7,2,6,4,5]=>100000=>011111=>1
[1,3,7,2,6,5,4]=>100000=>011111=>1
[1,3,7,4,2,5,6]=>100000=>011111=>1
[1,3,7,4,2,6,5]=>100000=>011111=>1
[1,3,7,4,5,2,6]=>100000=>011111=>1
[1,3,7,4,5,6,2]=>100000=>011111=>1
[1,3,7,4,6,2,5]=>100000=>011111=>1
[1,3,7,4,6,5,2]=>100000=>011111=>1
[1,3,7,5,2,4,6]=>100000=>011111=>1
[1,3,7,5,2,6,4]=>100000=>011111=>1
[1,3,7,5,4,2,6]=>100000=>011111=>1
[1,3,7,5,4,6,2]=>100000=>011111=>1
[1,3,7,5,6,2,4]=>100000=>011111=>1
[1,3,7,5,6,4,2]=>100000=>011111=>1
[1,3,7,6,2,4,5]=>100000=>011111=>1
[1,3,7,6,2,5,4]=>100000=>011111=>1
[1,3,7,6,4,2,5]=>100000=>011111=>1
[1,3,7,6,4,5,2]=>100000=>011111=>1
[1,3,7,6,5,2,4]=>100000=>011111=>1
[1,3,7,6,5,4,2]=>100000=>011111=>1
[1,4,2,3,5,6,7]=>100111=>011000=>1
[1,4,2,3,5,7,6]=>100110=>011001=>2
[1,4,2,3,6,5,7]=>100101=>011010=>2
[1,4,2,3,6,7,5]=>100100=>011011=>2
[1,4,2,3,7,5,6]=>100100=>011011=>2
[1,4,2,3,7,6,5]=>100100=>011011=>2
[1,4,2,5,3,6,7]=>100011=>011100=>1
[1,4,2,5,3,7,6]=>100010=>011101=>2
[1,4,2,5,6,3,7]=>100001=>011110=>1
[1,4,2,5,6,7,3]=>100000=>011111=>1
[1,4,2,5,7,3,6]=>100000=>011111=>1
[1,4,2,5,7,6,3]=>100000=>011111=>1
[1,4,2,6,3,5,7]=>100001=>011110=>1
[1,4,2,6,3,7,5]=>100000=>011111=>1
[1,4,2,6,5,3,7]=>100001=>011110=>1
[1,4,2,6,5,7,3]=>100000=>011111=>1
[1,4,2,6,7,3,5]=>100000=>011111=>1
[1,4,2,6,7,5,3]=>100000=>011111=>1
[1,4,2,7,3,5,6]=>100000=>011111=>1
[1,4,2,7,3,6,5]=>100000=>011111=>1
[1,4,2,7,5,3,6]=>100000=>011111=>1
[1,4,2,7,5,6,3]=>100000=>011111=>1
[1,4,2,7,6,3,5]=>100000=>011111=>1
[1,4,2,7,6,5,3]=>100000=>011111=>1
[1,4,3,2,5,6,7]=>100111=>011000=>1
[1,4,3,2,5,7,6]=>100110=>011001=>2
[1,4,3,2,6,5,7]=>100101=>011010=>2
[1,4,3,2,6,7,5]=>100100=>011011=>2
[1,4,3,2,7,5,6]=>100100=>011011=>2
[1,4,3,2,7,6,5]=>100100=>011011=>2
[1,4,3,5,2,6,7]=>100011=>011100=>1
[1,4,3,5,2,7,6]=>100010=>011101=>2
[1,4,3,5,6,2,7]=>100001=>011110=>1
[1,4,3,5,6,7,2]=>100000=>011111=>1
[1,4,3,5,7,2,6]=>100000=>011111=>1
[1,4,3,5,7,6,2]=>100000=>011111=>1
[1,4,3,6,2,5,7]=>100001=>011110=>1
[1,4,3,6,2,7,5]=>100000=>011111=>1
[1,4,3,6,5,2,7]=>100001=>011110=>1
[1,4,3,6,5,7,2]=>100000=>011111=>1
[1,4,3,6,7,2,5]=>100000=>011111=>1
[1,4,3,6,7,5,2]=>100000=>011111=>1
[1,4,3,7,2,5,6]=>100000=>011111=>1
[1,4,3,7,2,6,5]=>100000=>011111=>1
[1,4,3,7,5,2,6]=>100000=>011111=>1
[1,4,3,7,5,6,2]=>100000=>011111=>1
[1,4,3,7,6,2,5]=>100000=>011111=>1
[1,4,3,7,6,5,2]=>100000=>011111=>1
[1,4,5,2,3,6,7]=>100011=>011100=>1
[1,4,5,2,3,7,6]=>100010=>011101=>2
[1,4,5,2,6,3,7]=>100001=>011110=>1
[1,4,5,2,6,7,3]=>100000=>011111=>1
[1,4,5,2,7,3,6]=>100000=>011111=>1
[1,4,5,2,7,6,3]=>100000=>011111=>1
[1,4,5,3,2,6,7]=>100011=>011100=>1
[1,4,5,3,2,7,6]=>100010=>011101=>2
[1,4,5,3,6,2,7]=>100001=>011110=>1
[1,4,5,3,6,7,2]=>100000=>011111=>1
[1,4,5,3,7,2,6]=>100000=>011111=>1
[1,4,5,3,7,6,2]=>100000=>011111=>1
[1,4,5,6,2,3,7]=>100001=>011110=>1
[1,4,5,6,2,7,3]=>100000=>011111=>1
[1,4,5,6,3,2,7]=>100001=>011110=>1
[1,4,5,6,3,7,2]=>100000=>011111=>1
[1,4,5,6,7,2,3]=>100000=>011111=>1
[1,4,5,6,7,3,2]=>100000=>011111=>1
[1,4,5,7,2,3,6]=>100000=>011111=>1
[1,4,5,7,2,6,3]=>100000=>011111=>1
[1,4,5,7,3,2,6]=>100000=>011111=>1
[1,4,5,7,3,6,2]=>100000=>011111=>1
[1,4,5,7,6,2,3]=>100000=>011111=>1
[1,4,5,7,6,3,2]=>100000=>011111=>1
[1,4,6,2,3,5,7]=>100001=>011110=>1
[1,4,6,2,3,7,5]=>100000=>011111=>1
[1,4,6,2,5,3,7]=>100001=>011110=>1
[1,4,6,2,5,7,3]=>100000=>011111=>1
[1,4,6,2,7,3,5]=>100000=>011111=>1
[1,4,6,2,7,5,3]=>100000=>011111=>1
[1,4,6,3,2,5,7]=>100001=>011110=>1
[1,4,6,3,2,7,5]=>100000=>011111=>1
[1,4,6,3,5,2,7]=>100001=>011110=>1
[1,4,6,3,5,7,2]=>100000=>011111=>1
[1,4,6,3,7,2,5]=>100000=>011111=>1
[1,4,6,3,7,5,2]=>100000=>011111=>1
[1,4,6,5,2,3,7]=>100001=>011110=>1
[1,4,6,5,2,7,3]=>100000=>011111=>1
[1,4,6,5,3,2,7]=>100001=>011110=>1
[1,4,6,5,3,7,2]=>100000=>011111=>1
[1,4,6,5,7,2,3]=>100000=>011111=>1
[1,4,6,5,7,3,2]=>100000=>011111=>1
[1,4,6,7,2,3,5]=>100000=>011111=>1
[1,4,6,7,2,5,3]=>100000=>011111=>1
[1,4,6,7,3,2,5]=>100000=>011111=>1
[1,4,6,7,3,5,2]=>100000=>011111=>1
[1,4,6,7,5,2,3]=>100000=>011111=>1
[1,4,6,7,5,3,2]=>100000=>011111=>1
[1,4,7,2,3,5,6]=>100000=>011111=>1
[1,4,7,2,3,6,5]=>100000=>011111=>1
[1,4,7,2,5,3,6]=>100000=>011111=>1
[1,4,7,2,5,6,3]=>100000=>011111=>1
[1,4,7,2,6,3,5]=>100000=>011111=>1
[1,4,7,2,6,5,3]=>100000=>011111=>1
[1,4,7,3,2,5,6]=>100000=>011111=>1
[1,4,7,3,2,6,5]=>100000=>011111=>1
[1,4,7,3,5,2,6]=>100000=>011111=>1
[1,4,7,3,5,6,2]=>100000=>011111=>1
[1,4,7,3,6,2,5]=>100000=>011111=>1
[1,4,7,3,6,5,2]=>100000=>011111=>1
[1,4,7,5,2,3,6]=>100000=>011111=>1
[1,4,7,5,2,6,3]=>100000=>011111=>1
[1,4,7,5,3,2,6]=>100000=>011111=>1
[1,4,7,5,3,6,2]=>100000=>011111=>1
[1,4,7,5,6,2,3]=>100000=>011111=>1
[1,4,7,5,6,3,2]=>100000=>011111=>1
[1,4,7,6,2,3,5]=>100000=>011111=>1
[1,4,7,6,2,5,3]=>100000=>011111=>1
[1,4,7,6,3,2,5]=>100000=>011111=>1
[1,4,7,6,3,5,2]=>100000=>011111=>1
[1,4,7,6,5,2,3]=>100000=>011111=>1
[1,4,7,6,5,3,2]=>100000=>011111=>1
[1,5,2,3,4,6,7]=>100011=>011100=>1
[1,5,2,3,4,7,6]=>100010=>011101=>2
[1,5,2,3,6,4,7]=>100001=>011110=>1
[1,5,2,3,6,7,4]=>100000=>011111=>1
[1,5,2,3,7,4,6]=>100000=>011111=>1
[1,5,2,3,7,6,4]=>100000=>011111=>1
[1,5,2,4,3,6,7]=>100011=>011100=>1
[1,5,2,4,3,7,6]=>100010=>011101=>2
[1,5,2,4,6,3,7]=>100001=>011110=>1
[1,5,2,4,6,7,3]=>100000=>011111=>1
[1,5,2,4,7,3,6]=>100000=>011111=>1
[1,5,2,4,7,6,3]=>100000=>011111=>1
[1,5,2,6,3,4,7]=>100001=>011110=>1
[1,5,2,6,3,7,4]=>100000=>011111=>1
[1,5,2,6,4,3,7]=>100001=>011110=>1
[1,5,2,6,4,7,3]=>100000=>011111=>1
[1,5,2,6,7,3,4]=>100000=>011111=>1
[1,5,2,6,7,4,3]=>100000=>011111=>1
[1,5,2,7,3,4,6]=>100000=>011111=>1
[1,5,2,7,3,6,4]=>100000=>011111=>1
[1,5,2,7,4,3,6]=>100000=>011111=>1
[1,5,2,7,4,6,3]=>100000=>011111=>1
[1,5,2,7,6,3,4]=>100000=>011111=>1
[1,5,2,7,6,4,3]=>100000=>011111=>1
[1,5,3,2,4,6,7]=>100011=>011100=>1
[1,5,3,2,4,7,6]=>100010=>011101=>2
[1,5,3,2,6,4,7]=>100001=>011110=>1
[1,5,3,2,6,7,4]=>100000=>011111=>1
[1,5,3,2,7,4,6]=>100000=>011111=>1
[1,5,3,2,7,6,4]=>100000=>011111=>1
[1,5,3,4,2,6,7]=>100011=>011100=>1
[1,5,3,4,2,7,6]=>100010=>011101=>2
[1,5,3,4,6,2,7]=>100001=>011110=>1
[1,5,3,4,6,7,2]=>100000=>011111=>1
[1,5,3,4,7,2,6]=>100000=>011111=>1
[1,5,3,4,7,6,2]=>100000=>011111=>1
[1,5,3,6,2,4,7]=>100001=>011110=>1
[1,5,3,6,2,7,4]=>100000=>011111=>1
[1,5,3,6,4,2,7]=>100001=>011110=>1
[1,5,3,6,4,7,2]=>100000=>011111=>1
[1,5,3,6,7,2,4]=>100000=>011111=>1
[1,5,3,6,7,4,2]=>100000=>011111=>1
[1,5,3,7,2,4,6]=>100000=>011111=>1
[1,5,3,7,2,6,4]=>100000=>011111=>1
[1,5,3,7,4,2,6]=>100000=>011111=>1
[1,5,3,7,4,6,2]=>100000=>011111=>1
[1,5,3,7,6,2,4]=>100000=>011111=>1
[1,5,3,7,6,4,2]=>100000=>011111=>1
[1,5,4,2,3,6,7]=>100011=>011100=>1
[1,5,4,2,3,7,6]=>100010=>011101=>2
[1,5,4,2,6,3,7]=>100001=>011110=>1
[1,5,4,2,6,7,3]=>100000=>011111=>1
[1,5,4,2,7,3,6]=>100000=>011111=>1
[1,5,4,2,7,6,3]=>100000=>011111=>1
[1,5,4,3,2,6,7]=>100011=>011100=>1
[1,5,4,3,2,7,6]=>100010=>011101=>2
[1,5,4,3,6,2,7]=>100001=>011110=>1
[1,5,4,3,6,7,2]=>100000=>011111=>1
[1,5,4,3,7,2,6]=>100000=>011111=>1
[1,5,4,3,7,6,2]=>100000=>011111=>1
[1,5,4,6,2,3,7]=>100001=>011110=>1
[1,5,4,6,2,7,3]=>100000=>011111=>1
[1,5,4,6,3,2,7]=>100001=>011110=>1
[1,5,4,6,3,7,2]=>100000=>011111=>1
[1,5,4,6,7,2,3]=>100000=>011111=>1
[1,5,4,6,7,3,2]=>100000=>011111=>1
[1,5,4,7,2,3,6]=>100000=>011111=>1
[1,5,4,7,2,6,3]=>100000=>011111=>1
[1,5,4,7,3,2,6]=>100000=>011111=>1
[1,5,4,7,3,6,2]=>100000=>011111=>1
[1,5,4,7,6,2,3]=>100000=>011111=>1
[1,5,4,7,6,3,2]=>100000=>011111=>1
[1,5,6,2,3,4,7]=>100001=>011110=>1
[1,5,6,2,3,7,4]=>100000=>011111=>1
[1,5,6,2,4,3,7]=>100001=>011110=>1
[1,5,6,2,4,7,3]=>100000=>011111=>1
[1,5,6,2,7,3,4]=>100000=>011111=>1
[1,5,6,2,7,4,3]=>100000=>011111=>1
[1,5,6,3,2,4,7]=>100001=>011110=>1
[1,5,6,3,2,7,4]=>100000=>011111=>1
[1,5,6,3,4,2,7]=>100001=>011110=>1
[1,5,6,3,4,7,2]=>100000=>011111=>1
[1,5,6,3,7,2,4]=>100000=>011111=>1
[1,5,6,3,7,4,2]=>100000=>011111=>1
[1,5,6,4,2,3,7]=>100001=>011110=>1
[1,5,6,4,2,7,3]=>100000=>011111=>1
[1,5,6,4,3,2,7]=>100001=>011110=>1
[1,5,6,4,3,7,2]=>100000=>011111=>1
[1,5,6,4,7,2,3]=>100000=>011111=>1
[1,5,6,4,7,3,2]=>100000=>011111=>1
[1,5,6,7,2,3,4]=>100000=>011111=>1
[1,5,6,7,2,4,3]=>100000=>011111=>1
[1,5,6,7,3,2,4]=>100000=>011111=>1
[1,5,6,7,3,4,2]=>100000=>011111=>1
[1,5,6,7,4,2,3]=>100000=>011111=>1
[1,5,6,7,4,3,2]=>100000=>011111=>1
[1,5,7,2,3,4,6]=>100000=>011111=>1
[1,5,7,2,3,6,4]=>100000=>011111=>1
[1,5,7,2,4,3,6]=>100000=>011111=>1
[1,5,7,2,4,6,3]=>100000=>011111=>1
[1,5,7,2,6,3,4]=>100000=>011111=>1
[1,5,7,2,6,4,3]=>100000=>011111=>1
[1,5,7,3,2,4,6]=>100000=>011111=>1
[1,5,7,3,2,6,4]=>100000=>011111=>1
[1,5,7,3,4,2,6]=>100000=>011111=>1
[1,5,7,3,4,6,2]=>100000=>011111=>1
[1,5,7,3,6,2,4]=>100000=>011111=>1
[1,5,7,3,6,4,2]=>100000=>011111=>1
[1,5,7,4,2,3,6]=>100000=>011111=>1
[1,5,7,4,2,6,3]=>100000=>011111=>1
[1,5,7,4,3,2,6]=>100000=>011111=>1
[1,5,7,4,3,6,2]=>100000=>011111=>1
[1,5,7,4,6,2,3]=>100000=>011111=>1
[1,5,7,4,6,3,2]=>100000=>011111=>1
[1,5,7,6,2,3,4]=>100000=>011111=>1
[1,5,7,6,2,4,3]=>100000=>011111=>1
[1,5,7,6,3,2,4]=>100000=>011111=>1
[1,5,7,6,3,4,2]=>100000=>011111=>1
[1,5,7,6,4,2,3]=>100000=>011111=>1
[1,5,7,6,4,3,2]=>100000=>011111=>1
[1,6,2,3,4,5,7]=>100001=>011110=>1
[1,6,2,3,4,7,5]=>100000=>011111=>1
[1,6,2,3,5,4,7]=>100001=>011110=>1
[1,6,2,3,5,7,4]=>100000=>011111=>1
[1,6,2,3,7,4,5]=>100000=>011111=>1
[1,6,2,3,7,5,4]=>100000=>011111=>1
[1,6,2,4,3,5,7]=>100001=>011110=>1
[1,6,2,4,3,7,5]=>100000=>011111=>1
[1,6,2,4,5,3,7]=>100001=>011110=>1
[1,6,2,4,5,7,3]=>100000=>011111=>1
[1,6,2,4,7,3,5]=>100000=>011111=>1
[1,6,2,4,7,5,3]=>100000=>011111=>1
[1,6,2,5,3,4,7]=>100001=>011110=>1
[1,6,2,5,3,7,4]=>100000=>011111=>1
[1,6,2,5,4,3,7]=>100001=>011110=>1
[1,6,2,5,4,7,3]=>100000=>011111=>1
[1,6,2,5,7,3,4]=>100000=>011111=>1
[1,6,2,5,7,4,3]=>100000=>011111=>1
[1,6,2,7,3,4,5]=>100000=>011111=>1
[1,6,2,7,3,5,4]=>100000=>011111=>1
[1,6,2,7,4,3,5]=>100000=>011111=>1
[1,6,2,7,4,5,3]=>100000=>011111=>1
[1,6,2,7,5,3,4]=>100000=>011111=>1
[1,6,2,7,5,4,3]=>100000=>011111=>1
[1,6,3,2,4,5,7]=>100001=>011110=>1
[1,6,3,2,4,7,5]=>100000=>011111=>1
[1,6,3,2,5,4,7]=>100001=>011110=>1
[1,6,3,2,5,7,4]=>100000=>011111=>1
[1,6,3,2,7,4,5]=>100000=>011111=>1
[1,6,3,2,7,5,4]=>100000=>011111=>1
[1,6,3,4,2,5,7]=>100001=>011110=>1
[1,6,3,4,2,7,5]=>100000=>011111=>1
[1,6,3,4,5,2,7]=>100001=>011110=>1
[1,6,3,4,5,7,2]=>100000=>011111=>1
[1,6,3,4,7,2,5]=>100000=>011111=>1
[1,6,3,4,7,5,2]=>100000=>011111=>1
[1,6,3,5,2,4,7]=>100001=>011110=>1
[1,6,3,5,2,7,4]=>100000=>011111=>1
[1,6,3,5,4,2,7]=>100001=>011110=>1
[1,6,3,5,4,7,2]=>100000=>011111=>1
[1,6,3,5,7,2,4]=>100000=>011111=>1
[1,6,3,5,7,4,2]=>100000=>011111=>1
[1,6,3,7,2,4,5]=>100000=>011111=>1
[1,6,3,7,2,5,4]=>100000=>011111=>1
[1,6,3,7,4,2,5]=>100000=>011111=>1
[1,6,3,7,4,5,2]=>100000=>011111=>1
[1,6,3,7,5,2,4]=>100000=>011111=>1
[1,6,3,7,5,4,2]=>100000=>011111=>1
[1,6,4,2,3,5,7]=>100001=>011110=>1
[1,6,4,2,3,7,5]=>100000=>011111=>1
[1,6,4,2,5,3,7]=>100001=>011110=>1
[1,6,4,2,5,7,3]=>100000=>011111=>1
[1,6,4,2,7,3,5]=>100000=>011111=>1
[1,6,4,2,7,5,3]=>100000=>011111=>1
[1,6,4,3,2,5,7]=>100001=>011110=>1
[1,6,4,3,2,7,5]=>100000=>011111=>1
[1,6,4,3,5,2,7]=>100001=>011110=>1
[1,6,4,3,5,7,2]=>100000=>011111=>1
[1,6,4,3,7,2,5]=>100000=>011111=>1
[1,6,4,3,7,5,2]=>100000=>011111=>1
[1,6,4,5,2,3,7]=>100001=>011110=>1
[1,6,4,5,2,7,3]=>100000=>011111=>1
[1,6,4,5,3,2,7]=>100001=>011110=>1
[1,6,4,5,3,7,2]=>100000=>011111=>1
[1,6,4,5,7,2,3]=>100000=>011111=>1
[1,6,4,5,7,3,2]=>100000=>011111=>1
[1,6,4,7,2,3,5]=>100000=>011111=>1
[1,6,4,7,2,5,3]=>100000=>011111=>1
[1,6,4,7,3,2,5]=>100000=>011111=>1
[1,6,4,7,3,5,2]=>100000=>011111=>1
[1,6,4,7,5,2,3]=>100000=>011111=>1
[1,6,4,7,5,3,2]=>100000=>011111=>1
[1,6,5,2,3,4,7]=>100001=>011110=>1
[1,6,5,2,3,7,4]=>100000=>011111=>1
[1,6,5,2,4,3,7]=>100001=>011110=>1
[1,6,5,2,4,7,3]=>100000=>011111=>1
[1,6,5,2,7,3,4]=>100000=>011111=>1
[1,6,5,2,7,4,3]=>100000=>011111=>1
[1,6,5,3,2,4,7]=>100001=>011110=>1
[1,6,5,3,2,7,4]=>100000=>011111=>1
[1,6,5,3,4,2,7]=>100001=>011110=>1
[1,6,5,3,4,7,2]=>100000=>011111=>1
[1,6,5,3,7,2,4]=>100000=>011111=>1
[1,6,5,3,7,4,2]=>100000=>011111=>1
[1,6,5,4,2,3,7]=>100001=>011110=>1
[1,6,5,4,2,7,3]=>100000=>011111=>1
[1,6,5,4,3,2,7]=>100001=>011110=>1
[1,6,5,4,3,7,2]=>100000=>011111=>1
[1,6,5,4,7,2,3]=>100000=>011111=>1
[1,6,5,4,7,3,2]=>100000=>011111=>1
[1,6,5,7,2,3,4]=>100000=>011111=>1
[1,6,5,7,2,4,3]=>100000=>011111=>1
[1,6,5,7,3,2,4]=>100000=>011111=>1
[1,6,5,7,3,4,2]=>100000=>011111=>1
[1,6,5,7,4,2,3]=>100000=>011111=>1
[1,6,5,7,4,3,2]=>100000=>011111=>1
[1,6,7,2,3,4,5]=>100000=>011111=>1
[1,6,7,2,3,5,4]=>100000=>011111=>1
[1,6,7,2,4,3,5]=>100000=>011111=>1
[1,6,7,2,4,5,3]=>100000=>011111=>1
[1,6,7,2,5,3,4]=>100000=>011111=>1
[1,6,7,2,5,4,3]=>100000=>011111=>1
[1,6,7,3,2,4,5]=>100000=>011111=>1
[1,6,7,3,2,5,4]=>100000=>011111=>1
[1,6,7,3,4,2,5]=>100000=>011111=>1
[1,6,7,3,4,5,2]=>100000=>011111=>1
[1,6,7,3,5,2,4]=>100000=>011111=>1
[1,6,7,3,5,4,2]=>100000=>011111=>1
[1,6,7,4,2,3,5]=>100000=>011111=>1
[1,6,7,4,2,5,3]=>100000=>011111=>1
[1,6,7,4,3,2,5]=>100000=>011111=>1
[1,6,7,4,3,5,2]=>100000=>011111=>1
[1,6,7,4,5,2,3]=>100000=>011111=>1
[1,6,7,4,5,3,2]=>100000=>011111=>1
[1,6,7,5,2,3,4]=>100000=>011111=>1
[1,6,7,5,2,4,3]=>100000=>011111=>1
[1,6,7,5,3,2,4]=>100000=>011111=>1
[1,6,7,5,3,4,2]=>100000=>011111=>1
[1,6,7,5,4,2,3]=>100000=>011111=>1
[1,6,7,5,4,3,2]=>100000=>011111=>1
[1,7,2,3,4,5,6]=>100000=>011111=>1
[1,7,2,3,4,6,5]=>100000=>011111=>1
[1,7,2,3,5,4,6]=>100000=>011111=>1
[1,7,2,3,5,6,4]=>100000=>011111=>1
[1,7,2,3,6,4,5]=>100000=>011111=>1
[1,7,2,3,6,5,4]=>100000=>011111=>1
[1,7,2,4,3,5,6]=>100000=>011111=>1
[1,7,2,4,3,6,5]=>100000=>011111=>1
[1,7,2,4,5,3,6]=>100000=>011111=>1
[1,7,2,4,5,6,3]=>100000=>011111=>1
[1,7,2,4,6,3,5]=>100000=>011111=>1
[1,7,2,4,6,5,3]=>100000=>011111=>1
[1,7,2,5,3,4,6]=>100000=>011111=>1
[1,7,2,5,3,6,4]=>100000=>011111=>1
[1,7,2,5,4,3,6]=>100000=>011111=>1
[1,7,2,5,4,6,3]=>100000=>011111=>1
[1,7,2,5,6,3,4]=>100000=>011111=>1
[1,7,2,5,6,4,3]=>100000=>011111=>1
[1,7,2,6,3,4,5]=>100000=>011111=>1
[1,7,2,6,3,5,4]=>100000=>011111=>1
[1,7,2,6,4,3,5]=>100000=>011111=>1
[1,7,2,6,4,5,3]=>100000=>011111=>1
[1,7,2,6,5,3,4]=>100000=>011111=>1
[1,7,2,6,5,4,3]=>100000=>011111=>1
[1,7,3,2,4,5,6]=>100000=>011111=>1
[1,7,3,2,4,6,5]=>100000=>011111=>1
[1,7,3,2,5,4,6]=>100000=>011111=>1
[1,7,3,2,5,6,4]=>100000=>011111=>1
[1,7,3,2,6,4,5]=>100000=>011111=>1
[1,7,3,2,6,5,4]=>100000=>011111=>1
[1,7,3,4,2,5,6]=>100000=>011111=>1
[1,7,3,4,2,6,5]=>100000=>011111=>1
[1,7,3,4,5,2,6]=>100000=>011111=>1
[1,7,3,4,5,6,2]=>100000=>011111=>1
[1,7,3,4,6,2,5]=>100000=>011111=>1
[1,7,3,4,6,5,2]=>100000=>011111=>1
[1,7,3,5,2,4,6]=>100000=>011111=>1
[1,7,3,5,2,6,4]=>100000=>011111=>1
[1,7,3,5,4,2,6]=>100000=>011111=>1
[1,7,3,5,4,6,2]=>100000=>011111=>1
[1,7,3,5,6,2,4]=>100000=>011111=>1
[1,7,3,5,6,4,2]=>100000=>011111=>1
[1,7,3,6,2,4,5]=>100000=>011111=>1
[1,7,3,6,2,5,4]=>100000=>011111=>1
[1,7,3,6,4,2,5]=>100000=>011111=>1
[1,7,3,6,4,5,2]=>100000=>011111=>1
[1,7,3,6,5,2,4]=>100000=>011111=>1
[1,7,3,6,5,4,2]=>100000=>011111=>1
[1,7,4,2,3,5,6]=>100000=>011111=>1
[1,7,4,2,3,6,5]=>100000=>011111=>1
[1,7,4,2,5,3,6]=>100000=>011111=>1
[1,7,4,2,5,6,3]=>100000=>011111=>1
[1,7,4,2,6,3,5]=>100000=>011111=>1
[1,7,4,2,6,5,3]=>100000=>011111=>1
[1,7,4,3,2,5,6]=>100000=>011111=>1
[1,7,4,3,2,6,5]=>100000=>011111=>1
[1,7,4,3,5,2,6]=>100000=>011111=>1
[1,7,4,3,5,6,2]=>100000=>011111=>1
[1,7,4,3,6,2,5]=>100000=>011111=>1
[1,7,4,3,6,5,2]=>100000=>011111=>1
[1,7,4,5,2,3,6]=>100000=>011111=>1
[1,7,4,5,2,6,3]=>100000=>011111=>1
[1,7,4,5,3,2,6]=>100000=>011111=>1
[1,7,4,5,3,6,2]=>100000=>011111=>1
[1,7,4,5,6,2,3]=>100000=>011111=>1
[1,7,4,5,6,3,2]=>100000=>011111=>1
[1,7,4,6,2,3,5]=>100000=>011111=>1
[1,7,4,6,2,5,3]=>100000=>011111=>1
[1,7,4,6,3,2,5]=>100000=>011111=>1
[1,7,4,6,3,5,2]=>100000=>011111=>1
[1,7,4,6,5,2,3]=>100000=>011111=>1
[1,7,4,6,5,3,2]=>100000=>011111=>1
[1,7,5,2,3,4,6]=>100000=>011111=>1
[1,7,5,2,3,6,4]=>100000=>011111=>1
[1,7,5,2,4,3,6]=>100000=>011111=>1
[1,7,5,2,4,6,3]=>100000=>011111=>1
[1,7,5,2,6,3,4]=>100000=>011111=>1
[1,7,5,2,6,4,3]=>100000=>011111=>1
[1,7,5,3,2,4,6]=>100000=>011111=>1
[1,7,5,3,2,6,4]=>100000=>011111=>1
[1,7,5,3,4,2,6]=>100000=>011111=>1
[1,7,5,3,4,6,2]=>100000=>011111=>1
[1,7,5,3,6,2,4]=>100000=>011111=>1
[1,7,5,3,6,4,2]=>100000=>011111=>1
[1,7,5,4,2,3,6]=>100000=>011111=>1
[1,7,5,4,2,6,3]=>100000=>011111=>1
[1,7,5,4,3,2,6]=>100000=>011111=>1
[1,7,5,4,3,6,2]=>100000=>011111=>1
[1,7,5,4,6,2,3]=>100000=>011111=>1
[1,7,5,4,6,3,2]=>100000=>011111=>1
[1,7,5,6,2,3,4]=>100000=>011111=>1
[1,7,5,6,2,4,3]=>100000=>011111=>1
[1,7,5,6,3,2,4]=>100000=>011111=>1
[1,7,5,6,3,4,2]=>100000=>011111=>1
[1,7,5,6,4,2,3]=>100000=>011111=>1
[1,7,5,6,4,3,2]=>100000=>011111=>1
[1,7,6,2,3,4,5]=>100000=>011111=>1
[1,7,6,2,3,5,4]=>100000=>011111=>1
[1,7,6,2,4,3,5]=>100000=>011111=>1
[1,7,6,2,4,5,3]=>100000=>011111=>1
[1,7,6,2,5,3,4]=>100000=>011111=>1
[1,7,6,2,5,4,3]=>100000=>011111=>1
[1,7,6,3,2,4,5]=>100000=>011111=>1
[1,7,6,3,2,5,4]=>100000=>011111=>1
[1,7,6,3,4,2,5]=>100000=>011111=>1
[1,7,6,3,4,5,2]=>100000=>011111=>1
[1,7,6,3,5,2,4]=>100000=>011111=>1
[1,7,6,3,5,4,2]=>100000=>011111=>1
[1,7,6,4,2,3,5]=>100000=>011111=>1
[1,7,6,4,2,5,3]=>100000=>011111=>1
[1,7,6,4,3,2,5]=>100000=>011111=>1
[1,7,6,4,3,5,2]=>100000=>011111=>1
[1,7,6,4,5,2,3]=>100000=>011111=>1
[1,7,6,4,5,3,2]=>100000=>011111=>1
[1,7,6,5,2,3,4]=>100000=>011111=>1
[1,7,6,5,2,4,3]=>100000=>011111=>1
[1,7,6,5,3,2,4]=>100000=>011111=>1
[1,7,6,5,3,4,2]=>100000=>011111=>1
[1,7,6,5,4,2,3]=>100000=>011111=>1
[1,7,6,5,4,3,2]=>100000=>011111=>1
[2,1,3,4,5,6,7]=>011111=>100000=>1
[2,1,3,4,5,7,6]=>011110=>100001=>2
[2,1,3,4,6,5,7]=>011101=>100010=>2
[2,1,3,4,6,7,5]=>011100=>100011=>2
[2,1,3,4,7,5,6]=>011100=>100011=>2
[2,1,3,4,7,6,5]=>011100=>100011=>2
[2,1,3,5,4,6,7]=>011011=>100100=>2
[2,1,3,5,4,7,6]=>011010=>100101=>3
[2,1,3,5,6,4,7]=>011001=>100110=>2
[2,1,3,5,6,7,4]=>011000=>100111=>2
[2,1,3,5,7,4,6]=>011000=>100111=>2
[2,1,3,5,7,6,4]=>011000=>100111=>2
[2,1,3,6,4,5,7]=>011001=>100110=>2
[2,1,3,6,4,7,5]=>011000=>100111=>2
[2,1,3,6,5,4,7]=>011001=>100110=>2
[2,1,3,6,5,7,4]=>011000=>100111=>2
[2,1,3,6,7,4,5]=>011000=>100111=>2
[2,1,3,6,7,5,4]=>011000=>100111=>2
[2,1,3,7,4,5,6]=>011000=>100111=>2
[2,1,3,7,4,6,5]=>011000=>100111=>2
[2,1,3,7,5,4,6]=>011000=>100111=>2
[2,1,3,7,5,6,4]=>011000=>100111=>2
[2,1,3,7,6,4,5]=>011000=>100111=>2
[2,1,3,7,6,5,4]=>011000=>100111=>2
[2,1,4,3,5,6,7]=>010111=>101000=>2
[2,1,4,3,5,7,6]=>010110=>101001=>3
[2,1,4,3,6,5,7]=>010101=>101010=>3
[2,1,4,3,6,7,5]=>010100=>101011=>3
[2,1,4,3,7,5,6]=>010100=>101011=>3
[2,1,4,3,7,6,5]=>010100=>101011=>3
[2,1,4,5,3,6,7]=>010011=>101100=>2
[2,1,4,5,3,7,6]=>010010=>101101=>3
[2,1,4,5,6,3,7]=>010001=>101110=>2
[2,1,4,5,6,7,3]=>010000=>101111=>2
[2,1,4,5,7,3,6]=>010000=>101111=>2
[2,1,4,5,7,6,3]=>010000=>101111=>2
[2,1,4,6,3,5,7]=>010001=>101110=>2
[2,1,4,6,3,7,5]=>010000=>101111=>2
[2,1,4,6,5,3,7]=>010001=>101110=>2
[2,1,4,6,5,7,3]=>010000=>101111=>2
[2,1,4,6,7,3,5]=>010000=>101111=>2
[2,1,4,6,7,5,3]=>010000=>101111=>2
[2,1,4,7,3,5,6]=>010000=>101111=>2
[2,1,4,7,3,6,5]=>010000=>101111=>2
[2,1,4,7,5,3,6]=>010000=>101111=>2
[2,1,4,7,5,6,3]=>010000=>101111=>2
[2,1,4,7,6,3,5]=>010000=>101111=>2
[2,1,4,7,6,5,3]=>010000=>101111=>2
[2,1,5,3,4,6,7]=>010011=>101100=>2
[2,1,5,3,4,7,6]=>010010=>101101=>3
[2,1,5,3,6,4,7]=>010001=>101110=>2
[2,1,5,3,6,7,4]=>010000=>101111=>2
[2,1,5,3,7,4,6]=>010000=>101111=>2
[2,1,5,3,7,6,4]=>010000=>101111=>2
[2,1,5,4,3,6,7]=>010011=>101100=>2
[2,1,5,4,3,7,6]=>010010=>101101=>3
[2,1,5,4,6,3,7]=>010001=>101110=>2
[2,1,5,4,6,7,3]=>010000=>101111=>2
[2,1,5,4,7,3,6]=>010000=>101111=>2
[2,1,5,4,7,6,3]=>010000=>101111=>2
[2,1,5,6,3,4,7]=>010001=>101110=>2
[2,1,5,6,3,7,4]=>010000=>101111=>2
[2,1,5,6,4,3,7]=>010001=>101110=>2
[2,1,5,6,4,7,3]=>010000=>101111=>2
[2,1,5,6,7,3,4]=>010000=>101111=>2
[2,1,5,6,7,4,3]=>010000=>101111=>2
[2,1,5,7,3,4,6]=>010000=>101111=>2
[2,1,5,7,3,6,4]=>010000=>101111=>2
[2,1,5,7,4,3,6]=>010000=>101111=>2
[2,1,5,7,4,6,3]=>010000=>101111=>2
[2,1,5,7,6,3,4]=>010000=>101111=>2
[2,1,5,7,6,4,3]=>010000=>101111=>2
[2,1,6,3,4,5,7]=>010001=>101110=>2
[2,1,6,3,4,7,5]=>010000=>101111=>2
[2,1,6,3,5,4,7]=>010001=>101110=>2
[2,1,6,3,5,7,4]=>010000=>101111=>2
[2,1,6,3,7,4,5]=>010000=>101111=>2
[2,1,6,3,7,5,4]=>010000=>101111=>2
[2,1,6,4,3,5,7]=>010001=>101110=>2
[2,1,6,4,3,7,5]=>010000=>101111=>2
[2,1,6,4,5,3,7]=>010001=>101110=>2
[2,1,6,4,5,7,3]=>010000=>101111=>2
[2,1,6,4,7,3,5]=>010000=>101111=>2
[2,1,6,4,7,5,3]=>010000=>101111=>2
[2,1,6,5,3,4,7]=>010001=>101110=>2
[2,1,6,5,3,7,4]=>010000=>101111=>2
[2,1,6,5,4,3,7]=>010001=>101110=>2
[2,1,6,5,4,7,3]=>010000=>101111=>2
[2,1,6,5,7,3,4]=>010000=>101111=>2
[2,1,6,5,7,4,3]=>010000=>101111=>2
[2,1,6,7,3,4,5]=>010000=>101111=>2
[2,1,6,7,3,5,4]=>010000=>101111=>2
[2,1,6,7,4,3,5]=>010000=>101111=>2
[2,1,6,7,4,5,3]=>010000=>101111=>2
[2,1,6,7,5,3,4]=>010000=>101111=>2
[2,1,6,7,5,4,3]=>010000=>101111=>2
[2,1,7,3,4,5,6]=>010000=>101111=>2
[2,1,7,3,4,6,5]=>010000=>101111=>2
[2,1,7,3,5,4,6]=>010000=>101111=>2
[2,1,7,3,5,6,4]=>010000=>101111=>2
[2,1,7,3,6,4,5]=>010000=>101111=>2
[2,1,7,3,6,5,4]=>010000=>101111=>2
[2,1,7,4,3,5,6]=>010000=>101111=>2
[2,1,7,4,3,6,5]=>010000=>101111=>2
[2,1,7,4,5,3,6]=>010000=>101111=>2
[2,1,7,4,5,6,3]=>010000=>101111=>2
[2,1,7,4,6,3,5]=>010000=>101111=>2
[2,1,7,4,6,5,3]=>010000=>101111=>2
[2,1,7,5,3,4,6]=>010000=>101111=>2
[2,1,7,5,3,6,4]=>010000=>101111=>2
[2,1,7,5,4,3,6]=>010000=>101111=>2
[2,1,7,5,4,6,3]=>010000=>101111=>2
[2,1,7,5,6,3,4]=>010000=>101111=>2
[2,1,7,5,6,4,3]=>010000=>101111=>2
[2,1,7,6,3,4,5]=>010000=>101111=>2
[2,1,7,6,3,5,4]=>010000=>101111=>2
[2,1,7,6,4,3,5]=>010000=>101111=>2
[2,1,7,6,4,5,3]=>010000=>101111=>2
[2,1,7,6,5,3,4]=>010000=>101111=>2
[2,1,7,6,5,4,3]=>010000=>101111=>2
[2,3,1,4,5,6,7]=>001111=>110000=>1
[2,3,1,4,5,7,6]=>001110=>110001=>2
[2,3,1,4,6,5,7]=>001101=>110010=>2
[2,3,1,4,6,7,5]=>001100=>110011=>2
[2,3,1,4,7,5,6]=>001100=>110011=>2
[2,3,1,4,7,6,5]=>001100=>110011=>2
[2,3,1,5,4,6,7]=>001011=>110100=>2
[2,3,1,5,4,7,6]=>001010=>110101=>3
[2,3,1,5,6,4,7]=>001001=>110110=>2
[2,3,1,5,6,7,4]=>001000=>110111=>2
[2,3,1,5,7,4,6]=>001000=>110111=>2
[2,3,1,5,7,6,4]=>001000=>110111=>2
[2,3,1,6,4,5,7]=>001001=>110110=>2
[2,3,1,6,4,7,5]=>001000=>110111=>2
[2,3,1,6,5,4,7]=>001001=>110110=>2
[2,3,1,6,5,7,4]=>001000=>110111=>2
[2,3,1,6,7,4,5]=>001000=>110111=>2
[2,3,1,6,7,5,4]=>001000=>110111=>2
[2,3,1,7,4,5,6]=>001000=>110111=>2
[2,3,1,7,4,6,5]=>001000=>110111=>2
[2,3,1,7,5,4,6]=>001000=>110111=>2
[2,3,1,7,5,6,4]=>001000=>110111=>2
[2,3,1,7,6,4,5]=>001000=>110111=>2
[2,3,1,7,6,5,4]=>001000=>110111=>2
[2,3,4,1,5,6,7]=>000111=>111000=>1
[2,3,4,1,5,7,6]=>000110=>111001=>2
[2,3,4,1,6,5,7]=>000101=>111010=>2
[2,3,4,1,6,7,5]=>000100=>111011=>2
[2,3,4,1,7,5,6]=>000100=>111011=>2
[2,3,4,1,7,6,5]=>000100=>111011=>2
[2,3,4,5,1,6,7]=>000011=>111100=>1
[2,3,4,5,1,7,6]=>000010=>111101=>2
[2,3,4,5,6,1,7]=>000001=>111110=>1
[2,3,4,5,6,7,1]=>000000=>111111=>1
[2,3,4,5,7,1,6]=>000000=>111111=>1
[2,3,4,5,7,6,1]=>000000=>111111=>1
[2,3,4,6,1,5,7]=>000001=>111110=>1
[2,3,4,6,1,7,5]=>000000=>111111=>1
[2,3,4,6,5,1,7]=>000001=>111110=>1
[2,3,4,6,5,7,1]=>000000=>111111=>1
[2,3,4,6,7,1,5]=>000000=>111111=>1
[2,3,4,6,7,5,1]=>000000=>111111=>1
[2,3,4,7,1,5,6]=>000000=>111111=>1
[2,3,4,7,1,6,5]=>000000=>111111=>1
[2,3,4,7,5,1,6]=>000000=>111111=>1
[2,3,4,7,5,6,1]=>000000=>111111=>1
[2,3,4,7,6,1,5]=>000000=>111111=>1
[2,3,4,7,6,5,1]=>000000=>111111=>1
[2,3,5,1,4,6,7]=>000011=>111100=>1
[2,3,5,1,4,7,6]=>000010=>111101=>2
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[2,7,6,1,3,4,5]=>000000=>111111=>1
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[2,7,6,3,1,4,5]=>000000=>111111=>1
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[2,7,6,4,1,3,5]=>000000=>111111=>1
[2,7,6,4,1,5,3]=>000000=>111111=>1
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[2,7,6,5,4,3,1]=>000000=>111111=>1
[3,1,2,4,5,6,7]=>001111=>110000=>1
[3,1,2,4,5,7,6]=>001110=>110001=>2
[3,1,2,4,6,5,7]=>001101=>110010=>2
[3,1,2,4,6,7,5]=>001100=>110011=>2
[3,1,2,4,7,5,6]=>001100=>110011=>2
[3,1,2,4,7,6,5]=>001100=>110011=>2
[3,1,2,5,4,6,7]=>001011=>110100=>2
[3,1,2,5,4,7,6]=>001010=>110101=>3
[3,1,2,5,6,4,7]=>001001=>110110=>2
[3,1,2,5,6,7,4]=>001000=>110111=>2
[3,1,2,5,7,4,6]=>001000=>110111=>2
[3,1,2,5,7,6,4]=>001000=>110111=>2
[3,1,2,6,4,5,7]=>001001=>110110=>2
[3,1,2,6,4,7,5]=>001000=>110111=>2
[3,1,2,6,5,4,7]=>001001=>110110=>2
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[3,1,2,7,4,5,6]=>001000=>110111=>2
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[3,1,2,7,5,4,6]=>001000=>110111=>2
[3,1,2,7,5,6,4]=>001000=>110111=>2
[3,1,2,7,6,4,5]=>001000=>110111=>2
[3,1,2,7,6,5,4]=>001000=>110111=>2
[3,1,4,2,5,6,7]=>000111=>111000=>1
[3,1,4,2,5,7,6]=>000110=>111001=>2
[3,1,4,2,6,5,7]=>000101=>111010=>2
[3,1,4,2,6,7,5]=>000100=>111011=>2
[3,1,4,2,7,5,6]=>000100=>111011=>2
[3,1,4,2,7,6,5]=>000100=>111011=>2
[3,1,4,5,2,6,7]=>000011=>111100=>1
[3,1,4,5,2,7,6]=>000010=>111101=>2
[3,1,4,5,6,2,7]=>000001=>111110=>1
[3,1,4,5,6,7,2]=>000000=>111111=>1
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[3,1,4,6,5,7,2]=>000000=>111111=>1
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[3,1,5,2,4,6,7]=>000011=>111100=>1
[3,1,5,2,4,7,6]=>000010=>111101=>2
[3,1,5,2,6,4,7]=>000001=>111110=>1
[3,1,5,2,6,7,4]=>000000=>111111=>1
[3,1,5,2,7,4,6]=>000000=>111111=>1
[3,1,5,2,7,6,4]=>000000=>111111=>1
[3,1,5,4,2,6,7]=>000011=>111100=>1
[3,1,5,4,2,7,6]=>000010=>111101=>2
[3,1,5,4,6,2,7]=>000001=>111110=>1
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[3,1,5,4,7,2,6]=>000000=>111111=>1
[3,1,5,4,7,6,2]=>000000=>111111=>1
[3,1,5,6,2,4,7]=>000001=>111110=>1
[3,1,5,6,2,7,4]=>000000=>111111=>1
[3,1,5,6,4,2,7]=>000001=>111110=>1
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[3,1,5,6,7,2,4]=>000000=>111111=>1
[3,1,5,6,7,4,2]=>000000=>111111=>1
[3,1,5,7,2,4,6]=>000000=>111111=>1
[3,1,5,7,2,6,4]=>000000=>111111=>1
[3,1,5,7,4,2,6]=>000000=>111111=>1
[3,1,5,7,4,6,2]=>000000=>111111=>1
[3,1,5,7,6,2,4]=>000000=>111111=>1
[3,1,5,7,6,4,2]=>000000=>111111=>1
[3,1,6,2,4,5,7]=>000001=>111110=>1
[3,1,6,2,4,7,5]=>000000=>111111=>1
[3,1,6,2,5,4,7]=>000001=>111110=>1
[3,1,6,2,5,7,4]=>000000=>111111=>1
[3,1,6,2,7,4,5]=>000000=>111111=>1
[3,1,6,2,7,5,4]=>000000=>111111=>1
[3,1,6,4,2,5,7]=>000001=>111110=>1
[3,1,6,4,2,7,5]=>000000=>111111=>1
[3,1,6,4,5,2,7]=>000001=>111110=>1
[3,1,6,4,5,7,2]=>000000=>111111=>1
[3,1,6,4,7,2,5]=>000000=>111111=>1
[3,1,6,4,7,5,2]=>000000=>111111=>1
[3,1,6,5,2,4,7]=>000001=>111110=>1
[3,1,6,5,2,7,4]=>000000=>111111=>1
[3,1,6,5,4,2,7]=>000001=>111110=>1
[3,1,6,5,4,7,2]=>000000=>111111=>1
[3,1,6,5,7,2,4]=>000000=>111111=>1
[3,1,6,5,7,4,2]=>000000=>111111=>1
[3,1,6,7,2,4,5]=>000000=>111111=>1
[3,1,6,7,2,5,4]=>000000=>111111=>1
[3,1,6,7,4,2,5]=>000000=>111111=>1
[3,1,6,7,4,5,2]=>000000=>111111=>1
[3,1,6,7,5,2,4]=>000000=>111111=>1
[3,1,6,7,5,4,2]=>000000=>111111=>1
[3,1,7,2,4,5,6]=>000000=>111111=>1
[3,1,7,2,4,6,5]=>000000=>111111=>1
[3,1,7,2,5,4,6]=>000000=>111111=>1
[3,1,7,2,5,6,4]=>000000=>111111=>1
[3,1,7,2,6,4,5]=>000000=>111111=>1
[3,1,7,2,6,5,4]=>000000=>111111=>1
[3,1,7,4,2,5,6]=>000000=>111111=>1
[3,1,7,4,2,6,5]=>000000=>111111=>1
[3,1,7,4,5,2,6]=>000000=>111111=>1
[3,1,7,4,5,6,2]=>000000=>111111=>1
[3,1,7,4,6,2,5]=>000000=>111111=>1
[3,1,7,4,6,5,2]=>000000=>111111=>1
[3,1,7,5,2,4,6]=>000000=>111111=>1
[3,1,7,5,2,6,4]=>000000=>111111=>1
[3,1,7,5,4,2,6]=>000000=>111111=>1
[3,1,7,5,4,6,2]=>000000=>111111=>1
[3,1,7,5,6,2,4]=>000000=>111111=>1
[3,1,7,5,6,4,2]=>000000=>111111=>1
[3,1,7,6,2,4,5]=>000000=>111111=>1
[3,1,7,6,2,5,4]=>000000=>111111=>1
[3,1,7,6,4,2,5]=>000000=>111111=>1
[3,1,7,6,4,5,2]=>000000=>111111=>1
[3,1,7,6,5,2,4]=>000000=>111111=>1
[3,1,7,6,5,4,2]=>000000=>111111=>1
[3,2,1,4,5,6,7]=>001111=>110000=>1
[3,2,1,4,5,7,6]=>001110=>110001=>2
[3,2,1,4,6,5,7]=>001101=>110010=>2
[3,2,1,4,6,7,5]=>001100=>110011=>2
[3,2,1,4,7,5,6]=>001100=>110011=>2
[3,2,1,4,7,6,5]=>001100=>110011=>2
[3,2,1,5,4,6,7]=>001011=>110100=>2
[3,2,1,5,4,7,6]=>001010=>110101=>3
[3,2,1,5,6,4,7]=>001001=>110110=>2
[3,2,1,5,6,7,4]=>001000=>110111=>2
[3,2,1,5,7,4,6]=>001000=>110111=>2
[3,2,1,5,7,6,4]=>001000=>110111=>2
[3,2,1,6,4,5,7]=>001001=>110110=>2
[3,2,1,6,4,7,5]=>001000=>110111=>2
[3,2,1,6,5,4,7]=>001001=>110110=>2
[3,2,1,6,5,7,4]=>001000=>110111=>2
[3,2,1,6,7,4,5]=>001000=>110111=>2
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[3,2,1,7,4,5,6]=>001000=>110111=>2
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[3,2,1,7,6,5,4]=>001000=>110111=>2
[3,2,4,1,5,6,7]=>000111=>111000=>1
[3,2,4,1,5,7,6]=>000110=>111001=>2
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[3,2,6,1,4,5,7]=>000001=>111110=>1
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[3,2,6,1,5,4,7]=>000001=>111110=>1
[3,2,6,1,5,7,4]=>000000=>111111=>1
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[3,2,6,7,1,5,4]=>000000=>111111=>1
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[3,4,1,2,6,5,7]=>000101=>111010=>2
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[3,4,1,2,7,5,6]=>000100=>111011=>2
[3,4,1,2,7,6,5]=>000100=>111011=>2
[3,4,1,5,2,6,7]=>000011=>111100=>1
[3,4,1,5,2,7,6]=>000010=>111101=>2
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[3,4,2,1,7,5,6]=>000100=>111011=>2
[3,4,2,1,7,6,5]=>000100=>111011=>2
[3,4,2,5,1,6,7]=>000011=>111100=>1
[3,4,2,5,1,7,6]=>000010=>111101=>2
[3,4,2,5,6,1,7]=>000001=>111110=>1
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[3,4,5,1,2,6,7]=>000011=>111100=>1
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[3,4,5,1,6,2,7]=>000001=>111110=>1
[3,4,5,1,6,7,2]=>000000=>111111=>1
[3,4,5,1,7,2,6]=>000000=>111111=>1
[3,4,5,1,7,6,2]=>000000=>111111=>1
[3,4,5,2,1,6,7]=>000011=>111100=>1
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[3,4,5,2,6,1,7]=>000001=>111110=>1
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[3,4,5,2,7,1,6]=>000000=>111111=>1
[3,4,5,2,7,6,1]=>000000=>111111=>1
[3,4,5,6,1,2,7]=>000001=>111110=>1
[3,4,5,6,1,7,2]=>000000=>111111=>1
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[3,4,5,6,7,1,2]=>000000=>111111=>1
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[3,4,5,7,1,2,6]=>000000=>111111=>1
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[3,4,6,2,5,1,7]=>000001=>111110=>1
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[3,4,6,5,1,2,7]=>000001=>111110=>1
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[4,3,5,6,2,7,8,1]=>0000000=>1111111=>1
[3,4,5,6,2,7,8,1]=>0000000=>1111111=>1
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[5,6,4,2,3,7,8,1]=>0000000=>1111111=>1
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[3,4,5,2,6,7,8,1]=>0000000=>1111111=>1
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[3,4,2,5,6,7,8,1]=>0000000=>1111111=>1
[4,2,3,5,6,7,8,1]=>0000000=>1111111=>1
[3,2,4,5,6,7,8,1]=>0000000=>1111111=>1
[2,3,4,5,6,7,8,1]=>0000000=>1111111=>1
[8,7,6,5,4,3,1,2]=>0000000=>1111111=>1
[7,8,6,5,4,3,1,2]=>0000000=>1111111=>1
[8,6,7,5,4,3,1,2]=>0000000=>1111111=>1
[7,6,8,5,4,3,1,2]=>0000000=>1111111=>1
[6,7,8,5,4,3,1,2]=>0000000=>1111111=>1
[8,7,5,6,4,3,1,2]=>0000000=>1111111=>1
[8,6,5,7,4,3,1,2]=>0000000=>1111111=>1
[7,6,5,8,4,3,1,2]=>0000000=>1111111=>1
[6,7,5,8,4,3,1,2]=>0000000=>1111111=>1
[7,5,6,8,4,3,1,2]=>0000000=>1111111=>1
[5,6,7,8,4,3,1,2]=>0000000=>1111111=>1
[8,7,6,4,5,3,1,2]=>0000000=>1111111=>1
[8,6,7,4,5,3,1,2]=>0000000=>1111111=>1
[6,7,8,4,5,3,1,2]=>0000000=>1111111=>1
[7,8,4,5,6,3,1,2]=>0000000=>1111111=>1
[8,6,4,5,7,3,1,2]=>0000000=>1111111=>1
[7,6,5,4,8,3,1,2]=>0000000=>1111111=>1
[7,5,6,4,8,3,1,2]=>0000000=>1111111=>1
[6,5,7,4,8,3,1,2]=>0000000=>1111111=>1
[7,6,4,5,8,3,1,2]=>0000000=>1111111=>1
[6,7,4,5,8,3,1,2]=>0000000=>1111111=>1
[6,5,4,7,8,3,1,2]=>0000000=>1111111=>1
[5,4,6,7,8,3,1,2]=>0000000=>1111111=>1
[4,5,6,7,8,3,1,2]=>0000000=>1111111=>1
[8,7,6,5,3,4,1,2]=>0000000=>1111111=>1
[8,7,5,6,3,4,1,2]=>0000000=>1111111=>1
[7,8,5,6,3,4,1,2]=>0000000=>1111111=>1
[7,6,5,8,3,4,1,2]=>0000000=>1111111=>1
[6,7,5,8,3,4,1,2]=>0000000=>1111111=>1
[7,5,6,8,3,4,1,2]=>0000000=>1111111=>1
[6,5,7,8,3,4,1,2]=>0000000=>1111111=>1
[5,6,7,8,3,4,1,2]=>0000000=>1111111=>1
[8,7,6,3,4,5,1,2]=>0000000=>1111111=>1
[7,8,6,3,4,5,1,2]=>0000000=>1111111=>1
[8,6,7,3,4,5,1,2]=>0000000=>1111111=>1
[7,8,5,4,3,6,1,2]=>0000000=>1111111=>1
[8,7,4,5,3,6,1,2]=>0000000=>1111111=>1
[7,8,4,5,3,6,1,2]=>0000000=>1111111=>1
[7,8,5,3,4,6,1,2]=>0000000=>1111111=>1
[8,7,4,3,5,6,1,2]=>0000000=>1111111=>1
[7,8,4,3,5,6,1,2]=>0000000=>1111111=>1
[7,8,3,4,5,6,1,2]=>0000000=>1111111=>1
[8,6,5,4,3,7,1,2]=>0000000=>1111111=>1
[8,5,4,6,3,7,1,2]=>0000000=>1111111=>1
[8,3,4,5,6,7,1,2]=>0000000=>1111111=>1
[7,6,5,4,3,8,1,2]=>0000000=>1111111=>1
[7,5,6,4,3,8,1,2]=>0000000=>1111111=>1
[5,6,7,4,3,8,1,2]=>0000000=>1111111=>1
[6,7,4,5,3,8,1,2]=>0000000=>1111111=>1
[7,5,4,6,3,8,1,2]=>0000000=>1111111=>1
[6,5,4,7,3,8,1,2]=>0000000=>1111111=>1
[5,6,4,7,3,8,1,2]=>0000000=>1111111=>1
[4,5,6,7,3,8,1,2]=>0000000=>1111111=>1
[7,6,5,3,4,8,1,2]=>0000000=>1111111=>1
[7,6,3,4,5,8,1,2]=>0000000=>1111111=>1
[7,4,5,3,6,8,1,2]=>0000000=>1111111=>1
[7,3,4,5,6,8,1,2]=>0000000=>1111111=>1
[6,5,4,3,7,8,1,2]=>0000000=>1111111=>1
[5,6,4,3,7,8,1,2]=>0000000=>1111111=>1
[5,4,6,3,7,8,1,2]=>0000000=>1111111=>1
[4,5,6,3,7,8,1,2]=>0000000=>1111111=>1
[5,6,3,4,7,8,1,2]=>0000000=>1111111=>1
[6,4,3,5,7,8,1,2]=>0000000=>1111111=>1
[6,3,4,5,7,8,1,2]=>0000000=>1111111=>1
[5,4,3,6,7,8,1,2]=>0000000=>1111111=>1
[4,5,3,6,7,8,1,2]=>0000000=>1111111=>1
[5,3,4,6,7,8,1,2]=>0000000=>1111111=>1
[4,3,5,6,7,8,1,2]=>0000000=>1111111=>1
[3,4,5,6,7,8,1,2]=>0000000=>1111111=>1
[8,7,6,5,4,2,1,3]=>0000000=>1111111=>1
[7,8,6,5,4,2,1,3]=>0000000=>1111111=>1
[8,6,7,5,4,2,1,3]=>0000000=>1111111=>1
[7,6,8,5,4,2,1,3]=>0000000=>1111111=>1
[8,7,5,6,4,2,1,3]=>0000000=>1111111=>1
[7,8,5,6,4,2,1,3]=>0000000=>1111111=>1
[7,6,5,8,4,2,1,3]=>0000000=>1111111=>1
[6,7,5,8,4,2,1,3]=>0000000=>1111111=>1
[7,5,6,8,4,2,1,3]=>0000000=>1111111=>1
[5,6,7,8,4,2,1,3]=>0000000=>1111111=>1
[8,7,6,4,5,2,1,3]=>0000000=>1111111=>1
[7,6,5,4,8,2,1,3]=>0000000=>1111111=>1
[6,7,5,4,8,2,1,3]=>0000000=>1111111=>1
[6,5,7,4,8,2,1,3]=>0000000=>1111111=>1
[5,6,7,4,8,2,1,3]=>0000000=>1111111=>1
[7,6,4,5,8,2,1,3]=>0000000=>1111111=>1
[7,4,5,6,8,2,1,3]=>0000000=>1111111=>1
[5,4,6,7,8,2,1,3]=>0000000=>1111111=>1
[4,5,6,7,8,2,1,3]=>0000000=>1111111=>1
[8,7,6,5,4,1,2,3]=>0000000=>1111111=>1
[7,8,6,5,4,1,2,3]=>0000000=>1111111=>1
[7,6,8,5,4,1,2,3]=>0000000=>1111111=>1
[6,7,8,5,4,1,2,3]=>0000000=>1111111=>1
[8,5,6,7,4,1,2,3]=>0000000=>1111111=>1
[7,6,5,8,4,1,2,3]=>0000000=>1111111=>1
[6,7,5,8,4,1,2,3]=>0000000=>1111111=>1
[6,5,7,8,4,1,2,3]=>0000000=>1111111=>1
[5,6,7,8,4,1,2,3]=>0000000=>1111111=>1
[8,7,6,4,5,1,2,3]=>0000000=>1111111=>1
[8,6,7,4,5,1,2,3]=>0000000=>1111111=>1
[6,7,8,4,5,1,2,3]=>0000000=>1111111=>1
[8,7,5,4,6,1,2,3]=>0000000=>1111111=>1
[8,7,4,5,6,1,2,3]=>0000000=>1111111=>1
[7,8,4,5,6,1,2,3]=>0000000=>1111111=>1
[8,6,5,4,7,1,2,3]=>0000000=>1111111=>1
[8,6,4,5,7,1,2,3]=>0000000=>1111111=>1
[8,5,4,6,7,1,2,3]=>0000000=>1111111=>1
[8,4,5,6,7,1,2,3]=>0000000=>1111111=>1
[7,6,5,4,8,1,2,3]=>0000000=>1111111=>1
[6,7,5,4,8,1,2,3]=>0000000=>1111111=>1
[6,5,7,4,8,1,2,3]=>0000000=>1111111=>1
[6,7,4,5,8,1,2,3]=>0000000=>1111111=>1
[6,5,4,7,8,1,2,3]=>0000000=>1111111=>1
[5,4,6,7,8,1,2,3]=>0000000=>1111111=>1
[4,5,6,7,8,1,2,3]=>0000000=>1111111=>1
[8,7,6,5,3,2,1,4]=>0000000=>1111111=>1
[7,8,6,5,3,2,1,4]=>0000000=>1111111=>1
[8,6,7,5,3,2,1,4]=>0000000=>1111111=>1
[7,6,8,5,3,2,1,4]=>0000000=>1111111=>1
[6,7,8,5,3,2,1,4]=>0000000=>1111111=>1
[8,7,5,6,3,2,1,4]=>0000000=>1111111=>1
[7,8,5,6,3,2,1,4]=>0000000=>1111111=>1
[8,6,5,7,3,2,1,4]=>0000000=>1111111=>1
[8,5,6,7,3,2,1,4]=>0000000=>1111111=>1
[7,6,5,8,3,2,1,4]=>0000000=>1111111=>1
[6,7,5,8,3,2,1,4]=>0000000=>1111111=>1
[7,5,6,8,3,2,1,4]=>0000000=>1111111=>1
[6,5,7,8,3,2,1,4]=>0000000=>1111111=>1
[5,6,7,8,3,2,1,4]=>0000000=>1111111=>1
[8,7,6,5,2,3,1,4]=>0000000=>1111111=>1
[7,8,6,5,2,3,1,4]=>0000000=>1111111=>1
[8,6,7,5,2,3,1,4]=>0000000=>1111111=>1
[7,6,8,5,2,3,1,4]=>0000000=>1111111=>1
[6,7,8,5,2,3,1,4]=>0000000=>1111111=>1
[8,7,5,6,2,3,1,4]=>0000000=>1111111=>1
[7,8,5,6,2,3,1,4]=>0000000=>1111111=>1
[8,6,5,7,2,3,1,4]=>0000000=>1111111=>1
[8,5,6,7,2,3,1,4]=>0000000=>1111111=>1
[7,6,5,8,2,3,1,4]=>0000000=>1111111=>1
[6,7,5,8,2,3,1,4]=>0000000=>1111111=>1
[7,5,6,8,2,3,1,4]=>0000000=>1111111=>1
[6,5,7,8,2,3,1,4]=>0000000=>1111111=>1
[5,6,7,8,2,3,1,4]=>0000000=>1111111=>1
[8,7,6,5,3,1,2,4]=>0000000=>1111111=>1
[7,6,8,5,3,1,2,4]=>0000000=>1111111=>1
[7,8,5,6,3,1,2,4]=>0000000=>1111111=>1
[8,6,5,7,3,1,2,4]=>0000000=>1111111=>1
[7,6,5,8,3,1,2,4]=>0000000=>1111111=>1
[6,7,5,8,3,1,2,4]=>0000000=>1111111=>1
[7,5,6,8,3,1,2,4]=>0000000=>1111111=>1
[6,5,7,8,3,1,2,4]=>0000000=>1111111=>1
[5,6,7,8,3,1,2,4]=>0000000=>1111111=>1
[8,7,6,5,2,1,3,4]=>0000000=>1111111=>1
[7,8,6,5,2,1,3,4]=>0000000=>1111111=>1
[6,7,8,5,2,1,3,4]=>0000000=>1111111=>1
[8,7,5,6,2,1,3,4]=>0000000=>1111111=>1
[7,8,5,6,2,1,3,4]=>0000000=>1111111=>1
[8,6,5,7,2,1,3,4]=>0000000=>1111111=>1
[7,6,5,8,2,1,3,4]=>0000000=>1111111=>1
[6,7,5,8,2,1,3,4]=>0000000=>1111111=>1
[7,5,6,8,2,1,3,4]=>0000000=>1111111=>1
[6,5,7,8,2,1,3,4]=>0000000=>1111111=>1
[5,6,7,8,2,1,3,4]=>0000000=>1111111=>1
[8,7,6,5,1,2,3,4]=>0000000=>1111111=>1
[7,8,6,5,1,2,3,4]=>0000000=>1111111=>1
[8,6,7,5,1,2,3,4]=>0000000=>1111111=>1
[7,6,8,5,1,2,3,4]=>0000000=>1111111=>1
[6,7,8,5,1,2,3,4]=>0000000=>1111111=>1
[8,7,5,6,1,2,3,4]=>0000000=>1111111=>1
[7,8,5,6,1,2,3,4]=>0000000=>1111111=>1
[8,6,5,7,1,2,3,4]=>0000000=>1111111=>1
[8,5,6,7,1,2,3,4]=>0000000=>1111111=>1
[7,6,5,8,1,2,3,4]=>0000000=>1111111=>1
[6,7,5,8,1,2,3,4]=>0000000=>1111111=>1
[7,5,6,8,1,2,3,4]=>0000000=>1111111=>1
[6,5,7,8,1,2,3,4]=>0000000=>1111111=>1
[5,6,7,8,1,2,3,4]=>0000000=>1111111=>1
[8,7,6,4,3,2,1,5]=>0000000=>1111111=>1
[7,8,6,4,3,2,1,5]=>0000000=>1111111=>1
[8,6,7,4,3,2,1,5]=>0000000=>1111111=>1
[7,6,8,4,3,2,1,5]=>0000000=>1111111=>1
[6,7,8,4,3,2,1,5]=>0000000=>1111111=>1
[8,7,6,3,4,2,1,5]=>0000000=>1111111=>1
[6,7,8,3,4,2,1,5]=>0000000=>1111111=>1
[8,7,6,4,2,3,1,5]=>0000000=>1111111=>1
[7,6,8,4,2,3,1,5]=>0000000=>1111111=>1
[6,7,8,4,2,3,1,5]=>0000000=>1111111=>1
[8,7,6,3,2,4,1,5]=>0000000=>1111111=>1
[8,6,7,3,2,4,1,5]=>0000000=>1111111=>1
[6,7,8,3,2,4,1,5]=>0000000=>1111111=>1
[8,7,6,2,3,4,1,5]=>0000000=>1111111=>1
[7,6,8,2,3,4,1,5]=>0000000=>1111111=>1
[6,7,8,2,3,4,1,5]=>0000000=>1111111=>1
[8,7,6,4,3,1,2,5]=>0000000=>1111111=>1
[6,7,8,4,3,1,2,5]=>0000000=>1111111=>1
[8,7,6,3,4,1,2,5]=>0000000=>1111111=>1
[7,8,6,3,4,1,2,5]=>0000000=>1111111=>1
[6,7,8,3,4,1,2,5]=>0000000=>1111111=>1
[8,7,6,4,2,1,3,5]=>0000000=>1111111=>1
[6,7,8,4,2,1,3,5]=>0000000=>1111111=>1
[8,7,6,4,1,2,3,5]=>0000000=>1111111=>1
[7,6,8,4,1,2,3,5]=>0000000=>1111111=>1
[6,7,8,4,1,2,3,5]=>0000000=>1111111=>1
[8,7,6,3,2,1,4,5]=>0000000=>1111111=>1
[7,8,6,3,2,1,4,5]=>0000000=>1111111=>1
[7,6,8,3,2,1,4,5]=>0000000=>1111111=>1
[6,7,8,3,2,1,4,5]=>0000000=>1111111=>1
[8,7,6,2,3,1,4,5]=>0000000=>1111111=>1
[7,8,6,2,3,1,4,5]=>0000000=>1111111=>1
[7,6,8,2,3,1,4,5]=>0000000=>1111111=>1
[6,7,8,2,3,1,4,5]=>0000000=>1111111=>1
[8,7,6,3,1,2,4,5]=>0000000=>1111111=>1
[7,8,6,3,1,2,4,5]=>0000000=>1111111=>1
[8,6,7,3,1,2,4,5]=>0000000=>1111111=>1
[6,7,8,3,1,2,4,5]=>0000000=>1111111=>1
[8,7,6,2,1,3,4,5]=>0000000=>1111111=>1
[7,8,6,2,1,3,4,5]=>0000000=>1111111=>1
[6,7,8,2,1,3,4,5]=>0000000=>1111111=>1
[8,7,6,1,2,3,4,5]=>0000000=>1111111=>1
[7,8,6,1,2,3,4,5]=>0000000=>1111111=>1
[8,6,7,1,2,3,4,5]=>0000000=>1111111=>1
[7,6,8,1,2,3,4,5]=>0000000=>1111111=>1
[6,7,8,1,2,3,4,5]=>0000000=>1111111=>1
[8,7,5,4,3,2,1,6]=>0000000=>1111111=>1
[7,8,5,4,3,2,1,6]=>0000000=>1111111=>1
[8,7,4,5,3,2,1,6]=>0000000=>1111111=>1
[7,8,4,5,3,2,1,6]=>0000000=>1111111=>1
[8,7,3,4,5,2,1,6]=>0000000=>1111111=>1
[7,8,3,4,5,2,1,6]=>0000000=>1111111=>1
[8,7,4,5,2,3,1,6]=>0000000=>1111111=>1
[7,8,4,5,2,3,1,6]=>0000000=>1111111=>1
[8,7,5,3,2,4,1,6]=>0000000=>1111111=>1
[7,8,5,2,3,4,1,6]=>0000000=>1111111=>1
[8,7,4,3,2,5,1,6]=>0000000=>1111111=>1
[7,8,4,3,2,5,1,6]=>0000000=>1111111=>1
[7,8,3,4,2,5,1,6]=>0000000=>1111111=>1
[8,7,2,3,4,5,1,6]=>0000000=>1111111=>1
[7,8,2,3,4,5,1,6]=>0000000=>1111111=>1
[8,7,5,4,3,1,2,6]=>0000000=>1111111=>1
[8,7,5,3,4,1,2,6]=>0000000=>1111111=>1
[7,8,3,4,5,1,2,6]=>0000000=>1111111=>1
[7,8,5,4,2,1,3,6]=>0000000=>1111111=>1
[8,7,5,4,1,2,3,6]=>0000000=>1111111=>1
[7,8,5,4,1,2,3,6]=>0000000=>1111111=>1
[7,8,4,5,1,2,3,6]=>0000000=>1111111=>1
[8,7,5,3,2,1,4,6]=>0000000=>1111111=>1
[7,8,5,3,2,1,4,6]=>0000000=>1111111=>1
[8,7,5,2,1,3,4,6]=>0000000=>1111111=>1
[7,8,5,2,1,3,4,6]=>0000000=>1111111=>1
[8,7,5,1,2,3,4,6]=>0000000=>1111111=>1
[7,8,5,1,2,3,4,6]=>0000000=>1111111=>1
[8,7,4,3,2,1,5,6]=>0000000=>1111111=>1
[7,8,4,3,2,1,5,6]=>0000000=>1111111=>1
[8,7,3,4,2,1,5,6]=>0000000=>1111111=>1
[7,8,3,4,2,1,5,6]=>0000000=>1111111=>1
[7,8,4,2,3,1,5,6]=>0000000=>1111111=>1
[8,7,3,2,4,1,5,6]=>0000000=>1111111=>1
[7,8,3,2,4,1,5,6]=>0000000=>1111111=>1
[8,7,2,3,4,1,5,6]=>0000000=>1111111=>1
[7,8,2,3,4,1,5,6]=>0000000=>1111111=>1
[7,8,4,3,1,2,5,6]=>0000000=>1111111=>1
[7,8,3,4,1,2,5,6]=>0000000=>1111111=>1
[8,7,4,2,1,3,5,6]=>0000000=>1111111=>1
[7,8,4,2,1,3,5,6]=>0000000=>1111111=>1
[8,7,4,1,2,3,5,6]=>0000000=>1111111=>1
[7,8,4,1,2,3,5,6]=>0000000=>1111111=>1
[8,7,3,2,1,4,5,6]=>0000000=>1111111=>1
[7,8,3,2,1,4,5,6]=>0000000=>1111111=>1
[7,8,2,3,1,4,5,6]=>0000000=>1111111=>1
[7,8,3,1,2,4,5,6]=>0000000=>1111111=>1
[8,7,2,1,3,4,5,6]=>0000000=>1111111=>1
[7,8,2,1,3,4,5,6]=>0000000=>1111111=>1
[8,7,1,2,3,4,5,6]=>0000000=>1111111=>1
[7,8,1,2,3,4,5,6]=>0000000=>1111111=>1
[8,6,5,4,3,2,1,7]=>0000000=>1111111=>1
[8,5,6,4,3,2,1,7]=>0000000=>1111111=>1
[8,6,4,5,3,2,1,7]=>0000000=>1111111=>1
[8,4,5,6,3,2,1,7]=>0000000=>1111111=>1
[8,6,5,3,4,2,1,7]=>0000000=>1111111=>1
[8,5,6,3,4,2,1,7]=>0000000=>1111111=>1
[8,4,5,3,6,2,1,7]=>0000000=>1111111=>1
[8,4,3,5,6,2,1,7]=>0000000=>1111111=>1
[8,3,4,5,6,2,1,7]=>0000000=>1111111=>1
[8,6,5,4,2,3,1,7]=>0000000=>1111111=>1
[8,4,5,6,2,3,1,7]=>0000000=>1111111=>1
[8,6,5,2,3,4,1,7]=>0000000=>1111111=>1
[8,6,4,2,3,5,1,7]=>0000000=>1111111=>1
[8,5,4,3,2,6,1,7]=>0000000=>1111111=>1
[8,4,3,5,2,6,1,7]=>0000000=>1111111=>1
[8,4,5,2,3,6,1,7]=>0000000=>1111111=>1
[8,5,3,2,4,6,1,7]=>0000000=>1111111=>1
[8,3,4,2,5,6,1,7]=>0000000=>1111111=>1
[8,3,2,4,5,6,1,7]=>0000000=>1111111=>1
[8,2,3,4,5,6,1,7]=>0000000=>1111111=>1
[8,6,5,4,3,1,2,7]=>0000000=>1111111=>1
[8,6,4,5,3,1,2,7]=>0000000=>1111111=>1
[8,6,5,3,4,1,2,7]=>0000000=>1111111=>1
[8,5,6,3,4,1,2,7]=>0000000=>1111111=>1
[8,5,4,3,6,1,2,7]=>0000000=>1111111=>1
[8,4,3,5,6,1,2,7]=>0000000=>1111111=>1
[8,3,4,5,6,1,2,7]=>0000000=>1111111=>1
[8,6,5,4,2,1,3,7]=>0000000=>1111111=>1
[8,5,6,4,2,1,3,7]=>0000000=>1111111=>1
[8,6,5,4,1,2,3,7]=>0000000=>1111111=>1
[8,4,5,6,1,2,3,7]=>0000000=>1111111=>1
[8,6,5,3,2,1,4,7]=>0000000=>1111111=>1
[8,6,5,2,3,1,4,7]=>0000000=>1111111=>1
[8,5,6,2,3,1,4,7]=>0000000=>1111111=>1
[8,5,6,2,1,3,4,7]=>0000000=>1111111=>1
[8,6,5,1,2,3,4,7]=>0000000=>1111111=>1
[8,5,6,1,2,3,4,7]=>0000000=>1111111=>1
[8,6,4,3,2,1,5,7]=>0000000=>1111111=>1
[8,6,3,4,2,1,5,7]=>0000000=>1111111=>1
[8,6,4,2,3,1,5,7]=>0000000=>1111111=>1
[8,6,3,2,4,1,5,7]=>0000000=>1111111=>1
[8,6,2,3,4,1,5,7]=>0000000=>1111111=>1
[8,6,3,4,1,2,5,7]=>0000000=>1111111=>1
[8,6,4,2,1,3,5,7]=>0000000=>1111111=>1
[8,6,3,2,1,4,5,7]=>0000000=>1111111=>1
[8,6,1,2,3,4,5,7]=>0000000=>1111111=>1
[8,5,4,3,2,1,6,7]=>0000000=>1111111=>1
[8,4,5,3,2,1,6,7]=>0000000=>1111111=>1
[8,4,3,5,2,1,6,7]=>0000000=>1111111=>1
[8,3,4,5,2,1,6,7]=>0000000=>1111111=>1
[8,2,3,4,5,1,6,7]=>0000000=>1111111=>1
[8,5,4,2,1,3,6,7]=>0000000=>1111111=>1
[8,5,2,1,3,4,6,7]=>0000000=>1111111=>1
[8,5,1,2,3,4,6,7]=>0000000=>1111111=>1
[8,4,3,2,1,5,6,7]=>0000000=>1111111=>1
[8,4,2,3,1,5,6,7]=>0000000=>1111111=>1
[8,2,3,4,1,5,6,7]=>0000000=>1111111=>1
[8,4,1,2,3,5,6,7]=>0000000=>1111111=>1
[8,3,2,1,4,5,6,7]=>0000000=>1111111=>1
[8,2,3,1,4,5,6,7]=>0000000=>1111111=>1
[8,3,1,2,4,5,6,7]=>0000000=>1111111=>1
[8,2,1,3,4,5,6,7]=>0000000=>1111111=>1
[8,1,2,3,4,5,6,7]=>0000000=>1111111=>1
[7,6,5,4,3,2,1,8]=>0000001=>1111110=>1
[6,7,5,4,3,2,1,8]=>0000001=>1111110=>1
[7,5,6,4,3,2,1,8]=>0000001=>1111110=>1
[6,5,7,4,3,2,1,8]=>0000001=>1111110=>1
[5,6,7,4,3,2,1,8]=>0000001=>1111110=>1
[7,6,4,5,3,2,1,8]=>0000001=>1111110=>1
[6,7,4,5,3,2,1,8]=>0000001=>1111110=>1
[7,5,4,6,3,2,1,8]=>0000001=>1111110=>1
[7,4,5,6,3,2,1,8]=>0000001=>1111110=>1
[6,5,4,7,3,2,1,8]=>0000001=>1111110=>1
[5,6,4,7,3,2,1,8]=>0000001=>1111110=>1
[5,4,6,7,3,2,1,8]=>0000001=>1111110=>1
[4,5,6,7,3,2,1,8]=>0000001=>1111110=>1
[7,6,5,3,4,2,1,8]=>0000001=>1111110=>1
[6,7,5,3,4,2,1,8]=>0000001=>1111110=>1
[7,5,6,3,4,2,1,8]=>0000001=>1111110=>1
[5,6,7,3,4,2,1,8]=>0000001=>1111110=>1
[7,6,4,3,5,2,1,8]=>0000001=>1111110=>1
[6,7,4,3,5,2,1,8]=>0000001=>1111110=>1
[7,6,3,4,5,2,1,8]=>0000001=>1111110=>1
[7,5,4,3,6,2,1,8]=>0000001=>1111110=>1
[7,3,4,5,6,2,1,8]=>0000001=>1111110=>1
[6,5,4,3,7,2,1,8]=>0000001=>1111110=>1
[5,6,4,3,7,2,1,8]=>0000001=>1111110=>1
[5,4,6,3,7,2,1,8]=>0000001=>1111110=>1
[5,4,3,6,7,2,1,8]=>0000001=>1111110=>1
[3,4,5,6,7,2,1,8]=>0000001=>1111110=>1
[7,6,5,4,2,3,1,8]=>0000001=>1111110=>1
[6,7,5,4,2,3,1,8]=>0000001=>1111110=>1
[7,5,6,4,2,3,1,8]=>0000001=>1111110=>1
[5,6,7,4,2,3,1,8]=>0000001=>1111110=>1
[7,6,4,5,2,3,1,8]=>0000001=>1111110=>1
[6,7,4,5,2,3,1,8]=>0000001=>1111110=>1
[7,5,4,6,2,3,1,8]=>0000001=>1111110=>1
[6,5,4,7,2,3,1,8]=>0000001=>1111110=>1
[5,6,4,7,2,3,1,8]=>0000001=>1111110=>1
[5,4,6,7,2,3,1,8]=>0000001=>1111110=>1
[4,5,6,7,2,3,1,8]=>0000001=>1111110=>1
[7,6,5,3,2,4,1,8]=>0000001=>1111110=>1
[6,5,7,3,2,4,1,8]=>0000001=>1111110=>1
[5,6,7,3,2,4,1,8]=>0000001=>1111110=>1
[7,6,5,2,3,4,1,8]=>0000001=>1111110=>1
[6,7,5,2,3,4,1,8]=>0000001=>1111110=>1
[7,5,6,2,3,4,1,8]=>0000001=>1111110=>1
[6,5,7,2,3,4,1,8]=>0000001=>1111110=>1
[5,6,7,2,3,4,1,8]=>0000001=>1111110=>1
[7,6,4,3,2,5,1,8]=>0000001=>1111110=>1
[6,7,4,3,2,5,1,8]=>0000001=>1111110=>1
[6,7,3,4,2,5,1,8]=>0000001=>1111110=>1
[7,6,4,2,3,5,1,8]=>0000001=>1111110=>1
[6,7,4,2,3,5,1,8]=>0000001=>1111110=>1
[7,6,3,2,4,5,1,8]=>0000001=>1111110=>1
[6,7,3,2,4,5,1,8]=>0000001=>1111110=>1
[7,6,2,3,4,5,1,8]=>0000001=>1111110=>1
[6,7,2,3,4,5,1,8]=>0000001=>1111110=>1
[7,5,4,3,2,6,1,8]=>0000001=>1111110=>1
[7,4,5,3,2,6,1,8]=>0000001=>1111110=>1
[7,5,3,4,2,6,1,8]=>0000001=>1111110=>1
[7,4,3,5,2,6,1,8]=>0000001=>1111110=>1
[7,4,5,2,3,6,1,8]=>0000001=>1111110=>1
[7,5,3,2,4,6,1,8]=>0000001=>1111110=>1
[7,2,3,4,5,6,1,8]=>0000001=>1111110=>1
[6,5,4,3,2,7,1,8]=>0000001=>1111110=>1
[5,6,4,3,2,7,1,8]=>0000001=>1111110=>1
[5,4,6,3,2,7,1,8]=>0000001=>1111110=>1
[5,6,3,4,2,7,1,8]=>0000001=>1111110=>1
[6,3,4,5,2,7,1,8]=>0000001=>1111110=>1
[5,4,3,6,2,7,1,8]=>0000001=>1111110=>1
[4,5,3,6,2,7,1,8]=>0000001=>1111110=>1
[3,4,5,6,2,7,1,8]=>0000001=>1111110=>1
[6,3,2,4,5,7,1,8]=>0000001=>1111110=>1
[6,2,3,4,5,7,1,8]=>0000001=>1111110=>1
[5,4,3,2,6,7,1,8]=>0000001=>1111110=>1
[5,4,2,3,6,7,1,8]=>0000001=>1111110=>1
[5,2,3,4,6,7,1,8]=>0000001=>1111110=>1
[4,3,2,5,6,7,1,8]=>0000001=>1111110=>1
[3,4,2,5,6,7,1,8]=>0000001=>1111110=>1
[4,2,3,5,6,7,1,8]=>0000001=>1111110=>1
[3,2,4,5,6,7,1,8]=>0000001=>1111110=>1
[2,3,4,5,6,7,1,8]=>0000001=>1111110=>1
[7,6,5,4,3,1,2,8]=>0000001=>1111110=>1
[6,7,5,4,3,1,2,8]=>0000001=>1111110=>1
[7,5,6,4,3,1,2,8]=>0000001=>1111110=>1
[7,6,4,5,3,1,2,8]=>0000001=>1111110=>1
[5,4,6,7,3,1,2,8]=>0000001=>1111110=>1
[4,5,6,7,3,1,2,8]=>0000001=>1111110=>1
[7,6,5,3,4,1,2,8]=>0000001=>1111110=>1
[6,5,7,3,4,1,2,8]=>0000001=>1111110=>1
[6,7,3,4,5,1,2,8]=>0000001=>1111110=>1
[6,5,4,3,7,1,2,8]=>0000001=>1111110=>1
[6,4,5,3,7,1,2,8]=>0000001=>1111110=>1
[5,6,3,4,7,1,2,8]=>0000001=>1111110=>1
[4,3,5,6,7,1,2,8]=>0000001=>1111110=>1
[3,4,5,6,7,1,2,8]=>0000001=>1111110=>1
[7,6,5,4,2,1,3,8]=>0000001=>1111110=>1
[6,5,7,4,2,1,3,8]=>0000001=>1111110=>1
[7,6,4,5,2,1,3,8]=>0000001=>1111110=>1
[4,5,6,7,2,1,3,8]=>0000001=>1111110=>1
[7,6,5,4,1,2,3,8]=>0000001=>1111110=>1
[5,6,7,4,1,2,3,8]=>0000001=>1111110=>1
[7,4,5,6,1,2,3,8]=>0000001=>1111110=>1
[5,6,4,7,1,2,3,8]=>0000001=>1111110=>1
[5,4,6,7,1,2,3,8]=>0000001=>1111110=>1
[7,6,5,3,2,1,4,8]=>0000001=>1111110=>1
[7,6,5,2,3,1,4,8]=>0000001=>1111110=>1
[5,6,7,3,1,2,4,8]=>0000001=>1111110=>1
[7,6,5,2,1,3,4,8]=>0000001=>1111110=>1
[6,7,5,2,1,3,4,8]=>0000001=>1111110=>1
[5,6,7,2,1,3,4,8]=>0000001=>1111110=>1
[7,6,5,1,2,3,4,8]=>0000001=>1111110=>1
[6,7,5,1,2,3,4,8]=>0000001=>1111110=>1
[7,5,6,1,2,3,4,8]=>0000001=>1111110=>1
[6,5,7,1,2,3,4,8]=>0000001=>1111110=>1
[5,6,7,1,2,3,4,8]=>0000001=>1111110=>1
[7,6,4,3,2,1,5,8]=>0000001=>1111110=>1
[6,7,4,3,2,1,5,8]=>0000001=>1111110=>1
[7,6,3,4,2,1,5,8]=>0000001=>1111110=>1
[6,7,3,4,2,1,5,8]=>0000001=>1111110=>1
[7,6,4,2,3,1,5,8]=>0000001=>1111110=>1
[7,6,3,2,4,1,5,8]=>0000001=>1111110=>1
[6,7,3,2,4,1,5,8]=>0000001=>1111110=>1
[7,6,2,3,4,1,5,8]=>0000001=>1111110=>1
[6,7,2,3,4,1,5,8]=>0000001=>1111110=>1
[7,6,4,3,1,2,5,8]=>0000001=>1111110=>1
[6,7,3,4,1,2,5,8]=>0000001=>1111110=>1
[7,6,4,2,1,3,5,8]=>0000001=>1111110=>1
[7,6,3,2,1,4,5,8]=>0000001=>1111110=>1
[6,7,3,2,1,4,5,8]=>0000001=>1111110=>1
[6,7,2,3,1,4,5,8]=>0000001=>1111110=>1
[6,7,3,1,2,4,5,8]=>0000001=>1111110=>1
[7,6,1,2,3,4,5,8]=>0000001=>1111110=>1
[6,7,1,2,3,4,5,8]=>0000001=>1111110=>1
[7,5,4,3,2,1,6,8]=>0000001=>1111110=>1
[7,4,5,3,2,1,6,8]=>0000001=>1111110=>1
[7,4,3,5,2,1,6,8]=>0000001=>1111110=>1
[7,3,4,5,2,1,6,8]=>0000001=>1111110=>1
[7,5,4,2,3,1,6,8]=>0000001=>1111110=>1
[7,5,3,2,4,1,6,8]=>0000001=>1111110=>1
[7,5,2,3,4,1,6,8]=>0000001=>1111110=>1
[7,2,3,4,5,1,6,8]=>0000001=>1111110=>1
[7,5,4,3,1,2,6,8]=>0000001=>1111110=>1
[7,4,5,2,1,3,6,8]=>0000001=>1111110=>1
[7,4,5,1,2,3,6,8]=>0000001=>1111110=>1
[7,5,3,2,1,4,6,8]=>0000001=>1111110=>1
[7,5,2,3,1,4,6,8]=>0000001=>1111110=>1
[7,5,3,1,2,4,6,8]=>0000001=>1111110=>1
[7,5,1,2,3,4,6,8]=>0000001=>1111110=>1
[7,4,3,2,1,5,6,8]=>0000001=>1111110=>1
[7,2,3,4,1,5,6,8]=>0000001=>1111110=>1
[7,4,3,1,2,5,6,8]=>0000001=>1111110=>1
[7,4,1,2,3,5,6,8]=>0000001=>1111110=>1
[7,3,2,1,4,5,6,8]=>0000001=>1111110=>1
[7,2,3,1,4,5,6,8]=>0000001=>1111110=>1
[7,3,1,2,4,5,6,8]=>0000001=>1111110=>1
[7,2,1,3,4,5,6,8]=>0000001=>1111110=>1
[7,1,2,3,4,5,6,8]=>0000001=>1111110=>1
[6,5,4,3,2,1,7,8]=>0000011=>1111100=>1
[5,6,4,3,2,1,7,8]=>0000011=>1111100=>1
[5,4,6,3,2,1,7,8]=>0000011=>1111100=>1
[4,5,6,3,2,1,7,8]=>0000011=>1111100=>1
[6,5,3,4,2,1,7,8]=>0000011=>1111100=>1
[5,6,3,4,2,1,7,8]=>0000011=>1111100=>1
[5,4,3,6,2,1,7,8]=>0000011=>1111100=>1
[3,4,5,6,2,1,7,8]=>0000011=>1111100=>1
[6,5,2,3,4,1,7,8]=>0000011=>1111100=>1
[5,6,2,3,4,1,7,8]=>0000011=>1111100=>1
[6,4,3,2,5,1,7,8]=>0000011=>1111100=>1
[6,2,3,4,5,1,7,8]=>0000011=>1111100=>1
[5,4,3,2,6,1,7,8]=>0000011=>1111100=>1
[4,5,3,2,6,1,7,8]=>0000011=>1111100=>1
[3,4,5,2,6,1,7,8]=>0000011=>1111100=>1
[5,3,2,4,6,1,7,8]=>0000011=>1111100=>1
[5,2,3,4,6,1,7,8]=>0000011=>1111100=>1
[4,3,2,5,6,1,7,8]=>0000011=>1111100=>1
[3,4,2,5,6,1,7,8]=>0000011=>1111100=>1
[4,2,3,5,6,1,7,8]=>0000011=>1111100=>1
[3,2,4,5,6,1,7,8]=>0000011=>1111100=>1
[2,3,4,5,6,1,7,8]=>0000011=>1111100=>1
[6,5,4,3,1,2,7,8]=>0000011=>1111100=>1
[5,6,4,3,1,2,7,8]=>0000011=>1111100=>1
[6,4,5,3,1,2,7,8]=>0000011=>1111100=>1
[5,4,6,3,1,2,7,8]=>0000011=>1111100=>1
[5,6,3,4,1,2,7,8]=>0000011=>1111100=>1
[6,4,3,5,1,2,7,8]=>0000011=>1111100=>1
[5,4,3,6,1,2,7,8]=>0000011=>1111100=>1
[4,3,5,6,1,2,7,8]=>0000011=>1111100=>1
[3,4,5,6,1,2,7,8]=>0000011=>1111100=>1
[6,5,4,2,1,3,7,8]=>0000011=>1111100=>1
[5,6,4,2,1,3,7,8]=>0000011=>1111100=>1
[5,4,6,2,1,3,7,8]=>0000011=>1111100=>1
[4,5,6,2,1,3,7,8]=>0000011=>1111100=>1
[6,5,4,1,2,3,7,8]=>0000011=>1111100=>1
[4,5,6,1,2,3,7,8]=>0000011=>1111100=>1
[6,5,3,2,1,4,7,8]=>0000011=>1111100=>1
[5,6,3,2,1,4,7,8]=>0000011=>1111100=>1
[5,6,2,1,3,4,7,8]=>0000011=>1111100=>1
[6,4,3,2,1,5,7,8]=>0000011=>1111100=>1
[6,3,4,2,1,5,7,8]=>0000011=>1111100=>1
[6,4,3,1,2,5,7,8]=>0000011=>1111100=>1
[6,4,2,1,3,5,7,8]=>0000011=>1111100=>1
[6,4,1,2,3,5,7,8]=>0000011=>1111100=>1
[6,2,3,1,4,5,7,8]=>0000011=>1111100=>1
[6,3,1,2,4,5,7,8]=>0000011=>1111100=>1
[6,1,2,3,4,5,7,8]=>0000011=>1111100=>1
[5,4,3,2,1,6,7,8]=>0000111=>1111000=>1
[4,5,3,2,1,6,7,8]=>0000111=>1111000=>1
[5,3,4,2,1,6,7,8]=>0000111=>1111000=>1
[4,3,5,2,1,6,7,8]=>0000111=>1111000=>1
[3,4,5,2,1,6,7,8]=>0000111=>1111000=>1
[5,4,2,3,1,6,7,8]=>0000111=>1111000=>1
[4,5,2,3,1,6,7,8]=>0000111=>1111000=>1
[5,3,2,4,1,6,7,8]=>0000111=>1111000=>1
[5,2,3,4,1,6,7,8]=>0000111=>1111000=>1
[4,3,2,5,1,6,7,8]=>0000111=>1111000=>1
[3,4,2,5,1,6,7,8]=>0000111=>1111000=>1
[4,2,3,5,1,6,7,8]=>0000111=>1111000=>1
[3,2,4,5,1,6,7,8]=>0000111=>1111000=>1
[2,3,4,5,1,6,7,8]=>0000111=>1111000=>1
[5,4,3,1,2,6,7,8]=>0000111=>1111000=>1
[5,3,4,1,2,6,7,8]=>0000111=>1111000=>1
[4,3,5,1,2,6,7,8]=>0000111=>1111000=>1
[3,4,5,1,2,6,7,8]=>0000111=>1111000=>1
[5,4,2,1,3,6,7,8]=>0000111=>1111000=>1
[4,5,2,1,3,6,7,8]=>0000111=>1111000=>1
[5,4,1,2,3,6,7,8]=>0000111=>1111000=>1
[4,5,1,2,3,6,7,8]=>0000111=>1111000=>1
[5,3,2,1,4,6,7,8]=>0000111=>1111000=>1
[5,2,3,1,4,6,7,8]=>0000111=>1111000=>1
[5,3,1,2,4,6,7,8]=>0000111=>1111000=>1
[5,2,1,3,4,6,7,8]=>0000111=>1111000=>1
[5,1,2,3,4,6,7,8]=>0000111=>1111000=>1
[4,3,2,1,5,6,7,8]=>0001111=>1110000=>1
[3,4,2,1,5,6,7,8]=>0001111=>1110000=>1
[4,2,3,1,5,6,7,8]=>0001111=>1110000=>1
[3,2,4,1,5,6,7,8]=>0001111=>1110000=>1
[2,3,4,1,5,6,7,8]=>0001111=>1110000=>1
[4,3,1,2,5,6,7,8]=>0001111=>1110000=>1
[3,4,1,2,5,6,7,8]=>0001111=>1110000=>1
[4,2,1,3,5,6,7,8]=>0001111=>1110000=>1
[4,1,2,3,5,6,7,8]=>0001111=>1110000=>1
[3,2,1,4,5,6,7,8]=>0011111=>1100000=>1
[2,3,1,4,5,6,7,8]=>0011111=>1100000=>1
[3,1,2,4,5,6,7,8]=>0011111=>1100000=>1
[2,1,3,4,5,6,7,8]=>0111111=>1000000=>1
[1,2,3,4,5,6,7,8]=>1111111=>0000000=>0
[6,8,7,5,4,3,2,1]=>0000000=>1111111=>1
[5,8,7,6,4,3,2,1]=>0000000=>1111111=>1
[5,7,8,6,4,3,2,1]=>0000000=>1111111=>1
[6,5,8,7,4,3,2,1]=>0000000=>1111111=>1
[5,7,6,8,4,3,2,1]=>0000000=>1111111=>1
[4,8,7,6,5,3,2,1]=>0000000=>1111111=>1
[4,7,8,6,5,3,2,1]=>0000000=>1111111=>1
[4,6,8,7,5,3,2,1]=>0000000=>1111111=>1
[4,7,6,8,5,3,2,1]=>0000000=>1111111=>1
[4,6,7,8,5,3,2,1]=>0000000=>1111111=>1
[4,5,8,7,6,3,2,1]=>0000000=>1111111=>1
[4,5,7,8,6,3,2,1]=>0000000=>1111111=>1
[4,6,5,8,7,3,2,1]=>0000000=>1111111=>1
[4,5,6,8,7,3,2,1]=>0000000=>1111111=>1
[5,7,6,4,8,3,2,1]=>0000000=>1111111=>1
[4,7,6,5,8,3,2,1]=>0000000=>1111111=>1
[4,6,7,5,8,3,2,1]=>0000000=>1111111=>1
[5,4,7,6,8,3,2,1]=>0000000=>1111111=>1
[4,5,7,6,8,3,2,1]=>0000000=>1111111=>1
[4,6,5,7,8,3,2,1]=>0000000=>1111111=>1
[3,8,7,6,5,4,2,1]=>0000000=>1111111=>1
[3,7,8,6,5,4,2,1]=>0000000=>1111111=>1
[3,6,8,7,5,4,2,1]=>0000000=>1111111=>1
[3,5,8,7,6,4,2,1]=>0000000=>1111111=>1
[3,5,7,8,6,4,2,1]=>0000000=>1111111=>1
[3,5,6,8,7,4,2,1]=>0000000=>1111111=>1
[3,5,6,7,8,4,2,1]=>0000000=>1111111=>1
[4,3,8,7,6,5,2,1]=>0000000=>1111111=>1
[4,3,6,7,8,5,2,1]=>0000000=>1111111=>1
[3,4,8,7,6,5,2,1]=>0000000=>1111111=>1
[3,4,6,7,8,5,2,1]=>0000000=>1111111=>1
[5,4,3,8,7,6,2,1]=>0000000=>1111111=>1
[5,4,3,7,8,6,2,1]=>0000000=>1111111=>1
[4,5,3,7,8,6,2,1]=>0000000=>1111111=>1
[4,3,5,7,8,6,2,1]=>0000000=>1111111=>1
[3,4,5,8,7,6,2,1]=>0000000=>1111111=>1
[6,5,4,3,8,7,2,1]=>0000000=>1111111=>1
[5,6,4,3,8,7,2,1]=>0000000=>1111111=>1
[4,5,6,3,8,7,2,1]=>0000000=>1111111=>1
[4,3,6,5,8,7,2,1]=>0000000=>1111111=>1
[5,4,3,6,8,7,2,1]=>0000000=>1111111=>1
[4,5,3,6,8,7,2,1]=>0000000=>1111111=>1
[4,3,5,6,8,7,2,1]=>0000000=>1111111=>1
[3,4,5,6,8,7,2,1]=>0000000=>1111111=>1
[5,4,7,6,3,8,2,1]=>0000000=>1111111=>1
[3,7,6,5,4,8,2,1]=>0000000=>1111111=>1
[4,3,7,6,5,8,2,1]=>0000000=>1111111=>1
[3,4,7,6,5,8,2,1]=>0000000=>1111111=>1
[4,5,3,7,6,8,2,1]=>0000000=>1111111=>1
[4,3,5,7,6,8,2,1]=>0000000=>1111111=>1
[3,6,5,4,7,8,2,1]=>0000000=>1111111=>1
[3,4,6,5,7,8,2,1]=>0000000=>1111111=>1
[2,8,7,6,5,4,3,1]=>0000000=>1111111=>1
[2,7,8,6,5,4,3,1]=>0000000=>1111111=>1
[2,6,8,7,5,4,3,1]=>0000000=>1111111=>1
[2,7,6,8,5,4,3,1]=>0000000=>1111111=>1
[2,6,7,8,5,4,3,1]=>0000000=>1111111=>1
[2,5,8,7,6,4,3,1]=>0000000=>1111111=>1
[2,5,6,7,8,4,3,1]=>0000000=>1111111=>1
[2,4,8,7,6,5,3,1]=>0000000=>1111111=>1
[2,4,7,8,6,5,3,1]=>0000000=>1111111=>1
[2,4,6,8,7,5,3,1]=>0000000=>1111111=>1
[2,4,6,7,8,5,3,1]=>0000000=>1111111=>1
[2,5,4,8,7,6,3,1]=>0000000=>1111111=>1
[2,4,5,7,8,6,3,1]=>0000000=>1111111=>1
[2,6,5,4,8,7,3,1]=>0000000=>1111111=>1
[2,5,6,4,8,7,3,1]=>0000000=>1111111=>1
[2,4,6,5,8,7,3,1]=>0000000=>1111111=>1
[2,4,5,6,8,7,3,1]=>0000000=>1111111=>1
[2,4,7,6,5,8,3,1]=>0000000=>1111111=>1
[2,4,6,7,5,8,3,1]=>0000000=>1111111=>1
[2,6,5,4,7,8,3,1]=>0000000=>1111111=>1
[2,4,6,5,7,8,3,1]=>0000000=>1111111=>1
[2,4,5,6,7,8,3,1]=>0000000=>1111111=>1
[3,2,8,7,6,5,4,1]=>0000000=>1111111=>1
[3,2,6,8,7,5,4,1]=>0000000=>1111111=>1
[3,2,5,7,6,8,4,1]=>0000000=>1111111=>1
[3,2,5,6,7,8,4,1]=>0000000=>1111111=>1
[2,3,8,7,6,5,4,1]=>0000000=>1111111=>1
[2,3,6,7,8,5,4,1]=>0000000=>1111111=>1
[2,3,5,8,7,6,4,1]=>0000000=>1111111=>1
[2,3,5,6,8,7,4,1]=>0000000=>1111111=>1
[2,3,5,6,7,8,4,1]=>0000000=>1111111=>1
[4,3,2,8,7,6,5,1]=>0000000=>1111111=>1
[4,3,2,7,8,6,5,1]=>0000000=>1111111=>1
[4,3,2,6,8,7,5,1]=>0000000=>1111111=>1
[3,4,2,8,7,6,5,1]=>0000000=>1111111=>1
[3,4,2,7,8,6,5,1]=>0000000=>1111111=>1
[2,4,3,8,7,6,5,1]=>0000000=>1111111=>1
[2,4,3,6,8,7,5,1]=>0000000=>1111111=>1
[2,4,3,6,7,8,5,1]=>0000000=>1111111=>1
[3,2,4,8,7,6,5,1]=>0000000=>1111111=>1
[2,3,4,8,7,6,5,1]=>0000000=>1111111=>1
[2,3,4,6,8,7,5,1]=>0000000=>1111111=>1
[2,3,4,6,7,8,5,1]=>0000000=>1111111=>1
[5,4,3,2,8,7,6,1]=>0000000=>1111111=>1
[5,4,3,2,7,8,6,1]=>0000000=>1111111=>1
[4,5,3,2,8,7,6,1]=>0000000=>1111111=>1
[4,3,5,2,8,7,6,1]=>0000000=>1111111=>1
[2,5,4,3,8,7,6,1]=>0000000=>1111111=>1
[2,5,4,3,7,8,6,1]=>0000000=>1111111=>1
[2,4,5,3,8,7,6,1]=>0000000=>1111111=>1
[2,4,5,3,7,8,6,1]=>0000000=>1111111=>1
[2,3,5,4,8,7,6,1]=>0000000=>1111111=>1
[4,3,2,5,8,7,6,1]=>0000000=>1111111=>1
[2,3,4,5,8,7,6,1]=>0000000=>1111111=>1
[2,3,4,5,7,8,6,1]=>0000000=>1111111=>1
[6,5,4,3,2,8,7,1]=>0000000=>1111111=>1
[4,6,5,3,2,8,7,1]=>0000000=>1111111=>1
[5,4,6,3,2,8,7,1]=>0000000=>1111111=>1
[4,5,6,3,2,8,7,1]=>0000000=>1111111=>1
[4,3,6,5,2,8,7,1]=>0000000=>1111111=>1
[2,6,5,4,3,8,7,1]=>0000000=>1111111=>1
[2,4,6,5,3,8,7,1]=>0000000=>1111111=>1
[2,4,5,6,3,8,7,1]=>0000000=>1111111=>1
[3,2,6,5,4,8,7,1]=>0000000=>1111111=>1
[4,3,2,6,5,8,7,1]=>0000000=>1111111=>1
[3,4,2,6,5,8,7,1]=>0000000=>1111111=>1
[2,4,3,6,5,8,7,1]=>0000000=>1111111=>1
[2,3,4,6,5,8,7,1]=>0000000=>1111111=>1
[5,4,3,2,6,8,7,1]=>0000000=>1111111=>1
[2,5,4,3,6,8,7,1]=>0000000=>1111111=>1
[2,4,5,3,6,8,7,1]=>0000000=>1111111=>1
[4,3,2,5,6,8,7,1]=>0000000=>1111111=>1
[3,4,2,5,6,8,7,1]=>0000000=>1111111=>1
[2,4,3,5,6,8,7,1]=>0000000=>1111111=>1
[2,3,4,5,6,8,7,1]=>0000000=>1111111=>1
[5,7,6,4,3,2,8,1]=>0000000=>1111111=>1
[4,7,6,5,3,2,8,1]=>0000000=>1111111=>1
[4,6,7,5,3,2,8,1]=>0000000=>1111111=>1
[4,6,5,7,3,2,8,1]=>0000000=>1111111=>1
[3,5,7,6,4,2,8,1]=>0000000=>1111111=>1
[4,3,6,7,5,2,8,1]=>0000000=>1111111=>1
[5,4,3,7,6,2,8,1]=>0000000=>1111111=>1
[3,5,4,7,6,2,8,1]=>0000000=>1111111=>1
[3,4,5,7,6,2,8,1]=>0000000=>1111111=>1
[4,6,5,3,7,2,8,1]=>0000000=>1111111=>1
[3,6,5,4,7,2,8,1]=>0000000=>1111111=>1
[3,5,6,4,7,2,8,1]=>0000000=>1111111=>1
[4,3,6,5,7,2,8,1]=>0000000=>1111111=>1
[3,4,6,5,7,2,8,1]=>0000000=>1111111=>1
[2,7,6,5,4,3,8,1]=>0000000=>1111111=>1
[2,6,5,7,4,3,8,1]=>0000000=>1111111=>1
[2,4,6,7,5,3,8,1]=>0000000=>1111111=>1
[2,5,4,7,6,3,8,1]=>0000000=>1111111=>1
[2,4,6,5,7,3,8,1]=>0000000=>1111111=>1
[2,4,5,6,7,3,8,1]=>0000000=>1111111=>1
[3,2,7,6,5,4,8,1]=>0000000=>1111111=>1
[3,2,6,7,5,4,8,1]=>0000000=>1111111=>1
[2,3,7,6,5,4,8,1]=>0000000=>1111111=>1
[2,3,5,7,6,4,8,1]=>0000000=>1111111=>1
[2,3,5,6,7,4,8,1]=>0000000=>1111111=>1
[4,3,2,7,6,5,8,1]=>0000000=>1111111=>1
[3,4,2,7,6,5,8,1]=>0000000=>1111111=>1
[3,4,2,6,7,5,8,1]=>0000000=>1111111=>1
[2,4,3,7,6,5,8,1]=>0000000=>1111111=>1
[2,4,3,6,7,5,8,1]=>0000000=>1111111=>1
[3,2,4,7,6,5,8,1]=>0000000=>1111111=>1
[2,3,4,7,6,5,8,1]=>0000000=>1111111=>1
[2,3,4,6,7,5,8,1]=>0000000=>1111111=>1
[5,4,3,2,7,6,8,1]=>0000000=>1111111=>1
[4,3,5,2,7,6,8,1]=>0000000=>1111111=>1
[2,5,4,3,7,6,8,1]=>0000000=>1111111=>1
[3,2,5,4,7,6,8,1]=>0000000=>1111111=>1
[2,3,5,4,7,6,8,1]=>0000000=>1111111=>1
[4,3,2,5,7,6,8,1]=>0000000=>1111111=>1
[2,4,3,5,7,6,8,1]=>0000000=>1111111=>1
[3,2,4,5,7,6,8,1]=>0000000=>1111111=>1
[2,3,4,5,7,6,8,1]=>0000000=>1111111=>1
[3,4,6,5,2,7,8,1]=>0000000=>1111111=>1
[2,6,5,4,3,7,8,1]=>0000000=>1111111=>1
[2,5,6,4,3,7,8,1]=>0000000=>1111111=>1
[2,4,6,5,3,7,8,1]=>0000000=>1111111=>1
[2,4,5,6,3,7,8,1]=>0000000=>1111111=>1
[2,3,6,5,4,7,8,1]=>0000000=>1111111=>1
[2,3,5,6,4,7,8,1]=>0000000=>1111111=>1
[4,3,2,6,5,7,8,1]=>0000000=>1111111=>1
[2,4,3,6,5,7,8,1]=>0000000=>1111111=>1
[2,3,4,6,5,7,8,1]=>0000000=>1111111=>1
[3,5,4,2,6,7,8,1]=>0000000=>1111111=>1
[2,5,4,3,6,7,8,1]=>0000000=>1111111=>1
[2,4,5,3,6,7,8,1]=>0000000=>1111111=>1
[3,2,5,4,6,7,8,1]=>0000000=>1111111=>1
[2,3,5,4,6,7,8,1]=>0000000=>1111111=>1
[2,4,3,5,6,7,8,1]=>0000000=>1111111=>1
[1,8,7,6,5,4,3,2]=>1000000=>0111111=>1
[1,7,8,6,5,4,3,2]=>1000000=>0111111=>1
[1,6,8,7,5,4,3,2]=>1000000=>0111111=>1
[1,7,6,8,5,4,3,2]=>1000000=>0111111=>1
[1,6,7,8,5,4,3,2]=>1000000=>0111111=>1
[1,5,8,7,6,4,3,2]=>1000000=>0111111=>1
[1,6,5,8,7,4,3,2]=>1000000=>0111111=>1
[1,7,6,5,8,4,3,2]=>1000000=>0111111=>1
[1,6,7,5,8,4,3,2]=>1000000=>0111111=>1
[1,5,7,6,8,4,3,2]=>1000000=>0111111=>1
[1,6,5,7,8,4,3,2]=>1000000=>0111111=>1
[1,5,6,7,8,4,3,2]=>1000000=>0111111=>1
[1,4,8,7,6,5,3,2]=>1000000=>0111111=>1
[1,4,7,8,6,5,3,2]=>1000000=>0111111=>1
[1,4,6,8,7,5,3,2]=>1000000=>0111111=>1
[1,4,6,7,8,5,3,2]=>1000000=>0111111=>1
[1,5,4,7,8,6,3,2]=>1000000=>0111111=>1
[1,4,5,8,7,6,3,2]=>1000000=>0111111=>1
[1,4,6,5,8,7,3,2]=>1000000=>0111111=>1
[1,4,7,6,5,8,3,2]=>1000000=>0111111=>1
[1,6,5,4,7,8,3,2]=>1000000=>0111111=>1
[1,5,4,6,7,8,3,2]=>1000000=>0111111=>1
[1,4,5,6,7,8,3,2]=>1000000=>0111111=>1
[1,3,8,7,6,5,4,2]=>1000000=>0111111=>1
[1,3,7,8,6,5,4,2]=>1000000=>0111111=>1
[1,3,6,8,7,5,4,2]=>1000000=>0111111=>1
[1,3,6,7,8,5,4,2]=>1000000=>0111111=>1
[1,3,5,8,7,6,4,2]=>1000000=>0111111=>1
[1,3,5,7,8,6,4,2]=>1000000=>0111111=>1
[1,3,5,6,8,7,4,2]=>1000000=>0111111=>1
[1,3,6,5,7,8,4,2]=>1000000=>0111111=>1
[1,3,5,6,7,8,4,2]=>1000000=>0111111=>1
[1,4,3,8,7,6,5,2]=>1000000=>0111111=>1
[1,4,3,7,8,6,5,2]=>1000000=>0111111=>1
[1,4,3,6,8,7,5,2]=>1000000=>0111111=>1
[1,4,3,7,6,8,5,2]=>1000000=>0111111=>1
[1,4,3,6,7,8,5,2]=>1000000=>0111111=>1
[1,3,4,8,7,6,5,2]=>1000000=>0111111=>1
[1,3,4,7,6,8,5,2]=>1000000=>0111111=>1
[1,3,4,6,7,8,5,2]=>1000000=>0111111=>1
[1,3,5,4,8,7,6,2]=>1000000=>0111111=>1
[1,4,3,5,8,7,6,2]=>1000000=>0111111=>1
[1,4,3,5,7,8,6,2]=>1000000=>0111111=>1
[1,3,4,5,7,8,6,2]=>1000000=>0111111=>1
[1,6,5,4,3,8,7,2]=>1000000=>0111111=>1
[1,5,6,4,3,8,7,2]=>1000000=>0111111=>1
[1,4,6,5,3,8,7,2]=>1000000=>0111111=>1
[1,4,5,6,3,8,7,2]=>1000000=>0111111=>1
[1,3,6,5,4,8,7,2]=>1000000=>0111111=>1
[1,4,3,6,5,8,7,2]=>1000000=>0111111=>1
[1,5,4,3,6,8,7,2]=>1000000=>0111111=>1
[1,4,5,3,6,8,7,2]=>1000000=>0111111=>1
[1,3,4,5,6,8,7,2]=>1000000=>0111111=>1
[1,7,6,5,4,3,8,2]=>1000000=>0111111=>1
[1,4,6,7,5,3,8,2]=>1000000=>0111111=>1
[1,5,4,6,7,3,8,2]=>1000000=>0111111=>1
[1,3,5,6,7,4,8,2]=>1000000=>0111111=>1
[1,3,4,7,6,5,8,2]=>1000000=>0111111=>1
[1,3,4,6,7,5,8,2]=>1000000=>0111111=>1
[1,4,3,6,5,7,8,2]=>1000000=>0111111=>1
[1,3,4,6,5,7,8,2]=>1000000=>0111111=>1
[1,5,4,3,6,7,8,2]=>1000000=>0111111=>1
[1,4,5,3,6,7,8,2]=>1000000=>0111111=>1
[1,4,3,5,6,7,8,2]=>1000000=>0111111=>1
[1,3,4,5,6,7,8,2]=>1000000=>0111111=>1
[2,1,8,7,6,5,4,3]=>0100000=>1011111=>2
[2,1,6,7,8,5,4,3]=>0100000=>1011111=>2
[2,1,5,7,8,6,4,3]=>0100000=>1011111=>2
[2,1,6,5,8,7,4,3]=>0100000=>1011111=>2
[2,1,5,7,6,8,4,3]=>0100000=>1011111=>2
[2,1,5,6,7,8,4,3]=>0100000=>1011111=>2
[2,1,4,8,7,6,5,3]=>0100000=>1011111=>2
[2,1,4,7,8,6,5,3]=>0100000=>1011111=>2
[2,1,4,6,8,7,5,3]=>0100000=>1011111=>2
[2,1,4,6,7,8,5,3]=>0100000=>1011111=>2
[2,1,5,4,8,7,6,3]=>0100000=>1011111=>2
[2,1,4,5,8,7,6,3]=>0100000=>1011111=>2
[2,1,4,5,7,8,6,3]=>0100000=>1011111=>2
[2,1,4,6,5,8,7,3]=>0100000=>1011111=>2
[2,1,5,4,6,8,7,3]=>0100000=>1011111=>2
[2,1,4,5,6,8,7,3]=>0100000=>1011111=>2
[2,1,7,6,5,4,8,3]=>0100000=>1011111=>2
[2,1,6,7,5,4,8,3]=>0100000=>1011111=>2
[2,1,5,7,6,4,8,3]=>0100000=>1011111=>2
[2,1,5,6,7,4,8,3]=>0100000=>1011111=>2
[2,1,4,7,6,5,8,3]=>0100000=>1011111=>2
[2,1,5,4,7,6,8,3]=>0100000=>1011111=>2
[2,1,5,4,6,7,8,3]=>0100000=>1011111=>2
[2,1,4,5,6,7,8,3]=>0100000=>1011111=>2
[1,2,8,7,6,5,4,3]=>1100000=>0011111=>1
[1,2,7,8,6,5,4,3]=>1100000=>0011111=>1
[1,2,6,7,8,5,4,3]=>1100000=>0011111=>1
[1,2,5,8,7,6,4,3]=>1100000=>0011111=>1
[1,2,5,6,8,7,4,3]=>1100000=>0011111=>1
[1,2,7,6,5,8,4,3]=>1100000=>0011111=>1
[1,2,5,6,7,8,4,3]=>1100000=>0011111=>1
[1,2,4,8,7,6,5,3]=>1100000=>0011111=>1
[1,2,4,7,8,6,5,3]=>1100000=>0011111=>1
[1,2,4,6,8,7,5,3]=>1100000=>0011111=>1
[1,2,4,6,7,8,5,3]=>1100000=>0011111=>1
[1,2,5,4,8,7,6,3]=>1100000=>0011111=>1
[1,2,5,4,7,8,6,3]=>1100000=>0011111=>1
[1,2,4,5,8,7,6,3]=>1100000=>0011111=>1
[1,2,4,5,7,8,6,3]=>1100000=>0011111=>1
[1,2,6,5,4,8,7,3]=>1100000=>0011111=>1
[1,2,4,6,5,8,7,3]=>1100000=>0011111=>1
[1,2,5,4,6,8,7,3]=>1100000=>0011111=>1
[1,2,4,5,6,8,7,3]=>1100000=>0011111=>1
[1,2,5,6,7,4,8,3]=>1100000=>0011111=>1
[1,2,4,7,6,5,8,3]=>1100000=>0011111=>1
[1,2,5,4,7,6,8,3]=>1100000=>0011111=>1
[1,2,6,5,4,7,8,3]=>1100000=>0011111=>1
[1,2,5,4,6,7,8,3]=>1100000=>0011111=>1
[1,2,4,5,6,7,8,3]=>1100000=>0011111=>1
[3,2,1,8,7,6,5,4]=>0010000=>1101111=>2
[3,2,1,7,8,6,5,4]=>0010000=>1101111=>2
[3,2,1,6,8,7,5,4]=>0010000=>1101111=>2
[3,2,1,7,6,8,5,4]=>0010000=>1101111=>2
[3,2,1,6,7,8,5,4]=>0010000=>1101111=>2
[3,2,1,5,8,7,6,4]=>0010000=>1101111=>2
[3,2,1,5,7,8,6,4]=>0010000=>1101111=>2
[3,2,1,6,5,8,7,4]=>0010000=>1101111=>2
[3,2,1,5,6,8,7,4]=>0010000=>1101111=>2
[3,2,1,7,6,5,8,4]=>0010000=>1101111=>2
[3,2,1,6,7,5,8,4]=>0010000=>1101111=>2
[3,2,1,5,7,6,8,4]=>0010000=>1101111=>2
[3,2,1,6,5,7,8,4]=>0010000=>1101111=>2
[3,2,1,5,6,7,8,4]=>0010000=>1101111=>2
[2,3,1,8,7,6,5,4]=>0010000=>1101111=>2
[2,3,1,6,8,7,5,4]=>0010000=>1101111=>2
[2,3,1,7,6,8,5,4]=>0010000=>1101111=>2
[2,3,1,6,7,8,5,4]=>0010000=>1101111=>2
[2,3,1,6,5,8,7,4]=>0010000=>1101111=>2
[2,3,1,5,6,7,8,4]=>0010000=>1101111=>2
[1,3,2,8,7,6,5,4]=>1010000=>0101111=>2
[1,3,2,6,8,7,5,4]=>1010000=>0101111=>2
[1,3,2,6,7,8,5,4]=>1010000=>0101111=>2
[1,3,2,5,8,7,6,4]=>1010000=>0101111=>2
[1,3,2,5,7,8,6,4]=>1010000=>0101111=>2
[1,3,2,6,5,8,7,4]=>1010000=>0101111=>2
[1,3,2,5,6,8,7,4]=>1010000=>0101111=>2
[1,3,2,7,6,5,8,4]=>1010000=>0101111=>2
[2,1,3,8,7,6,5,4]=>0110000=>1001111=>2
[2,1,3,7,8,6,5,4]=>0110000=>1001111=>2
[2,1,3,6,8,7,5,4]=>0110000=>1001111=>2
[2,1,3,6,5,8,7,4]=>0110000=>1001111=>2
[2,1,3,5,6,7,8,4]=>0110000=>1001111=>2
[1,2,3,8,7,6,5,4]=>1110000=>0001111=>1
[1,2,3,7,8,6,5,4]=>1110000=>0001111=>1
[1,2,3,6,8,7,5,4]=>1110000=>0001111=>1
[1,2,3,7,6,8,5,4]=>1110000=>0001111=>1
[1,2,3,6,7,8,5,4]=>1110000=>0001111=>1
[1,2,3,5,8,7,6,4]=>1110000=>0001111=>1
[1,2,3,5,7,8,6,4]=>1110000=>0001111=>1
[1,2,3,6,5,8,7,4]=>1110000=>0001111=>1
[1,2,3,5,6,8,7,4]=>1110000=>0001111=>1
[1,2,3,7,6,5,8,4]=>1110000=>0001111=>1
[1,2,3,6,7,5,8,4]=>1110000=>0001111=>1
[1,2,3,5,7,6,8,4]=>1110000=>0001111=>1
[1,2,3,6,5,7,8,4]=>1110000=>0001111=>1
[1,2,3,5,6,7,8,4]=>1110000=>0001111=>1
[4,3,2,1,8,7,6,5]=>0001000=>1110111=>2
[4,3,2,1,7,8,6,5]=>0001000=>1110111=>2
[4,3,2,1,6,8,7,5]=>0001000=>1110111=>2
[4,3,2,1,7,6,8,5]=>0001000=>1110111=>2
[4,3,2,1,6,7,8,5]=>0001000=>1110111=>2
[3,4,2,1,8,7,6,5]=>0001000=>1110111=>2
[3,4,2,1,7,8,6,5]=>0001000=>1110111=>2
[3,4,2,1,6,7,8,5]=>0001000=>1110111=>2
[2,4,3,1,8,7,6,5]=>0001000=>1110111=>2
[2,4,3,1,7,6,8,5]=>0001000=>1110111=>2
[3,2,4,1,8,7,6,5]=>0001000=>1110111=>2
[3,2,4,1,7,8,6,5]=>0001000=>1110111=>2
[3,2,4,1,6,8,7,5]=>0001000=>1110111=>2
[3,2,4,1,7,6,8,5]=>0001000=>1110111=>2
[2,3,4,1,8,7,6,5]=>0001000=>1110111=>2
[2,3,4,1,6,7,8,5]=>0001000=>1110111=>2
[1,4,3,2,8,7,6,5]=>1001000=>0110111=>2
[1,4,3,2,6,8,7,5]=>1001000=>0110111=>2
[1,4,3,2,7,6,8,5]=>1001000=>0110111=>2
[1,4,3,2,6,7,8,5]=>1001000=>0110111=>2
[1,3,4,2,8,7,6,5]=>1001000=>0110111=>2
[1,3,4,2,7,8,6,5]=>1001000=>0110111=>2
[1,3,4,2,6,8,7,5]=>1001000=>0110111=>2
[2,1,4,3,8,7,6,5]=>0101000=>1010111=>3
[2,1,4,3,7,8,6,5]=>0101000=>1010111=>3
[2,1,4,3,6,8,7,5]=>0101000=>1010111=>3
[1,2,4,3,8,7,6,5]=>1101000=>0010111=>2
[1,2,4,3,7,8,6,5]=>1101000=>0010111=>2
[1,2,4,3,6,8,7,5]=>1101000=>0010111=>2
[1,2,4,3,6,7,8,5]=>1101000=>0010111=>2
[3,2,1,4,8,7,6,5]=>0011000=>1100111=>2
[3,2,1,4,7,8,6,5]=>0011000=>1100111=>2
[3,2,1,4,6,8,7,5]=>0011000=>1100111=>2
[2,3,1,4,8,7,6,5]=>0011000=>1100111=>2
[2,3,1,4,7,8,6,5]=>0011000=>1100111=>2
[2,3,1,4,6,7,8,5]=>0011000=>1100111=>2
[1,3,2,4,8,7,6,5]=>1011000=>0100111=>2
[1,3,2,4,6,8,7,5]=>1011000=>0100111=>2
[1,3,2,4,6,7,8,5]=>1011000=>0100111=>2
[2,1,3,4,8,7,6,5]=>0111000=>1000111=>2
[2,1,3,4,7,8,6,5]=>0111000=>1000111=>2
[2,1,3,4,6,7,8,5]=>0111000=>1000111=>2
[1,2,3,4,8,7,6,5]=>1111000=>0000111=>1
[1,2,3,4,7,8,6,5]=>1111000=>0000111=>1
[1,2,3,4,6,8,7,5]=>1111000=>0000111=>1
[1,2,3,4,7,6,8,5]=>1111000=>0000111=>1
[1,2,3,4,6,7,8,5]=>1111000=>0000111=>1
[5,4,3,2,1,8,7,6]=>0000100=>1111011=>2
[5,4,3,2,1,7,8,6]=>0000100=>1111011=>2
[4,5,3,2,1,8,7,6]=>0000100=>1111011=>2
[3,5,4,2,1,8,7,6]=>0000100=>1111011=>2
[3,5,4,2,1,7,8,6]=>0000100=>1111011=>2
[4,3,5,2,1,8,7,6]=>0000100=>1111011=>2
[3,4,5,2,1,8,7,6]=>0000100=>1111011=>2
[2,5,4,3,1,8,7,6]=>0000100=>1111011=>2
[2,4,5,3,1,8,7,6]=>0000100=>1111011=>2
[2,4,5,3,1,7,8,6]=>0000100=>1111011=>2
[3,2,5,4,1,8,7,6]=>0000100=>1111011=>2
[3,2,5,4,1,7,8,6]=>0000100=>1111011=>2
[2,3,5,4,1,8,7,6]=>0000100=>1111011=>2
[4,3,2,5,1,8,7,6]=>0000100=>1111011=>2
[3,4,2,5,1,8,7,6]=>0000100=>1111011=>2
[2,4,3,5,1,8,7,6]=>0000100=>1111011=>2
[3,2,4,5,1,8,7,6]=>0000100=>1111011=>2
[2,3,4,5,1,8,7,6]=>0000100=>1111011=>2
[2,3,4,5,1,7,8,6]=>0000100=>1111011=>2
[1,5,4,3,2,8,7,6]=>1000100=>0111011=>2
[1,5,4,3,2,7,8,6]=>1000100=>0111011=>2
[1,3,5,4,2,7,8,6]=>1000100=>0111011=>2
[1,3,4,5,2,8,7,6]=>1000100=>0111011=>2
[1,3,4,5,2,7,8,6]=>1000100=>0111011=>2
[2,1,5,4,3,8,7,6]=>0100100=>1011011=>3
[2,1,4,5,3,8,7,6]=>0100100=>1011011=>3
[1,2,5,4,3,8,7,6]=>1100100=>0011011=>2
[1,2,5,4,3,7,8,6]=>1100100=>0011011=>2
[1,2,4,5,3,8,7,6]=>1100100=>0011011=>2
[1,2,4,5,3,7,8,6]=>1100100=>0011011=>2
[1,3,2,5,4,8,7,6]=>1010100=>0101011=>3
[1,3,2,5,4,7,8,6]=>1010100=>0101011=>3
[2,1,3,5,4,8,7,6]=>0110100=>1001011=>3
[2,1,3,5,4,7,8,6]=>0110100=>1001011=>3
[1,2,3,5,4,8,7,6]=>1110100=>0001011=>2
[1,2,3,5,4,7,8,6]=>1110100=>0001011=>2
[4,3,2,1,5,8,7,6]=>0001100=>1110011=>2
[4,3,2,1,5,7,8,6]=>0001100=>1110011=>2
[2,4,3,1,5,8,7,6]=>0001100=>1110011=>2
[3,2,4,1,5,8,7,6]=>0001100=>1110011=>2
[1,4,3,2,5,8,7,6]=>1001100=>0110011=>2
[1,4,3,2,5,7,8,6]=>1001100=>0110011=>2
[1,3,4,2,5,7,8,6]=>1001100=>0110011=>2
[2,1,4,3,5,8,7,6]=>0101100=>1010011=>3
[2,1,4,3,5,7,8,6]=>0101100=>1010011=>3
[1,2,4,3,5,8,7,6]=>1101100=>0010011=>2
[1,2,4,3,5,7,8,6]=>1101100=>0010011=>2
[3,2,1,4,5,8,7,6]=>0011100=>1100011=>2
[3,2,1,4,5,7,8,6]=>0011100=>1100011=>2
[2,3,1,4,5,7,8,6]=>0011100=>1100011=>2
[1,3,2,4,5,8,7,6]=>1011100=>0100011=>2
[1,3,2,4,5,7,8,6]=>1011100=>0100011=>2
[2,1,3,4,5,8,7,6]=>0111100=>1000011=>2
[2,1,3,4,5,7,8,6]=>0111100=>1000011=>2
[1,2,3,4,5,8,7,6]=>1111100=>0000011=>1
[1,2,3,4,5,7,8,6]=>1111100=>0000011=>1
[6,5,4,3,2,1,8,7]=>0000010=>1111101=>2
[5,6,4,3,2,1,8,7]=>0000010=>1111101=>2
[4,6,5,3,2,1,8,7]=>0000010=>1111101=>2
[5,4,6,3,2,1,8,7]=>0000010=>1111101=>2
[4,5,6,3,2,1,8,7]=>0000010=>1111101=>2
[3,6,5,4,2,1,8,7]=>0000010=>1111101=>2
[4,3,6,5,2,1,8,7]=>0000010=>1111101=>2
[3,4,5,6,2,1,8,7]=>0000010=>1111101=>2
[2,6,5,4,3,1,8,7]=>0000010=>1111101=>2
[4,3,2,6,5,1,8,7]=>0000010=>1111101=>2
[5,4,3,2,6,1,8,7]=>0000010=>1111101=>2
[4,5,3,2,6,1,8,7]=>0000010=>1111101=>2
[3,5,4,2,6,1,8,7]=>0000010=>1111101=>2
[3,2,5,4,6,1,8,7]=>0000010=>1111101=>2
[4,3,2,5,6,1,8,7]=>0000010=>1111101=>2
[2,4,3,5,6,1,8,7]=>0000010=>1111101=>2
[2,3,4,5,6,1,8,7]=>0000010=>1111101=>2
[1,6,5,4,3,2,8,7]=>1000010=>0111101=>2
[1,5,6,4,3,2,8,7]=>1000010=>0111101=>2
[1,5,4,6,3,2,8,7]=>1000010=>0111101=>2
[1,3,6,5,4,2,8,7]=>1000010=>0111101=>2
[1,3,4,5,6,2,8,7]=>1000010=>0111101=>2
[2,1,6,5,4,3,8,7]=>0100010=>1011101=>3
[2,1,5,6,4,3,8,7]=>0100010=>1011101=>3
[2,1,5,4,6,3,8,7]=>0100010=>1011101=>3
[2,1,4,5,6,3,8,7]=>0100010=>1011101=>3
[1,2,4,5,6,3,8,7]=>1100010=>0011101=>2
[3,2,1,6,5,4,8,7]=>0010010=>1101101=>3
[2,3,1,6,5,4,8,7]=>0010010=>1101101=>3
[1,3,2,6,5,4,8,7]=>1010010=>0101101=>3
[1,3,2,5,6,4,8,7]=>1010010=>0101101=>3
[2,1,3,6,5,4,8,7]=>0110010=>1001101=>3
[2,1,3,5,6,4,8,7]=>0110010=>1001101=>3
[1,2,3,6,5,4,8,7]=>1110010=>0001101=>2
[1,2,3,5,6,4,8,7]=>1110010=>0001101=>2
[4,3,2,1,6,5,8,7]=>0001010=>1110101=>3
[3,4,2,1,6,5,8,7]=>0001010=>1110101=>3
[3,2,4,1,6,5,8,7]=>0001010=>1110101=>3
[2,3,4,1,6,5,8,7]=>0001010=>1110101=>3
[1,3,4,2,6,5,8,7]=>1001010=>0110101=>3
[2,1,4,3,6,5,8,7]=>0101010=>1010101=>4
[1,2,4,3,6,5,8,7]=>1101010=>0010101=>3
[2,3,1,4,6,5,8,7]=>0011010=>1100101=>3
[1,3,2,4,6,5,8,7]=>1011010=>0100101=>3
[2,1,3,4,6,5,8,7]=>0111010=>1000101=>3
[1,2,3,4,6,5,8,7]=>1111010=>0000101=>2
[5,4,3,2,1,6,8,7]=>0000110=>1111001=>2
[4,5,3,2,1,6,8,7]=>0000110=>1111001=>2
[3,5,4,2,1,6,8,7]=>0000110=>1111001=>2
[4,3,5,2,1,6,8,7]=>0000110=>1111001=>2
[3,4,5,2,1,6,8,7]=>0000110=>1111001=>2
[2,5,4,3,1,6,8,7]=>0000110=>1111001=>2
[2,4,5,3,1,6,8,7]=>0000110=>1111001=>2
[3,2,5,4,1,6,8,7]=>0000110=>1111001=>2
[2,3,5,4,1,6,8,7]=>0000110=>1111001=>2
[2,4,3,5,1,6,8,7]=>0000110=>1111001=>2
[2,3,4,5,1,6,8,7]=>0000110=>1111001=>2
[1,4,5,3,2,6,8,7]=>1000110=>0111001=>2
[1,3,5,4,2,6,8,7]=>1000110=>0111001=>2
[2,1,5,4,3,6,8,7]=>0100110=>1011001=>3
[1,2,5,4,3,6,8,7]=>1100110=>0011001=>2
[2,1,3,5,4,6,8,7]=>0110110=>1001001=>3
[1,2,3,5,4,6,8,7]=>1110110=>0001001=>2
[4,3,2,1,5,6,8,7]=>0001110=>1110001=>2
[2,3,4,1,5,6,8,7]=>0001110=>1110001=>2
[1,4,3,2,5,6,8,7]=>1001110=>0110001=>2
[1,3,4,2,5,6,8,7]=>1001110=>0110001=>2
[2,1,4,3,5,6,8,7]=>0101110=>1010001=>3
[1,2,4,3,5,6,8,7]=>1101110=>0010001=>2
[3,2,1,4,5,6,8,7]=>0011110=>1100001=>2
[2,3,1,4,5,6,8,7]=>0011110=>1100001=>2
[1,3,2,4,5,6,8,7]=>1011110=>0100001=>2
[2,1,3,4,5,6,8,7]=>0111110=>1000001=>2
[1,2,3,4,5,6,8,7]=>1111110=>0000001=>1
[5,7,6,4,3,2,1,8]=>0000001=>1111110=>1
[4,7,6,5,3,2,1,8]=>0000001=>1111110=>1
[4,6,7,5,3,2,1,8]=>0000001=>1111110=>1
[5,4,7,6,3,2,1,8]=>0000001=>1111110=>1
[4,5,7,6,3,2,1,8]=>0000001=>1111110=>1
[4,6,5,7,3,2,1,8]=>0000001=>1111110=>1
[3,5,7,6,4,2,1,8]=>0000001=>1111110=>1
[3,5,6,7,4,2,1,8]=>0000001=>1111110=>1
[4,3,7,6,5,2,1,8]=>0000001=>1111110=>1
[3,4,7,6,5,2,1,8]=>0000001=>1111110=>1
[4,5,3,7,6,2,1,8]=>0000001=>1111110=>1
[3,5,4,7,6,2,1,8]=>0000001=>1111110=>1
[4,3,5,7,6,2,1,8]=>0000001=>1111110=>1
[3,6,5,4,7,2,1,8]=>0000001=>1111110=>1
[4,3,6,5,7,2,1,8]=>0000001=>1111110=>1
[2,7,6,5,4,3,1,8]=>0000001=>1111110=>1
[2,6,7,5,4,3,1,8]=>0000001=>1111110=>1
[2,5,7,6,4,3,1,8]=>0000001=>1111110=>1
[2,5,6,7,4,3,1,8]=>0000001=>1111110=>1
[2,4,6,7,5,3,1,8]=>0000001=>1111110=>1
[2,5,6,4,7,3,1,8]=>0000001=>1111110=>1
[3,2,7,6,5,4,1,8]=>0000001=>1111110=>1
[3,2,6,7,5,4,1,8]=>0000001=>1111110=>1
[3,2,5,7,6,4,1,8]=>0000001=>1111110=>1
[3,2,6,5,7,4,1,8]=>0000001=>1111110=>1
[3,2,5,6,7,4,1,8]=>0000001=>1111110=>1
[2,3,7,6,5,4,1,8]=>0000001=>1111110=>1
[2,3,6,7,5,4,1,8]=>0000001=>1111110=>1
[2,3,5,7,6,4,1,8]=>0000001=>1111110=>1
[2,3,6,5,7,4,1,8]=>0000001=>1111110=>1
[2,3,5,6,7,4,1,8]=>0000001=>1111110=>1
[3,2,4,6,7,5,1,8]=>0000001=>1111110=>1
[2,3,4,7,6,5,1,8]=>0000001=>1111110=>1
[5,4,3,2,7,6,1,8]=>0000001=>1111110=>1
[4,5,3,2,7,6,1,8]=>0000001=>1111110=>1
[3,5,4,2,7,6,1,8]=>0000001=>1111110=>1
[4,3,5,2,7,6,1,8]=>0000001=>1111110=>1
[3,4,5,2,7,6,1,8]=>0000001=>1111110=>1
[3,2,5,4,7,6,1,8]=>0000001=>1111110=>1
[2,3,4,5,7,6,1,8]=>0000001=>1111110=>1
[3,4,6,5,2,7,1,8]=>0000001=>1111110=>1
[3,5,4,6,2,7,1,8]=>0000001=>1111110=>1
[2,5,4,6,3,7,1,8]=>0000001=>1111110=>1
[3,2,6,5,4,7,1,8]=>0000001=>1111110=>1
[4,3,2,6,5,7,1,8]=>0000001=>1111110=>1
[3,4,2,6,5,7,1,8]=>0000001=>1111110=>1
[2,4,3,6,5,7,1,8]=>0000001=>1111110=>1
[2,3,4,6,5,7,1,8]=>0000001=>1111110=>1
[3,5,4,2,6,7,1,8]=>0000001=>1111110=>1
[2,5,4,3,6,7,1,8]=>0000001=>1111110=>1
[1,7,6,5,4,3,2,8]=>1000001=>0111110=>1
[1,6,7,5,4,3,2,8]=>1000001=>0111110=>1
[1,6,5,7,4,3,2,8]=>1000001=>0111110=>1
[1,5,6,7,4,3,2,8]=>1000001=>0111110=>1
[1,5,6,4,7,3,2,8]=>1000001=>0111110=>1
[1,4,6,5,7,3,2,8]=>1000001=>0111110=>1
[1,3,6,7,5,4,2,8]=>1000001=>0111110=>1
[1,3,5,7,6,4,2,8]=>1000001=>0111110=>1
[1,3,5,6,7,4,2,8]=>1000001=>0111110=>1
[1,3,4,6,7,5,2,8]=>1000001=>0111110=>1
[1,3,5,4,7,6,2,8]=>1000001=>0111110=>1
[1,4,3,5,7,6,2,8]=>1000001=>0111110=>1
[1,5,4,6,3,7,2,8]=>1000001=>0111110=>1
[1,3,6,5,4,7,2,8]=>1000001=>0111110=>1
[1,3,5,6,4,7,2,8]=>1000001=>0111110=>1
[1,4,3,6,5,7,2,8]=>1000001=>0111110=>1
[1,4,5,3,6,7,2,8]=>1000001=>0111110=>1
[1,3,4,5,6,7,2,8]=>1000001=>0111110=>1
[2,1,7,6,5,4,3,8]=>0100001=>1011110=>2
[2,1,6,7,5,4,3,8]=>0100001=>1011110=>2
[2,1,5,6,7,4,3,8]=>0100001=>1011110=>2
[2,1,5,4,6,7,3,8]=>0100001=>1011110=>2
[2,1,4,5,6,7,3,8]=>0100001=>1011110=>2
[1,2,7,6,5,4,3,8]=>1100001=>0011110=>1
[1,2,6,7,5,4,3,8]=>1100001=>0011110=>1
[1,2,5,7,6,4,3,8]=>1100001=>0011110=>1
[1,2,5,6,7,4,3,8]=>1100001=>0011110=>1
[1,2,4,6,7,5,3,8]=>1100001=>0011110=>1
[1,2,5,6,4,7,3,8]=>1100001=>0011110=>1
[1,2,5,4,6,7,3,8]=>1100001=>0011110=>1
[1,2,4,5,6,7,3,8]=>1100001=>0011110=>1
[3,2,1,7,6,5,4,8]=>0010001=>1101110=>2
[3,2,1,5,7,6,4,8]=>0010001=>1101110=>2
[3,2,1,6,5,7,4,8]=>0010001=>1101110=>2
[2,3,1,6,5,7,4,8]=>0010001=>1101110=>2
[2,3,1,5,6,7,4,8]=>0010001=>1101110=>2
[1,3,2,5,7,6,4,8]=>1010001=>0101110=>2
[1,3,2,6,5,7,4,8]=>1010001=>0101110=>2
[2,1,3,6,7,5,4,8]=>0110001=>1001110=>2
[1,2,3,7,6,5,4,8]=>1110001=>0001110=>1
[1,2,3,6,7,5,4,8]=>1110001=>0001110=>1
[1,2,3,5,7,6,4,8]=>1110001=>0001110=>1
[1,2,3,6,5,7,4,8]=>1110001=>0001110=>1
[1,2,3,5,6,7,4,8]=>1110001=>0001110=>1
[4,3,2,1,7,6,5,8]=>0001001=>1110110=>2
[4,3,2,1,6,7,5,8]=>0001001=>1110110=>2
[2,3,4,1,7,6,5,8]=>0001001=>1110110=>2
[2,3,4,1,6,7,5,8]=>0001001=>1110110=>2
[1,4,3,2,7,6,5,8]=>1001001=>0110110=>2
[1,4,3,2,6,7,5,8]=>1001001=>0110110=>2
[1,3,4,2,6,7,5,8]=>1001001=>0110110=>2
[2,1,4,3,6,7,5,8]=>0101001=>1010110=>3
[1,2,4,3,6,7,5,8]=>1101001=>0010110=>2
[3,2,1,4,7,6,5,8]=>0011001=>1100110=>2
[1,3,2,4,7,6,5,8]=>1011001=>0100110=>2
[1,2,3,4,7,6,5,8]=>1111001=>0000110=>1
[1,2,3,4,6,7,5,8]=>1111001=>0000110=>1
[5,4,3,2,1,7,6,8]=>0000101=>1111010=>2
[3,5,4,2,1,7,6,8]=>0000101=>1111010=>2
[3,4,5,2,1,7,6,8]=>0000101=>1111010=>2
[2,4,5,3,1,7,6,8]=>0000101=>1111010=>2
[3,2,5,4,1,7,6,8]=>0000101=>1111010=>2
[2,3,5,4,1,7,6,8]=>0000101=>1111010=>2
[3,4,2,5,1,7,6,8]=>0000101=>1111010=>2
[2,4,3,5,1,7,6,8]=>0000101=>1111010=>2
[2,3,4,5,1,7,6,8]=>0000101=>1111010=>2
[1,3,5,4,2,7,6,8]=>1000101=>0111010=>2
[1,4,3,5,2,7,6,8]=>1000101=>0111010=>2
[1,3,4,5,2,7,6,8]=>1000101=>0111010=>2
[2,1,5,4,3,7,6,8]=>0100101=>1011010=>3
[1,2,4,5,3,7,6,8]=>1100101=>0011010=>2
[3,2,1,5,4,7,6,8]=>0010101=>1101010=>3
[2,3,1,5,4,7,6,8]=>0010101=>1101010=>3
[1,3,2,5,4,7,6,8]=>1010101=>0101010=>3
[1,2,3,5,4,7,6,8]=>1110101=>0001010=>2
[4,3,2,1,5,7,6,8]=>0001101=>1110010=>2
[1,4,3,2,5,7,6,8]=>1001101=>0110010=>2
[1,2,4,3,5,7,6,8]=>1101101=>0010010=>2
[3,2,1,4,5,7,6,8]=>0011101=>1100010=>2
[2,3,1,4,5,7,6,8]=>0011101=>1100010=>2
[1,3,2,4,5,7,6,8]=>1011101=>0100010=>2
[2,1,3,4,5,7,6,8]=>0111101=>1000010=>2
[1,2,3,4,5,7,6,8]=>1111101=>0000010=>1
[3,6,5,4,2,1,7,8]=>0000011=>1111100=>1
[4,3,6,5,2,1,7,8]=>0000011=>1111100=>1
[2,4,6,5,3,1,7,8]=>0000011=>1111100=>1
[2,4,5,6,3,1,7,8]=>0000011=>1111100=>1
[4,3,2,6,5,1,7,8]=>0000011=>1111100=>1
[2,4,3,6,5,1,7,8]=>0000011=>1111100=>1
[2,3,4,6,5,1,7,8]=>0000011=>1111100=>1
[3,5,4,2,6,1,7,8]=>0000011=>1111100=>1
[2,3,5,4,6,1,7,8]=>0000011=>1111100=>1
[1,6,5,4,3,2,7,8]=>1000011=>0111100=>1
[1,5,6,4,3,2,7,8]=>1000011=>0111100=>1
[1,4,6,5,3,2,7,8]=>1000011=>0111100=>1
[1,5,4,6,3,2,7,8]=>1000011=>0111100=>1
[1,4,5,6,3,2,7,8]=>1000011=>0111100=>1
[1,3,5,6,4,2,7,8]=>1000011=>0111100=>1
[1,4,3,6,5,2,7,8]=>1000011=>0111100=>1
[1,5,4,3,6,2,7,8]=>1000011=>0111100=>1
[1,4,5,3,6,2,7,8]=>1000011=>0111100=>1
[1,4,3,5,6,2,7,8]=>1000011=>0111100=>1
[1,3,4,5,6,2,7,8]=>1000011=>0111100=>1
[2,1,5,6,4,3,7,8]=>0100011=>1011100=>2
[2,1,4,6,5,3,7,8]=>0100011=>1011100=>2
[1,2,6,5,4,3,7,8]=>1100011=>0011100=>1
[1,2,5,6,4,3,7,8]=>1100011=>0011100=>1
[1,2,4,5,6,3,7,8]=>1100011=>0011100=>1
[3,2,1,6,5,4,7,8]=>0010011=>1101100=>2
[3,2,1,5,6,4,7,8]=>0010011=>1101100=>2
[2,3,1,6,5,4,7,8]=>0010011=>1101100=>2
[2,3,1,5,6,4,7,8]=>0010011=>1101100=>2
[1,3,2,6,5,4,7,8]=>1010011=>0101100=>2
[1,2,3,6,5,4,7,8]=>1110011=>0001100=>1
[1,2,3,5,6,4,7,8]=>1110011=>0001100=>1
[4,3,2,1,6,5,7,8]=>0001011=>1110100=>2
[2,4,3,1,6,5,7,8]=>0001011=>1110100=>2
[3,2,4,1,6,5,7,8]=>0001011=>1110100=>2
[2,3,4,1,6,5,7,8]=>0001011=>1110100=>2
[2,1,4,3,6,5,7,8]=>0101011=>1010100=>3
[1,2,4,3,6,5,7,8]=>1101011=>0010100=>2
[1,3,2,4,6,5,7,8]=>1011011=>0100100=>2
[2,1,3,4,6,5,7,8]=>0111011=>1000100=>2
[1,2,3,4,6,5,7,8]=>1111011=>0000100=>1
[3,5,4,2,1,6,7,8]=>0000111=>1111000=>1
[2,5,4,3,1,6,7,8]=>0000111=>1111000=>1
[2,4,5,3,1,6,7,8]=>0000111=>1111000=>1
[3,2,5,4,1,6,7,8]=>0000111=>1111000=>1
[2,3,5,4,1,6,7,8]=>0000111=>1111000=>1
[2,4,3,5,1,6,7,8]=>0000111=>1111000=>1
[1,3,4,5,2,6,7,8]=>1000111=>0111000=>1
[2,1,5,4,3,6,7,8]=>0100111=>1011000=>2
[2,1,4,5,3,6,7,8]=>0100111=>1011000=>2
[1,2,5,4,3,6,7,8]=>1100111=>0011000=>1
[3,2,1,5,4,6,7,8]=>0010111=>1101000=>2
[2,3,1,5,4,6,7,8]=>0010111=>1101000=>2
[1,3,2,5,4,6,7,8]=>1010111=>0101000=>2
[2,1,3,5,4,6,7,8]=>0110111=>1001000=>2
[1,2,3,5,4,6,7,8]=>1110111=>0001000=>1
[2,4,3,1,5,6,7,8]=>0001111=>1110000=>1
[1,4,3,2,5,6,7,8]=>1001111=>0110000=>1
[1,3,4,2,5,6,7,8]=>1001111=>0110000=>1
[2,1,4,3,5,6,7,8]=>0101111=>1010000=>2
[1,2,4,3,5,6,7,8]=>1101111=>0010000=>1
[1,3,2,4,5,6,7,8]=>1011111=>0100000=>1
[1,2,3,4,8,6,7,5]=>1111000=>0000111=>1
[1,2,3,5,8,6,7,4]=>1110000=>0001111=>1
[1,2,3,7,5,6,4,8]=>1110001=>0001110=>1
[1,2,3,7,5,6,8,4]=>1110000=>0001111=>1
[1,2,3,8,5,6,7,4]=>1110000=>0001111=>1
[1,2,3,8,5,7,6,4]=>1110000=>0001111=>1
[1,2,3,8,6,5,7,4]=>1110000=>0001111=>1
[1,2,3,8,6,7,5,4]=>1110000=>0001111=>1
[1,2,4,3,8,6,7,5]=>1101000=>0010111=>2
[1,2,4,5,8,6,7,3]=>1100000=>0011111=>1
[1,2,4,7,5,6,8,3]=>1100000=>0011111=>1
[1,2,4,8,6,5,7,3]=>1100000=>0011111=>1
[1,2,5,4,8,6,7,3]=>1100000=>0011111=>1
[1,2,6,4,5,3,7,8]=>1100011=>0011100=>1
[1,2,6,4,5,7,8,3]=>1100000=>0011111=>1
[1,2,7,4,5,6,8,3]=>1100000=>0011111=>1
[1,2,8,4,5,6,7,3]=>1100000=>0011111=>1
[1,2,8,4,7,6,5,3]=>1100000=>0011111=>1
[1,2,7,5,4,6,3,8]=>1100001=>0011110=>1
[1,2,7,5,4,6,8,3]=>1100000=>0011111=>1
[1,2,8,5,4,6,7,3]=>1100000=>0011111=>1
[1,2,8,5,4,7,6,3]=>1100000=>0011111=>1
[1,2,8,6,5,4,7,3]=>1100000=>0011111=>1
[1,2,8,6,5,7,4,3]=>1100000=>0011111=>1
[1,2,8,7,5,6,4,3]=>1100000=>0011111=>1
[1,3,2,4,8,6,7,5]=>1011000=>0100111=>2
[1,3,2,7,5,6,8,4]=>1010000=>0101111=>2
[1,3,2,8,5,7,6,4]=>1010000=>0101111=>2
[1,3,2,8,6,5,7,4]=>1010000=>0101111=>2
[1,3,2,8,6,7,5,4]=>1010000=>0101111=>2
[1,3,4,2,8,6,7,5]=>1001000=>0110111=>2
[1,3,6,4,5,2,8,7]=>1000010=>0111101=>2
[1,3,6,4,5,7,2,8]=>1000001=>0111110=>1
[1,3,6,4,5,7,8,2]=>1000000=>0111111=>1
[1,3,6,4,5,8,7,2]=>1000000=>0111111=>1
[1,3,7,4,5,6,8,2]=>1000000=>0111111=>1
[1,3,8,4,5,6,7,2]=>1000000=>0111111=>1
[1,3,8,4,6,7,5,2]=>1000000=>0111111=>1
[1,3,8,5,4,6,7,2]=>1000000=>0111111=>1
[1,3,8,5,4,7,6,2]=>1000000=>0111111=>1
[1,3,8,5,6,7,4,2]=>1000000=>0111111=>1
[1,3,8,5,7,6,4,2]=>1000000=>0111111=>1
[1,3,8,6,5,7,4,2]=>1000000=>0111111=>1
[1,3,8,7,5,6,4,2]=>1000000=>0111111=>1
[1,4,3,2,8,6,7,5]=>1001000=>0110111=>2
[1,4,3,5,8,6,7,2]=>1000000=>0111111=>1
[1,4,3,8,5,6,7,2]=>1000000=>0111111=>1
[1,4,3,8,5,7,6,2]=>1000000=>0111111=>1
[1,4,3,8,6,5,7,2]=>1000000=>0111111=>1
[1,4,3,8,6,7,5,2]=>1000000=>0111111=>1
[1,5,3,4,2,6,7,8]=>1000111=>0111000=>1
[1,5,3,4,2,7,8,6]=>1000100=>0111011=>2
[1,5,3,4,2,8,7,6]=>1000100=>0111011=>2
[1,5,3,4,6,2,8,7]=>1000010=>0111101=>2
[1,5,3,4,6,7,2,8]=>1000001=>0111110=>1
[1,5,3,4,6,7,8,2]=>1000000=>0111111=>1
[1,5,3,4,8,6,7,2]=>1000000=>0111111=>1
[1,6,3,4,5,2,7,8]=>1000011=>0111100=>1
[1,6,3,4,5,8,7,2]=>1000000=>0111111=>1
[1,7,3,4,5,6,2,8]=>1000001=>0111110=>1
[1,7,3,4,5,6,8,2]=>1000000=>0111111=>1
[1,8,3,4,5,6,7,2]=>1000000=>0111111=>1
[1,8,3,4,6,7,5,2]=>1000000=>0111111=>1
[1,8,3,4,7,6,5,2]=>1000000=>0111111=>1
[1,6,3,5,4,2,7,8]=>1000011=>0111100=>1
[1,6,3,5,4,8,7,2]=>1000000=>0111111=>1
[1,7,3,5,4,6,2,8]=>1000001=>0111110=>1
[1,8,3,5,4,6,7,2]=>1000000=>0111111=>1
[1,8,3,5,6,4,7,2]=>1000000=>0111111=>1
[1,8,3,5,7,6,4,2]=>1000000=>0111111=>1
[1,7,3,6,5,4,2,8]=>1000001=>0111110=>1
[1,8,3,6,5,4,7,2]=>1000000=>0111111=>1
[1,8,3,7,5,6,4,2]=>1000000=>0111111=>1
[1,8,3,7,6,5,4,2]=>1000000=>0111111=>1
[1,6,4,3,5,2,7,8]=>1000011=>0111100=>1
[1,6,4,3,5,8,7,2]=>1000000=>0111111=>1
[1,8,4,3,5,6,7,2]=>1000000=>0111111=>1
[1,8,4,3,5,7,6,2]=>1000000=>0111111=>1
[1,8,4,3,6,5,7,2]=>1000000=>0111111=>1
[1,8,4,3,6,7,5,2]=>1000000=>0111111=>1
[1,6,4,5,3,2,8,7]=>1000010=>0111101=>2
[1,6,4,5,3,8,7,2]=>1000000=>0111111=>1
[1,8,4,5,3,6,7,2]=>1000000=>0111111=>1
[1,7,4,5,6,3,8,2]=>1000000=>0111111=>1
[1,8,4,5,6,7,3,2]=>1000000=>0111111=>1
[1,7,4,6,5,3,2,8]=>1000001=>0111110=>1
[1,8,4,6,5,3,7,2]=>1000000=>0111111=>1
[1,8,4,6,5,7,3,2]=>1000000=>0111111=>1
[1,8,4,7,6,5,3,2]=>1000000=>0111111=>1
[1,7,5,4,3,6,2,8]=>1000001=>0111110=>1
[1,7,5,4,3,6,8,2]=>1000000=>0111111=>1
[1,8,5,4,3,6,7,2]=>1000000=>0111111=>1
[1,8,5,4,6,3,7,2]=>1000000=>0111111=>1
[1,8,5,4,6,7,3,2]=>1000000=>0111111=>1
[1,8,5,4,7,6,3,2]=>1000000=>0111111=>1
[1,7,6,4,5,3,2,8]=>1000001=>0111110=>1
[1,8,6,4,5,3,7,2]=>1000000=>0111111=>1
[1,8,6,4,5,7,3,2]=>1000000=>0111111=>1
[1,8,7,4,5,6,3,2]=>1000000=>0111111=>1
[1,8,7,4,6,5,3,2]=>1000000=>0111111=>1
[1,8,6,5,4,3,7,2]=>1000000=>0111111=>1
[1,8,6,5,4,7,3,2]=>1000000=>0111111=>1
[1,8,7,5,4,6,3,2]=>1000000=>0111111=>1
[1,8,7,5,6,4,3,2]=>1000000=>0111111=>1
[2,1,3,4,8,6,7,5]=>0111000=>1000111=>2
[2,1,3,8,5,7,6,4]=>0110000=>1001111=>2
[2,1,3,8,6,5,7,4]=>0110000=>1001111=>2
[2,1,3,8,6,7,5,4]=>0110000=>1001111=>2
[2,1,4,5,8,6,7,3]=>0100000=>1011111=>2
[2,1,4,8,6,5,7,3]=>0100000=>1011111=>2
[2,1,6,4,5,3,8,7]=>0100010=>1011101=>3
[2,1,6,4,5,8,7,3]=>0100000=>1011111=>2
[2,1,8,4,5,7,6,3]=>0100000=>1011111=>2
[2,1,8,4,6,7,5,3]=>0100000=>1011111=>2
[2,1,8,4,7,6,5,3]=>0100000=>1011111=>2
[2,1,8,5,4,6,7,3]=>0100000=>1011111=>2
[2,1,8,5,4,7,6,3]=>0100000=>1011111=>2
[2,1,7,5,6,4,8,3]=>0100000=>1011111=>2
[2,1,8,5,6,7,4,3]=>0100000=>1011111=>2
[2,1,8,5,7,6,4,3]=>0100000=>1011111=>2
[2,1,8,6,5,4,7,3]=>0100000=>1011111=>2
[2,1,8,6,5,7,4,3]=>0100000=>1011111=>2
[2,1,8,7,5,6,4,3]=>0100000=>1011111=>2
[2,3,1,8,5,6,7,4]=>0010000=>1101111=>2
[2,3,1,8,6,7,5,4]=>0010000=>1101111=>2
[2,3,4,5,8,6,7,1]=>0000000=>1111111=>1
[2,3,4,8,5,6,7,1]=>0000000=>1111111=>1
[2,3,4,8,6,5,7,1]=>0000000=>1111111=>1
[2,3,4,8,6,7,5,1]=>0000000=>1111111=>1
[2,3,6,4,5,7,8,1]=>0000000=>1111111=>1
[2,3,7,4,5,6,8,1]=>0000000=>1111111=>1
[2,3,8,4,5,6,7,1]=>0000000=>1111111=>1
[2,3,7,4,6,5,8,1]=>0000000=>1111111=>1
[2,3,7,5,4,6,8,1]=>0000000=>1111111=>1
[2,3,8,5,4,6,7,1]=>0000000=>1111111=>1
[2,3,7,5,6,4,1,8]=>0000001=>1111110=>1
[2,3,7,5,6,4,8,1]=>0000000=>1111111=>1
[2,3,8,5,6,4,7,1]=>0000000=>1111111=>1
[2,3,8,6,5,4,7,1]=>0000000=>1111111=>1
[2,4,3,5,8,6,7,1]=>0000000=>1111111=>1
[2,5,3,4,1,6,7,8]=>0000111=>1111000=>1
[2,5,3,4,1,8,7,6]=>0000100=>1111011=>2
[2,5,3,4,6,7,1,8]=>0000001=>1111110=>1
[2,5,3,4,6,7,8,1]=>0000000=>1111111=>1
[2,5,3,4,8,6,7,1]=>0000000=>1111111=>1
[2,5,3,4,8,7,6,1]=>0000000=>1111111=>1
[2,6,3,4,5,7,8,1]=>0000000=>1111111=>1
[2,8,3,4,5,6,7,1]=>0000000=>1111111=>1
[2,6,3,5,4,1,8,7]=>0000010=>1111101=>2
[2,6,3,5,4,7,8,1]=>0000000=>1111111=>1
[2,7,3,5,4,6,8,1]=>0000000=>1111111=>1
[2,7,3,5,6,4,8,1]=>0000000=>1111111=>1
[2,8,3,5,7,6,4,1]=>0000000=>1111111=>1
[2,7,3,6,5,4,1,8]=>0000001=>1111110=>1
[2,8,3,7,6,5,4,1]=>0000000=>1111111=>1
[2,5,4,3,8,6,7,1]=>0000000=>1111111=>1
[2,6,4,3,5,7,8,1]=>0000000=>1111111=>1
[2,7,4,3,5,6,8,1]=>0000000=>1111111=>1
[2,8,4,3,5,6,7,1]=>0000000=>1111111=>1
[2,8,4,3,5,7,6,1]=>0000000=>1111111=>1
[2,8,4,3,6,7,5,1]=>0000000=>1111111=>1
[2,8,4,3,7,6,5,1]=>0000000=>1111111=>1
[2,6,4,5,3,1,7,8]=>0000011=>1111100=>1
[2,6,4,5,3,7,8,1]=>0000000=>1111111=>1
[2,8,4,5,3,6,7,1]=>0000000=>1111111=>1
[2,7,4,6,5,3,1,8]=>0000001=>1111110=>1
[2,7,5,4,3,6,8,1]=>0000000=>1111111=>1
[2,8,5,4,3,6,7,1]=>0000000=>1111111=>1
[2,7,5,4,6,3,8,1]=>0000000=>1111111=>1
[2,8,5,4,6,7,3,1]=>0000000=>1111111=>1
[2,8,5,4,7,6,3,1]=>0000000=>1111111=>1
[2,8,7,4,6,5,3,1]=>0000000=>1111111=>1
[2,8,7,5,4,6,3,1]=>0000000=>1111111=>1
[2,8,7,5,6,4,3,1]=>0000000=>1111111=>1
[3,2,1,4,8,6,7,5]=>0011000=>1100111=>2
[3,2,1,5,8,6,7,4]=>0010000=>1101111=>2
[3,2,1,7,5,6,4,8]=>0010001=>1101110=>2
[3,2,1,7,5,6,8,4]=>0010000=>1101111=>2
[3,2,1,8,5,6,7,4]=>0010000=>1101111=>2
[3,2,1,8,5,7,6,4]=>0010000=>1101111=>2
[3,2,1,8,6,5,7,4]=>0010000=>1101111=>2
[3,2,1,8,6,7,5,4]=>0010000=>1101111=>2
[3,2,4,1,8,6,7,5]=>0001000=>1110111=>2
[3,2,4,5,8,6,7,1]=>0000000=>1111111=>1
[3,2,4,8,6,7,5,1]=>0000000=>1111111=>1
[3,2,5,4,8,6,7,1]=>0000000=>1111111=>1
[3,2,7,4,5,6,1,8]=>0000001=>1111110=>1
[3,2,8,4,5,6,7,1]=>0000000=>1111111=>1
[3,2,7,4,6,5,1,8]=>0000001=>1111110=>1
[3,2,7,4,6,5,8,1]=>0000000=>1111111=>1
[3,2,7,5,4,6,1,8]=>0000001=>1111110=>1
[3,2,8,5,4,6,7,1]=>0000000=>1111111=>1
[3,2,8,5,4,7,6,1]=>0000000=>1111111=>1
[3,2,7,5,6,4,1,8]=>0000001=>1111110=>1
[3,2,7,5,6,4,8,1]=>0000000=>1111111=>1
[3,2,8,5,7,6,4,1]=>0000000=>1111111=>1
[4,2,3,1,5,7,6,8]=>0001101=>1110010=>2
[4,2,3,1,5,8,7,6]=>0001100=>1110011=>2
[4,2,3,1,6,5,7,8]=>0001011=>1110100=>2
[4,2,3,1,7,6,5,8]=>0001001=>1110110=>2
[4,2,3,1,8,6,7,5]=>0001000=>1110111=>2
[4,2,3,1,8,7,6,5]=>0001000=>1110111=>2
[4,2,3,5,1,6,8,7]=>0000110=>1111001=>2
[4,2,3,5,1,7,8,6]=>0000100=>1111011=>2
[4,2,3,5,1,8,7,6]=>0000100=>1111011=>2
[4,2,3,5,6,1,8,7]=>0000010=>1111101=>2
[4,2,3,5,6,8,7,1]=>0000000=>1111111=>1
[4,2,3,6,5,8,7,1]=>0000000=>1111111=>1
[4,2,3,7,5,6,1,8]=>0000001=>1111110=>1
[4,2,3,7,5,6,8,1]=>0000000=>1111111=>1
[4,2,3,8,5,6,7,1]=>0000000=>1111111=>1
[4,2,3,7,6,5,8,1]=>0000000=>1111111=>1
[4,2,3,8,7,6,5,1]=>0000000=>1111111=>1
[5,2,3,4,1,7,8,6]=>0000100=>1111011=>2
[5,2,3,4,1,8,7,6]=>0000100=>1111011=>2
[5,2,3,4,6,1,8,7]=>0000010=>1111101=>2
[5,2,3,4,7,6,1,8]=>0000001=>1111110=>1
[5,2,3,4,8,7,6,1]=>0000000=>1111111=>1
[7,2,3,4,6,5,1,8]=>0000001=>1111110=>1
[6,2,3,5,4,1,7,8]=>0000011=>1111100=>1
[6,2,3,5,4,1,8,7]=>0000010=>1111101=>2
[6,2,3,5,4,7,1,8]=>0000001=>1111110=>1
[7,2,3,5,4,6,1,8]=>0000001=>1111110=>1
[8,2,3,5,4,6,7,1]=>0000000=>1111111=>1
[7,2,3,5,6,4,1,8]=>0000001=>1111110=>1
[7,2,3,6,5,4,1,8]=>0000001=>1111110=>1
[8,2,3,6,5,4,7,1]=>0000000=>1111111=>1
[8,2,3,7,5,6,4,1]=>0000000=>1111111=>1
[5,2,4,3,1,6,7,8]=>0000111=>1111000=>1
[5,2,4,3,1,6,8,7]=>0000110=>1111001=>2
[5,2,4,3,1,7,6,8]=>0000101=>1111010=>2
[5,2,4,3,1,8,7,6]=>0000100=>1111011=>2
[5,2,4,3,6,1,7,8]=>0000011=>1111100=>1
[5,2,4,3,6,1,8,7]=>0000010=>1111101=>2
[5,2,4,3,6,7,1,8]=>0000001=>1111110=>1
[5,2,4,3,7,6,1,8]=>0000001=>1111110=>1
[5,2,4,3,7,6,8,1]=>0000000=>1111111=>1
[7,2,4,3,6,5,1,8]=>0000001=>1111110=>1
[7,2,4,3,6,5,8,1]=>0000000=>1111111=>1
[8,2,4,3,6,5,7,1]=>0000000=>1111111=>1
[8,2,4,3,6,7,5,1]=>0000000=>1111111=>1
[6,2,4,5,3,1,7,8]=>0000011=>1111100=>1
[7,2,4,5,3,6,1,8]=>0000001=>1111110=>1
[7,2,4,5,3,6,8,1]=>0000000=>1111111=>1
[8,2,4,5,3,7,6,1]=>0000000=>1111111=>1
[7,2,4,6,5,3,1,8]=>0000001=>1111110=>1
[8,2,4,7,6,5,3,1]=>0000000=>1111111=>1
[6,2,5,4,3,1,7,8]=>0000011=>1111100=>1
[6,2,5,4,3,1,8,7]=>0000010=>1111101=>2
[7,2,5,4,3,6,1,8]=>0000001=>1111110=>1
[8,2,5,4,3,6,7,1]=>0000000=>1111111=>1
[8,2,5,4,3,7,6,1]=>0000000=>1111111=>1
[7,2,6,4,5,3,1,8]=>0000001=>1111110=>1
[8,2,6,4,5,3,7,1]=>0000000=>1111111=>1
[8,2,6,4,5,7,3,1]=>0000000=>1111111=>1
[8,2,7,4,5,6,3,1]=>0000000=>1111111=>1
[8,2,7,4,6,5,3,1]=>0000000=>1111111=>1
[8,2,6,5,4,3,7,1]=>0000000=>1111111=>1
[8,2,6,5,4,7,3,1]=>0000000=>1111111=>1
[8,2,7,5,4,6,3,1]=>0000000=>1111111=>1
[8,2,7,5,6,4,3,1]=>0000000=>1111111=>1
[8,2,7,6,5,4,3,1]=>0000000=>1111111=>1
[4,3,2,1,8,6,7,5]=>0001000=>1110111=>2
[4,3,2,7,5,6,8,1]=>0000000=>1111111=>1
[4,3,2,8,5,6,7,1]=>0000000=>1111111=>1
[4,3,2,8,5,7,6,1]=>0000000=>1111111=>1
[4,3,2,8,6,7,5,1]=>0000000=>1111111=>1
[5,3,2,4,1,6,8,7]=>0000110=>1111001=>2
[5,3,2,4,1,7,6,8]=>0000101=>1111010=>2
[5,3,2,4,1,8,7,6]=>0000100=>1111011=>2
[5,3,2,4,6,1,8,7]=>0000010=>1111101=>2
[5,3,2,4,7,6,1,8]=>0000001=>1111110=>1
[8,3,2,4,6,7,5,1]=>0000000=>1111111=>1
[6,3,2,5,4,1,7,8]=>0000011=>1111100=>1
[6,3,2,5,4,1,8,7]=>0000010=>1111101=>2
[6,3,2,5,4,7,1,8]=>0000001=>1111110=>1
[6,3,2,5,4,7,8,1]=>0000000=>1111111=>1
[7,3,2,5,4,6,1,8]=>0000001=>1111110=>1
[8,3,2,5,4,7,6,1]=>0000000=>1111111=>1
[8,3,2,5,6,4,7,1]=>0000000=>1111111=>1
[8,3,2,6,5,7,4,1]=>0000000=>1111111=>1
[8,3,2,7,5,6,4,1]=>0000000=>1111111=>1
[8,3,2,7,6,5,4,1]=>0000000=>1111111=>1
[5,3,4,2,1,6,8,7]=>0000110=>1111001=>2
[5,3,4,2,1,7,8,6]=>0000100=>1111011=>2
[5,3,4,2,1,8,7,6]=>0000100=>1111011=>2
[5,3,4,2,7,6,1,8]=>0000001=>1111110=>1
[7,3,4,2,6,5,1,8]=>0000001=>1111110=>1
[7,3,4,2,6,5,8,1]=>0000000=>1111111=>1
[8,3,4,2,6,5,7,1]=>0000000=>1111111=>1
[6,3,4,5,2,1,8,7]=>0000010=>1111101=>2
[6,3,4,5,2,8,7,1]=>0000000=>1111111=>1
[8,3,4,5,7,6,2,1]=>0000000=>1111111=>1
[7,3,4,6,5,2,1,8]=>0000001=>1111110=>1
[6,3,5,4,2,1,8,7]=>0000010=>1111101=>2
[6,3,5,4,2,7,1,8]=>0000001=>1111110=>1
[7,3,5,4,2,6,1,8]=>0000001=>1111110=>1
[7,3,5,4,6,2,1,8]=>0000001=>1111110=>1
[8,3,5,4,6,7,2,1]=>0000000=>1111111=>1
[8,3,5,4,7,6,2,1]=>0000000=>1111111=>1
[7,3,6,4,5,2,1,8]=>0000001=>1111110=>1
[8,3,7,4,6,5,2,1]=>0000000=>1111111=>1
[7,3,6,5,4,2,1,8]=>0000001=>1111110=>1
[7,3,6,5,4,2,8,1]=>0000000=>1111111=>1
[8,3,6,5,4,2,7,1]=>0000000=>1111111=>1
[8,3,6,5,4,7,2,1]=>0000000=>1111111=>1
[8,3,7,5,4,6,2,1]=>0000000=>1111111=>1
[8,3,7,6,5,4,2,1]=>0000000=>1111111=>1
[5,4,3,2,8,6,7,1]=>0000000=>1111111=>1
[6,4,3,2,5,1,8,7]=>0000010=>1111101=>2
[7,4,3,2,6,5,8,1]=>0000000=>1111111=>1
[6,4,3,5,2,1,8,7]=>0000010=>1111101=>2
[7,4,3,6,5,2,1,8]=>0000001=>1111110=>1
[7,4,3,6,5,2,8,1]=>0000000=>1111111=>1
[8,4,3,7,5,6,2,1]=>0000000=>1111111=>1
[6,5,3,4,2,1,8,7]=>0000010=>1111101=>2
[8,5,3,4,2,7,6,1]=>0000000=>1111111=>1
[8,5,3,4,7,6,2,1]=>0000000=>1111111=>1
[8,7,3,4,6,5,2,1]=>0000000=>1111111=>1
[7,6,3,5,4,2,1,8]=>0000001=>1111110=>1
[7,6,3,5,4,2,8,1]=>0000000=>1111111=>1
[8,7,3,5,4,6,2,1]=>0000000=>1111111=>1
[8,7,3,5,6,4,2,1]=>0000000=>1111111=>1
[8,7,3,6,5,4,2,1]=>0000000=>1111111=>1
[8,5,4,3,2,7,6,1]=>0000000=>1111111=>1
[8,7,4,3,6,5,2,1]=>0000000=>1111111=>1
[8,7,4,6,5,3,2,1]=>0000000=>1111111=>1
[2,4,1,3,6,5,8,7]=>0001010=>1110101=>3
[2,4,1,6,3,5,8,7]=>0000010=>1111101=>2
[2,4,6,1,3,5,8,7]=>0000010=>1111101=>2
[2,4,1,3,6,8,5,7]=>0001000=>1110111=>2
[2,1,4,6,3,8,5,7]=>0100000=>1011111=>2
[2,4,1,6,3,8,5,7]=>0000000=>1111111=>1
[2,4,6,1,3,8,5,7]=>0000000=>1111111=>1
[2,4,1,6,8,3,5,7]=>0000000=>1111111=>1
[2,4,6,1,8,3,5,7]=>0000000=>1111111=>1
[2,4,6,8,1,3,5,7]=>0000000=>1111111=>1
[2,4,1,3,6,5,7,8]=>0001011=>1110100=>2
[2,1,4,6,3,5,7,8]=>0100011=>1011100=>2
[2,4,1,6,3,5,7,8]=>0000011=>1111100=>1
[2,4,6,1,3,5,7,8]=>0000011=>1111100=>1
[2,1,4,6,3,7,5,8]=>0100001=>1011110=>2
[2,4,1,6,3,7,5,8]=>0000001=>1111110=>1
[2,4,6,1,3,7,5,8]=>0000001=>1111110=>1
[2,1,4,6,3,7,8,5]=>0100000=>1011111=>2
[2,4,1,6,3,7,8,5]=>0000000=>1111111=>1
[2,1,4,6,7,3,8,5]=>0100000=>1011111=>2
[2,4,1,6,7,3,8,5]=>0000000=>1111111=>1
[2,4,6,1,7,3,8,5]=>0000000=>1111111=>1
[2,4,6,7,1,3,8,5]=>0000000=>1111111=>1
[2,4,1,6,7,8,3,5]=>0000000=>1111111=>1
[2,4,6,7,8,1,3,5]=>0000000=>1111111=>1
[2,1,4,3,7,5,8,6]=>0101000=>1010111=>3
[2,4,1,3,7,5,8,6]=>0001000=>1110111=>2
[2,1,4,7,3,5,8,6]=>0100000=>1011111=>2
[2,4,1,7,3,5,8,6]=>0000000=>1111111=>1
[2,4,7,1,3,5,8,6]=>0000000=>1111111=>1
[2,1,4,3,7,8,5,6]=>0101000=>1010111=>3
[2,4,1,3,7,8,5,6]=>0001000=>1110111=>2
[2,4,1,7,3,8,5,6]=>0000000=>1111111=>1
[2,4,1,7,8,3,5,6]=>0000000=>1111111=>1
[2,4,7,8,1,3,5,6]=>0000000=>1111111=>1
[2,4,1,5,3,7,6,8]=>0000101=>1111010=>2
[2,4,5,1,3,7,6,8]=>0000101=>1111010=>2
[2,4,1,3,5,7,8,6]=>0001100=>1110011=>2
[2,4,1,5,3,7,8,6]=>0000100=>1111011=>2
[2,4,5,1,3,7,8,6]=>0000100=>1111011=>2
[2,1,4,5,7,3,8,6]=>0100000=>1011111=>2
[2,4,1,5,7,3,8,6]=>0000000=>1111111=>1
[2,4,5,1,7,3,8,6]=>0000000=>1111111=>1
[2,4,5,1,7,8,3,6]=>0000000=>1111111=>1
[2,4,5,7,8,1,3,6]=>0000000=>1111111=>1
[2,1,4,3,8,5,6,7]=>0101000=>1010111=>3
[2,4,1,3,8,5,6,7]=>0001000=>1110111=>2
[2,1,4,8,3,5,6,7]=>0100000=>1011111=>2
[2,4,1,8,3,5,6,7]=>0000000=>1111111=>1
[2,1,4,3,5,8,6,7]=>0101100=>1010011=>3
[2,4,1,5,3,8,6,7]=>0000100=>1111011=>2
[2,1,4,5,8,3,6,7]=>0100000=>1011111=>2
[2,4,5,1,8,3,6,7]=>0000000=>1111111=>1
[2,4,1,5,3,6,8,7]=>0000110=>1111001=>2
[2,4,1,5,6,3,8,7]=>0000010=>1111101=>2
[2,4,5,1,6,3,8,7]=>0000010=>1111101=>2
[2,1,4,5,6,8,3,7]=>0100000=>1011111=>2
[2,4,1,5,6,8,3,7]=>0000000=>1111111=>1
[2,4,5,6,8,1,3,7]=>0000000=>1111111=>1
[2,4,1,3,5,6,7,8]=>0001111=>1110000=>1
[2,4,1,5,3,6,7,8]=>0000111=>1111000=>1
[2,4,5,1,3,6,7,8]=>0000111=>1111000=>1
[2,4,1,5,6,3,7,8]=>0000011=>1111100=>1
[2,4,5,6,1,3,7,8]=>0000011=>1111100=>1
[2,4,1,5,6,7,3,8]=>0000001=>1111110=>1
[2,4,5,6,1,7,3,8]=>0000001=>1111110=>1
[2,4,5,6,7,1,3,8]=>0000001=>1111110=>1
[2,4,5,6,1,7,8,3]=>0000000=>1111111=>1
[2,4,5,6,7,1,8,3]=>0000000=>1111111=>1
[2,4,5,6,7,8,1,3]=>0000000=>1111111=>1
[2,1,5,3,6,4,8,7]=>0100010=>1011101=>3
[2,5,1,3,6,4,8,7]=>0000010=>1111101=>2
[2,1,5,6,3,4,8,7]=>0100010=>1011101=>3
[2,5,1,6,3,4,8,7]=>0000010=>1111101=>2
[2,1,5,3,6,8,4,7]=>0100000=>1011111=>2
[2,5,1,3,6,8,4,7]=>0000000=>1111111=>1
[2,5,6,1,3,8,4,7]=>0000000=>1111111=>1
[2,5,6,8,1,3,4,7]=>0000000=>1111111=>1
[2,5,1,3,6,4,7,8]=>0000011=>1111100=>1
[2,1,5,6,3,4,7,8]=>0100011=>1011100=>2
[2,5,1,6,3,4,7,8]=>0000011=>1111100=>1
[2,1,5,3,6,7,4,8]=>0100001=>1011110=>2
[2,1,5,6,3,7,4,8]=>0100001=>1011110=>2
[2,5,1,6,3,7,4,8]=>0000001=>1111110=>1
[2,5,6,1,3,7,4,8]=>0000001=>1111110=>1
[2,1,5,6,7,3,4,8]=>0100001=>1011110=>2
[2,5,6,1,7,3,4,8]=>0000001=>1111110=>1
[2,5,1,3,6,7,8,4]=>0000000=>1111111=>1
[2,1,5,6,3,7,8,4]=>0100000=>1011111=>2
[2,5,1,6,3,7,8,4]=>0000000=>1111111=>1
[2,5,6,1,3,7,8,4]=>0000000=>1111111=>1
[2,1,5,6,7,3,8,4]=>0100000=>1011111=>2
[2,5,1,6,7,3,8,4]=>0000000=>1111111=>1
[2,5,6,7,1,3,8,4]=>0000000=>1111111=>1
[2,1,5,6,7,8,3,4]=>0100000=>1011111=>2
[2,5,1,6,7,8,3,4]=>0000000=>1111111=>1
[2,5,6,1,7,8,3,4]=>0000000=>1111111=>1
[2,5,6,7,1,8,3,4]=>0000000=>1111111=>1
[2,5,6,7,8,1,3,4]=>0000000=>1111111=>1
[2,1,5,3,7,4,8,6]=>0100000=>1011111=>2
[2,5,1,3,7,4,8,6]=>0000000=>1111111=>1
[2,1,5,7,3,4,8,6]=>0100000=>1011111=>2
[2,5,1,7,3,4,8,6]=>0000000=>1111111=>1
[2,5,7,1,3,4,8,6]=>0000000=>1111111=>1
[2,1,5,3,7,8,4,6]=>0100000=>1011111=>2
[2,5,1,3,7,8,4,6]=>0000000=>1111111=>1
[2,1,5,7,3,8,4,6]=>0100000=>1011111=>2
[2,1,5,7,8,3,4,6]=>0100000=>1011111=>2
[2,5,1,7,8,3,4,6]=>0000000=>1111111=>1
[2,5,7,1,8,3,4,6]=>0000000=>1111111=>1
[2,5,7,8,1,3,4,6]=>0000000=>1111111=>1
[2,5,1,3,7,4,6,8]=>0000001=>1111110=>1
[2,1,5,7,3,4,6,8]=>0100001=>1011110=>2
[2,3,5,1,4,7,6,8]=>0000101=>1111010=>2
[2,3,5,7,1,4,6,8]=>0000001=>1111110=>1
[2,3,5,7,1,4,8,6]=>0000000=>1111111=>1
[2,3,1,5,7,8,4,6]=>0010000=>1101111=>2
[2,1,5,3,8,4,6,7]=>0100000=>1011111=>2
[2,5,1,8,3,4,6,7]=>0000000=>1111111=>1
[2,5,8,1,3,4,6,7]=>0000000=>1111111=>1
[2,3,5,1,4,8,6,7]=>0000100=>1111011=>2
[2,1,3,5,8,4,6,7]=>0110000=>1001111=>2
[2,3,5,8,1,4,6,7]=>0000000=>1111111=>1
[2,1,3,5,6,8,4,7]=>0110000=>1001111=>2
[2,3,1,5,6,8,4,7]=>0010000=>1101111=>2
[2,3,5,6,1,8,4,7]=>0000000=>1111111=>1
[2,3,5,6,8,1,4,7]=>0000000=>1111111=>1
[2,5,1,3,4,6,7,8]=>0000111=>1111000=>1
[2,3,5,1,4,6,7,8]=>0000111=>1111000=>1
[2,3,5,1,6,4,7,8]=>0000011=>1111100=>1
[2,3,5,6,1,4,7,8]=>0000011=>1111100=>1
[2,3,5,6,1,7,8,4]=>0000000=>1111111=>1
[2,3,5,6,7,8,1,4]=>0000000=>1111111=>1
[2,1,6,3,7,4,8,5]=>0100000=>1011111=>2
[2,6,1,3,7,4,8,5]=>0000000=>1111111=>1
[2,6,1,7,3,4,8,5]=>0000000=>1111111=>1
[2,6,7,1,3,4,8,5]=>0000000=>1111111=>1
[2,1,6,3,7,8,4,5]=>0100000=>1011111=>2
[2,6,1,7,3,8,4,5]=>0000000=>1111111=>1
[2,6,7,1,3,8,4,5]=>0000000=>1111111=>1
[2,1,6,7,8,3,4,5]=>0100000=>1011111=>2
[2,6,1,7,8,3,4,5]=>0000000=>1111111=>1
[2,6,7,8,1,3,4,5]=>0000000=>1111111=>1
[2,1,6,3,7,4,5,8]=>0100001=>1011110=>2
[2,6,1,7,3,4,5,8]=>0000001=>1111110=>1
[2,6,7,1,3,4,5,8]=>0000001=>1111110=>1
[2,6,1,3,4,7,5,8]=>0000001=>1111110=>1
[2,3,1,6,4,7,5,8]=>0010001=>1101110=>2
[2,3,6,1,4,7,5,8]=>0000001=>1111110=>1
[2,1,6,3,4,7,8,5]=>0100000=>1011111=>2
[2,6,1,3,4,7,8,5]=>0000000=>1111111=>1
[2,3,6,1,4,7,8,5]=>0000000=>1111111=>1
[2,1,3,6,7,4,8,5]=>0110000=>1001111=>2
[2,1,3,6,7,8,4,5]=>0110000=>1001111=>2
[2,3,1,6,7,8,4,5]=>0010000=>1101111=>2
[2,3,6,1,7,8,4,5]=>0000000=>1111111=>1
[2,3,6,7,1,8,4,5]=>0000000=>1111111=>1
[2,3,6,7,8,1,4,5]=>0000000=>1111111=>1
[2,1,6,3,8,4,5,7]=>0100000=>1011111=>2
[2,1,6,8,3,4,5,7]=>0100000=>1011111=>2
[2,6,1,8,3,4,5,7]=>0000000=>1111111=>1
[2,6,8,1,3,4,5,7]=>0000000=>1111111=>1
[2,1,6,3,4,8,5,7]=>0100000=>1011111=>2
[2,3,1,6,4,8,5,7]=>0010000=>1101111=>2
[2,3,6,1,8,4,5,7]=>0000000=>1111111=>1
[2,1,6,3,4,5,8,7]=>0100010=>1011101=>3
[2,1,3,6,4,5,8,7]=>0110010=>1001101=>3
[2,3,6,1,4,5,8,7]=>0000010=>1111101=>2
[2,3,4,1,6,8,5,7]=>0001000=>1110111=>2
[2,3,4,6,8,1,5,7]=>0000000=>1111111=>1
[2,6,1,3,4,5,7,8]=>0000011=>1111100=>1
[2,1,3,6,4,5,7,8]=>0110011=>1001100=>2
[2,3,1,6,4,5,7,8]=>0010011=>1101100=>2
[2,3,6,1,4,5,7,8]=>0000011=>1111100=>1
[2,3,4,6,1,5,7,8]=>0000011=>1111100=>1
[2,3,4,6,1,7,5,8]=>0000001=>1111110=>1
[2,3,4,6,7,1,5,8]=>0000001=>1111110=>1
[2,3,4,6,7,8,1,5]=>0000000=>1111111=>1
[2,1,7,8,3,4,5,6]=>0100000=>1011111=>2
[2,7,1,8,3,4,5,6]=>0000000=>1111111=>1
[2,7,8,1,3,4,5,6]=>0000000=>1111111=>1
[2,1,7,3,4,8,5,6]=>0100000=>1011111=>2
[2,1,3,7,4,8,5,6]=>0110000=>1001111=>2
[2,3,1,7,4,8,5,6]=>0010000=>1101111=>2
[2,3,7,1,4,8,5,6]=>0000000=>1111111=>1
[2,1,3,7,8,4,5,6]=>0110000=>1001111=>2
[2,3,7,8,1,4,5,6]=>0000000=>1111111=>1
[2,7,1,3,4,5,8,6]=>0000000=>1111111=>1
[2,3,7,1,4,5,8,6]=>0000000=>1111111=>1
[2,1,3,4,7,5,8,6]=>0111000=>1000111=>2
[2,3,4,1,7,5,8,6]=>0001000=>1110111=>2
[2,1,3,4,7,8,5,6]=>0111000=>1000111=>2
[2,3,1,4,7,8,5,6]=>0011000=>1100111=>2
[2,3,4,1,7,8,5,6]=>0001000=>1110111=>2
[2,3,4,7,1,8,5,6]=>0000000=>1111111=>1
[2,1,7,3,4,5,6,8]=>0100001=>1011110=>2
[2,7,1,3,4,5,6,8]=>0000001=>1111110=>1
[2,1,3,4,7,5,6,8]=>0111001=>1000110=>2
[2,3,1,4,7,5,6,8]=>0011001=>1100110=>2
[2,3,4,1,7,5,6,8]=>0001001=>1110110=>2
[2,3,4,7,1,5,6,8]=>0000001=>1111110=>1
[2,3,4,5,7,1,6,8]=>0000001=>1111110=>1
[2,3,4,5,7,1,8,6]=>0000000=>1111111=>1
[2,3,4,5,7,8,1,6]=>0000000=>1111111=>1
[2,1,8,3,4,5,6,7]=>0100000=>1011111=>2
[2,8,1,3,4,5,6,7]=>0000000=>1111111=>1
[2,1,3,8,4,5,6,7]=>0110000=>1001111=>2
[2,3,1,8,4,5,6,7]=>0010000=>1101111=>2
[2,3,8,1,4,5,6,7]=>0000000=>1111111=>1
[2,1,3,4,8,5,6,7]=>0111000=>1000111=>2
[2,3,4,1,8,5,6,7]=>0001000=>1110111=>2
[2,3,4,8,1,5,6,7]=>0000000=>1111111=>1
[2,1,3,4,5,8,6,7]=>0111100=>1000011=>2
[2,3,1,4,5,8,6,7]=>0011100=>1100011=>2
[2,3,4,1,5,8,6,7]=>0001100=>1110011=>2
[2,3,4,5,1,8,6,7]=>0000100=>1111011=>2
[2,3,4,5,8,1,6,7]=>0000000=>1111111=>1
[2,3,4,5,6,8,1,7]=>0000000=>1111111=>1
[3,1,4,2,6,5,8,7]=>0001010=>1110101=>3
[3,4,1,2,6,5,8,7]=>0001010=>1110101=>3
[3,1,4,6,2,5,8,7]=>0000010=>1111101=>2
[3,4,1,6,2,5,8,7]=>0000010=>1111101=>2
[3,4,6,1,2,5,8,7]=>0000010=>1111101=>2
[3,1,4,2,6,8,5,7]=>0001000=>1110111=>2
[3,4,1,6,2,8,5,7]=>0000000=>1111111=>1
[3,1,4,6,8,2,5,7]=>0000000=>1111111=>1
[3,4,6,8,1,2,5,7]=>0000000=>1111111=>1
[3,1,4,2,6,5,7,8]=>0001011=>1110100=>2
[3,4,1,2,6,5,7,8]=>0001011=>1110100=>2
[3,1,4,2,6,7,5,8]=>0001001=>1110110=>2
[3,4,1,2,6,7,5,8]=>0001001=>1110110=>2
[3,4,1,6,2,7,5,8]=>0000001=>1111110=>1
[3,4,1,6,7,2,5,8]=>0000001=>1111110=>1
[3,4,6,7,1,2,5,8]=>0000001=>1111110=>1
[3,1,4,2,6,7,8,5]=>0001000=>1110111=>2
[3,4,1,2,6,7,8,5]=>0001000=>1110111=>2
[3,4,1,6,2,7,8,5]=>0000000=>1111111=>1
[3,4,6,1,2,7,8,5]=>0000000=>1111111=>1
[3,4,1,6,7,2,8,5]=>0000000=>1111111=>1
[3,4,6,1,7,2,8,5]=>0000000=>1111111=>1
[3,4,6,7,1,2,8,5]=>0000000=>1111111=>1
[3,1,4,6,7,8,2,5]=>0000000=>1111111=>1
[3,4,1,6,7,8,2,5]=>0000000=>1111111=>1
[3,4,6,1,7,8,2,5]=>0000000=>1111111=>1
[3,4,6,7,1,8,2,5]=>0000000=>1111111=>1
[3,4,6,7,8,1,2,5]=>0000000=>1111111=>1
[3,1,4,2,7,5,8,6]=>0001000=>1110111=>2
[3,4,1,2,7,5,8,6]=>0001000=>1110111=>2
[3,4,7,1,2,5,8,6]=>0000000=>1111111=>1
[3,1,4,2,7,8,5,6]=>0001000=>1110111=>2
[3,4,1,2,7,8,5,6]=>0001000=>1110111=>2
[3,4,7,1,8,2,5,6]=>0000000=>1111111=>1
[3,4,7,8,1,2,5,6]=>0000000=>1111111=>1
[3,1,4,2,7,5,6,8]=>0001001=>1110110=>2
[3,4,1,5,2,7,6,8]=>0000101=>1111010=>2
[3,4,1,5,7,2,6,8]=>0000001=>1111110=>1
[3,4,5,7,1,2,6,8]=>0000001=>1111110=>1
[3,1,4,2,5,7,8,6]=>0001100=>1110011=>2
[3,4,1,2,5,7,8,6]=>0001100=>1110011=>2
[3,1,4,5,2,7,8,6]=>0000100=>1111011=>2
[3,4,5,1,2,7,8,6]=>0000100=>1111011=>2
[3,4,5,7,1,2,8,6]=>0000000=>1111111=>1
[3,1,4,5,7,8,2,6]=>0000000=>1111111=>1
[3,4,1,5,7,8,2,6]=>0000000=>1111111=>1
[3,4,5,1,7,8,2,6]=>0000000=>1111111=>1
[3,4,5,7,8,1,2,6]=>0000000=>1111111=>1
[3,1,4,2,8,5,6,7]=>0001000=>1110111=>2
[3,1,4,8,2,5,6,7]=>0000000=>1111111=>1
[3,4,1,8,2,5,6,7]=>0000000=>1111111=>1
[3,1,4,2,5,8,6,7]=>0001100=>1110011=>2
[3,4,1,5,2,8,6,7]=>0000100=>1111011=>2
[3,4,1,5,8,2,6,7]=>0000000=>1111111=>1
[3,4,5,8,1,2,6,7]=>0000000=>1111111=>1
[3,4,1,2,5,6,8,7]=>0001110=>1110001=>2
[3,4,5,1,2,6,8,7]=>0000110=>1111001=>2
[3,4,5,1,6,2,8,7]=>0000010=>1111101=>2
[3,4,5,6,1,2,8,7]=>0000010=>1111101=>2
[3,1,4,5,6,8,2,7]=>0000000=>1111111=>1
[3,4,1,5,6,8,2,7]=>0000000=>1111111=>1
[3,4,5,6,1,8,2,7]=>0000000=>1111111=>1
[3,4,5,6,8,1,2,7]=>0000000=>1111111=>1
[3,1,4,2,5,6,7,8]=>0001111=>1110000=>1
[3,1,4,5,2,6,7,8]=>0000111=>1111000=>1
[3,4,1,5,2,6,7,8]=>0000111=>1111000=>1
[3,4,1,5,6,2,7,8]=>0000011=>1111100=>1
[3,4,5,1,6,2,7,8]=>0000011=>1111100=>1
[3,1,4,5,6,7,2,8]=>0000001=>1111110=>1
[3,4,1,5,6,7,2,8]=>0000001=>1111110=>1
[3,4,5,6,1,7,2,8]=>0000001=>1111110=>1
[3,1,4,5,6,7,8,2]=>0000000=>1111111=>1
[3,4,1,5,6,7,8,2]=>0000000=>1111111=>1
[3,4,5,1,6,7,8,2]=>0000000=>1111111=>1
[3,4,5,6,1,7,8,2]=>0000000=>1111111=>1
[3,4,5,6,7,1,8,2]=>0000000=>1111111=>1
[3,1,5,2,6,4,8,7]=>0000010=>1111101=>2
[3,5,1,2,6,4,8,7]=>0000010=>1111101=>2
[3,1,5,6,2,4,8,7]=>0000010=>1111101=>2
[3,5,1,6,2,4,8,7]=>0000010=>1111101=>2
[3,5,1,2,6,8,4,7]=>0000000=>1111111=>1
[3,1,5,6,2,8,4,7]=>0000000=>1111111=>1
[3,5,6,1,2,8,4,7]=>0000000=>1111111=>1
[3,1,5,6,8,2,4,7]=>0000000=>1111111=>1
[3,5,1,6,8,2,4,7]=>0000000=>1111111=>1
[3,5,6,1,8,2,4,7]=>0000000=>1111111=>1
[3,5,6,8,1,2,4,7]=>0000000=>1111111=>1
[3,1,5,6,2,4,7,8]=>0000011=>1111100=>1
[3,5,1,6,2,4,7,8]=>0000011=>1111100=>1
[3,5,1,2,6,7,4,8]=>0000001=>1111110=>1
[3,5,1,6,2,7,4,8]=>0000001=>1111110=>1
[3,5,6,1,2,7,4,8]=>0000001=>1111110=>1
[3,5,1,6,7,2,4,8]=>0000001=>1111110=>1
[3,1,5,2,6,7,8,4]=>0000000=>1111111=>1
[3,5,1,2,6,7,8,4]=>0000000=>1111111=>1
[3,1,5,6,2,7,8,4]=>0000000=>1111111=>1
[3,5,1,6,2,7,8,4]=>0000000=>1111111=>1
[3,5,6,1,2,7,8,4]=>0000000=>1111111=>1
[3,1,5,6,7,2,8,4]=>0000000=>1111111=>1
[3,5,1,6,7,2,8,4]=>0000000=>1111111=>1
[3,5,6,1,7,2,8,4]=>0000000=>1111111=>1
[3,5,6,7,1,2,8,4]=>0000000=>1111111=>1
[3,1,5,6,7,8,2,4]=>0000000=>1111111=>1
[3,5,1,6,7,8,2,4]=>0000000=>1111111=>1
[3,5,6,1,7,8,2,4]=>0000000=>1111111=>1
[3,5,6,7,1,8,2,4]=>0000000=>1111111=>1
[3,5,6,7,8,1,2,4]=>0000000=>1111111=>1
[3,1,5,2,7,4,8,6]=>0000000=>1111111=>1
[3,5,1,2,7,4,8,6]=>0000000=>1111111=>1
[3,1,5,7,2,4,8,6]=>0000000=>1111111=>1
[3,5,1,7,2,4,8,6]=>0000000=>1111111=>1
[3,5,7,1,2,4,8,6]=>0000000=>1111111=>1
[3,1,5,2,7,8,4,6]=>0000000=>1111111=>1
[3,5,1,2,7,8,4,6]=>0000000=>1111111=>1
[3,1,5,7,2,8,4,6]=>0000000=>1111111=>1
[3,5,1,7,2,8,4,6]=>0000000=>1111111=>1
[3,1,5,7,8,2,4,6]=>0000000=>1111111=>1
[3,5,1,7,8,2,4,6]=>0000000=>1111111=>1
[3,5,7,8,1,2,4,6]=>0000000=>1111111=>1
[3,1,5,2,7,4,6,8]=>0000001=>1111110=>1
[3,5,1,2,7,4,6,8]=>0000001=>1111110=>1
[3,1,5,7,2,4,6,8]=>0000001=>1111110=>1
[3,5,1,7,2,4,6,8]=>0000001=>1111110=>1
[3,5,7,1,2,4,6,8]=>0000001=>1111110=>1
[3,1,5,2,4,7,6,8]=>0000101=>1111010=>2
[3,5,1,2,4,7,6,8]=>0000101=>1111010=>2
[3,1,2,5,4,7,6,8]=>0010101=>1101010=>3
[1,3,5,2,4,7,6,8]=>1000101=>0111010=>2
[3,1,2,5,7,4,6,8]=>0010001=>1101110=>2
[1,3,2,5,7,4,6,8]=>1010001=>0101110=>2
[1,3,5,2,7,4,6,8]=>1000001=>0111110=>1
[1,3,5,7,2,4,6,8]=>1000001=>0111110=>1
[3,5,1,2,4,7,8,6]=>0000100=>1111011=>2
[3,1,2,5,7,4,8,6]=>0010000=>1101111=>2
[1,3,5,2,7,4,8,6]=>1000000=>0111111=>1
[1,3,5,7,2,4,8,6]=>1000000=>0111111=>1
[1,3,2,5,7,8,4,6]=>1010000=>0101111=>2
[1,3,5,2,7,8,4,6]=>1000000=>0111111=>1
[1,3,5,7,2,8,4,6]=>1000000=>0111111=>1
[1,3,5,7,8,2,4,6]=>1000000=>0111111=>1
[3,1,5,2,8,4,6,7]=>0000000=>1111111=>1
[3,5,1,2,8,4,6,7]=>0000000=>1111111=>1
[3,1,5,8,2,4,6,7]=>0000000=>1111111=>1
[3,5,1,8,2,4,6,7]=>0000000=>1111111=>1
[3,1,5,2,4,8,6,7]=>0000100=>1111011=>2
[3,5,1,2,4,8,6,7]=>0000100=>1111011=>2
[1,3,2,5,4,8,6,7]=>1010100=>0101011=>3
[1,3,5,2,4,8,6,7]=>1000100=>0111011=>2
[3,1,2,5,8,4,6,7]=>0010000=>1101111=>2
[1,3,2,5,8,4,6,7]=>1010000=>0101111=>2
[1,3,5,2,8,4,6,7]=>1000000=>0111111=>1
[1,3,5,8,2,4,6,7]=>1000000=>0111111=>1
[3,5,1,2,4,6,8,7]=>0000110=>1111001=>2
[3,1,2,5,4,6,8,7]=>0010110=>1101001=>3
[1,3,5,2,4,6,8,7]=>1000110=>0111001=>2
[1,3,5,2,6,4,8,7]=>1000010=>0111101=>2
[1,3,5,6,2,4,8,7]=>1000010=>0111101=>2
[3,1,2,5,6,8,4,7]=>0010000=>1101111=>2
[1,3,5,2,6,8,4,7]=>1000000=>0111111=>1
[1,3,5,6,2,8,4,7]=>1000000=>0111111=>1
[1,3,5,6,8,2,4,7]=>1000000=>0111111=>1
[3,5,1,2,4,6,7,8]=>0000111=>1111000=>1
[1,3,5,2,4,6,7,8]=>1000111=>0111000=>1
[1,3,5,6,2,4,7,8]=>1000011=>0111100=>1
[3,1,2,5,6,7,4,8]=>0010001=>1101110=>2
[1,3,5,2,6,7,4,8]=>1000001=>0111110=>1
[1,3,5,6,2,7,4,8]=>1000001=>0111110=>1
[1,3,5,6,7,2,4,8]=>1000001=>0111110=>1
[3,1,2,5,6,7,8,4]=>0010000=>1101111=>2
[1,3,5,6,7,8,2,4]=>1000000=>0111111=>1
[3,1,6,2,7,4,8,5]=>0000000=>1111111=>1
[3,6,1,2,7,4,8,5]=>0000000=>1111111=>1
[3,6,1,7,2,4,8,5]=>0000000=>1111111=>1
[3,6,7,1,2,4,8,5]=>0000000=>1111111=>1
[3,1,6,7,2,8,4,5]=>0000000=>1111111=>1
[3,6,1,7,2,8,4,5]=>0000000=>1111111=>1
[3,6,7,1,2,8,4,5]=>0000000=>1111111=>1
[3,6,1,7,8,2,4,5]=>0000000=>1111111=>1
[3,6,7,8,1,2,4,5]=>0000000=>1111111=>1
[3,1,6,2,7,4,5,8]=>0000001=>1111110=>1
[3,1,6,7,2,4,5,8]=>0000001=>1111110=>1
[3,6,7,1,2,4,5,8]=>0000001=>1111110=>1
[3,1,6,2,4,7,5,8]=>0000001=>1111110=>1
[3,6,1,2,4,7,5,8]=>0000001=>1111110=>1
[3,1,2,6,4,7,5,8]=>0010001=>1101110=>2
[1,3,2,6,4,7,5,8]=>1010001=>0101110=>2
[1,3,6,2,4,7,5,8]=>1000001=>0111110=>1
[1,3,6,2,7,4,5,8]=>1000001=>0111110=>1
[3,1,6,2,4,7,8,5]=>0000000=>1111111=>1
[3,6,1,2,4,7,8,5]=>0000000=>1111111=>1
[3,1,2,6,4,7,8,5]=>0010000=>1101111=>2
[1,3,6,2,4,7,8,5]=>1000000=>0111111=>1
[3,1,2,6,7,4,8,5]=>0010000=>1101111=>2
[1,3,6,2,7,4,8,5]=>1000000=>0111111=>1
[1,3,6,7,2,4,8,5]=>1000000=>0111111=>1
[3,1,2,6,7,8,4,5]=>0010000=>1101111=>2
[1,3,2,6,7,8,4,5]=>1010000=>0101111=>2
[1,3,6,2,7,8,4,5]=>1000000=>0111111=>1
[1,3,6,7,8,2,4,5]=>1000000=>0111111=>1
[3,1,6,2,8,4,5,7]=>0000000=>1111111=>1
[3,1,6,8,2,4,5,7]=>0000000=>1111111=>1
[3,6,1,8,2,4,5,7]=>0000000=>1111111=>1
[3,1,6,2,4,8,5,7]=>0000000=>1111111=>1
[3,6,1,2,4,8,5,7]=>0000000=>1111111=>1
[1,3,2,6,4,8,5,7]=>1010000=>0101111=>2
[1,3,6,2,4,8,5,7]=>1000000=>0111111=>1
[3,1,6,2,4,5,8,7]=>0000010=>1111101=>2
[3,1,2,6,4,5,8,7]=>0010010=>1101101=>3
[1,3,6,2,4,5,8,7]=>1000010=>0111101=>2
[3,1,2,4,6,5,8,7]=>0011010=>1100101=>3
[1,3,4,6,2,5,8,7]=>1000010=>0111101=>2
[3,1,2,4,6,8,5,7]=>0011000=>1100111=>2
[1,3,2,4,6,8,5,7]=>1011000=>0100111=>2
[1,3,4,6,8,2,5,7]=>1000000=>0111111=>1
[3,1,6,2,4,5,7,8]=>0000011=>1111100=>1
[3,6,1,2,4,5,7,8]=>0000011=>1111100=>1
[1,3,2,6,4,5,7,8]=>1010011=>0101100=>2
[1,3,6,2,4,5,7,8]=>1000011=>0111100=>1
[1,3,4,6,2,5,7,8]=>1000011=>0111100=>1
[3,1,2,4,6,7,5,8]=>0011001=>1100110=>2
[1,3,4,6,2,7,5,8]=>1000001=>0111110=>1
[3,1,2,4,6,7,8,5]=>0011000=>1100111=>2
[1,3,4,6,7,2,8,5]=>1000000=>0111111=>1
[3,7,1,2,8,4,5,6]=>0000000=>1111111=>1
[3,1,7,8,2,4,5,6]=>0000000=>1111111=>1
[3,7,8,1,2,4,5,6]=>0000000=>1111111=>1
[3,7,1,2,4,8,5,6]=>0000000=>1111111=>1
[3,1,2,7,4,8,5,6]=>0010000=>1101111=>2
[1,3,2,7,4,8,5,6]=>1010000=>0101111=>2
[1,3,7,2,4,8,5,6]=>1000000=>0111111=>1
[1,3,7,2,8,4,5,6]=>1000000=>0111111=>1
[1,3,7,8,2,4,5,6]=>1000000=>0111111=>1
[3,7,1,2,4,5,8,6]=>0000000=>1111111=>1
[1,3,7,2,4,5,8,6]=>1000000=>0111111=>1
[3,1,2,4,7,5,8,6]=>0011000=>1100111=>2
[1,3,2,4,7,5,8,6]=>1011000=>0100111=>2
[1,3,4,2,7,5,8,6]=>1001000=>0110111=>2
[1,3,4,7,2,5,8,6]=>1000000=>0111111=>1
[3,1,2,4,7,8,5,6]=>0011000=>1100111=>2
[1,3,4,7,8,2,5,6]=>1000000=>0111111=>1
[3,1,7,2,4,5,6,8]=>0000001=>1111110=>1
[3,7,1,2,4,5,6,8]=>0000001=>1111110=>1
[1,3,2,7,4,5,6,8]=>1010001=>0101110=>2
[1,3,7,2,4,5,6,8]=>1000001=>0111110=>1
[3,1,2,4,7,5,6,8]=>0011001=>1100110=>2
[1,3,4,7,2,5,6,8]=>1000001=>0111110=>1
[3,1,2,4,5,7,6,8]=>0011101=>1100010=>2
[1,3,4,5,7,2,6,8]=>1000001=>0111110=>1
[3,1,2,4,5,7,8,6]=>0011100=>1100011=>2
[1,3,4,5,7,8,2,6]=>1000000=>0111111=>1
[3,1,8,2,4,5,6,7]=>0000000=>1111111=>1
[3,8,1,2,4,5,6,7]=>0000000=>1111111=>1
[3,1,2,8,4,5,6,7]=>0010000=>1101111=>2
[1,3,2,8,4,5,6,7]=>1010000=>0101111=>2
[1,3,8,2,4,5,6,7]=>1000000=>0111111=>1
[3,1,2,4,8,5,6,7]=>0011000=>1100111=>2
[1,3,2,4,8,5,6,7]=>1011000=>0100111=>2
[1,3,4,2,8,5,6,7]=>1001000=>0110111=>2
[1,3,4,8,2,5,6,7]=>1000000=>0111111=>1
[3,1,2,4,5,8,6,7]=>0011100=>1100011=>2
[1,3,2,4,5,8,6,7]=>1011100=>0100011=>2
[1,3,4,2,5,8,6,7]=>1001100=>0110011=>2
[1,3,4,5,2,8,6,7]=>1000100=>0111011=>2
[1,3,4,5,8,2,6,7]=>1000000=>0111111=>1
[3,1,2,4,5,6,8,7]=>0011110=>1100001=>2
[1,3,4,5,6,8,2,7]=>1000000=>0111111=>1
[4,1,5,2,6,3,8,7]=>0000010=>1111101=>2
[4,5,1,2,6,3,8,7]=>0000010=>1111101=>2
[4,1,5,6,2,3,8,7]=>0000010=>1111101=>2
[4,5,1,6,2,3,8,7]=>0000010=>1111101=>2
[4,5,6,1,2,3,8,7]=>0000010=>1111101=>2
[4,1,5,2,6,8,3,7]=>0000000=>1111111=>1
[4,5,1,2,6,8,3,7]=>0000000=>1111111=>1
[4,5,1,6,2,8,3,7]=>0000000=>1111111=>1
[4,1,5,6,8,2,3,7]=>0000000=>1111111=>1
[4,5,6,1,8,2,3,7]=>0000000=>1111111=>1
[4,5,6,8,1,2,3,7]=>0000000=>1111111=>1
[4,1,5,2,6,3,7,8]=>0000011=>1111100=>1
[4,5,1,2,6,7,3,8]=>0000001=>1111110=>1
[4,5,1,6,2,7,3,8]=>0000001=>1111110=>1
[4,5,6,1,2,7,3,8]=>0000001=>1111110=>1
[4,1,5,6,7,2,3,8]=>0000001=>1111110=>1
[4,5,1,6,7,2,3,8]=>0000001=>1111110=>1
[4,5,6,1,7,2,3,8]=>0000001=>1111110=>1
[4,1,5,2,6,7,8,3]=>0000000=>1111111=>1
[4,5,1,2,6,7,8,3]=>0000000=>1111111=>1
[4,5,1,6,2,7,8,3]=>0000000=>1111111=>1
[4,5,6,1,2,7,8,3]=>0000000=>1111111=>1
[4,1,5,6,7,2,8,3]=>0000000=>1111111=>1
[4,5,1,6,7,2,8,3]=>0000000=>1111111=>1
[4,5,6,1,7,2,8,3]=>0000000=>1111111=>1
[4,5,6,7,1,2,8,3]=>0000000=>1111111=>1
[4,1,5,6,7,8,2,3]=>0000000=>1111111=>1
[4,5,1,6,7,8,2,3]=>0000000=>1111111=>1
[4,5,6,1,7,8,2,3]=>0000000=>1111111=>1
[4,5,6,7,1,8,2,3]=>0000000=>1111111=>1
[4,1,5,2,7,3,8,6]=>0000000=>1111111=>1
[4,5,1,2,7,3,8,6]=>0000000=>1111111=>1
[4,5,1,7,2,3,8,6]=>0000000=>1111111=>1
[4,1,5,2,7,8,3,6]=>0000000=>1111111=>1
[4,5,1,2,7,8,3,6]=>0000000=>1111111=>1
[4,1,5,7,2,8,3,6]=>0000000=>1111111=>1
[4,5,1,7,2,8,3,6]=>0000000=>1111111=>1
[4,5,7,1,2,8,3,6]=>0000000=>1111111=>1
[4,5,1,7,8,2,3,6]=>0000000=>1111111=>1
[4,5,7,8,1,2,3,6]=>0000000=>1111111=>1
[4,1,5,2,7,3,6,8]=>0000001=>1111110=>1
[4,5,1,2,7,3,6,8]=>0000001=>1111110=>1
[4,1,5,2,3,7,6,8]=>0000101=>1111010=>2
[4,5,1,2,3,7,6,8]=>0000101=>1111010=>2
[4,1,2,5,3,7,6,8]=>0000101=>1111010=>2
[1,4,2,5,3,7,6,8]=>1000101=>0111010=>2
[4,1,2,5,7,3,6,8]=>0000001=>1111110=>1
[1,4,2,5,7,3,6,8]=>1000001=>0111110=>1
[1,4,5,2,7,3,6,8]=>1000001=>0111110=>1
[1,4,5,7,2,3,6,8]=>1000001=>0111110=>1
[4,1,5,2,3,7,8,6]=>0000100=>1111011=>2
[4,1,2,5,3,7,8,6]=>0000100=>1111011=>2
[1,4,5,2,3,7,8,6]=>1000100=>0111011=>2
[4,1,2,5,7,3,8,6]=>0000000=>1111111=>1
[1,4,2,5,7,3,8,6]=>1000000=>0111111=>1
[1,4,5,2,7,3,8,6]=>1000000=>0111111=>1
[1,4,2,5,7,8,3,6]=>1000000=>0111111=>1
[1,4,5,2,7,8,3,6]=>1000000=>0111111=>1
[1,4,5,7,8,2,3,6]=>1000000=>0111111=>1
[4,1,5,2,8,3,6,7]=>0000000=>1111111=>1
[4,5,1,2,8,3,6,7]=>0000000=>1111111=>1
[4,5,1,8,2,3,6,7]=>0000000=>1111111=>1
[4,5,8,1,2,3,6,7]=>0000000=>1111111=>1
[4,1,5,2,3,8,6,7]=>0000100=>1111011=>2
[4,5,1,2,3,8,6,7]=>0000100=>1111011=>2
[4,1,2,5,3,8,6,7]=>0000100=>1111011=>2
[1,4,2,5,3,8,6,7]=>1000100=>0111011=>2
[1,4,5,2,3,8,6,7]=>1000100=>0111011=>2
[4,1,2,5,8,3,6,7]=>0000000=>1111111=>1
[1,4,2,5,8,3,6,7]=>1000000=>0111111=>1
[1,4,2,5,3,6,8,7]=>1000110=>0111001=>2
[4,1,2,5,6,3,8,7]=>0000010=>1111101=>2
[1,4,5,2,6,3,8,7]=>1000010=>0111101=>2
[4,1,2,5,6,8,3,7]=>0000000=>1111111=>1
[1,4,2,5,6,8,3,7]=>1000000=>0111111=>1
[1,4,5,2,6,8,3,7]=>1000000=>0111111=>1
[1,4,5,6,8,2,3,7]=>1000000=>0111111=>1
[4,1,2,5,3,6,7,8]=>0000111=>1111000=>1
[1,4,2,5,3,6,7,8]=>1000111=>0111000=>1
[1,4,5,2,3,6,7,8]=>1000111=>0111000=>1
[4,1,2,5,6,3,7,8]=>0000011=>1111100=>1
[1,4,5,2,6,3,7,8]=>1000011=>0111100=>1
[4,1,2,5,6,7,3,8]=>0000001=>1111110=>1
[1,4,2,5,6,7,3,8]=>1000001=>0111110=>1
[1,4,5,6,7,2,3,8]=>1000001=>0111110=>1
[4,1,2,5,6,7,8,3]=>0000000=>1111111=>1
[1,4,2,5,6,7,8,3]=>1000000=>0111111=>1
[1,4,5,2,6,7,8,3]=>1000000=>0111111=>1
[1,4,5,6,2,7,8,3]=>1000000=>0111111=>1
[1,4,5,6,7,2,8,3]=>1000000=>0111111=>1
[1,4,5,6,7,8,2,3]=>1000000=>0111111=>1
[4,1,6,2,7,3,8,5]=>0000000=>1111111=>1
[4,6,7,1,2,3,8,5]=>0000000=>1111111=>1
[4,6,7,1,8,2,3,5]=>0000000=>1111111=>1
[4,6,7,8,1,2,3,5]=>0000000=>1111111=>1
[4,1,6,2,7,3,5,8]=>0000001=>1111110=>1
[4,6,1,2,7,3,5,8]=>0000001=>1111110=>1
[4,1,6,7,2,3,5,8]=>0000001=>1111110=>1
[4,6,1,7,2,3,5,8]=>0000001=>1111110=>1
[4,6,1,2,3,7,5,8]=>0000001=>1111110=>1
[4,1,2,6,3,7,5,8]=>0000001=>1111110=>1
[1,4,2,6,3,7,5,8]=>1000001=>0111110=>1
[4,1,2,6,7,3,5,8]=>0000001=>1111110=>1
[1,4,2,6,7,3,5,8]=>1000001=>0111110=>1
[1,4,6,2,7,3,5,8]=>1000001=>0111110=>1
[1,4,6,7,2,3,5,8]=>1000001=>0111110=>1
[4,1,6,2,3,7,8,5]=>0000000=>1111111=>1
[4,1,2,6,3,7,8,5]=>0000000=>1111111=>1
[1,4,6,2,3,7,8,5]=>1000000=>0111111=>1
[4,1,2,6,7,3,8,5]=>0000000=>1111111=>1
[1,4,6,2,7,3,8,5]=>1000000=>0111111=>1
[1,4,2,6,7,8,3,5]=>1000000=>0111111=>1
[1,4,6,2,7,8,3,5]=>1000000=>0111111=>1
[1,4,6,7,2,8,3,5]=>1000000=>0111111=>1
[4,1,6,2,8,3,5,7]=>0000000=>1111111=>1
[4,6,1,2,8,3,5,7]=>0000000=>1111111=>1
[4,1,6,8,2,3,5,7]=>0000000=>1111111=>1
[4,6,1,8,2,3,5,7]=>0000000=>1111111=>1
[4,6,8,1,2,3,5,7]=>0000000=>1111111=>1
[4,6,1,2,3,8,5,7]=>0000000=>1111111=>1
[4,1,2,6,3,8,5,7]=>0000000=>1111111=>1
[1,4,2,6,3,8,5,7]=>1000000=>0111111=>1
[1,4,6,2,3,8,5,7]=>1000000=>0111111=>1
[1,4,2,6,8,3,5,7]=>1000000=>0111111=>1
[1,4,6,8,2,3,5,7]=>1000000=>0111111=>1
[4,1,6,2,3,5,8,7]=>0000010=>1111101=>2
[4,6,1,2,3,5,8,7]=>0000010=>1111101=>2
[1,4,2,6,3,5,8,7]=>1000010=>0111101=>2
[1,4,6,2,3,5,8,7]=>1000010=>0111101=>2
[4,1,2,3,6,5,8,7]=>0001010=>1110101=>3
[1,4,2,3,6,5,8,7]=>1001010=>0110101=>3
[1,2,4,6,3,5,8,7]=>1100010=>0011101=>2
[1,2,4,3,6,8,5,7]=>1101000=>0010111=>2
[1,2,4,6,3,8,5,7]=>1100000=>0011111=>1
[1,2,4,6,8,3,5,7]=>1100000=>0011111=>1
[4,1,6,2,3,5,7,8]=>0000011=>1111100=>1
[4,6,1,2,3,5,7,8]=>0000011=>1111100=>1
[1,4,2,6,3,5,7,8]=>1000011=>0111100=>1
[1,4,6,2,3,5,7,8]=>1000011=>0111100=>1
[1,4,2,3,6,5,7,8]=>1001011=>0110100=>2
[1,2,4,6,3,5,7,8]=>1100011=>0011100=>1
[1,4,2,3,6,7,5,8]=>1001001=>0110110=>2
[4,1,2,3,6,7,8,5]=>0001000=>1110111=>2
[1,4,2,3,6,7,8,5]=>1001000=>0110111=>2
[1,2,4,6,7,8,3,5]=>1100000=>0011111=>1
[4,1,7,2,8,3,5,6]=>0000000=>1111111=>1
[4,1,7,8,2,3,5,6]=>0000000=>1111111=>1
[4,7,1,8,2,3,5,6]=>0000000=>1111111=>1
[4,1,7,2,3,8,5,6]=>0000000=>1111111=>1
[4,7,1,2,3,8,5,6]=>0000000=>1111111=>1
[1,4,2,7,3,8,5,6]=>1000000=>0111111=>1
[1,4,7,2,3,8,5,6]=>1000000=>0111111=>1
[4,1,2,7,8,3,5,6]=>0000000=>1111111=>1
[1,4,2,7,8,3,5,6]=>1000000=>0111111=>1
[1,4,7,2,8,3,5,6]=>1000000=>0111111=>1
[1,4,7,8,2,3,5,6]=>1000000=>0111111=>1
[4,1,7,2,3,5,8,6]=>0000000=>1111111=>1
[4,1,2,7,3,5,8,6]=>0000000=>1111111=>1
[1,4,2,7,3,5,8,6]=>1000000=>0111111=>1
[1,4,7,2,3,5,8,6]=>1000000=>0111111=>1
[4,1,2,3,7,5,8,6]=>0001000=>1110111=>2
[1,4,2,3,7,5,8,6]=>1001000=>0110111=>2
[1,2,4,3,7,5,8,6]=>1101000=>0010111=>2
[1,2,4,7,3,5,8,6]=>1100000=>0011111=>1
[1,4,2,3,7,8,5,6]=>1001000=>0110111=>2
[1,2,4,3,7,8,5,6]=>1101000=>0010111=>2
[1,2,4,7,3,8,5,6]=>1100000=>0011111=>1
[1,2,4,7,8,3,5,6]=>1100000=>0011111=>1
[4,1,7,2,3,5,6,8]=>0000001=>1111110=>1
[4,1,2,7,3,5,6,8]=>0000001=>1111110=>1
[1,4,2,7,3,5,6,8]=>1000001=>0111110=>1
[1,4,7,2,3,5,6,8]=>1000001=>0111110=>1
[4,1,2,3,7,5,6,8]=>0001001=>1110110=>2
[1,4,2,3,7,5,6,8]=>1001001=>0110110=>2
[1,2,4,3,7,5,6,8]=>1101001=>0010110=>2
[1,2,4,7,3,5,6,8]=>1100001=>0011110=>1
[4,1,2,3,5,7,6,8]=>0001101=>1110010=>2
[1,4,2,3,5,7,6,8]=>1001101=>0110010=>2
[1,2,4,5,7,3,6,8]=>1100001=>0011110=>1
[4,1,2,3,5,7,8,6]=>0001100=>1110011=>2
[1,4,2,3,5,7,8,6]=>1001100=>0110011=>2
[1,2,4,5,7,3,8,6]=>1100000=>0011111=>1
[1,2,4,5,7,8,3,6]=>1100000=>0011111=>1
[4,1,8,2,3,5,6,7]=>0000000=>1111111=>1
[4,8,1,2,3,5,6,7]=>0000000=>1111111=>1
[1,4,2,8,3,5,6,7]=>1000000=>0111111=>1
[1,4,8,2,3,5,6,7]=>1000000=>0111111=>1
[4,1,2,3,8,5,6,7]=>0001000=>1110111=>2
[1,4,2,3,8,5,6,7]=>1001000=>0110111=>2
[1,2,4,3,8,5,6,7]=>1101000=>0010111=>2
[1,2,4,8,3,5,6,7]=>1100000=>0011111=>1
[4,1,2,3,5,8,6,7]=>0001100=>1110011=>2
[1,4,2,3,5,8,6,7]=>1001100=>0110011=>2
[1,2,4,3,5,8,6,7]=>1101100=>0010011=>2
[1,2,4,5,8,3,6,7]=>1100000=>0011111=>1
[1,4,2,3,5,6,8,7]=>1001110=>0110001=>2
[1,2,4,5,6,8,3,7]=>1100000=>0011111=>1
[1,4,2,3,5,6,7,8]=>1001111=>0110000=>1
[5,1,6,2,7,3,8,4]=>0000000=>1111111=>1
[5,6,1,2,7,3,8,4]=>0000000=>1111111=>1
[5,6,1,7,2,3,8,4]=>0000000=>1111111=>1
[5,6,7,1,2,3,8,4]=>0000000=>1111111=>1
[5,6,1,2,7,8,3,4]=>0000000=>1111111=>1
[5,1,6,7,2,8,3,4]=>0000000=>1111111=>1
[5,6,7,1,2,8,3,4]=>0000000=>1111111=>1
[5,1,6,7,8,2,3,4]=>0000000=>1111111=>1
[5,6,1,7,8,2,3,4]=>0000000=>1111111=>1
[5,6,7,1,8,2,3,4]=>0000000=>1111111=>1
[5,1,6,2,7,3,4,8]=>0000001=>1111110=>1
[5,1,6,2,3,7,4,8]=>0000001=>1111110=>1
[5,1,2,6,3,7,4,8]=>0000001=>1111110=>1
[1,5,2,6,3,7,4,8]=>1000001=>0111110=>1
[5,1,2,6,7,3,4,8]=>0000001=>1111110=>1
[1,5,2,6,7,3,4,8]=>1000001=>0111110=>1
[1,5,6,7,2,3,4,8]=>1000001=>0111110=>1
[5,1,6,2,3,7,8,4]=>0000000=>1111111=>1
[5,6,1,2,3,7,8,4]=>0000000=>1111111=>1
[5,1,2,6,3,7,8,4]=>0000000=>1111111=>1
[1,5,2,6,3,7,8,4]=>1000000=>0111111=>1
[1,5,6,2,3,7,8,4]=>1000000=>0111111=>1
[5,1,2,6,7,3,8,4]=>0000000=>1111111=>1
[1,5,6,7,2,3,8,4]=>1000000=>0111111=>1
[5,1,2,6,7,8,3,4]=>0000000=>1111111=>1
[1,5,6,7,2,8,3,4]=>1000000=>0111111=>1
[1,5,6,7,8,2,3,4]=>1000000=>0111111=>1
[5,1,6,2,8,3,4,7]=>0000000=>1111111=>1
[5,6,1,2,8,3,4,7]=>0000000=>1111111=>1
[5,6,1,8,2,3,4,7]=>0000000=>1111111=>1
[5,6,8,1,2,3,4,7]=>0000000=>1111111=>1
[5,1,6,2,3,8,4,7]=>0000000=>1111111=>1
[5,6,1,2,3,8,4,7]=>0000000=>1111111=>1
[5,1,2,6,3,8,4,7]=>0000000=>1111111=>1
[1,5,2,6,3,8,4,7]=>1000000=>0111111=>1
[1,5,6,2,3,8,4,7]=>1000000=>0111111=>1
[5,1,2,6,8,3,4,7]=>0000000=>1111111=>1
[1,5,2,6,8,3,4,7]=>1000000=>0111111=>1
[1,5,6,2,8,3,4,7]=>1000000=>0111111=>1
[1,5,2,6,3,4,8,7]=>1000010=>0111101=>2
[1,5,6,2,3,4,8,7]=>1000010=>0111101=>2
[1,5,2,3,6,4,8,7]=>1000010=>0111101=>2
[1,2,5,3,6,4,8,7]=>1100010=>0011101=>2
[1,2,5,6,3,4,8,7]=>1100010=>0011101=>2
[5,1,2,3,6,8,4,7]=>0000000=>1111111=>1
[1,5,2,3,6,8,4,7]=>1000000=>0111111=>1
[1,2,5,6,3,8,4,7]=>1100000=>0011111=>1
[1,2,5,6,8,3,4,7]=>1100000=>0011111=>1
[5,1,6,2,3,4,7,8]=>0000011=>1111100=>1
[5,1,2,6,3,4,7,8]=>0000011=>1111100=>1
[1,5,2,6,3,4,7,8]=>1000011=>0111100=>1
[1,5,6,2,3,4,7,8]=>1000011=>0111100=>1
[5,1,2,3,6,4,7,8]=>0000011=>1111100=>1
[1,5,2,3,6,4,7,8]=>1000011=>0111100=>1
[1,2,5,6,3,4,7,8]=>1100011=>0011100=>1
[1,5,2,3,6,7,4,8]=>1000001=>0111110=>1
[1,2,5,3,6,7,4,8]=>1100001=>0011110=>1
[1,2,5,6,3,7,4,8]=>1100001=>0011110=>1
[5,1,2,3,6,7,8,4]=>0000000=>1111111=>1
[1,5,2,3,6,7,8,4]=>1000000=>0111111=>1
[1,2,5,3,6,7,8,4]=>1100000=>0011111=>1
[1,2,5,6,3,7,8,4]=>1100000=>0011111=>1
[1,2,5,6,7,3,8,4]=>1100000=>0011111=>1
[1,2,5,6,7,8,3,4]=>1100000=>0011111=>1
[5,1,7,2,8,3,4,6]=>0000000=>1111111=>1
[5,7,1,2,8,3,4,6]=>0000000=>1111111=>1
[5,1,7,8,2,3,4,6]=>0000000=>1111111=>1
[5,7,8,1,2,3,4,6]=>0000000=>1111111=>1
[5,1,2,7,3,8,4,6]=>0000000=>1111111=>1
[1,5,2,7,3,8,4,6]=>1000000=>0111111=>1
[1,5,7,2,3,8,4,6]=>1000000=>0111111=>1
[5,1,2,7,8,3,4,6]=>0000000=>1111111=>1
[1,5,2,7,8,3,4,6]=>1000000=>0111111=>1
[1,5,7,2,8,3,4,6]=>1000000=>0111111=>1
[1,5,7,8,2,3,4,6]=>1000000=>0111111=>1
[5,1,2,7,3,4,8,6]=>0000000=>1111111=>1
[1,5,2,7,3,4,8,6]=>1000000=>0111111=>1
[1,5,7,2,3,4,8,6]=>1000000=>0111111=>1
[5,1,2,3,7,4,8,6]=>0000000=>1111111=>1
[1,5,2,3,7,4,8,6]=>1000000=>0111111=>1
[1,2,5,3,7,4,8,6]=>1100000=>0011111=>1
[1,2,5,7,3,4,8,6]=>1100000=>0011111=>1
[5,1,2,3,7,8,4,6]=>0000000=>1111111=>1
[1,5,2,3,7,8,4,6]=>1000000=>0111111=>1
[1,2,5,3,7,8,4,6]=>1100000=>0011111=>1
[1,2,5,7,3,8,4,6]=>1100000=>0011111=>1
[1,2,5,7,8,3,4,6]=>1100000=>0011111=>1
[5,1,7,2,3,4,6,8]=>0000001=>1111110=>1
[5,7,1,2,3,4,6,8]=>0000001=>1111110=>1
[1,5,2,7,3,4,6,8]=>1000001=>0111110=>1
[1,5,2,3,7,4,6,8]=>1000001=>0111110=>1
[1,2,5,3,7,4,6,8]=>1100001=>0011110=>1
[1,2,5,7,3,4,6,8]=>1100001=>0011110=>1
[1,5,2,3,4,7,6,8]=>1000101=>0111010=>2
[1,2,5,3,4,7,6,8]=>1100101=>0011010=>2
[1,2,3,5,7,4,6,8]=>1110001=>0001110=>1
[1,5,2,3,4,7,8,6]=>1000100=>0111011=>2
[1,2,5,3,4,7,8,6]=>1100100=>0011011=>2
[1,2,3,5,7,4,8,6]=>1110000=>0001111=>1
[1,2,3,5,7,8,4,6]=>1110000=>0001111=>1
[5,8,1,2,3,4,6,7]=>0000000=>1111111=>1
[5,1,2,8,3,4,6,7]=>0000000=>1111111=>1
[1,5,2,8,3,4,6,7]=>1000000=>0111111=>1
[1,5,2,3,8,4,6,7]=>1000000=>0111111=>1
[1,2,5,3,8,4,6,7]=>1100000=>0011111=>1
[1,2,5,8,3,4,6,7]=>1100000=>0011111=>1
[5,1,2,3,4,8,6,7]=>0000100=>1111011=>2
[1,5,2,3,4,8,6,7]=>1000100=>0111011=>2
[1,2,5,3,4,8,6,7]=>1100100=>0011011=>2
[1,2,3,5,4,8,6,7]=>1110100=>0001011=>2
[1,2,3,5,8,4,6,7]=>1110000=>0001111=>1
[5,1,2,3,4,6,8,7]=>0000110=>1111001=>2
[1,5,2,3,4,6,8,7]=>1000110=>0111001=>2
[1,2,5,3,4,6,8,7]=>1100110=>0011001=>2
[1,2,3,5,6,8,4,7]=>1110000=>0001111=>1
[1,5,2,3,4,6,7,8]=>1000111=>0111000=>1
[1,2,5,3,4,6,7,8]=>1100111=>0011000=>1
[6,1,7,2,8,3,4,5]=>0000000=>1111111=>1
[6,7,1,2,8,3,4,5]=>0000000=>1111111=>1
[6,1,7,8,2,3,4,5]=>0000000=>1111111=>1
[6,7,1,8,2,3,4,5]=>0000000=>1111111=>1
[6,1,7,2,3,8,4,5]=>0000000=>1111111=>1
[6,7,1,2,3,8,4,5]=>0000000=>1111111=>1
[6,1,2,7,3,8,4,5]=>0000000=>1111111=>1
[1,6,2,7,3,8,4,5]=>1000000=>0111111=>1
[1,6,7,2,3,8,4,5]=>1000000=>0111111=>1
[6,1,2,7,8,3,4,5]=>0000000=>1111111=>1
[1,6,2,7,8,3,4,5]=>1000000=>0111111=>1
[1,6,7,2,8,3,4,5]=>1000000=>0111111=>1
[1,6,7,8,2,3,4,5]=>1000000=>0111111=>1
[6,1,7,2,3,4,8,5]=>0000000=>1111111=>1
[6,7,1,2,3,4,8,5]=>0000000=>1111111=>1
[6,1,2,7,3,4,8,5]=>0000000=>1111111=>1
[1,6,2,7,3,4,8,5]=>1000000=>0111111=>1
[1,6,7,2,3,4,8,5]=>1000000=>0111111=>1
[6,1,2,3,7,4,8,5]=>0000000=>1111111=>1
[1,6,2,3,7,4,8,5]=>1000000=>0111111=>1
[1,2,6,3,7,4,8,5]=>1100000=>0011111=>1
[1,2,6,7,3,4,8,5]=>1100000=>0011111=>1
[6,1,2,3,7,8,4,5]=>0000000=>1111111=>1
[1,6,2,3,7,8,4,5]=>1000000=>0111111=>1
[1,2,6,3,7,8,4,5]=>1100000=>0011111=>1
[1,2,6,7,3,8,4,5]=>1100000=>0011111=>1
[1,2,6,7,8,3,4,5]=>1100000=>0011111=>1
[6,1,7,2,3,4,5,8]=>0000001=>1111110=>1
[6,1,2,7,3,4,5,8]=>0000001=>1111110=>1
[1,6,2,7,3,4,5,8]=>1000001=>0111110=>1
[1,6,7,2,3,4,5,8]=>1000001=>0111110=>1
[1,6,2,3,7,4,5,8]=>1000001=>0111110=>1
[1,2,6,3,7,4,5,8]=>1100001=>0011110=>1
[1,2,6,7,3,4,5,8]=>1100001=>0011110=>1
[6,1,2,3,4,7,5,8]=>0000001=>1111110=>1
[1,6,2,3,4,7,5,8]=>1000001=>0111110=>1
[1,2,6,3,4,7,5,8]=>1100001=>0011110=>1
[1,2,3,6,4,7,5,8]=>1110001=>0001110=>1
[1,2,3,6,7,4,5,8]=>1110001=>0001110=>1
[6,1,2,3,4,7,8,5]=>0000000=>1111111=>1
[1,6,2,3,4,7,8,5]=>1000000=>0111111=>1
[1,2,6,3,4,7,8,5]=>1100000=>0011111=>1
[1,2,3,6,4,7,8,5]=>1110000=>0001111=>1
[1,2,3,6,7,4,8,5]=>1110000=>0001111=>1
[1,2,3,6,7,8,4,5]=>1110000=>0001111=>1
[6,1,8,2,3,4,5,7]=>0000000=>1111111=>1
[6,8,1,2,3,4,5,7]=>0000000=>1111111=>1
[6,1,2,8,3,4,5,7]=>0000000=>1111111=>1
[1,6,2,8,3,4,5,7]=>1000000=>0111111=>1
[1,6,8,2,3,4,5,7]=>1000000=>0111111=>1
[6,1,2,3,8,4,5,7]=>0000000=>1111111=>1
[1,6,2,3,8,4,5,7]=>1000000=>0111111=>1
[1,2,6,3,8,4,5,7]=>1100000=>0011111=>1
[1,2,6,8,3,4,5,7]=>1100000=>0011111=>1
[6,1,2,3,4,8,5,7]=>0000000=>1111111=>1
[1,6,2,3,4,8,5,7]=>1000000=>0111111=>1
[1,2,6,3,4,8,5,7]=>1100000=>0011111=>1
[1,2,3,6,4,8,5,7]=>1110000=>0001111=>1
[1,2,3,6,8,4,5,7]=>1110000=>0001111=>1
[6,1,2,3,4,5,8,7]=>0000010=>1111101=>2
[1,6,2,3,4,5,8,7]=>1000010=>0111101=>2
[1,2,6,3,4,5,8,7]=>1100010=>0011101=>2
[1,2,3,6,4,5,8,7]=>1110010=>0001101=>2
[1,2,3,4,6,8,5,7]=>1111000=>0000111=>1
[1,6,2,3,4,5,7,8]=>1000011=>0111100=>1
[1,2,6,3,4,5,7,8]=>1100011=>0011100=>1
[1,2,3,6,4,5,7,8]=>1110011=>0001100=>1
[7,1,8,2,3,4,5,6]=>0000000=>1111111=>1
[7,1,2,8,3,4,5,6]=>0000000=>1111111=>1
[1,7,2,8,3,4,5,6]=>1000000=>0111111=>1
[1,7,8,2,3,4,5,6]=>1000000=>0111111=>1
[7,1,2,3,8,4,5,6]=>0000000=>1111111=>1
[1,7,2,3,8,4,5,6]=>1000000=>0111111=>1
[1,2,7,3,8,4,5,6]=>1100000=>0011111=>1
[1,2,7,8,3,4,5,6]=>1100000=>0011111=>1
[7,1,2,3,4,8,5,6]=>0000000=>1111111=>1
[1,7,2,3,4,8,5,6]=>1000000=>0111111=>1
[1,2,7,3,4,8,5,6]=>1100000=>0011111=>1
[1,2,3,7,4,8,5,6]=>1110000=>0001111=>1
[1,2,3,7,8,4,5,6]=>1110000=>0001111=>1
[7,1,2,3,4,5,8,6]=>0000000=>1111111=>1
[1,7,2,3,4,5,8,6]=>1000000=>0111111=>1
[1,2,7,3,4,5,8,6]=>1100000=>0011111=>1
[1,2,3,7,4,5,8,6]=>1110000=>0001111=>1
[1,2,3,4,7,5,8,6]=>1111000=>0000111=>1
[1,2,3,4,7,8,5,6]=>1111000=>0000111=>1
[1,7,2,3,4,5,6,8]=>1000001=>0111110=>1
[1,2,7,3,4,5,6,8]=>1100001=>0011110=>1
[1,2,3,7,4,5,6,8]=>1110001=>0001110=>1
[1,2,3,4,7,5,6,8]=>1111001=>0000110=>1
[1,8,2,3,4,5,6,7]=>1000000=>0111111=>1
[1,2,8,3,4,5,6,7]=>1100000=>0011111=>1
[1,2,3,8,4,5,6,7]=>1110000=>0001111=>1
[1,2,3,4,8,5,6,7]=>1111000=>0000111=>1
[1,2,3,4,5,8,6,7]=>1111100=>0000011=>1
[5,3,2,6,1,4,8,7]=>0000010=>1111101=>2
[7,3,2,5,4,8,1,6]=>0000000=>1111111=>1
[8,4,5,2,3,7,6,1]=>0000000=>1111111=>1
[7,4,5,2,3,8,1,6]=>0000000=>1111111=>1
[6,4,5,2,3,1,8,7]=>0000010=>1111101=>2
[5,4,6,2,1,3,8,7]=>0000010=>1111101=>2
[3,6,1,5,4,2,8,7]=>0000010=>1111101=>2
[4,6,5,1,3,2,8,7]=>0000010=>1111101=>2
[5,6,4,3,1,2,8,7]=>0000010=>1111101=>2
[7,5,4,3,2,8,1,6]=>0000000=>1111111=>1
[8,6,4,3,7,2,5,1]=>0000000=>1111111=>1
[7,6,4,3,8,2,1,5]=>0000000=>1111111=>1
[6,7,4,3,8,1,2,5]=>0000000=>1111111=>1
[5,7,4,3,1,8,2,6]=>0000000=>1111111=>1
[4,7,5,1,3,8,2,6]=>0000000=>1111111=>1
[3,7,1,5,4,8,2,6]=>0000000=>1111111=>1
[2,1,7,5,4,8,3,6]=>0100000=>1011111=>2
[3,8,1,5,4,7,6,2]=>0000000=>1111111=>1
[4,8,5,1,3,7,6,2]=>0000000=>1111111=>1
[5,8,4,3,1,7,6,2]=>0000000=>1111111=>1
[6,8,4,3,7,1,5,2]=>0000000=>1111111=>1
[7,8,4,3,6,5,1,2]=>0000000=>1111111=>1
[6,8,5,7,3,1,4,2]=>0000000=>1111111=>1
[5,8,6,7,1,3,4,2]=>0000000=>1111111=>1
[4,8,6,1,7,3,5,2]=>0000000=>1111111=>1
[3,8,1,6,7,4,5,2]=>0000000=>1111111=>1
[2,1,8,6,7,4,5,3]=>0100000=>1011111=>2
[2,1,7,6,8,4,3,5]=>0100000=>1011111=>2
[3,7,1,6,8,4,2,5]=>0000000=>1111111=>1
[4,7,6,1,8,3,2,5]=>0000000=>1111111=>1
[5,7,6,8,1,3,2,4]=>0000000=>1111111=>1
[5,4,7,2,1,8,3,6]=>0000000=>1111111=>1
[6,4,7,2,8,1,3,5]=>0000000=>1111111=>1
[7,4,6,2,8,3,1,5]=>0000000=>1111111=>1
[8,4,6,2,7,3,5,1]=>0000000=>1111111=>1
[8,3,2,6,7,4,5,1]=>0000000=>1111111=>1
[7,3,2,6,8,4,1,5]=>0000000=>1111111=>1
[6,3,2,7,8,1,4,5]=>0000000=>1111111=>1
[5,3,2,7,1,8,4,6]=>0000000=>1111111=>1
[4,3,2,1,7,8,5,6]=>0001000=>1110111=>2
[3,4,1,2,8,7,6,5]=>0001000=>1110111=>2
[5,3,2,8,1,7,6,4]=>0000000=>1111111=>1
[6,3,2,8,7,1,5,4]=>0000000=>1111111=>1
[7,3,2,8,6,5,1,4]=>0000000=>1111111=>1
[8,4,7,2,6,5,3,1]=>0000000=>1111111=>1
[7,4,8,2,6,5,1,3]=>0000000=>1111111=>1
[6,4,8,2,7,1,5,3]=>0000000=>1111111=>1
[5,4,8,2,1,7,6,3]=>0000000=>1111111=>1
[4,5,8,1,2,7,6,3]=>0000000=>1111111=>1
[3,5,1,8,2,7,6,4]=>0000000=>1111111=>1
[2,1,5,8,3,7,6,4]=>0100000=>1011111=>2
[2,1,6,8,7,3,5,4]=>0100000=>1011111=>2
[3,6,1,8,7,2,5,4]=>0000000=>1111111=>1
[4,6,8,1,7,2,5,3]=>0000000=>1111111=>1
[5,6,8,7,1,2,4,3]=>0000000=>1111111=>1
[6,5,8,7,2,1,4,3]=>0000000=>1111111=>1
[7,5,8,6,2,4,1,3]=>0000000=>1111111=>1
[8,5,7,6,2,4,3,1]=>0000000=>1111111=>1
[5,7,8,6,1,4,2,3]=>0000000=>1111111=>1
[4,7,8,1,6,5,2,3]=>0000000=>1111111=>1
[3,7,1,8,6,5,2,4]=>0000000=>1111111=>1
[2,1,7,8,6,5,3,4]=>0100000=>1011111=>2
[3,8,1,7,6,5,4,2]=>0000000=>1111111=>1
[4,8,7,1,6,5,3,2]=>0000000=>1111111=>1
[5,8,7,6,1,4,3,2]=>0000000=>1111111=>1
[6,8,7,5,4,1,3,2]=>0000000=>1111111=>1
[2,1,4,3,6,5,8,7,10,9]=>010101010=>101010101=>5
[3,4,1,2,6,5,8,7,10,9]=>000101010=>111010101=>4
[4,3,2,1,6,5,8,7,10,9]=>000101010=>111010101=>4
[6,3,2,5,4,1,8,7,10,9]=>000001010=>111110101=>3
[8,3,2,5,4,7,6,1,10,9]=>000000010=>111111101=>2
[10,3,2,5,4,7,6,9,8,1]=>000000000=>111111111=>1
[2,1,6,5,4,3,8,7,10,9]=>010001010=>101110101=>4
[6,5,4,3,2,1,8,7,10,9]=>000001010=>111110101=>3
[8,5,4,3,2,7,6,1,10,9]=>000000010=>111111101=>2
[10,5,4,3,2,7,6,9,8,1]=>000000000=>111111111=>1
[2,1,8,5,4,7,6,3,10,9]=>010000010=>101111101=>3
[8,7,4,3,6,5,2,1,10,9]=>000000010=>111111101=>2
[10,7,4,3,6,5,2,9,8,1]=>000000000=>111111111=>1
[2,1,10,5,4,7,6,9,8,3]=>010000000=>101111111=>2
[10,9,4,3,6,5,8,7,2,1]=>000000000=>111111111=>1
[8,9,5,6,3,4,10,1,2,7]=>000000000=>111111111=>1
[2,1,4,3,8,7,6,5,10,9]=>010100010=>101011101=>4
[4,3,2,1,8,7,6,5,10,9]=>000100010=>111011101=>3
[8,3,2,7,6,5,4,1,10,9]=>000000010=>111111101=>2
[10,3,2,7,6,5,4,9,8,1]=>000000000=>111111111=>1
[2,1,8,7,6,5,4,3,10,9]=>010000010=>101111101=>3
[8,7,6,5,4,3,2,1,10,9]=>000000010=>111111101=>2
[9,7,6,5,4,3,2,10,1,8]=>000000000=>111111111=>1
[10,7,6,5,4,3,2,9,8,1]=>000000000=>111111111=>1
[2,1,10,7,6,5,4,9,8,3]=>010000000=>101111111=>2
[10,9,6,5,4,3,8,7,2,1]=>000000000=>111111111=>1
[2,1,4,3,10,7,6,9,8,5]=>010100000=>101011111=>3
[4,3,2,1,10,7,6,9,8,5]=>000100000=>111011111=>2
[10,3,2,9,6,5,8,7,4,1]=>000000000=>111111111=>1
[2,1,10,9,6,5,8,7,4,3]=>010000000=>101111111=>2
[10,9,8,5,4,7,6,3,2,1]=>000000000=>111111111=>1
[10,8,9,6,7,4,5,2,3,1]=>000000000=>111111111=>1
[6,7,8,9,10,1,2,3,4,5]=>000000000=>111111111=>1
[7,3,2,8,9,10,1,4,5,6]=>000000000=>111111111=>1
[8,5,4,3,2,9,10,1,6,7]=>000000000=>111111111=>1
[2,1,4,3,6,5,10,9,8,7]=>010101000=>101010111=>4
[4,3,2,1,6,5,10,9,8,7]=>000101000=>111010111=>3
[6,3,2,5,4,1,10,9,8,7]=>000001000=>111110111=>2
[10,3,2,5,4,9,8,7,6,1]=>000000000=>111111111=>1
[2,1,6,5,4,3,10,9,8,7]=>010001000=>101110111=>3
[6,5,4,3,2,1,10,9,8,7]=>000001000=>111110111=>2
[10,5,4,3,2,9,8,7,6,1]=>000000000=>111111111=>1
[2,1,10,5,4,9,8,7,6,3]=>010000000=>101111111=>2
[10,9,4,3,8,7,6,5,2,1]=>000000000=>111111111=>1
[9,7,5,10,3,8,2,6,1,4]=>000000000=>111111111=>1
[2,1,4,3,10,9,8,7,6,5]=>010100000=>101011111=>3
[4,3,2,1,10,9,8,7,6,5]=>000100000=>111011111=>2
[10,3,2,9,8,7,6,5,4,1]=>000000000=>111111111=>1
[2,1,10,9,8,7,6,5,4,3]=>010000000=>101111111=>2
[9,10,8,7,6,5,4,3,1,2]=>000000000=>111111111=>1
[10,9,8,7,6,5,4,3,2,1]=>000000000=>111111111=>1
[3,2,5,1,4,6,7,8]=>0000111=>1111000=>1
[4,2,5,1,3,6,7,8]=>0000111=>1111000=>1
[5,2,4,1,3,6,7,8]=>0000111=>1111000=>1
[3,2,6,1,4,5,7,8]=>0000011=>1111100=>1
[4,2,6,1,3,5,7,8]=>0000011=>1111100=>1
[5,3,6,1,2,4,7,8]=>0000011=>1111100=>1
[6,2,4,1,3,5,7,8]=>0000011=>1111100=>1
[5,3,7,1,2,4,6,8]=>0000001=>1111110=>1
[5,4,7,1,2,3,6,8]=>0000001=>1111110=>1
[6,2,7,1,3,4,5,8]=>0000001=>1111110=>1
[6,3,7,1,2,4,5,8]=>0000001=>1111110=>1
[6,4,7,1,2,3,5,8]=>0000001=>1111110=>1
[7,3,5,1,2,4,6,8]=>0000001=>1111110=>1
[7,3,6,1,2,4,5,8]=>0000001=>1111110=>1
[7,4,6,1,2,3,5,8]=>0000001=>1111110=>1
[3,2,8,1,4,5,6,7]=>0000000=>1111111=>1
[4,2,8,1,3,5,6,7]=>0000000=>1111111=>1
[5,4,8,1,2,3,6,7]=>0000000=>1111111=>1
[6,2,8,1,3,4,5,7]=>0000000=>1111111=>1
[6,3,8,1,2,4,5,7]=>0000000=>1111111=>1
[6,5,8,1,2,3,4,7]=>0000000=>1111111=>1
[7,2,8,1,3,4,5,6]=>0000000=>1111111=>1
[7,5,8,1,2,3,4,6]=>0000000=>1111111=>1
[8,3,5,1,2,4,6,7]=>0000000=>1111111=>1
[8,5,7,1,2,3,4,6]=>0000000=>1111111=>1
[3,2,5,7,1,4,6,8]=>0000001=>1111110=>1
[4,2,5,7,1,3,6,8]=>0000001=>1111110=>1
[5,2,4,7,1,3,6,8]=>0000001=>1111110=>1
[4,2,6,7,1,3,5,8]=>0000001=>1111110=>1
[5,2,6,7,1,3,4,8]=>0000001=>1111110=>1
[5,3,6,7,1,2,4,8]=>0000001=>1111110=>1
[6,2,5,7,1,3,4,8]=>0000001=>1111110=>1
[6,3,5,7,1,2,4,8]=>0000001=>1111110=>1
[3,2,5,8,1,4,6,7]=>0000000=>1111111=>1
[4,2,5,8,1,3,6,7]=>0000000=>1111111=>1
[4,3,5,8,1,2,6,7]=>0000000=>1111111=>1
[5,2,4,8,1,3,6,7]=>0000000=>1111111=>1
[3,2,6,8,1,4,5,7]=>0000000=>1111111=>1
[4,2,6,8,1,3,5,7]=>0000000=>1111111=>1
[5,2,6,8,1,3,4,7]=>0000000=>1111111=>1
[6,2,4,8,1,3,5,7]=>0000000=>1111111=>1
[6,2,5,8,1,3,4,7]=>0000000=>1111111=>1
[6,3,5,8,1,2,4,7]=>0000000=>1111111=>1
[3,2,7,8,1,4,5,6]=>0000000=>1111111=>1
[4,3,7,8,1,2,5,6]=>0000000=>1111111=>1
[5,3,7,8,1,2,4,6]=>0000000=>1111111=>1
[5,4,7,8,1,2,3,6]=>0000000=>1111111=>1
[6,2,7,8,1,3,4,5]=>0000000=>1111111=>1
[6,3,7,8,1,2,4,5]=>0000000=>1111111=>1
[6,4,7,8,1,2,3,5]=>0000000=>1111111=>1
[7,2,4,8,1,3,5,6]=>0000000=>1111111=>1
[7,3,4,8,1,2,5,6]=>0000000=>1111111=>1
[7,4,5,8,1,2,3,6]=>0000000=>1111111=>1
[8,3,5,7,1,2,4,6]=>0000000=>1111111=>1
[8,2,6,7,1,3,4,5]=>0000000=>1111111=>1
[8,4,6,7,1,2,3,5]=>0000000=>1111111=>1
[3,6,2,5,1,4,7,8]=>0000011=>1111100=>1
[4,6,2,5,1,3,7,8]=>0000011=>1111100=>1
[4,6,3,5,1,2,7,8]=>0000011=>1111100=>1
[5,6,2,4,1,3,7,8]=>0000011=>1111100=>1
[3,7,2,5,1,4,6,8]=>0000001=>1111110=>1
[4,7,3,5,1,2,6,8]=>0000001=>1111110=>1
[5,7,2,4,1,3,6,8]=>0000001=>1111110=>1
[3,7,2,6,1,4,5,8]=>0000001=>1111110=>1
[4,7,3,6,1,2,5,8]=>0000001=>1111110=>1
[5,7,2,6,1,3,4,8]=>0000001=>1111110=>1
[6,7,2,5,1,3,4,8]=>0000001=>1111110=>1
[4,8,2,5,1,3,6,7]=>0000000=>1111111=>1
[5,8,3,4,1,2,6,7]=>0000000=>1111111=>1
[3,8,2,6,1,4,5,7]=>0000000=>1111111=>1
[5,8,3,6,1,2,4,7]=>0000000=>1111111=>1
[5,8,4,6,1,2,3,7]=>0000000=>1111111=>1
[6,8,3,5,1,2,4,7]=>0000000=>1111111=>1
[3,8,2,7,1,4,5,6]=>0000000=>1111111=>1
[4,8,2,7,1,3,5,6]=>0000000=>1111111=>1
[4,8,3,7,1,2,5,6]=>0000000=>1111111=>1
[5,8,2,7,1,3,4,6]=>0000000=>1111111=>1
[5,8,4,7,1,2,3,6]=>0000000=>1111111=>1
[6,8,2,7,1,3,4,5]=>0000000=>1111111=>1
[6,8,3,7,1,2,4,5]=>0000000=>1111111=>1
[6,8,5,7,1,2,3,4]=>0000000=>1111111=>1
[7,8,2,4,1,3,5,6]=>0000000=>1111111=>1
[7,8,2,5,1,3,4,6]=>0000000=>1111111=>1
[7,8,4,6,1,2,3,5]=>0000000=>1111111=>1
[4,3,2,6,1,5,7,8]=>0000011=>1111100=>1
[5,3,2,6,1,4,7,8]=>0000011=>1111100=>1
[5,4,2,6,1,3,7,8]=>0000011=>1111100=>1
[6,3,2,5,1,4,7,8]=>0000011=>1111100=>1
[4,3,2,7,1,5,6,8]=>0000001=>1111110=>1
[5,3,2,7,1,4,6,8]=>0000001=>1111110=>1
[5,4,3,7,1,2,6,8]=>0000001=>1111110=>1
[6,3,2,7,1,4,5,8]=>0000001=>1111110=>1
[6,4,2,7,1,3,5,8]=>0000001=>1111110=>1
[6,4,3,7,1,2,5,8]=>0000001=>1111110=>1
[6,5,2,7,1,3,4,8]=>0000001=>1111110=>1
[6,5,3,7,1,2,4,8]=>0000001=>1111110=>1
[7,3,2,5,1,4,6,8]=>0000001=>1111110=>1
[7,4,2,5,1,3,6,8]=>0000001=>1111110=>1
[7,3,2,6,1,4,5,8]=>0000001=>1111110=>1
[7,4,2,6,1,3,5,8]=>0000001=>1111110=>1
[7,4,3,6,1,2,5,8]=>0000001=>1111110=>1
[7,5,2,6,1,3,4,8]=>0000001=>1111110=>1
[7,5,3,6,1,2,4,8]=>0000001=>1111110=>1
[7,6,3,5,1,2,4,8]=>0000001=>1111110=>1
[4,3,2,8,1,5,6,7]=>0000000=>1111111=>1
[5,3,2,8,1,4,6,7]=>0000000=>1111111=>1
[5,4,3,8,1,2,6,7]=>0000000=>1111111=>1
[6,3,2,8,1,4,5,7]=>0000000=>1111111=>1
[6,4,2,8,1,3,5,7]=>0000000=>1111111=>1
[6,4,3,8,1,2,5,7]=>0000000=>1111111=>1
[6,5,2,8,1,3,4,7]=>0000000=>1111111=>1
[6,5,3,8,1,2,4,7]=>0000000=>1111111=>1
[7,4,2,8,1,3,5,6]=>0000000=>1111111=>1
[7,4,3,8,1,2,5,6]=>0000000=>1111111=>1
[7,5,3,8,1,2,4,6]=>0000000=>1111111=>1
[7,6,2,8,1,3,4,5]=>0000000=>1111111=>1
[8,3,2,5,1,4,6,7]=>0000000=>1111111=>1
[8,4,2,5,1,3,6,7]=>0000000=>1111111=>1
[8,4,2,6,1,3,5,7]=>0000000=>1111111=>1
[8,5,3,6,1,2,4,7]=>0000000=>1111111=>1
[8,6,2,5,1,3,4,7]=>0000000=>1111111=>1
[8,4,2,7,1,3,5,6]=>0000000=>1111111=>1
[8,4,3,7,1,2,5,6]=>0000000=>1111111=>1
[8,5,2,7,1,3,4,6]=>0000000=>1111111=>1
[8,5,3,7,1,2,4,6]=>0000000=>1111111=>1
[8,7,2,4,1,3,5,6]=>0000000=>1111111=>1
[8,7,2,5,1,3,4,6]=>0000000=>1111111=>1
[8,7,3,5,1,2,4,6]=>0000000=>1111111=>1
[8,7,2,6,1,3,4,5]=>0000000=>1111111=>1
[8,7,3,6,1,2,4,5]=>0000000=>1111111=>1
[8,7,4,6,1,2,3,5]=>0000000=>1111111=>1
[3,6,2,5,8,1,4,7]=>0000000=>1111111=>1
[4,6,3,5,8,1,2,7]=>0000000=>1111111=>1
[5,6,2,4,8,1,3,7]=>0000000=>1111111=>1
[4,7,3,5,8,1,2,6]=>0000000=>1111111=>1
[5,7,2,4,8,1,3,6]=>0000000=>1111111=>1
[5,7,3,4,8,1,2,6]=>0000000=>1111111=>1
[4,7,3,6,8,1,2,5]=>0000000=>1111111=>1
[5,7,2,6,8,1,3,4]=>0000000=>1111111=>1
[5,7,4,6,8,1,2,3]=>0000000=>1111111=>1
[6,7,3,4,8,1,2,5]=>0000000=>1111111=>1
[4,8,3,5,7,1,2,6]=>0000000=>1111111=>1
[5,8,2,4,7,1,3,6]=>0000000=>1111111=>1
[5,8,2,6,7,1,3,4]=>0000000=>1111111=>1
[7,8,2,4,6,1,3,5]=>0000000=>1111111=>1
[7,8,3,4,6,1,2,5]=>0000000=>1111111=>1
[7,8,2,5,6,1,3,4]=>0000000=>1111111=>1
[7,8,3,5,6,1,2,4]=>0000000=>1111111=>1
[4,3,2,6,8,1,5,7]=>0000000=>1111111=>1
[5,3,2,6,8,1,4,7]=>0000000=>1111111=>1
[5,4,2,6,8,1,3,7]=>0000000=>1111111=>1
[5,4,3,6,8,1,2,7]=>0000000=>1111111=>1
[6,3,2,5,8,1,4,7]=>0000000=>1111111=>1
[6,5,2,4,8,1,3,7]=>0000000=>1111111=>1
[4,3,2,7,8,1,5,6]=>0000000=>1111111=>1
[5,3,2,7,8,1,4,6]=>0000000=>1111111=>1
[5,4,2,7,8,1,3,6]=>0000000=>1111111=>1
[5,4,3,7,8,1,2,6]=>0000000=>1111111=>1
[6,4,2,7,8,1,3,5]=>0000000=>1111111=>1
[6,4,3,7,8,1,2,5]=>0000000=>1111111=>1
[6,5,2,7,8,1,3,4]=>0000000=>1111111=>1
[7,4,3,5,8,1,2,6]=>0000000=>1111111=>1
[7,5,2,6,8,1,3,4]=>0000000=>1111111=>1
[7,6,2,4,8,1,3,5]=>0000000=>1111111=>1
[7,6,3,5,8,1,2,4]=>0000000=>1111111=>1
[8,3,2,5,7,1,4,6]=>0000000=>1111111=>1
[8,4,2,5,7,1,3,6]=>0000000=>1111111=>1
[8,5,2,4,7,1,3,6]=>0000000=>1111111=>1
[8,5,2,6,7,1,3,4]=>0000000=>1111111=>1
[8,5,3,6,7,1,2,4]=>0000000=>1111111=>1
[8,6,2,4,7,1,3,5]=>0000000=>1111111=>1
[8,6,2,5,7,1,3,4]=>0000000=>1111111=>1
[8,6,3,5,7,1,2,4]=>0000000=>1111111=>1
[8,7,2,4,6,1,3,5]=>0000000=>1111111=>1
[8,7,3,4,6,1,2,5]=>0000000=>1111111=>1
[8,7,2,5,6,1,3,4]=>0000000=>1111111=>1
[4,3,7,2,6,1,5,8]=>0000001=>1111110=>1
[5,3,7,2,6,1,4,8]=>0000001=>1111110=>1
[5,4,7,2,6,1,3,8]=>0000001=>1111110=>1
[6,3,7,2,5,1,4,8]=>0000001=>1111110=>1
[6,4,7,2,5,1,3,8]=>0000001=>1111110=>1
[6,4,7,3,5,1,2,8]=>0000001=>1111110=>1
[7,3,6,2,5,1,4,8]=>0000001=>1111110=>1
[4,3,8,2,6,1,5,7]=>0000000=>1111111=>1
[5,3,8,2,6,1,4,7]=>0000000=>1111111=>1
[5,4,8,2,6,1,3,7]=>0000000=>1111111=>1
[5,4,8,3,6,1,2,7]=>0000000=>1111111=>1
[6,3,8,2,5,1,4,7]=>0000000=>1111111=>1
[6,4,8,2,5,1,3,7]=>0000000=>1111111=>1
[6,4,8,3,5,1,2,7]=>0000000=>1111111=>1
[6,5,8,2,4,1,3,7]=>0000000=>1111111=>1
[4,3,8,2,7,1,5,6]=>0000000=>1111111=>1
[5,4,8,2,7,1,3,6]=>0000000=>1111111=>1
[5,4,8,3,7,1,2,6]=>0000000=>1111111=>1
[6,3,8,2,7,1,4,5]=>0000000=>1111111=>1
[6,4,8,2,7,1,3,5]=>0000000=>1111111=>1
[7,3,8,2,5,1,4,6]=>0000000=>1111111=>1
[7,4,8,3,5,1,2,6]=>0000000=>1111111=>1
[7,5,8,2,4,1,3,6]=>0000000=>1111111=>1
[7,5,8,2,6,1,3,4]=>0000000=>1111111=>1
[7,5,8,4,6,1,2,3]=>0000000=>1111111=>1
[8,3,6,2,5,1,4,7]=>0000000=>1111111=>1
[8,4,6,2,5,1,3,7]=>0000000=>1111111=>1
[8,3,7,2,5,1,4,6]=>0000000=>1111111=>1
[8,4,7,3,5,1,2,6]=>0000000=>1111111=>1
[8,5,7,2,4,1,3,6]=>0000000=>1111111=>1
[8,3,7,2,6,1,4,5]=>0000000=>1111111=>1
[8,4,7,2,6,1,3,5]=>0000000=>1111111=>1
[8,4,7,3,6,1,2,5]=>0000000=>1111111=>1
[8,5,7,2,6,1,3,4]=>0000000=>1111111=>1
[8,6,7,2,4,1,3,5]=>0000000=>1111111=>1
[8,6,7,2,5,1,3,4]=>0000000=>1111111=>1
[5,4,3,2,7,1,6,8]=>0000001=>1111110=>1
[6,4,3,2,7,1,5,8]=>0000001=>1111110=>1
[6,5,3,2,7,1,4,8]=>0000001=>1111110=>1
[6,5,4,2,7,1,3,8]=>0000001=>1111110=>1
[7,5,3,2,6,1,4,8]=>0000001=>1111110=>1
[7,5,4,2,6,1,3,8]=>0000001=>1111110=>1
[5,4,3,2,8,1,6,7]=>0000000=>1111111=>1
[6,5,3,2,8,1,4,7]=>0000000=>1111111=>1
[6,5,4,2,8,1,3,7]=>0000000=>1111111=>1
[7,5,3,2,8,1,4,6]=>0000000=>1111111=>1
[7,6,3,2,8,1,4,5]=>0000000=>1111111=>1
[7,6,4,3,8,1,2,5]=>0000000=>1111111=>1
[8,5,3,2,6,1,4,7]=>0000000=>1111111=>1
[8,5,4,2,6,1,3,7]=>0000000=>1111111=>1
[8,5,3,2,7,1,4,6]=>0000000=>1111111=>1
[8,6,3,2,7,1,4,5]=>0000000=>1111111=>1
[8,6,4,3,7,1,2,5]=>0000000=>1111111=>1
[8,7,3,2,6,1,4,5]=>0000000=>1111111=>1
[8,7,5,2,6,1,3,4]=>0000000=>1111111=>1
[8,7,5,3,6,1,2,4]=>0000000=>1111111=>1
[8,7,6,2,4,1,3,5]=>0000000=>1111111=>1
[8,7,6,3,5,1,2,4]=>0000000=>1111111=>1
[4,8,3,7,2,6,1,5]=>0000000=>1111111=>1
[5,8,3,7,2,6,1,4]=>0000000=>1111111=>1
[5,8,4,7,2,6,1,3]=>0000000=>1111111=>1
[5,8,4,7,3,6,1,2]=>0000000=>1111111=>1
[6,8,3,7,2,5,1,4]=>0000000=>1111111=>1
[6,8,4,7,2,5,1,3]=>0000000=>1111111=>1
[6,8,4,7,3,5,1,2]=>0000000=>1111111=>1
[6,8,5,7,2,4,1,3]=>0000000=>1111111=>1
[6,8,5,7,3,4,1,2]=>0000000=>1111111=>1
[7,8,3,6,2,5,1,4]=>0000000=>1111111=>1
[7,8,4,6,2,5,1,3]=>0000000=>1111111=>1
[7,8,4,6,3,5,1,2]=>0000000=>1111111=>1
[7,8,5,6,2,4,1,3]=>0000000=>1111111=>1
[5,4,3,8,2,7,1,6]=>0000000=>1111111=>1
[6,4,3,8,2,7,1,5]=>0000000=>1111111=>1
[6,5,4,8,3,7,1,2]=>0000000=>1111111=>1
[7,4,3,8,2,6,1,5]=>0000000=>1111111=>1
[7,5,3,8,2,6,1,4]=>0000000=>1111111=>1
[7,5,4,8,2,6,1,3]=>0000000=>1111111=>1
[7,6,3,8,2,5,1,4]=>0000000=>1111111=>1
[7,6,4,8,2,5,1,3]=>0000000=>1111111=>1
[7,6,5,8,2,4,1,3]=>0000000=>1111111=>1
[8,5,3,7,2,6,1,4]=>0000000=>1111111=>1
[8,5,4,7,2,6,1,3]=>0000000=>1111111=>1
[8,5,4,7,3,6,1,2]=>0000000=>1111111=>1
[8,6,3,7,2,5,1,4]=>0000000=>1111111=>1
[8,6,4,7,2,5,1,3]=>0000000=>1111111=>1
[8,6,4,7,3,5,1,2]=>0000000=>1111111=>1
[8,6,5,7,2,4,1,3]=>0000000=>1111111=>1
[8,7,3,6,2,5,1,4]=>0000000=>1111111=>1
[8,7,4,6,2,5,1,3]=>0000000=>1111111=>1
[8,7,4,6,3,5,1,2]=>0000000=>1111111=>1
[6,5,4,3,2,8,1,7]=>0000000=>1111111=>1
[7,6,5,4,2,8,1,3]=>0000000=>1111111=>1
[8,5,4,3,2,7,1,6]=>0000000=>1111111=>1
[8,6,5,3,2,7,1,4]=>0000000=>1111111=>1
[8,7,4,3,2,6,1,5]=>0000000=>1111111=>1
[8,7,5,4,2,6,1,3]=>0000000=>1111111=>1
[8,7,6,3,2,5,1,4]=>0000000=>1111111=>1
[8,7,6,4,2,5,1,3]=>0000000=>1111111=>1
[8,7,6,5,2,4,1,3]=>0000000=>1111111=>1
[5,1,2,3,8,7,4,6]=>0000000=>1111111=>1
[8,1,2,3,6,7,4,5]=>0000000=>1111111=>1
[8,1,2,5,3,4,6,7]=>0000000=>1111111=>1
[8,1,2,6,3,4,5,7]=>0000000=>1111111=>1
[6,1,2,5,3,8,4,7]=>0000000=>1111111=>1
[8,1,2,6,3,7,4,5]=>0000000=>1111111=>1
[6,1,2,5,3,7,8,4]=>0000000=>1111111=>1
[4,1,2,8,7,3,5,6]=>0000000=>1111111=>1
[4,1,2,7,6,3,8,5]=>0000000=>1111111=>1
[8,1,2,5,6,3,4,7]=>0000000=>1111111=>1
[8,1,2,7,6,3,4,5]=>0000000=>1111111=>1
[7,1,2,5,6,3,8,4]=>0000000=>1111111=>1
[8,1,2,5,6,7,3,4]=>0000000=>1111111=>1
[3,1,8,2,6,4,5,7]=>0000000=>1111111=>1
[3,1,7,2,6,4,8,5]=>0000000=>1111111=>1
[3,1,5,2,8,7,4,6]=>0000000=>1111111=>1
[3,1,8,2,6,7,4,5]=>0000000=>1111111=>1
[8,1,4,2,3,5,6,7]=>0000000=>1111111=>1
[6,1,4,2,3,8,5,7]=>0000000=>1111111=>1
[8,1,4,2,3,7,5,6]=>0000000=>1111111=>1
[8,1,5,2,3,4,6,7]=>0000000=>1111111=>1
[7,1,5,2,3,4,8,6]=>0000000=>1111111=>1
[6,1,5,2,3,8,4,7]=>0000000=>1111111=>1
[8,1,5,2,3,7,4,6]=>0000000=>1111111=>1
[6,1,8,2,3,7,4,5]=>0000000=>1111111=>1
[6,1,5,2,3,7,8,4]=>0000000=>1111111=>1
[5,1,4,2,8,3,6,7]=>0000000=>1111111=>1
[5,1,4,2,7,3,8,6]=>0000000=>1111111=>1
[7,1,4,2,6,3,8,5]=>0000000=>1111111=>1
[8,1,5,2,7,3,4,6]=>0000000=>1111111=>1
[5,1,4,2,8,7,3,6]=>0000000=>1111111=>1
[8,1,4,2,6,7,3,5]=>0000000=>1111111=>1
[8,1,5,2,6,7,3,4]=>0000000=>1111111=>1
[5,1,4,2,6,7,8,3]=>0000000=>1111111=>1
[3,1,8,6,2,4,5,7]=>0000000=>1111111=>1
[3,1,8,5,2,7,4,6]=>0000000=>1111111=>1
[3,1,8,6,2,7,4,5]=>0000000=>1111111=>1
[8,1,4,5,2,3,6,7]=>0000000=>1111111=>1
[8,1,4,6,2,3,5,7]=>0000000=>1111111=>1
[7,1,8,6,2,3,4,5]=>0000000=>1111111=>1
[7,1,6,5,2,3,8,4]=>0000000=>1111111=>1
[8,1,4,6,2,7,3,5]=>0000000=>1111111=>1
[3,1,4,8,6,2,5,7]=>0000000=>1111111=>1
[3,1,7,5,6,2,8,4]=>0000000=>1111111=>1
[8,1,4,7,6,2,3,5]=>0000000=>1111111=>1
[3,1,4,5,8,7,2,6]=>0000000=>1111111=>1
[3,1,8,5,6,7,2,4]=>0000000=>1111111=>1
[8,1,4,5,6,7,2,3]=>0000000=>1111111=>1
[2,8,1,3,4,7,5,6]=>0000000=>1111111=>1
[2,8,1,3,6,7,4,5]=>0000000=>1111111=>1
[2,4,1,8,3,7,5,6]=>0000000=>1111111=>1
[2,8,1,6,3,4,5,7]=>0000000=>1111111=>1
[2,6,1,5,3,8,4,7]=>0000000=>1111111=>1
[2,8,1,5,3,7,4,6]=>0000000=>1111111=>1
[2,6,1,5,3,7,8,4]=>0000000=>1111111=>1
[2,8,1,7,6,3,4,5]=>0000000=>1111111=>1
[2,7,1,5,6,3,8,4]=>0000000=>1111111=>1
[2,4,1,8,6,7,3,5]=>0000000=>1111111=>1
[7,3,1,2,4,5,8,6]=>0000000=>1111111=>1
[5,3,1,2,8,4,6,7]=>0000000=>1111111=>1
[8,3,1,2,6,4,5,7]=>0000000=>1111111=>1
[5,3,1,2,8,7,4,6]=>0000000=>1111111=>1
[8,4,1,2,3,7,5,6]=>0000000=>1111111=>1
[7,6,1,2,3,4,8,5]=>0000000=>1111111=>1
[5,8,1,2,3,7,4,6]=>0000000=>1111111=>1
[5,4,1,2,8,3,6,7]=>0000000=>1111111=>1
[7,4,1,2,6,3,8,5]=>0000000=>1111111=>1
[5,8,1,2,7,3,4,6]=>0000000=>1111111=>1
[8,7,1,2,6,3,4,5]=>0000000=>1111111=>1
[5,7,1,2,6,3,8,4]=>0000000=>1111111=>1
[8,4,1,2,6,7,3,5]=>0000000=>1111111=>1
[5,8,1,2,6,7,3,4]=>0000000=>1111111=>1
[5,4,1,2,6,7,8,3]=>0000000=>1111111=>1
[4,3,1,6,2,8,5,7]=>0000000=>1111111=>1
[4,3,1,6,2,7,8,5]=>0000000=>1111111=>1
[8,3,1,5,2,4,6,7]=>0000000=>1111111=>1
[8,3,1,6,2,4,5,7]=>0000000=>1111111=>1
[7,3,1,6,2,4,8,5]=>0000000=>1111111=>1
[8,3,1,5,2,7,4,6]=>0000000=>1111111=>1
[8,3,1,6,2,7,4,5]=>0000000=>1111111=>1
[6,3,1,5,2,7,8,4]=>0000000=>1111111=>1
[7,4,1,5,2,3,8,6]=>0000000=>1111111=>1
[8,4,1,6,2,3,5,7]=>0000000=>1111111=>1
[7,4,1,8,2,3,5,6]=>0000000=>1111111=>1
[7,4,1,6,2,3,8,5]=>0000000=>1111111=>1
[8,7,1,6,2,3,4,5]=>0000000=>1111111=>1
[6,7,1,5,2,3,8,4]=>0000000=>1111111=>1
[6,8,1,5,2,7,3,4]=>0000000=>1111111=>1
[6,4,1,5,2,7,8,3]=>0000000=>1111111=>1
[4,3,1,5,8,2,6,7]=>0000000=>1111111=>1
[4,3,1,8,6,2,5,7]=>0000000=>1111111=>1
[4,3,1,8,7,2,5,6]=>0000000=>1111111=>1
[8,3,1,5,6,2,4,7]=>0000000=>1111111=>1
[8,3,1,5,7,2,4,6]=>0000000=>1111111=>1
[7,3,1,5,6,2,8,4]=>0000000=>1111111=>1
[7,8,1,5,6,2,3,4]=>0000000=>1111111=>1
[4,3,1,5,6,8,2,7]=>0000000=>1111111=>1
[8,4,1,5,6,7,2,3]=>0000000=>1111111=>1
[4,3,1,5,6,7,8,2]=>0000000=>1111111=>1
[2,3,7,1,6,4,8,5]=>0000000=>1111111=>1
[2,3,5,1,8,7,4,6]=>0000000=>1111111=>1
[2,3,8,1,6,7,4,5]=>0000000=>1111111=>1
[2,8,4,1,3,5,6,7]=>0000000=>1111111=>1
[2,6,4,1,3,8,5,7]=>0000000=>1111111=>1
[2,6,4,1,3,7,8,5]=>0000000=>1111111=>1
[2,7,5,1,3,4,8,6]=>0000000=>1111111=>1
[2,6,5,1,3,8,4,7]=>0000000=>1111111=>1
[2,8,5,1,3,7,4,6]=>0000000=>1111111=>1
[2,6,5,1,3,7,8,4]=>0000000=>1111111=>1
[2,7,4,1,6,3,8,5]=>0000000=>1111111=>1
[2,8,5,1,7,3,4,6]=>0000000=>1111111=>1
[2,7,5,1,6,3,8,4]=>0000000=>1111111=>1
[6,3,4,1,2,7,8,5]=>0000000=>1111111=>1
[7,3,5,1,2,4,8,6]=>0000000=>1111111=>1
[6,3,7,1,2,4,8,5]=>0000000=>1111111=>1
[6,3,8,1,2,7,4,5]=>0000000=>1111111=>1
[6,7,4,1,2,3,8,5]=>0000000=>1111111=>1
[6,8,5,1,2,3,4,7]=>0000000=>1111111=>1
[8,5,4,1,2,7,3,6]=>0000000=>1111111=>1
[6,8,4,1,2,7,3,5]=>0000000=>1111111=>1
[6,8,5,1,2,7,3,4]=>0000000=>1111111=>1
[6,5,4,1,2,7,8,3]=>0000000=>1111111=>1
[5,3,4,1,7,2,8,6]=>0000000=>1111111=>1
[8,3,4,1,7,2,5,6]=>0000000=>1111111=>1
[7,3,4,1,6,2,8,5]=>0000000=>1111111=>1
[8,3,5,1,6,2,4,7]=>0000000=>1111111=>1
[7,3,8,1,6,2,4,5]=>0000000=>1111111=>1
[7,3,5,1,6,2,8,4]=>0000000=>1111111=>1
[8,5,4,1,6,2,3,7]=>0000000=>1111111=>1
[8,5,4,1,7,2,3,6]=>0000000=>1111111=>1
[7,8,4,1,6,2,3,5]=>0000000=>1111111=>1
[7,8,5,1,6,2,3,4]=>0000000=>1111111=>1
[5,3,4,1,6,7,8,2]=>0000000=>1111111=>1
[2,3,7,6,1,4,8,5]=>0000000=>1111111=>1
[2,3,6,5,1,8,4,7]=>0000000=>1111111=>1
[2,3,6,5,1,7,8,4]=>0000000=>1111111=>1
[2,7,4,8,1,3,5,6]=>0000000=>1111111=>1
[2,7,4,6,1,3,8,5]=>0000000=>1111111=>1
[2,7,6,5,1,3,8,4]=>0000000=>1111111=>1
[2,6,4,5,1,8,3,7]=>0000000=>1111111=>1
[2,8,4,5,1,7,3,6]=>0000000=>1111111=>1
[2,8,4,6,1,7,3,5]=>0000000=>1111111=>1
[2,8,6,5,1,7,3,4]=>0000000=>1111111=>1
[7,3,8,5,1,2,4,6]=>0000000=>1111111=>1
[7,3,8,6,1,2,4,5]=>0000000=>1111111=>1
[7,3,6,5,1,2,8,4]=>0000000=>1111111=>1
[8,3,6,5,1,7,2,4]=>0000000=>1111111=>1
[8,6,4,5,1,7,2,3]=>0000000=>1111111=>1
[2,3,8,5,7,1,4,6]=>0000000=>1111111=>1
[2,3,7,5,6,1,8,4]=>0000000=>1111111=>1
[2,8,4,7,6,1,3,5]=>0000000=>1111111=>1
[2,8,7,5,6,1,3,4]=>0000000=>1111111=>1
[8,3,7,5,6,1,2,4]=>0000000=>1111111=>1
[2,8,4,5,6,7,1,3]=>0000000=>1111111=>1
[9,1,2,3,4,5,6,7,8]=>00000000=>11111111=>1
[8,1,2,3,4,5,6,9,7]=>00000000=>11111111=>1
[7,1,2,3,4,5,9,6,8]=>00000000=>11111111=>1
[7,1,2,3,4,5,8,9,6]=>00000000=>11111111=>1
[6,1,2,3,4,7,8,9,5]=>00000000=>11111111=>1
[5,1,2,3,9,4,6,7,8]=>00000000=>11111111=>1
[9,1,2,3,6,4,5,7,8]=>00000000=>11111111=>1
[5,1,2,3,6,7,8,9,4]=>00000000=>11111111=>1
[9,1,2,5,3,4,6,7,8]=>00000000=>11111111=>1
[4,1,2,5,6,7,8,9,3]=>00000000=>11111111=>1
[3,1,9,2,4,5,6,7,8]=>00000000=>11111111=>1
[3,1,5,2,7,4,9,6,8]=>00000000=>11111111=>1
[3,1,4,8,9,2,5,6,7]=>00000000=>11111111=>1
[3,1,4,5,6,7,9,2,8]=>00000000=>11111111=>1
[3,1,4,5,6,7,8,9,2]=>00000000=>11111111=>1
[2,9,1,3,4,5,6,7,8]=>00000000=>11111111=>1
[2,5,1,3,6,7,8,9,4]=>00000000=>11111111=>1
[2,4,1,6,3,8,5,9,7]=>00000000=>11111111=>1
[9,3,1,2,4,5,6,7,8]=>00000000=>11111111=>1
[9,7,1,2,3,4,5,6,8]=>00000000=>11111111=>1
[8,9,1,2,3,4,5,6,7]=>00000000=>11111111=>1
[8,7,1,2,3,4,5,9,6]=>00000000=>11111111=>1
[9,6,1,2,3,4,8,5,7]=>00000000=>11111111=>1
[7,6,1,2,3,4,8,9,5]=>00000000=>11111111=>1
[5,6,1,2,3,7,8,9,4]=>00000000=>11111111=>1
[5,4,1,2,6,7,8,9,3]=>00000000=>11111111=>1
[9,4,1,6,2,8,3,5,7]=>00000000=>11111111=>1
[8,9,1,5,6,7,2,3,4]=>00000000=>11111111=>1
[4,3,1,5,6,7,8,9,2]=>00000000=>11111111=>1
[2,3,5,1,6,7,8,9,4]=>00000000=>11111111=>1
[2,6,7,1,3,4,8,9,5]=>00000000=>11111111=>1
[6,3,4,1,2,7,8,9,5]=>00000000=>11111111=>1
[9,7,8,1,2,3,4,5,6]=>00000000=>11111111=>1
[6,7,8,1,2,3,4,9,5]=>00000000=>11111111=>1
[9,8,5,1,7,2,3,4,6]=>00000000=>11111111=>1
[9,5,4,1,8,7,2,3,6]=>00000000=>11111111=>1
[2,7,8,9,1,3,4,5,6]=>00000000=>11111111=>1
[7,3,4,8,1,2,5,9,6]=>00000000=>11111111=>1
[7,3,8,9,1,2,4,5,6]=>00000000=>11111111=>1
[8,9,4,5,6,1,2,3,7]=>00000000=>11111111=>1
[2,3,4,5,6,7,9,1,8]=>00000000=>11111111=>1
[9,3,4,5,6,7,8,1,2]=>00000000=>11111111=>1
[2,3,4,5,6,7,8,9,1]=>00000000=>11111111=>1
[3,5,2,6,1,4,8,7]=>0000010=>1111101=>2
[3,5,2,6,4,1,8,7]=>0000010=>1111101=>2
[3,5,2,7,4,8,1,6]=>0000000=>1111111=>1
[3,5,2,7,4,8,6,1]=>0000000=>1111111=>1
[4,5,7,2,3,8,6,1]=>0000000=>1111111=>1
[4,5,7,2,3,8,1,6]=>0000000=>1111111=>1
[4,5,6,2,3,1,8,7]=>0000010=>1111101=>2
[4,5,6,2,1,3,8,7]=>0000010=>1111101=>2
[3,5,1,6,4,2,8,7]=>0000010=>1111101=>2
[4,5,6,1,3,2,8,7]=>0000010=>1111101=>2
[4,5,6,3,1,2,8,7]=>0000010=>1111101=>2
[4,5,7,3,2,8,1,6]=>0000000=>1111111=>1
[4,5,7,3,2,8,6,1]=>0000000=>1111111=>1
[4,6,7,3,8,2,5,1]=>0000000=>1111111=>1
[4,6,7,3,8,2,1,5]=>0000000=>1111111=>1
[4,6,7,3,8,1,2,5]=>0000000=>1111111=>1
[4,5,7,3,1,8,2,6]=>0000000=>1111111=>1
[4,5,7,1,3,8,2,6]=>0000000=>1111111=>1
[3,5,1,7,4,8,2,6]=>0000000=>1111111=>1
[2,1,5,7,4,8,3,6]=>0100000=>1011111=>2
[2,1,5,7,4,8,6,3]=>0100000=>1011111=>2
[3,5,1,7,4,8,6,2]=>0000000=>1111111=>1
[4,5,7,1,3,8,6,2]=>0000000=>1111111=>1
[4,5,7,3,1,8,6,2]=>0000000=>1111111=>1
[4,6,7,3,8,1,5,2]=>0000000=>1111111=>1
[4,6,7,3,8,5,1,2]=>0000000=>1111111=>1
[4,6,7,3,8,5,2,1]=>0000000=>1111111=>1
[5,6,7,8,3,1,4,2]=>0000000=>1111111=>1
[5,6,7,8,1,3,4,2]=>0000000=>1111111=>1
[4,6,7,1,8,3,5,2]=>0000000=>1111111=>1
[3,6,1,7,8,4,5,2]=>0000000=>1111111=>1
[2,1,6,7,8,4,5,3]=>0100000=>1011111=>2
[2,1,6,7,8,4,3,5]=>0100000=>1011111=>2
[3,6,1,7,8,4,2,5]=>0000000=>1111111=>1
[4,6,7,1,8,3,2,5]=>0000000=>1111111=>1
[5,6,7,8,1,3,2,4]=>0000000=>1111111=>1
[4,5,7,2,1,8,3,6]=>0000000=>1111111=>1
[4,6,7,2,8,1,3,5]=>0000000=>1111111=>1
[4,6,7,2,8,3,1,5]=>0000000=>1111111=>1
[4,6,7,2,8,3,5,1]=>0000000=>1111111=>1
[3,6,2,7,8,4,5,1]=>0000000=>1111111=>1
[3,6,2,7,8,4,1,5]=>0000000=>1111111=>1
[3,6,2,7,8,1,4,5]=>0000000=>1111111=>1
[3,5,2,7,1,8,4,6]=>0000000=>1111111=>1
[3,4,2,1,7,8,5,6]=>0001000=>1110111=>2
[3,4,1,2,7,8,6,5]=>0001000=>1110111=>2
[3,5,2,7,1,8,6,4]=>0000000=>1111111=>1
[3,6,2,7,8,1,5,4]=>0000000=>1111111=>1
[3,6,2,7,8,5,1,4]=>0000000=>1111111=>1
[3,6,2,7,8,5,4,1]=>0000000=>1111111=>1
[4,6,7,2,8,5,3,1]=>0000000=>1111111=>1
[4,6,7,2,8,5,1,3]=>0000000=>1111111=>1
[4,6,7,2,8,1,5,3]=>0000000=>1111111=>1
[4,5,7,2,1,8,6,3]=>0000000=>1111111=>1
[4,5,7,1,2,8,6,3]=>0000000=>1111111=>1
[3,5,1,7,2,8,6,4]=>0000000=>1111111=>1
[2,1,5,7,3,8,6,4]=>0100000=>1011111=>2
[2,1,6,7,8,3,5,4]=>0100000=>1011111=>2
[3,6,1,7,8,2,5,4]=>0000000=>1111111=>1
[4,6,7,1,8,2,5,3]=>0000000=>1111111=>1
[5,6,7,8,1,2,4,3]=>0000000=>1111111=>1
[5,6,7,8,2,1,4,3]=>0000000=>1111111=>1
[5,6,7,8,2,4,1,3]=>0000000=>1111111=>1
[5,6,7,8,2,4,3,1]=>0000000=>1111111=>1
[5,6,7,8,1,4,2,3]=>0000000=>1111111=>1
[4,6,7,1,8,5,2,3]=>0000000=>1111111=>1
[3,6,1,7,8,5,2,4]=>0000000=>1111111=>1
[2,1,6,7,8,5,3,4]=>0100000=>1011111=>2
[3,6,1,7,8,5,4,2]=>0000000=>1111111=>1
[4,6,7,1,8,5,3,2]=>0000000=>1111111=>1
[5,6,7,8,1,4,3,2]=>0000000=>1111111=>1
[5,6,7,8,4,1,3,2]=>0000000=>1111111=>1
[3,5,2,7,4,9,6,10,8,1]=>000000000=>111111111=>1
[4,6,8,3,9,5,10,7,2,1]=>000000000=>111111111=>1
[5,7,8,9,4,10,6,3,2,1]=>000000000=>111111111=>1
[6,7,8,9,10,1,4,5,3,2]=>000000000=>111111111=>1
[6,7,8,9,10,1,4,5,2,3]=>000000000=>111111111=>1
[6,7,8,9,10,4,3,2,1,5]=>000000000=>111111111=>1
[6,7,8,9,10,1,3,4,5,2]=>000000000=>111111111=>1
[6,7,8,9,10,3,4,1,2,5]=>000000000=>111111111=>1
[6,7,8,9,10,3,4,2,1,5]=>000000000=>111111111=>1
[6,7,8,9,10,2,3,4,1,5]=>000000000=>111111111=>1
[6,7,8,9,10,1,5,4,3,2]=>000000000=>111111111=>1
[6,7,8,9,10,5,4,3,2,1]=>000000000=>111111111=>1
[6,5,8,7,3,4,1,2]=>0000000=>1111111=>1
[3,6,7,4,5,8,1,2]=>0000000=>1111111=>1
[2,6,7,4,5,1,8,3]=>0000000=>1111111=>1
[1,6,7,4,5,2,3,8]=>1000001=>0111110=>1
[1,5,4,7,6,2,3,8]=>1000001=>0111110=>1
[2,5,4,7,6,1,8,3]=>0000000=>1111111=>1
[3,5,4,7,6,8,1,2]=>0000000=>1111111=>1
[4,5,3,7,8,6,1,2]=>0000000=>1111111=>1
[5,4,3,8,7,6,1,2]=>0000000=>1111111=>1
[6,4,8,3,7,5,1,2]=>0000000=>1111111=>1
[6,3,8,4,5,7,1,2]=>0000000=>1111111=>1
[5,3,4,8,6,7,1,2]=>0000000=>1111111=>1
[4,3,5,6,8,7,1,2]=>0000000=>1111111=>1
[3,2,5,6,1,8,7,4]=>0000000=>1111111=>1
[4,2,5,6,8,1,7,3]=>0000000=>1111111=>1
[5,2,4,8,6,1,7,3]=>0000000=>1111111=>1
[6,2,8,4,5,1,7,3]=>0000000=>1111111=>1
[7,8,2,4,5,1,6,3]=>0000000=>1111111=>1
[7,8,1,4,5,2,3,6]=>0000000=>1111111=>1
[6,1,8,4,5,2,3,7]=>0000000=>1111111=>1
[5,1,4,8,6,2,3,7]=>0000000=>1111111=>1
[4,1,3,2,8,6,5,7]=>0001000=>1110111=>2
[5,1,3,8,2,6,4,7]=>0000000=>1111111=>1
[6,1,8,3,2,5,4,7]=>0000000=>1111111=>1
[7,8,1,3,2,5,4,6]=>0000000=>1111111=>1
[7,8,2,3,1,5,6,4]=>0000000=>1111111=>1
[6,2,8,3,1,5,7,4]=>0000000=>1111111=>1
[5,2,3,8,1,6,7,4]=>0000000=>1111111=>1
[6,3,8,2,1,7,5,4]=>0000000=>1111111=>1
[7,8,3,2,1,6,5,4]=>0000000=>1111111=>1
[7,8,4,2,6,1,5,3]=>0000000=>1111111=>1
[5,4,2,8,7,1,6,3]=>0000000=>1111111=>1
[4,5,2,7,8,1,6,3]=>0000000=>1111111=>1
[2,5,3,7,1,6,8,4]=>0000000=>1111111=>1
[1,5,3,7,2,6,4,8]=>1000001=>0111110=>1
[1,6,7,3,2,5,4,8]=>1000001=>0111110=>1
[2,6,7,3,1,5,8,4]=>0000000=>1111111=>1
[3,6,7,2,1,8,5,4]=>0000000=>1111111=>1
[7,8,5,6,2,1,4,3]=>0000000=>1111111=>1
[6,5,8,7,1,2,3,4]=>0000000=>1111111=>1
[5,4,1,8,7,2,3,6]=>0000000=>1111111=>1
[6,4,8,1,7,2,3,5]=>0000000=>1111111=>1
[7,8,3,1,2,6,4,5]=>0000000=>1111111=>1
[5,3,1,8,2,7,4,6]=>0000000=>1111111=>1
[4,3,1,2,8,7,5,6]=>0001000=>1110111=>2
[4,2,1,3,8,5,7,6]=>0001000=>1110111=>2
[5,2,1,8,3,4,7,6]=>0000000=>1111111=>1
[6,2,8,1,3,4,7,5]=>0000000=>1111111=>1
[7,8,2,1,3,4,6,5]=>0000000=>1111111=>1
[6,3,1,5,2,4,8,7]=>0000010=>1111101=>2
[7,4,5,1,2,8,3,6]=>0000000=>1111111=>1
[6,4,5,1,2,3,8,7]=>0000010=>1111101=>2
[5,4,6,1,2,3,8,7]=>0000010=>1111101=>2
[4,6,5,1,2,3,8,7]=>0000010=>1111101=>2
[5,6,4,1,2,3,8,7]=>0000010=>1111101=>2
[6,5,4,1,2,3,8,7]=>0000010=>1111101=>2
[7,5,4,1,2,8,3,6]=>0000000=>1111111=>1
[8,6,4,1,7,2,3,5]=>0000000=>1111111=>1
[7,6,4,1,8,2,3,5]=>0000000=>1111111=>1
[6,7,4,1,8,2,3,5]=>0000000=>1111111=>1
[2,1,7,5,3,8,4,6]=>0100000=>1011111=>2
[2,1,8,5,3,7,4,6]=>0100000=>1011111=>2
[3,8,1,5,2,7,4,6]=>0000000=>1111111=>1
[8,7,4,1,6,2,3,5]=>0000000=>1111111=>1
[5,8,6,7,1,2,3,4]=>0000000=>1111111=>1
[3,8,1,6,7,2,4,5]=>0000000=>1111111=>1
[2,1,8,6,7,3,4,5]=>0100000=>1011111=>2
[3,7,1,6,8,2,4,5]=>0000000=>1111111=>1
[5,7,6,8,1,2,3,4]=>0000000=>1111111=>1
[6,4,7,1,8,2,3,5]=>0000000=>1111111=>1
[7,4,6,1,8,2,3,5]=>0000000=>1111111=>1
[8,4,6,1,7,2,3,5]=>0000000=>1111111=>1
[8,3,1,6,7,2,4,5]=>0000000=>1111111=>1
[7,3,1,6,8,2,4,5]=>0000000=>1111111=>1
[6,3,1,7,8,2,4,5]=>0000000=>1111111=>1
[4,3,1,2,7,8,5,6]=>0001000=>1110111=>2
[2,1,4,3,8,7,5,6]=>0101000=>1010111=>3
[3,4,1,2,8,7,5,6]=>0001000=>1110111=>2
[6,3,1,8,7,2,4,5]=>0000000=>1111111=>1
[7,4,8,1,6,2,3,5]=>0000000=>1111111=>1
[5,4,8,1,2,7,3,6]=>0000000=>1111111=>1
[4,5,8,1,2,7,3,6]=>0000000=>1111111=>1
[3,5,1,8,2,7,4,6]=>0000000=>1111111=>1
[2,1,5,8,3,7,4,6]=>0100000=>1011111=>2
[3,6,1,8,7,2,4,5]=>0000000=>1111111=>1
[5,6,8,7,1,2,3,4]=>0000000=>1111111=>1
[7,5,8,6,1,2,3,4]=>0000000=>1111111=>1
[8,5,7,6,1,2,3,4]=>0000000=>1111111=>1
[5,7,8,6,1,2,3,4]=>0000000=>1111111=>1
[2,1,7,8,6,3,4,5]=>0100000=>1011111=>2
[2,1,8,7,6,3,4,5]=>0100000=>1011111=>2
[3,8,1,7,6,2,4,5]=>0000000=>1111111=>1
[5,8,7,6,1,2,3,4]=>0000000=>1111111=>1
[6,8,7,5,1,2,3,4]=>0000000=>1111111=>1
[6,4,7,3,8,5,1,2]=>0000000=>1111111=>1
[6,4,7,3,5,8,1,2]=>0000000=>1111111=>1
[6,4,7,2,5,1,8,3]=>0000000=>1111111=>1
[5,4,2,7,6,1,3,8]=>0000001=>1111110=>1
[5,4,2,7,6,1,8,3]=>0000000=>1111111=>1
[5,4,3,7,6,8,1,2]=>0000000=>1111111=>1
[5,4,3,7,8,6,1,2]=>0000000=>1111111=>1
[6,4,8,3,5,7,1,2]=>0000000=>1111111=>1
[5,4,3,8,6,7,1,2]=>0000000=>1111111=>1
[5,4,3,6,8,7,1,2]=>0000000=>1111111=>1
[5,4,2,6,7,1,8,3]=>0000000=>1111111=>1
[5,4,2,6,7,1,3,8]=>0000001=>1111110=>1
[5,3,2,6,1,7,4,8]=>0000001=>1111110=>1
[5,3,2,6,1,7,8,4]=>0000000=>1111111=>1
[5,3,2,6,1,8,7,4]=>0000000=>1111111=>1
[5,4,2,6,8,1,7,3]=>0000000=>1111111=>1
[5,4,2,8,6,1,7,3]=>0000000=>1111111=>1
[6,4,8,2,5,1,7,3]=>0000000=>1111111=>1
[7,8,4,2,5,1,6,3]=>0000000=>1111111=>1
[7,8,4,2,5,1,3,6]=>0000000=>1111111=>1
[5,4,2,8,6,1,3,7]=>0000000=>1111111=>1
[5,3,2,6,1,8,4,7]=>0000000=>1111111=>1
[4,3,2,1,6,8,5,7]=>0001000=>1110111=>2
[4,3,2,1,8,6,5,7]=>0001000=>1110111=>2
[5,3,2,8,1,6,4,7]=>0000000=>1111111=>1
[6,3,8,2,1,5,4,7]=>0000000=>1111111=>1
[7,8,3,2,1,5,4,6]=>0000000=>1111111=>1
[7,8,3,2,1,5,6,4]=>0000000=>1111111=>1
[6,3,8,2,1,5,7,4]=>0000000=>1111111=>1
[5,3,2,8,1,6,7,4]=>0000000=>1111111=>1
[5,4,2,7,8,1,6,3]=>0000000=>1111111=>1
[5,3,2,7,1,8,6,4]=>0000000=>1111111=>1
[5,3,2,7,1,6,8,4]=>0000000=>1111111=>1
[5,3,2,7,1,6,4,8]=>0000001=>1111110=>1
[6,3,7,2,1,5,4,8]=>0000001=>1111110=>1
[6,3,7,2,1,5,8,4]=>0000000=>1111111=>1
[6,3,7,2,1,8,5,4]=>0000000=>1111111=>1
[6,4,7,2,8,1,5,3]=>0000000=>1111111=>1
[6,5,7,8,2,1,4,3]=>0000000=>1111111=>1
[6,5,8,7,2,1,3,4]=>0000000=>1111111=>1
[6,3,7,2,1,8,4,5]=>0000000=>1111111=>1
[6,3,7,2,1,4,8,5]=>0000000=>1111111=>1
[6,3,7,2,1,4,5,8]=>0000001=>1111110=>1
[5,3,2,7,1,4,8,6]=>0000000=>1111111=>1
[5,4,2,8,7,1,3,6]=>0000000=>1111111=>1
[7,8,4,2,6,1,3,5]=>0000000=>1111111=>1
[7,8,3,2,1,6,4,5]=>0000000=>1111111=>1
[6,3,8,2,1,7,4,5]=>0000000=>1111111=>1
[5,3,2,8,1,7,4,6]=>0000000=>1111111=>1
[4,3,2,1,8,7,5,6]=>0001000=>1110111=>2
[4,3,2,1,7,5,8,6]=>0001000=>1110111=>2
[4,3,2,1,7,5,6,8]=>0001001=>1110110=>2
[4,3,2,1,8,5,7,6]=>0001000=>1110111=>2
[5,3,2,8,1,4,7,6]=>0000000=>1111111=>1
[6,3,8,2,1,4,7,5]=>0000000=>1111111=>1
[7,8,3,2,1,4,6,5]=>0000000=>1111111=>1
[6,3,8,2,1,4,5,7]=>0000000=>1111111=>1
[4,3,2,1,8,5,6,7]=>0001000=>1110111=>2
[4,3,2,1,5,8,6,7]=>0001100=>1110011=>2
[7,8,5,6,1,2,4,3]=>0000000=>1111111=>1
[7,8,4,1,6,2,5,3]=>0000000=>1111111=>1
[7,8,1,4,6,2,5,3]=>0000000=>1111111=>1
[6,1,8,4,7,2,5,3]=>0000000=>1111111=>1
[1,6,8,4,7,2,5,3]=>1000000=>0111111=>1
[1,6,8,3,2,7,5,4]=>1000000=>0111111=>1
[6,1,8,3,2,7,5,4]=>0000000=>1111111=>1
[7,8,1,3,2,6,5,4]=>0000000=>1111111=>1
[7,8,3,1,2,6,5,4]=>0000000=>1111111=>1
[7,8,3,4,6,5,1,2]=>0000000=>1111111=>1
[7,8,2,4,6,1,5,3]=>0000000=>1111111=>1
[7,8,2,3,1,6,5,4]=>0000000=>1111111=>1
[7,8,2,1,3,6,5,4]=>0000000=>1111111=>1
[7,8,1,2,3,6,5,4]=>0000000=>1111111=>1
[6,1,8,2,3,7,5,4]=>0000000=>1111111=>1
[1,6,8,2,3,7,5,4]=>1000000=>0111111=>1
[1,5,2,8,3,7,6,4]=>1000000=>0111111=>1
[5,1,2,8,3,7,6,4]=>0000000=>1111111=>1
[5,2,1,8,3,7,6,4]=>0000000=>1111111=>1
[6,2,8,1,3,7,5,4]=>0000000=>1111111=>1
[6,2,8,3,1,7,5,4]=>0000000=>1111111=>1
[6,2,8,4,7,1,5,3]=>0000000=>1111111=>1
[6,3,8,4,7,5,1,2]=>0000000=>1111111=>1
[3,6,8,4,7,5,1,2]=>0000000=>1111111=>1
[2,6,8,4,7,1,5,3]=>0000000=>1111111=>1
[2,6,8,3,1,7,5,4]=>0000000=>1111111=>1
[2,6,8,1,3,7,5,4]=>0000000=>1111111=>1
[2,5,1,8,3,7,6,4]=>0000000=>1111111=>1
[1,2,5,8,3,7,6,4]=>1100000=>0011111=>1
[2,4,1,3,8,7,6,5]=>0001000=>1110111=>2
[2,5,3,8,1,7,6,4]=>0000000=>1111111=>1
[2,5,4,8,7,1,6,3]=>0000000=>1111111=>1
[3,5,4,8,7,6,1,2]=>0000000=>1111111=>1
[5,3,4,8,7,6,1,2]=>0000000=>1111111=>1
[5,2,4,8,7,1,6,3]=>0000000=>1111111=>1
[5,2,3,8,1,7,6,4]=>0000000=>1111111=>1
[4,2,1,3,8,7,6,5]=>0001000=>1110111=>2
[4,1,2,3,8,7,6,5]=>0001000=>1110111=>2
[1,4,2,3,8,7,6,5]=>1001000=>0110111=>2
[4,1,3,2,8,7,6,5]=>0001000=>1110111=>2
[4,3,1,2,8,7,6,5]=>0001000=>1110111=>2
[6,3,8,1,2,7,5,4]=>0000000=>1111111=>1
[5,3,1,8,2,7,6,4]=>0000000=>1111111=>1
[5,1,3,8,2,7,6,4]=>0000000=>1111111=>1
[1,5,3,8,2,7,6,4]=>1000000=>0111111=>1
[1,5,4,8,7,2,6,3]=>1000000=>0111111=>1
[5,1,4,8,7,2,6,3]=>0000000=>1111111=>1
[5,4,1,8,7,2,6,3]=>0000000=>1111111=>1
[6,4,8,1,7,2,5,3]=>0000000=>1111111=>1
[6,5,8,7,1,2,4,3]=>0000000=>1111111=>1
[5,6,8,7,3,4,1,2]=>0000000=>1111111=>1
[5,6,8,7,2,1,4,3]=>0000000=>1111111=>1
[4,5,1,8,7,2,6,3]=>0000000=>1111111=>1
[4,1,5,8,7,2,6,3]=>0000000=>1111111=>1
[1,4,5,8,7,2,6,3]=>1000000=>0111111=>1
[1,3,5,8,2,7,6,4]=>1000000=>0111111=>1
[3,1,5,8,2,7,6,4]=>0000000=>1111111=>1
[3,6,8,1,2,7,5,4]=>0000000=>1111111=>1
[3,6,8,2,1,7,5,4]=>0000000=>1111111=>1
[4,6,8,2,7,1,5,3]=>0000000=>1111111=>1
[4,6,8,3,7,5,1,2]=>0000000=>1111111=>1
[4,5,3,8,7,6,1,2]=>0000000=>1111111=>1
[4,5,2,8,7,1,6,3]=>0000000=>1111111=>1
[3,5,2,8,1,7,6,4]=>0000000=>1111111=>1
[3,1,4,2,8,7,6,5]=>0001000=>1110111=>2
[3,1,2,4,8,7,6,5]=>0011000=>1100111=>2
[3,2,5,8,1,7,6,4]=>0000000=>1111111=>1
[4,2,5,8,7,1,6,3]=>0000000=>1111111=>1
[4,3,5,8,7,6,1,2]=>0000000=>1111111=>1
[3,4,5,8,7,6,1,2]=>0000000=>1111111=>1
[2,4,5,8,7,1,6,3]=>0000000=>1111111=>1
[2,3,5,8,1,7,6,4]=>0000000=>1111111=>1
[4,1,3,2,6,5,8,7]=>0001010=>1110101=>3
[7,1,3,2,5,4,8,6]=>0000000=>1111111=>1
[8,1,3,2,5,4,7,6]=>0000000=>1111111=>1
[8,1,4,2,5,3,7,6]=>0000000=>1111111=>1
[7,1,4,2,5,3,8,6]=>0000000=>1111111=>1
[5,1,4,2,6,3,8,7]=>0000010=>1111101=>2
[2,1,6,3,5,4,8,7]=>0100010=>1011101=>3
[3,1,6,2,5,4,8,7]=>0000010=>1111101=>2
[4,1,6,2,5,3,8,7]=>0000010=>1111101=>2
[5,2,7,1,4,3,8,6]=>0000000=>1111111=>1
[5,2,8,1,4,3,7,6]=>0000000=>1111111=>1
[6,2,8,1,4,3,7,5]=>0000000=>1111111=>1
[6,2,7,1,4,3,8,5]=>0000000=>1111111=>1
[4,1,7,2,5,3,8,6]=>0000000=>1111111=>1
[3,1,7,2,5,4,8,6]=>0000000=>1111111=>1
[2,1,7,3,5,4,8,6]=>0100000=>1011111=>2
[2,1,8,3,5,4,7,6]=>0100000=>1011111=>2
[3,1,8,2,5,4,7,6]=>0000000=>1111111=>1
[4,1,8,2,5,3,7,6]=>0000000=>1111111=>1
[8,2,6,1,4,3,7,5]=>0000000=>1111111=>1
[7,1,4,3,8,2,6,5]=>0000000=>1111111=>1
[8,1,5,3,7,2,6,4]=>0000000=>1111111=>1
[7,1,5,3,8,2,6,4]=>0000000=>1111111=>1
[5,1,8,2,6,3,7,4]=>0000000=>1111111=>1
[4,1,8,2,6,3,7,5]=>0000000=>1111111=>1
[3,1,8,2,6,4,7,5]=>0000000=>1111111=>1
[2,1,8,3,6,4,7,5]=>0100000=>1011111=>2
[2,1,7,3,6,4,8,5]=>0100000=>1011111=>2
[4,1,7,2,6,3,8,5]=>0000000=>1111111=>1
[5,1,7,2,6,3,8,4]=>0000000=>1111111=>1
[6,2,7,1,5,3,8,4]=>0000000=>1111111=>1
[8,1,5,2,6,3,7,4]=>0000000=>1111111=>1
[6,1,4,2,7,3,8,5]=>0000000=>1111111=>1
[8,1,4,2,6,3,7,5]=>0000000=>1111111=>1
[8,1,3,2,6,4,7,5]=>0000000=>1111111=>1
[7,1,3,2,6,4,8,5]=>0000000=>1111111=>1
[6,1,3,2,7,4,8,5]=>0000000=>1111111=>1
[5,1,3,2,7,4,8,6]=>0000000=>1111111=>1
[2,1,4,3,8,5,7,6]=>0101000=>1010111=>3
[3,1,4,2,8,5,7,6]=>0001000=>1110111=>2
[4,1,3,2,8,5,7,6]=>0001000=>1110111=>2
[5,1,3,2,8,4,7,6]=>0000000=>1111111=>1
[6,1,3,2,8,4,7,5]=>0000000=>1111111=>1
[8,4,7,1,3,2,6,5]=>0000000=>1111111=>1
[7,4,8,1,3,2,6,5]=>0000000=>1111111=>1
[7,3,8,1,4,2,6,5]=>0000000=>1111111=>1
[8,3,7,1,4,2,6,5]=>0000000=>1111111=>1
[6,1,4,2,8,3,7,5]=>0000000=>1111111=>1
[5,1,4,2,8,3,7,6]=>0000000=>1111111=>1
[4,1,5,2,8,3,7,6]=>0000000=>1111111=>1
[3,1,5,2,8,4,7,6]=>0000000=>1111111=>1
[2,1,5,3,8,4,7,6]=>0100000=>1011111=>2
[2,1,6,3,8,4,7,5]=>0100000=>1011111=>2
[3,1,6,2,8,4,7,5]=>0000000=>1111111=>1
[4,1,6,2,8,3,7,5]=>0000000=>1111111=>1
[5,1,6,2,8,3,7,4]=>0000000=>1111111=>1
[6,1,5,2,8,3,7,4]=>0000000=>1111111=>1
[6,2,7,3,8,1,5,4]=>0000000=>1111111=>1
[6,2,8,3,7,1,5,4]=>0000000=>1111111=>1
[8,3,7,2,6,1,5,4]=>0000000=>1111111=>1
[5,1,8,3,7,2,6,4]=>0000000=>1111111=>1
[4,1,8,3,7,2,6,5]=>0000000=>1111111=>1
[3,1,8,4,7,2,6,5]=>0000000=>1111111=>1
[2,1,8,4,7,3,6,5]=>0100000=>1011111=>2
[3,1,7,4,8,2,6,5]=>0000000=>1111111=>1
[5,1,7,3,8,2,6,4]=>0000000=>1111111=>1
[7,3,8,2,6,1,5,4]=>0000000=>1111111=>1
[8,2,6,3,7,1,5,4]=>0000000=>1111111=>1
[7,2,6,3,8,1,5,4]=>0000000=>1111111=>1
[3,4,2,6,8,1,5,7]=>0000000=>1111111=>1
[5,3,6,2,8,1,4,7]=>0000000=>1111111=>1
[5,3,6,2,4,8,1,7]=>0000000=>1111111=>1
[5,7,3,8,2,4,1,6]=>0000000=>1111111=>1
[5,7,3,8,2,4,6,1]=>0000000=>1111111=>1
[7,4,2,5,8,3,6,1]=>0000000=>1111111=>1
[7,4,2,5,8,3,1,6]=>0000000=>1111111=>1
[4,5,2,6,3,8,1,7]=>0000000=>1111111=>1
[4,5,2,1,6,8,3,7]=>0000000=>1111111=>1
[5,3,1,6,8,2,4,7]=>0000000=>1111111=>1
[5,6,2,8,1,3,4,7]=>0000000=>1111111=>1
[3,5,6,1,4,8,2,7]=>0000000=>1111111=>1
[4,1,5,6,3,8,2,7]=>0000000=>1111111=>1
[4,5,1,6,3,8,2,7]=>0000000=>1111111=>1
[4,5,6,3,2,8,1,7]=>0000000=>1111111=>1
[7,4,5,3,8,2,1,6]=>0000000=>1111111=>1
[7,4,5,3,8,2,6,1]=>0000000=>1111111=>1
[6,7,4,8,3,2,5,1]=>0000000=>1111111=>1
[6,7,4,8,3,2,1,5]=>0000000=>1111111=>1
[6,7,4,1,8,3,2,5]=>0000000=>1111111=>1
[7,4,5,3,1,8,2,6]=>0000000=>1111111=>1
[4,7,1,5,8,3,2,6]=>0000000=>1111111=>1
[5,3,7,8,1,4,2,6]=>0000000=>1111111=>1
[7,5,8,2,4,6,1,3]=>0000000=>1111111=>1
[7,3,5,8,1,4,6,2]=>0000000=>1111111=>1
[4,5,1,7,8,3,6,2]=>0000000=>1111111=>1
[7,4,1,5,8,3,6,2]=>0000000=>1111111=>1
[6,7,4,3,8,1,5,2]=>0000000=>1111111=>1
[6,7,4,8,3,1,5,2]=>0000000=>1111111=>1
[6,7,4,8,3,5,2,1]=>0000000=>1111111=>1
[5,6,7,3,8,4,2,1]=>0000000=>1111111=>1
[5,6,7,3,1,8,4,2]=>0000000=>1111111=>1
[5,6,1,7,3,8,4,2]=>0000000=>1111111=>1
[5,1,6,7,3,8,4,2]=>0000000=>1111111=>1
[6,4,7,1,8,3,5,2]=>0000000=>1111111=>1
[6,7,8,3,1,4,5,2]=>0000000=>1111111=>1
[6,7,2,8,4,5,1,3]=>0000000=>1111111=>1
[6,7,2,8,4,1,3,5]=>0000000=>1111111=>1
[6,1,7,4,8,3,2,5]=>0000000=>1111111=>1
[5,1,6,7,3,2,8,4]=>0000000=>1111111=>1
[5,6,1,7,3,2,8,4]=>0000000=>1111111=>1
[5,6,7,3,2,1,8,4]=>0000000=>1111111=>1
[5,6,7,3,2,8,4,1]=>0000000=>1111111=>1
[5,6,2,7,3,8,4,1]=>0000000=>1111111=>1
[5,6,2,7,3,1,8,4]=>0000000=>1111111=>1
[5,6,2,1,7,3,8,4]=>0000000=>1111111=>1
[6,1,7,4,2,8,3,5]=>0000000=>1111111=>1
[6,7,2,1,8,3,4,5]=>0000000=>1111111=>1
[7,5,8,2,1,3,4,6]=>0000000=>1111111=>1
[5,7,3,1,8,2,4,6]=>0000000=>1111111=>1
[4,7,1,5,2,8,3,6]=>0000000=>1111111=>1
[7,4,2,5,1,8,3,6]=>0000000=>1111111=>1
[6,7,4,2,1,8,3,5]=>0000000=>1111111=>1
[6,7,4,2,8,3,1,5]=>0000000=>1111111=>1
[6,7,4,2,8,3,5,1]=>0000000=>1111111=>1
[3,6,7,2,8,4,5,1]=>0000000=>1111111=>1
[3,6,7,2,8,4,1,5]=>0000000=>1111111=>1
[3,6,7,2,1,8,4,5]=>0000000=>1111111=>1
[5,7,3,8,2,1,4,6]=>0000000=>1111111=>1
[3,4,7,8,2,1,5,6]=>0000000=>1111111=>1
[3,7,8,1,4,6,2,5]=>0000000=>1111111=>1
[3,4,7,8,2,6,1,5]=>0000000=>1111111=>1
[5,7,3,8,2,6,1,4]=>0000000=>1111111=>1
[3,6,7,2,8,5,1,4]=>0000000=>1111111=>1
[3,6,7,8,5,2,1,4]=>0000000=>1111111=>1
[3,6,7,8,5,2,4,1]=>0000000=>1111111=>1
[6,4,7,8,2,5,3,1]=>0000000=>1111111=>1
[6,4,7,8,2,1,5,3]=>0000000=>1111111=>1
[4,1,5,7,8,2,6,3]=>0000000=>1111111=>1
[5,3,7,8,1,6,2,4]=>0000000=>1111111=>1
[6,7,2,8,5,1,3,4]=>0000000=>1111111=>1
[6,4,1,7,8,2,5,3]=>0000000=>1111111=>1
[5,1,6,2,7,8,4,3]=>0000000=>1111111=>1
[5,6,2,1,7,8,4,3]=>0000000=>1111111=>1
[5,6,2,7,1,8,4,3]=>0000000=>1111111=>1
[5,6,2,7,8,4,3,1]=>0000000=>1111111=>1
[5,6,7,2,8,4,3,1]=>0000000=>1111111=>1
[5,6,7,2,1,8,4,3]=>0000000=>1111111=>1
[5,6,1,7,2,8,4,3]=>0000000=>1111111=>1
[5,1,6,7,2,8,4,3]=>0000000=>1111111=>1
[6,4,7,1,8,2,5,3]=>0000000=>1111111=>1
[3,6,7,1,8,5,2,4]=>0000000=>1111111=>1
[6,7,8,5,2,4,1,3]=>0000000=>1111111=>1
[6,7,8,3,5,1,4,2]=>0000000=>1111111=>1
[4,6,7,8,1,5,3,2]=>0000000=>1111111=>1
[5,1,6,7,8,4,3,2]=>0000000=>1111111=>1
[5,6,1,7,8,4,3,2]=>0000000=>1111111=>1
[5,6,7,1,8,4,3,2]=>0000000=>1111111=>1
[8,6,1,3,4,2,5,7]=>0000000=>1111111=>1
[8,3,2,5,1,6,4,7]=>0000000=>1111111=>1
[8,5,3,6,2,4,1,7]=>0000000=>1111111=>1
[5,3,2,7,4,1,8,6]=>0000000=>1111111=>1
[7,5,3,8,2,4,6,1]=>0000000=>1111111=>1
[7,2,4,5,8,3,6,1]=>0000000=>1111111=>1
[2,4,5,3,7,1,8,6]=>0000000=>1111111=>1
[8,2,4,5,6,3,1,7]=>0000000=>1111111=>1
[8,2,4,5,6,1,3,7]=>0000000=>1111111=>1
[8,1,2,4,5,6,3,7]=>0000000=>1111111=>1
[8,2,5,1,3,6,4,7]=>0000000=>1111111=>1
[8,5,6,2,1,4,3,7]=>0000000=>1111111=>1
[8,5,3,6,4,1,2,7]=>0000000=>1111111=>1
[8,4,1,5,6,3,2,7]=>0000000=>1111111=>1
[8,1,4,5,6,3,2,7]=>0000000=>1111111=>1
[4,5,3,7,2,1,8,6]=>0000000=>1111111=>1
[7,4,5,8,3,2,6,1]=>0000000=>1111111=>1
[4,3,6,7,2,8,5,1]=>0000000=>1111111=>1
[4,3,6,7,2,8,1,5]=>0000000=>1111111=>1
[1,4,3,6,7,2,8,5]=>1000000=>0111111=>1
[4,5,3,7,1,8,2,6]=>0000000=>1111111=>1
[4,1,5,3,7,2,8,6]=>0000000=>1111111=>1
[5,3,4,7,1,2,8,6]=>0000000=>1111111=>1
[7,5,8,2,1,4,6,3]=>0000000=>1111111=>1
[7,5,3,8,4,1,6,2]=>0000000=>1111111=>1
[7,4,5,8,3,6,1,2]=>0000000=>1111111=>1
[4,3,6,7,8,1,5,2]=>0000000=>1111111=>1
[1,6,4,7,8,3,5,2]=>1000000=>0111111=>1
[6,4,7,8,3,5,2,1]=>0000000=>1111111=>1
[3,5,6,7,8,4,1,2]=>0000000=>1111111=>1
[3,1,5,6,7,8,4,2]=>0000000=>1111111=>1
[4,6,1,7,8,3,5,2]=>0000000=>1111111=>1
[3,6,7,1,4,8,5,2]=>0000000=>1111111=>1
[6,2,4,1,7,8,5,3]=>0000000=>1111111=>1
[2,6,7,1,4,8,3,5]=>0000000=>1111111=>1
[4,3,6,7,8,1,2,5]=>0000000=>1111111=>1
[1,5,3,6,7,8,2,4]=>1000000=>0111111=>1
[3,5,6,7,8,2,1,4]=>0000000=>1111111=>1
[3,5,6,7,8,2,4,1]=>0000000=>1111111=>1
[5,2,7,1,3,8,4,6]=>0000000=>1111111=>1
[5,3,1,7,8,2,4,6]=>0000000=>1111111=>1
[4,5,2,7,8,1,3,6]=>0000000=>1111111=>1
[4,2,6,7,8,3,1,5]=>0000000=>1111111=>1
[4,2,6,7,8,3,5,1]=>0000000=>1111111=>1
[3,6,2,7,4,8,5,1]=>0000000=>1111111=>1
[3,6,2,7,4,8,1,5]=>0000000=>1111111=>1
[3,2,1,6,4,7,8,5]=>0010000=>1101111=>2
[3,7,4,2,1,5,8,6]=>0000000=>1111111=>1
[1,7,3,4,2,5,8,6]=>1000000=>0111111=>1
[4,7,2,1,3,5,8,6]=>0000000=>1111111=>1
[7,8,4,2,1,3,6,5]=>0000000=>1111111=>1
[7,8,1,3,4,2,6,5]=>0000000=>1111111=>1
[7,8,3,4,2,1,6,5]=>0000000=>1111111=>1
[6,3,2,7,1,8,5,4]=>0000000=>1111111=>1
[3,6,2,7,1,8,5,4]=>0000000=>1111111=>1
[6,7,3,8,2,5,4,1]=>0000000=>1111111=>1
[6,4,7,8,5,2,3,1]=>0000000=>1111111=>1
[2,6,4,7,8,1,5,3]=>0000000=>1111111=>1
[4,6,2,7,8,1,5,3]=>0000000=>1111111=>1
[7,4,5,8,6,2,1,3]=>0000000=>1111111=>1
[7,4,1,5,8,6,2,3]=>0000000=>1111111=>1
[7,5,3,8,6,1,2,4]=>0000000=>1111111=>1
[7,5,8,2,1,6,3,4]=>0000000=>1111111=>1
[6,2,7,1,3,8,5,4]=>0000000=>1111111=>1
[6,3,1,7,8,2,5,4]=>0000000=>1111111=>1
[4,6,1,7,8,5,2,3]=>0000000=>1111111=>1
[5,1,2,6,7,8,4,3]=>0000000=>1111111=>1
[5,2,6,7,8,4,1,3]=>0000000=>1111111=>1
[5,2,6,7,8,4,3,1]=>0000000=>1111111=>1
[2,5,6,7,8,4,1,3]=>0000000=>1111111=>1
[1,5,2,6,7,8,4,3]=>1000000=>0111111=>1
[1,6,4,7,8,5,2,3]=>1000000=>0111111=>1
[2,6,7,1,3,8,5,4]=>0000000=>1111111=>1
[6,7,8,2,1,5,4,3]=>0000000=>1111111=>1
[6,7,3,8,5,1,4,2]=>0000000=>1111111=>1
[6,4,7,8,5,3,1,2]=>0000000=>1111111=>1
[4,5,2,3,7,6,1,8]=>0000001=>1111110=>1
[6,4,3,7,2,5,1,8]=>0000001=>1111110=>1
[8,4,3,6,5,1,2,7]=>0000000=>1111111=>1
[1,5,6,3,4,8,7,2]=>1000000=>0111111=>1
[4,6,2,7,3,5,1,8]=>0000001=>1111110=>1
[3,2,6,7,4,5,1,8]=>0000001=>1111110=>1
[4,7,2,6,5,3,1,8]=>0000001=>1111110=>1
[5,7,6,2,4,3,1,8]=>0000001=>1111110=>1
[1,7,5,4,8,3,6,2]=>1000000=>0111111=>1
[8,7,5,4,1,3,2,6]=>0000000=>1111111=>1
[6,8,5,4,2,1,3,7]=>0000000=>1111111=>1
[5,8,6,2,4,1,3,7]=>0000000=>1111111=>1
[4,8,2,6,5,1,3,7]=>0000000=>1111111=>1
[3,2,8,6,5,1,4,7]=>0000000=>1111111=>1
[4,1,2,6,5,8,7,3]=>0000000=>1111111=>1
[5,1,6,2,4,8,7,3]=>0000000=>1111111=>1
[6,1,5,4,2,8,7,3]=>0000000=>1111111=>1
[7,1,5,4,8,2,6,3]=>0000000=>1111111=>1
[8,1,5,4,7,6,2,3]=>0000000=>1111111=>1
[1,8,6,7,4,5,3,2]=>1000000=>0111111=>1
[8,1,6,7,4,5,2,3]=>0000000=>1111111=>1
[7,1,6,8,4,2,5,3]=>0000000=>1111111=>1
[6,1,7,8,2,4,5,3]=>0000000=>1111111=>1
[5,1,7,2,8,4,6,3]=>0000000=>1111111=>1
[4,1,2,7,8,5,6,3]=>0000000=>1111111=>1
[3,2,1,7,8,5,6,4]=>0010000=>1101111=>2
[3,2,8,7,1,5,4,6]=>0000000=>1111111=>1
[4,8,2,7,1,5,3,6]=>0000000=>1111111=>1
[5,8,7,2,1,4,3,6]=>0000000=>1111111=>1
[6,8,7,1,2,4,3,5]=>0000000=>1111111=>1
[7,8,6,1,4,2,3,5]=>0000000=>1111111=>1
[8,7,6,1,4,3,2,5]=>0000000=>1111111=>1
[1,7,6,8,4,3,5,2]=>1000000=>0111111=>1
[1,6,7,8,3,4,5,2]=>1000000=>0111111=>1
[8,6,7,1,3,4,2,5]=>0000000=>1111111=>1
[7,6,8,1,3,2,4,5]=>0000000=>1111111=>1
[5,7,8,2,1,3,4,6]=>0000000=>1111111=>1
[4,7,2,8,1,3,5,6]=>0000000=>1111111=>1
[3,2,6,8,4,1,5,7]=>0000000=>1111111=>1
[4,6,2,8,3,1,5,7]=>0000000=>1111111=>1
[5,6,8,2,3,1,4,7]=>0000000=>1111111=>1
[6,5,8,3,2,1,4,7]=>0000000=>1111111=>1
[7,5,8,3,1,2,4,6]=>0000000=>1111111=>1
[8,5,7,3,1,4,2,6]=>0000000=>1111111=>1
[1,5,7,3,8,4,6,2]=>1000000=>0111111=>1
[1,4,3,7,8,5,6,2]=>1000000=>0111111=>1
[8,4,3,7,1,5,2,6]=>0000000=>1111111=>1
[6,4,3,8,2,1,5,7]=>0000000=>1111111=>1
[4,5,2,3,8,1,6,7]=>0000000=>1111111=>1
[3,2,5,4,8,1,6,7]=>0000000=>1111111=>1
[4,5,2,3,1,8,7,6]=>0000100=>1111011=>2
[6,4,3,1,2,8,7,5]=>0000000=>1111111=>1
[7,4,3,1,8,2,6,5]=>0000000=>1111111=>1
[8,4,3,1,7,6,2,5]=>0000000=>1111111=>1
[1,5,8,3,7,6,4,2]=>1000000=>0111111=>1
[8,5,1,3,7,6,2,4]=>0000000=>1111111=>1
[7,5,1,3,8,2,6,4]=>0000000=>1111111=>1
[6,5,1,3,2,8,7,4]=>0000000=>1111111=>1
[5,6,1,2,3,8,7,4]=>0000000=>1111111=>1
[4,6,2,1,3,8,7,5]=>0000000=>1111111=>1
[3,2,6,1,4,8,7,5]=>0000000=>1111111=>1
[3,2,7,1,8,4,6,5]=>0000000=>1111111=>1
[4,7,2,1,8,3,6,5]=>0000000=>1111111=>1
[5,7,1,2,8,3,6,4]=>0000000=>1111111=>1
[6,7,1,8,2,3,5,4]=>0000000=>1111111=>1
[7,6,1,8,3,2,5,4]=>0000000=>1111111=>1
[8,6,1,7,3,5,2,4]=>0000000=>1111111=>1
[1,6,8,7,3,5,4,2]=>1000000=>0111111=>1
[1,7,8,6,5,3,4,2]=>1000000=>0111111=>1
[8,7,1,6,5,3,2,4]=>0000000=>1111111=>1
[7,8,1,6,5,2,3,4]=>0000000=>1111111=>1
[6,8,1,7,2,5,3,4]=>0000000=>1111111=>1
[5,8,1,2,7,6,3,4]=>0000000=>1111111=>1
[4,8,2,1,7,6,3,5]=>0000000=>1111111=>1
[3,2,8,1,7,6,4,5]=>0000000=>1111111=>1
[4,1,2,8,7,6,5,3]=>0000000=>1111111=>1
[5,1,8,2,7,6,4,3]=>0000000=>1111111=>1
[6,1,8,7,2,5,4,3]=>0000000=>1111111=>1
[7,1,8,6,5,2,4,3]=>0000000=>1111111=>1
[8,1,7,6,5,4,2,3]=>0000000=>1111111=>1
[3,1,2,6,5,8,7,4]=>0010000=>1101111=>2
[3,1,6,2,4,8,7,5]=>0000000=>1111111=>1
[3,1,5,2,4,8,7,6]=>0000100=>1111011=>2
[4,5,1,2,3,8,7,6]=>0000100=>1111011=>2
[4,6,1,2,3,8,7,5]=>0000000=>1111111=>1
[1,6,5,3,4,8,7,2]=>1000000=>0111111=>1
[6,1,5,2,4,8,7,3]=>0000000=>1111111=>1
[6,5,1,2,3,8,7,4]=>0000000=>1111111=>1
[6,4,1,2,3,8,7,5]=>0000000=>1111111=>1
[5,4,1,2,3,8,7,6]=>0000100=>1111011=>2
[5,4,1,2,7,3,6,8]=>0000001=>1111110=>1
[6,4,1,7,2,3,5,8]=>0000001=>1111110=>1
[6,4,1,8,2,3,5,7]=>0000000=>1111111=>1
[7,4,1,2,8,3,6,5]=>0000000=>1111111=>1
[7,5,1,2,8,3,6,4]=>0000000=>1111111=>1
[7,1,5,2,8,4,6,3]=>0000000=>1111111=>1
[1,7,5,3,8,4,6,2]=>1000000=>0111111=>1
[1,8,5,3,7,4,6,2]=>1000000=>0111111=>1
[8,1,5,2,7,4,6,3]=>0000000=>1111111=>1
[8,5,1,2,7,3,6,4]=>0000000=>1111111=>1
[8,4,1,2,7,3,6,5]=>0000000=>1111111=>1
[8,4,1,7,2,3,5,6]=>0000000=>1111111=>1
[7,4,1,6,2,3,5,8]=>0000001=>1111110=>1
[8,6,1,7,2,3,5,4]=>0000000=>1111111=>1
[8,1,6,7,2,4,5,3]=>0000000=>1111111=>1
[1,8,6,7,3,4,5,2]=>1000000=>0111111=>1
[1,7,6,8,3,4,5,2]=>1000000=>0111111=>1
[7,1,6,8,2,4,5,3]=>0000000=>1111111=>1
[7,6,1,8,2,3,5,4]=>0000000=>1111111=>1
[4,7,1,2,8,3,6,5]=>0000000=>1111111=>1
[3,1,7,2,8,4,6,5]=>0000000=>1111111=>1
[3,1,2,7,8,5,6,4]=>0010000=>1101111=>2
[1,4,3,8,7,5,6,2]=>1000000=>0111111=>1
[4,1,2,8,7,5,6,3]=>0000000=>1111111=>1
[3,1,2,8,7,5,6,4]=>0010000=>1101111=>2
[3,1,8,2,7,4,6,5]=>0000000=>1111111=>1
[3,1,8,7,2,4,5,6]=>0000000=>1111111=>1
[3,1,7,6,2,4,5,8]=>0000001=>1111110=>1
[4,7,1,6,2,3,5,8]=>0000001=>1111110=>1
[4,8,1,6,2,3,5,7]=>0000000=>1111111=>1
[4,8,1,7,2,3,5,6]=>0000000=>1111111=>1
[4,8,1,2,7,3,6,5]=>0000000=>1111111=>1
[5,8,1,2,7,3,6,4]=>0000000=>1111111=>1
[5,1,8,2,7,4,6,3]=>0000000=>1111111=>1
[1,5,8,3,7,4,6,2]=>1000000=>0111111=>1
[1,6,8,7,3,4,5,2]=>1000000=>0111111=>1
[6,1,8,7,2,4,5,3]=>0000000=>1111111=>1
[6,8,1,7,2,3,5,4]=>0000000=>1111111=>1
[6,8,7,1,2,3,4,5]=>0000000=>1111111=>1
[5,8,7,1,2,3,4,6]=>0000000=>1111111=>1
[5,8,6,1,2,3,4,7]=>0000000=>1111111=>1
[5,7,6,1,2,3,4,8]=>0000001=>1111110=>1
[7,8,1,6,2,3,5,4]=>0000000=>1111111=>1
[7,1,8,6,2,4,5,3]=>0000000=>1111111=>1
[1,7,8,6,3,4,5,2]=>1000000=>0111111=>1
[1,8,7,6,3,4,5,2]=>1000000=>0111111=>1
[8,1,7,6,2,4,5,3]=>0000000=>1111111=>1
[8,7,1,6,2,3,5,4]=>0000000=>1111111=>1
[3,2,5,4,7,1,8,6]=>0000000=>1111111=>1
[4,2,5,3,7,6,8,1]=>0000000=>1111111=>1
[4,2,5,3,7,1,8,6]=>0000000=>1111111=>1
[4,2,5,3,6,1,8,7]=>0000010=>1111101=>2
[4,2,5,1,6,3,8,7]=>0000010=>1111101=>2
[3,1,5,4,6,2,8,7]=>0000010=>1111101=>2
[4,1,5,3,6,2,8,7]=>0000010=>1111101=>2
[4,3,5,1,6,2,8,7]=>0000010=>1111101=>2
[4,3,5,2,7,1,8,6]=>0000000=>1111111=>1
[4,3,6,2,7,5,8,1]=>0000000=>1111111=>1
[4,3,6,2,7,1,8,5]=>0000000=>1111111=>1
[4,3,6,1,7,2,8,5]=>0000000=>1111111=>1
[4,3,5,1,7,2,8,6]=>0000000=>1111111=>1
[3,1,5,4,7,2,8,6]=>0000000=>1111111=>1
[2,1,5,4,7,3,8,6]=>0100000=>1011111=>2
[4,1,5,3,7,6,8,2]=>0000000=>1111111=>1
[4,3,5,1,7,6,8,2]=>0000000=>1111111=>1
[4,3,6,1,7,5,8,2]=>0000000=>1111111=>1
[4,3,6,5,7,1,8,2]=>0000000=>1111111=>1
[5,3,6,4,7,2,8,1]=>0000000=>1111111=>1
[5,3,6,4,7,1,8,2]=>0000000=>1111111=>1
[5,3,6,1,7,4,8,2]=>0000000=>1111111=>1
[5,1,6,3,7,4,8,2]=>0000000=>1111111=>1
[4,1,6,3,7,5,8,2]=>0000000=>1111111=>1
[3,1,6,4,7,5,8,2]=>0000000=>1111111=>1
[2,1,6,4,7,3,8,5]=>0100000=>1011111=>2
[3,1,6,4,7,2,8,5]=>0000000=>1111111=>1
[4,1,6,3,7,2,8,5]=>0000000=>1111111=>1
[5,1,6,3,7,2,8,4]=>0000000=>1111111=>1
[5,3,6,1,7,2,8,4]=>0000000=>1111111=>1
[5,3,6,2,7,1,8,4]=>0000000=>1111111=>1
[5,3,6,2,7,4,8,1]=>0000000=>1111111=>1
[5,2,6,3,7,4,8,1]=>0000000=>1111111=>1
[5,2,6,3,7,1,8,4]=>0000000=>1111111=>1
[5,2,6,1,7,3,8,4]=>0000000=>1111111=>1
[4,2,5,1,7,3,8,6]=>0000000=>1111111=>1
[4,2,6,1,7,3,8,5]=>0000000=>1111111=>1
[4,2,6,3,7,1,8,5]=>0000000=>1111111=>1
[4,2,6,3,7,5,8,1]=>0000000=>1111111=>1
[3,2,6,4,7,5,8,1]=>0000000=>1111111=>1
[3,2,6,4,7,1,8,5]=>0000000=>1111111=>1
[3,2,6,1,7,4,8,5]=>0000000=>1111111=>1
[3,2,5,1,7,4,8,6]=>0000000=>1111111=>1
[3,1,4,2,7,6,8,5]=>0001000=>1110111=>2
[3,2,5,1,7,6,8,4]=>0000000=>1111111=>1
[3,2,6,1,7,5,8,4]=>0000000=>1111111=>1
[3,2,6,5,7,1,8,4]=>0000000=>1111111=>1
[4,2,6,5,7,1,8,3]=>0000000=>1111111=>1
[4,2,6,1,7,5,8,3]=>0000000=>1111111=>1
[4,2,5,1,7,6,8,3]=>0000000=>1111111=>1
[4,1,6,2,7,5,8,3]=>0000000=>1111111=>1
[5,1,6,2,7,4,8,3]=>0000000=>1111111=>1
[5,2,6,1,7,4,8,3]=>0000000=>1111111=>1
[5,2,6,4,7,1,8,3]=>0000000=>1111111=>1
[5,2,6,4,7,3,8,1]=>0000000=>1111111=>1
[5,4,6,2,7,3,8,1]=>0000000=>1111111=>1
[5,4,6,2,7,1,8,3]=>0000000=>1111111=>1
[5,4,6,1,7,2,8,3]=>0000000=>1111111=>1
[5,1,6,4,7,2,8,3]=>0000000=>1111111=>1
[4,1,6,5,7,2,8,3]=>0000000=>1111111=>1
[3,1,6,5,7,2,8,4]=>0000000=>1111111=>1
[2,1,6,5,7,3,8,4]=>0100000=>1011111=>2
[4,1,6,5,7,3,8,2]=>0000000=>1111111=>1
[5,1,6,4,7,3,8,2]=>0000000=>1111111=>1
[5,4,6,1,7,3,8,2]=>0000000=>1111111=>1
[5,4,6,3,7,1,8,2]=>0000000=>1111111=>1
[8,3,5,2,1,6,4,7]=>0000000=>1111111=>1
[8,6,3,5,2,4,1,7]=>0000000=>1111111=>1
[3,7,5,2,4,1,8,6]=>0000000=>1111111=>1
[8,3,7,5,2,4,6,1]=>0000000=>1111111=>1
[8,2,4,5,7,3,6,1]=>0000000=>1111111=>1
[2,4,5,7,3,1,8,6]=>0000000=>1111111=>1
[8,2,4,6,5,3,1,7]=>0000000=>1111111=>1
[8,2,5,4,6,1,3,7]=>0000000=>1111111=>1
[8,6,3,5,1,4,2,7]=>0000000=>1111111=>1
[8,6,1,4,5,3,2,7]=>0000000=>1111111=>1
[8,1,5,6,4,3,2,7]=>0000000=>1111111=>1
[5,7,4,3,2,1,8,6]=>0000000=>1111111=>1
[8,5,7,4,3,2,6,1]=>0000000=>1111111=>1
[4,6,8,3,2,7,5,1]=>0000000=>1111111=>1
[4,7,6,3,2,8,1,5]=>0000000=>1111111=>1
[1,4,6,7,3,2,8,5]=>1000000=>0111111=>1
[5,4,7,3,1,8,2,6]=>0000000=>1111111=>1
[1,7,4,5,3,2,8,6]=>1000000=>0111111=>1
[3,7,5,1,4,2,8,6]=>0000000=>1111111=>1
[5,7,4,2,1,3,8,6]=>0000000=>1111111=>1
[8,5,7,4,2,1,6,3]=>0000000=>1111111=>1
[8,3,7,5,1,4,6,2]=>0000000=>1111111=>1
[8,4,1,7,5,3,6,2]=>0000000=>1111111=>1
[4,6,3,8,7,1,5,2]=>0000000=>1111111=>1
[1,7,4,8,6,3,5,2]=>1000000=>0111111=>1
[8,4,7,6,3,5,2,1]=>0000000=>1111111=>1
[3,6,5,8,7,4,1,2]=>0000000=>1111111=>1
[3,1,5,8,6,7,4,2]=>0000000=>1111111=>1
[4,8,1,6,7,3,5,2]=>0000000=>1111111=>1
[3,6,4,1,8,7,5,2]=>0000000=>1111111=>1
[8,2,6,1,4,7,5,3]=>0000000=>1111111=>1
[2,7,6,8,1,4,3,5]=>0000000=>1111111=>1
[3,7,1,6,4,8,2,5]=>0000000=>1111111=>1
[1,7,3,5,6,8,2,4]=>1000000=>0111111=>1
[1,3,6,7,5,8,2,4]=>1000000=>0111111=>1
[3,7,6,5,8,2,1,4]=>0000000=>1111111=>1
[3,6,8,5,7,2,4,1]=>0000000=>1111111=>1
[2,3,5,7,6,8,1,4]=>0000000=>1111111=>1
[2,1,6,5,7,8,3,4]=>0100000=>1011111=>2
[4,2,7,6,8,3,1,5]=>0000000=>1111111=>1
[4,2,6,8,7,3,5,1]=>0000000=>1111111=>1
[3,8,2,4,6,7,5,1]=>0000000=>1111111=>1
[3,7,2,6,4,8,1,5]=>0000000=>1111111=>1
[3,2,6,1,4,7,8,5]=>0000000=>1111111=>1
[5,3,7,2,1,8,4,6]=>0000000=>1111111=>1
[4,7,3,2,1,5,8,6]=>0000000=>1111111=>1
[8,7,6,1,3,4,2,5]=>0000000=>1111111=>1
[8,5,7,3,2,1,6,4]=>0000000=>1111111=>1
[8,3,6,7,2,1,5,4]=>0000000=>1111111=>1
[3,7,8,6,2,1,5,4]=>0000000=>1111111=>1
[8,7,6,3,5,2,4,1]=>0000000=>1111111=>1
[2,7,4,8,1,6,5,3]=>0000000=>1111111=>1
[4,6,8,2,1,7,5,3]=>0000000=>1111111=>1
[8,4,1,5,7,2,6,3]=>0000000=>1111111=>1
[8,5,3,7,1,6,2,4]=>0000000=>1111111=>1
[8,5,7,2,1,3,6,4]=>0000000=>1111111=>1
[8,2,6,7,1,3,5,4]=>0000000=>1111111=>1
[8,3,6,1,7,5,2,4]=>0000000=>1111111=>1
[4,6,1,8,7,2,5,3]=>0000000=>1111111=>1
[8,1,2,5,6,7,4,3]=>0000000=>1111111=>1
[8,2,6,5,7,4,1,3]=>0000000=>1111111=>1
[2,1,7,8,5,6,4,3]=>0100000=>1011111=>2
[8,2,5,7,6,4,3,1]=>0000000=>1111111=>1
[2,7,6,8,5,4,1,3]=>0000000=>1111111=>1
[1,7,2,5,8,6,4,3]=>1000000=>0111111=>1
[1,7,4,8,2,6,5,3]=>1000000=>0111111=>1
[3,7,8,1,6,5,2,4]=>0000000=>1111111=>1
[2,7,8,6,1,3,5,4]=>0000000=>1111111=>1
[8,7,6,3,5,1,4,2]=>0000000=>1111111=>1
[8,4,7,6,5,1,3,2]=>0000000=>1111111=>1
[8,7,1,5,6,4,3,2]=>0000000=>1111111=>1
[8,1,6,7,5,4,3,2]=>0000000=>1111111=>1
[6,5,3,1,2,4,8,7]=>0000010=>1111101=>2
[4,6,3,5,1,2,8,7]=>0000010=>1111101=>2
[8,5,3,7,2,1,4,6]=>0000000=>1111111=>1
[5,4,3,6,1,2,8,7]=>0000010=>1111101=>2
[3,1,6,4,5,2,8,7]=>0000010=>1111101=>2
[5,8,7,4,2,6,3,1]=>0000000=>1111111=>1
[3,7,8,4,5,1,2,6]=>0000000=>1111111=>1
[2,1,8,7,5,3,4,6]=>0100000=>1011111=>2
[2,1,6,8,5,7,3,4]=>0100000=>1011111=>2
[5,6,3,8,1,7,2,4]=>0000000=>1111111=>1
[7,6,1,4,5,8,3,2]=>0000000=>1111111=>1
[3,7,6,4,5,8,2,1]=>0000000=>1111111=>1
[8,5,7,4,1,6,3,2]=>0000000=>1111111=>1
[2,5,8,4,7,6,1,3]=>0000000=>1111111=>1
[2,4,8,3,5,6,7,1]=>0000000=>1111111=>1
[3,8,4,2,5,6,7,1]=>0000000=>1111111=>1
[7,5,8,4,3,6,1,2]=>0000000=>1111111=>1
[2,1,5,8,4,6,7,3]=>0100000=>1011111=>2
[6,4,3,8,2,1,7,5]=>0000000=>1111111=>1
[7,3,8,4,2,6,1,5]=>0000000=>1111111=>1
[3,1,8,2,5,6,7,4]=>0000000=>1111111=>1
[2,3,8,1,5,6,7,4]=>0000000=>1111111=>1
[4,8,2,3,5,6,7,1]=>0000000=>1111111=>1
[3,8,2,1,5,6,7,4]=>0000000=>1111111=>1
[2,8,1,3,5,6,7,4]=>0000000=>1111111=>1
[8,1,2,3,5,6,7,4]=>0000000=>1111111=>1
[7,8,2,4,3,6,1,5]=>0000000=>1111111=>1
[6,8,3,2,4,1,7,5]=>0000000=>1111111=>1
[2,1,7,8,5,4,3,6]=>0100000=>1011111=>2
[5,7,3,8,1,4,2,6]=>0000000=>1111111=>1
[3,8,7,4,2,6,1,5]=>0000000=>1111111=>1
[5,6,3,8,4,2,7,1]=>0000000=>1111111=>1
[4,8,3,6,2,1,7,5]=>0000000=>1111111=>1
[7,5,3,8,2,4,1,6]=>0000000=>1111111=>1
[2,4,3,1,8,5,7,6]=>0001000=>1110111=>2
[4,1,3,2,6,8,7,5]=>0001000=>1110111=>2
[8,6,3,5,1,2,7,4]=>0000000=>1111111=>1
[5,7,3,6,1,8,2,4]=>0000000=>1111111=>1
[2,1,7,6,5,8,3,4]=>0100000=>1011111=>2
[6,8,3,5,2,1,7,4]=>0000000=>1111111=>1
[7,8,5,4,2,6,1,3]=>0000000=>1111111=>1
[8,1,4,2,5,6,7,3]=>0000000=>1111111=>1
[4,8,1,2,5,6,7,3]=>0000000=>1111111=>1
[3,4,8,1,5,6,7,2]=>0000000=>1111111=>1
[3,4,2,8,5,6,7,1]=>0000000=>1111111=>1
[4,1,2,8,5,6,7,3]=>0000000=>1111111=>1
[8,4,2,1,5,6,7,3]=>0000000=>1111111=>1
[6,5,3,2,8,1,7,4]=>0000000=>1111111=>1
[6,4,3,5,8,1,7,2]=>0000000=>1111111=>1
[8,3,4,1,5,6,7,2]=>0000000=>1111111=>1
[4,3,1,8,5,6,7,2]=>0000000=>1111111=>1
[5,1,7,4,8,6,3,2]=>0000000=>1111111=>1
[3,8,7,4,5,2,1,6]=>0000000=>1111111=>1
[5,7,1,4,8,6,2,3]=>0000000=>1111111=>1
[5,6,3,1,8,2,7,4]=>0000000=>1111111=>1
[4,6,3,5,8,2,7,1]=>0000000=>1111111=>1
[4,6,3,8,1,2,7,5]=>0000000=>1111111=>1
[3,2,5,1,6,8,4,7]=>0000000=>1111111=>1
[3,6,2,5,4,8,1,7]=>0000000=>1111111=>1
[3,5,2,4,7,1,8,6]=>0000000=>1111111=>1
[3,5,8,2,4,7,6,1]=>0000000=>1111111=>1
[4,2,5,8,3,7,6,1]=>0000000=>1111111=>1
[4,2,6,5,3,8,1,7]=>0000000=>1111111=>1
[5,4,2,1,6,8,3,7]=>0000000=>1111111=>1
[6,3,5,1,4,8,2,7]=>0000000=>1111111=>1
[4,6,1,5,3,8,2,7]=>0000000=>1111111=>1
[5,1,6,4,3,8,2,7]=>0000000=>1111111=>1
[5,4,3,2,7,1,8,6]=>0000000=>1111111=>1
[5,4,3,8,2,7,6,1]=>0000000=>1111111=>1
[4,3,6,2,8,7,5,1]=>0000000=>1111111=>1
[4,3,7,6,2,1,8,5]=>0000000=>1111111=>1
[6,4,3,1,7,2,8,5]=>0000000=>1111111=>1
[7,5,4,3,1,8,2,6]=>0000000=>1111111=>1
[1,4,7,5,8,3,2,6]=>1000000=>0111111=>1
[7,1,3,5,8,4,2,6]=>0000000=>1111111=>1
[7,2,5,8,4,1,3,6]=>0000000=>1111111=>1
[2,8,5,7,4,6,1,3]=>0000000=>1111111=>1
[3,5,8,7,1,4,6,2]=>0000000=>1111111=>1
[1,4,5,8,7,3,6,2]=>1000000=>0111111=>1
[1,5,4,8,7,3,6,2]=>1000000=>0111111=>1
[6,4,3,8,1,7,5,2]=>0000000=>1111111=>1
[4,3,7,1,8,6,5,2]=>0000000=>1111111=>1
[4,8,3,7,6,5,2,1]=>0000000=>1111111=>1
[5,3,8,7,6,4,2,1]=>0000000=>1111111=>1
[7,5,3,1,8,6,4,2]=>0000000=>1111111=>1
[1,8,6,5,3,7,4,2]=>1000000=>0111111=>1
[1,5,8,6,3,7,4,2]=>1000000=>0111111=>1
[4,6,1,8,7,3,5,2]=>0000000=>1111111=>1
[6,8,7,3,1,4,5,2]=>0000000=>1111111=>1
[6,2,8,7,4,5,1,3]=>0000000=>1111111=>1
[7,6,2,8,4,1,3,5]=>0000000=>1111111=>1
[7,3,1,6,8,4,2,5]=>0000000=>1111111=>1
[1,7,6,4,8,3,2,5]=>1000000=>0111111=>1
[5,7,1,6,3,2,8,4]=>0000000=>1111111=>1
[6,1,7,5,3,2,8,4]=>0000000=>1111111=>1
[7,6,5,3,2,1,8,4]=>0000000=>1111111=>1
[6,5,3,2,8,7,4,1]=>0000000=>1111111=>1
[5,2,6,3,8,7,4,1]=>0000000=>1111111=>1
[5,2,7,6,3,1,8,4]=>0000000=>1111111=>1
[6,5,2,1,7,3,8,4]=>0000000=>1111111=>1
[5,2,7,4,1,8,3,6]=>0000000=>1111111=>1
[4,7,2,6,3,1,8,5]=>0000000=>1111111=>1
[2,4,8,6,3,7,5,1]=>0000000=>1111111=>1
[3,8,6,2,4,7,5,1]=>0000000=>1111111=>1
[7,3,6,2,4,1,8,5]=>0000000=>1111111=>1
[3,6,7,2,1,4,8,5]=>0000000=>1111111=>1
[4,3,7,8,2,1,5,6]=>0000000=>1111111=>1
[8,3,7,1,4,6,2,5]=>0000000=>1111111=>1
[3,8,2,5,7,1,6,4]=>0000000=>1111111=>1
[8,3,6,2,7,1,5,4]=>0000000=>1111111=>1
[7,8,3,6,2,1,5,4]=>0000000=>1111111=>1
[8,7,3,6,2,5,4,1]=>0000000=>1111111=>1
[4,7,8,2,1,6,5,3]=>0000000=>1111111=>1
[4,2,6,8,1,7,5,3]=>0000000=>1111111=>1
[5,4,8,2,7,1,6,3]=>0000000=>1111111=>1
[4,8,1,5,7,2,6,3]=>0000000=>1111111=>1
[5,8,3,7,1,6,2,4]=>0000000=>1111111=>1
[5,8,7,2,6,1,3,4]=>0000000=>1111111=>1
[8,6,2,7,5,1,3,4]=>0000000=>1111111=>1
[3,6,8,1,7,5,2,4]=>0000000=>1111111=>1
[5,1,6,8,2,7,4,3]=>0000000=>1111111=>1
[6,5,2,8,1,7,4,3]=>0000000=>1111111=>1
[5,2,7,1,8,6,4,3]=>0000000=>1111111=>1
[5,8,2,7,6,4,3,1]=>0000000=>1111111=>1
[6,2,8,7,5,4,3,1]=>0000000=>1111111=>1
[7,6,2,1,8,5,4,3]=>0000000=>1111111=>1
[6,1,7,2,8,5,4,3]=>0000000=>1111111=>1
[7,5,1,8,2,6,4,3]=>0000000=>1111111=>1
[4,7,1,8,6,2,5,3]=>0000000=>1111111=>1
[7,8,3,1,6,5,2,4]=>0000000=>1111111=>1
[8,7,4,6,1,5,3,2]=>0000000=>1111111=>1
[8,5,7,1,6,4,3,2]=>0000000=>1111111=>1
[6,8,1,7,5,4,3,2]=>0000000=>1111111=>1
[7,1,8,6,5,4,3,2]=>0000000=>1111111=>1
[5,4,2,3,7,6,1,8]=>0000001=>1111110=>1
[6,4,2,7,3,5,1,8]=>0000001=>1111110=>1
[7,4,2,6,3,5,1,8]=>0000001=>1111110=>1
[8,4,2,6,3,1,5,7]=>0000000=>1111111=>1
[3,2,7,6,4,5,1,8]=>0000001=>1111110=>1
[4,7,2,6,3,5,1,8]=>0000001=>1111110=>1
[5,7,6,2,3,4,1,8]=>0000001=>1111110=>1
[1,6,5,2,3,8,4,7]=>1000000=>0111111=>1
[1,7,5,2,8,3,4,6]=>1000000=>0111111=>1
[6,8,5,2,3,1,4,7]=>0000000=>1111111=>1
[5,8,6,2,3,1,4,7]=>0000000=>1111111=>1
[4,8,2,6,3,1,5,7]=>0000000=>1111111=>1
[3,2,8,6,4,1,5,7]=>0000000=>1111111=>1
[3,2,1,6,4,8,5,7]=>0010000=>1101111=>2
[7,1,5,2,8,3,4,6]=>0000000=>1111111=>1
[1,8,5,2,7,3,4,6]=>1000000=>0111111=>1
[1,8,6,7,2,3,4,5]=>1000000=>0111111=>1
[8,1,6,7,2,3,4,5]=>0000000=>1111111=>1
[7,1,6,8,2,3,4,5]=>0000000=>1111111=>1
[3,2,1,7,8,4,5,6]=>0010000=>1101111=>2
[3,2,8,7,1,4,5,6]=>0000000=>1111111=>1
[5,8,7,2,1,3,4,6]=>0000000=>1111111=>1
[1,7,6,8,2,3,4,5]=>1000000=>0111111=>1
[6,5,8,2,3,1,4,7]=>0000000=>1111111=>1
[8,5,7,2,1,3,4,6]=>0000000=>1111111=>1
[6,4,2,8,3,1,5,7]=>0000000=>1111111=>1
[5,4,2,3,8,1,6,7]=>0000000=>1111111=>1
[3,2,5,4,1,8,6,7]=>0000100=>1111011=>2
[4,5,2,3,1,8,6,7]=>0000100=>1111011=>2
[5,4,2,3,1,8,6,7]=>0000100=>1111011=>2
[6,4,2,1,3,8,5,7]=>0000000=>1111111=>1
[7,4,2,1,8,3,5,6]=>0000000=>1111111=>1
[8,4,2,1,7,3,5,6]=>0000000=>1111111=>1
[1,4,2,8,7,3,5,6]=>1000000=>0111111=>1
[1,5,8,2,7,3,4,6]=>1000000=>0111111=>1
[8,5,1,2,7,3,4,6]=>0000000=>1111111=>1
[7,5,1,2,8,3,4,6]=>0000000=>1111111=>1
[6,5,1,2,3,8,4,7]=>0000000=>1111111=>1
[4,6,2,1,3,8,5,7]=>0000000=>1111111=>1
[3,2,6,1,4,8,5,7]=>0000000=>1111111=>1
[3,2,7,1,8,4,5,6]=>0000000=>1111111=>1
[4,7,2,1,8,3,5,6]=>0000000=>1111111=>1
[7,6,1,8,2,3,4,5]=>0000000=>1111111=>1
[8,6,1,7,2,3,4,5]=>0000000=>1111111=>1
[1,6,8,7,2,3,4,5]=>1000000=>0111111=>1
[1,7,8,6,2,3,4,5]=>1000000=>0111111=>1
[7,8,1,6,2,3,4,5]=>0000000=>1111111=>1
[6,8,1,7,2,3,4,5]=>0000000=>1111111=>1
[4,8,2,1,7,3,5,6]=>0000000=>1111111=>1
[3,2,8,1,7,4,5,6]=>0000000=>1111111=>1
[3,2,1,8,7,4,5,6]=>0010000=>1101111=>2
[5,1,8,2,7,3,4,6]=>0000000=>1111111=>1
[6,1,8,7,2,3,4,5]=>0000000=>1111111=>1
[8,1,7,6,2,3,4,5]=>0000000=>1111111=>1
[1,8,7,6,2,3,4,5]=>1000000=>0111111=>1
[4,3,5,6,1,2,8,7]=>0000010=>1111101=>2
[6,5,2,7,1,8,3,4]=>0000000=>1111111=>1
[5,3,1,4,6,2,8,7]=>0000010=>1111101=>2
[5,7,4,6,2,8,3,1]=>0000000=>1111111=>1
[3,4,7,8,5,2,1,6]=>0000000=>1111111=>1
[7,5,4,8,1,6,3,2]=>0000000=>1111111=>1
[2,4,6,3,7,5,8,1]=>0000000=>1111111=>1
[4,1,6,3,8,5,7,2]=>0000000=>1111111=>1
[3,7,4,2,8,6,5,1]=>0000000=>1111111=>1
[7,4,1,3,5,8,6,2]=>0000000=>1111111=>1
[2,1,4,8,3,7,6,5]=>0100000=>1011111=>2
[8,3,1,2,5,7,6,4]=>0000000=>1111111=>1
[3,1,8,2,7,6,5,4]=>0000000=>1111111=>1
[2,3,8,1,6,7,5,4]=>0000000=>1111111=>1
[4,3,7,2,6,8,5,1]=>0000000=>1111111=>1
[2,8,1,3,6,5,7,4]=>0000000=>1111111=>1
[2,7,8,5,4,3,1,6]=>0000000=>1111111=>1
[3,8,6,7,2,4,1,5]=>0000000=>1111111=>1
[5,3,8,7,4,2,6,1]=>0000000=>1111111=>1
[4,3,8,7,2,1,6,5]=>0000000=>1111111=>1
[8,3,6,1,4,2,7,5]=>0000000=>1111111=>1
[4,1,3,2,6,7,8,5]=>0001000=>1110111=>2
[5,3,6,1,8,7,2,4]=>0000000=>1111111=>1
[5,6,2,8,7,4,1,3]=>0000000=>1111111=>1
[7,8,5,6,1,4,2,3]=>0000000=>1111111=>1
[8,1,6,4,5,7,2,3]=>0000000=>1111111=>1
[2,1,8,6,5,7,3,4]=>0100000=>1011111=>2
[2,1,7,5,3,6,8,4]=>0100000=>1011111=>2
[6,7,3,5,2,1,8,4]=>0000000=>1111111=>1
[4,1,2,5,8,6,7,3]=>0000000=>1111111=>1
[8,5,2,4,6,1,7,3]=>0000000=>1111111=>1
[3,1,4,5,6,8,7,2]=>0000000=>1111111=>1
[3,1,6,5,4,2,8,7]=>0000010=>1111101=>2
[5,1,7,3,8,4,6,2]=>0000000=>1111111=>1
[2,5,7,3,8,6,4,1]=>0000000=>1111111=>1
[7,6,1,3,5,8,4,2]=>0000000=>1111111=>1
[5,6,3,7,4,8,1,2]=>0000000=>1111111=>1
[2,1,6,7,4,8,5,3]=>0100000=>1011111=>2
[2,1,8,7,4,3,6,5]=>0100000=>1011111=>2
[5,8,3,7,4,2,6,1]=>0000000=>1111111=>1
[5,8,7,3,2,6,1,4]=>0000000=>1111111=>1
[2,8,6,3,1,5,7,4]=>0000000=>1111111=>1
[8,1,6,3,2,5,4,7]=>0000000=>1111111=>1
[2,8,4,1,6,3,7,5]=>0000000=>1111111=>1
[4,8,1,2,7,6,3,5]=>0000000=>1111111=>1
[3,8,4,2,5,7,1,6]=>0000000=>1111111=>1
[2,1,5,3,8,7,6,4]=>0100000=>1011111=>2
[6,5,3,2,8,7,1,4]=>0000000=>1111111=>1
[2,4,1,8,7,6,5,3]=>0000000=>1111111=>1
[8,4,2,1,7,5,3,6]=>0000000=>1111111=>1
[4,3,1,8,6,7,5,2]=>0000000=>1111111=>1
[8,6,2,5,1,7,4,3]=>0000000=>1111111=>1
[5,6,2,1,8,7,3,4]=>0000000=>1111111=>1
[7,5,2,8,3,4,6,1]=>0000000=>1111111=>1
[5,6,2,8,4,3,1,7]=>0000000=>1111111=>1
[4,7,2,8,1,5,3,6]=>0000000=>1111111=>1
[8,7,2,1,4,5,6,3]=>0000000=>1111111=>1
[3,6,8,7,1,5,4,2]=>0000000=>1111111=>1
[5,7,8,6,3,4,1,2]=>0000000=>1111111=>1
[5,7,3,8,1,4,6,2]=>0000000=>1111111=>1
[2,1,7,8,5,4,6,3]=>0100000=>1011111=>2
[2,1,5,8,4,6,3,7]=>0100000=>1011111=>2
[7,5,8,4,3,6,2,1]=>0000000=>1111111=>1
[8,4,1,3,7,2,6,5]=>0000000=>1111111=>1
[2,3,8,1,4,6,7,5]=>0000000=>1111111=>1
[4,3,8,2,5,1,7,6]=>0000000=>1111111=>1
[2,1,4,8,3,5,7,6]=>0100000=>1011111=>2
[2,8,4,1,6,5,3,7]=>0000000=>1111111=>1
[2,8,4,1,6,5,7,3]=>0000000=>1111111=>1
[2,8,7,6,1,4,3,5]=>0000000=>1111111=>1
[2,8,5,6,7,4,3,1]=>0000000=>1111111=>1
[7,5,8,6,1,4,2,3]=>0000000=>1111111=>1
[3,5,7,2,4,1,6,8]=>0000001=>1111110=>1
[2,8,5,3,4,1,6,7]=>0000000=>1111111=>1
[3,5,7,2,4,6,1,8]=>0000001=>1111110=>1
[7,5,8,2,4,6,3,1]=>0000000=>1111111=>1
[7,5,8,6,1,4,3,2]=>0000000=>1111111=>1
[6,5,8,2,1,3,7,4]=>0000000=>1111111=>1
[3,5,7,6,1,4,8,2]=>0000000=>1111111=>1
[3,5,7,2,4,1,8,6]=>0000000=>1111111=>1
[3,5,7,2,4,6,8,1]=>0000000=>1111111=>1
[6,5,2,7,3,4,8,1]=>0000000=>1111111=>1
[5,1,6,7,4,3,8,2]=>0000000=>1111111=>1
[4,1,2,3,8,7,5,6]=>0001000=>1110111=>2
[4,1,2,3,8,6,5,7]=>0001000=>1110111=>2
[4,1,2,3,8,6,7,5]=>0001000=>1110111=>2
[4,1,2,3,8,5,7,6]=>0001000=>1110111=>2
[7,1,6,8,4,3,5,2]=>0000000=>1111111=>1
[5,6,8,2,3,1,7,4]=>0000000=>1111111=>1
[6,5,8,2,4,3,7,1]=>0000000=>1111111=>1
[7,5,2,8,3,4,1,6]=>0000000=>1111111=>1
[6,5,2,8,3,7,1,4]=>0000000=>1111111=>1
[7,1,6,8,4,3,2,5]=>0000000=>1111111=>1
[4,1,8,3,6,5,7,2]=>0000000=>1111111=>1
[4,1,8,3,6,2,7,5]=>0000000=>1111111=>1
[7,1,6,5,8,3,2,4]=>0000000=>1111111=>1
[4,5,2,6,3,7,1,8]=>0000001=>1111110=>1
[7,5,2,6,3,8,4,1]=>0000000=>1111111=>1
[4,1,2,3,7,8,6,5]=>0001000=>1110111=>2
[4,5,2,7,3,8,6,1]=>0000000=>1111111=>1
[4,1,6,7,8,3,5,2]=>0000000=>1111111=>1
[4,1,2,6,8,5,7,3]=>0000000=>1111111=>1
[7,8,5,6,1,4,3,2]=>0000000=>1111111=>1
[7,8,4,2,1,5,3,6]=>0000000=>1111111=>1
[7,8,2,1,6,5,3,4]=>0000000=>1111111=>1
[6,4,1,2,5,7,3,8]=>0000001=>1111110=>1
[2,4,8,1,5,7,3,6]=>0000000=>1111111=>1
[4,3,8,1,7,2,5,6]=>0000000=>1111111=>1
[6,3,1,4,7,2,5,8]=>0000001=>1111110=>1
[7,8,3,4,5,1,6,2]=>0000000=>1111111=>1
[7,8,3,5,4,2,1,6]=>0000000=>1111111=>1
[7,8,4,1,2,3,6,5]=>0000000=>1111111=>1
[7,8,3,6,5,4,1,2]=>0000000=>1111111=>1
[7,8,2,1,5,3,4,6]=>0000000=>1111111=>1
[7,8,2,6,4,1,3,5]=>0000000=>1111111=>1
[7,8,2,5,6,4,1,3]=>0000000=>1111111=>1
[7,8,1,6,5,4,3,2]=>0000000=>1111111=>1
[6,2,1,7,5,4,3,8]=>0000001=>1111110=>1
[2,1,8,7,5,4,3,6]=>0100000=>1011111=>2
[1,3,8,2,6,4,7,5]=>1000000=>0111111=>1
[5,3,7,1,6,4,8,2]=>0000000=>1111111=>1
[5,3,6,2,7,4,1,8]=>0000001=>1111110=>1
[6,1,2,5,8,7,4,3]=>0000000=>1111111=>1
[6,3,1,8,4,2,7,5]=>0000000=>1111111=>1
[6,4,2,1,5,3,8,7]=>0000010=>1111101=>2
[6,4,3,7,5,8,1,2]=>0000000=>1111111=>1
[4,3,8,7,5,6,1,2]=>0000000=>1111111=>1
[2,4,7,1,5,3,6,8]=>0000001=>1111110=>1
[1,3,7,6,4,2,8,5]=>1000000=>0111111=>1
[2,1,7,5,6,8,4,3]=>0100000=>1011111=>2
[3,7,2,8,6,4,1,5]=>0000000=>1111111=>1
[3,8,1,7,6,4,5,2]=>0000000=>1111111=>1
[1,8,5,7,3,6,4,2]=>1000000=>0111111=>1
[2,7,5,8,3,6,1,4]=>0000000=>1111111=>1
[1,5,6,8,2,4,7,3]=>1000000=>0111111=>1
[2,6,8,5,3,1,4,7]=>0000000=>1111111=>1
[2,6,1,4,7,3,5,8]=>0000001=>1111110=>1
[5,6,7,3,8,4,1,2]=>0000000=>1111111=>1
[5,2,8,1,4,7,3,6]=>0000000=>1111111=>1
[4,6,7,5,2,1,3,8]=>0000001=>1111110=>1
[4,5,6,7,2,8,1,3]=>0000000=>1111111=>1
[4,5,7,6,1,8,3,2]=>0000000=>1111111=>1
[1,5,8,6,2,7,3,4]=>1000000=>0111111=>1
[1,6,5,8,3,2,7,4]=>1000000=>0111111=>1
[4,6,5,7,1,2,8,3]=>0000000=>1111111=>1
[4,7,5,6,3,1,8,2]=>0000000=>1111111=>1
[5,1,6,3,4,2,8,7]=>0000010=>1111101=>2
[5,7,1,4,2,3,8,6]=>0000000=>1111111=>1
[5,7,6,4,3,8,1,2]=>0000000=>1111111=>1
[6,3,4,5,8,7,1,2]=>0000000=>1111111=>1
[6,2,4,1,8,3,7,5]=>0000000=>1111111=>1
[6,2,3,5,4,8,1,7]=>0000000=>1111111=>1
[6,1,3,4,5,8,7,2]=>0000000=>1111111=>1
[5,1,4,2,7,6,8,3]=>0000000=>1111111=>1
[1,6,2,4,7,8,3,5]=>1000000=>0111111=>1
[5,7,2,4,1,6,3,8]=>0000001=>1111110=>1
[6,1,4,2,8,5,3,7]=>0000000=>1111111=>1
[6,7,5,8,1,4,3,2]=>0000000=>1111111=>1
[5,8,7,6,3,4,1,2]=>0000000=>1111111=>1
[5,8,7,6,2,3,1,4]=>0000000=>1111111=>1
[4,1,7,2,6,5,3,8]=>0000001=>1111110=>1
[4,8,2,1,5,6,3,7]=>0000000=>1111111=>1
[4,2,7,8,1,6,3,5]=>0000000=>1111111=>1
[2,1,8,7,6,5,3,4]=>0100000=>1011111=>2
[3,1,4,7,8,2,6,5]=>0000000=>1111111=>1
[3,1,7,4,5,6,8,2]=>0000000=>1111111=>1
[4,2,7,1,6,3,8,5]=>0000000=>1111111=>1
[4,3,7,5,6,8,1,2]=>0000000=>1111111=>1
[4,8,6,3,5,7,1,2]=>0000000=>1111111=>1
[4,8,1,2,5,3,7,6]=>0000000=>1111111=>1
[3,8,6,5,2,4,1,7]=>0000000=>1111111=>1
[3,8,5,6,1,4,7,2]=>0000000=>1111111=>1
[5,3,7,8,2,1,6,4]=>0000000=>1111111=>1
[5,2,8,7,1,6,4,3]=>0000000=>1111111=>1
[1,6,8,7,5,2,4,3]=>1000000=>0111111=>1
[3,6,7,8,5,1,4,2]=>0000000=>1111111=>1
[3,7,6,8,5,2,1,4]=>0000000=>1111111=>1
[3,7,8,5,1,2,4,6]=>0000000=>1111111=>1
[3,7,1,6,4,2,5,8]=>0000001=>1111110=>1
[4,1,8,6,2,3,5,7]=>0000000=>1111111=>1
[4,7,8,6,3,5,1,2]=>0000000=>1111111=>1
[3,8,7,6,5,4,1,2]=>0000000=>1111111=>1
[2,1,7,6,5,3,4,8]=>0100001=>1011110=>2
[2,8,1,6,4,5,3,7]=>0000000=>1111111=>1
[2,8,7,5,1,4,3,6]=>0000000=>1111111=>1
[2,8,6,7,5,1,3,4]=>0000000=>1111111=>1
[2,7,8,6,5,4,1,3]=>0000000=>1111111=>1
[6,4,2,7,1,3,8,5]=>0000000=>1111111=>1
[8,5,3,6,1,7,2,4]=>0000000=>1111111=>1
[7,3,6,2,4,8,1,5]=>0000000=>1111111=>1
[4,3,7,1,2,5,8,6]=>0000000=>1111111=>1
[3,6,2,7,1,4,8,5]=>0000000=>1111111=>1
[5,3,6,7,1,2,8,4]=>0000000=>1111111=>1
[4,7,1,5,2,3,8,6]=>0000000=>1111111=>1
[3,7,5,1,2,4,8,6]=>0000000=>1111111=>1
[7,6,4,2,3,8,1,5]=>0000000=>1111111=>1
[5,7,4,2,3,8,1,6]=>0000000=>1111111=>1
[3,7,6,1,4,8,2,5]=>0000000=>1111111=>1
[6,4,7,5,2,8,1,3]=>0000000=>1111111=>1
[7,4,8,5,2,6,1,3]=>0000000=>1111111=>1
[5,8,2,6,3,7,1,4]=>0000000=>1111111=>1
[3,8,6,2,4,7,1,5]=>0000000=>1111111=>1
[4,8,6,2,7,1,3,5]=>0000000=>1111111=>1
[2,6,5,8,1,3,4,7]=>0000000=>1111111=>1
[5,4,6,7,2,8,1,3]=>0000000=>1111111=>1
[3,5,7,1,4,8,2,6]=>0000000=>1111111=>1
[5,3,7,2,4,8,1,6]=>0000000=>1111111=>1
[5,4,7,3,8,1,2,6]=>0000000=>1111111=>1
[8,4,1,6,7,2,3,5]=>0000000=>1111111=>1
[7,4,1,6,8,2,3,5]=>0000000=>1111111=>1
[6,5,3,7,1,8,2,4]=>0000000=>1111111=>1
[5,3,6,4,7,8,1,2]=>0000000=>1111111=>1
[6,3,7,4,8,5,1,2]=>0000000=>1111111=>1
[4,7,1,5,8,6,2,3]=>0000000=>1111111=>1
[7,5,1,2,8,6,3,4]=>0000000=>1111111=>1
[8,6,1,7,5,2,3,4]=>0000000=>1111111=>1
[5,7,2,8,1,6,3,4]=>0000000=>1111111=>1
[6,3,7,8,5,1,2,4]=>0000000=>1111111=>1
[2,4,8,7,1,3,5,6]=>0000000=>1111111=>1
[4,3,8,7,1,2,5,6]=>0000000=>1111111=>1
[8,3,7,6,1,2,4,5]=>0000000=>1111111=>1
[8,4,7,6,1,2,3,5]=>0000000=>1111111=>1
[3,5,8,7,1,2,4,6]=>0000000=>1111111=>1
[2,5,8,7,1,3,4,6]=>0000000=>1111111=>1
[6,8,4,7,5,1,2,3]=>0000000=>1111111=>1
[5,8,7,1,6,2,3,4]=>0000000=>1111111=>1
[2,8,7,6,1,3,4,5]=>0000000=>1111111=>1
[3,8,7,6,1,2,4,5]=>0000000=>1111111=>1
[4,8,7,6,1,2,3,5]=>0000000=>1111111=>1
[7,5,3,8,2,1,6,4]=>0000000=>1111111=>1
[3,8,7,4,5,1,6,2]=>0000000=>1111111=>1
[5,7,3,8,1,2,6,4]=>0000000=>1111111=>1
[2,7,8,4,1,6,5,3]=>0000000=>1111111=>1
[7,1,8,4,2,6,5,3]=>0000000=>1111111=>1
[7,5,1,4,8,6,3,2]=>0000000=>1111111=>1
[6,5,3,1,8,4,7,2]=>0000000=>1111111=>1
[2,3,4,5,6,7,8,1,9]=>00000001=>11111110=>1
[2,3,4,5,6,8,9,1,7]=>00000000=>11111111=>1
[2,3,4,5,7,8,9,1,6]=>00000000=>11111111=>1
[2,3,4,6,7,8,9,1,5]=>00000000=>11111111=>1
[2,3,5,6,7,8,9,1,4]=>00000000=>11111111=>1
[2,4,5,6,7,8,9,1,3]=>00000000=>11111111=>1
[3,4,5,6,7,8,9,1,2]=>00000000=>11111111=>1
[2,3,4,5,6,7,8,9,10,1]=>000000000=>111111111=>1
[2,3,4,5,6,7,8,9,1,10]=>000000001=>111111110=>1
[2,3,4,5,6,7,1,8,9]=>00000011=>11111100=>1
[2,3,4,5,6,7,8,10,1,9]=>000000000=>111111111=>1
[2,3,4,5,6,1,9,7,8]=>00000100=>11111011=>2
[2,3,4,5,6,7,9,10,1,8]=>000000000=>111111111=>1
[2,3,4,5,1,8,9,6,7]=>00001000=>11110111=>2
[2,3,4,5,6,8,9,10,1,7]=>000000000=>111111111=>1
[2,3,4,1,7,8,9,5,6]=>00010000=>11101111=>2
[2,3,4,5,7,8,9,10,1,6]=>000000000=>111111111=>1
[2,3,1,6,7,8,9,4,5]=>00100000=>11011111=>2
[2,3,4,6,7,8,9,10,1,5]=>000000000=>111111111=>1
[2,1,5,6,7,8,9,3,4]=>01000000=>10111111=>2
[2,3,5,6,7,8,9,10,1,4]=>000000000=>111111111=>1
[1,4,5,6,7,8,9,2,3]=>10000000=>01111111=>1
[2,4,5,6,7,8,9,10,1,3]=>000000000=>111111111=>1
[3,4,5,6,7,8,9,10,1,2]=>000000000=>111111111=>1
[3,6,4,5,7,2,8,1]=>0000000=>1111111=>1
[5,3,2,7,4,6,8,1]=>0000000=>1111111=>1
[7,5,3,6,2,4,8,1]=>0000000=>1111111=>1
[6,3,2,5,1,8,4,7]=>0000000=>1111111=>1
[8,5,3,6,2,7,1,4]=>0000000=>1111111=>1
[8,2,6,3,4,7,1,5]=>0000000=>1111111=>1
[7,2,6,3,4,5,8,1]=>0000000=>1111111=>1
[6,2,7,3,4,5,8,1]=>0000000=>1111111=>1
[4,2,5,7,3,6,8,1]=>0000000=>1111111=>1
[5,4,7,6,2,3,8,1]=>0000000=>1111111=>1
[6,7,3,5,2,4,8,1]=>0000000=>1111111=>1
[3,7,6,2,4,5,8,1]=>0000000=>1111111=>1
[2,7,6,3,4,5,8,1]=>0000000=>1111111=>1
[6,5,3,1,2,8,4,7]=>0000000=>1111111=>1
[8,6,5,2,3,7,1,4]=>0000000=>1111111=>1
[8,5,2,1,7,3,4,6]=>0000000=>1111111=>1
[7,5,2,1,8,3,4,6]=>0000000=>1111111=>1
[1,6,3,2,8,4,5,7]=>1000000=>0111111=>1
[5,6,2,3,1,8,4,7]=>0000000=>1111111=>1
[5,4,8,6,2,7,1,3]=>0000000=>1111111=>1
[6,8,3,5,2,7,1,4]=>0000000=>1111111=>1
[7,8,5,2,3,6,1,4]=>0000000=>1111111=>1
[1,8,6,3,7,2,4,5]=>1000000=>0111111=>1
[1,8,2,7,3,4,5,6]=>1000000=>0111111=>1
[2,8,1,7,3,4,5,6]=>0000000=>1111111=>1
[3,8,6,1,7,2,4,5]=>0000000=>1111111=>1
[4,8,1,5,7,2,3,6]=>0000000=>1111111=>1
[4,2,8,3,7,1,5,6]=>0000000=>1111111=>1
[8,1,2,7,3,4,5,6]=>0000000=>1111111=>1
[3,6,2,7,1,8,4,5]=>0000000=>1111111=>1
[7,2,6,1,8,3,4,5]=>0000000=>1111111=>1
[7,3,1,5,8,2,4,6]=>0000000=>1111111=>1
[3,2,1,5,8,4,6,7]=>0010000=>1101111=>2
[5,4,1,3,6,8,2,7]=>0000000=>1111111=>1
[1,5,3,4,6,8,2,7]=>1000000=>0111111=>1
[4,3,5,1,6,8,2,7]=>0000000=>1111111=>1
[5,4,6,3,8,7,1,2]=>0000000=>1111111=>1
[3,6,4,5,8,7,1,2]=>0000000=>1111111=>1
[6,5,3,4,8,7,1,2]=>0000000=>1111111=>1
[5,3,2,8,7,1,4,6]=>0000000=>1111111=>1
[5,3,1,8,7,2,4,6]=>0000000=>1111111=>1
[8,5,3,7,6,1,2,4]=>0000000=>1111111=>1
[6,1,8,3,7,2,4,5]=>0000000=>1111111=>1
[6,3,8,1,7,2,4,5]=>0000000=>1111111=>1
[7,6,8,2,3,5,1,4]=>0000000=>1111111=>1
[3,7,8,2,4,6,1,5]=>0000000=>1111111=>1
[6,7,3,8,2,5,1,4]=>0000000=>1111111=>1
[5,4,7,8,2,6,1,3]=>0000000=>1111111=>1
[4,2,5,8,7,1,3,6]=>0000000=>1111111=>1
[2,3,8,7,1,4,5,6]=>0000000=>1111111=>1
[7,2,8,6,1,3,4,5]=>0000000=>1111111=>1
[2,1,8,7,3,4,5,6]=>0100000=>1011111=>2
[8,2,7,6,1,3,4,5]=>0000000=>1111111=>1
[1,2,8,7,3,4,5,6]=>1100000=>0011111=>1
[1,3,8,7,2,4,5,6]=>1000000=>0111111=>1
[1,7,8,3,6,2,4,5]=>1000000=>0111111=>1
[4,1,5,8,7,2,3,6]=>0000000=>1111111=>1
[5,4,8,7,6,1,2,3]=>0000000=>1111111=>1
[6,8,3,7,5,1,2,4]=>0000000=>1111111=>1
[7,8,6,2,5,1,3,4]=>0000000=>1111111=>1
[8,1,6,7,3,2,5,4]=>0000000=>1111111=>1
[8,1,6,7,3,2,4,5]=>0000000=>1111111=>1
[8,1,5,3,7,2,4,6]=>0000000=>1111111=>1
[8,1,5,3,6,2,4,7]=>0000000=>1111111=>1
[7,5,1,3,6,2,4,8]=>0000001=>1111110=>1
[7,5,8,3,6,2,4,1]=>0000000=>1111111=>1
[7,4,8,3,2,6,5,1]=>0000000=>1111111=>1
[7,4,1,3,2,6,5,8]=>0000001=>1111110=>1
[8,1,4,3,2,6,5,7]=>0000000=>1111111=>1
[8,1,4,3,2,7,5,6]=>0000000=>1111111=>1
[8,1,4,3,2,7,6,5]=>0000000=>1111111=>1
[8,1,5,4,6,7,2,3]=>0000000=>1111111=>1
[8,1,5,3,6,2,7,4]=>0000000=>1111111=>1
[8,1,4,3,2,6,7,5]=>0000000=>1111111=>1
[8,1,4,3,2,5,7,6]=>0000000=>1111111=>1
[8,1,4,3,2,5,6,7]=>0000000=>1111111=>1
[7,4,1,3,2,5,6,8]=>0000001=>1111110=>1
[7,4,8,3,2,5,6,1]=>0000000=>1111111=>1
[6,4,3,8,2,5,7,1]=>0000000=>1111111=>1
[6,4,3,1,2,5,8,7]=>0000010=>1111101=>2
[7,4,1,3,2,5,8,6]=>0000000=>1111111=>1
[7,4,1,3,2,6,8,5]=>0000000=>1111111=>1
[7,5,1,3,6,2,8,4]=>0000000=>1111111=>1
[7,5,1,4,6,8,2,3]=>0000000=>1111111=>1
[7,5,8,3,6,2,1,4]=>0000000=>1111111=>1
[7,4,8,3,2,6,1,5]=>0000000=>1111111=>1
[7,4,8,3,2,5,1,6]=>0000000=>1111111=>1
[6,4,3,8,2,5,1,7]=>0000000=>1111111=>1
[6,4,3,7,2,5,8,1]=>0000000=>1111111=>1
[5,4,3,2,8,6,1,7]=>0000000=>1111111=>1
[5,4,3,2,8,7,1,6]=>0000000=>1111111=>1
[6,5,3,8,7,2,1,4]=>0000000=>1111111=>1
[6,5,4,8,7,1,2,3]=>0000000=>1111111=>1
[6,5,4,1,7,8,2,3]=>0000000=>1111111=>1
[6,5,3,1,7,2,8,4]=>0000000=>1111111=>1
[6,4,3,1,2,7,8,5]=>0000000=>1111111=>1
[5,4,3,2,1,8,6,7]=>0000100=>1111011=>2
[6,5,3,1,8,2,7,4]=>0000000=>1111111=>1
[6,5,4,1,8,7,2,3]=>0000000=>1111111=>1
[7,5,1,4,8,6,2,3]=>0000000=>1111111=>1
[7,4,1,3,2,8,6,5]=>0000000=>1111111=>1
[7,4,1,3,2,8,5,6]=>0000000=>1111111=>1
[6,4,3,1,2,8,5,7]=>0000000=>1111111=>1
[6,4,3,1,2,7,5,8]=>0000001=>1111110=>1
[6,4,3,8,2,7,5,1]=>0000000=>1111111=>1
[6,5,3,8,7,2,4,1]=>0000000=>1111111=>1
[6,5,3,1,7,2,4,8]=>0000001=>1111110=>1
[6,5,3,1,8,2,4,7]=>0000000=>1111111=>1
[7,5,1,3,8,2,4,6]=>0000000=>1111111=>1
[7,6,1,8,3,2,4,5]=>0000000=>1111111=>1
[7,6,1,8,4,5,2,3]=>0000000=>1111111=>1
[7,6,8,1,4,5,2,3]=>0000000=>1111111=>1
[7,6,8,1,3,2,5,4]=>0000000=>1111111=>1
[6,5,3,7,8,2,4,1]=>0000000=>1111111=>1
[6,4,3,7,2,8,5,1]=>0000000=>1111111=>1
[6,4,3,7,2,1,5,8]=>0000001=>1111110=>1
[7,4,8,3,2,1,5,6]=>0000000=>1111111=>1
[7,4,8,3,2,1,6,5]=>0000000=>1111111=>1
[7,5,8,3,1,2,6,4]=>0000000=>1111111=>1
[7,5,8,4,1,6,2,3]=>0000000=>1111111=>1
[6,5,4,8,1,7,2,3]=>0000000=>1111111=>1
[6,5,3,8,1,2,7,4]=>0000000=>1111111=>1
[5,4,3,2,8,1,7,6]=>0000000=>1111111=>1
[6,4,3,7,2,1,8,5]=>0000000=>1111111=>1
[6,5,3,7,1,2,8,4]=>0000000=>1111111=>1
[6,5,4,7,1,8,2,3]=>0000000=>1111111=>1
[6,5,3,7,8,2,1,4]=>0000000=>1111111=>1
[6,4,3,7,2,8,1,5]=>0000000=>1111111=>1
[5,4,3,2,7,8,1,6]=>0000000=>1111111=>1
[5,4,3,2,6,8,1,7]=>0000000=>1111111=>1
[5,3,7,8,2,1,4,6]=>0000000=>1111111=>1
[7,6,1,2,5,8,3,4]=>0000000=>1111111=>1
[2,1,7,8,4,3,5,6]=>0100000=>1011111=>2
[7,8,1,2,5,4,6,3]=>0000000=>1111111=>1
[8,4,1,3,7,6,2,5]=>0000000=>1111111=>1
[6,5,2,1,8,7,4,3]=>0000000=>1111111=>1
[4,7,2,8,1,3,6,5]=>0000000=>1111111=>1
[7,3,8,6,1,2,5,4]=>0000000=>1111111=>1
[3,4,7,1,8,2,6,5]=>0000000=>1111111=>1
[1,8,2,4,3,5,6,7]=>1000000=>0111111=>1
[1,7,2,4,3,5,6,8]=>1000001=>0111110=>1
[1,6,2,4,3,5,7,8]=>1000011=>0111100=>1
[1,5,2,4,3,6,7,8]=>1000111=>0111000=>1
[1,6,2,5,3,4,7,8]=>1000011=>0111100=>1
[1,7,2,5,3,4,6,8]=>1000001=>0111110=>1
[1,8,2,5,3,4,6,7]=>1000000=>0111111=>1
[1,8,2,6,3,4,5,7]=>1000000=>0111111=>1
[1,7,2,6,3,4,5,8]=>1000001=>0111110=>1
[1,8,2,7,3,5,4,6]=>1000000=>0111111=>1
[1,7,2,8,3,5,4,6]=>1000000=>0111111=>1
[1,6,2,8,3,5,4,7]=>1000000=>0111111=>1
[1,5,2,8,3,6,4,7]=>1000000=>0111111=>1
[1,4,2,8,3,6,5,7]=>1000000=>0111111=>1
[1,3,2,8,4,6,5,7]=>1010000=>0101111=>2
[1,2,3,8,4,6,5,7]=>1110000=>0001111=>1
[1,2,3,7,4,6,5,8]=>1110001=>0001110=>1
[1,3,2,7,4,6,5,8]=>1010001=>0101110=>2
[1,4,2,7,3,6,5,8]=>1000001=>0111110=>1
[1,5,2,7,3,6,4,8]=>1000001=>0111110=>1
[1,6,2,7,3,5,4,8]=>1000001=>0111110=>1
[1,7,2,6,3,5,4,8]=>1000001=>0111110=>1
[1,8,2,6,3,5,4,7]=>1000000=>0111111=>1
[1,8,2,5,3,6,4,7]=>1000000=>0111111=>1
[1,7,2,5,3,6,4,8]=>1000001=>0111110=>1
[1,6,2,5,3,7,4,8]=>1000001=>0111110=>1
[1,5,2,4,3,7,6,8]=>1000101=>0111010=>2
[1,6,2,4,3,7,5,8]=>1000001=>0111110=>1
[1,7,2,4,3,6,5,8]=>1000001=>0111110=>1
[1,8,2,4,3,6,5,7]=>1000000=>0111111=>1
[1,8,2,3,4,6,5,7]=>1000000=>0111111=>1
[1,7,2,3,4,6,5,8]=>1000001=>0111110=>1
[1,8,2,3,4,7,5,6]=>1000000=>0111111=>1
[1,8,2,4,3,7,5,6]=>1000000=>0111111=>1
[1,7,2,4,3,8,5,6]=>1000000=>0111111=>1
[1,6,2,4,3,8,5,7]=>1000000=>0111111=>1
[1,5,2,4,3,8,6,7]=>1000100=>0111011=>2
[1,6,2,5,3,8,4,7]=>1000000=>0111111=>1
[1,7,2,5,3,8,4,6]=>1000000=>0111111=>1
[1,8,2,5,3,7,4,6]=>1000000=>0111111=>1
[1,8,2,6,3,7,4,5]=>1000000=>0111111=>1
[1,7,2,6,3,8,4,5]=>1000000=>0111111=>1
[1,2,3,8,4,7,5,6]=>1110000=>0001111=>1
[1,3,2,8,4,7,5,6]=>1010000=>0101111=>2
[1,4,2,8,3,7,5,6]=>1000000=>0111111=>1
[1,5,2,8,3,7,4,6]=>1000000=>0111111=>1
[1,6,2,8,3,7,4,5]=>1000000=>0111111=>1
[1,7,2,8,3,6,4,5]=>1000000=>0111111=>1
[1,8,2,7,3,6,4,5]=>1000000=>0111111=>1
[4,6,3,7,2,5,1,8]=>0000001=>1111110=>1
[4,6,3,7,5,2,1,8]=>0000001=>1111110=>1
[4,6,3,8,5,1,7,2]=>0000000=>1111111=>1
[4,6,3,8,5,1,2,7]=>0000000=>1111111=>1
[5,6,8,3,4,1,2,7]=>0000000=>1111111=>1
[5,6,8,3,4,1,7,2]=>0000000=>1111111=>1
[4,6,2,7,5,3,1,8]=>0000001=>1111110=>1
[5,6,7,2,4,3,1,8]=>0000001=>1111110=>1
[5,6,8,4,3,1,7,2]=>0000000=>1111111=>1
[5,6,8,4,3,1,2,7]=>0000000=>1111111=>1
[5,7,8,4,1,6,2,3]=>0000000=>1111111=>1
[5,7,8,4,1,6,3,2]=>0000000=>1111111=>1
[5,7,8,4,1,3,6,2]=>0000000=>1111111=>1
[5,6,8,4,2,1,7,3]=>0000000=>1111111=>1
[5,6,8,2,4,1,7,3]=>0000000=>1111111=>1
[4,6,2,8,5,1,7,3]=>0000000=>1111111=>1
[3,2,6,8,5,1,7,4]=>0000000=>1111111=>1
[3,2,6,8,5,1,4,7]=>0000000=>1111111=>1
[4,6,2,8,5,1,3,7]=>0000000=>1111111=>1
[5,6,8,2,4,1,3,7]=>0000000=>1111111=>1
[5,6,8,4,2,1,3,7]=>0000000=>1111111=>1
[5,7,8,4,1,3,2,6]=>0000000=>1111111=>1
[5,7,8,4,1,2,6,3]=>0000000=>1111111=>1
[5,7,8,4,1,2,3,6]=>0000000=>1111111=>1
[6,7,8,1,5,2,3,4]=>0000000=>1111111=>1
[6,7,8,1,5,2,4,3]=>0000000=>1111111=>1
[6,7,8,1,5,3,2,4]=>0000000=>1111111=>1
[6,7,8,1,3,5,2,4]=>0000000=>1111111=>1
[5,7,8,2,1,6,3,4]=>0000000=>1111111=>1
[4,7,2,8,1,6,3,5]=>0000000=>1111111=>1
[3,2,7,8,1,6,4,5]=>0000000=>1111111=>1
[3,2,7,8,1,6,5,4]=>0000000=>1111111=>1
[4,7,2,8,1,6,5,3]=>0000000=>1111111=>1
[5,7,8,2,1,6,4,3]=>0000000=>1111111=>1
[6,7,8,1,3,5,4,2]=>0000000=>1111111=>1
[6,7,8,1,5,3,4,2]=>0000000=>1111111=>1
[6,7,8,1,5,4,3,2]=>0000000=>1111111=>1
[6,7,8,1,5,4,2,3]=>0000000=>1111111=>1
[6,7,8,1,4,5,2,3]=>0000000=>1111111=>1
[6,7,8,1,4,5,3,2]=>0000000=>1111111=>1
[6,7,8,1,4,3,5,2]=>0000000=>1111111=>1
[6,7,8,1,3,4,5,2]=>0000000=>1111111=>1
[5,7,8,2,1,4,6,3]=>0000000=>1111111=>1
[4,7,2,8,1,5,6,3]=>0000000=>1111111=>1
[3,2,7,8,1,5,6,4]=>0000000=>1111111=>1
[3,2,6,8,4,1,7,5]=>0000000=>1111111=>1
[4,6,2,8,3,1,7,5]=>0000000=>1111111=>1
[5,6,8,3,2,1,7,4]=>0000000=>1111111=>1
[5,7,8,3,1,4,6,2]=>0000000=>1111111=>1
[5,7,8,3,1,6,4,2]=>0000000=>1111111=>1
[5,7,8,3,1,6,2,4]=>0000000=>1111111=>1
[4,7,3,8,1,6,2,5]=>0000000=>1111111=>1
[4,7,3,8,1,6,5,2]=>0000000=>1111111=>1
[4,7,3,8,1,5,6,2]=>0000000=>1111111=>1
[4,6,3,8,2,1,7,5]=>0000000=>1111111=>1
[4,5,3,2,8,1,7,6]=>0000000=>1111111=>1
[4,5,2,3,8,1,7,6]=>0000000=>1111111=>1
[3,2,5,4,8,1,7,6]=>0000000=>1111111=>1
[4,5,3,2,8,1,6,7]=>0000000=>1111111=>1
[4,6,3,8,2,1,5,7]=>0000000=>1111111=>1
[4,7,3,8,1,5,2,6]=>0000000=>1111111=>1
[4,7,3,8,1,2,6,5]=>0000000=>1111111=>1
[4,7,3,8,1,2,5,6]=>0000000=>1111111=>1
[5,7,8,3,1,2,4,6]=>0000000=>1111111=>1
[5,7,8,3,1,2,6,4]=>0000000=>1111111=>1
[5,7,8,3,1,4,2,6]=>0000000=>1111111=>1
[5,6,8,3,2,1,4,7]=>0000000=>1111111=>1
[3,2,7,8,1,5,4,6]=>0000000=>1111111=>1
[5,7,8,2,1,4,3,6]=>0000000=>1111111=>1
[6,7,8,1,3,4,2,5]=>0000000=>1111111=>1
[6,7,8,1,4,3,2,5]=>0000000=>1111111=>1
[6,7,8,1,4,2,5,3]=>0000000=>1111111=>1
[6,7,8,1,4,2,3,5]=>0000000=>1111111=>1
[6,7,8,1,2,5,3,4]=>0000000=>1111111=>1
[6,7,8,1,2,5,4,3]=>0000000=>1111111=>1
[6,7,8,1,2,4,5,3]=>0000000=>1111111=>1
[6,7,8,1,3,2,5,4]=>0000000=>1111111=>1
[5,7,8,2,1,3,6,4]=>0000000=>1111111=>1
[3,2,7,8,1,4,6,5]=>0000000=>1111111=>1
[6,7,8,1,3,2,4,5]=>0000000=>1111111=>1
[6,7,8,1,2,4,3,5]=>0000000=>1111111=>1
[6,7,8,1,2,3,5,4]=>0000000=>1111111=>1
[7,2,8,5,1,6,4,3]=>0000000=>1111111=>1
[1,3,7,5,2,6,4,8]=>1000001=>0111110=>1
[1,3,7,5,4,2,6,8]=>1000001=>0111110=>1
[7,2,8,4,5,6,1,3]=>0000000=>1111111=>1
[1,6,3,7,5,2,4,8]=>1000001=>0111110=>1
[6,2,3,8,5,1,7,4]=>0000000=>1111111=>1
[6,3,2,8,5,1,4,7]=>0000000=>1111111=>1
[7,4,8,5,2,1,3,6]=>0000000=>1111111=>1
[4,3,7,1,5,6,8,2]=>0000000=>1111111=>1
[6,2,5,8,3,7,1,4]=>0000000=>1111111=>1
[1,5,2,7,4,6,3,8]=>1000001=>0111110=>1
[5,2,1,8,7,6,3,4]=>0000000=>1111111=>1
[2,3,4,8,6,1,7,5]=>0000000=>1111111=>1
[2,3,4,8,6,5,1,7]=>0000000=>1111111=>1
[1,5,4,6,2,7,3,8]=>1000001=>0111110=>1
[7,3,5,6,8,4,2,1]=>0000000=>1111111=>1
[6,3,5,1,8,2,7,4]=>0000000=>1111111=>1
[5,7,1,6,3,8,4,2]=>0000000=>1111111=>1
[3,2,4,1,7,8,5,6]=>0001000=>1110111=>2
[2,5,4,6,1,7,8,3]=>0000000=>1111111=>1
[7,2,1,4,3,6,5,8]=>0000001=>1111110=>1
[7,3,4,1,2,6,5,8]=>0000001=>1111110=>1
[7,4,3,2,1,6,5,8]=>0000001=>1111110=>1
[7,6,3,2,5,4,1,8]=>0000001=>1111110=>1
[6,7,3,2,5,4,8,1]=>0000000=>1111111=>1
[1,8,3,2,5,4,7,6]=>1000000=>0111111=>1
[1,8,4,5,2,3,7,6]=>1000000=>0111111=>1
[7,3,5,1,6,2,4,8]=>0000001=>1111110=>1
[7,2,1,5,6,3,4,8]=>0000001=>1111110=>1
[7,2,1,6,5,4,3,8]=>0000001=>1111110=>1
[7,4,6,5,1,3,2,8]=>0000001=>1111110=>1
[1,8,5,4,3,2,7,6]=>1000000=>0111111=>1
[1,8,6,4,3,7,2,5]=>1000000=>0111111=>1
[6,5,7,4,3,1,8,2]=>0000000=>1111111=>1
[6,3,7,1,5,4,8,2]=>0000000=>1111111=>1
[3,2,1,8,5,4,7,6]=>0010000=>1101111=>2
[2,3,8,1,5,4,7,6]=>0000000=>1111111=>1
[2,5,8,4,3,1,7,6]=>0000000=>1111111=>1
[2,6,8,4,3,7,1,5]=>0000000=>1111111=>1
[2,7,8,4,3,6,5,1]=>0000000=>1111111=>1
[1,8,7,4,3,6,5,2]=>1000000=>0111111=>1
[1,8,7,5,6,3,4,2]=>1000000=>0111111=>1
[2,7,8,5,6,3,4,1]=>0000000=>1111111=>1
[2,6,8,5,7,3,1,4]=>0000000=>1111111=>1
[2,4,8,6,1,7,3,5]=>0000000=>1111111=>1
[3,2,1,8,6,7,4,5]=>0010000=>1101111=>2
[5,3,7,1,6,8,4,2]=>0000000=>1111111=>1
[5,4,7,6,1,8,3,2]=>0000000=>1111111=>1
[4,5,7,6,8,1,3,2]=>0000000=>1111111=>1
[1,8,6,5,7,3,2,4]=>1000000=>0111111=>1
[1,8,5,6,7,2,3,4]=>1000000=>0111111=>1
[4,6,5,7,8,2,1,3]=>0000000=>1111111=>1
[5,4,6,7,1,8,2,3]=>0000000=>1111111=>1
[5,2,1,6,7,8,3,4]=>0000000=>1111111=>1
[6,2,1,5,7,3,8,4]=>0000000=>1111111=>1
[6,3,5,1,7,2,8,4]=>0000000=>1111111=>1
[5,6,4,7,2,8,1,3]=>0000000=>1111111=>1
[1,8,4,6,2,7,3,5]=>1000000=>0111111=>1
[1,8,3,2,6,7,4,5]=>1000000=>0111111=>1
[6,5,3,2,7,1,8,4]=>0000000=>1111111=>1
[6,4,3,2,1,7,8,5]=>0000000=>1111111=>1
[6,2,1,4,3,7,8,5]=>0000000=>1111111=>1
[4,6,3,2,8,7,1,5]=>0000000=>1111111=>1
[4,7,3,2,8,6,5,1]=>0000000=>1111111=>1
[1,8,3,2,7,6,5,4]=>1000000=>0111111=>1
[1,8,4,7,2,6,5,3]=>1000000=>0111111=>1
[3,6,4,8,2,7,1,5]=>0000000=>1111111=>1
[3,4,5,8,1,2,7,6]=>0000000=>1111111=>1
[4,2,1,5,8,3,7,6]=>0000000=>1111111=>1
[4,2,1,6,8,7,3,5]=>0000000=>1111111=>1
[3,4,6,8,1,7,2,5]=>0000000=>1111111=>1
[3,5,6,8,7,1,2,4]=>0000000=>1111111=>1
[3,6,5,8,7,2,1,4]=>0000000=>1111111=>1
[1,8,5,7,6,2,4,3]=>1000000=>0111111=>1
[1,8,6,7,5,4,2,3]=>1000000=>0111111=>1
[3,6,7,8,5,4,1,2]=>0000000=>1111111=>1
[3,5,7,8,6,1,4,2]=>0000000=>1111111=>1
[3,4,7,8,1,6,5,2]=>0000000=>1111111=>1
[4,2,1,7,8,6,5,3]=>0000000=>1111111=>1
[2,3,8,1,7,6,5,4]=>0000000=>1111111=>1
[2,4,8,7,1,6,5,3]=>0000000=>1111111=>1
[2,1,4,3,6,5,8,7,10,9,12,11]=>01010101010=>10101010101=>6
[10,3,2,5,4,7,6,9,8,1,12,11]=>00000000010=>11111111101=>2
[10,3,2,5,4,9,8,7,6,1,12,11]=>00000000010=>11111111101=>2
[10,3,2,7,6,5,4,9,8,1,12,11]=>00000000010=>11111111101=>2
[10,3,2,9,6,5,8,7,4,1,12,11]=>00000000010=>11111111101=>2
[10,3,2,9,8,7,6,5,4,1,12,11]=>00000000010=>11111111101=>2
[10,5,4,3,2,7,6,9,8,1,12,11]=>00000000010=>11111111101=>2
[10,5,4,3,2,9,8,7,6,1,12,11]=>00000000010=>11111111101=>2
[10,7,4,3,6,5,2,9,8,1,12,11]=>00000000010=>11111111101=>2
[10,9,4,3,6,5,8,7,2,1,12,11]=>00000000010=>11111111101=>2
[10,9,4,3,8,7,6,5,2,1,12,11]=>00000000010=>11111111101=>2
[10,7,6,5,4,3,2,9,8,1,12,11]=>00000000010=>11111111101=>2
[10,9,6,5,4,3,8,7,2,1,12,11]=>00000000010=>11111111101=>2
[10,9,8,5,4,7,6,3,2,1,12,11]=>00000000010=>11111111101=>2
[10,9,8,7,6,5,4,3,2,1,12,11]=>00000000010=>11111111101=>2
[4,6,2,1,7,5,8,3]=>0000000=>1111111=>1
[3,6,8,4,1,7,5,2]=>0000000=>1111111=>1
[7,5,6,1,8,3,4,2]=>0000000=>1111111=>1
[3,4,6,5,7,1,8,2]=>0000000=>1111111=>1
[6,7,5,1,8,4,3,2]=>0000000=>1111111=>1
[6,8,4,1,7,5,3,2]=>0000000=>1111111=>1
[2,8,4,1,6,7,5,3]=>0000000=>1111111=>1
[2,4,6,1,7,5,8,3]=>0000000=>1111111=>1
[4,8,2,6,5,7,1,3]=>0000000=>1111111=>1
[4,6,1,2,7,5,8,3]=>0000000=>1111111=>1
[7,5,1,2,6,8,4,3]=>0000000=>1111111=>1
[6,7,1,5,8,2,3,4]=>0000000=>1111111=>1
[3,6,7,1,5,8,2,4]=>0000000=>1111111=>1
[8,4,1,6,7,5,2,3]=>0000000=>1111111=>1
[1,7,6,2,5,8,3,4]=>1000000=>0111111=>1
[7,6,2,1,5,8,3,4]=>0000000=>1111111=>1
[8,3,1,5,7,6,2,4]=>0000000=>1111111=>1
[6,2,4,1,7,5,8,3]=>0000000=>1111111=>1
[6,2,5,1,7,4,8,3]=>0000000=>1111111=>1
[8,3,5,7,6,2,1,4]=>0000000=>1111111=>1
[8,4,2,6,7,5,1,3]=>0000000=>1111111=>1
[6,1,4,2,7,5,8,3]=>0000000=>1111111=>1
[3,6,8,2,5,7,1,4]=>0000000=>1111111=>1
[8,3,2,5,7,6,1,4]=>0000000=>1111111=>1
[4,2,1,3,7,6,8,5]=>0001000=>1110111=>2
[2,5,1,3,7,6,8,4]=>0000000=>1111111=>1
[3,1,2,4,7,6,8,5]=>0011000=>1100111=>2
[10,8,9,5,6,7,1,2,3,4]=>000000000=>111111111=>1
[10,8,9,4,5,6,1,2,3,7]=>000000000=>111111111=>1
[10,7,8,5,6,9,1,2,3,4]=>000000000=>111111111=>1
[10,7,8,4,5,9,1,2,3,6]=>000000000=>111111111=>1
[10,6,7,4,5,8,1,2,3,9]=>000000000=>111111111=>1
[10,7,8,3,4,9,1,2,5,6]=>000000000=>111111111=>1
[10,6,7,3,4,8,1,2,5,9]=>000000000=>111111111=>1
[9,8,10,5,6,7,1,2,3,4]=>000000000=>111111111=>1
[9,8,10,4,5,6,1,2,3,7]=>000000000=>111111111=>1
[9,7,10,5,6,8,1,2,3,4]=>000000000=>111111111=>1
[9,7,10,4,5,8,1,2,3,6]=>000000000=>111111111=>1
[9,6,10,4,5,7,1,2,3,8]=>000000000=>111111111=>1
[9,7,10,3,4,8,1,2,5,6]=>000000000=>111111111=>1
[9,6,10,3,4,7,1,2,5,8]=>000000000=>111111111=>1
[8,7,9,5,6,10,1,2,3,4]=>000000000=>111111111=>1
[8,7,9,4,5,10,1,2,3,6]=>000000000=>111111111=>1
[8,6,9,4,5,10,1,2,3,7]=>000000000=>111111111=>1
[7,6,8,4,5,9,1,2,3,10]=>000000001=>111111110=>1
[8,7,9,3,4,10,1,2,5,6]=>000000000=>111111111=>1
[8,6,9,3,4,10,1,2,5,7]=>000000000=>111111111=>1
[7,6,8,3,4,9,1,2,5,10]=>000000001=>111111110=>1
[9,6,10,5,7,8,1,2,3,4]=>000000000=>111111111=>1
[9,6,10,4,7,8,1,2,3,5]=>000000000=>111111111=>1
[9,5,10,4,6,7,1,2,3,8]=>000000000=>111111111=>1
[9,6,10,3,7,8,1,2,4,5]=>000000000=>111111111=>1
[9,5,10,3,6,7,1,2,4,8]=>000000000=>111111111=>1
[8,6,9,5,7,10,1,2,3,4]=>000000000=>111111111=>1
[8,6,9,4,7,10,1,2,3,5]=>000000000=>111111111=>1
[8,5,9,4,6,10,1,2,3,7]=>000000000=>111111111=>1
[7,5,8,4,6,9,1,2,3,10]=>000000001=>111111110=>1
[8,6,9,3,7,10,1,2,4,5]=>000000000=>111111111=>1
[8,5,9,3,6,10,1,2,4,7]=>000000000=>111111111=>1
[7,5,8,3,6,9,1,2,4,10]=>000000001=>111111110=>1
[8,4,9,3,5,10,1,2,6,7]=>000000000=>111111111=>1
[7,4,8,3,5,9,1,2,6,10]=>000000001=>111111110=>1
[9,6,10,2,7,8,1,3,4,5]=>000000000=>111111111=>1
[9,5,10,2,6,7,1,3,4,8]=>000000000=>111111111=>1
[8,6,9,2,7,10,1,3,4,5]=>000000000=>111111111=>1
[8,5,9,2,6,10,1,3,4,7]=>000000000=>111111111=>1
[7,5,8,2,6,9,1,3,4,10]=>000000001=>111111110=>1
[8,4,9,2,5,10,1,3,6,7]=>000000000=>111111111=>1
[7,4,8,2,5,9,1,3,6,10]=>000000001=>111111110=>1
[8,1,2,4,3,6,5,7]=>0000000=>1111111=>1
[8,1,3,5,6,2,7,4]=>0000000=>1111111=>1
[8,1,3,4,2,6,7,5]=>0000000=>1111111=>1
[8,1,3,2,4,5,7,6]=>0000000=>1111111=>1
[2,7,8,3,4,5,6,1]=>0000000=>1111111=>1
[2,6,3,8,4,5,7,1]=>0000000=>1111111=>1
[6,3,2,1,4,5,8,7]=>0000010=>1111101=>2
[7,3,1,4,2,6,8,5]=>0000000=>1111111=>1
[7,4,1,5,6,8,2,3]=>0000000=>1111111=>1
[4,7,8,5,6,1,2,3]=>0000000=>1111111=>1
[3,7,8,5,6,2,1,4]=>0000000=>1111111=>1
[3,7,8,4,2,6,1,5]=>0000000=>1111111=>1
[3,7,8,2,4,5,1,6]=>0000000=>1111111=>1
[3,6,2,8,4,5,1,7]=>0000000=>1111111=>1
[2,3,6,7,4,5,8,1]=>0000000=>1111111=>1
[3,5,2,4,8,6,1,7]=>0000000=>1111111=>1
[3,5,4,2,8,7,1,6]=>0000000=>1111111=>1
[4,6,5,8,7,1,2,3]=>0000000=>1111111=>1
[6,4,5,1,7,8,2,3]=>0000000=>1111111=>1
[7,4,1,2,3,8,5,6]=>0000000=>1111111=>1
[6,2,4,1,3,7,5,8]=>0000001=>1111110=>1
[2,6,4,8,3,7,5,1]=>0000000=>1111111=>1
[2,6,5,8,7,3,4,1]=>0000000=>1111111=>1
[6,2,5,1,7,3,4,8]=>0000001=>1111110=>1
[6,5,2,1,8,3,4,7]=>0000000=>1111111=>1
[2,5,6,7,8,3,4,1]=>0000000=>1111111=>1
[2,4,6,7,3,8,5,1]=>0000000=>1111111=>1
[4,2,6,7,3,1,5,8]=>0000001=>1111110=>1
[4,7,8,2,3,1,5,6]=>0000000=>1111111=>1
[4,7,8,3,2,1,6,5]=>0000000=>1111111=>1
[5,6,4,8,1,7,2,3]=>0000000=>1111111=>1
[5,6,3,8,1,2,7,4]=>0000000=>1111111=>1
[4,2,5,3,7,1,6,8]=>0000001=>1111110=>1
[4,3,6,7,2,1,8,5]=>0000000=>1111111=>1
[3,4,6,7,2,8,1,5]=>0000000=>1111111=>1
[3,4,5,2,7,8,1,6]=>0000000=>1111111=>1
[3,4,2,5,6,8,1,7]=>0000000=>1111111=>1
[5,2,7,8,6,4,1,3]=>0000000=>1111111=>1
[5,1,2,7,8,6,4,3]=>0000000=>1111111=>1
[4,7,1,8,6,5,2,3]=>0000000=>1111111=>1
[4,7,1,2,8,6,5,3]=>0000000=>1111111=>1
[4,6,8,1,2,7,5,3]=>0000000=>1111111=>1
[6,8,7,1,5,3,2,4]=>0000000=>1111111=>1
[6,8,7,3,5,1,2,4]=>0000000=>1111111=>1
[7,8,1,6,3,5,2,4]=>0000000=>1111111=>1
[7,8,1,3,6,5,2,4]=>0000000=>1111111=>1
[7,8,3,6,5,2,1,4]=>0000000=>1111111=>1
[4,7,2,8,6,1,5,3]=>0000000=>1111111=>1
[1,7,3,4,8,6,5,2]=>1000000=>0111111=>1
[4,2,7,1,8,6,5,3]=>0000000=>1111111=>1
[7,8,2,3,6,5,1,4]=>0000000=>1111111=>1
[8,5,7,1,6,2,3,4]=>0000000=>1111111=>1
[8,5,7,1,2,6,3,4]=>0000000=>1111111=>1
[6,8,2,7,1,3,5,4]=>0000000=>1111111=>1
[6,8,7,2,5,3,1,4]=>0000000=>1111111=>1
[6,2,4,8,7,1,5,3]=>0000000=>1111111=>1
[1,6,8,3,7,4,5,2]=>1000000=>0111111=>1
[1,6,8,3,4,7,5,2]=>1000000=>0111111=>1
[6,2,4,8,1,7,5,3]=>0000000=>1111111=>1
[6,8,7,2,3,5,1,4]=>0000000=>1111111=>1
[6,8,2,1,7,3,5,4]=>0000000=>1111111=>1
[8,5,7,2,1,6,3,4]=>0000000=>1111111=>1
[8,5,7,1,2,3,6,4]=>0000000=>1111111=>1
[8,7,6,2,1,4,3,5]=>0000000=>1111111=>1
[8,5,7,2,3,1,6,4]=>0000000=>1111111=>1
[5,8,4,2,7,1,6,3]=>0000000=>1111111=>1
[1,8,7,5,3,4,6,2]=>1000000=>0111111=>1
[1,8,7,3,5,4,6,2]=>1000000=>0111111=>1
[8,2,5,4,7,1,6,3]=>0000000=>1111111=>1
[8,5,2,7,3,1,6,4]=>0000000=>1111111=>1
[8,7,6,2,4,3,1,5]=>0000000=>1111111=>1
[8,7,6,1,2,4,3,5]=>0000000=>1111111=>1
[8,7,6,1,4,2,3,5]=>0000000=>1111111=>1
[8,7,6,4,1,3,2,5]=>0000000=>1111111=>1
[5,8,4,7,2,1,6,3]=>0000000=>1111111=>1
[1,8,7,5,4,3,6,2]=>1000000=>0111111=>1
[1,6,8,4,3,7,5,2]=>1000000=>0111111=>1
[6,8,7,3,2,5,1,4]=>0000000=>1111111=>1
[6,8,1,7,3,2,5,4]=>0000000=>1111111=>1
[8,5,7,3,1,6,2,4]=>0000000=>1111111=>1
[8,5,7,1,3,2,6,4]=>0000000=>1111111=>1
[8,5,7,3,1,2,6,4]=>0000000=>1111111=>1
[5,8,4,7,1,2,6,3]=>0000000=>1111111=>1
[5,8,4,1,7,2,6,3]=>0000000=>1111111=>1
[5,8,4,7,1,6,2,3]=>0000000=>1111111=>1
[8,1,2,6,5,7,4,3]=>0000000=>1111111=>1
[8,2,5,6,7,4,1,3]=>0000000=>1111111=>1
[4,8,5,7,1,6,2,3]=>0000000=>1111111=>1
[4,8,5,7,1,2,6,3]=>0000000=>1111111=>1
[4,8,5,1,7,2,6,3]=>0000000=>1111111=>1
[8,5,3,1,7,2,6,4]=>0000000=>1111111=>1
[8,5,3,7,1,2,6,4]=>0000000=>1111111=>1
[6,8,1,3,7,2,5,4]=>0000000=>1111111=>1
[4,6,2,8,1,7,5,3]=>0000000=>1111111=>1
[1,6,4,8,3,7,5,2]=>1000000=>0111111=>1
[1,8,7,4,5,3,6,2]=>1000000=>0111111=>1
[4,8,5,7,2,1,6,3]=>0000000=>1111111=>1
[8,5,3,7,2,1,6,4]=>0000000=>1111111=>1
[8,7,6,3,1,4,2,5]=>0000000=>1111111=>1
[8,7,6,1,3,2,4,5]=>0000000=>1111111=>1
[8,5,3,2,7,1,6,4]=>0000000=>1111111=>1
[4,8,5,2,7,1,6,3]=>0000000=>1111111=>1
[1,8,7,4,3,5,6,2]=>1000000=>0111111=>1
[1,8,7,3,4,5,6,2]=>1000000=>0111111=>1
[8,2,4,5,7,1,6,3]=>0000000=>1111111=>1
[8,5,2,3,7,1,6,4]=>0000000=>1111111=>1
[8,3,1,5,2,7,6,4]=>0000000=>1111111=>1
[8,7,4,1,6,3,2,5]=>0000000=>1111111=>1
[8,7,4,1,6,3,5,2]=>0000000=>1111111=>1
[8,7,4,1,6,5,3,2]=>0000000=>1111111=>1
[8,3,2,5,1,7,4,6]=>0000000=>1111111=>1
[8,5,4,3,1,7,2,6]=>0000000=>1111111=>1
[8,7,4,1,6,5,2,3]=>0000000=>1111111=>1
[8,7,4,1,6,2,5,3]=>0000000=>1111111=>1
[8,7,6,5,2,1,4,3]=>0000000=>1111111=>1
[8,7,4,3,6,2,1,5]=>0000000=>1111111=>1
[8,3,2,7,6,4,1,5]=>0000000=>1111111=>1
[2,1,8,7,6,4,5,3]=>0100000=>1011111=>2
[8,3,2,7,6,4,5,1]=>0000000=>1111111=>1
[8,5,4,2,3,7,6,1]=>0000000=>1111111=>1
[8,7,4,2,6,3,5,1]=>0000000=>1111111=>1
[8,7,4,2,6,3,1,5]=>0000000=>1111111=>1
[8,3,1,7,6,5,4,2]=>0000000=>1111111=>1
[8,3,1,5,4,7,6,2]=>0000000=>1111111=>1
[8,3,1,5,4,7,2,6]=>0000000=>1111111=>1
[8,3,2,5,4,7,1,6]=>0000000=>1111111=>1
[8,7,6,5,3,1,4,2]=>0000000=>1111111=>1
[8,7,6,5,1,3,2,4]=>0000000=>1111111=>1
[8,7,6,5,1,4,3,2]=>0000000=>1111111=>1
[8,7,6,5,4,1,3,2]=>0000000=>1111111=>1
[8,3,2,7,6,1,5,4]=>0000000=>1111111=>1
[2,1,8,7,6,3,5,4]=>0100000=>1011111=>2
[8,3,2,7,6,1,4,5]=>0000000=>1111111=>1
[8,7,6,5,1,4,2,3]=>0000000=>1111111=>1
[7,3,5,1,8,4,6,2]=>0000000=>1111111=>1
[4,5,6,2,1,8,7,3]=>0000000=>1111111=>1
[1,6,5,2,7,4,3,8]=>1000001=>0111110=>1
[7,4,3,1,8,6,5,2]=>0000000=>1111111=>1
[7,6,5,1,8,4,3,2]=>0000000=>1111111=>1
[6,4,2,1,8,7,5,3]=>0000000=>1111111=>1
[1,5,3,2,7,6,4,8]=>1000001=>0111110=>1
[5,3,2,1,8,7,6,4]=>0000000=>1111111=>1
[2,6,4,1,7,8,5,3]=>0000000=>1111111=>1
[2,6,5,1,7,8,4,3]=>0000000=>1111111=>1
[6,4,1,2,8,5,3,7]=>0000000=>1111111=>1
[4,3,1,2,8,6,5,7]=>0001000=>1110111=>2
[6,1,2,5,8,3,4,7]=>0000000=>1111111=>1
[7,1,3,4,8,2,5,6]=>0000000=>1111111=>1
[2,6,1,5,7,8,3,4]=>0000000=>1111111=>1
[5,2,3,1,8,6,7,4]=>0000000=>1111111=>1
[1,6,2,5,7,3,4,8]=>1000001=>0111110=>1
[6,2,1,5,8,7,3,4]=>0000000=>1111111=>1
[6,2,5,1,8,4,7,3]=>0000000=>1111111=>1
[7,3,1,4,8,6,2,5]=>0000000=>1111111=>1
[6,2,1,4,8,7,3,5]=>0000000=>1111111=>1
[5,2,1,3,8,7,4,6]=>0000000=>1111111=>1
[7,5,1,3,8,4,2,6]=>0000000=>1111111=>1
[3,6,7,1,4,8,2,5]=>0000000=>1111111=>1
[7,6,1,4,8,3,2,5]=>0000000=>1111111=>1
[4,2,1,3,8,7,5,6]=>0001000=>1110111=>2
[2,6,1,4,7,8,3,5]=>0000000=>1111111=>1
[7,1,4,6,8,2,3,5]=>0000000=>1111111=>1
[7,1,3,5,8,2,4,6]=>0000000=>1111111=>1
[7,4,5,2,3,1,8,6]=>0000000=>1111111=>1
[8,6,7,3,5,2,4,1]=>0000000=>1111111=>1
[6,3,5,2,4,1,8,7]=>0000010=>1111101=>2
[5,2,7,3,4,1,8,6]=>0000000=>1111111=>1
[5,2,8,6,7,3,4,1]=>0000000=>1111111=>1
[6,2,7,3,4,1,8,5]=>0000000=>1111111=>1
[3,1,8,6,7,4,5,2]=>0000000=>1111111=>1
[8,5,7,3,4,1,6,2]=>0000000=>1111111=>1
[8,4,7,3,5,1,6,2]=>0000000=>1111111=>1
[4,1,8,5,7,3,6,2]=>0000000=>1111111=>1
[2,1,8,5,7,4,6,3]=>0100000=>1011111=>2
[6,2,7,3,5,1,8,4]=>0000000=>1111111=>1
[6,2,8,4,7,3,5,1]=>0000000=>1111111=>1
[8,4,7,3,6,2,5,1]=>0000000=>1111111=>1
[7,3,6,2,5,1,8,4]=>0000000=>1111111=>1
[6,2,5,1,7,3,8,4]=>0000000=>1111111=>1
[5,2,4,1,7,3,8,6]=>0000000=>1111111=>1
[6,2,4,1,7,3,8,5]=>0000000=>1111111=>1
[8,5,7,3,6,2,4,1]=>0000000=>1111111=>1
[8,5,7,4,6,2,3,1]=>0000000=>1111111=>1
[8,5,6,2,3,1,7,4]=>0000000=>1111111=>1
[7,4,8,5,6,2,3,1]=>0000000=>1111111=>1
[7,3,8,5,6,2,4,1]=>0000000=>1111111=>1
[3,1,5,2,8,6,7,4]=>0000000=>1111111=>1
[2,1,6,3,8,5,7,4]=>0100000=>1011111=>2
[3,1,6,2,8,5,7,4]=>0000000=>1111111=>1
[4,1,6,2,8,5,7,3]=>0000000=>1111111=>1
[5,1,6,2,8,4,7,3]=>0000000=>1111111=>1
[7,3,8,4,6,2,5,1]=>0000000=>1111111=>1
[5,1,8,4,6,2,7,3]=>0000000=>1111111=>1
[4,1,8,5,6,2,7,3]=>0000000=>1111111=>1
[3,1,8,5,6,2,7,4]=>0000000=>1111111=>1
[4,1,7,3,8,5,6,2]=>0000000=>1111111=>1
[7,3,8,4,5,1,6,2]=>0000000=>1111111=>1
[7,3,6,2,8,4,5,1]=>0000000=>1111111=>1
[7,8,5,6,1,3,4,2]=>0000000=>1111111=>1
[7,8,1,3,6,2,5,4]=>0000000=>1111111=>1
[1,3,8,4,7,2,5,6]=>1000000=>0111111=>1
[3,6,1,4,7,2,5,8]=>0000001=>1111110=>1
[4,6,1,2,5,7,3,8]=>0000001=>1111110=>1
[1,4,8,2,5,7,3,6]=>1000000=>0111111=>1
[7,8,2,4,5,6,1,3]=>0000000=>1111111=>1
[7,8,1,5,4,6,3,2]=>0000000=>1111111=>1
[7,8,2,1,6,3,4,5]=>0000000=>1111111=>1
[7,8,3,5,6,4,1,2]=>0000000=>1111111=>1
[7,8,1,4,2,3,6,5]=>0000000=>1111111=>1
[7,8,5,1,4,2,6,3]=>0000000=>1111111=>1
[7,8,4,5,3,1,6,2]=>0000000=>1111111=>1
[1,5,8,4,3,2,7,6]=>1000000=>0111111=>1
[5,6,1,4,3,2,7,8]=>0000011=>1111100=>1
[2,6,4,8,3,7,1,5]=>0000000=>1111111=>1
[1,4,6,8,3,7,5,2]=>1000000=>0111111=>1
[2,4,8,5,3,1,6,7]=>0000000=>1111111=>1
[2,5,8,1,4,7,6,3]=>0000000=>1111111=>1
[3,5,8,4,7,6,1,2]=>0000000=>1111111=>1
[1,6,2,4,7,3,8,5]=>1000000=>0111111=>1
[5,6,2,1,4,7,8,3]=>0000000=>1111111=>1
[4,6,2,5,3,1,8,7]=>0000010=>1111101=>2
[4,7,5,1,3,6,8,2]=>0000000=>1111111=>1
[7,5,3,6,2,4,1,8]=>0000001=>1111110=>1
[5,7,3,6,1,4,8,2]=>0000000=>1111111=>1
[5,3,6,7,2,1,8,4]=>0000000=>1111111=>1
[6,1,7,5,2,4,8,3]=>0000000=>1111111=>1
[6,3,1,2,4,5,8,7]=>0000010=>1111101=>2
[1,4,7,2,5,3,8,6]=>1000000=>0111111=>1
[4,6,7,8,3,5,1,2]=>0000000=>1111111=>1
[3,6,1,8,4,2,5,7]=>0000000=>1111111=>1
[1,6,7,5,8,2,4,3]=>1000000=>0111111=>1
[3,5,6,7,8,1,4,2]=>0000000=>1111111=>1
[3,6,5,7,8,2,1,4]=>0000000=>1111111=>1
[5,2,7,6,1,4,3,8]=>0000001=>1111110=>1
[2,5,7,6,8,1,3,4]=>0000000=>1111111=>1
[2,7,5,6,8,4,1,3]=>0000000=>1111111=>1
[2,1,6,8,4,5,3,7]=>0100000=>1011111=>2
[2,7,1,8,5,3,4,6]=>0000000=>1111111=>1
[3,7,6,8,5,4,1,2]=>0000000=>1111111=>1
[4,3,8,5,6,7,1,2]=>0000000=>1111111=>1
[4,2,8,1,6,3,7,5]=>0000000=>1111111=>1
[3,1,8,5,4,6,7,2]=>0000000=>1111111=>1
[3,2,8,4,5,6,1,7]=>0000000=>1111111=>1
[3,4,2,8,6,1,7,5]=>0000000=>1111111=>1
[3,4,7,1,5,2,6,8]=>0000001=>1111110=>1
[4,3,7,8,1,2,6,5]=>0000000=>1111111=>1
[1,7,3,8,5,2,6,4]=>1000000=>0111111=>1
[4,1,8,3,6,2,5,7]=>0000000=>1111111=>1
[5,7,8,6,3,2,1,4]=>0000000=>1111111=>1
[5,7,8,6,1,3,4,2]=>0000000=>1111111=>1
[7,6,5,8,1,3,4,2]=>0000000=>1111111=>1
[1,6,4,3,8,2,5,7]=>1000000=>0111111=>1
[7,1,3,4,8,2,6,5]=>0000000=>1111111=>1
[3,6,5,4,1,2,7,8]=>0000011=>1111100=>1
[2,4,5,1,7,8,6,3]=>0000000=>1111111=>1
[2,6,3,4,5,8,1,7]=>0000000=>1111111=>1
[2,6,4,1,8,3,7,5]=>0000000=>1111111=>1
[7,3,6,4,8,5,1,2]=>0000000=>1111111=>1
[7,2,1,4,8,3,5,6]=>0000000=>1111111=>1
[7,1,6,5,3,8,4,2]=>0000000=>1111111=>1
[7,2,5,6,3,8,1,4]=>0000000=>1111111=>1
[6,5,2,7,1,8,4,3]=>0000000=>1111111=>1
[5,6,2,7,3,1,4,8]=>0000001=>1111110=>1
[5,6,7,4,2,8,1,3]=>0000000=>1111111=>1
[5,7,6,4,1,8,3,2]=>0000000=>1111111=>1
[6,7,1,5,2,8,3,4]=>0000000=>1111111=>1
[1,7,5,2,4,8,3,6]=>1000000=>0111111=>1
[6,1,5,2,8,3,4,7]=>0000000=>1111111=>1
[6,7,5,3,8,4,1,2]=>0000000=>1111111=>1
[1,6,5,4,2,3,8,7]=>1000010=>0111101=>2
[7,1,5,3,4,2,8,6]=>0000000=>1111111=>1
[7,6,1,5,3,2,8,4]=>0000000=>1111111=>1
[7,5,6,4,1,2,8,3]=>0000000=>1111111=>1
[6,7,5,4,3,1,8,2]=>0000000=>1111111=>1
[7,5,2,4,3,1,6,8]=>0000001=>1111110=>1
[7,4,6,1,2,5,3,8]=>0000001=>1111110=>1
[7,1,4,2,5,3,6,8]=>0000001=>1111110=>1
[6,8,1,4,2,5,7,3]=>0000000=>1111111=>1
[1,6,4,2,5,7,3,8]=>1000001=>0111110=>1
[1,6,3,7,5,4,2,8]=>1000001=>0111110=>1
[6,8,1,3,7,5,4,2]=>0000000=>1111111=>1
[7,1,3,5,6,4,2,8]=>0000001=>1111110=>1
[7,3,1,6,4,5,2,8]=>0000001=>1111110=>1
[7,4,2,6,5,1,3,8]=>0000001=>1111110=>1
[7,4,6,3,1,5,2,8]=>0000001=>1111110=>1
[7,2,4,1,5,3,6,8]=>0000001=>1111110=>1
[7,2,3,5,4,1,6,8]=>0000001=>1111110=>1
[6,8,1,2,3,4,7,5]=>0000000=>1111111=>1
[1,5,7,2,3,8,6,4]=>1000000=>0111111=>1
[5,1,8,2,3,6,7,4]=>0000000=>1111111=>1
[5,8,2,3,7,6,4,1]=>0000000=>1111111=>1
[6,2,8,1,3,7,4,5]=>0000000=>1111111=>1
[6,8,2,3,5,4,7,1]=>0000000=>1111111=>1
[6,8,2,4,1,5,7,3]=>0000000=>1111111=>1
[6,8,3,1,2,4,7,5]=>0000000=>1111111=>1
[2,6,4,1,5,7,3,8]=>0000001=>1111110=>1
[2,6,3,5,7,1,4,8]=>0000001=>1111110=>1
[2,5,1,7,8,3,6,4]=>0000000=>1111111=>1
[2,5,3,6,8,4,7,1]=>0000000=>1111111=>1
[2,1,4,7,8,5,6,3]=>0100000=>1011111=>2
[2,4,7,6,8,5,1,3]=>0000000=>1111111=>1
[2,5,3,7,6,1,8,4]=>0000000=>1111111=>1
[2,5,7,8,1,4,6,3]=>0000000=>1111111=>1
[3,5,7,4,1,6,2,8]=>0000001=>1111110=>1
[5,3,4,1,8,6,7,2]=>0000000=>1111111=>1
[5,2,8,4,6,1,7,3]=>0000000=>1111111=>1
[5,2,1,8,6,3,7,4]=>0000000=>1111111=>1
[4,2,8,6,5,3,7,1]=>0000000=>1111111=>1
[4,2,8,5,7,6,3,1]=>0000000=>1111111=>1
[1,4,2,7,5,8,6,3]=>1000000=>0111111=>1
[4,1,8,6,7,5,3,2]=>0000000=>1111111=>1
[5,3,8,7,6,2,4,1]=>0000000=>1111111=>1
[5,8,4,7,6,2,1,3]=>0000000=>1111111=>1
[5,8,7,4,3,6,1,2]=>0000000=>1111111=>1
[6,4,8,3,1,7,2,5]=>0000000=>1111111=>1
[6,4,2,8,7,1,3,5]=>0000000=>1111111=>1
[6,3,8,7,2,5,1,4]=>0000000=>1111111=>1
[5,8,3,7,1,6,4,2]=>0000000=>1111111=>1
[5,1,3,8,6,7,2,4]=>0000000=>1111111=>1
[1,5,3,7,8,6,2,4]=>1000000=>0111111=>1
[1,5,7,6,4,2,8,3]=>1000000=>0111111=>1
[5,8,7,4,1,6,2,3]=>0000000=>1111111=>1
[6,4,8,1,2,7,3,5]=>0000000=>1111111=>1
[6,8,5,1,2,3,7,4]=>0000000=>1111111=>1
[6,8,5,2,4,3,7,1]=>0000000=>1111111=>1
[6,8,5,3,1,2,7,4]=>0000000=>1111111=>1
[4,5,1,2,7,6,3,8]=>0000001=>1111110=>1
[4,5,1,2,6,8,7,3]=>0000000=>1111111=>1
[3,5,6,1,8,4,7,2]=>0000000=>1111111=>1
[3,5,7,1,2,8,6,4]=>0000000=>1111111=>1
[3,6,2,7,5,1,4,8]=>0000001=>1111110=>1
[4,2,6,1,7,3,5,8]=>0000001=>1111110=>1
[4,6,3,1,2,7,5,8]=>0000001=>1111110=>1
[4,5,3,1,7,6,2,8]=>0000001=>1111110=>1
[4,2,5,7,1,6,3,8]=>0000001=>1111110=>1
[3,5,2,7,8,1,6,4]=>0000000=>1111111=>1
[3,1,4,7,5,6,2,8]=>0000001=>1111110=>1
[3,4,6,5,8,7,1,2]=>0000000=>1111111=>1
[3,1,4,5,8,6,7,2]=>0000000=>1111111=>1
[3,4,6,8,5,2,7,1]=>0000000=>1111111=>1
[3,5,6,2,8,4,7,1]=>0000000=>1111111=>1
[4,2,5,6,1,8,7,3]=>0000000=>1111111=>1
[4,5,3,1,6,8,7,2]=>0000000=>1111111=>1
[2,1,7,5,8,6,4,3]=>0100000=>1011111=>2
[1,2,7,5,3,8,6,4]=>1100000=>0011111=>1
[4,1,2,7,3,8,6,5]=>0000000=>1111111=>1
[6,4,1,7,5,2,3,8]=>0000001=>1111110=>1
[6,1,3,7,5,2,4,8]=>0000001=>1111110=>1
[3,1,2,6,8,5,4,7]=>0010000=>1101111=>2
[3,7,1,2,5,4,8,6]=>0000000=>1111111=>1
[1,3,7,2,4,8,6,5]=>1000000=>0111111=>1
[2,4,1,7,8,6,5,3]=>0000000=>1111111=>1
[3,4,7,5,1,8,6,2]=>0000000=>1111111=>1
[2,7,4,1,5,8,6,3]=>0000000=>1111111=>1
[2,3,7,1,5,8,6,4]=>0000000=>1111111=>1
[5,2,8,1,3,7,4,6]=>0000000=>1111111=>1
[2,1,6,8,3,4,7,5]=>0100000=>1011111=>2
[2,6,8,3,1,5,7,4]=>0000000=>1111111=>1
[2,8,6,4,1,5,7,3]=>0000000=>1111111=>1
[3,6,4,8,5,1,7,2]=>0000000=>1111111=>1
[6,3,7,4,5,1,8,2]=>0000000=>1111111=>1
[2,6,3,7,5,8,1,4]=>0000000=>1111111=>1
[5,2,1,7,8,3,4,6]=>0000000=>1111111=>1
[4,7,2,3,6,8,1,5]=>0000000=>1111111=>1
[5,2,7,3,6,8,1,4]=>0000000=>1111111=>1
[5,7,4,6,2,8,1,3]=>0000000=>1111111=>1
[5,7,3,4,6,1,8,2]=>0000000=>1111111=>1
[5,3,8,4,6,1,7,2]=>0000000=>1111111=>1
[8,5,2,4,1,6,7,3]=>0000000=>1111111=>1
[8,2,3,5,1,6,7,4]=>0000000=>1111111=>1
[4,2,8,3,6,7,1,5]=>0000000=>1111111=>1
[2,4,8,1,7,3,5,6]=>0000000=>1111111=>1
[8,4,1,3,6,2,5,7]=>0000000=>1111111=>1
[4,8,3,1,7,2,5,6]=>0000000=>1111111=>1
[5,2,8,4,7,1,6,3]=>0000000=>1111111=>1
[5,8,4,7,3,1,6,2]=>0000000=>1111111=>1
[4,6,8,3,1,7,5,2]=>0000000=>1111111=>1
[6,3,8,2,7,1,5,4]=>0000000=>1111111=>1
[6,3,1,8,2,4,7,5]=>0000000=>1111111=>1
[5,3,8,1,2,6,4,7]=>0000000=>1111111=>1
[5,7,4,1,6,2,3,8]=>0000001=>1111110=>1
[8,5,4,1,2,6,3,7]=>0000000=>1111111=>1
[5,1,8,4,2,7,3,6]=>0000000=>1111111=>1
[1,6,2,8,5,3,7,4]=>1000000=>0111111=>1
[6,8,5,3,1,7,4,2]=>0000000=>1111111=>1
[8,4,5,1,2,6,3,7]=>0000000=>1111111=>1
[5,6,3,7,1,2,4,8]=>0000001=>1111110=>1
[1,6,3,7,2,8,4,5]=>1000000=>0111111=>1
[6,3,2,7,8,5,1,4]=>0000000=>1111111=>1
[4,5,7,8,3,1,6,2]=>0000000=>1111111=>1
[4,7,2,5,8,1,6,3]=>0000000=>1111111=>1
[8,1,3,4,6,2,5,7]=>0000000=>1111111=>1
[3,8,2,4,6,7,1,5]=>0000000=>1111111=>1
[3,5,6,8,2,7,1,4]=>0000000=>1111111=>1
[2,4,5,6,8,1,7,3]=>0000000=>1111111=>1
[4,8,3,5,6,1,7,2]=>0000000=>1111111=>1
[5,6,2,3,7,8,1,4]=>0000000=>1111111=>1
[5,8,7,3,4,1,2,6]=>0000000=>1111111=>1
[6,8,7,3,4,1,2,5]=>0000000=>1111111=>1
[6,8,4,7,1,5,3,2]=>0000000=>1111111=>1
[6,8,4,7,2,5,3,1]=>0000000=>1111111=>1
[5,4,8,7,2,6,3,1]=>0000000=>1111111=>1
[5,4,8,7,1,6,3,2]=>0000000=>1111111=>1
[5,3,8,7,6,1,2,4]=>0000000=>1111111=>1
[4,3,8,7,6,1,2,5]=>0000000=>1111111=>1
[4,8,3,7,5,1,2,6]=>0000000=>1111111=>1
[8,3,4,6,5,1,2,7]=>0000000=>1111111=>1
[3,8,4,7,5,1,2,6]=>0000000=>1111111=>1
[3,4,8,7,6,1,2,5]=>0000000=>1111111=>1
[3,5,8,7,6,1,2,4]=>0000000=>1111111=>1
[4,5,8,7,6,1,2,3]=>0000000=>1111111=>1
[4,5,8,7,1,6,3,2]=>0000000=>1111111=>1
[4,5,8,7,2,6,3,1]=>0000000=>1111111=>1
[3,5,8,2,7,6,4,1]=>0000000=>1111111=>1
[3,5,8,1,7,6,4,2]=>0000000=>1111111=>1
[2,5,8,1,7,6,4,3]=>0000000=>1111111=>1
[2,5,8,7,1,6,3,4]=>0000000=>1111111=>1
[2,4,8,7,1,6,3,5]=>0000000=>1111111=>1
[2,8,4,7,1,5,3,6]=>0000000=>1111111=>1
[8,2,4,6,1,5,3,7]=>0000000=>1111111=>1
[8,1,4,6,2,5,3,7]=>0000000=>1111111=>1
[1,8,4,7,2,5,3,6]=>1000000=>0111111=>1
[1,4,8,7,2,6,3,5]=>1000000=>0111111=>1
[1,5,8,7,2,6,3,4]=>1000000=>0111111=>1
[1,5,8,2,7,6,4,3]=>1000000=>0111111=>1
[2,5,8,3,7,6,4,1]=>0000000=>1111111=>1
[1,4,2,8,7,6,5,3]=>1000000=>0111111=>1
[1,3,8,2,7,6,4,5]=>1000000=>0111111=>1
[1,8,3,2,7,5,4,6]=>1000000=>0111111=>1
[8,1,3,2,6,5,4,7]=>0000000=>1111111=>1
[8,2,3,1,6,5,4,7]=>0000000=>1111111=>1
[2,8,3,1,7,5,4,6]=>0000000=>1111111=>1
[2,3,8,1,7,6,4,5]=>0000000=>1111111=>1
[3,4,1,8,7,6,5,2]=>0000000=>1111111=>1
[4,3,1,8,7,6,5,2]=>0000000=>1111111=>1
[4,2,1,8,7,6,5,3]=>0000000=>1111111=>1
[3,8,2,1,7,5,4,6]=>0000000=>1111111=>1
[8,3,2,1,6,5,4,7]=>0000000=>1111111=>1
[8,4,2,6,1,5,3,7]=>0000000=>1111111=>1
[4,2,8,7,1,6,3,5]=>0000000=>1111111=>1
[5,2,8,7,1,6,3,4]=>0000000=>1111111=>1
[5,2,8,1,7,6,4,3]=>0000000=>1111111=>1
[5,3,8,1,7,6,4,2]=>0000000=>1111111=>1
[5,3,8,2,7,6,4,1]=>0000000=>1111111=>1
[6,8,3,2,7,5,4,1]=>0000000=>1111111=>1
[6,8,3,1,7,5,4,2]=>0000000=>1111111=>1
[6,8,2,1,7,5,4,3]=>0000000=>1111111=>1
[6,8,2,7,1,5,3,4]=>0000000=>1111111=>1
[6,8,7,2,1,4,3,5]=>0000000=>1111111=>1
[8,5,6,1,2,4,3,7]=>0000000=>1111111=>1
[5,8,7,1,2,4,3,6]=>0000000=>1111111=>1
[6,8,1,2,7,5,4,3]=>0000000=>1111111=>1
[6,8,2,3,7,5,4,1]=>0000000=>1111111=>1
[5,2,8,3,7,6,4,1]=>0000000=>1111111=>1
[5,1,8,3,7,6,4,2]=>0000000=>1111111=>1
[5,1,8,7,2,6,3,4]=>0000000=>1111111=>1
[4,1,8,7,2,6,3,5]=>0000000=>1111111=>1
[4,8,1,7,2,5,3,6]=>0000000=>1111111=>1
[8,4,1,6,2,5,3,7]=>0000000=>1111111=>1
[8,3,1,2,6,5,4,7]=>0000000=>1111111=>1
[3,8,1,2,7,5,4,6]=>0000000=>1111111=>1
[3,1,8,2,7,6,4,5]=>0000000=>1111111=>1
[3,1,2,8,7,6,5,4]=>0010000=>1101111=>2
[4,1,3,8,7,6,5,2]=>0000000=>1111111=>1
[3,1,4,8,7,6,5,2]=>0000000=>1111111=>1
[2,1,8,3,7,6,4,5]=>0100000=>1011111=>2
[2,8,1,3,7,5,4,6]=>0000000=>1111111=>1
[8,2,1,3,6,5,4,7]=>0000000=>1111111=>1
[8,1,2,3,6,5,4,7]=>0000000=>1111111=>1
[1,8,2,3,7,5,4,6]=>1000000=>0111111=>1
[1,2,8,3,7,6,4,5]=>1100000=>0011111=>1
[1,4,3,6,8,2,5,7]=>1000000=>0111111=>1
[3,1,6,2,5,8,4,7]=>0000000=>1111111=>1
[3,5,1,8,2,4,7,6]=>0000000=>1111111=>1
[1,4,5,2,8,3,7,6]=>1000000=>0111111=>1
[1,4,2,6,5,8,3,7]=>1000000=>0111111=>1
[1,5,4,2,6,8,3,7]=>1000000=>0111111=>1
[3,1,6,5,8,2,4,7]=>0000000=>1111111=>1
[1,6,4,2,5,8,3,7]=>1000000=>0111111=>1
[1,5,2,6,4,8,3,7]=>1000000=>0111111=>1
[1,2,6,5,4,8,3,7]=>1100000=>0011111=>1
[1,2,5,4,7,3,8,6]=>1100000=>0011111=>1
[4,1,2,6,3,8,7,5]=>0000000=>1111111=>1
[7,1,5,4,2,8,3,6]=>0000000=>1111111=>1
[1,4,7,5,2,8,3,6]=>1000000=>0111111=>1
[7,1,3,5,2,8,4,6]=>0000000=>1111111=>1
[7,2,5,1,8,3,4,6]=>0000000=>1111111=>1
[1,4,5,2,8,7,3,6]=>1000000=>0111111=>1
[1,6,4,2,8,3,7,5]=>1000000=>0111111=>1
[1,4,2,8,3,7,6,5]=>1000000=>0111111=>1
[1,2,5,3,8,7,6,4]=>1100000=>0011111=>1
[1,2,8,6,5,3,7,4]=>1100000=>0011111=>1
[1,5,2,8,6,3,7,4]=>1000000=>0111111=>1
[1,6,4,2,8,7,3,5]=>1000000=>0111111=>1
[6,2,1,8,7,3,4,5]=>0000000=>1111111=>1
[7,6,2,1,8,3,4,5]=>0000000=>1111111=>1
[7,3,1,6,2,8,4,5]=>0000000=>1111111=>1
[1,7,6,4,2,8,3,5]=>1000000=>0111111=>1
[1,7,5,2,6,3,8,4]=>1000000=>0111111=>1
[1,6,2,7,5,3,8,4]=>1000000=>0111111=>1
[1,2,7,6,5,3,8,4]=>1100000=>0011111=>1
[1,2,6,5,3,8,7,4]=>1100000=>0011111=>1
[1,5,2,6,3,8,7,4]=>1000000=>0111111=>1
[1,5,2,7,6,3,8,4]=>1000000=>0111111=>1
[1,6,5,2,7,3,8,4]=>1000000=>0111111=>1
[1,5,7,4,2,8,3,6]=>1000000=>0111111=>1
[4,1,2,8,6,3,7,5]=>0000000=>1111111=>1
[3,1,8,6,2,4,7,5]=>0000000=>1111111=>1
[4,3,7,1,8,2,5,6]=>0000000=>1111111=>1
[8,3,1,6,2,4,7,5]=>0000000=>1111111=>1
[7,1,8,3,2,4,6,5]=>0000000=>1111111=>1
[1,8,7,3,2,4,6,5]=>1000000=>0111111=>1
[1,4,2,8,7,3,6,5]=>1000000=>0111111=>1
[1,7,4,2,8,3,6,5]=>1000000=>0111111=>1
[8,1,5,4,2,7,3,6]=>0000000=>1111111=>1
[1,4,8,5,2,7,3,6]=>1000000=>0111111=>1
[8,5,3,1,7,2,4,6]=>0000000=>1111111=>1
[8,6,2,1,7,3,4,5]=>0000000=>1111111=>1
[1,8,6,4,2,7,3,5]=>1000000=>0111111=>1
[1,8,5,2,6,3,7,4]=>1000000=>0111111=>1
[1,5,2,7,3,8,6,4]=>1000000=>0111111=>1
[1,2,8,5,3,7,6,4]=>1100000=>0011111=>1
[1,2,6,3,8,7,5,4]=>1100000=>0011111=>1
[1,2,7,6,3,8,5,4]=>1100000=>0011111=>1
[1,6,2,7,3,8,5,4]=>1000000=>0111111=>1
[1,7,2,8,5,3,6,4]=>1000000=>0111111=>1
[1,7,4,2,8,6,3,5]=>1000000=>0111111=>1
[7,1,8,3,2,6,4,5]=>0000000=>1111111=>1
[7,2,1,8,6,3,4,5]=>0000000=>1111111=>1
[1,8,7,3,2,6,4,5]=>1000000=>0111111=>1
[1,4,2,8,7,6,3,5]=>1000000=>0111111=>1
[1,2,8,7,5,3,6,4]=>1100000=>0011111=>1
[1,2,8,6,3,7,5,4]=>1100000=>0011111=>1
[1,2,7,3,8,6,5,4]=>1100000=>0011111=>1
[8,1,7,6,3,4,5,2]=>0000000=>1111111=>1
[5,7,1,6,2,4,3,8]=>0000001=>1111110=>1
[6,1,4,5,3,8,7,2]=>0000000=>1111111=>1
[6,1,4,8,3,5,7,2]=>0000000=>1111111=>1
[7,1,8,6,3,4,5,2]=>0000000=>1111111=>1
[6,3,5,7,2,1,4,8]=>0000001=>1111110=>1
[6,3,5,8,2,1,7,4]=>0000000=>1111111=>1
[8,4,5,7,3,6,1,2]=>0000000=>1111111=>1
[5,8,7,6,2,4,1,3]=>0000000=>1111111=>1
[5,4,1,8,2,3,7,6]=>0000000=>1111111=>1
[8,4,1,5,2,6,3,7]=>0000000=>1111111=>1
[8,3,5,6,2,1,4,7]=>0000000=>1111111=>1
[2,3,8,5,1,4,7,6]=>0000000=>1111111=>1
[8,7,5,6,1,4,2,3]=>0000000=>1111111=>1
[2,6,4,1,8,5,7,3]=>0000000=>1111111=>1
[2,6,1,3,8,5,7,4]=>0000000=>1111111=>1
[8,4,1,5,2,3,7,6]=>0000000=>1111111=>1
[7,8,1,6,3,4,2,5]=>0000000=>1111111=>1
[6,4,1,8,3,2,7,5]=>0000000=>1111111=>1
[2,3,4,1,8,7,5,6]=>0001000=>1110111=>2
[2,3,8,1,6,4,7,5]=>0000000=>1111111=>1
[1,2,3,4,5,6,7,9,8]=>11111110=>00000001=>1
[2,1,3,4,5,6,7,8,9]=>01111111=>10000000=>1
[1,2,3,4,5,6,7,8,10,9]=>111111110=>000000001=>1
[2,1,3,4,5,6,7,8,9,10]=>011111111=>100000000=>1
[1,2,3,4,5,6,7,8,9,11,10]=>1111111110=>0000000001=>1
[9,1,2,3,4,5,6,7,10,8]=>000000000=>111111111=>1
[1,8,2,3,4,5,6,9,7]=>10000000=>01111111=>1
[7,1,2,3,4,5,6,9,8]=>00000010=>11111101=>2
[2,1,9,3,4,5,6,7,8]=>01000000=>10111111=>2
[2,8,1,3,4,5,6,7,9]=>00000001=>11111110=>1
[2,10,1,3,4,5,6,7,8,9]=>000000000=>111111111=>1
[2,1,3,4,5,6,7,8,9,10,11]=>0111111111=>1000000000=>1
[8,4,3,6,5,1,7,2]=>0000000=>1111111=>1
[8,5,6,3,4,1,7,2]=>0000000=>1111111=>1
[8,6,5,4,3,1,7,2]=>0000000=>1111111=>1
[1,7,6,5,4,2,3,8]=>1000001=>0111110=>1
[1,8,6,5,2,7,3,4]=>1000000=>0111111=>1
[8,7,5,4,1,6,3,2]=>0000000=>1111111=>1
[7,8,5,4,1,3,6,2]=>0000000=>1111111=>1
[6,8,5,4,2,1,7,3]=>0000000=>1111111=>1
[5,8,6,2,4,1,7,3]=>0000000=>1111111=>1
[4,8,2,6,5,1,7,3]=>0000000=>1111111=>1
[3,2,8,6,5,1,7,4]=>0000000=>1111111=>1
[3,2,1,7,6,4,5,8]=>0010001=>1101110=>2
[4,1,3,7,6,2,5,8]=>0000001=>1111110=>1
[5,1,7,3,6,2,4,8]=>0000001=>1111110=>1
[6,1,7,5,3,2,4,8]=>0000001=>1111110=>1
[7,1,6,5,2,4,3,8]=>0000001=>1111110=>1
[8,1,6,5,2,3,7,4]=>0000000=>1111111=>1
[1,2,7,6,3,4,5,8]=>1100001=>0011110=>1
[1,2,8,3,7,4,5,6]=>1100000=>0011111=>1
[8,1,7,2,6,3,5,4]=>0000000=>1111111=>1
[7,1,8,2,6,4,3,5]=>0000000=>1111111=>1
[6,1,8,2,4,7,3,5]=>0000000=>1111111=>1
[5,1,8,3,2,7,4,6]=>0000000=>1111111=>1
[4,1,3,8,2,7,5,6]=>0000000=>1111111=>1
[3,2,1,8,4,7,5,6]=>0010000=>1101111=>2
[3,2,8,7,1,6,5,4]=>0000000=>1111111=>1
[4,8,2,7,1,6,5,3]=>0000000=>1111111=>1
[5,8,7,2,1,6,4,3]=>0000000=>1111111=>1
[6,8,7,1,3,5,4,2]=>0000000=>1111111=>1
[7,8,6,1,5,3,4,2]=>0000000=>1111111=>1
[8,7,6,1,5,4,3,2]=>0000000=>1111111=>1
[1,8,7,2,6,5,3,4]=>1000000=>0111111=>1
[1,7,8,2,5,6,3,4]=>1000000=>0111111=>1
[8,6,7,1,4,5,3,2]=>0000000=>1111111=>1
[7,6,8,1,4,3,5,2]=>0000000=>1111111=>1
[6,5,8,3,2,1,7,4]=>0000000=>1111111=>1
[7,5,8,3,1,4,6,2]=>0000000=>1111111=>1
[8,5,7,3,1,6,4,2]=>0000000=>1111111=>1
[1,6,8,4,2,7,3,5]=>1000000=>0111111=>1
[1,5,4,8,2,7,3,6]=>1000000=>0111111=>1
[8,4,3,7,1,6,5,2]=>0000000=>1111111=>1
[7,4,3,8,1,5,6,2]=>0000000=>1111111=>1
[6,4,3,1,5,2,7,8]=>0000011=>1111100=>1
[7,4,3,1,2,6,5,8]=>0000001=>1111110=>1
[8,4,3,1,2,5,7,6]=>0000000=>1111111=>1
[1,5,4,2,3,6,7,8]=>1000111=>0111000=>1
[8,5,1,4,2,3,7,6]=>0000000=>1111111=>1
[7,5,1,4,2,6,3,8]=>0000001=>1111110=>1
[6,5,1,4,3,2,7,8]=>0000011=>1111100=>1
[5,6,1,3,4,2,7,8]=>0000011=>1111100=>1
[4,6,2,1,5,3,7,8]=>0000011=>1111100=>1
[3,2,6,1,5,4,7,8]=>0000011=>1111100=>1
[3,2,7,1,4,6,5,8]=>0000001=>1111110=>1
[4,7,2,1,3,6,5,8]=>0000001=>1111110=>1
[5,7,1,3,2,6,4,8]=>0000001=>1111110=>1
[6,7,1,2,4,5,3,8]=>0000001=>1111110=>1
[7,6,1,2,5,4,3,8]=>0000001=>1111110=>1
[8,6,1,2,5,3,7,4]=>0000000=>1111111=>1
[1,7,2,3,6,4,5,8]=>1000001=>0111110=>1
[8,7,1,2,3,6,5,4]=>0000000=>1111111=>1
[7,8,1,2,3,5,6,4]=>0000000=>1111111=>1
[6,8,1,2,4,3,7,5]=>0000000=>1111111=>1
[5,8,1,3,2,4,7,6]=>0000000=>1111111=>1
[4,8,2,1,3,5,7,6]=>0000000=>1111111=>1
[3,2,8,1,4,5,7,6]=>0000000=>1111111=>1
[4,1,3,2,5,6,7,8]=>0001111=>1110000=>1
[5,1,2,4,3,6,7,8]=>0000111=>1111000=>1
[6,1,2,3,5,4,7,8]=>0000011=>1111100=>1
[7,1,2,3,4,6,5,8]=>0000001=>1111110=>1
[8,1,2,3,4,5,7,6]=>0000000=>1111111=>1
[6,7,3,8,5,1,2,4]=>0000000=>1111111=>1
[6,7,4,5,1,8,3,2]=>0000000=>1111111=>1
[5,4,7,6,8,1,2,3]=>0000000=>1111111=>1
[5,3,7,8,6,1,2,4]=>0000000=>1111111=>1
[3,8,4,5,7,1,2,6]=>0000000=>1111111=>1
[3,4,8,6,7,1,2,5]=>0000000=>1111111=>1
[4,5,6,7,1,8,3,2]=>0000000=>1111111=>1
[3,5,6,2,7,4,8,1]=>0000000=>1111111=>1
[3,5,6,1,7,8,4,2]=>0000000=>1111111=>1
[2,5,6,1,8,7,4,3]=>0000000=>1111111=>1
[2,5,6,8,1,7,3,4]=>0000000=>1111111=>1
[8,2,4,5,1,6,3,7]=>0000000=>1111111=>1
[1,4,8,6,2,3,7,5]=>1000000=>0111111=>1
[1,5,6,8,2,3,7,4]=>1000000=>0111111=>1
[1,5,6,2,8,4,7,3]=>1000000=>0111111=>1
[2,5,6,3,4,7,8,1]=>0000000=>1111111=>1
[1,4,2,6,8,5,7,3]=>1000000=>0111111=>1
[8,1,3,2,5,4,6,7]=>0000000=>1111111=>1
[8,2,3,1,5,6,4,7]=>0000000=>1111111=>1
[2,8,3,1,5,7,4,6]=>0000000=>1111111=>1
[2,4,1,6,8,7,5,3]=>0000000=>1111111=>1
[3,4,1,6,7,8,5,2]=>0000000=>1111111=>1
[4,3,1,7,6,8,5,2]=>0000000=>1111111=>1
[5,2,7,8,1,6,3,4]=>0000000=>1111111=>1
[5,3,7,2,6,4,8,1]=>0000000=>1111111=>1
[6,7,3,1,5,8,4,2]=>0000000=>1111111=>1
[6,7,2,1,8,5,4,3]=>0000000=>1111111=>1
[6,7,2,8,1,5,3,4]=>0000000=>1111111=>1
[6,7,8,2,1,4,3,5]=>0000000=>1111111=>1
[6,7,1,2,8,4,5,3]=>0000000=>1111111=>1
[6,7,1,3,4,8,5,2]=>0000000=>1111111=>1
[5,2,7,3,4,6,8,1]=>0000000=>1111111=>1
[5,1,7,3,4,8,6,2]=>0000000=>1111111=>1
[5,1,7,8,2,3,6,4]=>0000000=>1111111=>1
[4,1,8,7,2,3,6,5]=>0000000=>1111111=>1
[3,8,1,2,7,4,5,6]=>0000000=>1111111=>1
[4,1,3,7,5,8,6,2]=>0000000=>1111111=>1
[3,1,4,5,7,8,6,2]=>0000000=>1111111=>1
[2,1,8,3,4,7,6,5]=>0100000=>1011111=>2
[8,2,1,3,4,6,5,7]=>0000000=>1111111=>1
[1,8,2,3,4,5,7,6]=>1000000=>0111111=>1
[1,2,8,3,4,6,7,5]=>1100000=>0011111=>1
[4,2,1,6,5,8,7,3]=>0000000=>1111111=>1
[5,2,6,1,4,8,7,3]=>0000000=>1111111=>1
[5,2,6,4,1,8,7,3]=>0000000=>1111111=>1
[5,2,7,4,8,1,6,3]=>0000000=>1111111=>1
[5,2,7,4,8,6,1,3]=>0000000=>1111111=>1
[5,7,2,3,8,6,1,4]=>0000000=>1111111=>1
[5,7,2,3,8,1,6,4]=>0000000=>1111111=>1
[5,6,2,3,1,8,7,4]=>0000000=>1111111=>1
[5,6,2,1,3,8,7,4]=>0000000=>1111111=>1
[5,1,6,4,2,8,7,3]=>0000000=>1111111=>1
[5,6,1,3,2,8,7,4]=>0000000=>1111111=>1
[5,6,3,1,2,8,7,4]=>0000000=>1111111=>1
[5,6,3,2,1,8,7,4]=>0000000=>1111111=>1
[5,7,3,2,8,1,6,4]=>0000000=>1111111=>1
[5,7,3,2,8,6,1,4]=>0000000=>1111111=>1
[6,7,3,8,2,1,5,4]=>0000000=>1111111=>1
[6,7,3,8,1,2,5,4]=>0000000=>1111111=>1
[5,7,3,1,8,2,6,4]=>0000000=>1111111=>1
[5,7,1,3,8,2,6,4]=>0000000=>1111111=>1
[5,1,7,4,8,2,6,3]=>0000000=>1111111=>1
[1,5,7,4,8,3,6,2]=>1000000=>0111111=>1
[1,5,7,4,8,6,3,2]=>1000000=>0111111=>1
[5,1,7,4,8,6,2,3]=>0000000=>1111111=>1
[5,7,1,3,8,6,2,4]=>0000000=>1111111=>1
[5,7,3,1,8,6,2,4]=>0000000=>1111111=>1
[6,7,3,8,1,5,2,4]=>0000000=>1111111=>1
[6,7,3,8,5,2,1,4]=>0000000=>1111111=>1
[6,7,8,3,1,4,2,5]=>0000000=>1111111=>1
[6,7,1,8,3,5,2,4]=>0000000=>1111111=>1
[6,1,7,8,4,5,2,3]=>0000000=>1111111=>1
[1,6,7,8,4,5,3,2]=>1000000=>0111111=>1
[1,6,7,8,4,3,5,2]=>1000000=>0111111=>1
[6,1,7,8,4,2,5,3]=>0000000=>1111111=>1
[6,7,1,8,3,2,5,4]=>0000000=>1111111=>1
[5,7,2,1,8,3,6,4]=>0000000=>1111111=>1
[6,7,2,8,1,3,5,4]=>0000000=>1111111=>1
[6,7,2,8,3,1,5,4]=>0000000=>1111111=>1
[6,7,2,8,3,5,1,4]=>0000000=>1111111=>1
[6,2,7,8,4,5,1,3]=>0000000=>1111111=>1
[6,2,7,8,4,1,5,3]=>0000000=>1111111=>1
[6,2,7,8,1,4,5,3]=>0000000=>1111111=>1
[5,2,7,1,8,4,6,3]=>0000000=>1111111=>1
[4,2,1,7,8,5,6,3]=>0000000=>1111111=>1
[4,1,2,7,8,6,5,3]=>0000000=>1111111=>1
[6,2,7,8,1,5,4,3]=>0000000=>1111111=>1
[6,2,7,8,5,1,4,3]=>0000000=>1111111=>1
[6,2,7,8,5,4,1,3]=>0000000=>1111111=>1
[6,7,2,8,5,3,1,4]=>0000000=>1111111=>1
[5,7,2,1,8,6,3,4]=>0000000=>1111111=>1
[5,7,1,2,8,6,3,4]=>0000000=>1111111=>1
[5,1,7,2,8,6,4,3]=>0000000=>1111111=>1
[1,5,7,3,8,6,4,2]=>1000000=>0111111=>1
[1,6,7,8,3,5,4,2]=>1000000=>0111111=>1
[6,1,7,8,2,5,4,3]=>0000000=>1111111=>1
[6,7,1,8,2,5,3,4]=>0000000=>1111111=>1
[6,7,8,2,4,1,3,5]=>0000000=>1111111=>1
[6,7,8,2,4,3,1,5]=>0000000=>1111111=>1
[6,7,1,8,5,2,3,4]=>0000000=>1111111=>1
[6,1,7,8,5,2,4,3]=>0000000=>1111111=>1
[1,6,7,8,5,3,4,2]=>1000000=>0111111=>1
[6,1,7,8,5,4,2,3]=>0000000=>1111111=>1
[6,7,1,8,5,3,2,4]=>0000000=>1111111=>1
[6,7,8,4,1,3,2,5]=>0000000=>1111111=>1
[6,5,2,8,4,7,3,1]=>0000000=>1111111=>1
[3,6,4,8,5,7,1,2]=>0000000=>1111111=>1
[5,1,4,8,6,3,7,2]=>0000000=>1111111=>1
[3,4,7,1,8,6,5,2]=>0000000=>1111111=>1
[6,3,8,4,2,7,1,5]=>0000000=>1111111=>1
[3,6,8,7,1,4,2,5]=>0000000=>1111111=>1
[4,6,1,2,7,8,5,3]=>0000000=>1111111=>1
[3,6,4,2,8,7,5,1]=>0000000=>1111111=>1
[6,3,7,5,2,8,1,4]=>0000000=>1111111=>1
[5,7,1,4,8,3,2,6]=>0000000=>1111111=>1
[5,8,1,4,6,7,2,3]=>0000000=>1111111=>1
[5,3,8,7,4,1,2,6]=>0000000=>1111111=>1
[5,4,2,7,3,6,8,1]=>0000000=>1111111=>1
[7,5,3,6,4,2,8,1]=>0000000=>1111111=>1
[8,2,6,3,4,7,5,1]=>0000000=>1111111=>1
[7,2,6,3,5,4,8,1]=>0000000=>1111111=>1
[6,2,7,4,3,5,8,1]=>0000000=>1111111=>1
[3,7,6,4,5,2,8,1]=>0000000=>1111111=>1
[2,7,6,5,3,4,8,1]=>0000000=>1111111=>1
[6,5,4,3,1,8,2,7]=>0000000=>1111111=>1
[8,6,5,4,2,7,3,1]=>0000000=>1111111=>1
[8,5,4,1,7,2,6,3]=>0000000=>1111111=>1
[7,5,4,1,8,3,2,6]=>0000000=>1111111=>1
[1,6,5,2,8,3,4,7]=>1000000=>0111111=>1
[1,6,5,3,4,8,2,7]=>1000000=>0111111=>1
[5,4,6,3,1,8,2,7]=>0000000=>1111111=>1
[6,5,8,4,2,7,3,1]=>0000000=>1111111=>1
[5,8,2,6,4,7,3,1]=>0000000=>1111111=>1
[1,8,6,3,7,5,2,4]=>1000000=>0111111=>1
[8,7,5,2,6,4,3,1]=>0000000=>1111111=>1
[8,7,1,6,2,5,4,3]=>0000000=>1111111=>1
[7,8,1,6,3,2,5,4]=>0000000=>1111111=>1
[2,8,1,7,3,5,6,4]=>0000000=>1111111=>1
[4,8,1,3,7,2,6,5]=>0000000=>1111111=>1
[4,2,8,5,7,3,6,1]=>0000000=>1111111=>1
[5,1,7,6,8,3,2,4]=>0000000=>1111111=>1
[6,7,3,1,8,4,2,5]=>0000000=>1111111=>1
[1,7,3,8,4,5,2,6]=>1000000=>0111111=>1
[1,7,2,8,5,3,4,6]=>1000000=>0111111=>1
[7,6,1,8,4,3,2,5]=>0000000=>1111111=>1
[8,6,1,7,4,2,5,3]=>0000000=>1111111=>1
[8,1,2,7,3,4,6,5]=>0000000=>1111111=>1
[7,1,2,8,3,5,4,6]=>0000000=>1111111=>1
[8,2,6,1,7,3,5,4]=>0000000=>1111111=>1
[4,2,1,5,8,3,6,7]=>0000000=>1111111=>1
[5,4,3,1,6,8,2,7]=>0000000=>1111111=>1
[4,7,5,6,8,3,2,1]=>0000000=>1111111=>1
[8,6,4,7,5,3,2,1]=>0000000=>1111111=>1
[5,1,8,3,7,6,2,4]=>0000000=>1111111=>1
[5,4,8,1,7,2,6,3]=>0000000=>1111111=>1
[5,7,3,8,2,6,4,1]=>0000000=>1111111=>1
[2,3,8,7,4,5,6,1]=>0000000=>1111111=>1
[7,2,8,6,4,3,5,1]=>0000000=>1111111=>1
[8,2,7,6,3,5,4,1]=>0000000=>1111111=>1
[8,1,7,6,5,2,4,3]=>0000000=>1111111=>1
[7,1,8,6,5,3,2,4]=>0000000=>1111111=>1
[1,2,8,7,6,3,4,5]=>1100000=>0011111=>1
[1,3,8,7,4,6,2,5]=>1000000=>0111111=>1
[5,1,6,8,7,4,2,3]=>0000000=>1111111=>1
[3,8,7,6,4,5,2,1]=>0000000=>1111111=>1
[2,8,7,6,5,3,4,1]=>0000000=>1111111=>1
[1,8,7,6,5,4,2,3]=>1000000=>0111111=>1
[5,8,6,7,3,4,1,2]=>0000000=>1111111=>1
[4,8,6,7,3,5,1,2]=>0000000=>1111111=>1
[3,8,6,7,4,5,1,2]=>0000000=>1111111=>1
[2,8,6,7,4,5,1,3]=>0000000=>1111111=>1
[1,8,6,7,4,5,2,3]=>1000000=>0111111=>1
[1,8,5,7,4,6,2,3]=>1000000=>0111111=>1
[3,8,5,7,4,6,1,2]=>0000000=>1111111=>1
[4,8,5,7,3,6,1,2]=>0000000=>1111111=>1
[7,8,3,6,4,5,1,2]=>0000000=>1111111=>1
[6,8,3,7,4,5,1,2]=>0000000=>1111111=>1
[5,8,3,7,4,6,1,2]=>0000000=>1111111=>1
[3,7,4,8,5,6,1,2]=>0000000=>1111111=>1
[4,7,3,8,5,6,1,2]=>0000000=>1111111=>1
[4,7,2,8,5,6,1,3]=>0000000=>1111111=>1
[4,7,1,8,5,6,2,3]=>0000000=>1111111=>1
[3,7,1,8,5,6,2,4]=>0000000=>1111111=>1
[3,7,2,8,5,6,1,4]=>0000000=>1111111=>1
[2,7,3,8,5,6,1,4]=>0000000=>1111111=>1
[2,7,4,8,5,6,1,3]=>0000000=>1111111=>1
[5,8,2,7,4,6,1,3]=>0000000=>1111111=>1
[6,8,2,7,4,5,1,3]=>0000000=>1111111=>1
[7,8,2,6,4,5,1,3]=>0000000=>1111111=>1
[7,8,1,6,4,5,2,3]=>0000000=>1111111=>1
[6,8,1,7,4,5,2,3]=>0000000=>1111111=>1
[5,8,1,7,4,6,2,3]=>0000000=>1111111=>1
[1,7,4,8,5,6,2,3]=>1000000=>0111111=>1
[1,7,3,8,5,6,2,4]=>1000000=>0111111=>1
[2,8,5,6,1,7,3,4]=>0000000=>1111111=>1
[1,8,5,6,2,7,3,4]=>1000000=>0111111=>1
[1,7,3,8,4,6,2,5]=>1000000=>0111111=>1
[4,8,1,7,3,6,2,5]=>0000000=>1111111=>1
[5,8,1,7,3,6,2,4]=>0000000=>1111111=>1
[6,8,1,7,3,5,2,4]=>0000000=>1111111=>1
[7,8,2,6,3,5,1,4]=>0000000=>1111111=>1
[6,8,2,7,3,5,1,4]=>0000000=>1111111=>1
[5,8,2,7,3,6,1,4]=>0000000=>1111111=>1
[4,8,2,7,3,6,1,5]=>0000000=>1111111=>1
[2,7,3,8,4,6,1,5]=>0000000=>1111111=>1
[3,7,2,8,4,6,1,5]=>0000000=>1111111=>1
[3,7,1,8,4,6,2,5]=>0000000=>1111111=>1
[1,8,4,7,3,6,2,5]=>1000000=>0111111=>1
[2,8,4,7,3,6,1,5]=>0000000=>1111111=>1
[3,8,4,7,2,6,1,5]=>0000000=>1111111=>1
[4,8,5,7,2,6,1,3]=>0000000=>1111111=>1
[3,8,5,7,2,6,1,4]=>0000000=>1111111=>1
[2,8,5,7,3,6,1,4]=>0000000=>1111111=>1
[1,8,5,7,3,6,2,4]=>1000000=>0111111=>1
[1,8,6,7,3,5,2,4]=>1000000=>0111111=>1
[2,8,6,7,3,5,1,4]=>0000000=>1111111=>1
[3,8,6,7,2,5,1,4]=>0000000=>1111111=>1
[4,8,6,7,2,5,1,3]=>0000000=>1111111=>1
[5,8,6,7,2,4,1,3]=>0000000=>1111111=>1
[6,8,5,7,1,4,2,3]=>0000000=>1111111=>1
[5,8,6,7,1,4,2,3]=>0000000=>1111111=>1
[4,8,6,7,1,5,2,3]=>0000000=>1111111=>1
[3,8,6,7,1,5,2,4]=>0000000=>1111111=>1
[1,5,2,8,6,7,3,4]=>1000000=>0111111=>1
[2,5,1,8,6,7,3,4]=>0000000=>1111111=>1
[2,6,1,8,5,7,3,4]=>0000000=>1111111=>1
[1,6,2,8,5,7,3,4]=>1000000=>0111111=>1
[3,8,5,7,1,6,2,4]=>0000000=>1111111=>1
[6,8,4,7,1,5,2,3]=>0000000=>1111111=>1
[7,8,4,6,1,5,2,3]=>0000000=>1111111=>1
[7,8,3,6,1,5,2,4]=>0000000=>1111111=>1
[6,8,3,7,1,5,2,4]=>0000000=>1111111=>1
[4,8,3,7,1,6,2,5]=>0000000=>1111111=>1
[3,8,4,7,1,6,2,5]=>0000000=>1111111=>1
[1,6,2,8,4,7,3,5]=>1000000=>0111111=>1
[2,6,1,8,4,7,3,5]=>0000000=>1111111=>1
[3,7,2,6,1,8,4,5]=>0000000=>1111111=>1
[3,7,1,6,2,8,4,5]=>0000000=>1111111=>1
[4,8,1,6,2,7,3,5]=>0000000=>1111111=>1
[5,8,1,6,2,7,3,4]=>0000000=>1111111=>1
[7,8,1,5,2,6,3,4]=>0000000=>1111111=>1
[7,8,2,5,1,6,3,4]=>0000000=>1111111=>1
[6,8,2,5,1,7,3,4]=>0000000=>1111111=>1
[5,8,2,6,1,7,3,4]=>0000000=>1111111=>1
[4,8,2,6,1,7,3,5]=>0000000=>1111111=>1
[1,7,3,6,2,8,4,5]=>1000000=>0111111=>1
[2,7,3,6,1,8,4,5]=>0000000=>1111111=>1
[1,2,3,4,5,6,7,8,9]=>11111111=>00000000=>0
[1,2,3,4,5,6,8,9,7]=>11111100=>00000011=>1
[1,2,3,4,5,7,8,9,6]=>11111000=>00000111=>1
[1,2,3,4,6,7,8,9,5]=>11110000=>00001111=>1
[1,2,3,5,6,7,8,9,4]=>11100000=>00011111=>1
[1,2,4,5,6,7,8,9,3]=>11000000=>00111111=>1
[1,3,4,5,6,7,8,9,2]=>10000000=>01111111=>1
[1,2,3,4,5,6,7,8,9,10]=>111111111=>000000000=>0
[1,2,3,4,5,6,9,8,7]=>11111100=>00000011=>1
[1,2,3,4,5,6,7,9,10,8]=>111111100=>000000011=>1
[1,2,3,4,5,8,7,9,6]=>11111000=>00000111=>1
[1,2,3,4,5,6,8,9,10,7]=>111111000=>000000111=>1
[1,2,3,4,7,6,8,9,5]=>11110000=>00001111=>1
[1,2,3,4,5,7,8,9,10,6]=>111110000=>000001111=>1
[1,2,3,6,5,7,8,9,4]=>11100000=>00011111=>1
[1,2,3,4,6,7,8,9,10,5]=>111100000=>000011111=>1
[1,2,5,4,6,7,8,9,3]=>11000000=>00111111=>1
[1,2,3,5,6,7,8,9,10,4]=>111000000=>000111111=>1
[1,4,3,5,6,7,8,9,2]=>10000000=>01111111=>1
[1,2,4,5,6,7,8,9,10,3]=>110000000=>001111111=>1
[3,2,4,5,6,7,8,9,1]=>00000000=>11111111=>1
[1,3,4,5,6,7,8,9,10,2]=>100000000=>011111111=>1
[6,7,4,8,3,5,1,2]=>0000000=>1111111=>1
[6,7,4,5,2,8,1,3]=>0000000=>1111111=>1
[5,7,4,6,2,3,1,8]=>0000001=>1111110=>1
[5,7,4,6,3,8,1,2]=>0000000=>1111111=>1
[5,7,4,8,3,6,1,2]=>0000000=>1111111=>1
[6,8,4,5,3,7,1,2]=>0000000=>1111111=>1
[5,8,4,6,3,7,1,2]=>0000000=>1111111=>1
[5,6,4,8,3,7,1,2]=>0000000=>1111111=>1
[5,6,3,7,2,4,1,8]=>0000001=>1111110=>1
[5,6,3,7,2,8,1,4]=>0000000=>1111111=>1
[5,6,3,8,2,7,1,4]=>0000000=>1111111=>1
[5,6,4,8,2,7,1,3]=>0000000=>1111111=>1
[5,8,4,6,2,7,1,3]=>0000000=>1111111=>1
[6,8,4,5,2,7,1,3]=>0000000=>1111111=>1
[7,8,4,5,2,6,1,3]=>0000000=>1111111=>1
[6,8,4,5,2,3,1,7]=>0000000=>1111111=>1
[5,8,4,6,2,3,1,7]=>0000000=>1111111=>1
[5,6,4,8,2,3,1,7]=>0000000=>1111111=>1
[5,6,3,8,2,4,1,7]=>0000000=>1111111=>1
[5,6,3,4,2,8,1,7]=>0000000=>1111111=>1
[4,6,3,5,2,7,1,8]=>0000001=>1111110=>1
[4,6,3,5,2,8,1,7]=>0000000=>1111111=>1
[4,6,3,8,2,5,1,7]=>0000000=>1111111=>1
[4,8,3,6,2,5,1,7]=>0000000=>1111111=>1
[5,8,3,6,2,4,1,7]=>0000000=>1111111=>1
[6,8,3,5,2,4,1,7]=>0000000=>1111111=>1
[7,8,3,5,2,4,1,6]=>0000000=>1111111=>1
[7,8,3,5,2,6,1,4]=>0000000=>1111111=>1
[5,8,3,6,2,7,1,4]=>0000000=>1111111=>1
[4,8,3,6,2,7,1,5]=>0000000=>1111111=>1
[4,6,3,8,2,7,1,5]=>0000000=>1111111=>1
[4,6,3,7,2,8,1,5]=>0000000=>1111111=>1
[4,7,3,6,2,5,1,8]=>0000001=>1111110=>1
[4,7,3,6,2,8,1,5]=>0000000=>1111111=>1
[4,7,3,8,2,6,1,5]=>0000000=>1111111=>1
[5,7,4,8,2,6,1,3]=>0000000=>1111111=>1
[5,7,3,6,2,8,1,4]=>0000000=>1111111=>1
[5,7,3,6,2,4,1,8]=>0000001=>1111110=>1
[6,7,3,5,2,4,1,8]=>0000001=>1111110=>1
[6,7,3,5,2,8,1,4]=>0000000=>1111111=>1
[6,7,4,8,2,5,1,3]=>0000000=>1111111=>1
[6,7,5,8,2,4,1,3]=>0000000=>1111111=>1
[6,8,5,7,2,3,1,4]=>0000000=>1111111=>1
[6,7,4,8,2,3,1,5]=>0000000=>1111111=>1
[6,7,3,8,2,4,1,5]=>0000000=>1111111=>1
[6,7,3,4,2,8,1,5]=>0000000=>1111111=>1
[5,7,3,4,2,6,1,8]=>0000001=>1111110=>1
[5,7,3,4,2,8,1,6]=>0000000=>1111111=>1
[5,7,4,8,2,3,1,6]=>0000000=>1111111=>1
[5,8,4,7,2,3,1,6]=>0000000=>1111111=>1
[6,8,4,7,2,3,1,5]=>0000000=>1111111=>1
[7,8,4,6,2,3,1,5]=>0000000=>1111111=>1
[7,8,3,6,2,4,1,5]=>0000000=>1111111=>1
[6,8,3,7,2,4,1,5]=>0000000=>1111111=>1
[5,8,3,7,2,4,1,6]=>0000000=>1111111=>1
[4,8,3,7,2,5,1,6]=>0000000=>1111111=>1
[4,7,3,8,2,5,1,6]=>0000000=>1111111=>1
[4,7,3,5,2,8,1,6]=>0000000=>1111111=>1
[4,7,3,5,2,6,1,8]=>0000001=>1111110=>1
[4,5,3,7,2,6,1,8]=>0000001=>1111110=>1
[4,5,3,7,2,8,1,6]=>0000000=>1111111=>1
[4,5,3,8,2,7,1,6]=>0000000=>1111111=>1
[4,8,3,5,2,7,1,6]=>0000000=>1111111=>1
[5,8,3,4,2,7,1,6]=>0000000=>1111111=>1
[6,8,3,4,2,7,1,5]=>0000000=>1111111=>1
[7,8,3,4,2,6,1,5]=>0000000=>1111111=>1
[6,8,3,4,2,5,1,7]=>0000000=>1111111=>1
[5,8,3,4,2,6,1,7]=>0000000=>1111111=>1
[4,8,3,5,2,6,1,7]=>0000000=>1111111=>1
[4,5,3,8,2,6,1,7]=>0000000=>1111111=>1
[4,5,3,6,2,8,1,7]=>0000000=>1111111=>1
[4,6,5,2,1,3,8,7]=>0000010=>1111101=>2
[7,4,8,1,6,5,3,2]=>0000000=>1111111=>1
[5,4,7,1,3,8,2,6]=>0000000=>1111111=>1
[6,4,8,1,7,5,2,3]=>0000000=>1111111=>1
[6,3,2,8,7,4,1,5]=>0000000=>1111111=>1
[5,7,8,6,2,3,1,4]=>0000000=>1111111=>1
[5,8,7,6,3,2,1,4]=>0000000=>1111111=>1
[3,7,1,8,6,4,5,2]=>0000000=>1111111=>1
[3,8,1,6,7,5,2,4]=>0000000=>1111111=>1
[4,7,6,2,8,1,3,5]=>0000000=>1111111=>1
[6,7,4,2,8,1,5,3]=>0000000=>1111111=>1
[6,8,4,2,7,5,1,3]=>0000000=>1111111=>1
[2,1,8,6,7,5,3,4]=>0100000=>1011111=>2
[5,8,6,7,3,1,2,4]=>0000000=>1111111=>1
[6,7,5,8,1,3,4,2]=>0000000=>1111111=>1
[7,6,5,8,1,4,3,2]=>0000000=>1111111=>1
[2,1,7,6,8,3,5,4]=>0100000=>1011111=>2
[7,5,6,8,1,4,2,3]=>0000000=>1111111=>1
[8,1,3,7,4,6,5,2]=>0000000=>1111111=>1
[5,2,8,7,4,6,1,3]=>0000000=>1111111=>1
[8,1,3,5,4,7,6,2]=>0000000=>1111111=>1
[6,1,5,4,3,8,7,2]=>0000000=>1111111=>1
[6,1,8,3,4,5,7,2]=>0000000=>1111111=>1
[8,1,3,4,5,6,7,2]=>0000000=>1111111=>1
[6,3,2,7,5,1,8,4]=>0000000=>1111111=>1
[8,4,7,2,5,6,1,3]=>0000000=>1111111=>1
[8,5,2,1,4,3,7,6]=>0000000=>1111111=>1
[5,6,2,1,4,8,3,7]=>0000000=>1111111=>1
[6,3,8,5,2,1,4,7]=>0000000=>1111111=>1
[8,3,1,5,2,4,7,6]=>0000000=>1111111=>1
[3,8,6,7,2,1,5,4]=>0000000=>1111111=>1
[8,5,6,4,2,1,7,3]=>0000000=>1111111=>1
[7,2,1,3,8,6,4,5]=>0000000=>1111111=>1
[1,5,7,3,2,4,6,8]=>1000001=>0111110=>1
[5,8,2,4,1,3,7,6]=>0000000=>1111111=>1
[4,8,1,6,3,2,7,5]=>0000000=>1111111=>1
[3,1,8,6,4,2,7,5]=>0000000=>1111111=>1
[4,2,1,3,7,8,5,6]=>0001000=>1110111=>2
[8,6,1,3,7,2,4,5]=>0000000=>1111111=>1
[9,8,7,6,5,4,3,2,1]=>00000000=>11111111=>1
[8,9,7,6,5,4,3,2,1]=>00000000=>11111111=>1
[8,7,9,6,5,4,3,2,1]=>00000000=>11111111=>1
[8,7,6,9,5,4,3,2,1]=>00000000=>11111111=>1
[8,7,6,5,9,4,3,2,1]=>00000000=>11111111=>1
[8,7,6,5,4,9,3,2,1]=>00000000=>11111111=>1
[8,7,6,5,4,3,9,2,1]=>00000000=>11111111=>1
[8,7,6,5,4,3,2,9,1]=>00000000=>11111111=>1
[8,7,6,5,4,3,2,1,9]=>00000001=>11111110=>1
[9,10,8,7,6,5,4,3,2,1]=>000000000=>111111111=>1
[7,8,9,6,5,4,3,2,1]=>00000000=>11111111=>1
[9,8,10,7,6,5,4,3,2,1]=>000000000=>111111111=>1
[8,6,7,9,5,4,3,2,1]=>00000000=>11111111=>1
[9,8,7,10,6,5,4,3,2,1]=>000000000=>111111111=>1
[8,7,5,6,9,4,3,2,1]=>00000000=>11111111=>1
[9,8,7,6,10,5,4,3,2,1]=>000000000=>111111111=>1
[8,7,6,4,5,9,3,2,1]=>00000000=>11111111=>1
[9,8,7,6,5,10,4,3,2,1]=>000000000=>111111111=>1
[8,7,6,5,3,4,9,2,1]=>00000000=>11111111=>1
[9,8,7,6,5,4,10,3,2,1]=>000000000=>111111111=>1
[8,7,6,5,4,2,3,9,1]=>00000000=>11111111=>1
[9,8,7,6,5,4,3,10,2,1]=>000000000=>111111111=>1
[8,7,6,5,4,3,1,2,9]=>00000001=>11111110=>1
[9,8,7,6,5,4,3,2,10,1]=>000000000=>111111111=>1
[9,8,7,6,5,4,3,2,1,10]=>000000001=>111111110=>1
[1,4,2,7,8,6,3,5]=>1000000=>0111111=>1
[1,6,2,4,8,5,3,7]=>1000000=>0111111=>1
[1,6,2,4,7,5,3,8]=>1000001=>0111110=>1
[1,7,3,8,5,2,4,6]=>1000000=>0111111=>1
[1,7,3,2,8,6,4,5]=>1000000=>0111111=>1
[4,2,5,7,8,6,1,3]=>0000000=>1111111=>1
[7,2,3,1,8,5,6,4]=>0000000=>1111111=>1
[8,2,5,1,7,3,4,6]=>0000000=>1111111=>1
[6,2,1,8,3,4,7,5]=>0000000=>1111111=>1
[6,2,8,3,5,1,7,4]=>0000000=>1111111=>1
[6,2,4,8,5,7,1,3]=>0000000=>1111111=>1
[1,3,6,4,8,5,7,2]=>1000000=>0111111=>1
[1,3,6,4,7,5,8,2]=>1000000=>0111111=>1
[6,2,4,7,5,8,1,3]=>0000000=>1111111=>1
[6,2,1,3,7,8,4,5]=>0000000=>1111111=>1
[7,8,2,1,4,3,5,6]=>0000000=>1111111=>1
[7,6,4,2,3,1,8,5]=>0000000=>1111111=>1
[5,7,2,3,1,6,8,4]=>0000000=>1111111=>1
[7,5,4,2,6,8,1,3]=>0000000=>1111111=>1
[1,7,5,3,4,6,8,2]=>1000000=>0111111=>1
[8,2,5,4,6,7,1,3]=>0000000=>1111111=>1
[5,2,6,3,1,8,7,4]=>0000000=>1111111=>1
[8,2,6,4,3,1,7,5]=>0000000=>1111111=>1
[8,2,7,4,1,3,5,6]=>0000000=>1111111=>1
[1,2,8,4,3,5,6,7]=>1100000=>0011111=>1
[1,7,4,2,3,5,6,8]=>1000001=>0111110=>1
[6,8,4,1,3,2,5,7]=>0000000=>1111111=>1
[1,8,7,4,3,2,5,6]=>1000000=>0111111=>1
[1,6,3,8,2,4,7,5]=>1000000=>0111111=>1
[5,3,8,1,2,7,4,6]=>0000000=>1111111=>1
[5,1,8,3,2,6,4,7]=>0000000=>1111111=>1
[5,7,3,1,2,6,4,8]=>0000001=>1111110=>1
[1,7,5,4,2,6,3,8]=>1000001=>0111110=>1
[1,5,8,2,4,6,3,7]=>1000000=>0111111=>1
[1,5,8,4,2,7,3,6]=>1000000=>0111111=>1
[1,4,6,2,8,3,7,5]=>1000000=>0111111=>1
[5,3,1,6,7,2,4,8]=>0000001=>1111110=>1
[5,3,6,1,2,8,4,7]=>0000000=>1111111=>1
[1,6,3,2,7,8,4,5]=>1000000=>0111111=>1
[1,7,4,5,3,8,6,2]=>1000000=>0111111=>1
[6,3,4,1,2,5,8,7]=>0000010=>1111101=>2
[6,3,1,4,2,7,5,8]=>0000001=>1111110=>1
[1,8,3,2,4,5,6,7]=>1000000=>0111111=>1
[8,6,3,2,4,1,7,5]=>0000000=>1111111=>1
[8,5,3,2,6,7,1,4]=>0000000=>1111111=>1
[4,5,2,6,8,1,7,3]=>0000000=>1111111=>1
[4,2,5,6,7,8,1,3]=>0000000=>1111111=>1
[5,2,3,6,7,1,8,4]=>0000000=>1111111=>1
[6,2,3,4,1,7,8,5]=>0000000=>1111111=>1
[7,2,3,1,4,5,8,6]=>0000000=>1111111=>1
[8,6,1,4,3,2,5,7]=>0000000=>1111111=>1
[8,3,1,6,5,2,4,7]=>0000000=>1111111=>1
[3,7,5,1,8,2,4,6]=>0000000=>1111111=>1
[4,1,5,2,8,7,3,6]=>0000000=>1111111=>1
[8,1,2,4,6,5,3,7]=>0000000=>1111111=>1
[8,1,2,5,4,6,3,7]=>0000000=>1111111=>1
[8,2,6,5,1,3,4,7]=>0000000=>1111111=>1
[8,3,1,6,2,5,4,7]=>0000000=>1111111=>1
[8,1,2,6,4,5,3,7]=>0000000=>1111111=>1
[8,1,2,5,6,4,3,7]=>0000000=>1111111=>1
[8,1,2,6,5,4,3,7]=>0000000=>1111111=>1
[1,7,5,4,2,8,3,6]=>1000000=>0111111=>1
[5,1,4,8,2,7,3,6]=>0000000=>1111111=>1
[1,4,6,8,2,7,3,5]=>1000000=>0111111=>1
[1,4,7,6,2,8,3,5]=>1000000=>0111111=>1
[5,1,4,7,2,8,3,6]=>0000000=>1111111=>1
[1,7,4,5,2,8,3,6]=>1000000=>0111111=>1
[3,7,5,1,2,8,4,6]=>0000000=>1111111=>1
[5,7,2,8,1,3,4,6]=>0000000=>1111111=>1
[5,2,8,7,1,3,4,6]=>0000000=>1111111=>1
[4,1,5,8,2,7,3,6]=>0000000=>1111111=>1
[1,4,6,2,8,7,3,5]=>1000000=>0111111=>1
[1,4,2,8,6,7,3,5]=>1000000=>0111111=>1
[3,1,2,6,4,8,7,5]=>0010000=>1101111=>2
[2,1,7,6,3,4,8,5]=>0100000=>1011111=>2
[3,1,2,7,4,6,8,5]=>0010000=>1101111=>2
[1,4,7,2,6,8,3,5]=>1000000=>0111111=>1
[1,2,3,6,8,5,7,4]=>1110000=>0001111=>1
[5,1,4,2,7,8,3,6]=>0000000=>1111111=>1
[1,4,2,7,6,8,3,5]=>1000000=>0111111=>1
[1,4,2,6,8,7,3,5]=>1000000=>0111111=>1
[3,1,2,8,4,6,7,5]=>0010000=>1101111=>2
[3,1,2,7,6,4,8,5]=>0010000=>1101111=>2
[5,3,7,1,8,2,4,6]=>0000000=>1111111=>1
[1,7,4,3,2,5,8,6]=>1000000=>0111111=>1
[4,8,7,2,1,3,5,6]=>0000000=>1111111=>1
[1,8,7,3,4,2,5,6]=>1000000=>0111111=>1
[3,1,7,8,2,6,4,5]=>0000000=>1111111=>1
[1,4,2,7,8,3,6,5]=>1000000=>0111111=>1
[5,2,8,1,3,4,7,6]=>0000000=>1111111=>1
[2,1,8,6,3,4,7,5]=>0100000=>1011111=>2
[1,4,2,6,8,3,7,5]=>1000000=>0111111=>1
[1,2,3,7,8,5,6,4]=>1110000=>0001111=>1
[1,2,3,7,5,8,6,4]=>1110000=>0001111=>1
[1,4,2,7,3,8,6,5]=>1000000=>0111111=>1
[3,1,7,2,8,6,4,5]=>0000000=>1111111=>1
[2,1,7,8,3,4,6,5]=>0100000=>1011111=>2
[1,2,3,8,7,5,6,4]=>1110000=>0001111=>1
[10,1,2,3,4,5,6,7,8,9]=>000000000=>111111111=>1
[9,1,10,2,3,4,5,6,7,8]=>000000000=>111111111=>1
[10,9,1,2,3,4,5,6,7,8]=>000000000=>111111111=>1
[8,1,2,3,4,5,6,9,10,7]=>000000000=>111111111=>1
[2,9,10,1,3,4,5,6,7,8]=>000000000=>111111111=>1
[4,7,8,5,6,2,1,3]=>0000000=>1111111=>1
[5,7,8,4,2,6,1,3]=>0000000=>1111111=>1
[6,7,8,4,2,5,1,3]=>0000000=>1111111=>1
[8,6,3,7,2,1,5,4]=>0000000=>1111111=>1
[7,6,3,8,2,1,5,4]=>0000000=>1111111=>1
[6,7,8,3,2,1,5,4]=>0000000=>1111111=>1
[5,7,8,3,2,1,6,4]=>0000000=>1111111=>1
[2,7,8,4,3,5,6,1]=>0000000=>1111111=>1
[3,7,8,4,2,5,1,6]=>0000000=>1111111=>1
[4,7,8,3,2,1,5,6]=>0000000=>1111111=>1
[5,7,8,3,2,1,4,6]=>0000000=>1111111=>1
[7,6,3,8,2,1,4,5]=>0000000=>1111111=>1
[8,6,3,7,2,1,4,5]=>0000000=>1111111=>1
[5,6,3,8,2,1,4,7]=>0000000=>1111111=>1
[3,6,4,8,2,5,1,7]=>0000000=>1111111=>1
[2,6,4,8,3,5,7,1]=>0000000=>1111111=>1
[2,6,4,7,3,5,8,1]=>0000000=>1111111=>1
[3,6,4,7,2,5,1,8]=>0000001=>1111110=>1
[4,6,3,7,2,1,5,8]=>0000001=>1111110=>1
[5,6,3,7,2,1,4,8]=>0000001=>1111110=>1
[8,4,3,2,1,6,5,7]=>0000000=>1111111=>1
[6,4,3,2,1,7,5,8]=>0000001=>1111110=>1
[4,5,3,2,7,1,6,8]=>0000001=>1111110=>1
[3,5,4,2,8,6,1,7]=>0000000=>1111111=>1
[6,4,3,2,1,8,5,7]=>0000000=>1111111=>1
[7,4,3,2,1,8,5,6]=>0000000=>1111111=>1
[8,4,3,2,1,7,5,6]=>0000000=>1111111=>1
[8,4,3,2,1,7,6,5]=>0000000=>1111111=>1
[7,4,3,2,1,8,6,5]=>0000000=>1111111=>1
[6,4,3,2,1,8,7,5]=>0000000=>1111111=>1
[5,6,3,8,2,1,7,4]=>0000000=>1111111=>1
[7,5,3,2,8,1,6,4]=>0000000=>1111111=>1
[8,5,4,2,7,6,1,3]=>0000000=>1111111=>1
[7,5,4,2,8,6,1,3]=>0000000=>1111111=>1
[6,5,4,2,8,7,1,3]=>0000000=>1111111=>1
[4,6,5,8,7,2,1,3]=>0000000=>1111111=>1
[2,6,5,7,8,3,4,1]=>0000000=>1111111=>1
[6,5,4,2,7,8,1,3]=>0000000=>1111111=>1
[8,5,4,2,6,7,1,3]=>0000000=>1111111=>1
[8,5,3,2,6,1,7,4]=>0000000=>1111111=>1
[7,5,3,2,6,1,8,4]=>0000000=>1111111=>1
[5,6,3,7,2,1,8,4]=>0000000=>1111111=>1
[4,6,3,7,2,1,8,5]=>0000000=>1111111=>1
[3,6,4,7,2,8,1,5]=>0000000=>1111111=>1
[2,6,4,7,3,8,5,1]=>0000000=>1111111=>1
[3,5,4,2,7,8,1,6]=>0000000=>1111111=>1
[4,5,3,2,7,1,8,6]=>0000000=>1111111=>1
[7,4,3,2,1,6,8,5]=>0000000=>1111111=>1
[8,4,3,2,1,6,7,5]=>0000000=>1111111=>1
[8,4,3,2,1,5,7,6]=>0000000=>1111111=>1
[7,4,3,2,1,5,8,6]=>0000000=>1111111=>1
[6,4,3,2,1,5,8,7]=>0000010=>1111101=>2
[3,5,4,2,6,8,1,7]=>0000000=>1111111=>1
[8,5,7,4,2,6,3,1]=>0000000=>1111111=>1
[6,8,3,7,5,1,4,2]=>0000000=>1111111=>1
[5,7,3,8,1,6,2,4]=>0000000=>1111111=>1
[3,2,6,4,8,5,1,7]=>0000000=>1111111=>1
[3,2,5,8,4,6,1,7]=>0000000=>1111111=>1
[3,5,2,4,1,7,6,8]=>0000101=>1111010=>2
[4,2,1,5,7,3,6,8]=>0000001=>1111110=>1
[4,5,2,3,7,1,6,8]=>0000001=>1111110=>1
[4,2,5,3,8,1,6,7]=>0000000=>1111111=>1
[4,2,5,8,3,1,6,7]=>0000000=>1111111=>1
[3,1,5,4,2,8,6,7]=>0000100=>1111011=>2
[4,1,5,3,8,2,6,7]=>0000000=>1111111=>1
[4,1,5,8,3,2,6,7]=>0000000=>1111111=>1
[4,3,8,5,2,1,6,7]=>0000000=>1111111=>1
[4,7,3,5,2,1,6,8]=>0000001=>1111110=>1
[4,3,2,7,5,1,6,8]=>0000001=>1111110=>1
[4,3,6,2,5,1,7,8]=>0000011=>1111100=>1
[4,6,3,2,5,1,7,8]=>0000011=>1111100=>1
[4,6,7,1,3,2,5,8]=>0000001=>1111110=>1
[4,5,1,7,3,2,6,8]=>0000001=>1111110=>1
[4,5,1,3,7,2,6,8]=>0000001=>1111110=>1
[3,5,1,4,2,7,6,8]=>0000101=>1111010=>2
[2,5,1,4,3,7,8,6]=>0000100=>1111011=>2
[5,2,1,4,3,7,8,6]=>0000100=>1111011=>2
[5,3,1,4,2,7,6,8]=>0000101=>1111010=>2
[4,3,1,5,7,2,6,8]=>0000001=>1111110=>1
[4,3,1,7,5,2,6,8]=>0000001=>1111110=>1
[4,3,6,1,5,2,7,8]=>0000011=>1111100=>1
[4,6,3,1,5,2,7,8]=>0000011=>1111100=>1
[5,3,6,4,1,2,7,8]=>0000011=>1111100=>1
[4,3,6,1,7,2,5,8]=>0000001=>1111110=>1
[6,3,4,1,2,7,5,8]=>0000001=>1111110=>1
[6,2,4,1,3,7,8,5]=>0000000=>1111111=>1
[3,6,4,1,2,7,5,8]=>0000001=>1111110=>1
[4,6,3,1,7,2,5,8]=>0000001=>1111110=>1
[5,3,6,2,1,4,7,8]=>0000011=>1111100=>1
[5,6,2,7,1,3,4,8]=>0000001=>1111110=>1
[4,5,2,7,3,1,6,8]=>0000001=>1111110=>1
[4,6,7,2,3,1,5,8]=>0000001=>1111110=>1
[4,6,2,1,7,3,5,8]=>0000001=>1111110=>1
[3,2,6,1,4,7,5,8]=>0000001=>1111110=>1
[3,6,2,1,4,7,5,8]=>0000001=>1111110=>1
[3,6,7,2,4,5,1,8]=>0000001=>1111110=>1
[3,5,2,7,4,6,1,8]=>0000001=>1111110=>1
[3,7,2,4,8,5,1,6]=>0000000=>1111111=>1
[7,2,1,4,6,3,8,5]=>0000000=>1111111=>1
[7,3,1,4,6,8,2,5]=>0000000=>1111111=>1
[3,2,6,1,5,7,4,8]=>0000001=>1111110=>1
[3,6,2,1,5,7,4,8]=>0000001=>1111110=>1
[6,3,2,1,5,7,4,8]=>0000001=>1111110=>1
[6,4,2,1,5,3,7,8]=>0000011=>1111100=>1
[4,2,6,1,5,3,7,8]=>0000011=>1111100=>1
[4,2,1,7,5,3,6,8]=>0000001=>1111110=>1
[7,4,1,5,6,2,3,8]=>0000001=>1111110=>1
[7,3,1,5,2,6,4,8]=>0000001=>1111110=>1
[7,2,1,5,3,6,8,4]=>0000000=>1111111=>1
[6,2,5,1,3,7,8,4]=>0000000=>1111111=>1
[6,3,5,1,2,7,4,8]=>0000001=>1111110=>1
[6,4,5,1,7,2,3,8]=>0000001=>1111110=>1
[5,2,6,4,1,3,7,8]=>0000011=>1111100=>1
[4,6,5,1,7,2,3,8]=>0000001=>1111110=>1
[3,6,5,1,2,7,4,8]=>0000001=>1111110=>1
[6,5,2,1,4,7,8,3]=>0000000=>1111111=>1
[6,5,3,1,4,7,2,8]=>0000001=>1111110=>1
[2,3,1,8,5,4,7,6]=>0010000=>1101111=>2
[2,4,1,5,8,3,7,6]=>0000000=>1111111=>1
[2,4,1,5,3,8,7,6]=>0000100=>1111011=>2
[3,4,5,1,2,8,7,6]=>0000100=>1111011=>2
[3,4,5,1,8,2,7,6]=>0000000=>1111111=>1
[3,4,5,8,2,1,7,6]=>0000000=>1111111=>1
[3,4,5,2,8,1,7,6]=>0000000=>1111111=>1
[3,5,6,2,7,1,4,8]=>0000001=>1111110=>1
[3,5,6,2,7,1,8,4]=>0000000=>1111111=>1
[2,4,8,6,3,7,1,5]=>0000000=>1111111=>1
[1,8,4,6,3,7,2,5]=>1000000=>0111111=>1
[3,4,6,8,2,7,5,1]=>0000000=>1111111=>1
[3,4,6,2,8,7,5,1]=>0000000=>1111111=>1
[3,5,6,2,7,8,4,1]=>0000000=>1111111=>1
[3,5,6,2,7,4,1,8]=>0000001=>1111110=>1
[4,5,6,7,2,8,3,1]=>0000000=>1111111=>1
[3,5,6,8,7,2,4,1]=>0000000=>1111111=>1
[2,5,8,6,7,3,4,1]=>0000000=>1111111=>1
[2,5,8,6,7,3,1,4]=>0000000=>1111111=>1
[3,5,6,8,7,2,1,4]=>0000000=>1111111=>1
[4,5,6,7,2,1,8,3]=>0000000=>1111111=>1
[2,3,1,8,6,7,4,5]=>0010000=>1101111=>2
[1,8,3,2,6,7,5,4]=>1000000=>0111111=>1
[2,5,1,6,7,8,4,3]=>0000000=>1111111=>1
[2,5,1,6,7,4,8,3]=>0000000=>1111111=>1
[3,4,6,8,1,7,5,2]=>0000000=>1111111=>1
[2,4,8,6,1,7,5,3]=>0000000=>1111111=>1
[3,5,6,8,7,1,4,2]=>0000000=>1111111=>1
[4,5,6,7,8,1,3,2]=>0000000=>1111111=>1
[4,5,6,7,1,3,8,2]=>0000000=>1111111=>1
[4,5,6,7,1,3,2,8]=>0000001=>1111110=>1
[4,5,6,7,3,1,8,2]=>0000000=>1111111=>1
[3,5,6,8,7,4,1,2]=>0000000=>1111111=>1
[2,5,8,6,7,4,1,3]=>0000000=>1111111=>1
[1,8,5,6,7,4,3,2]=>1000000=>0111111=>1
[2,5,8,6,7,4,3,1]=>0000000=>1111111=>1
[8,2,4,3,7,1,6,5]=>0000000=>1111111=>1
[5,8,2,4,3,7,1,6]=>0000000=>1111111=>1
[6,1,5,7,3,2,4,8]=>0000001=>1111110=>1
[6,1,5,8,3,2,4,7]=>0000000=>1111111=>1
[4,3,5,6,7,1,8,2]=>0000000=>1111111=>1
[3,7,1,5,6,8,2,4]=>0000000=>1111111=>1
[8,3,2,4,6,1,5,7]=>0000000=>1111111=>1
[7,3,2,4,6,1,5,8]=>0000001=>1111110=>1
[3,2,5,1,7,4,6,8]=>0000001=>1111110=>1
[3,2,5,1,7,8,4,6]=>0000000=>1111111=>1
[5,7,6,1,8,3,4,2]=>0000000=>1111111=>1
[3,2,5,1,6,4,7,8]=>0000011=>1111100=>1
[3,8,6,5,1,7,4,2]=>0000000=>1111111=>1
[3,7,6,5,1,8,4,2]=>0000000=>1111111=>1
[3,2,5,1,6,7,8,4]=>0000000=>1111111=>1
[3,2,4,1,6,8,5,7]=>0001000=>1110111=>2
[8,3,2,4,7,6,1,5]=>0000000=>1111111=>1
[3,2,5,1,8,4,7,6]=>0000000=>1111111=>1
[3,2,5,1,6,7,4,8]=>0000001=>1111110=>1
[8,4,2,3,7,5,1,6]=>0000000=>1111111=>1
[4,2,6,1,8,3,7,5]=>0000000=>1111111=>1
[5,2,6,1,8,3,7,4]=>0000000=>1111111=>1
[8,4,6,1,7,3,5,2]=>0000000=>1111111=>1
[5,2,6,1,8,4,7,3]=>0000000=>1111111=>1
[7,4,2,3,8,5,1,6]=>0000000=>1111111=>1
[8,5,1,6,4,2,3,7]=>0000000=>1111111=>1
[7,5,1,6,4,2,3,8]=>0000001=>1111110=>1
[3,2,5,1,7,6,4,8]=>0000001=>1111110=>1
[7,3,2,4,8,6,1,5]=>0000000=>1111111=>1
[4,2,6,1,8,5,7,3]=>0000000=>1111111=>1
[8,5,6,1,7,3,4,2]=>0000000=>1111111=>1
[3,6,8,5,1,7,4,2]=>0000000=>1111111=>1
[3,2,5,1,8,6,7,4]=>0000000=>1111111=>1
[3,2,4,1,8,6,5,7]=>0001000=>1110111=>2
[3,2,5,1,7,8,6,4]=>0000000=>1111111=>1
[7,8,5,1,6,4,2,3]=>0000000=>1111111=>1
[3,7,5,1,8,6,4,2]=>0000000=>1111111=>1
[8,7,5,1,6,4,2,3]=>0000000=>1111111=>1
[6,5,7,3,1,8,4,2]=>0000000=>1111111=>1
[4,6,3,7,1,8,5,2]=>0000000=>1111111=>1
[4,6,3,7,5,1,8,2]=>0000000=>1111111=>1
[4,2,6,1,7,5,3,8]=>0000001=>1111110=>1
[2,5,7,4,1,6,3,8]=>0000001=>1111110=>1
[2,5,7,4,1,6,8,3]=>0000000=>1111111=>1
[5,4,7,3,6,1,8,2]=>0000000=>1111111=>1
[5,4,7,8,3,1,6,2]=>0000000=>1111111=>1
[4,3,7,5,1,8,6,2]=>0000000=>1111111=>1
[6,4,3,8,5,1,7,2]=>0000000=>1111111=>1
[5,8,4,3,6,1,7,2]=>0000000=>1111111=>1
[5,4,8,3,6,1,7,2]=>0000000=>1111111=>1
[5,4,3,6,7,1,8,2]=>0000000=>1111111=>1
[2,5,4,6,1,7,3,8]=>0000001=>1111110=>1
[3,2,5,8,1,6,7,4]=>0000000=>1111111=>1
[2,5,4,6,8,1,7,3]=>0000000=>1111111=>1
[5,2,8,4,1,6,7,3]=>0000000=>1111111=>1
[4,6,2,1,8,5,7,3]=>0000000=>1111111=>1
[2,4,1,7,5,8,6,3]=>0000000=>1111111=>1
[2,4,1,7,5,3,8,6]=>0000000=>1111111=>1
[2,6,4,1,8,5,3,7]=>0000000=>1111111=>1
[5,4,8,2,1,6,3,7]=>0000000=>1111111=>1
[2,5,8,4,1,6,3,7]=>0000000=>1111111=>1
[3,2,5,6,1,8,4,7]=>0000000=>1111111=>1
[4,8,3,2,6,1,5,7]=>0000000=>1111111=>1
[3,5,2,8,1,6,4,7]=>0000000=>1111111=>1
[3,2,1,6,8,5,4,7]=>0010000=>1101111=>2
[3,2,7,1,5,4,8,6]=>0000000=>1111111=>1
[3,2,7,1,5,8,6,4]=>0000000=>1111111=>1
[3,8,2,5,1,6,7,4]=>0000000=>1111111=>1
[4,8,3,2,6,7,1,5]=>0000000=>1111111=>1
[4,3,8,2,6,7,1,5]=>0000000=>1111111=>1
[4,3,2,6,7,8,1,5]=>0000000=>1111111=>1
[4,3,2,6,7,1,5,8]=>0000001=>1111110=>1
[4,3,7,2,6,8,1,5]=>0000000=>1111111=>1
[4,3,7,8,2,6,1,5]=>0000000=>1111111=>1
[2,5,7,4,8,1,6,3]=>0000000=>1111111=>1
[3,2,5,7,8,1,6,4]=>0000000=>1111111=>1
[3,2,5,7,1,6,8,4]=>0000000=>1111111=>1
[3,2,5,7,1,6,4,8]=>0000001=>1111110=>1
[6,3,2,7,1,5,4,8]=>0000001=>1111110=>1
[6,3,2,7,1,5,8,4]=>0000000=>1111111=>1
[6,3,2,7,8,1,5,4]=>0000000=>1111111=>1
[4,2,6,1,7,8,5,3]=>0000000=>1111111=>1
[6,5,2,1,7,8,4,3]=>0000000=>1111111=>1
[2,1,7,5,3,8,6,4]=>0100000=>1011111=>2
[6,2,1,8,5,3,7,4]=>0000000=>1111111=>1
[6,3,2,7,1,4,8,5]=>0000000=>1111111=>1
[6,3,2,1,4,7,8,5]=>0000000=>1111111=>1
[6,3,2,1,4,7,5,8]=>0000001=>1111110=>1
[3,5,2,1,7,4,6,8]=>0000001=>1111110=>1
[3,5,2,1,7,8,4,6]=>0000000=>1111111=>1
[5,8,4,2,1,7,3,6]=>0000000=>1111111=>1
[4,6,2,1,8,3,7,5]=>0000000=>1111111=>1
[2,4,1,7,3,8,6,5]=>0000000=>1111111=>1
[3,2,7,1,4,8,6,5]=>0000000=>1111111=>1
[3,5,8,2,1,7,4,6]=>0000000=>1111111=>1
[4,8,3,7,2,1,5,6]=>0000000=>1111111=>1
[4,3,7,2,8,1,5,6]=>0000000=>1111111=>1
[4,3,7,2,1,5,6,8]=>0000001=>1111110=>1
[4,8,3,2,7,1,5,6]=>0000000=>1111111=>1
[3,5,2,8,1,7,4,6]=>0000000=>1111111=>1
[6,3,2,8,1,4,7,5]=>0000000=>1111111=>1
[3,2,1,4,7,5,8,6]=>0011000=>1100111=>2
[5,3,2,1,8,4,6,7]=>0000000=>1111111=>1
[4,8,3,2,1,5,6,7]=>0000000=>1111111=>1
[4,3,8,2,1,5,6,7]=>0000000=>1111111=>1
[1,9,8,7,6,5,4,3,2]=>10000000=>01111111=>1
[8,7,6,4,5,3,2,1,9]=>00000001=>11111110=>1
[1,9,8,7,5,6,4,3,2]=>10000000=>01111111=>1
[1,10,9,8,7,6,5,4,3,2]=>100000000=>011111111=>1
[10,9,8,7,6,5,4,3,2,1,11]=>0000000001=>1111111110=>1
[9,8,7,5,6,4,3,2,1,10]=>000000001=>111111110=>1
[8,7,5,4,6,3,2,1,9]=>00000001=>11111110=>1
[8,7,4,6,5,3,2,1,9]=>00000001=>11111110=>1
[1,9,8,6,5,7,4,3,2]=>10000000=>01111111=>1
[1,9,8,5,7,6,4,3,2]=>10000000=>01111111=>1
[1,10,9,8,6,7,5,4,3,2]=>100000000=>011111111=>1
[1,11,10,9,8,7,6,5,4,3,2]=>1000000000=>0111111111=>1
[6,2,5,3,4,1,8,7]=>0000010=>1111101=>2
[6,1,5,2,4,3,8,7]=>0000010=>1111101=>2
[8,3,5,2,4,1,7,6]=>0000000=>1111111=>1
[8,1,5,3,4,2,7,6]=>0000000=>1111111=>1
[8,4,5,1,3,2,7,6]=>0000000=>1111111=>1
[8,6,7,4,5,1,3,2]=>0000000=>1111111=>1
[8,6,7,3,5,1,4,2]=>0000000=>1111111=>1
[8,5,7,3,6,1,4,2]=>0000000=>1111111=>1
[8,3,7,1,6,4,5,2]=>0000000=>1111111=>1
[8,1,7,5,6,3,4,2]=>0000000=>1111111=>1
[8,4,7,5,6,1,3,2]=>0000000=>1111111=>1
[2,1,8,4,7,5,6,3]=>0100000=>1011111=>2
[8,1,7,3,4,2,6,5]=>0000000=>1111111=>1
[8,1,7,3,6,2,5,4]=>0000000=>1111111=>1
[8,3,7,2,6,4,5,1]=>0000000=>1111111=>1
[8,2,7,3,6,4,5,1]=>0000000=>1111111=>1
[8,1,7,2,4,3,6,5]=>0000000=>1111111=>1
[8,1,5,2,4,3,7,6]=>0000000=>1111111=>1
[8,2,7,1,4,3,6,5]=>0000000=>1111111=>1
[8,2,3,1,5,4,7,6]=>0000000=>1111111=>1
[4,1,3,2,8,6,7,5]=>0001000=>1110111=>2
[8,6,7,2,3,1,5,4]=>0000000=>1111111=>1
[8,5,7,2,6,1,4,3]=>0000000=>1111111=>1
[8,2,7,5,6,1,4,3]=>0000000=>1111111=>1
[2,1,8,6,7,3,5,4]=>0100000=>1011111=>2
[2,1,8,3,7,5,6,4]=>0100000=>1011111=>2
[8,4,7,2,6,3,5,1]=>0000000=>1111111=>1
[2,1,8,5,7,3,6,4]=>0100000=>1011111=>2
[8,5,7,4,6,1,3,2]=>0000000=>1111111=>1
[2,4,8,3,6,1,7,5]=>0000000=>1111111=>1
[6,5,8,7,3,1,2,4]=>0000000=>1111111=>1
[1,7,2,8,4,6,5,3]=>1000000=>0111111=>1
[3,1,6,8,4,5,7,2]=>0000000=>1111111=>1
[2,3,6,8,4,5,7,1]=>0000000=>1111111=>1
[1,5,7,8,2,4,6,3]=>1000000=>0111111=>1
[5,1,7,8,2,4,6,3]=>0000000=>1111111=>1
[3,6,7,8,4,2,5,1]=>0000000=>1111111=>1
[5,6,8,7,3,2,1,4]=>0000000=>1111111=>1
[5,2,7,8,1,4,6,3]=>0000000=>1111111=>1
[2,8,4,5,3,1,6,7]=>0000000=>1111111=>1
[3,4,2,1,8,5,6,7]=>0001000=>1110111=>2
[2,7,6,8,4,3,5,1]=>0000000=>1111111=>1
[5,7,1,8,3,4,6,2]=>0000000=>1111111=>1
[3,7,5,8,1,4,6,2]=>0000000=>1111111=>1
[1,6,8,5,4,3,2,7]=>1000000=>0111111=>1
[4,6,8,5,1,3,2,7]=>0000000=>1111111=>1
[5,6,8,1,4,3,2,7]=>0000000=>1111111=>1
[2,4,8,3,6,5,1,7]=>0000000=>1111111=>1
[2,8,4,1,5,6,3,7]=>0000000=>1111111=>1
[1,7,3,8,5,4,6,2]=>1000000=>0111111=>1
[3,7,1,8,5,4,6,2]=>0000000=>1111111=>1
[5,7,8,4,3,6,1,2]=>0000000=>1111111=>1
[2,8,5,4,3,1,6,7]=>0000000=>1111111=>1
[6,5,8,4,2,3,1,7]=>0000000=>1111111=>1
[4,1,3,2,8,5,6,7]=>0001000=>1110111=>2
[1,4,3,2,8,5,6,7]=>1001000=>0110111=>2
[6,4,8,2,5,3,1,7]=>0000000=>1111111=>1
[2,8,3,4,5,1,6,7]=>0000000=>1111111=>1
[6,2,8,4,5,3,1,7]=>0000000=>1111111=>1
[3,2,1,4,8,5,6,7]=>0011000=>1100111=>2
[5,1,3,2,4,8,6,7]=>0000100=>1111011=>2
[2,8,1,5,3,4,7,6]=>0000000=>1111111=>1
[1,2,8,4,5,3,7,6]=>1100000=>0011111=>1
[1,4,2,8,5,3,6,7]=>1000000=>0111111=>1
[1,8,4,2,5,3,6,7]=>1000000=>0111111=>1
[8,1,5,3,2,4,6,7]=>0000000=>1111111=>1
[3,8,1,5,2,4,6,7]=>0000000=>1111111=>1
[3,5,1,4,8,2,6,7]=>0000000=>1111111=>1
[1,5,2,8,4,3,6,7]=>1000000=>0111111=>1
[1,2,8,5,4,3,6,7]=>1100000=>0011111=>1
[1,2,5,4,3,8,6,7]=>1100100=>0011011=>2
[1,2,4,8,5,3,7,6]=>1100000=>0011111=>1
[1,2,7,4,8,5,3,6]=>1100000=>0011111=>1
[1,5,2,7,8,4,3,6]=>1000000=>0111111=>1
[5,1,2,7,4,8,3,6]=>0000000=>1111111=>1
[8,3,5,1,4,7,2,6]=>0000000=>1111111=>1
[2,8,1,5,4,7,3,6]=>0000000=>1111111=>1
[1,2,8,5,7,4,3,6]=>1100000=>0011111=>1
[1,2,4,8,7,5,3,6]=>1100000=>0011111=>1
[2,8,1,4,3,7,6,5]=>0000000=>1111111=>1
[6,1,2,8,7,4,3,5]=>0000000=>1111111=>1
[6,4,1,2,8,7,3,5]=>0000000=>1111111=>1
[3,6,4,8,1,7,2,5]=>0000000=>1111111=>1
[7,6,1,4,2,8,3,5]=>0000000=>1111111=>1
[7,1,6,2,8,4,3,5]=>0000000=>1111111=>1
[1,6,7,2,8,4,3,5]=>1000000=>0111111=>1
[6,7,1,4,2,8,3,5]=>0000000=>1111111=>1
[6,3,7,1,4,8,2,5]=>0000000=>1111111=>1
[3,7,8,1,5,2,4,6]=>0000000=>1111111=>1
[7,1,2,8,5,3,4,6]=>0000000=>1111111=>1
[1,7,2,8,4,5,3,6]=>1000000=>0111111=>1
[1,4,2,7,8,5,3,6]=>1000000=>0111111=>1
[6,1,2,8,4,3,7,5]=>0000000=>1111111=>1
[6,4,1,2,8,3,7,5]=>0000000=>1111111=>1
[7,6,1,3,2,4,8,5]=>0000000=>1111111=>1
[6,7,1,3,2,4,8,5]=>0000000=>1111111=>1
[1,2,7,3,5,8,4,6]=>1100000=>0011111=>1
[1,2,7,5,8,3,4,6]=>1100000=>0011111=>1
[5,8,1,3,7,2,4,6]=>0000000=>1111111=>1
[1,2,5,8,7,3,4,6]=>1100000=>0011111=>1
[1,2,5,8,3,7,4,6]=>1100000=>0011111=>1
[2,8,1,7,3,5,4,6]=>0000000=>1111111=>1
[8,6,1,3,2,4,7,5]=>0000000=>1111111=>1
[4,2,8,1,7,3,6,5]=>0000000=>1111111=>1
[2,8,1,7,4,3,6,5]=>0000000=>1111111=>1
[7,1,2,8,4,3,6,5]=>0000000=>1111111=>1
[1,2,8,4,7,5,3,6]=>1100000=>0011111=>1
[1,2,8,7,4,5,3,6]=>1100000=>0011111=>1
[2,8,1,7,5,3,4,6]=>0000000=>1111111=>1
[8,3,7,1,5,2,4,6]=>0000000=>1111111=>1
[3,8,6,1,4,7,2,5]=>0000000=>1111111=>1
[8,6,1,4,2,7,3,5]=>0000000=>1111111=>1
[8,1,6,2,7,4,3,5]=>0000000=>1111111=>1
[7,1,2,8,6,4,3,5]=>0000000=>1111111=>1
[7,4,1,2,8,6,3,5]=>0000000=>1111111=>1
[3,7,4,8,1,6,2,5]=>0000000=>1111111=>1
[3,4,8,7,1,6,2,5]=>0000000=>1111111=>1
[4,2,8,1,7,6,3,5]=>0000000=>1111111=>1
[2,8,1,7,6,4,3,5]=>0000000=>1111111=>1
[7,8,3,4,1,5,2,6]=>0000000=>1111111=>1
[7,8,3,4,1,6,2,5]=>0000000=>1111111=>1
[6,8,3,4,1,7,2,5]=>0000000=>1111111=>1
[6,7,3,4,1,8,2,5]=>0000000=>1111111=>1
[5,7,3,4,1,8,2,6]=>0000000=>1111111=>1
[5,8,3,4,1,7,2,6]=>0000000=>1111111=>1
[5,8,3,4,1,6,2,7]=>0000000=>1111111=>1
[6,8,3,4,1,5,2,7]=>0000000=>1111111=>1
[6,7,3,4,1,5,2,8]=>0000001=>1111110=>1
[5,7,3,4,1,6,2,8]=>0000001=>1111110=>1
[5,6,2,8,3,4,1,7]=>0000000=>1111111=>1
[5,6,2,7,3,4,1,8]=>0000001=>1111110=>1
[4,6,2,8,3,5,1,7]=>0000000=>1111111=>1
[4,7,3,5,1,6,2,8]=>0000001=>1111110=>1
[4,8,3,5,1,6,2,7]=>0000000=>1111111=>1
[4,8,3,5,1,7,2,6]=>0000000=>1111111=>1
[4,7,3,5,1,8,2,6]=>0000000=>1111111=>1
[5,6,2,3,1,7,4,8]=>0000001=>1111110=>1
[5,6,2,4,1,8,3,7]=>0000000=>1111111=>1
[5,6,2,4,1,7,3,8]=>0000001=>1111110=>1
[4,6,2,5,1,7,3,8]=>0000001=>1111110=>1
[4,6,2,5,1,8,3,7]=>0000000=>1111111=>1
[4,5,1,8,3,7,2,6]=>0000000=>1111111=>1
[4,5,1,7,3,8,2,6]=>0000000=>1111111=>1
[4,6,2,7,3,8,1,5]=>0000000=>1111111=>1
[5,6,2,7,3,8,1,4]=>0000000=>1111111=>1
[5,6,2,7,4,8,1,3]=>0000000=>1111111=>1
[5,6,3,8,4,7,1,2]=>0000000=>1111111=>1
[5,6,2,8,4,7,1,3]=>0000000=>1111111=>1
[5,6,2,8,3,7,1,4]=>0000000=>1111111=>1
[4,6,2,8,3,7,1,5]=>0000000=>1111111=>1
[4,5,1,7,3,6,2,8]=>0000001=>1111110=>1
[4,5,1,8,3,6,2,7]=>0000000=>1111111=>1
[9,2,1,3,4,5,6,7,8]=>00000000=>11111111=>1
[10,2,1,3,4,5,6,7,8,9]=>000000000=>111111111=>1
[9,2,3,1,4,5,6,7,8]=>00000000=>11111111=>1
[4,2,3,5,6,7,8,9,1]=>00000000=>11111111=>1
[3,4,2,5,6,7,8,9,1]=>00000000=>11111111=>1
[3,2,4,5,6,7,8,9,10,1]=>000000000=>111111111=>1
[8,7,2,4,5,3,1,6]=>0000000=>1111111=>1
[6,3,8,4,5,7,2,1]=>0000000=>1111111=>1
[5,8,7,4,3,6,2,1]=>0000000=>1111111=>1
[2,8,7,4,3,6,1,5]=>0000000=>1111111=>1
[5,1,8,4,7,6,3,2]=>0000000=>1111111=>1
[2,5,8,4,7,6,3,1]=>0000000=>1111111=>1
[4,3,8,1,5,6,7,2]=>0000000=>1111111=>1
[4,8,1,3,5,6,7,2]=>0000000=>1111111=>1
[5,8,7,4,1,6,3,2]=>0000000=>1111111=>1
[5,8,3,6,1,4,7,2]=>0000000=>1111111=>1
[3,8,7,4,1,6,2,5]=>0000000=>1111111=>1
[8,1,7,4,5,2,3,6]=>0000000=>1111111=>1
[6,1,8,4,5,7,2,3]=>0000000=>1111111=>1
[6,8,3,5,1,7,2,4]=>0000000=>1111111=>1
[2,1,5,8,3,6,7,4]=>0100000=>1011111=>2
[4,1,8,2,5,6,7,3]=>0000000=>1111111=>1
[2,4,8,1,5,6,7,3]=>0000000=>1111111=>1
[4,8,2,1,5,6,7,3]=>0000000=>1111111=>1
[3,4,8,2,5,6,7,1]=>0000000=>1111111=>1
[5,8,1,4,7,6,2,3]=>0000000=>1111111=>1
[3,4,1,8,5,6,7,2]=>0000000=>1111111=>1
[2,4,6,8,10,1,3,5,7,9]=>000000000=>111111111=>1
[2,4,6,9,10,1,3,5,7,8]=>000000000=>111111111=>1
[2,4,7,8,10,1,3,5,6,9]=>000000000=>111111111=>1
[2,4,7,9,10,1,3,5,6,8]=>000000000=>111111111=>1
[2,4,8,9,10,1,3,5,6,7]=>000000000=>111111111=>1
[2,5,6,8,10,1,3,4,7,9]=>000000000=>111111111=>1
[2,5,6,9,10,1,3,4,7,8]=>000000000=>111111111=>1
[2,5,7,8,10,1,3,4,6,9]=>000000000=>111111111=>1
[2,5,7,9,10,1,3,4,6,8]=>000000000=>111111111=>1
[2,5,8,9,10,1,3,4,6,7]=>000000000=>111111111=>1
[2,6,7,8,10,1,3,4,5,9]=>000000000=>111111111=>1
[2,6,7,9,10,1,3,4,5,8]=>000000000=>111111111=>1
[2,6,8,9,10,1,3,4,5,7]=>000000000=>111111111=>1
[2,7,8,9,10,1,3,4,5,6]=>000000000=>111111111=>1
[3,4,6,8,10,1,2,5,7,9]=>000000000=>111111111=>1
[3,4,6,9,10,1,2,5,7,8]=>000000000=>111111111=>1
[3,4,7,8,10,1,2,5,6,9]=>000000000=>111111111=>1
[3,4,7,9,10,1,2,5,6,8]=>000000000=>111111111=>1
[3,4,8,9,10,1,2,5,6,7]=>000000000=>111111111=>1
[3,5,6,8,10,1,2,4,7,9]=>000000000=>111111111=>1
[3,5,6,9,10,1,2,4,7,8]=>000000000=>111111111=>1
[3,5,7,8,10,1,2,4,6,9]=>000000000=>111111111=>1
[3,5,7,9,10,1,2,4,6,8]=>000000000=>111111111=>1
[3,5,8,9,10,1,2,4,6,7]=>000000000=>111111111=>1
[3,6,7,8,10,1,2,4,5,9]=>000000000=>111111111=>1
[3,6,7,9,10,1,2,4,5,8]=>000000000=>111111111=>1
[3,6,8,9,10,1,2,4,5,7]=>000000000=>111111111=>1
[3,7,8,9,10,1,2,4,5,6]=>000000000=>111111111=>1
[4,5,6,8,10,1,2,3,7,9]=>000000000=>111111111=>1
[4,5,6,9,10,1,2,3,7,8]=>000000000=>111111111=>1
[4,5,7,8,10,1,2,3,6,9]=>000000000=>111111111=>1
[4,5,7,9,10,1,2,3,6,8]=>000000000=>111111111=>1
[4,5,8,9,10,1,2,3,6,7]=>000000000=>111111111=>1
[4,6,7,8,10,1,2,3,5,9]=>000000000=>111111111=>1
[4,6,7,9,10,1,2,3,5,8]=>000000000=>111111111=>1
[4,6,8,9,10,1,2,3,5,7]=>000000000=>111111111=>1
[4,7,8,9,10,1,2,3,5,6]=>000000000=>111111111=>1
[5,6,7,8,10,1,2,3,4,9]=>000000000=>111111111=>1
[5,6,7,9,10,1,2,3,4,8]=>000000000=>111111111=>1
[5,6,8,9,10,1,2,3,4,7]=>000000000=>111111111=>1
[5,7,8,9,10,1,2,3,4,6]=>000000000=>111111111=>1
[4,5,7,6,2,3,8,1]=>0000000=>1111111=>1
[3,5,7,2,6,4,8,1]=>0000000=>1111111=>1
[2,5,7,3,6,4,8,1]=>0000000=>1111111=>1
[1,5,7,3,6,8,4,2]=>1000000=>0111111=>1
[8,4,3,7,6,1,5,2]=>0000000=>1111111=>1
[6,7,2,3,5,4,8,1]=>0000000=>1111111=>1
[5,2,7,3,6,4,8,1]=>0000000=>1111111=>1
[8,3,4,7,6,1,5,2]=>0000000=>1111111=>1
[8,2,4,7,1,6,5,3]=>0000000=>1111111=>1
[3,1,4,7,6,8,5,2]=>0000000=>1111111=>1
[4,1,3,7,6,8,5,2]=>0000000=>1111111=>1
[5,1,7,3,6,8,4,2]=>0000000=>1111111=>1
[6,7,1,3,5,8,4,2]=>0000000=>1111111=>1
[5,8,7,3,6,1,4,2]=>0000000=>1111111=>1
[4,8,3,7,6,1,5,2]=>0000000=>1111111=>1
[3,8,4,7,6,1,5,2]=>0000000=>1111111=>1
[2,8,4,7,1,6,5,3]=>0000000=>1111111=>1
[8,1,4,7,2,6,5,3]=>0000000=>1111111=>1
[8,1,3,2,7,6,5,4]=>0000000=>1111111=>1
[2,8,3,1,7,6,5,4]=>0000000=>1111111=>1
[3,8,2,1,7,6,5,4]=>0000000=>1111111=>1
[6,7,1,2,8,5,4,3]=>0000000=>1111111=>1
[8,2,3,1,7,6,5,4]=>0000000=>1111111=>1
[8,3,2,1,7,6,5,4]=>0000000=>1111111=>1
[3,4,1,7,6,8,5,2]=>0000000=>1111111=>1
[1,4,2,7,8,6,5,3]=>1000000=>0111111=>1
[8,4,2,7,1,6,5,3]=>0000000=>1111111=>1
[8,5,7,2,1,6,4,3]=>0000000=>1111111=>1
[1,5,7,2,8,6,4,3]=>1000000=>0111111=>1
[2,5,7,1,8,6,4,3]=>0000000=>1111111=>1
[3,5,7,1,6,8,4,2]=>0000000=>1111111=>1
[6,7,4,5,8,1,3,2]=>0000000=>1111111=>1
[5,4,7,6,8,1,3,2]=>0000000=>1111111=>1
[2,5,7,8,1,6,4,3]=>0000000=>1111111=>1
[1,5,7,8,2,6,4,3]=>1000000=>0111111=>1
[8,5,7,1,2,6,4,3]=>0000000=>1111111=>1
[8,4,1,7,2,6,5,3]=>0000000=>1111111=>1
[1,4,8,7,2,6,5,3]=>1000000=>0111111=>1
[3,4,8,7,6,1,5,2]=>0000000=>1111111=>1
[4,3,8,7,6,1,5,2]=>0000000=>1111111=>1
[5,3,7,8,6,1,4,2]=>0000000=>1111111=>1
[6,7,2,8,1,5,4,3]=>0000000=>1111111=>1
[5,2,7,8,1,6,4,3]=>0000000=>1111111=>1
[4,2,8,7,1,6,5,3]=>0000000=>1111111=>1
[3,2,8,1,7,6,5,4]=>0000000=>1111111=>1
[1,3,8,2,7,6,5,4]=>1000000=>0111111=>1
[8,3,1,2,7,6,5,4]=>0000000=>1111111=>1
[8,2,1,3,7,6,5,4]=>0000000=>1111111=>1
[1,2,8,3,7,6,5,4]=>1100000=>0011111=>1
[2,1,8,3,7,6,5,4]=>0100000=>1011111=>2
[4,1,8,7,2,6,5,3]=>0000000=>1111111=>1
[5,1,7,8,2,6,4,3]=>0000000=>1111111=>1
[6,7,1,8,2,5,4,3]=>0000000=>1111111=>1
[5,8,7,1,2,6,4,3]=>0000000=>1111111=>1
[4,8,1,7,2,6,5,3]=>0000000=>1111111=>1
[3,8,1,2,7,6,5,4]=>0000000=>1111111=>1
[2,8,1,3,7,6,5,4]=>0000000=>1111111=>1
[1,8,2,3,7,6,5,4]=>1000000=>0111111=>1
[8,1,2,3,7,6,5,4]=>0000000=>1111111=>1
[3,1,4,5,6,7,8,9,10,2]=>000000000=>111111111=>1
[6,7,1,8,4,5,2,3]=>0000000=>1111111=>1
[3,7,1,5,8,2,6,4]=>0000000=>1111111=>1
[2,7,1,5,8,3,6,4]=>0000000=>1111111=>1
[2,6,5,1,8,3,7,4]=>0000000=>1111111=>1
[3,6,5,1,8,2,7,4]=>0000000=>1111111=>1
[4,6,5,1,8,7,2,3]=>0000000=>1111111=>1
[5,6,4,1,8,7,2,3]=>0000000=>1111111=>1
[8,1,4,5,7,6,2,3]=>0000000=>1111111=>1
[6,4,5,1,8,7,2,3]=>0000000=>1111111=>1
[5,4,6,1,8,7,2,3]=>0000000=>1111111=>1
[4,5,6,1,8,7,2,3]=>0000000=>1111111=>1
[3,5,6,1,8,2,7,4]=>0000000=>1111111=>1
[2,5,6,1,8,3,7,4]=>0000000=>1111111=>1
[2,4,6,1,3,8,7,5]=>0000000=>1111111=>1
[3,4,6,1,2,8,7,5]=>0000000=>1111111=>1
[4,3,6,1,2,8,7,5]=>0000000=>1111111=>1
[5,3,6,1,8,2,7,4]=>0000000=>1111111=>1
[7,3,1,5,8,2,6,4]=>0000000=>1111111=>1
[8,1,3,5,7,2,6,4]=>0000000=>1111111=>1
[8,1,2,5,7,3,6,4]=>0000000=>1111111=>1
[7,2,1,5,8,3,6,4]=>0000000=>1111111=>1
[6,2,5,1,8,3,7,4]=>0000000=>1111111=>1
[4,2,6,1,3,8,7,5]=>0000000=>1111111=>1
[2,3,6,1,4,8,7,5]=>0000000=>1111111=>1
[4,2,5,3,1,8,7,6]=>0000100=>1111011=>2
[6,2,4,1,3,8,7,5]=>0000000=>1111111=>1
[7,2,1,4,3,8,6,5]=>0000000=>1111111=>1
[8,1,2,4,3,7,6,5]=>0000000=>1111111=>1
[8,1,3,4,2,7,6,5]=>0000000=>1111111=>1
[7,3,1,4,2,8,6,5]=>0000000=>1111111=>1
[6,3,4,1,2,8,7,5]=>0000000=>1111111=>1
[4,6,3,1,2,8,7,5]=>0000000=>1111111=>1
[3,6,4,1,2,8,7,5]=>0000000=>1111111=>1
[2,6,4,1,3,8,7,5]=>0000000=>1111111=>1
[2,7,1,4,3,8,6,5]=>0000000=>1111111=>1
[3,7,1,4,2,8,6,5]=>0000000=>1111111=>1
[4,7,1,3,2,8,6,5]=>0000000=>1111111=>1
[8,1,6,7,2,3,5,4]=>0000000=>1111111=>1
[4,7,1,2,3,8,6,5]=>0000000=>1111111=>1
[3,7,1,2,4,8,6,5]=>0000000=>1111111=>1
[2,7,1,3,4,8,6,5]=>0000000=>1111111=>1
[2,6,3,1,4,8,7,5]=>0000000=>1111111=>1
[3,6,2,1,4,8,7,5]=>0000000=>1111111=>1
[5,6,2,1,8,3,7,4]=>0000000=>1111111=>1
[6,5,2,1,8,3,7,4]=>0000000=>1111111=>1
[8,1,5,2,7,3,6,4]=>0000000=>1111111=>1
[8,1,4,2,3,7,6,5]=>0000000=>1111111=>1
[7,4,1,2,3,8,6,5]=>0000000=>1111111=>1
[6,4,2,1,3,8,7,5]=>0000000=>1111111=>1
[5,4,2,3,1,8,7,6]=>0000100=>1111011=>2
[3,5,2,4,1,8,7,6]=>0000100=>1111011=>2
[6,3,2,1,4,8,7,5]=>0000000=>1111111=>1
[7,3,1,2,4,8,6,5]=>0000000=>1111111=>1
[8,1,3,2,4,7,6,5]=>0000000=>1111111=>1
[8,1,2,3,4,7,6,5]=>0000000=>1111111=>1
[7,2,1,3,4,8,6,5]=>0000000=>1111111=>1
[6,2,3,1,4,8,7,5]=>0000000=>1111111=>1
[2,4,3,6,5,8,1,7]=>0000000=>1111111=>1
[2,4,6,3,5,8,7,1]=>0000000=>1111111=>1
[2,4,6,3,5,8,1,7]=>0000000=>1111111=>1
[4,2,6,5,1,8,7,3]=>0000000=>1111111=>1
[4,2,6,5,8,1,3,7]=>0000000=>1111111=>1
[4,2,6,5,8,3,1,7]=>0000000=>1111111=>1
[2,4,6,1,5,8,3,7]=>0000000=>1111111=>1
[2,4,1,6,5,8,3,7]=>0000000=>1111111=>1
[4,2,6,5,8,3,7,1]=>0000000=>1111111=>1
[2,6,4,3,8,7,5,1]=>0000000=>1111111=>1
[4,2,6,8,5,3,7,1]=>0000000=>1111111=>1
[2,4,6,8,1,5,7,3]=>0000000=>1111111=>1
[2,4,6,1,8,5,7,3]=>0000000=>1111111=>1
[2,1,4,6,8,5,7,3]=>0100000=>1011111=>2
[2,1,4,6,8,5,3,7]=>0100000=>1011111=>2
[2,4,6,1,8,5,3,7]=>0000000=>1111111=>1
[2,4,6,8,1,5,3,7]=>0000000=>1111111=>1
[4,2,6,8,5,1,3,7]=>0000000=>1111111=>1
[2,4,6,8,3,5,7,1]=>0000000=>1111111=>1
[2,4,6,8,3,5,1,7]=>0000000=>1111111=>1
[2,4,6,8,3,1,5,7]=>0000000=>1111111=>1
[2,4,6,3,1,8,5,7]=>0000000=>1111111=>1
[2,4,6,3,8,1,5,7]=>0000000=>1111111=>1
[2,4,6,3,8,5,1,7]=>0000000=>1111111=>1
[2,4,6,3,8,5,7,1]=>0000000=>1111111=>1
[2,4,3,6,8,5,7,1]=>0000000=>1111111=>1
[2,4,3,6,8,5,1,7]=>0000000=>1111111=>1
[2,4,3,6,8,1,5,7]=>0000000=>1111111=>1
[2,4,3,6,1,8,7,5]=>0000000=>1111111=>1
[2,4,3,6,8,1,7,5]=>0000000=>1111111=>1
[4,6,5,2,8,7,1,3]=>0000000=>1111111=>1
[2,4,6,3,8,1,7,5]=>0000000=>1111111=>1
[2,4,6,8,1,3,7,5]=>0000000=>1111111=>1
[2,4,6,8,3,1,7,5]=>0000000=>1111111=>1
[6,2,4,8,7,1,3,5]=>0000000=>1111111=>1
[6,4,2,8,7,5,3,1]=>0000000=>1111111=>1
[2,6,4,8,1,7,5,3]=>0000000=>1111111=>1
[2,6,4,1,8,7,5,3]=>0000000=>1111111=>1
[2,6,1,4,8,7,5,3]=>0000000=>1111111=>1
[2,1,6,4,8,7,5,3]=>0100000=>1011111=>2
[2,6,1,4,8,7,3,5]=>0000000=>1111111=>1
[6,4,2,8,7,5,1,3]=>0000000=>1111111=>1
[1,6,4,7,3,8,2,5]=>1000000=>0111111=>1
[1,3,7,4,5,8,2,6]=>1000000=>0111111=>1
[5,2,4,7,3,6,8,1]=>0000000=>1111111=>1
[1,7,6,3,4,8,2,5]=>1000000=>0111111=>1
[8,1,6,3,7,2,4,5]=>0000000=>1111111=>1
[7,1,6,3,8,2,4,5]=>0000000=>1111111=>1
[1,2,7,4,8,3,5,6]=>1100000=>0011111=>1
[6,1,7,3,4,8,2,5]=>0000000=>1111111=>1
[2,1,7,4,5,8,3,6]=>0100000=>1011111=>2
[5,1,4,7,3,8,2,6]=>0000000=>1111111=>1
[4,3,1,7,5,8,2,6]=>0000000=>1111111=>1
[2,8,6,3,7,1,4,5]=>0000000=>1111111=>1
[6,8,1,3,7,2,4,5]=>0000000=>1111111=>1
[5,8,2,1,7,3,4,6]=>0000000=>1111111=>1
[5,7,2,1,8,3,4,6]=>0000000=>1111111=>1
[6,7,1,3,8,2,4,5]=>0000000=>1111111=>1
[5,1,2,4,8,3,6,7]=>0000000=>1111111=>1
[4,3,6,1,5,8,2,7]=>0000000=>1111111=>1
[2,6,1,4,5,8,3,7]=>0000000=>1111111=>1
[6,5,1,3,4,8,2,7]=>0000000=>1111111=>1
[1,6,2,4,8,3,5,7]=>1000000=>0111111=>1
[8,5,1,3,7,2,4,6]=>0000000=>1111111=>1
[1,5,3,2,8,4,6,7]=>1000000=>0111111=>1
[6,4,2,1,5,8,3,7]=>0000000=>1111111=>1
[2,5,3,4,1,8,6,7]=>0000100=>1111011=>2
[4,3,5,2,1,8,6,7]=>0000100=>1111011=>2
[2,6,4,8,7,1,3,5]=>0000000=>1111111=>1
[1,6,4,8,7,2,3,5]=>1000000=>0111111=>1
[2,7,8,3,6,1,4,5]=>0000000=>1111111=>1
[4,3,2,8,7,1,5,6]=>0000000=>1111111=>1
[5,2,4,8,7,1,3,6]=>0000000=>1111111=>1
[6,2,8,3,7,1,4,5]=>0000000=>1111111=>1
[5,1,4,8,7,2,3,6]=>0000000=>1111111=>1
[4,8,2,5,1,3,7,6]=>0000000=>1111111=>1
[4,7,2,5,1,3,8,6]=>0000000=>1111111=>1
[3,7,2,1,5,4,8,6]=>0000000=>1111111=>1
[3,8,2,1,5,4,7,6]=>0000000=>1111111=>1
[8,3,2,1,5,4,6,7]=>0000000=>1111111=>1
[8,3,2,1,6,4,5,7]=>0000000=>1111111=>1
[8,4,2,5,1,6,3,7]=>0000000=>1111111=>1
[8,3,2,1,5,6,4,7]=>0000000=>1111111=>1
[8,3,2,1,4,6,5,7]=>0000000=>1111111=>1
[3,8,2,1,4,5,7,6]=>0000000=>1111111=>1
[3,7,2,1,4,5,8,6]=>0000000=>1111111=>1
[3,2,7,1,4,6,8,5]=>0000000=>1111111=>1
[3,2,8,1,4,6,7,5]=>0000000=>1111111=>1
[3,2,8,1,4,7,6,5]=>0000000=>1111111=>1
[3,8,2,1,4,7,5,6]=>0000000=>1111111=>1
[3,8,2,1,5,7,4,6]=>0000000=>1111111=>1
[4,8,2,5,1,7,3,6]=>0000000=>1111111=>1
[4,7,2,5,1,8,3,6]=>0000000=>1111111=>1
[3,7,2,1,5,8,4,6]=>0000000=>1111111=>1
[3,7,2,1,4,8,5,6]=>0000000=>1111111=>1
[3,2,1,7,5,8,6,4]=>0010000=>1101111=>2
[3,2,7,1,6,8,4,5]=>0000000=>1111111=>1
[4,2,7,6,1,8,3,5]=>0000000=>1111111=>1
[4,3,7,6,8,1,2,5]=>0000000=>1111111=>1
[4,3,8,6,7,1,2,5]=>0000000=>1111111=>1
[4,2,8,6,1,7,3,5]=>0000000=>1111111=>1
[3,2,8,1,6,7,4,5]=>0000000=>1111111=>1
[3,2,1,8,7,5,6,4]=>0010000=>1101111=>2
[3,8,2,1,7,4,5,6]=>0000000=>1111111=>1
[3,2,8,1,7,4,6,5]=>0000000=>1111111=>1
[3,2,8,1,6,4,7,5]=>0000000=>1111111=>1
[3,2,7,1,6,4,8,5]=>0000000=>1111111=>1
[4,2,7,6,1,3,8,5]=>0000000=>1111111=>1
[4,2,8,6,1,3,7,5]=>0000000=>1111111=>1
[4,2,8,7,1,3,6,5]=>0000000=>1111111=>1
[5,7,8,3,4,1,2,6]=>0000000=>1111111=>1
[4,2,7,8,1,3,6,5]=>0000000=>1111111=>1
[4,2,6,8,1,3,7,5]=>0000000=>1111111=>1
[4,2,6,7,1,3,8,5]=>0000000=>1111111=>1
[3,2,6,1,8,4,7,5]=>0000000=>1111111=>1
[3,7,2,1,8,4,5,6]=>0000000=>1111111=>1
[3,7,2,1,8,5,4,6]=>0000000=>1111111=>1
[4,7,3,8,5,1,2,6]=>0000000=>1111111=>1
[4,3,7,8,6,1,2,5]=>0000000=>1111111=>1
[3,2,7,1,8,6,4,5]=>0000000=>1111111=>1
[3,2,1,6,8,5,7,4]=>0010000=>1101111=>2
[3,2,6,1,8,7,4,5]=>0000000=>1111111=>1
[4,2,6,8,1,7,3,5]=>0000000=>1111111=>1
[4,3,6,8,7,1,2,5]=>0000000=>1111111=>1
[4,2,6,7,1,8,3,5]=>0000000=>1111111=>1
[3,2,6,1,7,8,4,5]=>0000000=>1111111=>1
[3,4,6,8,7,5,1,2]=>0000000=>1111111=>1
[5,3,6,4,8,7,1,2]=>0000000=>1111111=>1
[1,4,6,2,7,8,5,3]=>1000000=>0111111=>1
[3,1,8,5,4,2,6,7]=>0000000=>1111111=>1
[1,2,7,5,4,8,6,3]=>1100000=>0011111=>1
[6,3,7,5,4,8,1,2]=>0000000=>1111111=>1
[7,3,8,5,4,6,1,2]=>0000000=>1111111=>1
[3,8,7,5,4,6,1,2]=>0000000=>1111111=>1
[4,3,6,7,8,5,1,2]=>0000000=>1111111=>1
[4,5,6,3,8,7,1,2]=>0000000=>1111111=>1
[3,6,8,5,4,7,1,2]=>0000000=>1111111=>1
[6,8,3,5,4,7,1,2]=>0000000=>1111111=>1
[7,6,3,5,4,8,1,2]=>0000000=>1111111=>1
[1,6,2,5,4,8,7,3]=>1000000=>0111111=>1
[7,1,2,5,8,3,6,4]=>0000000=>1111111=>1
[1,8,2,5,7,3,6,4]=>1000000=>0111111=>1
[6,2,1,5,4,8,7,3]=>0000000=>1111111=>1
[4,1,6,2,8,7,5,3]=>0000000=>1111111=>1
[7,8,1,2,4,6,5,3]=>0000000=>1111111=>1
[7,8,3,1,4,2,6,5]=>0000000=>1111111=>1
[4,3,6,1,8,2,7,5]=>0000000=>1111111=>1
[2,3,8,5,4,1,6,7]=>0000000=>1111111=>1
[4,8,1,5,2,3,7,6]=>0000000=>1111111=>1
[7,5,1,6,4,3,2,8]=>0000001=>1111110=>1
[5,8,1,6,4,3,2,7]=>0000000=>1111111=>1
[6,1,5,7,4,3,2,8]=>0000001=>1111110=>1
[1,5,8,6,4,3,2,7]=>1000000=>0111111=>1
[3,4,6,1,5,8,2,7]=>0000000=>1111111=>1
[7,8,4,1,5,3,2,6]=>0000000=>1111111=>1
[7,8,5,1,6,3,2,4]=>0000000=>1111111=>1
[2,6,1,5,7,3,8,4]=>0000000=>1111111=>1
[1,6,8,7,4,3,2,5]=>1000000=>0111111=>1
[6,8,1,7,4,3,2,5]=>0000000=>1111111=>1
[5,6,1,7,4,3,2,8]=>0000001=>1111110=>1
[5,1,7,6,4,3,2,8]=>0000001=>1111110=>1
[6,1,7,8,4,3,2,5]=>0000000=>1111111=>1
[7,1,8,6,4,3,2,5]=>0000000=>1111111=>1
[1,8,7,6,4,3,2,5]=>1000000=>0111111=>1
[2,1,7,5,6,3,8,4]=>0100000=>1011111=>2
[3,1,6,7,5,8,2,4]=>0000000=>1111111=>1
[7,8,1,6,5,3,2,4]=>0000000=>1111111=>1
[7,8,2,1,4,5,6,3]=>0000000=>1111111=>1
[2,8,1,5,4,6,7,3]=>0000000=>1111111=>1
[7,2,1,5,4,6,8,3]=>0000000=>1111111=>1
[1,2,8,5,6,3,7,4]=>1100000=>0011111=>1
[6,1,2,5,7,3,8,4]=>0000000=>1111111=>1
[4,2,1,5,6,3,7,8]=>0000011=>1111100=>1
[4,3,6,1,5,7,2,8]=>0000001=>1111110=>1
[5,1,6,3,7,8,2,4]=>0000000=>1111111=>1
[1,3,6,8,5,7,2,4]=>1000000=>0111111=>1
[2,4,6,3,7,1,8,5]=>0000000=>1111111=>1
[1,3,6,4,8,7,2,5]=>1000000=>0111111=>1
[4,1,6,7,3,8,2,5]=>0000000=>1111111=>1
[5,4,6,1,3,7,2,8]=>0000001=>1111110=>1
[6,4,1,5,2,3,7,8]=>0000011=>1111100=>1
[4,1,7,5,2,3,8,6]=>0000000=>1111111=>1
[1,2,4,5,8,3,7,6]=>1100000=>0011111=>1
[7,2,3,5,4,1,8,6]=>0000000=>1111111=>1
[2,8,3,5,4,1,7,6]=>0000000=>1111111=>1
[4,2,6,3,8,1,7,5]=>0000000=>1111111=>1
[7,8,2,3,4,1,6,5]=>0000000=>1111111=>1
[7,8,1,4,6,3,2,5]=>0000000=>1111111=>1
[3,1,6,4,7,8,2,5]=>0000000=>1111111=>1
[1,8,5,7,4,3,2,6]=>1000000=>0111111=>1
[7,1,5,8,4,3,2,6]=>0000000=>1111111=>1
[5,1,8,7,4,3,2,6]=>0000000=>1111111=>1
[6,5,1,8,4,3,2,7]=>0000000=>1111111=>1
[6,5,7,1,4,3,2,8]=>0000001=>1111110=>1
[7,5,8,1,4,3,2,6]=>0000000=>1111111=>1
[5,8,7,1,4,3,2,6]=>0000000=>1111111=>1
[1,5,7,8,4,3,2,6]=>1000000=>0111111=>1
[2,4,7,5,1,3,8,6]=>0000000=>1111111=>1
[7,8,4,6,1,3,2,5]=>0000000=>1111111=>1
[7,8,5,4,1,3,2,6]=>0000000=>1111111=>1
[3,5,6,4,1,8,2,7]=>0000000=>1111111=>1
[2,6,4,5,1,3,8,7]=>0000010=>1111101=>2
[1,6,5,8,4,3,2,7]=>1000000=>0111111=>1
[6,8,5,1,4,3,2,7]=>0000000=>1111111=>1
[7,6,5,1,4,3,2,8]=>0000001=>1111110=>1
[1,2,3,4,5,6,9,7,8]=>11111100=>00000011=>1
[1,2,3,4,5,8,6,9,7]=>11111000=>00000111=>1
[1,4,2,5,6,7,8,9,3]=>10000000=>01111111=>1
[9,8,1,2,3,4,5,6,7]=>00000000=>11111111=>1
[7,8,9,1,2,3,4,5,6]=>00000000=>11111111=>1
[9,8,7,1,2,3,4,5,6]=>00000000=>11111111=>1
[6,7,8,9,1,2,3,4,5]=>00000000=>11111111=>1
[9,6,7,8,1,2,3,4,5]=>00000000=>11111111=>1
[8,9,6,7,1,2,3,4,5]=>00000000=>11111111=>1
[9,8,6,7,1,2,3,4,5]=>00000000=>11111111=>1
[9,8,7,6,1,2,3,4,5]=>00000000=>11111111=>1
[9,5,6,7,8,1,2,3,4]=>00000000=>11111111=>1
[8,9,5,6,7,1,2,3,4]=>00000000=>11111111=>1
[9,8,5,6,7,1,2,3,4]=>00000000=>11111111=>1
[9,7,8,5,6,1,2,3,4]=>00000000=>11111111=>1
[9,8,7,5,6,1,2,3,4]=>00000000=>11111111=>1
[9,8,7,6,5,1,2,3,4]=>00000000=>11111111=>1
[7,8,9,4,5,6,1,2,3]=>00000000=>11111111=>1
[9,7,8,4,5,6,1,2,3]=>00000000=>11111111=>1
[9,8,7,4,5,6,1,2,3]=>00000000=>11111111=>1
[8,9,6,7,4,5,1,2,3]=>00000000=>11111111=>1
[9,8,6,7,4,5,1,2,3]=>00000000=>11111111=>1
[9,8,7,6,4,5,1,2,3]=>00000000=>11111111=>1
[9,8,7,6,5,4,1,2,3]=>00000000=>11111111=>1
[9,7,8,5,6,3,4,1,2]=>00000000=>11111111=>1
[9,8,7,5,6,3,4,1,2]=>00000000=>11111111=>1
[9,8,7,6,5,3,4,1,2]=>00000000=>11111111=>1
[9,8,7,6,5,4,3,1,2]=>00000000=>11111111=>1
[9,10,1,2,3,4,5,6,7,8]=>000000000=>111111111=>1
[8,9,10,1,2,3,4,5,6,7]=>000000000=>111111111=>1
[10,8,9,1,2,3,4,5,6,7]=>000000000=>111111111=>1
[10,9,8,1,2,3,4,5,6,7]=>000000000=>111111111=>1
[7,8,9,10,1,2,3,4,5,6]=>000000000=>111111111=>1
[10,7,8,9,1,2,3,4,5,6]=>000000000=>111111111=>1
[9,10,7,8,1,2,3,4,5,6]=>000000000=>111111111=>1
[10,9,7,8,1,2,3,4,5,6]=>000000000=>111111111=>1
[10,9,8,7,1,2,3,4,5,6]=>000000000=>111111111=>1
[10,6,7,8,9,1,2,3,4,5]=>000000000=>111111111=>1
[9,10,6,7,8,1,2,3,4,5]=>000000000=>111111111=>1
[10,9,6,7,8,1,2,3,4,5]=>000000000=>111111111=>1
[10,8,9,6,7,1,2,3,4,5]=>000000000=>111111111=>1
[10,9,8,6,7,1,2,3,4,5]=>000000000=>111111111=>1
[10,9,8,7,6,1,2,3,4,5]=>000000000=>111111111=>1
[9,10,5,6,7,8,1,2,3,4]=>000000000=>111111111=>1
[10,9,5,6,7,8,1,2,3,4]=>000000000=>111111111=>1
[8,9,10,5,6,7,1,2,3,4]=>000000000=>111111111=>1
[10,9,8,5,6,7,1,2,3,4]=>000000000=>111111111=>1
[9,10,7,8,5,6,1,2,3,4]=>000000000=>111111111=>1
[10,9,7,8,5,6,1,2,3,4]=>000000000=>111111111=>1
[10,9,8,7,5,6,1,2,3,4]=>000000000=>111111111=>1
[10,9,8,7,6,5,1,2,3,4]=>000000000=>111111111=>1
[10,7,8,9,4,5,6,1,2,3]=>000000000=>111111111=>1
[9,10,7,8,4,5,6,1,2,3]=>000000000=>111111111=>1
[10,9,7,8,4,5,6,1,2,3]=>000000000=>111111111=>1
[10,9,8,7,4,5,6,1,2,3]=>000000000=>111111111=>1
[10,8,9,6,7,4,5,1,2,3]=>000000000=>111111111=>1
[10,9,8,6,7,4,5,1,2,3]=>000000000=>111111111=>1
[10,9,8,7,6,4,5,1,2,3]=>000000000=>111111111=>1
[10,9,8,7,6,5,4,1,2,3]=>000000000=>111111111=>1
[9,10,7,8,5,6,3,4,1,2]=>000000000=>111111111=>1
[10,9,7,8,5,6,3,4,1,2]=>000000000=>111111111=>1
[10,9,8,7,5,6,3,4,1,2]=>000000000=>111111111=>1
[10,9,8,7,6,5,3,4,1,2]=>000000000=>111111111=>1
[10,9,8,7,6,5,4,3,1,2]=>000000000=>111111111=>1
[3,4,6,2,7,1,5,8]=>0000001=>1111110=>1
[3,6,2,5,4,1,7,8]=>0000011=>1111100=>1
[3,2,7,5,4,1,6,8]=>0000001=>1111110=>1
[4,3,6,2,8,1,5,7]=>0000000=>1111111=>1
[6,1,2,5,4,7,8,3]=>0000000=>1111111=>1
[6,2,4,5,1,3,7,8]=>0000011=>1111100=>1
[4,2,8,5,1,3,7,6]=>0000000=>1111111=>1
[4,3,6,8,1,7,2,5]=>0000000=>1111111=>1
[5,3,6,4,1,7,2,8]=>0000001=>1111110=>1
[6,2,1,5,8,3,7,4]=>0000000=>1111111=>1
[1,6,7,4,8,3,5,2]=>1000000=>0111111=>1
[1,4,6,3,7,5,8,2]=>1000000=>0111111=>1
[4,6,7,2,5,8,1,3]=>0000000=>1111111=>1
[2,4,6,1,7,5,3,8]=>0000001=>1111110=>1
[2,7,5,4,1,6,3,8]=>0000001=>1111110=>1
[7,5,4,6,2,8,1,3]=>0000000=>1111111=>1
[1,7,5,4,3,8,6,2]=>1000000=>0111111=>1
[1,4,6,3,5,8,7,2]=>1000000=>0111111=>1
[1,5,8,4,3,6,7,2]=>1000000=>0111111=>1
[5,4,6,2,7,8,1,3]=>0000000=>1111111=>1
[2,5,4,1,6,7,3,8]=>0000001=>1111110=>1
[5,6,3,2,7,1,4,8]=>0000001=>1111110=>1
[5,6,3,2,7,1,8,4]=>0000000=>1111111=>1
[8,5,6,3,2,7,1,4]=>0000000=>1111111=>1
[5,4,6,2,8,1,7,3]=>0000000=>1111111=>1
[2,4,1,7,8,5,3,6]=>0000000=>1111111=>1
[2,5,4,1,6,3,8,7]=>0000010=>1111101=>2
[5,6,3,2,1,8,4,7]=>0000000=>1111111=>1
[3,5,2,1,6,4,7,8]=>0000011=>1111100=>1
[6,8,4,3,2,1,5,7]=>0000000=>1111111=>1
[5,3,8,2,1,6,4,7]=>0000000=>1111111=>1
[3,7,5,8,2,1,4,6]=>0000000=>1111111=>1
[7,3,2,8,5,1,6,4]=>0000000=>1111111=>1
[8,4,6,3,2,1,7,5]=>0000000=>1111111=>1
[8,6,4,3,2,1,7,5]=>0000000=>1111111=>1
[7,6,4,3,2,1,8,5]=>0000000=>1111111=>1
[7,8,4,3,2,1,6,5]=>0000000=>1111111=>1
[5,4,7,2,1,8,6,3]=>0000000=>1111111=>1
[7,5,8,3,2,6,1,4]=>0000000=>1111111=>1
[5,7,3,2,1,6,8,4]=>0000000=>1111111=>1
[5,7,3,2,1,6,4,8]=>0000001=>1111110=>1
[6,3,7,2,5,1,8,4]=>0000000=>1111111=>1
[6,7,8,3,5,2,1,4]=>0000000=>1111111=>1
[6,2,5,7,8,4,1,3]=>0000000=>1111111=>1
[2,1,5,7,8,6,3,4]=>0100000=>1011111=>2
[3,6,7,2,8,1,4,5]=>0000000=>1111111=>1
[6,3,7,2,8,1,4,5]=>0000000=>1111111=>1
[3,2,6,1,7,4,5,8]=>0000001=>1111110=>1
[3,5,2,1,4,7,6,8]=>0000101=>1111010=>2
[7,3,5,2,1,8,4,6]=>0000000=>1111111=>1
[2,5,4,1,3,7,8,6]=>0000100=>1111011=>2
[2,5,8,4,1,3,7,6]=>0000000=>1111111=>1
[2,4,1,7,8,3,6,5]=>0000000=>1111111=>1
[3,7,2,8,6,1,4,5]=>0000000=>1111111=>1
[3,6,8,2,1,7,4,5]=>0000000=>1111111=>1
[5,3,8,2,1,4,7,6]=>0000000=>1111111=>1
[4,8,7,3,2,1,5,6]=>0000000=>1111111=>1
[4,7,3,2,1,5,6,8]=>0000001=>1111110=>1
[8,4,7,3,2,1,5,6]=>0000000=>1111111=>1
[8,3,5,2,1,4,7,6]=>0000000=>1111111=>1
[7,3,2,8,6,1,4,5]=>0000000=>1111111=>1
[3,5,2,1,4,6,8,7]=>0000110=>1111001=>2
[7,8,6,5,4,3,2,1,9]=>00000001=>11111110=>1
[8,9,7,6,5,4,3,2,1,10]=>000000001=>111111110=>1
[7,6,8,5,4,3,2,1,9]=>00000001=>11111110=>1
[7,8,3,5,4,6,1,2]=>0000000=>1111111=>1
[8,6,3,7,5,2,4,1]=>0000000=>1111111=>1
[5,4,1,6,2,3,8,7]=>0000010=>1111101=>2
[5,7,1,6,2,8,3,4]=>0000000=>1111111=>1
[2,7,6,5,1,8,3,4]=>0000000=>1111111=>1
[2,7,6,5,1,8,4,3]=>0000000=>1111111=>1
[2,3,6,1,5,4,8,7]=>0000010=>1111101=>2
[7,3,5,1,8,4,2,6]=>0000000=>1111111=>1
[7,3,5,1,8,6,4,2]=>0000000=>1111111=>1
[2,3,4,8,7,6,1,5]=>0000000=>1111111=>1
[2,1,4,5,8,7,3,6]=>0100000=>1011111=>2
[6,4,3,5,8,7,1,2]=>0000000=>1111111=>1
[7,3,5,4,8,1,6,2]=>0000000=>1111111=>1
[2,7,6,5,4,8,1,3]=>0000000=>1111111=>1
[7,4,1,5,8,2,3,6]=>0000000=>1111111=>1
[6,3,5,7,8,2,4,1]=>0000000=>1111111=>1
[2,7,6,4,5,8,3,1]=>0000000=>1111111=>1
[5,7,3,6,1,8,4,2]=>0000000=>1111111=>1
[2,1,4,5,8,6,3,7]=>0100000=>1011111=>2
[2,3,4,8,7,1,6,5]=>0000000=>1111111=>1
[2,3,4,8,1,7,6,5]=>0000000=>1111111=>1
[6,3,5,4,8,2,7,1]=>0000000=>1111111=>1
[2,1,4,5,8,3,7,6]=>0100000=>1011111=>2
[2,3,4,8,1,6,5,7]=>0000000=>1111111=>1
[2,3,4,8,1,5,7,6]=>0000000=>1111111=>1
[7,8,2,6,1,5,3,4]=>0000000=>1111111=>1
[7,8,1,6,2,5,3,4]=>0000000=>1111111=>1
[1,8,6,7,2,5,3,4]=>1000000=>0111111=>1
[1,8,5,7,2,6,3,4]=>1000000=>0111111=>1
[5,8,1,7,2,6,3,4]=>0000000=>1111111=>1
[5,8,2,7,1,6,3,4]=>0000000=>1111111=>1
[2,8,6,7,1,5,3,4]=>0000000=>1111111=>1
[2,8,5,7,1,6,3,4]=>0000000=>1111111=>1
[2,8,1,7,5,6,3,4]=>0000000=>1111111=>1
[1,8,2,7,5,6,3,4]=>1000000=>0111111=>1
[1,8,2,7,4,6,3,5]=>1000000=>0111111=>1
[2,8,1,7,4,6,3,5]=>0000000=>1111111=>1
[2,8,4,7,1,6,3,5]=>0000000=>1111111=>1
[4,8,2,7,1,6,3,5]=>0000000=>1111111=>1
[4,8,1,7,2,6,3,5]=>0000000=>1111111=>1
[1,8,4,7,2,6,3,5]=>1000000=>0111111=>1
[4,8,1,7,5,6,2,3]=>0000000=>1111111=>1
[1,8,4,7,5,6,2,3]=>1000000=>0111111=>1
[1,8,3,7,5,6,2,4]=>1000000=>0111111=>1
[3,8,1,7,5,6,2,4]=>0000000=>1111111=>1
[3,8,1,7,4,6,2,5]=>0000000=>1111111=>1
[1,8,3,7,4,6,2,5]=>1000000=>0111111=>1
[1,8,3,7,2,6,4,5]=>1000000=>0111111=>1
[3,8,1,7,2,6,4,5]=>0000000=>1111111=>1
[3,8,2,7,1,6,4,5]=>0000000=>1111111=>1
[3,8,2,7,4,6,1,5]=>0000000=>1111111=>1
[3,8,2,7,5,6,1,4]=>0000000=>1111111=>1
[4,8,2,7,5,6,1,3]=>0000000=>1111111=>1
[4,8,3,7,5,6,1,2]=>0000000=>1111111=>1
[3,8,4,7,5,6,1,2]=>0000000=>1111111=>1
[2,8,4,7,5,6,1,3]=>0000000=>1111111=>1
[2,8,3,7,5,6,1,4]=>0000000=>1111111=>1
[2,8,3,7,4,6,1,5]=>0000000=>1111111=>1
[2,8,3,7,1,6,4,5]=>0000000=>1111111=>1
[2,8,1,7,3,6,4,5]=>0000000=>1111111=>1
[7,5,2,8,6,4,1,3]=>0000000=>1111111=>1
[7,5,1,8,6,2,3,4]=>0000000=>1111111=>1
[7,4,8,6,1,5,2,3]=>0000000=>1111111=>1
[7,1,8,4,5,2,6,3]=>0000000=>1111111=>1
[6,8,1,7,4,2,5,3]=>0000000=>1111111=>1
[1,6,7,4,2,8,5,3]=>1000000=>0111111=>1
[1,6,7,3,8,5,2,4]=>1000000=>0111111=>1
[7,1,8,3,5,6,2,4]=>0000000=>1111111=>1
[7,3,8,6,2,5,1,4]=>0000000=>1111111=>1
[7,4,2,8,6,1,3,5]=>0000000=>1111111=>1
[7,3,1,8,4,2,5,6]=>0000000=>1111111=>1
[7,2,8,4,1,5,3,6]=>0000000=>1111111=>1
[7,2,8,3,5,1,6,4]=>0000000=>1111111=>1
[7,2,8,3,4,6,1,5]=>0000000=>1111111=>1
[1,5,7,8,2,6,3,4]=>1000000=>0111111=>1
[6,2,3,8,5,7,4,1]=>0000000=>1111111=>1
[6,2,4,8,5,3,1,7]=>0000000=>1111111=>1
[6,3,1,4,8,5,2,7]=>0000000=>1111111=>1
[2,6,3,7,8,5,4,1]=>0000000=>1111111=>1
[2,6,3,7,8,4,5,1]=>0000000=>1111111=>1
[2,4,7,3,5,6,8,1]=>0000000=>1111111=>1
[2,4,7,3,6,8,5,1]=>0000000=>1111111=>1
[2,5,3,7,8,1,6,4]=>0000000=>1111111=>1
[3,1,5,4,7,8,2,6]=>0000000=>1111111=>1
[5,3,1,4,8,2,6,7]=>0000000=>1111111=>1
[5,2,4,8,6,1,3,7]=>0000000=>1111111=>1
[5,2,3,8,4,6,7,1]=>0000000=>1111111=>1
[4,8,2,3,6,1,7,5]=>0000000=>1111111=>1
[4,8,2,3,5,7,1,6]=>0000000=>1111111=>1
[1,4,7,8,3,6,2,5]=>1000000=>0111111=>1
[4,8,1,3,6,7,2,5]=>0000000=>1111111=>1
[5,3,8,2,4,7,1,6]=>0000000=>1111111=>1
[5,4,3,8,1,2,7,6]=>0000000=>1111111=>1
[6,4,2,8,1,3,7,5]=>0000000=>1111111=>1
[6,3,8,2,5,1,7,4]=>0000000=>1111111=>1
[6,3,8,1,4,7,2,5]=>0000000=>1111111=>1
[5,8,1,3,6,2,7,4]=>0000000=>1111111=>1
[1,5,7,4,2,6,8,3]=>1000000=>0111111=>1
[5,8,1,4,2,6,3,7]=>0000000=>1111111=>1
[5,8,4,1,2,7,6,3]=>0000000=>1111111=>1
[6,5,1,2,8,7,3,4]=>0000000=>1111111=>1
[6,5,3,1,4,2,8,7]=>0000010=>1111101=>2
[5,3,1,6,4,2,7,8]=>0000011=>1111100=>1
[5,2,6,4,1,7,3,8]=>0000001=>1111110=>1
[4,6,1,7,5,2,8,3]=>0000000=>1111111=>1
[4,5,1,7,2,6,3,8]=>0000001=>1111110=>1
[3,5,6,1,2,8,7,4]=>0000000=>1111111=>1
[3,5,7,1,8,6,2,4]=>0000000=>1111111=>1
[3,6,2,7,5,1,8,4]=>0000000=>1111111=>1
[4,2,5,7,1,8,6,3]=>0000000=>1111111=>1
[3,4,7,2,8,6,1,5]=>0000000=>1111111=>1
[3,4,5,8,2,7,1,6]=>0000000=>1111111=>1
[3,4,6,2,8,1,5,7]=>0000000=>1111111=>1
[3,5,2,6,8,1,7,4]=>0000000=>1111111=>1
[4,2,5,6,1,3,8,7]=>0000010=>1111101=>2
[4,3,1,2,5,6,8,7]=>0001110=>1110001=>2
[5,3,6,8,4,7,2,1]=>0000000=>1111111=>1
[3,7,2,5,4,8,6,1]=>0000000=>1111111=>1
[8,4,2,5,7,3,6,1]=>0000000=>1111111=>1
[4,7,2,5,8,3,6,1]=>0000000=>1111111=>1
[5,2,6,8,4,3,7,1]=>0000000=>1111111=>1
[3,1,6,5,4,8,2,7]=>0000000=>1111111=>1
[4,1,6,5,8,3,2,7]=>0000000=>1111111=>1
[5,1,6,8,4,3,2,7]=>0000000=>1111111=>1
[8,5,4,7,6,3,2,1]=>0000000=>1111111=>1
[5,7,1,8,4,3,2,6]=>0000000=>1111111=>1
[2,7,1,5,4,3,8,6]=>0000000=>1111111=>1
[8,2,1,5,4,3,7,6]=>0000000=>1111111=>1
[8,4,1,5,7,3,2,6]=>0000000=>1111111=>1
[8,5,6,7,1,3,2,4]=>0000000=>1111111=>1
[8,4,6,1,7,3,2,5]=>0000000=>1111111=>1
[8,3,6,1,4,7,2,5]=>0000000=>1111111=>1
[2,7,6,1,4,3,8,5]=>0000000=>1111111=>1
[6,7,8,5,1,3,2,4]=>0000000=>1111111=>1
[5,7,6,8,2,3,4,1]=>0000000=>1111111=>1
[5,7,2,8,4,3,6,1]=>0000000=>1111111=>1
[6,7,8,2,4,3,5,1]=>0000000=>1111111=>1
[4,7,6,2,8,3,5,1]=>0000000=>1111111=>1
[8,3,6,2,4,7,5,1]=>0000000=>1111111=>1
[3,7,6,2,4,8,5,1]=>0000000=>1111111=>1
[5,7,3,8,4,6,2,1]=>0000000=>1111111=>1
[4,7,3,5,8,6,2,1]=>0000000=>1111111=>1
[8,7,2,1,4,3,6,5]=>0000000=>1111111=>1
[8,7,3,1,4,6,2,5]=>0000000=>1111111=>1
[8,7,6,3,2,5,4,1]=>0000000=>1111111=>1
[8,7,3,5,1,6,2,4]=>0000000=>1111111=>1
[8,7,2,5,1,3,6,4]=>0000000=>1111111=>1
[8,2,6,5,1,3,7,4]=>0000000=>1111111=>1
[8,4,6,5,7,1,2,3]=>0000000=>1111111=>1
[5,7,6,8,4,1,2,3]=>0000000=>1111111=>1
[4,7,6,5,8,1,2,3]=>0000000=>1111111=>1
[3,7,6,5,1,8,2,4]=>0000000=>1111111=>1
[8,1,2,3,4,5,6,7,9]=>00000001=>11111110=>1
[1,9,2,3,4,5,6,7,8]=>10000000=>01111111=>1
[9,1,2,3,4,5,6,7,8,10]=>000000001=>111111110=>1
[1,8,9,2,3,4,5,6,7]=>10000000=>01111111=>1
[1,10,2,3,4,5,6,7,8,9]=>100000000=>011111111=>1
[10,1,2,3,4,5,6,7,8,9,11]=>0000000001=>1111111110=>1
[1,11,2,3,4,5,6,7,8,9,10]=>1000000000=>0111111111=>1
[3,6,4,8,7,5,1,2]=>0000000=>1111111=>1
[5,6,4,3,8,7,1,2]=>0000000=>1111111=>1
[1,6,2,4,7,8,5,3]=>1000000=>0111111=>1
[3,6,2,4,8,1,5,7]=>0000000=>1111111=>1
[3,4,7,2,8,1,6,5]=>0000000=>1111111=>1
[1,4,7,2,5,8,6,3]=>1000000=>0111111=>1
[7,3,8,4,5,6,1,2]=>0000000=>1111111=>1
[3,5,6,4,8,7,1,2]=>0000000=>1111111=>1
[4,6,8,5,3,7,1,2]=>0000000=>1111111=>1
[6,8,5,3,4,7,1,2]=>0000000=>1111111=>1
[1,6,5,4,2,8,7,3]=>1000000=>0111111=>1
[1,8,5,2,7,3,6,4]=>1000000=>0111111=>1
[4,2,7,5,1,8,6,3]=>0000000=>1111111=>1
[7,8,1,4,2,6,5,3]=>0000000=>1111111=>1
[1,3,6,4,8,2,5,7]=>1000000=>0111111=>1
[4,1,7,5,3,2,6,8]=>0000001=>1111110=>1
[6,5,1,3,4,2,8,7]=>0000010=>1111101=>2
[4,8,5,3,1,7,2,6]=>0000000=>1111111=>1
[7,4,5,3,2,8,1,6]=>0000000=>1111111=>1
[5,8,3,6,1,4,2,7]=>0000000=>1111111=>1
[2,5,8,6,4,1,3,7]=>0000000=>1111111=>1
[1,4,6,2,5,8,3,7]=>1000000=>0111111=>1
[3,6,2,5,8,1,7,4]=>0000000=>1111111=>1
[1,6,8,7,4,2,3,5]=>1000000=>0111111=>1
[6,1,7,8,2,4,3,5]=>0000000=>1111111=>1
[7,1,8,6,3,4,2,5]=>0000000=>1111111=>1
[7,2,1,4,5,6,8,3]=>0000000=>1111111=>1
[1,2,8,3,6,5,7,4]=>1100000=>0011111=>1
[6,1,3,2,7,5,8,4]=>0000000=>1111111=>1
[1,6,3,8,5,7,2,4]=>1000000=>0111111=>1
[2,6,4,1,7,5,8,3]=>0000000=>1111111=>1
[7,6,5,8,1,4,2,3]=>0000000=>1111111=>1
[5,8,6,7,3,2,1,4]=>0000000=>1111111=>1
[1,6,4,3,7,2,8,5]=>1000000=>0111111=>1
[2,6,3,4,8,7,1,5]=>0000000=>1111111=>1
[7,1,3,4,5,2,8,6]=>0000000=>1111111=>1
[1,8,3,5,4,2,7,6]=>1000000=>0111111=>1
[4,1,6,3,8,2,7,5]=>0000000=>1111111=>1
[7,8,2,4,6,3,1,5]=>0000000=>1111111=>1
[3,2,6,4,7,8,1,5]=>0000000=>1111111=>1
[2,8,5,7,4,3,1,6]=>0000000=>1111111=>1
[7,2,5,8,3,4,1,6]=>0000000=>1111111=>1
[5,3,8,7,1,2,6,4]=>0000000=>1111111=>1
[6,5,3,8,2,1,7,4]=>0000000=>1111111=>1
[7,5,8,4,1,2,3,6]=>0000000=>1111111=>1
[5,8,7,4,1,3,2,6]=>0000000=>1111111=>1
[3,5,7,8,4,1,2,6]=>0000000=>1111111=>1
[1,4,7,5,3,8,2,6]=>1000000=>0111111=>1
[2,4,6,7,3,1,8,5]=>0000000=>1111111=>1
[7,8,4,6,3,1,2,5]=>0000000=>1111111=>1
[2,6,4,5,3,8,1,7]=>0000000=>1111111=>1
[3,6,5,8,4,2,1,7]=>0000000=>1111111=>1
[5,6,8,4,2,3,1,7]=>0000000=>1111111=>1
[6,8,5,4,3,1,2,7]=>0000000=>1111111=>1
[6,1,4,2,8,5,7,3]=>0000000=>1111111=>1
[6,7,5,8,2,1,4,3]=>0000000=>1111111=>1
[1,3,8,5,7,6,2,4]=>1000000=>0111111=>1
[8,3,1,5,6,2,7,4]=>0000000=>1111111=>1
[2,8,1,5,6,3,7,4]=>0000000=>1111111=>1
[2,5,8,6,1,7,3,4]=>0000000=>1111111=>1
[8,6,1,5,7,2,3,4]=>0000000=>1111111=>1
[3,8,6,5,7,1,2,4]=>0000000=>1111111=>1
[7,6,5,8,1,2,4,3]=>0000000=>1111111=>1
[3,2,8,5,7,6,1,4]=>0000000=>1111111=>1
[4,2,1,3,6,7,8,5]=>0001000=>1110111=>2
[4,3,1,2,6,7,8,5]=>0001000=>1110111=>2
[8,1,6,5,7,3,2,4]=>0000000=>1111111=>1
[5,8,1,6,3,7,2,4]=>0000000=>1111111=>1
[1,7,6,5,4,2,8,3]=>1000000=>0111111=>1
[4,1,7,3,5,6,8,2]=>0000000=>1111111=>1
[1,8,3,6,5,7,2,4]=>1000000=>0111111=>1
[8,1,3,5,7,6,2,4]=>0000000=>1111111=>1
[7,8,5,4,1,6,2,3]=>0000000=>1111111=>1
[7,4,6,2,5,1,8,3]=>0000000=>1111111=>1
[7,2,6,4,5,1,8,3]=>0000000=>1111111=>1
[8,2,3,6,5,7,1,4]=>0000000=>1111111=>1
[5,4,7,3,6,8,1,2]=>0000000=>1111111=>1
[3,4,7,8,5,6,1,2]=>0000000=>1111111=>1
[3,4,7,2,5,1,6,8]=>0000001=>1111110=>1
[1,4,7,2,5,8,3,6]=>1000000=>0111111=>1
[3,6,2,4,7,1,5,8]=>0000001=>1111110=>1
[6,8,3,4,5,7,1,2]=>0000000=>1111111=>1
[4,3,6,7,5,8,1,2]=>0000000=>1111111=>1
[6,3,7,5,8,4,1,2]=>0000000=>1111111=>1
[7,3,8,6,4,5,1,2]=>0000000=>1111111=>1
[3,2,7,6,5,1,4,8]=>0000001=>1111110=>1
[1,2,7,6,5,8,3,4]=>1100000=>0011111=>1
[4,8,2,6,1,5,3,7]=>0000000=>1111111=>1
[2,3,8,6,4,1,5,7]=>0000000=>1111111=>1
[4,3,6,2,5,1,8,7]=>0000010=>1111101=>2
[7,8,3,2,5,1,4,6]=>0000000=>1111111=>1
[7,8,1,2,5,6,3,4]=>0000000=>1111111=>1
[4,1,6,2,5,7,3,8]=>0000001=>1111110=>1
[6,1,2,5,8,7,3,4]=>0000000=>1111111=>1
[2,1,8,6,4,7,3,5]=>0100000=>1011111=>2
[7,1,3,6,8,4,2,5]=>0000000=>1111111=>1
[1,8,3,6,7,4,5,2]=>1000000=>0111111=>1
[7,1,5,8,3,6,2,4]=>0000000=>1111111=>1
[5,1,8,7,2,3,6,4]=>0000000=>1111111=>1
[6,1,5,7,4,2,8,3]=>0000000=>1111111=>1
[3,1,6,4,7,2,5,8]=>0000001=>1111110=>1
[2,4,7,5,1,8,3,6]=>0000000=>1111111=>1
[6,5,7,1,4,2,3,8]=>0000001=>1111110=>1
[5,6,8,1,3,2,4,7]=>0000000=>1111111=>1
[6,8,5,1,3,4,2,7]=>0000000=>1111111=>1
[2,8,3,4,5,1,7,6]=>0000000=>1111111=>1
[6,2,4,3,1,5,7,8]=>0000011=>1111100=>1
[4,2,8,3,1,7,5,6]=>0000000=>1111111=>1
[1,3,7,4,8,2,5,6]=>1000000=>0111111=>1
[5,3,7,4,1,6,2,8]=>0000001=>1111110=>1
[2,4,7,3,6,1,8,5]=>0000000=>1111111=>1
[5,8,7,6,3,1,2,4]=>0000000=>1111111=>1
[7,5,6,8,1,4,3,2]=>0000000=>1111111=>1
[2,4,7,1,6,5,3,8]=>0000001=>1111110=>1
[1,2,7,8,5,4,3,6]=>1100000=>0011111=>1
[6,3,1,2,8,4,5,7]=>0000000=>1111111=>1
[4,2,1,3,6,5,8,7]=>0001010=>1110101=>3
[2,8,1,4,5,6,3,7]=>0000000=>1111111=>1
[7,2,1,5,4,6,3,8]=>0000001=>1111110=>1
[4,2,6,1,8,5,3,7]=>0000000=>1111111=>1
[7,8,2,1,4,5,3,6]=>0000000=>1111111=>1
[7,8,4,1,5,3,6,2]=>0000000=>1111111=>1
[3,4,6,1,5,8,7,2]=>0000000=>1111111=>1
[7,5,1,6,4,3,8,2]=>0000000=>1111111=>1
[5,8,1,6,3,4,7,2]=>0000000=>1111111=>1
[6,5,1,8,2,7,4,3]=>0000000=>1111111=>1
[6,8,1,7,5,2,3,4]=>0000000=>1111111=>1
[7,6,1,8,5,3,2,4]=>0000000=>1111111=>1
[5,6,1,7,4,8,2,3]=>0000000=>1111111=>1
[3,6,1,5,7,4,2,8]=>0000001=>1111110=>1
[2,5,6,1,7,4,8,3]=>0000000=>1111111=>1
[3,1,7,5,6,4,8,2]=>0000000=>1111111=>1
[5,1,7,6,4,8,3,2]=>0000000=>1111111=>1
[6,1,7,8,5,3,4,2]=>0000000=>1111111=>1
[7,1,8,6,5,4,2,3]=>0000000=>1111111=>1
[2,6,5,7,3,4,8,1]=>0000000=>1111111=>1
[1,6,4,7,5,8,2,3]=>1000000=>0111111=>1
[8,5,3,6,2,7,4,1]=>0000000=>1111111=>1
[1,3,7,4,6,8,2,5]=>1000000=>0111111=>1
[4,7,5,6,3,2,8,1]=>0000000=>1111111=>1
[1,7,6,5,4,8,2,3]=>1000000=>0111111=>1
[8,1,6,5,7,2,4,3]=>0000000=>1111111=>1
[1,2,7,6,8,3,4,5]=>1100000=>0011111=>1
[6,1,7,5,3,8,2,4]=>0000000=>1111111=>1
[2,1,7,5,6,8,3,4]=>0100000=>1011111=>2
[5,4,1,7,6,8,2,3]=>0000000=>1111111=>1
[4,8,5,6,2,7,3,1]=>0000000=>1111111=>1
[3,8,6,4,2,7,5,1]=>0000000=>1111111=>1
[7,8,5,2,4,6,3,1]=>0000000=>1111111=>1
[2,8,6,3,7,4,5,1]=>0000000=>1111111=>1
[7,8,1,6,2,4,5,3]=>0000000=>1111111=>1
[6,8,1,4,7,2,5,3]=>0000000=>1111111=>1
[3,8,4,1,7,2,6,5]=>0000000=>1111111=>1
[5,4,7,1,8,3,2,6]=>0000000=>1111111=>1
[3,7,4,1,8,5,2,6]=>0000000=>1111111=>1
[6,7,1,4,8,3,2,5]=>0000000=>1111111=>1
[2,7,1,8,4,5,3,6]=>0000000=>1111111=>1
[6,1,2,8,4,3,5,7]=>0000000=>1111111=>1
[6,5,1,4,3,8,2,7]=>0000000=>1111111=>1
[1,6,2,5,8,3,4,7]=>1000000=>0111111=>1
[8,5,1,3,7,2,6,4]=>0000000=>1111111=>1
[8,4,2,1,7,3,6,5]=>0000000=>1111111=>1
[7,4,2,1,8,5,3,6]=>0000000=>1111111=>1
[1,5,4,2,8,3,6,7]=>1000000=>0111111=>1
[6,4,3,1,5,8,2,7]=>0000000=>1111111=>1
[3,7,6,8,4,5,2,1]=>0000000=>1111111=>1
[2,7,6,8,5,3,4,1]=>0000000=>1111111=>1
[1,7,6,8,5,4,2,3]=>1000000=>0111111=>1
[1,4,8,6,7,5,2,3]=>1000000=>0111111=>1
[2,4,8,6,7,3,5,1]=>0000000=>1111111=>1
[7,3,8,5,4,6,2,1]=>0000000=>1111111=>1
[3,4,8,5,6,7,2,1]=>0000000=>1111111=>1
[6,3,5,8,4,7,2,1]=>0000000=>1111111=>1
[5,4,3,8,6,7,2,1]=>0000000=>1111111=>1
[5,4,2,8,7,3,6,1]=>0000000=>1111111=>1
[6,2,5,8,7,3,4,1]=>0000000=>1111111=>1
[3,2,8,5,7,4,6,1]=>0000000=>1111111=>1
[1,3,8,7,5,6,2,4]=>1000000=>0111111=>1
[2,1,8,7,4,6,3,5]=>0100000=>1011111=>2
[3,1,8,5,7,6,2,4]=>0000000=>1111111=>1
[6,1,5,8,7,4,2,3]=>0000000=>1111111=>1
[5,4,1,8,7,6,2,3]=>0000000=>1111111=>1
[5,8,6,7,4,3,2,1]=>0000000=>1111111=>1
[4,8,7,5,6,3,2,1]=>0000000=>1111111=>1
[4,2,1,6,3,5,8,7]=>0000010=>1111101=>2
[6,2,1,4,3,5,8,7]=>0000010=>1111101=>2
[6,2,1,4,3,8,5,7]=>0000000=>1111111=>1
[8,2,1,4,3,6,5,7]=>0000000=>1111111=>1
[6,2,4,1,3,5,8,7]=>0000010=>1111101=>2
[2,1,6,4,3,5,8,7]=>0100010=>1011101=>3
[6,4,2,1,3,5,8,7]=>0000010=>1111101=>2
[8,4,2,1,3,6,5,7]=>0000000=>1111111=>1
[8,4,2,1,6,3,5,7]=>0000000=>1111111=>1
[6,4,2,1,8,3,5,7]=>0000000=>1111111=>1
[2,6,1,4,3,8,5,7]=>0000000=>1111111=>1
[2,1,8,4,3,6,5,7]=>0100000=>1011111=>2
[4,8,2,1,3,6,5,7]=>0000000=>1111111=>1
[8,6,2,1,4,3,5,7]=>0000000=>1111111=>1
[2,8,1,4,6,3,5,7]=>0000000=>1111111=>1
[2,6,1,4,8,3,5,7]=>0000000=>1111111=>1
[2,6,4,1,8,3,5,7]=>0000000=>1111111=>1
[2,6,4,8,1,3,5,7]=>0000000=>1111111=>1
[4,6,2,8,1,3,5,7]=>0000000=>1111111=>1
[4,2,6,1,8,3,5,7]=>0000000=>1111111=>1
[6,2,4,1,8,3,5,7]=>0000000=>1111111=>1
[4,2,1,6,8,3,5,7]=>0000000=>1111111=>1
[4,2,1,6,3,8,5,7]=>0000000=>1111111=>1
[2,1,4,3,8,6,5,7]=>0101000=>1010111=>3
[4,2,1,3,8,6,5,7]=>0001000=>1110111=>2
[4,2,1,8,3,6,5,7]=>0000000=>1111111=>1
[8,2,1,6,4,3,5,7]=>0000000=>1111111=>1
[8,2,6,1,4,3,5,7]=>0000000=>1111111=>1
[4,2,8,1,3,6,5,7]=>0000000=>1111111=>1
[2,4,1,8,3,6,5,7]=>0000000=>1111111=>1
[2,4,8,1,6,3,5,7]=>0000000=>1111111=>1
[8,4,6,2,1,3,5,7]=>0000000=>1111111=>1
[4,6,8,2,1,3,5,7]=>0000000=>1111111=>1
[2,6,1,8,4,3,5,7]=>0000000=>1111111=>1
[2,1,8,6,4,3,5,7]=>0100000=>1011111=>2
[2,8,6,4,1,3,5,7]=>0000000=>1111111=>1
[4,8,6,2,1,3,5,7]=>0000000=>1111111=>1
[6,8,4,2,1,3,5,7]=>0000000=>1111111=>1
[3,2,6,1,5,4,8,7]=>0000010=>1111101=>2
[5,2,4,3,8,1,7,6]=>0000000=>1111111=>1
[4,3,6,1,5,2,8,7]=>0000010=>1111101=>2
[4,3,8,2,6,1,7,5]=>0000000=>1111111=>1
[4,3,8,1,7,2,6,5]=>0000000=>1111111=>1
[4,3,8,1,5,2,7,6]=>0000000=>1111111=>1
[2,1,5,4,8,3,7,6]=>0100000=>1011111=>2
[4,3,7,1,8,5,6,2]=>0000000=>1111111=>1
[4,3,6,5,8,1,7,2]=>0000000=>1111111=>1
[6,3,5,4,7,2,8,1]=>0000000=>1111111=>1
[6,3,5,4,8,1,7,2]=>0000000=>1111111=>1
[7,1,6,3,8,4,5,2]=>0000000=>1111111=>1
[7,4,6,5,8,1,3,2]=>0000000=>1111111=>1
[8,4,6,1,3,2,7,5]=>0000000=>1111111=>1
[8,1,6,3,4,2,7,5]=>0000000=>1111111=>1
[8,1,6,3,7,2,5,4]=>0000000=>1111111=>1
[8,3,5,2,6,1,7,4]=>0000000=>1111111=>1
[8,2,7,1,5,3,6,4]=>0000000=>1111111=>1
[8,2,4,1,5,3,7,6]=>0000000=>1111111=>1
[3,2,8,4,6,1,7,5]=>0000000=>1111111=>1
[3,2,7,6,8,1,5,4]=>0000000=>1111111=>1
[3,2,7,1,8,5,6,4]=>0000000=>1111111=>1
[3,2,6,5,8,1,7,4]=>0000000=>1111111=>1
[7,6,8,1,5,2,4,3]=>0000000=>1111111=>1
[7,1,8,2,6,4,5,3]=>0000000=>1111111=>1
[7,2,8,1,5,4,6,3]=>0000000=>1111111=>1
[6,2,7,4,5,3,8,1]=>0000000=>1111111=>1
[5,4,7,2,6,3,8,1]=>0000000=>1111111=>1
[2,1,6,5,8,3,7,4]=>0100000=>1011111=>2
[5,4,7,1,8,3,6,2]=>0000000=>1111111=>1
[5,4,6,3,8,1,7,2]=>0000000=>1111111=>1
[2,8,3,1,5,4,6,7]=>0000000=>1111111=>1
[2,5,3,4,7,1,8,6]=>0000000=>1111111=>1
[2,4,8,3,5,7,6,1]=>0000000=>1111111=>1
[4,2,5,3,1,8,6,7]=>0000100=>1111011=>2
[4,2,1,8,5,3,6,7]=>0000000=>1111111=>1
[5,4,1,3,8,2,6,7]=>0000000=>1111111=>1
[5,1,4,8,3,2,6,7]=>0000000=>1111111=>1
[1,5,8,4,3,2,6,7]=>1000000=>0111111=>1
[1,8,5,4,3,2,6,7]=>1000000=>0111111=>1
[1,7,4,3,8,5,2,6]=>1000000=>0111111=>1
[1,5,7,3,8,4,2,6]=>1000000=>0111111=>1
[5,1,4,7,8,3,2,6]=>0000000=>1111111=>1
[4,8,1,5,7,3,6,2]=>0000000=>1111111=>1
[8,1,5,3,7,4,6,2]=>0000000=>1111111=>1
[3,8,4,7,6,5,2,1]=>0000000=>1111111=>1
[1,6,8,5,3,7,4,2]=>1000000=>0111111=>1
[6,8,1,7,4,3,5,2]=>0000000=>1111111=>1
[6,4,8,1,7,3,5,2]=>0000000=>1111111=>1
[6,4,8,7,1,5,2,3]=>0000000=>1111111=>1
[7,6,4,1,3,8,2,5]=>0000000=>1111111=>1
[1,7,5,6,3,2,8,4]=>1000000=>0111111=>1
[4,2,1,7,8,5,3,6]=>0000000=>1111111=>1
[2,7,4,6,3,1,8,5]=>0000000=>1111111=>1
[2,6,8,4,3,7,5,1]=>0000000=>1111111=>1
[6,2,4,8,3,7,5,1]=>0000000=>1111111=>1
[7,2,6,3,4,1,8,5]=>0000000=>1111111=>1
[2,6,7,3,1,4,8,5]=>0000000=>1111111=>1
[2,7,1,8,3,5,4,6]=>0000000=>1111111=>1
[2,1,7,3,5,8,4,6]=>0100000=>1011111=>2
[8,7,1,3,6,2,4,5]=>0000000=>1111111=>1
[8,2,1,7,3,5,6,4]=>0000000=>1111111=>1
[7,8,2,6,3,1,5,4]=>0000000=>1111111=>1
[8,7,2,6,3,5,4,1]=>0000000=>1111111=>1
[1,2,8,7,4,5,6,3]=>1100000=>0011111=>1
[8,3,7,1,5,6,2,4]=>0000000=>1111111=>1
[8,6,1,2,7,5,3,4]=>0000000=>1111111=>1
[8,1,6,2,7,4,5,3]=>0000000=>1111111=>1
[1,8,5,2,6,7,4,3]=>1000000=>0111111=>1
[5,2,1,8,6,7,4,3]=>0000000=>1111111=>1
[2,8,5,7,6,4,3,1]=>0000000=>1111111=>1
[1,7,8,5,2,6,4,3]=>1000000=>0111111=>1
[7,8,1,6,4,2,5,3]=>0000000=>1111111=>1
[7,8,6,1,5,3,2,4]=>0000000=>1111111=>1
[7,3,8,6,1,5,2,4]=>0000000=>1111111=>1
[8,7,6,1,5,3,4,2]=>0000000=>1111111=>1
[8,7,1,6,4,5,3,2]=>0000000=>1111111=>1
[8,1,7,5,6,4,3,2]=>0000000=>1111111=>1
[1,8,6,7,5,4,3,2]=>1000000=>0111111=>1
[4,5,3,6,1,2,8,7]=>0000010=>1111101=>2
[8,1,4,7,3,6,2,5]=>0000000=>1111111=>1
[2,1,8,5,7,4,3,6]=>0100000=>1011111=>2
[6,5,3,7,1,8,4,2]=>0000000=>1111111=>1
[6,5,1,4,7,8,3,2]=>0000000=>1111111=>1
[6,3,4,7,5,8,1,2]=>0000000=>1111111=>1
[4,7,1,3,5,8,6,2]=>0000000=>1111111=>1
[4,8,3,7,1,2,6,5]=>0000000=>1111111=>1
[5,3,7,8,2,4,6,1]=>0000000=>1111111=>1
[5,3,7,6,2,1,8,4]=>0000000=>1111111=>1
[5,3,6,2,8,7,1,4]=>0000000=>1111111=>1
[6,7,3,5,1,8,2,4]=>0000000=>1111111=>1
[2,1,6,7,5,8,3,4]=>0100000=>1011111=>2
[2,1,5,7,3,6,8,4]=>0100000=>1011111=>2
[2,4,7,1,6,5,8,3]=>0000000=>1111111=>1
[3,4,6,2,7,8,5,1]=>0000000=>1111111=>1
[4,6,1,2,5,8,7,3]=>0000000=>1111111=>1
[5,6,1,4,8,2,7,3]=>0000000=>1111111=>1
[3,5,6,4,7,1,8,2]=>0000000=>1111111=>1
[3,4,6,1,5,7,8,2]=>0000000=>1111111=>1
[3,4,1,5,7,6,8,2]=>0000000=>1111111=>1
[3,8,2,7,1,6,5,4]=>0000000=>1111111=>1
[3,8,2,7,6,1,5,4]=>0000000=>1111111=>1
[3,8,2,7,6,5,1,4]=>0000000=>1111111=>1
[3,8,2,7,6,5,4,1]=>0000000=>1111111=>1
[4,8,7,2,6,5,3,1]=>0000000=>1111111=>1
[4,8,7,2,6,5,1,3]=>0000000=>1111111=>1
[4,8,7,2,6,1,5,3]=>0000000=>1111111=>1
[4,8,7,2,1,6,5,3]=>0000000=>1111111=>1
[4,8,7,3,1,6,5,2]=>0000000=>1111111=>1
[4,8,7,3,2,1,6,5]=>0000000=>1111111=>1
[4,8,7,3,2,6,1,5]=>0000000=>1111111=>1
[4,8,7,3,2,6,5,1]=>0000000=>1111111=>1
[4,8,7,3,6,2,5,1]=>0000000=>1111111=>1
[4,8,7,3,6,2,1,5]=>0000000=>1111111=>1
[4,8,7,3,6,1,5,2]=>0000000=>1111111=>1
[4,8,7,3,6,5,1,2]=>0000000=>1111111=>1
[4,8,7,3,6,5,2,1]=>0000000=>1111111=>1
[5,8,7,6,3,4,2,1]=>0000000=>1111111=>1
[5,8,7,6,3,1,4,2]=>0000000=>1111111=>1
[5,8,7,6,3,2,4,1]=>0000000=>1111111=>1
[5,8,7,6,2,4,3,1]=>0000000=>1111111=>1
[5,8,7,6,2,1,4,3]=>0000000=>1111111=>1
[5,8,7,6,4,2,3,1]=>0000000=>1111111=>1
[5,8,7,6,4,2,1,3]=>0000000=>1111111=>1
[5,8,7,6,4,1,3,2]=>0000000=>1111111=>1
[5,8,7,6,4,3,1,2]=>0000000=>1111111=>1
[7,3,5,2,6,4,1,8]=>0000001=>1111110=>1
[7,2,1,5,6,4,3,8]=>0000001=>1111110=>1
[1,4,6,7,3,8,2,5]=>1000000=>0111111=>1
[6,4,5,7,1,3,8,2]=>0000000=>1111111=>1
[6,2,1,5,7,4,8,3]=>0000000=>1111111=>1
[3,2,1,5,7,4,8,6]=>0010000=>1101111=>2
[2,4,6,7,3,8,1,5]=>0000000=>1111111=>1
[1,4,6,7,3,8,5,2]=>1000000=>0111111=>1
[1,5,6,7,8,3,4,2]=>1000000=>0111111=>1
[2,5,6,7,8,3,1,4]=>0000000=>1111111=>1
[3,2,1,6,7,8,4,5]=>0010000=>1101111=>2
[5,2,1,6,7,8,4,3]=>0000000=>1111111=>1
[5,3,6,1,7,8,4,2]=>0000000=>1111111=>1
[1,5,6,7,8,3,2,4]=>1000000=>0111111=>1
[6,4,5,7,2,1,8,3]=>0000000=>1111111=>1
[6,3,5,2,7,1,8,4]=>0000000=>1111111=>1
[6,3,4,2,1,7,8,5]=>0000000=>1111111=>1
[4,3,6,2,7,8,5,1]=>0000000=>1111111=>1
[4,2,1,5,7,3,8,6]=>0000000=>1111111=>1
[1,5,6,7,8,2,4,3]=>1000000=>0111111=>1
[1,5,6,7,8,4,2,3]=>1000000=>0111111=>1
[3,4,6,7,1,8,5,2]=>0000000=>1111111=>1
[4,3,6,1,7,8,5,2]=>0000000=>1111111=>1
[2,1,4,3,6,5,8,7,9]=>01010101=>10101010=>4
[2,4,1,3,6,5,8,7,9]=>00010101=>11101010=>3
[2,4,1,6,3,5,8,7,9]=>00000101=>11111010=>2
[2,4,1,6,3,8,5,7,9]=>00000001=>11111110=>1
[2,4,1,6,3,7,5,9,8]=>00000010=>11111101=>2
[2,4,1,5,3,7,6,9,8]=>00001010=>11110101=>3
[2,3,1,5,4,7,6,9,8]=>00101010=>11010101=>4
[1,3,2,5,4,7,6,9,8]=>10101010=>01010101=>4
[2,4,1,3,6,5,8,7,10,9]=>000101010=>111010101=>4
[2,4,6,1,3,5,8,7,9]=>00000101=>11111010=>2
[2,4,1,6,3,5,8,7,10,9]=>000001010=>111110101=>3
[2,4,1,6,8,3,5,7,9]=>00000001=>11111110=>1
[2,4,1,6,3,8,5,7,10,9]=>000000010=>111111101=>2
[2,4,1,6,3,8,9,5,7]=>00000000=>11111111=>1
[2,4,1,6,3,8,5,10,7,9]=>000000000=>111111111=>1
[2,4,1,6,3,7,5,8,9]=>00000011=>11111100=>1
[2,4,1,6,3,8,5,9,7,10]=>000000001=>111111110=>1
[2,4,1,5,3,8,6,9,7]=>00001000=>11110111=>2
[2,4,1,6,3,7,5,9,8,10]=>000000101=>111111010=>2
[2,3,1,6,4,7,5,9,8]=>00100010=>11011101=>3
[2,4,1,5,3,7,6,9,8,10]=>000010101=>111101010=>3
[1,4,2,5,3,7,6,9,8]=>10001010=>01110101=>3
[2,3,1,5,4,7,6,9,8,10]=>001010101=>110101010=>4
[1,3,2,5,4,7,6,9,8,10]=>101010101=>010101010=>4
[7,1,2,3,4,5,6,8,9]=>00000011=>11111100=>1
[1,4,3,6,2,5,7,8]=>1000011=>0111100=>1
[1,4,3,7,2,5,6,8]=>1000001=>0111110=>1
[1,4,3,7,6,8,2,5]=>1000000=>0111111=>1
[1,4,3,7,5,8,2,6]=>1000000=>0111111=>1
[1,4,3,7,2,6,5,8]=>1000001=>0111110=>1
[1,5,3,7,4,8,2,6]=>1000000=>0111111=>1
[1,3,2,6,5,8,4,7]=>1010000=>0101111=>2
[1,5,4,8,2,6,3,7]=>1000000=>0111111=>1
[1,5,4,8,3,7,2,6]=>1000000=>0111111=>1
[1,2,3,6,5,8,4,7]=>1110000=>0001111=>1
[6,8,2,4,5,7,1,3]=>0000000=>1111111=>1
[7,8,1,4,5,3,6,2]=>0000000=>1111111=>1
[3,8,7,4,1,6,5,2]=>0000000=>1111111=>1
[4,8,3,6,1,5,7,2]=>0000000=>1111111=>1
[5,8,3,1,6,4,7,2]=>0000000=>1111111=>1
[5,8,1,4,7,6,3,2]=>0000000=>1111111=>1
[7,5,1,8,6,2,4,3]=>0000000=>1111111=>1
[7,4,1,8,2,6,3,5]=>0000000=>1111111=>1
[7,1,8,4,2,6,3,5]=>0000000=>1111111=>1
[1,6,3,8,5,2,4,7]=>1000000=>0111111=>1
[6,1,3,8,5,2,4,7]=>0000000=>1111111=>1
[7,1,8,3,6,2,5,4]=>0000000=>1111111=>1
[7,3,1,8,4,2,6,5]=>0000000=>1111111=>1
[7,2,8,4,1,6,5,3]=>0000000=>1111111=>1
[7,2,8,3,6,5,1,4]=>0000000=>1111111=>1
[7,2,8,3,6,1,5,4]=>0000000=>1111111=>1
[7,1,8,2,3,6,5,4]=>0000000=>1111111=>1
[6,1,2,8,3,5,4,7]=>0000000=>1111111=>1
[1,5,2,3,8,4,7,6]=>1000000=>0111111=>1
[5,1,2,3,8,4,7,6]=>0000000=>1111111=>1
[5,2,3,8,1,4,7,6]=>0000000=>1111111=>1
[6,2,8,1,3,5,4,7]=>0000000=>1111111=>1
[6,2,4,1,8,7,3,5]=>0000000=>1111111=>1
[6,3,1,4,2,8,5,7]=>0000000=>1111111=>1
[3,1,6,4,2,8,5,7]=>0000000=>1111111=>1
[2,6,3,8,7,1,5,4]=>0000000=>1111111=>1
[2,6,3,8,5,1,4,7]=>0000000=>1111111=>1
[2,5,1,8,3,4,7,6]=>0000000=>1111111=>1
[2,5,1,3,8,4,7,6]=>0000000=>1111111=>1
[1,2,5,3,8,4,7,6]=>1100000=>0011111=>1
[1,2,4,8,3,7,6,5]=>1100000=>0011111=>1
[2,4,8,1,3,7,6,5]=>0000000=>1111111=>1
[2,4,8,3,7,1,6,5]=>0000000=>1111111=>1
[2,4,8,3,7,6,1,5]=>0000000=>1111111=>1
[2,5,3,8,1,7,4,6]=>0000000=>1111111=>1
[2,5,4,1,3,8,7,6]=>0000100=>1111011=>2
[3,1,5,4,8,2,7,6]=>0000000=>1111111=>1
[5,3,1,4,8,2,7,6]=>0000000=>1111111=>1
[5,2,3,8,4,7,1,6]=>0000000=>1111111=>1
[4,8,2,3,7,6,1,5]=>0000000=>1111111=>1
[4,8,2,3,7,1,6,5]=>0000000=>1111111=>1
[4,8,1,2,3,7,6,5]=>0000000=>1111111=>1
[1,4,8,2,3,7,6,5]=>1000000=>0111111=>1
[1,4,8,3,7,2,6,5]=>1000000=>0111111=>1
[6,3,8,1,5,2,4,7]=>0000000=>1111111=>1
[5,3,8,1,2,4,7,6]=>0000000=>1111111=>1
[5,1,3,8,2,4,7,6]=>0000000=>1111111=>1
[1,5,3,8,2,4,7,6]=>1000000=>0111111=>1
[1,5,4,8,2,7,6,3]=>1000000=>0111111=>1
[5,1,4,8,2,7,6,3]=>0000000=>1111111=>1
[5,4,8,1,2,7,6,3]=>0000000=>1111111=>1
[6,5,1,2,8,7,4,3]=>0000000=>1111111=>1
[5,3,1,6,4,2,8,7]=>0000010=>1111101=>2
[5,1,6,2,8,7,4,3]=>0000000=>1111111=>1
[4,1,5,8,2,7,6,3]=>0000000=>1111111=>1
[4,1,2,5,8,7,6,3]=>0000000=>1111111=>1
[1,4,2,5,8,7,6,3]=>1000000=>0111111=>1
[1,3,5,2,8,7,4,6]=>1000000=>0111111=>1
[3,5,1,2,8,7,4,6]=>0000000=>1111111=>1
[3,6,2,8,7,5,1,4]=>0000000=>1111111=>1
[4,2,6,1,8,7,3,5]=>0000000=>1111111=>1
[4,3,1,5,8,2,7,6]=>0000000=>1111111=>1
[3,5,2,8,7,1,4,6]=>0000000=>1111111=>1
[3,4,8,7,2,6,1,5]=>0000000=>1111111=>1
[3,4,8,7,1,2,6,5]=>0000000=>1111111=>1
[3,4,8,1,7,2,6,5]=>0000000=>1111111=>1
[1,3,4,8,7,2,6,5]=>1000000=>0111111=>1
[1,3,4,8,2,7,6,5]=>1000000=>0111111=>1
[3,4,8,1,2,7,6,5]=>0000000=>1111111=>1
[3,4,8,2,7,1,6,5]=>0000000=>1111111=>1
[3,4,8,2,7,6,1,5]=>0000000=>1111111=>1
[4,2,5,8,1,7,6,3]=>0000000=>1111111=>1
[4,3,1,2,5,8,7,6]=>0001100=>1110011=>2
[3,1,4,2,5,8,7,6]=>0001100=>1110011=>2
[2,3,5,1,8,7,6,4]=>0000000=>1111111=>1
[7,8,2,1,5,3,6,4]=>0000000=>1111111=>1
[6,4,1,2,7,3,5,8]=>0000001=>1111110=>1
[2,3,7,5,4,1,8,6]=>0000000=>1111111=>1
[6,3,1,5,4,2,7,8]=>0000011=>1111100=>1
[7,8,1,5,4,2,6,3]=>0000000=>1111111=>1
[7,8,3,5,4,1,6,2]=>0000000=>1111111=>1
[7,8,2,5,4,1,3,6]=>0000000=>1111111=>1
[7,8,2,5,4,6,1,3]=>0000000=>1111111=>1
[6,2,1,5,4,7,3,8]=>0000001=>1111110=>1
[5,3,6,1,4,7,8,2]=>0000000=>1111111=>1
[5,3,6,2,4,7,1,8]=>0000001=>1111110=>1
[6,4,2,1,7,3,8,5]=>0000000=>1111111=>1
[4,3,7,5,8,6,1,2]=>0000000=>1111111=>1
[4,2,7,1,8,3,6,5]=>0000000=>1111111=>1
[3,2,6,7,4,8,1,5]=>0000000=>1111111=>1
[3,1,6,7,4,8,5,2]=>0000000=>1111111=>1
[1,7,6,5,3,8,4,2]=>1000000=>0111111=>1
[2,7,6,5,3,8,1,4]=>0000000=>1111111=>1
[1,7,6,5,2,4,8,3]=>1000000=>0111111=>1
[2,7,6,5,3,1,4,8]=>0000001=>1111110=>1
[2,7,1,4,8,3,5,6]=>0000000=>1111111=>1
[3,7,6,4,8,5,1,2]=>0000000=>1111111=>1
[5,7,6,3,8,4,1,2]=>0000000=>1111111=>1
[5,1,6,2,4,8,3,7]=>0000000=>1111111=>1
[4,7,6,5,2,1,3,8]=>0000001=>1111110=>1
[4,7,6,5,2,8,1,3]=>0000000=>1111111=>1
[4,7,6,5,1,8,3,2]=>0000000=>1111111=>1
[1,7,6,5,2,8,3,4]=>1000000=>0111111=>1
[1,7,6,5,3,2,8,4]=>1000000=>0111111=>1
[4,7,6,5,1,2,8,3]=>0000000=>1111111=>1
[4,7,6,5,3,1,8,2]=>0000000=>1111111=>1
[6,1,3,5,4,8,7,2]=>0000000=>1111111=>1
[5,2,6,3,4,1,7,8]=>0000011=>1111100=>1
[5,1,6,2,4,7,8,3]=>0000000=>1111111=>1
[1,2,6,3,4,8,7,5]=>1100000=>0011111=>1
[1,7,2,4,8,3,6,5]=>1000000=>0111111=>1
[6,1,4,2,8,3,5,7]=>0000000=>1111111=>1
[4,1,8,2,6,3,5,7]=>0000000=>1111111=>1
[4,7,2,1,5,3,6,8]=>0000001=>1111110=>1
[4,7,1,6,2,3,8,5]=>0000000=>1111111=>1
[1,7,2,6,8,3,5,4]=>1000000=>0111111=>1
[1,2,6,7,4,8,5,3]=>1100000=>0011111=>1
[3,1,6,7,4,2,8,5]=>0000000=>1111111=>1
[3,2,8,5,4,6,1,7]=>0000000=>1111111=>1
[4,7,6,3,5,8,1,2]=>0000000=>1111111=>1
[4,7,1,2,5,3,8,6]=>0000000=>1111111=>1
[3,7,6,5,2,4,1,8]=>0000001=>1111110=>1
[3,7,6,5,1,4,8,2]=>0000000=>1111111=>1
[3,7,6,5,2,1,8,4]=>0000000=>1111111=>1
[1,7,6,5,8,2,4,3]=>1000000=>0111111=>1
[3,7,6,5,8,1,4,2]=>0000000=>1111111=>1
[3,7,6,5,1,2,4,8]=>0000001=>1111110=>1
[3,1,6,8,4,2,5,7]=>0000000=>1111111=>1
[4,7,6,8,3,5,1,2]=>0000000=>1111111=>1
[2,7,6,5,1,4,3,8]=>0000001=>1111110=>1
[2,7,6,5,8,1,3,4]=>0000000=>1111111=>1
[2,7,6,5,8,4,1,3]=>0000000=>1111111=>1
[6,3,2,1,7,4,8,5]=>0000000=>1111111=>1
[4,2,1,7,3,5,8,6]=>0000000=>1111111=>1
[7,3,1,5,4,2,8,6]=>0000000=>1111111=>1
[8,4,1,5,2,7,6,3]=>0000000=>1111111=>1
[4,3,7,2,1,5,8,6]=>0000000=>1111111=>1
[2,7,5,4,1,3,8,6]=>0000000=>1111111=>1
[7,5,4,3,2,1,8,6]=>0000000=>1111111=>1
[6,5,2,1,8,4,3,7]=>0000000=>1111111=>1
[5,7,4,3,2,8,1,6]=>0000000=>1111111=>1
[1,7,6,2,4,8,3,5]=>1000000=>0111111=>1
[6,2,7,5,3,8,1,4]=>0000000=>1111111=>1
[7,1,8,5,3,6,4,2]=>0000000=>1111111=>1
[5,8,3,2,7,1,6,4]=>0000000=>1111111=>1
[8,7,3,1,6,5,4,2]=>0000000=>1111111=>1
[8,7,2,6,1,5,4,3]=>0000000=>1111111=>1
[1,8,5,7,4,3,6,2]=>1000000=>0111111=>1
[1,8,5,7,2,4,6,3]=>1000000=>0111111=>1
[3,8,6,1,7,2,5,4]=>0000000=>1111111=>1
[7,2,8,5,6,1,4,3]=>0000000=>1111111=>1
[6,3,7,5,8,2,1,4]=>0000000=>1111111=>1
[3,6,5,8,1,4,2,7]=>0000000=>1111111=>1
[2,6,5,8,4,1,3,7]=>0000000=>1111111=>1
[6,5,4,8,3,2,1,7]=>0000000=>1111111=>1
[6,3,5,1,8,4,2,7]=>0000000=>1111111=>1
[8,4,1,5,7,3,6,2]=>0000000=>1111111=>1
[5,4,1,6,8,2,3,7]=>0000000=>1111111=>1
[6,3,7,4,8,5,2,1]=>0000000=>1111111=>1
[6,4,7,8,1,5,3,2]=>0000000=>1111111=>1
[6,3,7,8,5,2,4,1]=>0000000=>1111111=>1
[2,5,8,7,1,3,6,4]=>0000000=>1111111=>1
[5,3,8,7,2,1,6,4]=>0000000=>1111111=>1
[8,3,7,6,1,5,4,2]=>0000000=>1111111=>1
[8,2,7,6,5,1,4,3]=>0000000=>1111111=>1
[4,3,8,7,6,2,1,5]=>0000000=>1111111=>1
[2,4,8,7,6,1,3,5]=>0000000=>1111111=>1
[4,7,3,8,6,5,1,2]=>0000000=>1111111=>1
[7,5,8,6,4,3,2,1]=>0000000=>1111111=>1
[5,8,7,3,6,4,2,1]=>0000000=>1111111=>1
[4,8,7,6,2,5,3,1]=>0000000=>1111111=>1
[3,8,7,6,5,1,4,2]=>0000000=>1111111=>1
[2,8,7,6,5,4,1,3]=>0000000=>1111111=>1
[3,4,1,2,5,6,7,8,9]=>00011111=>11100000=>1
[3,2,1,4,5,6,7,8,9]=>00111111=>11000000=>1
[4,5,6,1,2,3,7,8,9]=>00000111=>11111000=>1
[4,2,5,1,3,6,7,8,9]=>00001111=>11110000=>1
[4,3,2,1,5,6,7,8,9]=>00011111=>11100000=>1
[5,6,7,8,1,2,3,4,9]=>00000001=>11111110=>1
[5,2,6,7,1,3,4,8,9]=>00000011=>11111100=>1
[5,6,3,4,1,2,7,8,9]=>00000111=>11111000=>1
[5,3,2,6,1,4,7,8,9]=>00000111=>11111000=>1
[5,4,3,2,1,6,7,8,9]=>00001111=>11110000=>1
[6,2,7,8,9,1,3,4,5]=>00000000=>11111111=>1
[6,7,3,4,8,1,2,5,9]=>00000001=>11111110=>1
[6,3,2,7,8,1,4,5,9]=>00000001=>11111110=>1
[6,4,7,2,5,1,3,8,9]=>00000011=>11111100=>1
[6,4,3,2,7,1,5,8,9]=>00000011=>11111100=>1
[6,5,4,3,2,1,7,8,9]=>00000111=>11111000=>1
[7,4,8,2,5,9,1,3,6]=>00000000=>11111111=>1
[7,4,3,2,8,9,1,5,6]=>00000000=>11111111=>1
[7,8,5,6,3,4,1,2,9]=>00000001=>11111110=>1
[7,5,3,8,2,6,1,4,9]=>00000001=>11111110=>1
[7,5,4,3,2,8,1,6,9]=>00000001=>11111110=>1
[7,6,5,4,3,2,1,8,9]=>00000011=>11111100=>1
[8,6,9,4,7,2,5,1,3]=>00000000=>11111111=>1
[8,6,4,3,9,2,7,1,5]=>00000000=>11111111=>1
[8,6,5,4,3,2,9,1,7]=>00000000=>11111111=>1
[3,4,1,2,5,6,7,8,9,10]=>000111111=>111000000=>1
[3,2,1,4,5,6,7,8,9,10]=>001111111=>110000000=>1
[4,5,6,1,2,3,7,8,9,10]=>000001111=>111110000=>1
[4,2,5,1,3,6,7,8,9,10]=>000011111=>111100000=>1
[4,3,2,1,5,6,7,8,9,10]=>000111111=>111000000=>1
[5,6,7,8,1,2,3,4,9,10]=>000000011=>111111100=>1
[5,2,6,7,1,3,4,8,9,10]=>000000111=>111111000=>1
[5,6,3,4,1,2,7,8,9,10]=>000001111=>111110000=>1
[5,3,2,6,1,4,7,8,9,10]=>000001111=>111110000=>1
[5,4,3,2,1,6,7,8,9,10]=>000011111=>111100000=>1
[6,2,7,8,9,1,3,4,5,10]=>000000001=>111111110=>1
[6,7,3,4,8,1,2,5,9,10]=>000000011=>111111100=>1
[6,3,2,7,8,1,4,5,9,10]=>000000011=>111111100=>1
[6,4,7,2,5,1,3,8,9,10]=>000000111=>111111000=>1
[6,4,3,2,7,1,5,8,9,10]=>000000111=>111111000=>1
[6,5,4,3,2,1,7,8,9,10]=>000001111=>111110000=>1
[7,8,3,4,9,10,1,2,5,6]=>000000000=>111111111=>1
[7,8,9,4,5,6,1,2,3,10]=>000000001=>111111110=>1
[7,4,3,2,8,9,1,5,6,10]=>000000001=>111111110=>1
[7,8,5,6,3,4,1,2,9,10]=>000000011=>111111100=>1
[7,5,3,8,2,6,1,4,9,10]=>000000011=>111111100=>1
[7,5,4,3,2,8,1,6,9,10]=>000000011=>111111100=>1
[7,6,5,4,3,2,1,8,9,10]=>000000111=>111111000=>1
[8,5,9,10,2,6,7,1,3,4]=>000000000=>111111111=>1
[8,5,3,9,2,6,10,1,4,7]=>000000000=>111111111=>1
[8,6,9,4,7,2,5,1,3,10]=>000000001=>111111110=>1
[8,6,4,3,9,2,7,1,5,10]=>000000001=>111111110=>1
[8,6,5,4,3,2,9,1,7,10]=>000000001=>111111110=>1
[8,7,6,5,4,3,2,1,9,10]=>000000011=>111111100=>1
[9,7,5,4,3,10,2,8,1,6]=>000000000=>111111111=>1
[3,6,5,1,2,4,8,7]=>0000010=>1111101=>2
[3,7,5,8,2,4,1,6]=>0000000=>1111111=>1
[3,8,5,7,2,4,1,6]=>0000000=>1111111=>1
[5,1,7,8,4,3,2,6]=>0000000=>1111111=>1
[4,7,1,8,3,6,2,5]=>0000000=>1111111=>1
[7,5,3,8,1,4,2,6]=>0000000=>1111111=>1
[2,1,5,8,7,3,4,6]=>0100000=>1011111=>2
[6,1,2,3,7,5,8,4]=>0000000=>1111111=>1
[7,1,2,3,8,6,5,4]=>0000000=>1111111=>1
[7,1,2,3,5,8,6,4]=>0000000=>1111111=>1
[6,8,1,4,3,7,2,5]=>0000000=>1111111=>1
[8,7,3,2,4,1,6,5]=>0000000=>1111111=>1
[2,1,7,3,4,8,6,5]=>0100000=>1011111=>2
[7,8,3,2,4,1,6,5]=>0000000=>1111111=>1
[7,1,2,3,6,8,5,4]=>0000000=>1111111=>1
[7,1,2,3,8,5,6,4]=>0000000=>1111111=>1
[8,1,2,3,6,5,7,4]=>0000000=>1111111=>1
[6,7,2,8,3,4,1,5]=>0000000=>1111111=>1
[3,8,7,1,4,2,6,5]=>0000000=>1111111=>1
[7,6,2,8,3,1,4,5]=>0000000=>1111111=>1
[5,8,3,7,1,4,2,6]=>0000000=>1111111=>1
[7,1,2,3,5,6,8,4]=>0000000=>1111111=>1
[5,1,2,3,7,8,6,4]=>0000000=>1111111=>1
[5,1,2,3,8,6,7,4]=>0000000=>1111111=>1
[2,1,6,3,4,8,7,5]=>0100000=>1011111=>2
[8,6,3,2,4,7,1,5]=>0000000=>1111111=>1
[6,1,2,3,5,7,8,4]=>0000000=>1111111=>1
[5,1,2,3,6,8,7,4]=>0000000=>1111111=>1
[7,8,1,2,6,3,5,4]=>0000000=>1111111=>1
[1,4,8,2,7,3,5,6]=>1000000=>0111111=>1
[1,2,8,5,4,7,3,6]=>1100000=>0011111=>1
[1,3,8,5,4,2,7,6]=>1000000=>0111111=>1
[2,3,6,8,4,7,1,5]=>0000000=>1111111=>1
[1,3,6,8,4,7,5,2]=>1000000=>0111111=>1
[2,4,8,1,7,3,6,5]=>0000000=>1111111=>1
[3,4,8,5,7,6,1,2]=>0000000=>1111111=>1
[1,2,6,8,4,5,7,3]=>1100000=>0011111=>1
[7,5,1,2,4,3,6,8]=>0000001=>1111110=>1
[7,4,6,1,5,2,3,8]=>0000001=>1111110=>1
[7,1,4,2,6,3,5,8]=>0000001=>1111110=>1
[6,8,1,4,7,2,3,5]=>0000000=>1111111=>1
[1,6,4,2,8,3,5,7]=>1000000=>0111111=>1
[1,6,3,8,5,4,2,7]=>1000000=>0111111=>1
[6,8,1,7,3,5,4,2]=>0000000=>1111111=>1
[7,1,3,6,5,4,2,8]=>0000001=>1111110=>1
[7,3,1,6,5,4,2,8]=>0000001=>1111110=>1
[7,2,1,4,6,3,5,8]=>0000001=>1111110=>1
[7,2,3,6,5,1,4,8]=>0000001=>1111110=>1
[7,1,2,3,6,5,4,8]=>0000001=>1111110=>1
[6,8,1,2,7,3,5,4]=>0000000=>1111111=>1
[1,6,2,3,8,5,4,7]=>1000000=>0111111=>1
[1,5,8,2,7,6,3,4]=>1000000=>0111111=>1
[5,1,8,2,7,6,3,4]=>0000000=>1111111=>1
[5,8,2,7,6,3,4,1]=>0000000=>1111111=>1
[6,2,8,1,7,3,5,4]=>0000000=>1111111=>1
[6,8,2,1,7,4,3,5]=>0000000=>1111111=>1
[3,6,4,1,2,8,5,7]=>0000000=>1111111=>1
[2,1,6,3,8,5,4,7]=>0100000=>1011111=>2
[2,5,1,8,7,6,3,4]=>0000000=>1111111=>1
[2,5,3,8,7,4,6,1]=>0000000=>1111111=>1
[1,2,5,3,8,7,4,6]=>1100000=>0011111=>1
[2,4,8,7,6,5,1,3]=>0000000=>1111111=>1
[2,5,3,8,7,1,6,4]=>0000000=>1111111=>1
[2,5,8,4,1,7,6,3]=>0000000=>1111111=>1
[3,5,8,7,1,4,2,6]=>0000000=>1111111=>1
[5,3,8,4,1,7,6,2]=>0000000=>1111111=>1
[4,2,8,7,6,3,5,1]=>0000000=>1111111=>1
[4,2,8,7,6,5,3,1]=>0000000=>1111111=>1
[4,1,8,7,6,5,3,2]=>0000000=>1111111=>1
[4,3,8,7,6,5,1,2]=>0000000=>1111111=>1
[6,3,1,8,7,2,5,4]=>0000000=>1111111=>1
[5,8,3,7,6,1,4,2]=>0000000=>1111111=>1
[5,1,3,8,7,6,2,4]=>0000000=>1111111=>1
[1,5,3,8,7,6,2,4]=>1000000=>0111111=>1
[1,5,8,4,7,2,6,3]=>1000000=>0111111=>1
[5,1,8,4,7,2,6,3]=>0000000=>1111111=>1
[5,8,7,4,6,1,2,3]=>0000000=>1111111=>1
[6,8,5,1,2,4,7,3]=>0000000=>1111111=>1
[5,6,3,1,2,4,8,7]=>0000010=>1111101=>2
[5,6,2,4,3,1,8,7]=>0000010=>1111101=>2
[5,6,1,2,4,3,8,7]=>0000010=>1111101=>2
[4,5,8,1,7,2,3,6]=>0000000=>1111111=>1
[4,5,8,1,7,2,6,3]=>0000000=>1111111=>1
[1,3,2,5,8,7,4,6]=>1010000=>0101111=>2
[3,5,1,8,7,4,6,2]=>0000000=>1111111=>1
[3,5,1,8,7,2,6,4]=>0000000=>1111111=>1
[4,3,6,1,2,8,5,7]=>0000000=>1111111=>1
[4,5,8,3,1,7,2,6]=>0000000=>1111111=>1
[4,5,2,8,7,1,3,6]=>0000000=>1111111=>1
[3,2,5,8,7,1,6,4]=>0000000=>1111111=>1
[3,4,8,7,6,2,1,5]=>0000000=>1111111=>1
[3,1,4,8,7,6,2,5]=>0000000=>1111111=>1
[3,4,8,7,6,5,1,2]=>0000000=>1111111=>1
[1,3,4,8,7,6,2,5]=>1000000=>0111111=>1
[3,4,8,7,6,2,5,1]=>0000000=>1111111=>1
[3,2,5,8,7,4,6,1]=>0000000=>1111111=>1
[4,5,8,3,1,7,6,2]=>0000000=>1111111=>1
[2,1,3,5,8,7,4,6]=>0110000=>1001111=>2
[1,2,7,5,8,6,4,3]=>1100000=>0011111=>1
[7,1,4,8,2,6,5,3]=>0000000=>1111111=>1
[6,8,1,3,7,5,2,4]=>0000000=>1111111=>1
[3,7,8,1,2,6,5,4]=>0000000=>1111111=>1
[1,3,7,8,2,6,5,4]=>1000000=>0111111=>1
[2,3,7,8,1,6,5,4]=>0000000=>1111111=>1
[2,7,8,1,3,6,5,4]=>0000000=>1111111=>1
[8,1,2,6,7,3,5,4]=>0000000=>1111111=>1
[8,1,2,6,7,5,3,4]=>0000000=>1111111=>1
[8,2,5,7,1,3,6,4]=>0000000=>1111111=>1
[2,8,1,6,7,3,5,4]=>0000000=>1111111=>1
[2,6,8,3,7,1,5,4]=>0000000=>1111111=>1
[2,8,6,4,7,1,5,3]=>0000000=>1111111=>1
[6,8,3,4,1,7,5,2]=>0000000=>1111111=>1
[6,8,3,7,4,1,5,2]=>0000000=>1111111=>1
[2,6,8,3,7,5,1,4]=>0000000=>1111111=>1
[2,8,1,6,7,5,3,4]=>0000000=>1111111=>1
[8,2,5,7,1,6,3,4]=>0000000=>1111111=>1
[8,4,7,2,3,6,1,5]=>0000000=>1111111=>1
[8,5,7,4,2,6,1,3]=>0000000=>1111111=>1
[8,3,5,7,4,1,6,2]=>0000000=>1111111=>1
[8,5,2,4,7,1,6,3]=>0000000=>1111111=>1
[8,2,3,5,7,1,6,4]=>0000000=>1111111=>1
[8,2,4,7,3,6,1,5]=>0000000=>1111111=>1
[8,2,7,1,4,6,3,5]=>0000000=>1111111=>1
[8,7,1,2,4,6,3,5]=>0000000=>1111111=>1
[8,7,1,4,6,2,3,5]=>0000000=>1111111=>1
[8,4,7,1,3,6,2,5]=>0000000=>1111111=>1
[1,6,8,3,7,2,5,4]=>1000000=>0111111=>1
[8,3,5,7,1,2,6,4]=>0000000=>1111111=>1
[5,8,7,1,3,6,2,4]=>0000000=>1111111=>1
[8,5,4,7,1,6,2,3]=>0000000=>1111111=>1
[8,5,4,7,1,2,6,3]=>0000000=>1111111=>1
[8,5,1,4,7,2,6,3]=>0000000=>1111111=>1
[1,4,6,8,2,7,5,3]=>1000000=>0111111=>1
[1,6,5,8,2,7,4,3]=>1000000=>0111111=>1
[8,5,6,3,1,7,4,2]=>0000000=>1111111=>1
[5,6,2,8,1,7,4,3]=>0000000=>1111111=>1
[1,8,4,5,7,2,6,3]=>1000000=>0111111=>1
[5,8,7,3,6,1,2,4]=>0000000=>1111111=>1
[8,3,5,7,1,6,2,4]=>0000000=>1111111=>1
[1,6,8,3,7,5,2,4]=>1000000=>0111111=>1
[6,3,8,2,7,5,1,4]=>0000000=>1111111=>1
[6,8,4,2,7,1,5,3]=>0000000=>1111111=>1
[8,6,4,7,3,1,5,2]=>0000000=>1111111=>1
[8,4,5,7,3,1,6,2]=>0000000=>1111111=>1
[8,4,2,5,7,1,6,3]=>0000000=>1111111=>1
[8,3,4,7,2,6,1,5]=>0000000=>1111111=>1
[8,7,1,3,4,6,2,5]=>0000000=>1111111=>1
[8,3,7,2,4,6,1,5]=>0000000=>1111111=>1
[2,8,4,5,7,1,6,3]=>0000000=>1111111=>1
[8,7,3,4,5,1,6,2]=>0000000=>1111111=>1
[8,7,4,5,2,6,1,3]=>0000000=>1111111=>1
[5,8,7,2,3,6,1,4]=>0000000=>1111111=>1
[8,7,2,3,4,6,1,5]=>0000000=>1111111=>1
[8,7,2,3,6,1,4,5]=>0000000=>1111111=>1
[1,3,2,8,5,4,7,6]=>1010000=>0101111=>2
[4,2,8,5,3,7,1,6]=>0000000=>1111111=>1
[5,2,1,8,4,3,7,6]=>0000000=>1111111=>1
[6,2,8,4,3,7,5,1]=>0000000=>1111111=>1
[7,2,8,4,3,1,6,5]=>0000000=>1111111=>1
[7,3,4,8,2,1,6,5]=>0000000=>1111111=>1
[6,3,4,8,2,7,5,1]=>0000000=>1111111=>1
[5,3,4,1,8,2,7,6]=>0000000=>1111111=>1
[8,1,4,5,2,3,7,6]=>0000000=>1111111=>1
[8,1,5,4,3,2,7,6]=>0000000=>1111111=>1
[3,5,4,2,8,1,7,6]=>0000000=>1111111=>1
[4,5,3,2,8,7,1,6]=>0000000=>1111111=>1
[6,4,3,2,8,7,5,1]=>0000000=>1111111=>1
[6,5,3,2,1,7,8,4]=>0000000=>1111111=>1
[5,6,3,2,7,8,4,1]=>0000000=>1111111=>1
[4,1,6,3,2,7,8,5]=>0000000=>1111111=>1
[3,6,4,2,7,8,1,5]=>0000000=>1111111=>1
[8,1,6,4,3,7,2,5]=>0000000=>1111111=>1
[8,1,7,4,3,6,5,2]=>0000000=>1111111=>1
[2,7,4,1,3,6,5,8]=>0000001=>1111110=>1
[3,7,4,2,6,1,5,8]=>0000001=>1111110=>1
[4,1,7,3,2,6,5,8]=>0000001=>1111110=>1
[5,7,3,2,6,4,8,1]=>0000000=>1111111=>1
[6,7,3,2,5,4,1,8]=>0000001=>1111110=>1
[7,6,3,2,1,5,4,8]=>0000001=>1111110=>1
[4,7,5,6,2,3,8,1]=>0000000=>1111111=>1
[3,1,7,5,6,2,4,8]=>0000001=>1111110=>1
[2,7,5,6,1,3,4,8]=>0000001=>1111110=>1
[2,6,5,7,1,3,8,4]=>0000000=>1111111=>1
[4,6,5,7,2,8,1,3]=>0000000=>1111111=>1
[5,6,4,7,2,8,3,1]=>0000000=>1111111=>1
[6,5,4,1,7,2,8,3]=>0000000=>1111111=>1
[7,5,4,6,2,1,8,3]=>0000000=>1111111=>1
[6,4,5,7,1,8,2,3]=>0000000=>1111111=>1
[5,4,6,1,7,8,2,3]=>0000000=>1111111=>1
[8,1,5,6,7,2,3,4]=>0000000=>1111111=>1
[2,1,4,6,8,7,3,5]=>0100000=>1011111=>2
[3,4,6,8,7,1,2,5]=>0000000=>1111111=>1
[4,3,1,6,8,7,2,5]=>0000000=>1111111=>1
[5,3,6,8,7,2,4,1]=>0000000=>1111111=>1
[6,3,5,1,8,7,2,4]=>0000000=>1111111=>1
[7,3,5,8,6,2,1,4]=>0000000=>1111111=>1
[7,2,8,5,6,3,1,4]=>0000000=>1111111=>1
[6,2,8,5,1,7,3,4]=>0000000=>1111111=>1
[4,2,1,8,6,7,3,5]=>0000000=>1111111=>1
[1,3,2,8,6,7,4,5]=>1010000=>0101111=>2
[2,3,8,6,7,1,4,5]=>0000000=>1111111=>1
[8,1,3,2,6,7,4,5]=>0000000=>1111111=>1
[2,3,8,7,1,6,5,4]=>0000000=>1111111=>1
[4,2,8,7,6,1,5,3]=>0000000=>1111111=>1
[5,2,8,7,6,4,1,3]=>0000000=>1111111=>1
[7,2,1,8,6,5,4,3]=>0000000=>1111111=>1
[7,3,6,1,8,5,4,2]=>0000000=>1111111=>1
[6,3,7,8,5,4,2,1]=>0000000=>1111111=>1
[5,3,7,8,6,4,1,2]=>0000000=>1111111=>1
[4,3,1,7,8,6,5,2]=>0000000=>1111111=>1
[3,4,7,8,6,1,5,2]=>0000000=>1111111=>1
[8,1,5,7,6,2,4,3]=>0000000=>1111111=>1
[3,5,7,6,8,1,4,2]=>0000000=>1111111=>1
[4,5,7,6,8,3,1,2]=>0000000=>1111111=>1
[5,4,1,7,6,8,3,2]=>0000000=>1111111=>1
[6,4,7,5,8,3,2,1]=>0000000=>1111111=>1
[7,4,6,5,1,8,3,2]=>0000000=>1111111=>1
[7,5,6,4,3,1,8,2]=>0000000=>1111111=>1
[6,5,1,7,4,3,8,2]=>0000000=>1111111=>1
[4,6,7,5,3,8,1,2]=>0000000=>1111111=>1
[3,6,7,5,1,4,8,2]=>0000000=>1111111=>1
[8,1,6,7,5,4,2,3]=>0000000=>1111111=>1
[8,1,7,6,5,4,3,2]=>0000000=>1111111=>1
[2,7,6,1,5,4,3,8]=>0000001=>1111110=>1
[3,7,6,5,1,4,2,8]=>0000001=>1111110=>1
[4,7,6,5,3,1,2,8]=>0000001=>1111110=>1
[8,6,4,3,1,5,7,2]=>0000000=>1111111=>1
[8,6,4,1,5,2,7,3]=>0000000=>1111111=>1
[8,6,5,1,3,2,7,4]=>0000000=>1111111=>1
[8,6,3,1,7,2,4,5]=>0000000=>1111111=>1
[8,7,3,1,5,2,4,6]=>0000000=>1111111=>1
[5,3,1,7,2,4,6,8]=>0000001=>1111110=>1
[8,7,1,2,4,5,3,6]=>0000000=>1111111=>1
[8,6,1,2,4,7,3,5]=>0000000=>1111111=>1
[8,5,1,2,6,7,3,4]=>0000000=>1111111=>1
[8,5,1,6,4,2,7,3]=>0000000=>1111111=>1
[8,5,1,3,6,4,7,2]=>0000000=>1111111=>1
[8,6,1,5,3,4,7,2]=>0000000=>1111111=>1
[8,6,1,5,2,4,7,3]=>0000000=>1111111=>1
[8,6,1,2,5,7,3,4]=>0000000=>1111111=>1
[8,6,1,2,7,4,3,5]=>0000000=>1111111=>1
[8,7,1,2,5,4,3,6]=>0000000=>1111111=>1
[5,1,4,2,3,8,6,7]=>0000100=>1111011=>2
[5,1,4,2,7,3,6,8]=>0000001=>1111110=>1
[7,1,5,8,2,6,3,4]=>0000000=>1111111=>1
[5,7,8,1,2,4,6,3]=>0000000=>1111111=>1
[5,7,8,1,3,4,6,2]=>0000000=>1111111=>1
[5,8,1,7,3,4,6,2]=>0000000=>1111111=>1
[8,1,5,7,2,4,6,3]=>0000000=>1111111=>1
[8,4,1,2,7,6,3,5]=>0000000=>1111111=>1
[1,4,2,3,8,7,5,6]=>1001000=>0110111=>2
[1,4,2,7,6,3,5,8]=>1000001=>0111110=>1
[6,1,2,8,7,5,3,4]=>0000000=>1111111=>1
[6,1,2,4,8,7,5,3]=>0000000=>1111111=>1
[3,1,8,4,6,7,5,2]=>0000000=>1111111=>1
[3,1,7,6,4,8,5,2]=>0000000=>1111111=>1
[7,1,2,4,6,8,5,3]=>0000000=>1111111=>1
[7,1,2,6,8,5,3,4]=>0000000=>1111111=>1
[6,1,2,7,8,5,3,4]=>0000000=>1111111=>1
[6,1,2,7,4,8,5,3]=>0000000=>1111111=>1
[3,1,6,4,7,8,5,2]=>0000000=>1111111=>1
[5,7,1,3,8,4,6,2]=>0000000=>1111111=>1
[5,7,1,8,4,2,6,3]=>0000000=>1111111=>1
[7,1,5,3,2,8,6,4]=>0000000=>1111111=>1
[7,1,4,5,2,8,6,3]=>0000000=>1111111=>1
[4,7,3,1,5,8,6,2]=>0000000=>1111111=>1
[4,8,7,3,1,5,6,2]=>0000000=>1111111=>1
[8,1,7,4,5,2,6,3]=>0000000=>1111111=>1
[8,1,7,5,3,2,6,4]=>0000000=>1111111=>1
[8,3,7,1,2,6,4,5]=>0000000=>1111111=>1
[3,1,2,8,4,7,5,6]=>0010000=>1101111=>2
[3,1,2,8,6,4,5,7]=>0010000=>1101111=>2
[3,1,7,2,6,4,5,8]=>0000001=>1111110=>1
[1,4,2,3,8,6,5,7]=>1001000=>0110111=>2
[1,4,2,3,8,5,7,6]=>1001000=>0110111=>2
[5,8,1,7,2,4,6,3]=>0000000=>1111111=>1
[5,8,1,3,4,7,6,2]=>0000000=>1111111=>1
[3,1,8,6,4,7,5,2]=>0000000=>1111111=>1
[8,1,2,6,7,4,5,3]=>0000000=>1111111=>1
[6,1,2,8,7,3,5,4]=>0000000=>1111111=>1
[1,2,3,5,8,4,7,6]=>1110000=>0001111=>1
[1,2,3,5,8,6,4,7]=>1110000=>0001111=>1
[7,1,2,8,3,6,5,4]=>0000000=>1111111=>1
[7,1,2,8,6,4,5,3]=>0000000=>1111111=>1
[3,1,7,8,4,6,5,2]=>0000000=>1111111=>1
[3,1,8,7,6,4,5,2]=>0000000=>1111111=>1
[8,1,2,7,4,6,5,3]=>0000000=>1111111=>1
[8,1,2,7,3,6,5,4]=>0000000=>1111111=>1
[1,2,3,5,8,7,4,6]=>1110000=>0001111=>1
[1,2,3,6,8,5,4,7]=>1110000=>0001111=>1
[7,8,5,6,3,1,4,2]=>0000000=>1111111=>1
[7,5,8,3,1,4,2,6]=>0000000=>1111111=>1
[7,8,5,3,1,4,2,6]=>0000000=>1111111=>1
[7,8,5,3,1,6,2,4]=>0000000=>1111111=>1
[7,8,5,3,1,6,4,2]=>0000000=>1111111=>1
[7,8,5,3,6,1,4,2]=>0000000=>1111111=>1
[7,8,5,3,6,4,1,2]=>0000000=>1111111=>1
[7,5,6,3,4,1,8,2]=>0000000=>1111111=>1
[7,5,6,3,1,2,8,4]=>0000000=>1111111=>1
[7,5,3,6,1,2,8,4]=>0000000=>1111111=>1
[7,5,3,1,4,2,6,8]=>0000001=>1111110=>1
[7,5,3,1,6,4,8,2]=>0000000=>1111111=>1
[7,5,3,6,4,1,8,2]=>0000000=>1111111=>1
[7,5,3,8,4,6,1,2]=>0000000=>1111111=>1
[7,5,3,8,1,4,6,2]=>0000000=>1111111=>1
[7,5,3,1,8,4,6,2]=>0000000=>1111111=>1
[7,5,3,1,8,2,6,4]=>0000000=>1111111=>1
[7,5,3,1,8,6,2,4]=>0000000=>1111111=>1
[7,5,3,8,1,6,4,2]=>0000000=>1111111=>1
[7,5,3,8,6,1,4,2]=>0000000=>1111111=>1
[7,5,3,8,6,4,1,2]=>0000000=>1111111=>1
[7,5,8,3,6,4,1,2]=>0000000=>1111111=>1
[7,5,8,3,6,1,4,2]=>0000000=>1111111=>1
[7,5,8,3,1,6,4,2]=>0000000=>1111111=>1
[7,5,3,6,1,4,2,8]=>0000001=>1111110=>1
[7,5,3,8,4,1,2,6]=>0000000=>1111111=>1
[7,5,8,6,3,1,2,4]=>0000000=>1111111=>1
[7,5,8,6,3,1,4,2]=>0000000=>1111111=>1
[7,5,8,6,3,4,1,2]=>0000000=>1111111=>1
[7,5,6,8,3,1,4,2]=>0000000=>1111111=>1
[7,5,6,3,8,1,2,4]=>0000000=>1111111=>1
[7,5,3,4,1,8,2,6]=>0000000=>1111111=>1
[7,5,6,3,1,8,4,2]=>0000000=>1111111=>1
[7,5,3,6,1,8,4,2]=>0000000=>1111111=>1
[7,5,3,1,6,8,2,4]=>0000000=>1111111=>1
[7,5,3,4,1,6,8,2]=>0000000=>1111111=>1
[7,5,3,1,4,6,8,2]=>0000000=>1111111=>1
[5,4,8,3,2,7,6,1]=>0000000=>1111111=>1
[2,1,5,8,4,7,6,3]=>0100000=>1011111=>2
[2,1,8,6,7,5,4,3]=>0100000=>1011111=>2
[8,3,2,6,7,5,4,1]=>0000000=>1111111=>1
[8,4,5,3,2,7,6,1]=>0000000=>1111111=>1
[8,4,7,3,6,5,2,1]=>0000000=>1111111=>1
[8,4,6,3,7,5,2,1]=>0000000=>1111111=>1
[3,8,2,5,4,7,6,1]=>0000000=>1111111=>1
[3,7,2,8,6,5,4,1]=>0000000=>1111111=>1
[3,6,2,8,7,5,4,1]=>0000000=>1111111=>1
[6,4,7,3,8,5,2,1]=>0000000=>1111111=>1
[7,5,4,3,2,8,6,1]=>0000000=>1111111=>1
[6,8,5,7,4,3,2,1]=>0000000=>1111111=>1
[2,3,1,4,5,6,7,8,9]=>00111111=>11000000=>1
[2,3,4,1,5,6,7,8,9]=>00011111=>11100000=>1
[2,3,4,5,1,6,7,8,9]=>00001111=>11110000=>1
[2,3,4,5,6,1,7,8,9]=>00000111=>11111000=>1
[2,3,1,4,5,6,7,8,9,10]=>001111111=>110000000=>1
[2,4,3,1,5,6,7,8,9]=>00011111=>11100000=>1
[2,3,4,1,5,6,7,8,9,10]=>000111111=>111000000=>1
[2,3,4,5,1,6,7,8,9,10]=>000011111=>111100000=>1
[2,3,4,5,6,1,7,8,9,10]=>000001111=>111110000=>1
[2,3,4,5,6,7,1,8,9,10]=>000000111=>111111000=>1
[2,3,4,5,6,7,8,1,9,10]=>000000011=>111111100=>1
[2,3,4,5,6,7,9,8,1]=>00000000=>11111111=>1
[4,6,8,3,5,7,1,2]=>0000000=>1111111=>1
[6,8,1,2,4,5,7,3]=>0000000=>1111111=>1
[3,5,8,2,4,7,1,6]=>0000000=>1111111=>1
[8,3,5,2,4,1,6,7]=>0000000=>1111111=>1
[4,2,5,7,3,6,1,8]=>0000001=>1111110=>1
[4,5,2,8,3,1,6,7]=>0000000=>1111111=>1
[4,2,5,8,3,7,1,6]=>0000000=>1111111=>1
[2,1,6,8,4,7,3,5]=>0100000=>1011111=>2
[1,2,5,8,3,6,7,4]=>1100000=>0011111=>1
[5,3,6,8,4,7,1,2]=>0000000=>1111111=>1
[1,6,5,8,2,4,7,3]=>1000000=>0111111=>1
[3,1,2,6,8,5,7,4]=>0010000=>1101111=>2
[1,4,3,8,2,6,7,5]=>1000000=>0111111=>1
[5,4,8,3,2,1,6,7]=>0000000=>1111111=>1
[5,4,3,7,2,6,1,8]=>0000001=>1111110=>1
[4,3,6,2,7,5,1,8]=>0000001=>1111110=>1
[4,6,3,2,1,8,5,7]=>0000000=>1111111=>1
[4,1,7,3,2,5,8,6]=>0000000=>1111111=>1
[4,3,1,7,8,2,6,5]=>0000000=>1111111=>1
[3,5,1,2,7,8,6,4]=>0000000=>1111111=>1
[7,5,1,4,8,2,6,3]=>0000000=>1111111=>1
[5,4,7,3,8,6,1,2]=>0000000=>1111111=>1
[5,8,4,7,6,3,1,2]=>0000000=>1111111=>1
[5,8,7,1,4,2,6,3]=>0000000=>1111111=>1
[8,3,5,1,2,7,6,4]=>0000000=>1111111=>1
[4,8,3,1,7,2,6,5]=>0000000=>1111111=>1
[1,8,4,3,5,2,7,6]=>1000000=>0111111=>1
[4,6,3,1,5,2,8,7]=>0000010=>1111101=>2
[4,7,3,6,5,2,1,8]=>0000001=>1111110=>1
[5,3,7,6,4,2,1,8]=>0000001=>1111110=>1
[1,6,3,4,2,8,7,5]=>1000000=>0111111=>1
[1,8,3,6,2,7,5,4]=>1000000=>0111111=>1
[1,6,8,7,4,2,5,3]=>1000000=>0111111=>1
[6,4,8,7,5,3,1,2]=>0000000=>1111111=>1
[7,6,4,3,8,5,1,2]=>0000000=>1111111=>1
[1,7,6,2,8,4,5,3]=>1000000=>0111111=>1
[7,1,3,2,6,8,5,4]=>0000000=>1111111=>1
[1,5,3,2,7,4,8,6]=>1000000=>0111111=>1
[6,3,2,1,8,5,4,7]=>0000000=>1111111=>1
[6,5,3,2,7,4,1,8]=>0000001=>1111110=>1
[5,2,6,3,7,4,1,8]=>0000001=>1111110=>1
[2,8,5,3,1,6,4,7]=>0000000=>1111111=>1
[2,1,7,3,8,5,4,6]=>0100000=>1011111=>2
[1,6,2,3,7,8,5,4]=>1000000=>0111111=>1
[1,6,7,2,8,4,5,3]=>1000000=>0111111=>1
[5,7,1,8,2,4,6,3]=>0000000=>1111111=>1
[5,1,2,7,8,3,6,4]=>0000000=>1111111=>1
[2,4,1,7,8,6,3,5]=>0000000=>1111111=>1
[4,2,1,7,3,8,5,6]=>0000000=>1111111=>1
[6,2,8,4,3,1,5,7]=>0000000=>1111111=>1
[7,3,2,1,8,4,5,6]=>0000000=>1111111=>1
[7,8,3,2,5,6,1,4]=>0000000=>1111111=>1
[7,1,8,2,4,5,6,3]=>0000000=>1111111=>1
[8,7,6,1,2,4,5,3]=>0000000=>1111111=>1
[8,3,7,6,2,1,4,5]=>0000000=>1111111=>1
[3,2,8,7,5,1,4,6]=>0000000=>1111111=>1
[8,3,6,5,2,1,4,7]=>0000000=>1111111=>1
[7,6,3,5,2,4,1,8]=>0000001=>1111110=>1
[7,4,6,2,5,3,1,8]=>0000001=>1111110=>1
[8,2,4,1,6,5,3,7]=>0000000=>1111111=>1
[4,2,8,1,7,5,3,6]=>0000000=>1111111=>1
[8,2,4,1,7,6,3,5]=>0000000=>1111111=>1
[8,7,1,5,6,2,4,3]=>0000000=>1111111=>1
[8,5,7,3,6,4,1,2]=>0000000=>1111111=>1
[6,8,3,7,5,4,1,2]=>0000000=>1111111=>1
[8,1,6,7,5,2,4,3]=>0000000=>1111111=>1
[8,1,2,6,4,3,7,5]=>0000000=>1111111=>1
[2,8,1,7,5,4,3,6]=>0000000=>1111111=>1
[2,5,1,8,6,4,3,7]=>0000000=>1111111=>1
[5,7,2,6,4,3,1,8]=>0000001=>1111110=>1
[6,2,7,5,4,3,1,8]=>0000001=>1111110=>1
[2,1,8,6,5,4,3,7]=>0100000=>1011111=>2
[1,2,7,5,4,3,8,6]=>1100000=>0011111=>1
[1,7,2,4,3,8,6,5]=>1000000=>0111111=>1
[1,7,2,8,3,6,5,4]=>1000000=>0111111=>1
[1,7,8,6,5,2,4,3]=>1000000=>0111111=>1
[7,3,8,6,5,4,1,2]=>0000000=>1111111=>1
[1,8,7,6,5,2,4,3]=>1000000=>0111111=>1
[8,1,7,3,2,6,5,4]=>0000000=>1111111=>1
[5,1,4,3,2,8,7,6]=>0000100=>1111011=>2
[8,6,5,3,2,1,7,4]=>0000000=>1111111=>1
[8,6,3,2,1,7,4,5]=>0000000=>1111111=>1
[8,6,5,4,1,7,2,3]=>0000000=>1111111=>1
[8,6,5,1,7,3,2,4]=>0000000=>1111111=>1
[8,6,1,7,4,3,2,5]=>0000000=>1111111=>1
[4,6,3,2,7,5,1,8]=>0000001=>1111110=>1
[1,4,3,7,2,5,8,6]=>1000000=>0111111=>1
[7,4,8,3,1,6,2,5]=>0000000=>1111111=>1
[7,1,5,8,3,2,6,4]=>0000000=>1111111=>1
[5,7,4,1,8,2,6,3]=>0000000=>1111111=>1
[5,7,4,3,1,8,6,2]=>0000000=>1111111=>1
[1,8,7,2,5,4,6,3]=>1000000=>0111111=>1
[1,8,5,3,7,2,6,4]=>1000000=>0111111=>1
[4,3,1,8,7,5,2,6]=>0000000=>1111111=>1
[1,4,8,6,3,5,2,7]=>1000000=>0111111=>1
[7,4,6,3,5,2,1,8]=>0000001=>1111110=>1
[1,3,5,6,8,4,2,7]=>1000000=>0111111=>1
[3,5,4,8,7,1,2,6]=>0000000=>1111111=>1
[3,1,4,6,8,7,2,5]=>0000000=>1111111=>1
[1,6,3,8,7,2,5,4]=>1000000=>0111111=>1
[1,6,2,4,8,7,5,3]=>1000000=>0111111=>1
[8,4,1,6,7,5,3,2]=>0000000=>1111111=>1
[7,1,6,4,8,5,2,3]=>0000000=>1111111=>1
[7,3,6,8,5,1,2,4]=>0000000=>1111111=>1
[1,3,7,2,6,8,4,5]=>1000000=>0111111=>1
[3,6,5,2,8,1,4,7]=>0000000=>1111111=>1
[3,6,5,7,2,4,1,8]=>0000001=>1111110=>1
[4,2,6,3,8,1,5,7]=>0000000=>1111111=>1
[4,2,6,7,3,5,1,8]=>0000001=>1111110=>1
[3,6,2,4,7,5,1,8]=>0000001=>1111110=>1
[3,6,2,4,1,8,5,7]=>0000000=>1111111=>1
[7,3,8,2,1,6,4,5]=>0000000=>1111111=>1
[7,3,5,2,1,8,6,4]=>0000000=>1111111=>1
[8,7,6,4,3,1,5,2]=>0000000=>1111111=>1
[8,7,6,4,1,5,2,3]=>0000000=>1111111=>1
[3,8,7,2,1,4,6,5]=>0000000=>1111111=>1
[3,8,2,7,1,5,4,6]=>0000000=>1111111=>1
[3,6,8,2,1,5,4,7]=>0000000=>1111111=>1
[2,4,8,1,6,5,3,7]=>0000000=>1111111=>1
[4,2,8,1,5,7,3,6]=>0000000=>1111111=>1
[8,5,7,6,1,4,2,3]=>0000000=>1111111=>1
[8,6,1,7,3,5,4,2]=>0000000=>1111111=>1
[8,6,1,7,5,4,2,3]=>0000000=>1111111=>1
[1,6,2,8,7,3,5,4]=>1000000=>0111111=>1
[1,8,2,4,6,7,3,5]=>1000000=>0111111=>1
[2,8,5,4,7,1,3,6]=>0000000=>1111111=>1
[2,1,5,8,6,4,3,7]=>0100000=>1011111=>2
[7,2,5,6,4,3,1,8]=>0000001=>1111110=>1
[1,2,5,7,8,4,3,6]=>1100000=>0011111=>1
[1,2,7,4,8,6,3,5]=>1100000=>0011111=>1
[1,2,7,8,3,6,5,4]=>1100000=>0011111=>1
[7,1,8,6,3,5,4,2]=>0000000=>1111111=>1
[1,8,7,6,3,5,2,4]=>1000000=>0111111=>1
[1,8,7,4,6,3,2,5]=>1000000=>0111111=>1
[7,1,5,8,3,4,6,2]=>0000000=>1111111=>1
[7,1,6,4,2,3,5,8]=>0000001=>1111110=>1
[8,6,2,4,7,3,5,1]=>0000000=>1111111=>1
[8,6,2,4,5,7,3,1]=>0000000=>1111111=>1
[2,7,1,4,5,8,3,6]=>0000000=>1111111=>1
[7,1,6,4,5,2,3,8]=>0000001=>1111110=>1
[7,1,4,5,6,8,2,3]=>0000000=>1111111=>1
[7,1,4,6,5,8,3,2]=>0000000=>1111111=>1
[7,1,2,3,8,5,4,6]=>0000000=>1111111=>1
[7,1,5,4,3,8,2,6]=>0000000=>1111111=>1
[7,1,3,4,2,6,8,5]=>0000000=>1111111=>1
[7,1,5,4,6,2,8,3]=>0000000=>1111111=>1
[7,1,5,6,4,3,8,2]=>0000000=>1111111=>1
[7,1,6,5,4,3,2,8]=>0000001=>1111110=>1
[8,6,2,5,4,3,7,1]=>0000000=>1111111=>1
[2,5,1,7,4,3,6,8]=>0000001=>1111110=>1
[2,5,1,4,7,8,6,3]=>0000000=>1111111=>1
[3,5,1,4,8,6,2,7]=>0000000=>1111111=>1
[3,6,2,4,7,8,1,5]=>0000000=>1111111=>1
[5,6,2,4,8,7,1,3]=>0000000=>1111111=>1
[6,3,8,2,4,7,1,5]=>0000000=>1111111=>1
[6,5,8,7,2,3,1,4]=>0000000=>1111111=>1
[6,5,7,8,2,4,1,3]=>0000000=>1111111=>1
[6,3,4,2,8,5,1,7]=>0000000=>1111111=>1
[3,4,7,2,5,8,1,6]=>0000000=>1111111=>1
[4,6,8,1,3,5,2,7]=>0000000=>1111111=>1
[4,3,8,1,2,7,5,6]=>0000000=>1111111=>1
[3,6,4,1,7,2,5,8]=>0000001=>1111110=>1
[2,8,3,1,5,6,4,7]=>0000000=>1111111=>1
[3,8,7,1,5,4,2,6]=>0000000=>1111111=>1
[4,3,1,7,6,8,2,5]=>0000000=>1111111=>1
[3,4,1,7,5,6,8,2]=>0000000=>1111111=>1
[3,4,1,5,7,6,2,8]=>0000001=>1111110=>1
[3,7,4,1,6,2,8,5]=>0000000=>1111111=>1
[8,4,7,2,5,3,6,1]=>0000000=>1111111=>1
[4,7,8,1,2,3,6,5]=>0000000=>1111111=>1
[2,8,6,1,5,3,7,4]=>0000000=>1111111=>1
[7,6,5,1,3,8,2,4]=>0000000=>1111111=>1
[7,6,5,1,3,4,8,2]=>0000000=>1111111=>1
[7,2,6,4,1,3,8,5]=>0000000=>1111111=>1
[6,7,5,2,1,3,8,4]=>0000000=>1111111=>1
[8,4,5,3,7,2,6,1]=>0000000=>1111111=>1
[4,7,5,2,8,1,6,3]=>0000000=>1111111=>1
[2,6,4,3,1,5,7,8]=>0000011=>1111100=>1
[7,3,8,4,1,5,2,6]=>0000000=>1111111=>1
[7,2,3,4,1,6,5,8]=>0000001=>1111110=>1
[4,2,8,3,6,1,5,7]=>0000000=>1111111=>1
[6,8,5,7,2,1,3,4]=>0000000=>1111111=>1
[4,8,5,2,7,1,3,6]=>0000000=>1111111=>1
[6,3,5,2,1,7,4,8]=>0000001=>1111110=>1
[6,8,5,3,1,4,2,7]=>0000000=>1111111=>1
[3,6,5,4,2,8,1,7]=>0000000=>1111111=>1
[1,6,4,7,2,5,3,8]=>1000001=>0111110=>1
[1,6,4,8,2,5,3,7]=>1000000=>0111111=>1
[1,6,5,8,2,4,3,7]=>1000000=>0111111=>1
[1,6,8,2,4,3,7,5]=>1000000=>0111111=>1
[1,6,2,4,3,7,8,5]=>1000000=>0111111=>1
[1,5,6,2,4,7,3,8]=>1000001=>0111110=>1
[1,5,6,2,4,7,8,3]=>1000000=>0111111=>1
[1,5,8,2,4,7,3,6]=>1000000=>0111111=>1
[1,5,7,2,4,8,3,6]=>1000000=>0111111=>1
[1,6,5,7,2,4,3,8]=>1000001=>0111110=>1
[1,6,7,2,4,3,8,5]=>1000000=>0111111=>1
[1,5,6,7,2,4,8,3]=>1000000=>0111111=>1
[1,5,8,2,4,6,7,3]=>1000000=>0111111=>1
[1,5,7,2,4,6,8,3]=>1000000=>0111111=>1
[1,5,7,8,3,2,4,6]=>1000000=>0111111=>1
[1,5,8,3,2,4,6,7]=>1000000=>0111111=>1
[1,5,6,2,4,8,3,7]=>1000000=>0111111=>1
[1,7,6,2,8,3,4,5]=>1000000=>0111111=>1
[1,7,3,4,2,8,6,5]=>1000000=>0111111=>1
[1,6,2,4,3,8,7,5]=>1000000=>0111111=>1
[1,5,6,2,4,8,7,3]=>1000000=>0111111=>1
[1,5,8,7,3,2,4,6]=>1000000=>0111111=>1
[1,4,2,3,5,8,7,6]=>1001100=>0110011=>2
[1,5,2,3,4,8,7,6]=>1000100=>0111011=>2
[1,6,5,2,3,8,7,4]=>1000000=>0111111=>1
[1,7,4,2,8,6,5,3]=>1000000=>0111111=>1
[1,7,6,5,2,8,4,3]=>1000000=>0111111=>1
[1,6,7,5,2,3,8,4]=>1000000=>0111111=>1
[1,7,5,2,8,4,3,6]=>1000000=>0111111=>1
[1,7,5,6,2,8,3,4]=>1000000=>0111111=>1
[1,5,7,6,2,4,8,3]=>1000000=>0111111=>1
[1,5,8,3,2,4,7,6]=>1000000=>0111111=>1
[1,6,5,2,3,7,4,8]=>1000001=>0111110=>1
[1,6,5,2,3,7,8,4]=>1000000=>0111111=>1
[1,6,8,4,2,3,7,5]=>1000000=>0111111=>1
[1,7,4,6,2,8,3,5]=>1000000=>0111111=>1
[1,7,3,5,2,8,4,6]=>1000000=>0111111=>1
[1,6,8,5,2,3,7,4]=>1000000=>0111111=>1
[1,6,4,2,3,7,8,5]=>1000000=>0111111=>1
[1,6,4,2,3,7,5,8]=>1000001=>0111110=>1
[1,5,8,6,2,4,7,3]=>1000000=>0111111=>1
[1,5,7,3,2,4,8,6]=>1000000=>0111111=>1
[1,7,3,4,2,8,5,6]=>1000000=>0111111=>1
[1,7,4,2,8,5,3,6]=>1000000=>0111111=>1
[1,6,7,4,2,3,8,5]=>1000000=>0111111=>1
[1,6,4,2,3,8,5,7]=>1000000=>0111111=>1
[1,7,6,4,2,8,5,3]=>1000000=>0111111=>1
[1,7,5,2,8,6,4,3]=>1000000=>0111111=>1
[1,6,4,2,3,8,7,5]=>1000000=>0111111=>1
[7,3,5,6,1,4,8,2]=>0000000=>1111111=>1
[3,7,5,6,1,4,8,2]=>0000000=>1111111=>1
[8,2,4,1,6,7,5,3]=>0000000=>1111111=>1
[8,6,1,4,2,7,5,3]=>0000000=>1111111=>1
[3,6,1,4,2,8,5,7]=>0000000=>1111111=>1
[1,6,7,4,3,5,8,2]=>1000000=>0111111=>1
[6,7,1,4,3,5,8,2]=>0000000=>1111111=>1
[7,6,1,4,3,5,8,2]=>0000000=>1111111=>1
[3,5,4,1,6,7,8,2]=>0000000=>1111111=>1
[4,7,1,6,3,5,8,2]=>0000000=>1111111=>1
[3,1,4,7,6,5,8,2]=>0000000=>1111111=>1
[6,1,7,4,3,5,8,2]=>0000000=>1111111=>1
[7,1,6,4,3,5,8,2]=>0000000=>1111111=>1
[1,7,6,4,3,5,8,2]=>1000000=>0111111=>1
[8,1,6,4,2,7,5,3]=>0000000=>1111111=>1
[8,4,1,3,7,2,5,6]=>0000000=>1111111=>1
[4,7,1,3,8,2,5,6]=>0000000=>1111111=>1
[7,4,1,3,8,2,5,6]=>0000000=>1111111=>1
[1,3,6,4,2,8,5,7]=>1000000=>0111111=>1
[4,7,3,1,2,8,5,6]=>0000000=>1111111=>1
[4,7,8,1,2,6,5,3]=>0000000=>1111111=>1
[6,8,1,4,2,7,5,3]=>0000000=>1111111=>1
[1,8,6,4,2,7,5,3]=>1000000=>0111111=>1
[4,8,1,3,7,2,5,6]=>0000000=>1111111=>1
[8,7,1,3,6,2,5,4]=>0000000=>1111111=>1
[6,8,5,7,3,2,1,4]=>0000000=>1111111=>1
[1,8,4,3,7,2,5,6]=>1000000=>0111111=>1
[2,8,3,4,7,6,1,5]=>0000000=>1111111=>1
[3,7,8,4,6,2,1,5]=>0000000=>1111111=>1
[3,7,4,6,8,2,1,5]=>0000000=>1111111=>1
[2,4,3,7,8,6,1,5]=>0000000=>1111111=>1
[1,4,7,3,8,2,5,6]=>1000000=>0111111=>1
[5,7,6,8,3,2,1,4]=>0000000=>1111111=>1
[2,5,3,4,8,6,1,7]=>0000000=>1111111=>1
[3,7,5,4,8,2,1,6]=>0000000=>1111111=>1
[7,1,3,4,2,8,5,6]=>0000000=>1111111=>1
[6,1,4,3,8,2,5,7]=>0000000=>1111111=>1
[4,1,7,3,8,2,5,6]=>0000000=>1111111=>1
[8,1,4,3,7,2,5,6]=>0000000=>1111111=>1
[8,2,3,4,7,6,1,5]=>0000000=>1111111=>1
[4,2,3,7,8,6,1,5]=>0000000=>1111111=>1
[5,2,3,4,8,6,1,7]=>0000000=>1111111=>1
[2,7,5,6,3,8,1,4]=>0000000=>1111111=>1
[5,7,2,6,3,8,1,4]=>0000000=>1111111=>1
[5,7,2,6,8,4,1,3]=>0000000=>1111111=>1
[7,2,5,6,8,4,1,3]=>0000000=>1111111=>1
[4,2,3,8,5,6,1,7]=>0000000=>1111111=>1
[5,2,3,8,7,6,1,4]=>0000000=>1111111=>1
[8,2,3,7,5,6,1,4]=>0000000=>1111111=>1
[6,1,8,3,7,2,5,4]=>0000000=>1111111=>1
[1,7,8,4,2,6,5,3]=>1000000=>0111111=>1
[4,7,1,8,2,5,6,3]=>0000000=>1111111=>1
[3,7,4,8,5,2,1,6]=>0000000=>1111111=>1
[2,4,3,8,5,6,1,7]=>0000000=>1111111=>1
[1,4,8,3,6,2,5,7]=>1000000=>0111111=>1
[7,5,8,6,3,2,1,4]=>0000000=>1111111=>1
[6,5,8,7,3,2,1,4]=>0000000=>1111111=>1
[8,5,7,6,3,2,1,4]=>0000000=>1111111=>1
[2,5,3,8,7,6,1,4]=>0000000=>1111111=>1
[3,7,5,8,6,2,1,4]=>0000000=>1111111=>1
[3,7,8,6,5,2,1,4]=>0000000=>1111111=>1
[1,8,7,3,6,2,5,4]=>1000000=>0111111=>1
[6,8,7,5,3,2,1,4]=>0000000=>1111111=>1
[5,7,6,8,3,4,1,2]=>0000000=>1111111=>1
[3,7,6,8,4,5,1,2]=>0000000=>1111111=>1
[1,5,4,7,6,8,2,3]=>1000000=>0111111=>1
[1,7,4,6,5,8,2,3]=>1000000=>0111111=>1
[3,7,4,6,5,8,1,2]=>0000000=>1111111=>1
[3,5,4,8,6,7,1,2]=>0000000=>1111111=>1
[3,8,4,6,5,7,1,2]=>0000000=>1111111=>1
[3,6,4,7,5,8,1,2]=>0000000=>1111111=>1
[1,6,2,7,5,8,3,4]=>1000000=>0111111=>1
[1,6,4,8,5,7,2,3]=>1000000=>0111111=>1
[1,8,4,6,5,7,2,3]=>1000000=>0111111=>1
[1,5,4,8,6,7,2,3]=>1000000=>0111111=>1
[7,8,1,5,4,6,2,3]=>0000000=>1111111=>1
[7,8,1,5,2,4,3,6]=>0000000=>1111111=>1
[1,8,2,6,5,7,3,4]=>1000000=>0111111=>1
[1,7,2,8,5,6,3,4]=>1000000=>0111111=>1
[1,7,2,6,5,8,3,4]=>1000000=>0111111=>1
[1,5,2,7,6,8,3,4]=>1000000=>0111111=>1
[1,7,6,8,2,5,3,4]=>1000000=>0111111=>1
[1,7,6,8,4,5,2,3]=>1000000=>0111111=>1
[5,7,6,8,1,4,2,3]=>0000000=>1111111=>1
[7,8,5,6,1,3,2,4]=>0000000=>1111111=>1
[5,8,6,7,1,3,2,4]=>0000000=>1111111=>1
[1,3,2,7,6,8,4,5]=>1010000=>0101111=>2
[1,7,6,8,2,4,3,5]=>1000000=>0111111=>1
[7,8,1,3,2,6,4,5]=>0000000=>1111111=>1
[7,8,1,6,2,4,3,5]=>0000000=>1111111=>1
[1,8,6,7,2,4,3,5]=>1000000=>0111111=>1
[7,8,1,4,2,6,3,5]=>0000000=>1111111=>1
[7,8,1,4,2,5,3,6]=>0000000=>1111111=>1
[7,8,2,1,4,3,6,5]=>0000000=>1111111=>1
[7,8,1,2,4,3,5,6]=>0000000=>1111111=>1
[4,3,6,5,8,7,1,2]=>0000000=>1111111=>1
[3,4,6,5,7,8,1,2]=>0000000=>1111111=>1
[3,4,1,5,6,7,8,9,2]=>00000000=>11111111=>1
[3,4,5,1,6,7,8,9,2]=>00000000=>11111111=>1
[3,4,5,6,1,7,8,9,2]=>00000000=>11111111=>1
[3,4,5,6,7,1,8,9,2]=>00000000=>11111111=>1
[3,4,5,6,7,8,1,9,2]=>00000000=>11111111=>1
[3,1,2,5,6,7,8,9,4]=>00100000=>11011111=>2
[3,4,1,5,6,7,8,9,10,2]=>000000000=>111111111=>1
[3,4,1,2,6,7,8,9,5]=>00010000=>11101111=>2
[3,4,5,1,6,7,8,9,10,2]=>000000000=>111111111=>1
[3,4,5,1,2,7,8,9,6]=>00001000=>11110111=>2
[3,4,5,6,1,7,8,9,10,2]=>000000000=>111111111=>1
[3,4,5,6,1,2,8,9,7]=>00000100=>11111011=>2
[3,4,5,6,7,1,8,9,10,2]=>000000000=>111111111=>1
[3,4,5,6,7,1,2,9,8]=>00000010=>11111101=>2
[3,4,5,6,7,8,1,9,10,2]=>000000000=>111111111=>1
[3,4,5,6,7,8,1,2,9]=>00000001=>11111110=>1
[3,4,5,6,7,8,9,1,10,2]=>000000000=>111111111=>1
[1,6,2,3,8,7,4,5]=>1000000=>0111111=>1
[1,7,4,3,2,8,6,5]=>1000000=>0111111=>1
[1,4,7,6,2,5,8,3]=>1000000=>0111111=>1
[1,2,6,5,3,7,4,8]=>1100001=>0011110=>1
[1,2,6,5,3,7,8,4]=>1100000=>0011111=>1
[1,3,7,5,2,6,8,4]=>1000000=>0111111=>1
[1,3,7,4,2,6,8,5]=>1000000=>0111111=>1
[1,2,6,4,3,7,8,5]=>1100000=>0011111=>1
[1,2,6,4,3,7,5,8]=>1100001=>0011110=>1
[1,4,7,3,2,5,8,6]=>1000000=>0111111=>1
[1,4,3,2,5,8,6,7]=>1001100=>0110011=>2
[1,5,3,2,4,8,6,7]=>1000100=>0111011=>2
[1,7,5,3,2,8,6,4]=>1000000=>0111111=>1
[1,5,3,2,4,8,7,6]=>1000100=>0111011=>2
[7,6,5,4,3,1,8,2]=>0000000=>1111111=>1
[6,8,5,4,3,2,1,7]=>0000000=>1111111=>1
[8,7,6,5,4,3,1,9,2]=>00000000=>11111111=>1
[7,9,6,5,4,3,2,1,8]=>00000000=>11111111=>1
[9,8,7,6,5,4,3,1,10,2]=>000000000=>111111111=>1
[1,7,6,5,4,3,9,8,2]=>10000000=>01111111=>1
[7,1,5,4,3,8,6,2]=>0000000=>1111111=>1
[3,6,5,4,8,1,7,2]=>0000000=>1111111=>1
[6,8,1,4,3,2,7,5]=>0000000=>1111111=>1
[2,8,5,4,3,7,1,6]=>0000000=>1111111=>1
[1,9,6,5,4,3,2,8,7]=>10000000=>01111111=>1
[8,10,7,6,5,4,3,2,1,9]=>000000000=>111111111=>1
[1,8,7,6,5,4,3,10,9,2]=>100000000=>011111111=>1
[8,1,6,5,4,3,9,7,2]=>00000000=>11111111=>1
[3,7,6,5,4,9,1,8,2]=>00000000=>11111111=>1
[7,6,1,4,3,8,5,2]=>0000000=>1111111=>1
[4,6,5,8,3,1,7,2]=>0000000=>1111111=>1
[6,8,5,1,3,2,7,4]=>0000000=>1111111=>1
[1,8,2,4,3,7,6,5]=>1000000=>0111111=>1
[7,9,1,5,4,3,2,8,6]=>00000000=>11111111=>1
[3,8,5,4,7,2,1,6]=>0000000=>1111111=>1
[2,9,6,5,4,3,8,1,7]=>00000000=>11111111=>1
[1,10,7,6,5,4,3,2,9,8]=>100000000=>011111111=>1
[1,9,8,7,6,5,4,3,11,10,2]=>1000000000=>0111111111=>1
[9,1,7,6,5,4,3,10,8,2]=>000000000=>111111111=>1
[3,8,7,6,5,4,10,1,9,2]=>000000000=>111111111=>1
[8,7,1,5,4,3,9,6,2]=>00000000=>11111111=>1
[1,3,6,5,4,9,8,7,2]=>10000000=>01111111=>1
[4,7,6,5,9,3,1,8,2]=>00000000=>11111111=>1
[7,6,5,1,3,8,4,2]=>0000000=>1111111=>1
[1,6,3,4,8,7,5,2]=>1000000=>0111111=>1
[1,4,5,8,3,7,6,2]=>1000000=>0111111=>1
[6,8,5,4,1,2,7,3]=>0000000=>1111111=>1
[1,8,5,2,3,7,6,4]=>1000000=>0111111=>1
[7,9,6,1,4,3,2,8,5]=>00000000=>11111111=>1
[6,8,2,4,3,7,1,5]=>0000000=>1111111=>1
[1,8,3,4,7,2,6,5]=>1000000=>0111111=>1
[1,9,2,5,4,3,8,7,6]=>10000000=>01111111=>1
[8,10,1,6,5,4,3,2,9,7]=>000000000=>111111111=>1
[7,5,8,4,3,2,1,6]=>0000000=>1111111=>1
[4,8,5,7,3,2,1,6]=>0000000=>1111111=>1
[3,9,6,5,4,8,2,1,7]=>00000000=>11111111=>1
[2,10,7,6,5,4,3,9,1,8]=>000000000=>111111111=>1
[1,11,8,7,6,5,4,3,2,10,9]=>1000000000=>0111111111=>1
[5,1,7,6,8,4,3,2]=>0000000=>1111111=>1
[8,4,7,5,2,6,1,3]=>0000000=>1111111=>1
[5,4,6,8,2,1,7,3]=>0000000=>1111111=>1
[8,4,6,5,2,1,7,3]=>0000000=>1111111=>1
[4,8,7,5,6,1,3,2]=>0000000=>1111111=>1
[5,1,8,7,4,2,3,6]=>0000000=>1111111=>1
[3,6,5,2,4,1,8,7]=>0000010=>1111101=>2
[3,8,7,1,4,6,5,2]=>0000000=>1111111=>1
[3,2,6,8,5,7,1,4]=>0000000=>1111111=>1
[6,3,7,2,4,8,5,1]=>0000000=>1111111=>1
[7,4,8,6,5,2,1,3]=>0000000=>1111111=>1
[2,5,3,7,4,1,8,6]=>0000000=>1111111=>1
[8,4,7,6,2,3,1,5]=>0000000=>1111111=>1
[4,2,8,7,3,5,6,1]=>0000000=>1111111=>1
[8,1,7,4,2,5,6,3]=>0000000=>1111111=>1
[7,4,3,8,2,5,6,1]=>0000000=>1111111=>1
[2,5,8,7,3,6,1,4]=>0000000=>1111111=>1
[4,1,7,2,8,5,6,3]=>0000000=>1111111=>1
[4,7,8,3,1,5,6,2]=>0000000=>1111111=>1
[3,4,7,2,8,5,6,1]=>0000000=>1111111=>1
[6,1,8,5,2,7,4,3]=>0000000=>1111111=>1
[8,2,1,6,4,7,5,3]=>0000000=>1111111=>1
[7,8,2,6,4,1,5,3]=>0000000=>1111111=>1
[2,6,3,5,8,7,1,4]=>0000000=>1111111=>1
[7,4,8,6,5,2,3,1]=>0000000=>1111111=>1
[8,1,6,4,7,3,2,5]=>0000000=>1111111=>1
[4,8,7,5,6,1,2,3]=>0000000=>1111111=>1
[6,1,4,8,7,3,5,2]=>0000000=>1111111=>1
[7,2,8,4,3,5,6,1]=>0000000=>1111111=>1
[3,8,1,7,2,5,6,4]=>0000000=>1111111=>1
[4,3,8,2,7,6,1,5]=>0000000=>1111111=>1
[2,8,3,7,1,5,6,4]=>0000000=>1111111=>1
[7,2,5,4,3,8,1,6]=>0000000=>1111111=>1
[3,8,6,1,2,5,4,7]=>0000000=>1111111=>1
[4,1,6,5,8,2,3,7]=>0000000=>1111111=>1
[8,3,6,1,4,5,2,7]=>0000000=>1111111=>1
[2,7,5,4,3,8,1,6]=>0000000=>1111111=>1
[8,7,4,3,1,6,2,5]=>0000000=>1111111=>1
[1,7,4,3,8,6,2,5]=>1000000=>0111111=>1
[2,8,6,1,7,4,5,3]=>0000000=>1111111=>1
[4,8,6,5,7,2,1,3]=>0000000=>1111111=>1
[6,1,8,7,4,3,5,2]=>0000000=>1111111=>1
[4,1,3,8,5,6,7,2]=>0000000=>1111111=>1
[6,5,8,4,3,1,7,2]=>0000000=>1111111=>1
[4,6,5,2,8,1,7,3]=>0000000=>1111111=>1
[7,2,8,1,3,6,4,5]=>0000000=>1111111=>1
[1,8,5,2,3,6,7,4]=>1000000=>0111111=>1
[1,8,3,2,5,6,7,4]=>1000000=>0111111=>1
[2,8,3,1,5,6,7,4]=>0000000=>1111111=>1
[4,8,3,2,5,6,7,1]=>0000000=>1111111=>1
[8,2,3,1,5,6,7,4]=>0000000=>1111111=>1
[2,1,8,3,5,6,7,4]=>0100000=>1011111=>2
[3,5,8,1,2,4,7,6]=>0000000=>1111111=>1
[4,5,8,1,2,3,7,6]=>0000000=>1111111=>1
[4,2,7,1,8,6,3,5]=>0000000=>1111111=>1
[3,8,4,1,2,6,7,5]=>0000000=>1111111=>1
[2,7,1,4,3,8,5,6]=>0000000=>1111111=>1
[3,5,2,8,6,1,7,4]=>0000000=>1111111=>1
[8,2,5,6,1,4,7,3]=>0000000=>1111111=>1
[2,6,1,8,3,7,5,4]=>0000000=>1111111=>1
[7,6,1,5,8,2,3,4]=>0000000=>1111111=>1
[3,6,8,5,1,2,7,4]=>0000000=>1111111=>1
[4,2,1,8,5,6,7,3]=>0000000=>1111111=>1
[7,6,1,2,8,3,5,4]=>0000000=>1111111=>1
[7,5,8,4,1,2,6,3]=>0000000=>1111111=>1
[7,5,8,4,6,1,3,2]=>0000000=>1111111=>1
[6,5,4,8,7,1,3,2]=>0000000=>1111111=>1
[6,5,4,8,1,2,7,3]=>0000000=>1111111=>1
[7,5,1,6,2,3,8,4]=>0000000=>1111111=>1
[7,5,1,6,8,2,4,3]=>0000000=>1111111=>1
[6,5,4,1,8,2,7,3]=>0000000=>1111111=>1
[6,5,4,7,1,2,8,3]=>0000000=>1111111=>1
[6,5,4,7,8,1,3,2]=>0000000=>1111111=>1
[6,5,3,7,1,4,2,8]=>0000001=>1111110=>1
[6,5,3,1,8,4,2,7]=>0000000=>1111111=>1
[7,5,1,4,8,3,2,6]=>0000000=>1111111=>1
[8,1,6,4,7,3,5,2]=>0000000=>1111111=>1
[7,5,1,4,8,3,6,2]=>0000000=>1111111=>1
[6,5,3,7,1,4,8,2]=>0000000=>1111111=>1
[6,4,3,1,5,8,7,2]=>0000000=>1111111=>1
[7,4,1,5,3,8,6,2]=>0000000=>1111111=>1
[8,1,5,4,3,7,6,2]=>0000000=>1111111=>1
[8,1,5,4,3,7,2,6]=>0000000=>1111111=>1
[7,4,1,5,3,8,2,6]=>0000000=>1111111=>1
[7,4,1,5,3,2,6,8]=>0000001=>1111110=>1
[8,1,5,4,3,2,6,7]=>0000000=>1111111=>1
[8,1,6,4,2,5,3,7]=>0000000=>1111111=>1
[6,5,3,1,2,7,4,8]=>0000001=>1111110=>1
[6,5,3,8,1,4,2,7]=>0000000=>1111111=>1
[7,6,8,1,4,3,2,5]=>0000000=>1111111=>1
[8,1,7,2,5,4,3,6]=>0000000=>1111111=>1
[8,1,7,2,5,4,6,3]=>0000000=>1111111=>1
[7,6,1,2,5,4,8,3]=>0000000=>1111111=>1
[6,5,3,8,1,4,7,2]=>0000000=>1111111=>1
[6,5,3,1,2,7,8,4]=>0000000=>1111111=>1
[7,5,1,4,2,6,8,3]=>0000000=>1111111=>1
[8,1,6,4,2,5,7,3]=>0000000=>1111111=>1
[7,4,1,5,3,2,8,6]=>0000000=>1111111=>1
[6,4,3,1,5,2,8,7]=>0000010=>1111101=>2
[6,4,3,1,5,7,2,8]=>0000001=>1111110=>1
[7,4,1,5,3,6,2,8]=>0000001=>1111110=>1
[8,1,5,4,3,6,2,7]=>0000000=>1111111=>1
[8,1,5,4,3,6,7,2]=>0000000=>1111111=>1
[7,4,1,5,3,6,8,2]=>0000000=>1111111=>1
[6,4,3,1,5,7,8,2]=>0000000=>1111111=>1
[6,7,3,8,4,5,1,2]=>0000000=>1111111=>1
[6,7,4,5,1,8,2,3]=>0000000=>1111111=>1
[4,7,5,6,2,3,1,8]=>0000001=>1111110=>1
[4,7,5,6,1,8,2,3]=>0000000=>1111111=>1
[4,7,5,6,3,8,1,2]=>0000000=>1111111=>1
[3,7,5,8,4,6,1,2]=>0000000=>1111111=>1
[4,5,3,8,6,7,1,2]=>0000000=>1111111=>1
[4,8,3,6,5,7,1,2]=>0000000=>1111111=>1
[5,6,4,7,1,8,2,3]=>0000000=>1111111=>1
[5,6,1,7,3,8,2,4]=>0000000=>1111111=>1
[5,6,1,8,2,7,3,4]=>0000000=>1111111=>1
[5,6,1,8,4,7,2,3]=>0000000=>1111111=>1
[4,8,1,6,5,7,2,3]=>0000000=>1111111=>1
[4,5,1,8,6,7,2,3]=>0000000=>1111111=>1
[7,8,4,5,1,6,2,3]=>0000000=>1111111=>1
[4,8,2,3,1,6,5,7]=>0000000=>1111111=>1
[5,6,2,8,1,4,3,7]=>0000000=>1111111=>1
[5,6,3,4,1,8,2,7]=>0000000=>1111111=>1
[3,6,4,5,2,7,1,8]=>0000001=>1111110=>1
[3,6,4,5,1,8,2,7]=>0000000=>1111111=>1
[2,6,4,8,1,5,3,7]=>0000000=>1111111=>1
[2,8,3,6,1,5,4,7]=>0000000=>1111111=>1
[2,8,3,4,1,6,5,7]=>0000000=>1111111=>1
[7,8,2,5,3,4,1,6]=>0000000=>1111111=>1
[7,8,1,5,3,6,2,4]=>0000000=>1111111=>1
[1,5,3,8,6,7,2,4]=>1000000=>0111111=>1
[1,8,3,6,2,7,4,5]=>1000000=>0111111=>1
[1,6,4,8,2,7,3,5]=>1000000=>0111111=>1
[2,6,4,7,3,5,1,8]=>0000001=>1111110=>1
[2,7,3,6,4,5,1,8]=>0000001=>1111110=>1
[1,7,3,6,4,8,2,5]=>1000000=>0111111=>1
[1,7,2,8,4,6,3,5]=>1000000=>0111111=>1
[1,7,5,8,4,6,2,3]=>1000000=>0111111=>1
[1,7,5,8,2,6,3,4]=>1000000=>0111111=>1
[1,7,5,6,3,8,2,4]=>1000000=>0111111=>1
[2,7,5,6,3,4,1,8]=>0000001=>1111110=>1
[6,7,2,5,3,4,1,8]=>0000001=>1111110=>1
[6,7,1,5,3,8,2,4]=>0000000=>1111111=>1
[6,7,5,8,1,4,2,3]=>0000000=>1111111=>1
[5,8,6,7,2,3,1,4]=>0000000=>1111111=>1
[6,7,2,3,1,8,4,5]=>0000000=>1111111=>1
[6,7,2,8,1,4,3,5]=>0000000=>1111111=>1
[3,4,2,7,5,6,1,8]=>0000001=>1111110=>1
[3,4,1,7,5,8,2,6]=>0000000=>1111111=>1
[2,7,5,8,1,4,3,6]=>0000000=>1111111=>1
[2,3,1,7,5,8,4,6]=>0010000=>1101111=>2
[2,3,1,8,4,7,5,6]=>0010000=>1101111=>2
[7,8,2,3,1,6,4,5]=>0000000=>1111111=>1
[7,8,2,6,1,4,3,5]=>0000000=>1111111=>1
[2,8,6,7,1,4,3,5]=>0000000=>1111111=>1
[2,8,1,4,3,7,5,6]=>0000000=>1111111=>1
[3,7,2,5,4,6,1,8]=>0000001=>1111110=>1
[4,5,2,7,3,6,1,8]=>0000001=>1111110=>1
[4,5,1,8,2,7,3,6]=>0000000=>1111111=>1
[3,4,1,8,2,7,5,6]=>0000000=>1111111=>1
[3,4,1,8,6,7,2,5]=>0000000=>1111111=>1
[3,4,2,5,1,8,6,7]=>0000100=>1111011=>2
[3,4,2,8,1,6,5,7]=>0000000=>1111111=>1
[3,8,2,5,1,6,4,7]=>0000000=>1111111=>1
[4,5,2,8,1,6,3,7]=>0000000=>1111111=>1
[4,5,3,6,1,8,2,7]=>0000000=>1111111=>1
[7,1,5,8,4,6,2,3]=>0000000=>1111111=>1
[8,6,7,1,4,2,5,3]=>0000000=>1111111=>1
[8,6,3,7,5,1,2,4]=>0000000=>1111111=>1
[8,6,1,7,3,2,5,4]=>0000000=>1111111=>1
[7,6,1,8,3,5,2,4]=>0000000=>1111111=>1
[7,6,1,3,8,5,2,4]=>0000000=>1111111=>1
[7,6,8,2,4,5,1,3]=>0000000=>1111111=>1
[7,6,2,8,3,5,1,4]=>0000000=>1111111=>1
[7,6,2,3,8,5,1,4]=>0000000=>1111111=>1
[8,7,1,5,2,6,3,4]=>0000000=>1111111=>1
[8,7,1,5,2,3,6,4]=>0000000=>1111111=>1
[8,5,2,3,1,7,6,4]=>0000000=>1111111=>1
[8,6,2,3,7,1,5,4]=>0000000=>1111111=>1
[8,6,2,7,3,1,5,4]=>0000000=>1111111=>1
[8,6,7,2,4,1,5,3]=>0000000=>1111111=>1
[6,8,7,3,4,1,5,2]=>0000000=>1111111=>1
[8,7,2,5,1,6,3,4]=>0000000=>1111111=>1
[8,7,2,1,4,6,3,5]=>0000000=>1111111=>1
[8,4,2,1,7,6,3,5]=>0000000=>1111111=>1
[8,5,2,7,1,6,3,4]=>0000000=>1111111=>1
[8,5,7,2,1,4,3,6]=>0000000=>1111111=>1
[5,8,7,3,1,4,2,6]=>0000000=>1111111=>1
[5,8,7,3,1,4,6,2]=>0000000=>1111111=>1
[8,5,7,2,1,4,6,3]=>0000000=>1111111=>1
[8,5,2,7,1,3,6,4]=>0000000=>1111111=>1
[8,4,2,1,3,7,6,5]=>0000000=>1111111=>1
[8,7,4,1,2,3,6,5]=>0000000=>1111111=>1
[8,7,4,1,2,6,3,5]=>0000000=>1111111=>1
[8,4,3,1,7,2,6,5]=>0000000=>1111111=>1
[8,4,3,1,2,7,6,5]=>0000000=>1111111=>1
[8,6,1,3,7,2,5,4]=>0000000=>1111111=>1
[8,5,1,3,2,7,6,4]=>0000000=>1111111=>1
[8,5,7,4,1,6,2,3]=>0000000=>1111111=>1
[8,5,7,4,1,2,6,3]=>0000000=>1111111=>1
[8,1,5,4,2,7,6,3]=>0000000=>1111111=>1
[8,1,6,4,7,2,5,3]=>0000000=>1111111=>1
[6,1,5,8,4,2,7,3]=>0000000=>1111111=>1
[5,8,3,6,4,1,2,7]=>0000000=>1111111=>1
[5,2,8,6,4,1,3,7]=>0000000=>1111111=>1
[8,4,7,5,1,6,2,3]=>0000000=>1111111=>1
[8,4,7,5,1,2,6,3]=>0000000=>1111111=>1
[8,4,7,5,1,2,3,6]=>0000000=>1111111=>1
[8,7,3,5,1,2,6,4]=>0000000=>1111111=>1
[8,3,2,6,5,1,4,7]=>0000000=>1111111=>1
[4,8,6,3,5,1,2,7]=>0000000=>1111111=>1
[4,8,7,3,1,5,2,6]=>0000000=>1111111=>1
[8,4,7,2,1,5,3,6]=>0000000=>1111111=>1
[8,3,2,7,1,5,4,6]=>0000000=>1111111=>1
[8,3,2,1,7,6,4,5]=>0000000=>1111111=>1
[8,7,3,1,4,2,6,5]=>0000000=>1111111=>1
[8,7,3,1,6,2,4,5]=>0000000=>1111111=>1
[8,7,3,1,2,6,4,5]=>0000000=>1111111=>1
[8,7,3,1,2,4,6,5]=>0000000=>1111111=>1
[8,3,2,1,4,7,6,5]=>0000000=>1111111=>1
[8,3,2,1,7,4,6,5]=>0000000=>1111111=>1
[8,3,2,7,1,5,6,4]=>0000000=>1111111=>1
[8,4,7,2,1,5,6,3]=>0000000=>1111111=>1
[3,8,7,4,1,2,5,6]=>0000000=>1111111=>1
[8,7,2,1,6,3,4,5]=>0000000=>1111111=>1
[8,7,2,1,3,6,4,5]=>0000000=>1111111=>1
[8,7,2,1,3,4,6,5]=>0000000=>1111111=>1
[2,1,4,7,6,3,8,5]=>0100000=>1011111=>2
[6,4,7,8,5,3,2,1]=>0000000=>1111111=>1
[4,1,3,7,6,2,8,5]=>0000000=>1111111=>1
[4,2,8,6,7,3,1,5]=>0000000=>1111111=>1
[7,4,3,8,2,1,5,6]=>0000000=>1111111=>1
[4,7,5,8,1,6,3,2]=>0000000=>1111111=>1
[4,2,5,1,6,7,8,3]=>0000000=>1111111=>1
[7,8,2,5,6,1,4,3]=>0000000=>1111111=>1
[6,5,7,2,8,4,3,1]=>0000000=>1111111=>1
[6,5,8,2,1,7,3,4]=>0000000=>1111111=>1
[7,4,3,5,1,6,8,2]=>0000000=>1111111=>1
[4,1,6,3,5,8,7,2]=>0000000=>1111111=>1
[8,6,7,1,5,4,3,2]=>0000000=>1111111=>1
[2,1,6,5,8,4,7,3]=>0100000=>1011111=>2
[4,1,8,5,6,2,3,7]=>0000000=>1111111=>1
[2,6,4,8,7,3,5,1]=>0000000=>1111111=>1
[7,4,8,6,3,2,5,1]=>0000000=>1111111=>1
[5,8,4,7,2,1,3,6]=>0000000=>1111111=>1
[2,1,8,4,3,7,5,6]=>0100000=>1011111=>2
[6,3,8,2,4,5,7,1]=>0000000=>1111111=>1
[5,8,4,2,3,6,1,7]=>0000000=>1111111=>1
[5,8,2,4,3,1,6,7]=>0000000=>1111111=>1
[2,8,3,1,6,4,5,7]=>0000000=>1111111=>1
[1,4,8,2,6,3,5,7]=>1000000=>0111111=>1
[1,2,7,3,5,4,8,6]=>1100000=>0011111=>1
[1,2,3,8,4,5,7,6]=>1110000=>0001111=>1
[1,2,8,3,4,5,7,6]=>1100000=>0011111=>1
[1,3,8,2,6,4,5,7]=>1000000=>0111111=>1
[1,5,7,2,3,6,4,8]=>1000001=>0111110=>1
[1,7,2,3,5,4,8,6]=>1000000=>0111111=>1
[1,3,8,2,4,5,7,6]=>1000000=>0111111=>1
[1,2,3,8,4,6,7,5]=>1110000=>0001111=>1
[1,8,2,3,5,4,6,7]=>1000000=>0111111=>1
[1,7,8,2,3,6,4,5]=>1000000=>0111111=>1
[1,6,7,8,2,3,5,4]=>1000000=>0111111=>1
[1,7,8,2,5,3,6,4]=>1000000=>0111111=>1
[1,7,8,2,4,5,3,6]=>1000000=>0111111=>1
[1,2,8,3,6,4,5,7]=>1100000=>0011111=>1
[1,8,2,3,6,4,5,7]=>1000000=>0111111=>1
[1,2,8,3,5,4,6,7]=>1100000=>0011111=>1
[1,2,7,8,3,6,4,5]=>1100000=>0011111=>1
[1,5,2,7,8,3,6,4]=>1000000=>0111111=>1
[1,3,2,8,4,6,7,5]=>1010000=>0101111=>2
[1,8,2,3,4,6,7,5]=>1000000=>0111111=>1
[1,7,8,2,4,3,6,5]=>1000000=>0111111=>1
[6,7,3,1,5,2,8,4]=>0000000=>1111111=>1
[7,3,6,1,5,2,4,8]=>0000001=>1111110=>1
[6,4,7,5,1,2,8,3]=>0000000=>1111111=>1
[6,2,1,7,5,3,8,4]=>0000000=>1111111=>1
[5,4,8,6,1,7,2,3]=>0000000=>1111111=>1
[5,4,7,6,1,8,2,3]=>0000000=>1111111=>1
[4,6,5,7,8,1,2,3]=>0000000=>1111111=>1
[5,7,4,6,1,8,2,3]=>0000000=>1111111=>1
[5,7,3,1,6,8,2,4]=>0000000=>1111111=>1
[5,7,4,8,1,6,2,3]=>0000000=>1111111=>1
[5,3,8,1,7,6,2,4]=>0000000=>1111111=>1
[5,4,8,7,1,6,2,3]=>0000000=>1111111=>1
[4,6,8,7,5,1,2,3]=>0000000=>1111111=>1
[4,7,8,6,5,1,2,3]=>0000000=>1111111=>1
[2,5,4,7,3,6,1,8]=>0000001=>1111110=>1
[2,4,6,3,7,5,1,8]=>0000001=>1111110=>1
[4,2,7,3,6,5,1,8]=>0000001=>1111110=>1
[4,2,6,3,1,5,8,7]=>0000010=>1111101=>2
[2,5,3,1,6,4,8,7]=>0000010=>1111101=>2
[2,5,3,7,6,4,1,8]=>0000001=>1111110=>1
[2,6,5,3,7,4,1,8]=>0000001=>1111110=>1
[4,2,7,6,3,5,1,8]=>0000001=>1111110=>1
[2,7,5,3,6,4,1,8]=>0000001=>1111110=>1
[2,6,3,7,5,4,1,8]=>0000001=>1111110=>1
[1,7,5,2,3,8,4,6]=>1000000=>0111111=>1
[2,1,3,7,5,4,8,6]=>0110000=>1001111=>2
[2,3,1,8,6,5,4,7]=>0010000=>1101111=>2
[2,5,3,1,8,6,4,7]=>0000000=>1111111=>1
[4,2,8,3,1,6,5,7]=>0000000=>1111111=>1
[8,3,2,6,4,1,5,7]=>0000000=>1111111=>1
[3,6,8,2,1,4,5,7]=>0000000=>1111111=>1
[1,5,2,8,3,4,7,6]=>1000000=>0111111=>1
[1,2,6,3,8,7,4,5]=>1100000=>0011111=>1
[1,2,8,3,6,4,7,5]=>1100000=>0011111=>1
[1,2,7,6,3,4,8,5]=>1100000=>0011111=>1
[2,1,3,8,7,5,4,6]=>0110000=>1001111=>2
[1,2,3,8,6,4,7,5]=>1110000=>0001111=>1
[1,2,3,7,4,8,6,5]=>1110000=>0001111=>1
[1,2,7,6,3,8,4,5]=>1100000=>0011111=>1
[1,2,3,6,4,8,7,5]=>1110000=>0001111=>1
[1,2,3,7,6,4,8,5]=>1110000=>0001111=>1
[2,6,3,1,8,5,4,7]=>0000000=>1111111=>1
[2,1,3,8,5,4,7,6]=>0110000=>1001111=>2
[7,1,8,4,2,3,5,6]=>0000000=>1111111=>1
[2,1,8,4,3,5,7,6]=>0100000=>1011111=>2
[4,2,6,3,1,8,5,7]=>0000000=>1111111=>1
[5,4,2,8,3,1,6,7]=>0000000=>1111111=>1
[3,5,8,2,4,1,6,7]=>0000000=>1111111=>1
[2,5,4,8,3,1,6,7]=>0000000=>1111111=>1
[4,2,1,8,3,5,7,6]=>0000000=>1111111=>1
[1,8,7,4,2,3,5,6]=>1000000=>0111111=>1
[1,5,2,8,7,3,4,6]=>1000000=>0111111=>1
[1,2,7,3,6,4,8,5]=>1100000=>0011111=>1
[1,2,8,6,3,7,4,5]=>1100000=>0011111=>1
[1,2,7,3,8,6,4,5]=>1100000=>0011111=>1
[1,2,3,8,4,7,6,5]=>1110000=>0001111=>1
[1,2,7,3,4,8,6,5]=>1100000=>0011111=>1
[1,2,6,3,8,4,7,5]=>1100000=>0011111=>1
[1,5,2,3,8,7,4,6]=>1000000=>0111111=>1
[4,2,1,8,3,7,5,6]=>0000000=>1111111=>1
[8,3,2,1,7,4,5,6]=>0000000=>1111111=>1
[1,8,4,2,7,3,5,6]=>1000000=>0111111=>1
[1,2,8,6,3,4,7,5]=>1100000=>0011111=>1
[1,2,7,3,8,4,6,5]=>1100000=>0011111=>1
[1,2,3,8,7,4,6,5]=>1110000=>0001111=>1
[1,2,3,8,7,6,4,5]=>1110000=>0001111=>1
[2,5,3,8,1,6,4,7]=>0000000=>1111111=>1
[2,6,4,7,1,5,3,8]=>0000001=>1111110=>1
[2,6,5,7,1,4,3,8]=>0000001=>1111110=>1
[3,8,5,7,1,2,6,4]=>0000000=>1111111=>1
[3,8,5,7,2,6,4,1]=>0000000=>1111111=>1
[3,4,8,6,2,5,7,1]=>0000000=>1111111=>1
[3,4,8,6,1,2,5,7]=>0000000=>1111111=>1
[2,5,7,1,4,8,6,3]=>0000000=>1111111=>1
[2,4,8,1,5,7,6,3]=>0000000=>1111111=>1
[2,4,3,8,1,6,5,7]=>0000000=>1111111=>1
[2,8,1,7,5,6,4,3]=>0000000=>1111111=>1
[2,3,8,1,6,5,7,4]=>0000000=>1111111=>1
[2,4,8,1,3,5,7,6]=>0000000=>1111111=>1
[3,5,7,6,1,2,4,8]=>0000001=>1111110=>1
[3,5,7,6,2,4,8,1]=>0000000=>1111111=>1
[4,8,6,7,2,3,5,1]=>0000000=>1111111=>1
[4,8,6,7,1,2,3,5]=>0000000=>1111111=>1
[4,8,6,7,1,3,5,2]=>0000000=>1111111=>1
[3,4,8,6,1,5,7,2]=>0000000=>1111111=>1
[3,8,5,7,1,6,4,2]=>0000000=>1111111=>1
[3,2,8,5,6,1,7,4]=>0000000=>1111111=>1
[3,8,5,7,2,1,6,4]=>0000000=>1111111=>1
[3,4,8,6,2,1,5,7]=>0000000=>1111111=>1
[3,5,7,6,2,1,4,8]=>0000001=>1111110=>1
[4,8,6,7,2,1,3,5]=>0000000=>1111111=>1
[4,8,6,7,3,5,2,1]=>0000000=>1111111=>1
[5,8,6,7,3,4,2,1]=>0000000=>1111111=>1
[5,8,6,7,2,1,3,4]=>0000000=>1111111=>1
[5,8,6,7,2,1,4,3]=>0000000=>1111111=>1
[4,8,6,7,2,1,5,3]=>0000000=>1111111=>1
[4,3,1,7,5,2,8,6]=>0000000=>1111111=>1
[4,3,2,8,5,1,7,6]=>0000000=>1111111=>1
[4,3,8,5,1,6,7,2]=>0000000=>1111111=>1
[4,8,6,7,1,5,3,2]=>0000000=>1111111=>1
[5,8,6,7,1,4,3,2]=>0000000=>1111111=>1
[5,8,6,7,2,3,4,1]=>0000000=>1111111=>1
[5,8,6,7,2,4,3,1]=>0000000=>1111111=>1
[5,8,6,7,1,2,4,3]=>0000000=>1111111=>1
[4,2,3,8,5,1,6,7]=>0000000=>1111111=>1
[4,2,8,5,1,7,6,3]=>0000000=>1111111=>1
[3,4,2,8,5,6,1,7]=>0000000=>1111111=>1
[3,2,4,8,6,1,5,7]=>0000000=>1111111=>1
[3,2,5,7,6,1,4,8]=>0000001=>1111110=>1
[4,8,6,7,1,3,2,5]=>0000000=>1111111=>1
[4,8,6,7,1,2,5,3]=>0000000=>1111111=>1
[4,8,6,7,2,5,3,1]=>0000000=>1111111=>1
[4,3,8,5,2,6,7,1]=>0000000=>1111111=>1
[4,3,8,5,1,2,6,7]=>0000000=>1111111=>1
[4,2,6,7,5,1,3,8]=>0000001=>1111110=>1
[3,8,5,7,1,4,2,6]=>0000000=>1111111=>1
[3,8,4,7,1,5,2,6]=>0000000=>1111111=>1
[3,5,2,8,4,6,1,7]=>0000000=>1111111=>1
[3,5,1,7,4,6,2,8]=>0000001=>1111110=>1
[3,8,4,7,2,5,1,6]=>0000000=>1111111=>1
[4,1,3,8,5,2,6,7]=>0000000=>1111111=>1
[4,1,2,6,7,5,3,8]=>0000001=>1111110=>1
[4,2,6,7,5,3,8,1]=>0000000=>1111111=>1
[4,8,6,7,3,2,5,1]=>0000000=>1111111=>1
[4,8,6,7,3,1,2,5]=>0000000=>1111111=>1
[3,1,5,7,6,2,4,8]=>0000001=>1111110=>1
[3,4,1,7,5,6,2,8]=>0000001=>1111110=>1
[4,1,7,5,2,8,6,3]=>0000000=>1111111=>1
[4,1,6,7,5,2,3,8]=>0000001=>1111110=>1
[4,8,6,7,2,3,1,5]=>0000000=>1111111=>1
[5,8,6,7,3,2,4,1]=>0000000=>1111111=>1
[5,8,6,7,4,2,3,1]=>0000000=>1111111=>1
[5,8,6,7,4,1,2,3]=>0000000=>1111111=>1
[5,8,6,7,4,1,3,2]=>0000000=>1111111=>1
[5,8,6,7,3,1,4,2]=>0000000=>1111111=>1
[4,8,6,7,3,1,5,2]=>0000000=>1111111=>1
[4,1,6,7,5,3,8,2]=>0000000=>1111111=>1
[4,1,7,5,3,2,8,6]=>0000000=>1111111=>1
[4,2,8,5,3,1,7,6]=>0000000=>1111111=>1
[4,2,1,6,7,5,3,8]=>0000001=>1111110=>1
[4,8,6,7,3,2,1,5]=>0000000=>1111111=>1
[5,8,6,7,4,2,1,3]=>0000000=>1111111=>1
[5,8,6,7,4,3,1,2]=>0000000=>1111111=>1
[7,3,5,8,1,4,2,6]=>0000000=>1111111=>1
[3,8,7,6,1,4,2,5]=>0000000=>1111111=>1
[5,1,8,3,6,7,2,4]=>0000000=>1111111=>1
[1,4,7,8,5,6,2,3]=>1000000=>0111111=>1
[3,4,7,1,5,8,6,2]=>0000000=>1111111=>1
[3,6,1,4,7,8,5,2]=>0000000=>1111111=>1
[1,6,8,4,7,5,2,3]=>1000000=>0111111=>1
[6,8,1,3,5,7,2,4]=>0000000=>1111111=>1
[7,6,1,4,3,8,2,5]=>0000000=>1111111=>1
[3,8,1,6,5,4,2,7]=>0000000=>1111111=>1
[4,1,3,7,5,8,2,6]=>0000000=>1111111=>1
[6,1,7,3,8,4,2,5]=>0000000=>1111111=>1
[7,1,8,6,3,5,2,4]=>0000000=>1111111=>1
[3,1,7,6,5,8,4,2]=>0000000=>1111111=>1
[8,2,7,6,5,3,4,1]=>0000000=>1111111=>1
[8,4,2,6,7,5,3,1]=>0000000=>1111111=>1
[4,8,1,6,7,5,3,2]=>0000000=>1111111=>1
[7,4,1,6,8,2,5,3]=>0000000=>1111111=>1
[1,3,8,6,2,7,5,4]=>1000000=>0111111=>1
[6,1,3,2,7,8,4,5]=>0000000=>1111111=>1
[1,8,6,2,5,3,4,7]=>1000000=>0111111=>1
[4,7,2,6,8,1,5,3]=>0000000=>1111111=>1
[8,7,3,6,4,5,2,1]=>0000000=>1111111=>1
[5,7,8,6,2,1,4,3]=>0000000=>1111111=>1
[2,7,4,1,6,8,3,5]=>0000000=>1111111=>1
[3,7,2,4,5,1,6,8]=>0000001=>1111110=>1
[1,8,6,4,5,2,3,7]=>1000000=>0111111=>1
[2,8,4,6,5,1,3,7]=>0000000=>1111111=>1
[3,4,1,7,5,2,6,8]=>0000001=>1111110=>1
[7,5,8,6,1,2,4,3]=>0000000=>1111111=>1
[5,6,8,7,3,1,4,2]=>0000000=>1111111=>1
[2,5,4,3,6,8,1,7]=>0000000=>1111111=>1
[3,8,5,4,6,2,1,7]=>0000000=>1111111=>1
[4,8,2,1,3,7,5,6]=>0000000=>1111111=>1
[6,4,1,2,7,5,8,3]=>0000000=>1111111=>1
[4,1,8,3,6,7,5,2]=>0000000=>1111111=>1
[8,3,7,4,5,2,6,1]=>0000000=>1111111=>1
[4,3,7,8,5,1,6,2]=>0000000=>1111111=>1
[5,4,8,2,7,6,1,3]=>0000000=>1111111=>1
[1,2,7,3,6,5,8,4]=>1100000=>0011111=>1
[2,8,7,6,3,4,1,5]=>0000000=>1111111=>1
[5,8,2,6,3,4,1,7]=>0000000=>1111111=>1
[4,1,7,5,8,6,2,3]=>0000000=>1111111=>1
[5,1,7,8,4,3,6,2]=>0000000=>1111111=>1
[8,2,7,5,4,3,6,1]=>0000000=>1111111=>1
[6,3,8,1,4,7,5,2]=>0000000=>1111111=>1
[3,8,4,5,6,1,2,7]=>0000000=>1111111=>1
[1,4,3,5,7,8,2,6]=>1000000=>0111111=>1
[6,5,8,7,1,3,4,2]=>0000000=>1111111=>1
[3,6,7,2,4,8,1,5]=>0000000=>1111111=>1
[1,5,2,7,4,3,8,6]=>1000000=>0111111=>1
[2,8,5,6,4,3,1,7]=>0000000=>1111111=>1
[1,8,6,5,4,3,2,7]=>1000000=>0111111=>1
[7,6,8,1,2,3,5,4]=>0000000=>1111111=>1
[2,7,1,5,8,6,3,4]=>0000000=>1111111=>1
[2,4,7,1,8,5,6,3]=>0000000=>1111111=>1
[4,7,5,8,3,1,6,2]=>0000000=>1111111=>1
[1,2,7,6,8,3,5,4]=>1100000=>0011111=>1
[7,4,2,1,6,8,5,3]=>0000000=>1111111=>1
[6,7,4,1,8,5,3,2]=>0000000=>1111111=>1
[7,2,8,1,6,4,5,3]=>0000000=>1111111=>1
[1,7,2,6,8,5,4,3]=>1000000=>0111111=>1
[7,2,5,8,6,3,1,4]=>0000000=>1111111=>1
[7,2,6,8,5,4,1,3]=>0000000=>1111111=>1
[6,7,3,1,8,5,4,2]=>0000000=>1111111=>1
[6,7,1,8,5,4,3,2]=>0000000=>1111111=>1
[7,6,8,3,2,1,5,4]=>0000000=>1111111=>1
[4,7,8,5,6,1,3,2]=>0000000=>1111111=>1
[4,6,5,8,7,1,3,2]=>0000000=>1111111=>1
[5,6,4,8,1,2,7,3]=>0000000=>1111111=>1
[8,1,5,6,7,2,4,3]=>0000000=>1111111=>1
[6,4,5,1,8,2,7,3]=>0000000=>1111111=>1
[5,4,6,7,1,2,8,3]=>0000000=>1111111=>1
[4,3,6,7,2,1,5,8]=>0000001=>1111110=>1
[5,3,6,7,1,4,2,8]=>0000001=>1111110=>1
[8,1,4,6,7,3,2,5]=>0000000=>1111111=>1
[8,1,3,6,7,4,5,2]=>0000000=>1111111=>1
[7,2,1,6,8,4,5,3]=>0000000=>1111111=>1
[5,2,6,7,1,4,8,3]=>0000000=>1111111=>1
[4,2,6,7,3,1,8,5]=>0000000=>1111111=>1
[6,2,4,1,5,8,7,3]=>0000000=>1111111=>1
[7,2,1,5,4,8,6,3]=>0000000=>1111111=>1
[8,1,4,5,3,7,2,6]=>0000000=>1111111=>1
[7,3,1,5,4,8,2,6]=>0000000=>1111111=>1
[6,3,4,1,5,8,2,7]=>0000000=>1111111=>1
[5,3,4,2,1,8,6,7]=>0000100=>1111011=>2
[4,3,5,2,7,1,6,8]=>0000001=>1111110=>1
[5,6,3,8,1,4,2,7]=>0000000=>1111111=>1
[8,1,7,2,4,5,6,3]=>0000000=>1111111=>1
[7,6,1,2,4,5,8,3]=>0000000=>1111111=>1
[4,7,8,2,3,1,6,5]=>0000000=>1111111=>1
[5,6,2,8,1,4,7,3]=>0000000=>1111111=>1
[6,5,2,1,3,7,8,4]=>0000000=>1111111=>1
[7,5,1,3,2,6,8,4]=>0000000=>1111111=>1
[8,1,6,3,2,5,7,4]=>0000000=>1111111=>1
[7,4,1,3,5,2,8,6]=>0000000=>1111111=>1
[5,4,2,3,1,6,8,7]=>0000110=>1111001=>2
[7,3,1,4,5,6,2,8]=>0000001=>1111110=>1
[8,1,4,3,5,6,2,7]=>0000000=>1111111=>1
[6,2,3,1,5,7,8,4]=>0000000=>1111111=>1
[7,8,4,2,1,6,5,3]=>0000000=>1111111=>1
[7,8,4,2,1,5,6,3]=>0000000=>1111111=>1
[6,2,3,4,8,7,1,5]=>0000000=>1111111=>1
[6,2,3,4,7,8,1,5]=>0000000=>1111111=>1
[7,8,3,4,6,2,1,5]=>0000000=>1111111=>1
[7,8,3,6,4,2,1,5]=>0000000=>1111111=>1
[7,8,3,5,6,2,1,4]=>0000000=>1111111=>1
[6,2,3,8,7,5,1,4]=>0000000=>1111111=>1
[6,2,3,7,8,5,1,4]=>0000000=>1111111=>1
[5,2,6,3,8,1,7,4]=>0000000=>1111111=>1
[6,3,2,5,8,7,1,4]=>0000000=>1111111=>1
[6,3,2,8,4,7,1,5]=>0000000=>1111111=>1
[6,4,3,8,7,5,1,2]=>0000000=>1111111=>1
[6,4,3,7,8,5,1,2]=>0000000=>1111111=>1
[6,2,4,1,7,3,5,8]=>0000001=>1111110=>1
[6,3,2,7,4,8,1,5]=>0000000=>1111111=>1
[6,3,2,5,7,8,1,4]=>0000000=>1111111=>1
[5,7,2,3,6,1,8,4]=>0000000=>1111111=>1
[5,8,2,3,6,1,7,4]=>0000000=>1111111=>1
[4,7,5,8,3,2,1,6]=>0000000=>1111111=>1
[4,5,6,8,3,2,1,7]=>0000000=>1111111=>1
[4,6,8,5,3,2,1,7]=>0000000=>1111111=>1
[5,6,1,4,2,3,7,8]=>0000011=>1111100=>1
[5,6,8,4,3,7,1,2]=>0000000=>1111111=>1
[5,6,1,4,2,3,8,7]=>0000010=>1111101=>2
[5,2,8,3,4,1,7,6]=>0000000=>1111111=>1
[4,5,8,6,3,2,1,7]=>0000000=>1111111=>1
[4,6,5,8,3,2,1,7]=>0000000=>1111111=>1
[4,7,5,6,3,2,1,8]=>0000001=>1111110=>1
[6,2,3,4,5,8,1,7]=>0000000=>1111111=>1
[5,1,4,3,6,2,8,7]=>0000010=>1111101=>2
[5,1,4,3,7,2,8,6]=>0000000=>1111111=>1
[5,1,4,3,8,2,7,6]=>0000000=>1111111=>1
[5,6,2,4,1,7,8,3]=>0000000=>1111111=>1
[5,6,2,4,1,8,7,3]=>0000000=>1111111=>1
[5,7,2,4,1,8,6,3]=>0000000=>1111111=>1
[6,1,4,2,8,7,5,3]=>0000000=>1111111=>1
[6,1,4,2,7,8,5,3]=>0000000=>1111111=>1
[5,8,2,4,1,7,6,3]=>0000000=>1111111=>1
[5,2,7,4,1,6,8,3]=>0000000=>1111111=>1
[5,4,1,3,7,2,6,8]=>0000001=>1111110=>1
[5,1,4,3,6,2,7,8]=>0000011=>1111100=>1
[5,8,6,4,3,7,1,2]=>0000000=>1111111=>1
[5,8,1,4,2,3,7,6]=>0000000=>1111111=>1
[5,1,6,3,4,2,7,8]=>0000011=>1111100=>1
[4,8,6,5,3,2,1,7]=>0000000=>1111111=>1
[4,8,5,6,3,2,1,7]=>0000000=>1111111=>1
[5,4,7,8,3,2,1,6]=>0000000=>1111111=>1
[5,4,8,7,3,2,1,6]=>0000000=>1111111=>1
[4,6,8,7,3,2,1,5]=>0000000=>1111111=>1
[4,6,7,8,3,2,1,5]=>0000000=>1111111=>1
[4,7,6,8,3,2,1,5]=>0000000=>1111111=>1
[4,7,8,5,3,2,1,6]=>0000000=>1111111=>1
[5,7,1,3,4,2,6,8]=>0000001=>1111110=>1
[5,1,8,4,2,3,6,7]=>0000000=>1111111=>1
[5,1,7,4,2,3,6,8]=>0000001=>1111110=>1
[5,8,1,3,4,2,6,7]=>0000000=>1111111=>1
[4,8,7,5,3,2,1,6]=>0000000=>1111111=>1
[4,7,8,6,3,2,1,5]=>0000000=>1111111=>1
[4,8,7,6,3,2,1,5]=>0000000=>1111111=>1
[4,8,2,6,3,7,5,1]=>0000000=>1111111=>1
[4,3,8,1,6,2,5,7]=>0000000=>1111111=>1
[6,8,1,2,4,3,5,7]=>0000000=>1111111=>1
[4,8,7,6,3,1,2,5]=>0000000=>1111111=>1
[1,4,3,8,2,6,5,7]=>1000000=>0111111=>1
[4,1,3,8,2,6,5,7]=>0000000=>1111111=>1
[4,1,8,3,7,5,6,2]=>0000000=>1111111=>1
[7,3,8,1,5,4,6,2]=>0000000=>1111111=>1
[3,6,7,8,4,1,2,5]=>0000000=>1111111=>1
[3,7,6,8,4,2,1,5]=>0000000=>1111111=>1
[3,7,8,2,6,4,5,1]=>0000000=>1111111=>1
[4,2,3,8,1,6,5,7]=>0000000=>1111111=>1
[4,3,1,8,2,6,5,7]=>0000000=>1111111=>1
[4,3,7,8,5,2,1,6]=>0000000=>1111111=>1
[7,3,6,8,4,2,1,5]=>0000000=>1111111=>1
[7,6,2,8,3,5,4,1]=>0000000=>1111111=>1
[3,2,4,8,1,6,5,7]=>0000000=>1111111=>1
[2,4,8,3,6,1,5,7]=>0000000=>1111111=>1
[7,4,1,8,5,2,6,3]=>0000000=>1111111=>1
[1,3,2,4,8,6,5,7]=>1011000=>0100111=>2
[3,1,2,4,8,6,5,7]=>0011000=>1100111=>2
[3,1,4,8,2,6,5,7]=>0000000=>1111111=>1
[3,7,4,8,5,1,2,6]=>0000000=>1111111=>1
[6,7,2,8,3,5,4,1]=>0000000=>1111111=>1
[2,1,3,4,8,6,5,7]=>0111000=>1000111=>2
[1,2,3,4,8,6,5,7]=>1111000=>0000111=>1
[4,8,3,6,2,1,5,7]=>0000000=>1111111=>1
[3,5,8,2,6,1,4,7]=>0000000=>1111111=>1
[3,6,5,8,2,4,1,7]=>0000000=>1111111=>1
[5,3,8,7,2,4,6,1]=>0000000=>1111111=>1
[2,8,4,5,7,3,6,1]=>0000000=>1111111=>1
[2,4,5,7,3,8,1,6]=>0000000=>1111111=>1
[6,2,4,5,8,3,1,7]=>0000000=>1111111=>1
[4,8,1,2,5,6,3,7]=>0000000=>1111111=>1
[8,1,3,5,2,6,4,7]=>0000000=>1111111=>1
[5,2,1,6,3,8,4,7]=>0000000=>1111111=>1
[6,2,5,1,8,4,3,7]=>0000000=>1111111=>1
[3,6,1,5,8,4,2,7]=>0000000=>1111111=>1
[6,1,4,5,8,3,2,7]=>0000000=>1111111=>1
[5,6,4,8,1,3,2,7]=>0000000=>1111111=>1
[6,5,4,3,8,2,1,7]=>0000000=>1111111=>1
[5,4,3,7,2,8,1,6]=>0000000=>1111111=>1
[5,8,4,3,7,2,6,1]=>0000000=>1111111=>1
[4,6,8,3,7,2,5,1]=>0000000=>1111111=>1
[7,4,6,3,2,8,1,5]=>0000000=>1111111=>1
[1,4,3,6,2,7,8,5]=>1000000=>0111111=>1
[1,5,4,3,7,2,8,6]=>1000000=>0111111=>1
[4,7,8,5,3,1,2,6]=>0000000=>1111111=>1
[5,7,3,4,1,2,8,6]=>0000000=>1111111=>1
[8,5,4,7,6,2,1,3]=>0000000=>1111111=>1
[8,5,7,4,3,6,1,2]=>0000000=>1111111=>1
[4,3,8,1,6,7,5,2]=>0000000=>1111111=>1
[4,7,8,3,6,1,5,2]=>0000000=>1111111=>1
[5,3,8,6,7,4,1,2]=>0000000=>1111111=>1
[1,3,8,6,4,7,5,2]=>1000000=>0111111=>1
[8,6,2,7,4,1,5,3]=>0000000=>1111111=>1
[7,6,2,1,4,3,8,5]=>0000000=>1111111=>1
[7,6,1,3,4,2,8,5]=>0000000=>1111111=>1
[1,5,7,3,2,6,8,4]=>1000000=>0111111=>1
[1,6,7,3,2,5,8,4]=>1000000=>0111111=>1
[3,2,6,8,5,7,4,1]=>0000000=>1111111=>1
[5,8,2,3,6,7,4,1]=>0000000=>1111111=>1
[7,5,2,3,1,6,8,4]=>0000000=>1111111=>1
[1,6,4,7,2,3,8,5]=>1000000=>0111111=>1
[3,1,7,5,2,8,4,6]=>0000000=>1111111=>1
[2,5,7,4,1,8,3,6]=>0000000=>1111111=>1
[4,2,6,1,7,8,3,5]=>0000000=>1111111=>1
[4,2,7,6,3,8,1,5]=>0000000=>1111111=>1
[6,4,8,7,2,3,5,1]=>0000000=>1111111=>1
[3,2,6,8,7,4,5,1]=>0000000=>1111111=>1
[3,2,7,4,1,6,8,5]=>0000000=>1111111=>1
[6,3,2,1,7,8,4,5]=>0000000=>1111111=>1
[3,7,1,8,4,2,5,6]=>0000000=>1111111=>1
[4,2,1,3,7,5,8,6]=>0001000=>1110111=>2
[8,1,3,7,4,2,6,5]=>0000000=>1111111=>1
[8,4,3,7,6,2,1,5]=>0000000=>1111111=>1
[8,3,5,2,7,6,1,4]=>0000000=>1111111=>1
[3,6,2,8,7,1,5,4]=>0000000=>1111111=>1
[7,3,2,8,1,6,5,4]=>0000000=>1111111=>1
[3,8,7,2,6,5,4,1]=>0000000=>1111111=>1
[4,2,7,8,6,1,5,3]=>0000000=>1111111=>1
[6,8,2,4,7,1,5,3]=>0000000=>1111111=>1
[5,2,1,8,7,3,6,4]=>0000000=>1111111=>1
[8,2,1,6,3,7,5,4]=>0000000=>1111111=>1
[6,8,3,1,7,5,2,4]=>0000000=>1111111=>1
[5,8,1,6,7,2,4,3]=>0000000=>1111111=>1
[6,2,8,1,5,7,4,3]=>0000000=>1111111=>1
[5,7,8,2,6,1,4,3]=>0000000=>1111111=>1
[8,7,2,5,6,4,3,1]=>0000000=>1111111=>1
[8,6,7,5,2,4,3,1]=>0000000=>1111111=>1
[7,2,6,8,1,5,4,3]=>0000000=>1111111=>1
[1,2,7,8,5,6,4,3]=>1100000=>0011111=>1
[7,4,8,1,6,2,5,3]=>0000000=>1111111=>1
[3,7,1,8,2,6,5,4]=>0000000=>1111111=>1
[2,1,7,3,8,6,5,4]=>0100000=>1011111=>2
[8,2,1,7,6,5,4,3]=>0000000=>1111111=>1
[8,1,4,7,6,5,3,2]=>0000000=>1111111=>1
[8,6,7,5,1,4,3,2]=>0000000=>1111111=>1
[7,8,6,5,4,1,3,2]=>0000000=>1111111=>1
[5,8,4,3,2,1,6,7]=>0000000=>1111111=>1
[6,4,7,3,2,1,8,5]=>0000000=>1111111=>1
[5,4,7,3,2,1,6,8]=>0000001=>1111110=>1
[6,5,3,7,2,1,4,8]=>0000001=>1111110=>1
[5,8,3,6,2,1,4,7]=>0000000=>1111111=>1
[6,3,7,8,2,1,4,5]=>0000000=>1111111=>1
[5,3,7,6,2,1,4,8]=>0000001=>1111110=>1
[3,8,7,6,2,1,4,5]=>0000000=>1111111=>1
[5,8,4,2,6,1,3,7]=>0000000=>1111111=>1
[4,8,7,2,5,1,3,6]=>0000000=>1111111=>1
[5,8,3,2,6,1,4,7]=>0000000=>1111111=>1
[4,8,3,2,5,1,7,6]=>0000000=>1111111=>1
[4,3,7,2,5,1,8,6]=>0000000=>1111111=>1
[3,8,7,2,5,1,4,6]=>0000000=>1111111=>1
[6,4,2,7,5,1,3,8]=>0000001=>1111110=>1
[6,3,2,7,5,1,4,8]=>0000001=>1111110=>1
[5,3,2,6,7,1,4,8]=>0000001=>1111110=>1
[3,8,2,6,5,1,4,7]=>0000000=>1111111=>1
[6,2,7,8,5,1,3,4]=>0000000=>1111111=>1
[5,2,7,6,8,1,3,4]=>0000000=>1111111=>1
[4,2,7,6,5,1,3,8]=>0000001=>1111110=>1
[2,8,7,6,5,1,3,4]=>0000000=>1111111=>1
[6,5,4,3,1,7,8,2]=>0000000=>1111111=>1
[6,4,7,3,1,5,8,2]=>0000000=>1111111=>1
[5,4,7,3,1,8,6,2]=>0000000=>1111111=>1
[6,4,3,7,1,5,8,2]=>0000000=>1111111=>1
[5,4,3,6,1,8,7,2]=>0000000=>1111111=>1
[6,3,7,8,1,4,5,2]=>0000000=>1111111=>1
[5,3,7,6,1,4,8,2]=>0000000=>1111111=>1
[4,3,7,6,1,5,8,2]=>0000000=>1111111=>1
[3,8,7,6,1,4,5,2]=>0000000=>1111111=>1
[6,5,4,2,1,7,3,8]=>0000001=>1111110=>1
[6,4,7,2,1,5,3,8]=>0000001=>1111110=>1
[4,8,7,2,1,5,3,6]=>0000000=>1111111=>1
[5,8,3,2,1,4,7,6]=>0000000=>1111111=>1
[4,8,3,2,1,5,7,6]=>0000000=>1111111=>1
[5,3,7,2,1,4,8,6]=>0000000=>1111111=>1
[3,8,7,2,1,4,5,6]=>0000000=>1111111=>1
[6,5,2,7,1,4,3,8]=>0000001=>1111110=>1
[5,8,2,6,1,4,3,7]=>0000000=>1111111=>1
[6,4,2,7,1,5,3,8]=>0000001=>1111110=>1
[5,4,2,6,1,8,3,7]=>0000000=>1111111=>1
[4,3,2,6,1,5,8,7]=>0000010=>1111101=>2
[6,2,7,8,1,4,3,5]=>0000000=>1111111=>1
[4,2,7,6,1,5,3,8]=>0000001=>1111110=>1
[3,2,7,6,1,4,5,8]=>0000001=>1111110=>1
[6,5,4,1,8,7,3,2]=>0000000=>1111111=>1
[5,8,4,1,6,7,3,2]=>0000000=>1111111=>1
[6,4,7,1,5,8,3,2]=>0000000=>1111111=>1
[5,4,7,1,6,8,3,2]=>0000000=>1111111=>1
[4,8,7,1,5,6,3,2]=>0000000=>1111111=>1
[5,4,3,1,6,8,7,2]=>0000000=>1111111=>1
[4,8,3,1,5,6,7,2]=>0000000=>1111111=>1
[3,8,7,1,5,4,6,2]=>0000000=>1111111=>1
[5,8,2,1,6,4,3,7]=>0000000=>1111111=>1
[6,3,2,1,5,4,8,7]=>0000010=>1111101=>2
[5,3,2,1,6,4,8,7]=>0000010=>1111101=>2
[3,8,2,1,5,4,6,7]=>0000000=>1111111=>1
[6,2,7,1,5,4,3,8]=>0000001=>1111110=>1
[5,2,7,1,6,4,3,8]=>0000001=>1111110=>1
[4,2,7,1,5,6,3,8]=>0000001=>1111110=>1
[3,2,7,1,5,4,6,8]=>0000001=>1111110=>1
[2,8,7,1,5,4,3,6]=>0000000=>1111111=>1
[6,5,1,7,8,4,3,2]=>0000000=>1111111=>1
[5,8,1,6,7,4,3,2]=>0000000=>1111111=>1
[6,4,1,7,5,8,3,2]=>0000000=>1111111=>1
[5,4,1,6,7,8,3,2]=>0000000=>1111111=>1
[4,8,1,6,5,7,3,2]=>0000000=>1111111=>1
[6,3,1,7,5,4,8,2]=>0000000=>1111111=>1
[5,3,1,6,7,4,8,2]=>0000000=>1111111=>1
[4,3,1,6,5,7,8,2]=>0000000=>1111111=>1
[3,8,1,6,5,4,7,2]=>0000000=>1111111=>1
[5,2,1,6,7,4,3,8]=>0000001=>1111110=>1
[4,2,1,6,5,7,3,8]=>0000001=>1111110=>1
[2,8,1,6,5,4,3,7]=>0000000=>1111111=>1
[6,1,7,8,5,4,3,2]=>0000000=>1111111=>1
[4,1,7,6,5,8,3,2]=>0000000=>1111111=>1
[3,1,7,6,5,4,8,2]=>0000000=>1111111=>1
[8,1,3,5,7,2,4,6]=>0000000=>1111111=>1
[3,6,8,1,7,2,4,5]=>0000000=>1111111=>1
[3,4,5,6,8,1,7,2]=>0000000=>1111111=>1
[8,2,3,5,6,7,1,4]=>0000000=>1111111=>1
[1,7,2,3,5,4,6,8]=>1000001=>0111110=>1
[8,1,2,3,5,4,6,7]=>0000000=>1111111=>1
[4,5,8,1,7,6,3,2]=>0000000=>1111111=>1
[3,6,8,7,2,1,5,4]=>0000000=>1111111=>1
[8,6,4,1,7,5,3,2]=>0000000=>1111111=>1
[2,3,6,7,8,1,5,4]=>0000000=>1111111=>1
[7,1,4,2,8,3,6,5]=>0000000=>1111111=>1
[7,1,8,2,5,3,6,4]=>0000000=>1111111=>1
[1,7,2,6,5,4,3,8]=>1000001=>0111110=>1
[3,6,8,1,7,5,4,2]=>0000000=>1111111=>1
[8,2,6,7,5,4,1,3]=>0000000=>1111111=>1
[7,3,1,8,6,5,4,2]=>0000000=>1111111=>1
[8,7,2,1,6,5,4,3]=>0000000=>1111111=>1
[8,6,1,5,2,7,4,3]=>0000000=>1111111=>1
[8,5,1,7,4,2,6,3]=>0000000=>1111111=>1
[2,1,7,5,4,3,8,6]=>0100000=>1011111=>2
[2,1,7,8,3,6,5,4]=>0100000=>1011111=>2
[2,1,4,8,5,7,3,6]=>0100000=>1011111=>2
[8,5,3,1,6,2,4,7]=>0000000=>1111111=>1
[6,4,1,5,2,3,8,7]=>0000010=>1111101=>2
[8,3,7,5,2,6,1,4]=>0000000=>1111111=>1
[5,3,7,4,6,8,1,2]=>0000000=>1111111=>1
[5,8,3,7,6,2,1,4]=>0000000=>1111111=>1
[4,2,6,3,8,5,1,7]=>0000000=>1111111=>1
[3,8,2,4,7,5,1,6]=>0000000=>1111111=>1
[5,8,2,1,7,6,4,3]=>0000000=>1111111=>1
[8,3,2,4,1,7,5,6]=>0000000=>1111111=>1
[7,8,3,1,5,4,6,2]=>0000000=>1111111=>1
[7,2,8,1,4,6,5,3]=>0000000=>1111111=>1
[5,6,1,4,3,2,8,7]=>0000010=>1111101=>2
[5,7,1,8,3,6,2,4]=>0000000=>1111111=>1
[8,3,5,6,1,7,4,2]=>0000000=>1111111=>1
[6,3,5,4,1,2,8,7]=>0000010=>1111101=>2
[3,4,7,2,8,1,5,6]=>0000000=>1111111=>1
[4,2,3,5,8,1,6,7]=>0000000=>1111111=>1
[3,2,4,6,1,5,8,7]=>0000010=>1111101=>2
[5,6,8,1,4,2,7,3]=>0000000=>1111111=>1
[1,3,5,7,8,6,2,4]=>1000000=>0111111=>1
[3,5,7,8,6,1,2,4]=>0000000=>1111111=>1
[3,5,1,6,8,2,7,4]=>0000000=>1111111=>1
[5,6,4,8,2,1,7,3]=>0000000=>1111111=>1
[5,1,6,3,8,4,7,2]=>0000000=>1111111=>1
[2,5,1,6,8,3,7,4]=>0000000=>1111111=>1
[5,1,2,6,8,3,7,4]=>0000000=>1111111=>1
[5,7,1,8,6,2,3,4]=>0000000=>1111111=>1
[1,5,2,7,8,6,3,4]=>1000000=>0111111=>1
[6,1,7,5,2,8,3,4]=>0000000=>1111111=>1
[5,7,2,8,6,1,3,4]=>0000000=>1111111=>1
[5,1,7,8,6,3,4,2]=>0000000=>1111111=>1
[5,1,3,7,8,6,4,2]=>0000000=>1111111=>1
[5,2,7,8,4,6,1,3]=>0000000=>1111111=>1
[1,2,6,7,5,8,3,4]=>1100000=>0011111=>1
[6,2,7,5,4,1,8,3]=>0000000=>1111111=>1
[5,1,7,8,6,4,3,2]=>0000000=>1111111=>1
[2,5,7,8,6,3,1,4]=>0000000=>1111111=>1
[2,4,7,1,5,6,8,3]=>0000000=>1111111=>1
[1,6,7,4,5,2,8,3]=>1000000=>0111111=>1
[1,6,3,7,5,8,2,4]=>1000000=>0111111=>1
[6,2,7,4,5,1,8,3]=>0000000=>1111111=>1
[7,5,1,6,3,8,2,4]=>0000000=>1111111=>1
[2,7,6,1,3,8,5,4]=>0000000=>1111111=>1
[7,3,5,1,8,2,6,4]=>0000000=>1111111=>1
[7,3,5,1,8,2,4,6]=>0000000=>1111111=>1
[2,6,7,4,1,8,3,5]=>0000000=>1111111=>1
[2,1,6,7,3,8,5,4]=>0100000=>1011111=>2
[3,7,5,4,8,1,6,2]=>0000000=>1111111=>1
[4,6,1,5,8,7,3,2]=>0000000=>1111111=>1
[7,5,1,6,2,8,4,3]=>0000000=>1111111=>1
[6,8,5,4,3,2,7,1]=>0000000=>1111111=>1
[7,9,6,5,4,3,2,8,1]=>00000000=>11111111=>1
[8,9,6,5,4,3,2,1,7]=>00000000=>11111111=>1
[6,8,5,4,3,7,2,1]=>0000000=>1111111=>1
[5,8,4,3,2,1,7,6]=>0000000=>1111111=>1
[6,5,4,3,1,8,7,2]=>0000000=>1111111=>1
[8,7,6,5,4,3,9,1,2]=>00000000=>11111111=>1
[8,7,5,4,3,1,6,2]=>0000000=>1111111=>1
[9,7,6,5,4,3,1,8,2]=>00000000=>11111111=>1
[8,3,4,6,2,1,5,7]=>0000000=>1111111=>1
[3,5,6,2,1,8,4,7]=>0000000=>1111111=>1
[3,5,2,6,8,4,1,7]=>0000000=>1111111=>1
[7,5,3,2,8,4,1,6]=>0000000=>1111111=>1
[7,5,3,2,8,4,6,1]=>0000000=>1111111=>1
[2,4,5,7,3,8,6,1]=>0000000=>1111111=>1
[4,2,5,6,8,3,1,7]=>0000000=>1111111=>1
[4,2,8,1,5,6,3,7]=>0000000=>1111111=>1
[2,5,6,1,8,4,3,7]=>0000000=>1111111=>1
[5,3,6,8,1,4,2,7]=>0000000=>1111111=>1
[4,5,6,8,1,3,2,7]=>0000000=>1111111=>1
[1,4,5,6,8,3,2,7]=>1000000=>0111111=>1
[4,5,6,3,8,2,1,7]=>0000000=>1111111=>1
[4,5,3,7,2,8,6,1]=>0000000=>1111111=>1
[6,4,7,3,2,8,5,1]=>0000000=>1111111=>1
[6,1,4,7,3,2,8,5]=>0000000=>1111111=>1
[1,7,8,4,5,3,2,6]=>1000000=>0111111=>1
[5,1,7,3,8,4,2,6]=>0000000=>1111111=>1
[2,5,1,7,4,3,8,6]=>0000000=>1111111=>1
[2,5,7,4,1,8,6,3]=>0000000=>1111111=>1
[5,3,7,1,4,8,6,2]=>0000000=>1111111=>1
[6,4,3,1,7,8,5,2]=>0000000=>1111111=>1
[6,4,1,7,3,8,5,2]=>0000000=>1111111=>1
[5,6,3,7,8,4,2,1]=>0000000=>1111111=>1
[5,1,6,3,7,8,4,2]=>0000000=>1111111=>1
[5,6,1,3,7,8,4,2]=>0000000=>1111111=>1
[5,6,1,7,8,3,4,2]=>0000000=>1111111=>1
[1,6,3,7,4,8,5,2]=>1000000=>0111111=>1
[6,7,2,4,1,8,5,3]=>0000000=>1111111=>1
[6,7,2,1,4,3,8,5]=>0000000=>1111111=>1
[6,4,7,3,1,2,8,5]=>0000000=>1111111=>1
[5,6,3,1,2,7,8,4]=>0000000=>1111111=>1
[5,6,1,3,2,7,8,4]=>0000000=>1111111=>1
[5,6,3,2,1,7,8,4]=>0000000=>1111111=>1
[2,5,6,3,7,8,4,1]=>0000000=>1111111=>1
[2,5,6,3,1,7,8,4]=>0000000=>1111111=>1
[2,6,4,7,3,1,8,5]=>0000000=>1111111=>1
[6,3,7,2,8,4,5,1]=>0000000=>1111111=>1
[6,3,7,2,8,4,1,5]=>0000000=>1111111=>1
[6,3,2,7,1,8,4,5]=>0000000=>1111111=>1
[7,5,3,2,1,8,4,6]=>0000000=>1111111=>1
[7,3,8,4,2,1,5,6]=>0000000=>1111111=>1
[4,7,2,1,3,8,6,5]=>0000000=>1111111=>1
[1,3,7,8,6,4,2,5]=>1000000=>0111111=>1
[7,3,8,4,6,2,1,5]=>0000000=>1111111=>1
[5,7,3,8,2,1,6,4]=>0000000=>1111111=>1
[6,3,7,8,5,2,1,4]=>0000000=>1111111=>1
[4,6,2,7,8,5,3,1]=>0000000=>1111111=>1
[4,6,2,1,7,8,5,3]=>0000000=>1111111=>1
[7,4,5,8,1,2,6,3]=>0000000=>1111111=>1
[2,5,1,7,3,8,6,4]=>0000000=>1111111=>1
[6,7,2,1,3,8,5,4]=>0000000=>1111111=>1
[5,1,6,7,8,2,4,3]=>0000000=>1111111=>1
[6,3,7,1,8,5,2,4]=>0000000=>1111111=>1
[6,2,1,7,3,8,5,4]=>0000000=>1111111=>1
[6,2,7,1,8,5,4,3]=>0000000=>1111111=>1
[6,3,1,7,8,5,4,2]=>0000000=>1111111=>1
[4,1,3,6,8,2,5,7]=>0000000=>1111111=>1
[4,2,3,6,8,1,5,7]=>0000000=>1111111=>1
[5,3,2,1,8,4,7,6]=>0000000=>1111111=>1
[3,6,5,8,2,1,7,4]=>0000000=>1111111=>1
[4,5,2,1,3,8,7,6]=>0000100=>1111011=>2
[3,2,6,4,5,8,1,7]=>0000000=>1111111=>1
[2,4,6,5,8,1,3,7]=>0000000=>1111111=>1
[1,6,2,4,5,8,3,7]=>1000000=>0111111=>1
[5,3,2,1,6,8,4,7]=>0000000=>1111111=>1
[6,2,4,5,8,1,3,7]=>0000000=>1111111=>1
[1,3,4,6,5,8,2,7]=>1000000=>0111111=>1
[1,6,3,4,5,8,2,7]=>1000000=>0111111=>1
[3,4,1,8,5,2,7,6]=>0000000=>1111111=>1
[2,8,4,1,7,6,3,5]=>0000000=>1111111=>1
[8,1,4,2,7,3,6,5]=>0000000=>1111111=>1
[1,5,3,2,8,7,4,6]=>1000000=>0111111=>1
[8,2,1,7,5,3,4,6]=>0000000=>1111111=>1
[1,7,6,4,5,8,3,2]=>1000000=>0111111=>1
[5,8,7,4,1,2,6,3]=>0000000=>1111111=>1
[5,8,7,4,6,2,1,3]=>0000000=>1111111=>1
[3,4,2,5,8,6,7,1]=>0000000=>1111111=>1
[4,1,3,5,6,8,7,2]=>0000000=>1111111=>1
[2,4,8,6,7,1,3,5]=>0000000=>1111111=>1
[4,3,6,2,8,1,7,5]=>0000000=>1111111=>1
[3,7,4,8,2,1,6,5]=>0000000=>1111111=>1
[2,3,5,8,6,7,1,4]=>0000000=>1111111=>1
[3,2,5,6,8,7,1,4]=>0000000=>1111111=>1
[2,1,8,5,6,7,3,4]=>0100000=>1011111=>2
[1,2,8,3,5,6,7,4]=>1100000=>0011111=>1
[4,2,3,7,1,8,6,5]=>0000000=>1111111=>1
[3,2,6,4,8,1,7,5]=>0000000=>1111111=>1
[8,2,1,6,7,3,4,5]=>0000000=>1111111=>1
[2,7,8,5,4,1,3,6]=>0000000=>1111111=>1
[1,7,5,3,8,4,2,6]=>1000000=>0111111=>1
[4,7,5,3,1,2,8,6]=>0000000=>1111111=>1
[7,2,4,8,5,3,1,6]=>0000000=>1111111=>1
[4,8,3,1,2,7,6,5]=>0000000=>1111111=>1
[3,5,2,7,4,1,8,6]=>0000000=>1111111=>1
[8,4,2,3,7,1,5,6]=>0000000=>1111111=>1
[2,8,4,7,1,3,5,6]=>0000000=>1111111=>1
[8,2,4,6,7,1,3,5]=>0000000=>1111111=>1
[4,8,2,3,6,7,1,5]=>0000000=>1111111=>1
[3,5,2,7,6,1,8,4]=>0000000=>1111111=>1
[1,6,3,2,5,8,7,4]=>1000000=>0111111=>1
[5,8,3,2,1,6,7,4]=>0000000=>1111111=>1
[5,8,7,3,4,6,2,1]=>0000000=>1111111=>1
[5,8,2,7,4,1,6,3]=>0000000=>1111111=>1
[5,1,4,2,8,7,6,3]=>0000000=>1111111=>1
[4,7,6,5,8,2,1,3]=>0000000=>1111111=>1
[5,3,7,1,6,2,8,4]=>0000000=>1111111=>1
[5,2,6,8,7,1,3,4]=>0000000=>1111111=>1
[6,3,2,1,8,5,7,4]=>0000000=>1111111=>1
[2,7,5,4,1,8,6,3]=>0000000=>1111111=>1
[4,2,5,6,8,7,1,3]=>0000000=>1111111=>1
[1,8,4,2,5,6,7,3]=>1000000=>0111111=>1
[3,8,4,1,5,6,7,2]=>0000000=>1111111=>1
[4,2,8,5,6,7,1,3]=>0000000=>1111111=>1
[5,2,4,7,1,8,6,3]=>0000000=>1111111=>1
[5,3,4,7,1,8,6,2]=>0000000=>1111111=>1
[8,6,4,1,3,2,5,7]=>0000000=>1111111=>1
[8,1,3,6,5,2,4,7]=>0000000=>1111111=>1
[8,1,4,3,6,5,2,7]=>0000000=>1111111=>1
[3,6,5,2,1,8,7,4]=>0000000=>1111111=>1
[8,3,2,4,6,5,1,7]=>0000000=>1111111=>1
[8,4,2,1,6,5,3,7]=>0000000=>1111111=>1
[8,4,1,2,6,5,3,7]=>0000000=>1111111=>1
[8,6,4,2,1,5,3,7]=>0000000=>1111111=>1
[8,3,6,4,1,5,2,7]=>0000000=>1111111=>1
[8,2,6,3,4,5,1,7]=>0000000=>1111111=>1
[1,3,4,8,5,7,2,6]=>1000000=>0111111=>1
[5,8,4,7,6,2,3,1]=>0000000=>1111111=>1
[1,3,4,7,5,8,2,6]=>1000000=>0111111=>1
[1,3,5,2,4,8,7,6]=>1000100=>0111011=>2
[2,6,5,1,3,8,7,4]=>0000000=>1111111=>1
[4,7,1,6,5,8,3,2]=>0000000=>1111111=>1
[5,4,8,7,6,3,1,2]=>0000000=>1111111=>1
[2,8,5,1,4,7,6,3]=>0000000=>1111111=>1
[4,3,1,5,8,6,7,2]=>0000000=>1111111=>1
[4,1,3,5,8,6,7,2]=>0000000=>1111111=>1
[6,5,3,8,4,7,1,2]=>0000000=>1111111=>1
[5,4,2,1,6,8,7,3]=>0000000=>1111111=>1
[6,8,4,3,2,7,1,5]=>0000000=>1111111=>1
[3,4,7,8,2,1,6,5]=>0000000=>1111111=>1
[5,1,3,2,8,6,7,4]=>0000000=>1111111=>1
[5,3,1,2,8,6,7,4]=>0000000=>1111111=>1
[5,2,3,1,6,8,7,4]=>0000000=>1111111=>1
[5,3,2,1,8,6,7,4]=>0000000=>1111111=>1
[5,2,1,3,6,8,7,4]=>0000000=>1111111=>1
[2,4,7,3,8,1,6,5]=>0000000=>1111111=>1
[6,3,8,2,7,4,1,5]=>0000000=>1111111=>1
[8,2,1,3,6,4,7,5]=>0000000=>1111111=>1
[3,5,1,7,8,4,2,6]=>0000000=>1111111=>1
[2,7,4,5,8,3,1,6]=>0000000=>1111111=>1
[1,8,4,3,7,2,6,5]=>1000000=>0111111=>1
[3,4,8,7,2,1,6,5]=>0000000=>1111111=>1
[5,4,7,8,3,6,2,1]=>0000000=>1111111=>1
[6,4,3,8,7,2,1,5]=>0000000=>1111111=>1
[6,3,8,7,4,1,2,5]=>0000000=>1111111=>1
[3,5,7,2,4,8,1,6]=>0000000=>1111111=>1
[8,4,7,2,3,1,5,6]=>0000000=>1111111=>1
[8,4,7,1,3,2,5,6]=>0000000=>1111111=>1
[8,4,7,2,1,3,5,6]=>0000000=>1111111=>1
[8,6,4,2,1,3,7,5]=>0000000=>1111111=>1
[8,6,4,1,3,2,7,5]=>0000000=>1111111=>1
[8,6,4,2,3,1,7,5]=>0000000=>1111111=>1
[3,5,7,2,6,1,8,4]=>0000000=>1111111=>1
[6,1,3,8,5,7,2,4]=>0000000=>1111111=>1
[5,8,3,2,6,7,1,4]=>0000000=>1111111=>1
[4,8,5,3,6,2,7,1]=>0000000=>1111111=>1
[2,8,1,5,4,7,6,3]=>0000000=>1111111=>1
[1,5,8,7,4,6,2,3]=>1000000=>0111111=>1
[2,1,7,6,4,5,8,3]=>0100000=>1011111=>2
[1,7,2,4,6,5,8,3]=>1000000=>0111111=>1
[3,5,1,7,6,8,2,4]=>0000000=>1111111=>1
[5,8,2,6,1,3,7,4]=>0000000=>1111111=>1
[6,3,5,8,7,2,1,4]=>0000000=>1111111=>1
[2,5,7,8,4,1,6,3]=>0000000=>1111111=>1
[4,2,8,1,5,6,7,3]=>0000000=>1111111=>1
[4,1,5,2,6,8,7,3]=>0000000=>1111111=>1
[3,4,5,1,6,8,7,2]=>0000000=>1111111=>1
[4,2,8,5,1,6,7,3]=>0000000=>1111111=>1
[4,1,8,5,2,6,7,3]=>0000000=>1111111=>1
[2,7,1,8,5,4,6,3]=>0000000=>1111111=>1
[5,8,6,2,1,3,7,4]=>0000000=>1111111=>1
[8,2,4,1,5,6,7,3]=>0000000=>1111111=>1
[4,6,3,5,8,1,7,2]=>0000000=>1111111=>1
[1,7,8,3,5,4,6,2]=>1000000=>0111111=>1
[3,4,5,1,8,6,7,2]=>0000000=>1111111=>1
[3,8,1,4,5,6,7,2]=>0000000=>1111111=>1
[3,4,6,2,8,5,1,7]=>0000000=>1111111=>1
[3,5,6,2,8,4,1,7]=>0000000=>1111111=>1
[3,5,7,2,4,8,6,1]=>0000000=>1111111=>1
[3,5,7,8,4,1,6,2]=>0000000=>1111111=>1
[3,6,8,2,4,5,1,7]=>0000000=>1111111=>1
[3,7,2,1,4,8,6,5]=>0000000=>1111111=>1
[3,7,2,8,4,5,6,1]=>0000000=>1111111=>1
[4,1,5,7,3,8,6,2]=>0000000=>1111111=>1
[4,1,6,3,7,8,5,2]=>0000000=>1111111=>1
[4,1,6,3,8,5,2,7]=>0000000=>1111111=>1
[4,1,6,8,3,5,2,7]=>0000000=>1111111=>1
[4,1,8,3,2,5,6,7]=>0000000=>1111111=>1
[4,5,7,3,8,1,6,2]=>0000000=>1111111=>1
[4,5,8,3,2,1,6,7]=>0000000=>1111111=>1
[4,6,2,7,8,5,1,3]=>0000000=>1111111=>1
[4,7,8,3,2,5,6,1]=>0000000=>1111111=>1
[5,1,2,6,8,4,3,7]=>0000000=>1111111=>1
[5,1,6,3,8,4,2,7]=>0000000=>1111111=>1
[5,1,6,7,4,8,2,3]=>0000000=>1111111=>1
[5,6,2,7,8,4,1,3]=>0000000=>1111111=>1
[5,7,8,3,4,2,6,1]=>0000000=>1111111=>1
[6,1,2,3,7,8,5,4]=>0000000=>1111111=>1
[6,1,2,7,8,5,4,3]=>0000000=>1111111=>1
[6,7,2,8,4,5,3,1]=>0000000=>1111111=>1
[7,1,8,3,4,5,6,2]=>0000000=>1111111=>1
[1,3,5,7,2,6,4,8]=>1000001=>0111110=>1
[3,5,8,6,1,2,4,7]=>0000000=>1111111=>1
[3,1,6,8,2,4,7,5]=>0000000=>1111111=>1
[2,6,1,3,8,4,7,5]=>0000000=>1111111=>1
[1,6,7,5,3,2,4,8]=>1000001=>0111110=>1
[8,4,1,2,5,6,3,7]=>0000000=>1111111=>1
[1,7,3,6,5,2,4,8]=>1000001=>0111110=>1
[8,2,3,6,5,1,7,4]=>0000000=>1111111=>1
[7,9,8,6,5,4,3,2,1]=>00000000=>11111111=>1
[6,9,8,7,5,4,3,2,1]=>00000000=>11111111=>1
[5,9,8,7,6,4,3,2,1]=>00000000=>11111111=>1
[4,9,8,7,6,5,3,2,1]=>00000000=>11111111=>1
[3,9,8,7,6,5,4,2,1]=>00000000=>11111111=>1
[2,9,8,7,6,5,4,3,1]=>00000000=>11111111=>1
[8,10,9,7,6,5,4,3,2,1]=>000000000=>111111111=>1
[6,9,7,8,5,4,3,2,1]=>00000000=>11111111=>1
[7,10,9,8,6,5,4,3,2,1]=>000000000=>111111111=>1
[4,8,6,5,7,3,2,1]=>0000000=>1111111=>1
[5,9,8,6,7,4,3,2,1]=>00000000=>11111111=>1
[6,10,9,8,7,5,4,3,2,1]=>000000000=>111111111=>1
[3,8,7,5,4,6,2,1]=>0000000=>1111111=>1
[4,8,5,6,7,3,2,1]=>0000000=>1111111=>1
[4,9,8,7,5,6,3,2,1]=>00000000=>11111111=>1
[5,10,9,8,7,6,4,3,2,1]=>000000000=>111111111=>1
[2,8,7,6,4,3,5,1]=>0000000=>1111111=>1
[3,8,7,4,5,6,2,1]=>0000000=>1111111=>1
[3,9,8,7,6,4,5,2,1]=>00000000=>11111111=>1
[4,10,9,8,7,6,5,3,2,1]=>000000000=>111111111=>1
[1,8,7,6,5,3,2,4]=>1000000=>0111111=>1
[2,8,7,6,3,4,5,1]=>0000000=>1111111=>1
[2,9,8,7,6,5,3,4,1]=>00000000=>11111111=>1
[3,10,9,8,7,6,5,4,2,1]=>000000000=>111111111=>1
[1,8,7,6,5,2,3,4]=>1000000=>0111111=>1
[1,9,8,7,6,5,4,2,3]=>10000000=>01111111=>1
[2,10,9,8,7,6,5,4,3,1]=>000000000=>111111111=>1
[7,2,8,6,5,4,1,3]=>0000000=>1111111=>1
[6,3,2,8,5,1,7,4]=>0000000=>1111111=>1
[6,8,5,4,3,1,7,2]=>0000000=>1111111=>1
[3,6,1,8,5,2,7,4]=>0000000=>1111111=>1
[3,4,1,2,8,6,7,5]=>0001000=>1110111=>2
[7,2,5,8,3,6,1,4]=>0000000=>1111111=>1
[7,6,3,8,5,2,1,4]=>0000000=>1111111=>1
[7,2,6,4,8,3,1,5]=>0000000=>1111111=>1
[1,5,7,4,2,6,3,8]=>1000001=>0111110=>1
[4,2,3,1,7,8,5,6]=>0001000=>1110111=>2
[5,2,8,4,1,7,6,3]=>0000000=>1111111=>1
[6,8,3,4,5,1,7,2]=>0000000=>1111111=>1
[1,6,3,2,5,8,4,7]=>1000000=>0111111=>1
[8,3,2,1,5,4,7,6]=>0000000=>1111111=>1
[6,3,7,1,5,8,4,2]=>0000000=>1111111=>1
[2,5,1,8,4,3,7,6]=>0000000=>1111111=>1
[6,2,5,4,8,1,3,7]=>0000000=>1111111=>1
[4,3,1,6,5,8,2,7]=>0000000=>1111111=>1
[1,3,5,4,6,8,2,7]=>1000000=>0111111=>1
[6,1,3,4,5,8,2,7]=>0000000=>1111111=>1
[8,3,4,1,5,2,7,6]=>0000000=>1111111=>1
[7,5,4,2,6,8,3,1]=>0000000=>1111111=>1
[8,2,6,4,1,7,3,5]=>0000000=>1111111=>1
[7,3,8,4,5,2,1,6]=>0000000=>1111111=>1
[7,2,5,1,8,4,3,6]=>0000000=>1111111=>1
[1,7,3,2,5,4,8,6]=>1000000=>0111111=>1
[8,7,2,1,5,3,4,6]=>0000000=>1111111=>1
[3,6,1,5,8,7,4,2]=>0000000=>1111111=>1
[8,3,6,4,5,1,7,2]=>0000000=>1111111=>1
[5,4,6,8,1,2,7,3]=>0000000=>1111111=>1
[6,4,7,2,3,5,8,1]=>0000000=>1111111=>1
[6,8,4,1,3,5,7,2]=>0000000=>1111111=>1
[3,4,7,8,6,2,5,1]=>0000000=>1111111=>1
[4,1,3,5,7,8,6,2]=>0000000=>1111111=>1
[6,5,1,8,4,7,3,2]=>0000000=>1111111=>1
[5,3,1,8,4,7,6,2]=>0000000=>1111111=>1
[8,2,7,4,6,1,3,5]=>0000000=>1111111=>1
[4,7,3,2,8,1,6,5]=>0000000=>1111111=>1
[6,3,1,4,7,2,8,5]=>0000000=>1111111=>1
[8,7,3,6,1,5,2,4]=>0000000=>1111111=>1
[7,4,3,6,8,2,5,1]=>0000000=>1111111=>1
[2,4,7,3,8,5,6,1]=>0000000=>1111111=>1
[2,8,6,1,5,7,3,4]=>0000000=>1111111=>1
[7,8,2,5,4,3,1,6]=>0000000=>1111111=>1
[1,8,3,4,2,7,6,5]=>1000000=>0111111=>1
[8,5,3,7,4,2,6,1]=>0000000=>1111111=>1
[5,7,3,2,4,1,8,6]=>0000000=>1111111=>1
[2,8,3,4,7,1,5,6]=>0000000=>1111111=>1
[4,1,3,6,7,8,2,5]=>0000000=>1111111=>1
[1,7,6,3,2,5,8,4]=>1000000=>0111111=>1
[3,8,1,5,6,2,7,4]=>0000000=>1111111=>1
[8,2,5,6,1,7,4,3]=>0000000=>1111111=>1
[7,1,5,2,8,6,4,3]=>0000000=>1111111=>1
[6,5,4,8,7,2,1,3]=>0000000=>1111111=>1
[1,8,6,4,5,2,7,3]=>1000000=>0111111=>1
[1,8,5,3,6,2,7,4]=>1000000=>0111111=>1
[3,6,2,1,7,5,8,4]=>0000000=>1111111=>1
[2,5,4,1,8,7,6,3]=>0000000=>1111111=>1
[4,7,2,6,5,8,1,3]=>0000000=>1111111=>1
[6,8,1,4,2,7,3,5]=>0000000=>1111111=>1
[6,3,4,7,1,8,2,5]=>0000000=>1111111=>1
[3,4,7,8,2,5,6,1]=>0000000=>1111111=>1
[1,8,2,4,5,6,7,3]=>1000000=>0111111=>1
[5,2,4,1,6,8,7,3]=>0000000=>1111111=>1
[3,2,5,7,6,1,8,4]=>0000000=>1111111=>1
[4,3,5,6,1,8,7,2]=>0000000=>1111111=>1
[5,3,4,1,7,6,8,2]=>0000000=>1111111=>1
[3,1,4,6,5,7,8,2]=>0000000=>1111111=>1
[1,4,7,3,5,6,8,2]=>1000000=>0111111=>1
[5,1,3,6,4,8,7,2]=>0000000=>1111111=>1
[1,3,2,7,5,8,6,4]=>1010000=>0101111=>2
[1,4,2,5,8,3,7,6]=>1000000=>0111111=>1
[1,4,2,7,8,5,6,3]=>1000000=>0111111=>1
[5,1,2,6,8,4,7,3]=>0000000=>1111111=>1
[3,1,2,6,5,8,4,7]=>0010000=>1101111=>2
[4,1,2,6,8,5,3,7]=>0000000=>1111111=>1
[1,5,2,4,8,7,6,3]=>1000000=>0111111=>1
[1,2,6,4,8,7,5,3]=>1100000=>0011111=>1
[1,2,7,4,8,6,5,3]=>1100000=>0011111=>1
[1,3,2,7,5,8,4,6]=>1010000=>0101111=>2
[2,3,1,7,5,4,8,6]=>0010000=>1101111=>2
[1,3,2,8,5,7,4,6]=>1010000=>0101111=>2
[1,4,2,5,8,7,3,6]=>1000000=>0111111=>1
[1,5,2,4,8,7,3,6]=>1000000=>0111111=>1
[1,2,6,4,8,7,3,5]=>1100000=>0011111=>1
[1,2,7,8,5,6,3,4]=>1100000=>0011111=>1
[1,2,6,8,5,7,3,4]=>1100000=>0011111=>1
[1,5,6,8,2,7,3,4]=>1000000=>0111111=>1
[1,3,8,2,6,7,4,5]=>1000000=>0111111=>1
[1,4,7,2,8,6,3,5]=>1000000=>0111111=>1
[1,6,7,8,2,5,3,4]=>1000000=>0111111=>1
[1,2,6,8,3,7,5,4]=>1100000=>0011111=>1
[1,5,7,8,2,3,6,4]=>1000000=>0111111=>1
[1,5,2,7,8,4,6,3]=>1000000=>0111111=>1
[1,4,7,2,8,3,6,5]=>1000000=>0111111=>1
[1,3,6,2,4,8,7,5]=>1000000=>0111111=>1
[1,6,7,3,4,8,5,2]=>1000000=>0111111=>1
[1,5,3,7,4,8,6,2]=>1000000=>0111111=>1
[2,8,4,1,5,3,7,6]=>0000000=>1111111=>1
[3,8,4,1,5,7,2,6]=>0000000=>1111111=>1
[1,3,6,4,2,8,7,5]=>1000000=>0111111=>1
[1,3,7,4,2,8,6,5]=>1000000=>0111111=>1
[1,3,8,4,2,7,6,5]=>1000000=>0111111=>1
[1,2,8,4,7,3,6,5]=>1100000=>0011111=>1
[1,2,7,4,8,3,6,5]=>1100000=>0011111=>1
[1,2,6,4,8,3,7,5]=>1100000=>0011111=>1
[1,5,2,4,8,3,7,6]=>1000000=>0111111=>1
[1,8,4,5,7,2,3,6]=>1000000=>0111111=>1
[1,8,3,5,2,7,4,6]=>1000000=>0111111=>1
[2,8,3,5,1,4,7,6]=>0000000=>1111111=>1
[2,3,8,6,1,4,7,5]=>0000000=>1111111=>1
[1,3,8,6,2,7,4,5]=>1000000=>0111111=>1
[1,4,8,6,7,2,3,5]=>1000000=>0111111=>1
[1,5,6,8,7,2,3,4]=>1000000=>0111111=>1
[1,2,6,8,5,3,7,4]=>1100000=>0011111=>1
[1,2,7,8,5,3,6,4]=>1100000=>0011111=>1
[1,2,5,8,7,3,6,4]=>1100000=>0011111=>1
[1,2,6,8,7,3,5,4]=>1100000=>0011111=>1
[1,2,7,8,6,3,5,4]=>1100000=>0011111=>1
[1,6,7,8,5,2,3,4]=>1000000=>0111111=>1
[1,5,7,8,6,2,3,4]=>1000000=>0111111=>1
[1,4,7,6,8,2,3,5]=>1000000=>0111111=>1
[1,3,7,6,2,8,4,5]=>1000000=>0111111=>1
[2,3,8,7,4,1,6,5]=>0000000=>1111111=>1
[1,2,8,4,7,6,3,5]=>1100000=>0011111=>1
[1,2,5,8,7,6,3,4]=>1100000=>0011111=>1
[1,2,6,8,7,5,3,4]=>1100000=>0011111=>1
[1,2,7,8,6,5,3,4]=>1100000=>0011111=>1
[5,2,6,7,3,4,8,1]=>0000000=>1111111=>1
[5,2,4,7,6,3,8,1]=>0000000=>1111111=>1
[5,6,2,1,7,8,3,4]=>0000000=>1111111=>1
[5,6,2,1,4,8,7,3]=>0000000=>1111111=>1
[2,6,1,4,5,8,7,3]=>0000000=>1111111=>1
[5,4,2,7,6,3,8,1]=>0000000=>1111111=>1
[2,3,7,6,4,5,8,1]=>0000000=>1111111=>1
[2,6,1,7,5,8,3,4]=>0000000=>1111111=>1
[2,6,1,7,4,8,5,3]=>0000000=>1111111=>1
[5,1,2,7,8,4,3,6]=>0000000=>1111111=>1
[2,6,1,7,4,8,3,5]=>0000000=>1111111=>1
[3,6,4,1,7,8,2,5]=>0000000=>1111111=>1
[5,4,6,1,3,8,7,2]=>0000000=>1111111=>1
[3,6,4,1,5,8,7,2]=>0000000=>1111111=>1
[2,6,1,5,4,8,7,3]=>0000000=>1111111=>1
[2,6,1,4,7,8,5,3]=>0000000=>1111111=>1
[5,1,2,4,8,6,7,3]=>0000000=>1111111=>1
[5,1,2,4,8,7,3,6]=>0000000=>1111111=>1
[5,1,2,4,8,7,6,3]=>0000000=>1111111=>1
[1,2,3,8,5,4,7,6]=>1110000=>0001111=>1
[4,3,1,2,8,5,7,6]=>0001000=>1110111=>2
[2,1,5,3,8,6,4,7]=>0100000=>1011111=>2
[1,2,3,8,5,6,4,7]=>1110000=>0001111=>1
[1,2,3,8,6,4,5,7]=>1110000=>0001111=>1
[1,2,3,8,6,5,4,7]=>1110000=>0001111=>1
[1,2,3,8,5,4,6,7]=>1110000=>0001111=>1
[2,6,1,5,4,8,3,7]=>0000000=>1111111=>1
[5,1,2,4,8,6,3,7]=>0000000=>1111111=>1
[5,1,2,4,8,3,7,6]=>0000000=>1111111=>1
[5,6,3,1,4,8,2,7]=>0000000=>1111111=>1
[2,5,4,3,1,8,6,7]=>0000100=>1111011=>2
[5,4,6,3,1,8,7,2]=>0000000=>1111111=>1
[3,6,4,5,1,8,7,2]=>0000000=>1111111=>1
[3,6,5,4,1,8,7,2]=>0000000=>1111111=>1
[5,2,6,1,7,8,4,3]=>0000000=>1111111=>1
[5,1,6,2,8,7,3,4]=>0000000=>1111111=>1
[2,1,3,7,8,6,4,5]=>0110000=>1001111=>2
[2,1,3,7,8,5,6,4]=>0110000=>1001111=>2
[5,2,4,1,7,8,6,3]=>0000000=>1111111=>1
[4,3,1,2,8,6,7,5]=>0001000=>1110111=>2
[5,1,4,2,8,6,7,3]=>0000000=>1111111=>1
[2,1,3,6,8,5,7,4]=>0110000=>1001111=>2
[1,2,3,8,6,7,4,5]=>1110000=>0001111=>1
[1,2,3,8,7,5,4,6]=>1110000=>0001111=>1
[1,2,3,8,7,4,5,6]=>1110000=>0001111=>1
[1,2,3,8,5,7,4,6]=>1110000=>0001111=>1
[2,1,3,6,8,7,4,5]=>0110000=>1001111=>2
[5,4,1,2,8,7,6,3]=>0000000=>1111111=>1
[3,1,6,2,8,7,5,4]=>0000000=>1111111=>1
[1,2,3,4,5,9,6,7,8]=>11111000=>00000111=>1
[1,2,3,4,9,5,6,7,8]=>11110000=>00001111=>1
[1,2,3,9,4,5,6,7,8]=>11100000=>00011111=>1
[1,2,9,3,4,5,6,7,8]=>11000000=>00111111=>1
[1,2,3,4,5,6,7,10,8,9]=>111111100=>000000011=>1
[1,2,3,4,5,6,10,7,8,9]=>111111000=>000000111=>1
[1,2,3,4,5,10,6,7,8,9]=>111110000=>000001111=>1
[1,2,3,4,10,5,6,7,8,9]=>111100000=>000011111=>1
[1,8,3,4,2,5,6,7]=>1000000=>0111111=>1
[1,2,3,10,4,5,6,7,8,9]=>111000000=>000111111=>1
[1,8,4,3,2,5,6,7]=>1000000=>0111111=>1
[1,2,10,3,4,5,6,7,8,9]=>110000000=>001111111=>1
[8,5,7,4,6,3,2,1]=>0000000=>1111111=>1
[8,1,7,4,6,5,3,2]=>0000000=>1111111=>1
[8,2,7,3,6,5,4,1]=>0000000=>1111111=>1
[8,3,7,2,6,5,4,1]=>0000000=>1111111=>1
[8,5,7,2,6,4,3,1]=>0000000=>1111111=>1
[8,4,7,1,6,5,3,2]=>0000000=>1111111=>1
[8,3,7,1,6,5,4,2]=>0000000=>1111111=>1
[8,2,7,1,6,5,4,3]=>0000000=>1111111=>1
[8,1,7,2,6,5,4,3]=>0000000=>1111111=>1
[8,1,7,6,5,3,4,2]=>0000000=>1111111=>1
[8,3,7,6,5,2,4,1]=>0000000=>1111111=>1
[8,4,7,6,5,2,3,1]=>0000000=>1111111=>1
[8,5,7,6,4,2,3,1]=>0000000=>1111111=>1
[8,3,7,6,5,1,4,2]=>0000000=>1111111=>1
[8,7,6,1,5,2,4,3]=>0000000=>1111111=>1
[6,8,1,3,2,5,4,7]=>0000000=>1111111=>1
[6,8,1,4,2,5,3,7]=>0000000=>1111111=>1
[7,8,3,6,1,4,2,5]=>0000000=>1111111=>1
[7,8,2,5,3,6,1,4]=>0000000=>1111111=>1
[7,8,2,5,1,4,3,6]=>0000000=>1111111=>1
[7,8,1,4,3,6,2,5]=>0000000=>1111111=>1
[5,8,1,4,3,7,2,6]=>0000000=>1111111=>1
[6,8,2,5,1,4,3,7]=>0000000=>1111111=>1
[6,8,2,5,3,7,1,4]=>0000000=>1111111=>1
[6,8,2,5,4,7,1,3]=>0000000=>1111111=>1
[2,5,4,7,6,8,1,3]=>0000000=>1111111=>1
[2,5,3,7,6,8,1,4]=>0000000=>1111111=>1
[2,5,1,4,3,7,6,8]=>0000101=>1111010=>2
[2,6,1,4,3,7,5,8]=>0000001=>1111110=>1
[2,6,5,8,1,4,3,7]=>0000000=>1111111=>1
[2,6,1,5,3,7,4,8]=>0000001=>1111110=>1
[2,6,3,7,4,8,1,5]=>0000000=>1111111=>1
[2,6,4,7,5,8,1,3]=>0000000=>1111111=>1
[5,8,3,6,4,7,1,2]=>0000000=>1111111=>1
[5,8,2,6,4,7,1,3]=>0000000=>1111111=>1
[4,8,2,6,3,7,1,5]=>0000000=>1111111=>1
[4,8,1,5,3,7,2,6]=>0000000=>1111111=>1
[4,8,1,5,2,6,3,7]=>0000000=>1111111=>1
[4,8,3,7,1,5,2,6]=>0000000=>1111111=>1
[6,8,3,7,1,4,2,5]=>0000000=>1111111=>1
[5,8,1,3,2,6,4,7]=>0000000=>1111111=>1
[5,8,4,7,1,3,2,6]=>0000000=>1111111=>1
[6,8,4,7,1,3,2,5]=>0000000=>1111111=>1
[6,8,5,7,1,3,2,4]=>0000000=>1111111=>1
[5,7,6,8,2,4,1,3]=>0000000=>1111111=>1
[4,7,6,8,1,3,2,5]=>0000000=>1111111=>1
[4,7,5,8,1,3,2,6]=>0000000=>1111111=>1
[4,7,1,3,2,6,5,8]=>0000001=>1111110=>1
[3,7,1,4,2,6,5,8]=>0000001=>1111110=>1
[3,7,5,8,1,4,2,6]=>0000000=>1111111=>1
[3,7,6,8,1,4,2,5]=>0000000=>1111111=>1
[3,7,6,8,2,5,1,4]=>0000000=>1111111=>1
[4,7,6,8,2,5,1,3]=>0000000=>1111111=>1
[4,7,5,8,3,6,1,2]=>0000000=>1111111=>1
[4,7,5,8,2,6,1,3]=>0000000=>1111111=>1
[3,7,5,8,2,6,1,4]=>0000000=>1111111=>1
[3,7,4,8,2,6,1,5]=>0000000=>1111111=>1
[3,7,4,8,1,5,2,6]=>0000000=>1111111=>1
[3,7,1,5,2,6,4,8]=>0000001=>1111110=>1
[3,7,2,6,1,5,4,8]=>0000001=>1111110=>1
[3,7,2,6,5,8,1,4]=>0000000=>1111111=>1
[4,7,3,6,5,8,1,2]=>0000000=>1111111=>1
[3,6,5,8,4,7,1,2]=>0000000=>1111111=>1
[2,6,5,8,4,7,1,3]=>0000000=>1111111=>1
[2,6,5,8,3,7,1,4]=>0000000=>1111111=>1
[2,6,3,7,1,5,4,8]=>0000001=>1111110=>1
[7,6,4,2,8,5,3,1]=>0000000=>1111111=>1
[7,6,4,3,8,2,5,1]=>0000000=>1111111=>1
[7,6,4,8,5,2,3,1]=>0000000=>1111111=>1
[6,8,4,3,7,2,1,5]=>0000000=>1111111=>1
[6,7,4,3,5,1,8,2]=>0000000=>1111111=>1
[6,7,3,5,4,8,2,1]=>0000000=>1111111=>1
[6,8,3,7,5,2,4,1]=>0000000=>1111111=>1
[7,6,8,3,5,2,4,1]=>0000000=>1111111=>1
[7,6,3,5,8,2,4,1]=>0000000=>1111111=>1
[7,6,3,5,2,4,8,1]=>0000000=>1111111=>1
[7,6,4,2,5,1,8,3]=>0000000=>1111111=>1
[7,6,2,8,4,1,5,3]=>0000000=>1111111=>1
[7,6,3,8,2,4,1,5]=>0000000=>1111111=>1
[7,6,3,4,8,2,5,1]=>0000000=>1111111=>1
[6,8,3,7,4,5,2,1]=>0000000=>1111111=>1
[6,7,3,5,8,4,2,1]=>0000000=>1111111=>1
[5,7,8,3,6,2,1,4]=>0000000=>1111111=>1
[5,8,3,6,7,2,1,4]=>0000000=>1111111=>1
[6,3,4,8,7,2,5,1]=>0000000=>1111111=>1
[6,3,8,4,7,2,1,5]=>0000000=>1111111=>1
[6,2,8,4,1,7,5,3]=>0000000=>1111111=>1
[6,2,7,4,1,5,3,8]=>0000001=>1111110=>1
[6,3,4,7,5,8,2,1]=>0000000=>1111111=>1
[6,3,5,7,8,4,2,1]=>0000000=>1111111=>1
[5,7,3,6,8,2,1,4]=>0000000=>1111111=>1
[5,6,8,3,7,2,1,4]=>0000000=>1111111=>1
[5,6,7,3,4,1,8,2]=>0000000=>1111111=>1
[4,6,7,8,3,5,2,1]=>0000000=>1111111=>1
[4,6,8,3,5,7,2,1]=>0000000=>1111111=>1
[4,7,3,5,6,8,2,1]=>0000000=>1111111=>1
[4,7,3,5,8,2,6,1]=>0000000=>1111111=>1
[5,3,4,7,8,2,1,6]=>0000000=>1111111=>1
[5,3,8,2,4,1,6,7]=>0000000=>1111111=>1
[5,3,4,8,2,6,1,7]=>0000000=>1111111=>1
[4,8,3,6,2,5,7,1]=>0000000=>1111111=>1
[4,8,3,5,7,2,6,1]=>0000000=>1111111=>1
[4,8,3,5,6,7,2,1]=>0000000=>1111111=>1
[4,7,8,3,5,6,2,1]=>0000000=>1111111=>1
[4,7,8,3,6,2,5,1]=>0000000=>1111111=>1
[4,8,3,6,7,2,5,1]=>0000000=>1111111=>1
[4,8,3,7,2,5,6,1]=>0000000=>1111111=>1
[5,3,4,8,2,7,6,1]=>0000000=>1111111=>1
[5,3,8,2,4,1,7,6]=>0000000=>1111111=>1
[5,2,8,4,1,7,3,6]=>0000000=>1111111=>1
[6,4,2,5,1,8,7,3]=>0000000=>1111111=>1
[6,4,3,5,8,2,1,7]=>0000000=>1111111=>1
[6,3,5,8,7,2,4,1]=>0000000=>1111111=>1
[5,8,3,7,2,6,4,1]=>0000000=>1111111=>1
[5,7,3,4,8,2,1,6]=>0000000=>1111111=>1
[5,8,4,2,3,1,6,7]=>0000000=>1111111=>1
[5,8,4,2,3,1,7,6]=>0000000=>1111111=>1
[6,4,5,3,8,2,1,7]=>0000000=>1111111=>1
[6,4,8,5,3,7,2,1]=>0000000=>1111111=>1
[6,4,3,8,5,7,2,1]=>0000000=>1111111=>1
[6,4,2,8,5,3,1,7]=>0000000=>1111111=>1
[6,4,2,7,3,1,8,5]=>0000000=>1111111=>1
[6,4,3,7,8,5,2,1]=>0000000=>1111111=>1
[6,4,5,3,7,1,8,2]=>0000000=>1111111=>1
[5,7,4,2,3,1,6,8]=>0000001=>1111110=>1
[5,6,3,7,1,8,2,4]=>0000000=>1111111=>1
[5,6,3,4,7,1,8,2]=>0000000=>1111111=>1
[5,6,3,4,8,2,1,7]=>0000000=>1111111=>1
[6,3,5,7,4,8,2,1]=>0000000=>1111111=>1
[6,3,5,4,7,8,2,1]=>0000000=>1111111=>1
[6,4,3,5,7,1,8,2]=>0000000=>1111111=>1
[6,4,2,5,1,7,3,8]=>0000001=>1111110=>1
[5,3,7,2,4,1,6,8]=>0000001=>1111110=>1
[5,3,4,7,2,6,1,8]=>0000001=>1111110=>1
[4,7,3,6,2,5,8,1]=>0000000=>1111111=>1
[4,7,3,6,8,2,5,1]=>0000000=>1111111=>1
[4,6,7,3,5,8,2,1]=>0000000=>1111111=>1
[4,5,7,8,3,6,2,1]=>0000000=>1111111=>1
[4,5,8,3,6,7,2,1]=>0000000=>1111111=>1
[4,5,8,3,7,2,6,1]=>0000000=>1111111=>1
[5,3,4,6,8,2,1,7]=>0000000=>1111111=>1
[5,3,6,8,2,1,4,7]=>0000000=>1111111=>1
[5,3,6,7,1,8,2,4]=>0000000=>1111111=>1
[5,3,4,6,7,1,8,2]=>0000000=>1111111=>1
[4,6,3,5,7,8,2,1]=>0000000=>1111111=>1
[4,5,7,3,6,8,2,1]=>0000000=>1111111=>1
[4,5,6,8,3,7,2,1]=>0000000=>1111111=>1
[5,7,4,8,6,3,2,1]=>0000000=>1111111=>1
[3,2,6,5,1,8,7,4]=>0000000=>1111111=>1
[3,5,6,7,2,8,4,1]=>0000000=>1111111=>1
[7,6,9,8,5,4,3,2,1]=>00000000=>11111111=>1
[6,5,4,9,8,7,3,2,1]=>00000000=>11111111=>1
[6,8,5,9,7,4,3,2,1]=>00000000=>11111111=>1
[6,7,8,9,5,4,3,2,1]=>00000000=>11111111=>1
[5,4,3,2,9,8,7,6,1]=>00000000=>11111111=>1
[5,8,4,3,9,7,6,2,1]=>00000000=>11111111=>1
[5,4,7,6,9,8,3,2,1]=>00000000=>11111111=>1
[5,7,8,4,9,6,3,2,1]=>00000000=>11111111=>1
[5,6,7,8,9,4,3,2,1]=>00000000=>11111111=>1
[4,8,3,2,1,9,7,6,5]=>00000000=>11111111=>1
[4,3,7,6,2,9,8,5,1]=>00000000=>11111111=>1
[4,7,8,3,2,9,6,5,1]=>00000000=>11111111=>1
[4,6,3,8,5,9,7,2,1]=>00000000=>11111111=>1
[4,6,7,8,3,9,5,2,1]=>00000000=>11111111=>1
[4,5,6,7,8,9,3,2,1]=>00000000=>11111111=>1
[3,2,1,6,5,4,9,8,7]=>00100100=>11011011=>3
[3,6,2,8,5,1,9,7,4]=>00000000=>11111111=>1
[3,6,7,8,2,1,9,5,4]=>00000000=>11111111=>1
[3,2,5,4,7,6,9,8,1]=>00000000=>11111111=>1
[3,5,7,2,8,4,9,6,1]=>00000000=>11111111=>1
[3,5,6,7,8,2,9,4,1]=>00000000=>11111111=>1
[3,4,5,6,7,8,9,2,1]=>00000000=>11111111=>1
[2,4,6,7,1,8,3,9,5]=>00000000=>11111111=>1
[2,4,5,6,7,8,1,9,3]=>00000000=>11111111=>1
[8,7,10,9,6,5,4,3,2,1]=>000000000=>111111111=>1
[8,9,10,7,6,5,4,3,2,1]=>000000000=>111111111=>1
[7,6,5,10,9,8,4,3,2,1]=>000000000=>111111111=>1
[7,9,6,10,8,5,4,3,2,1]=>000000000=>111111111=>1
[7,8,9,10,6,5,4,3,2,1]=>000000000=>111111111=>1
[6,5,4,3,10,9,8,7,2,1]=>000000000=>111111111=>1
[6,9,5,4,10,8,7,3,2,1]=>000000000=>111111111=>1
[6,5,8,7,10,9,4,3,2,1]=>000000000=>111111111=>1
[6,8,9,5,10,7,4,3,2,1]=>000000000=>111111111=>1
[5,4,3,2,1,10,9,8,7,6]=>000010000=>111101111=>2
[5,9,4,3,2,10,8,7,6,1]=>000000000=>111111111=>1
[5,4,8,7,3,10,9,6,2,1]=>000000000=>111111111=>1
[5,8,9,4,3,10,7,6,2,1]=>000000000=>111111111=>1
[5,7,4,9,6,10,8,3,2,1]=>000000000=>111111111=>1
[5,6,7,8,9,10,4,3,2,1]=>000000000=>111111111=>1
[4,3,8,7,2,1,10,9,6,5]=>000000000=>111111111=>1
[4,8,9,3,2,1,10,7,6,5]=>000000000=>111111111=>1
[4,3,2,7,6,5,10,9,8,1]=>000000000=>111111111=>1
[4,7,3,9,6,2,10,8,5,1]=>000000000=>111111111=>1
[4,7,8,9,3,2,10,6,5,1]=>000000000=>111111111=>1
[4,3,6,5,8,7,10,9,2,1]=>000000000=>111111111=>1
[4,6,7,8,9,3,10,5,2,1]=>000000000=>111111111=>1
[4,5,6,7,8,9,10,3,2,1]=>000000000=>111111111=>1
[3,6,2,1,9,5,4,10,8,7]=>000000000=>111111111=>1
[3,2,6,5,8,7,1,10,9,4]=>000000000=>111111111=>1
[3,6,8,2,9,5,1,10,7,4]=>000000000=>111111111=>1
[3,6,7,8,9,2,1,10,5,4]=>000000000=>111111111=>1
[3,5,7,8,2,9,4,10,6,1]=>000000000=>111111111=>1
[3,5,6,7,8,9,2,10,4,1]=>000000000=>111111111=>1
[3,4,5,6,7,8,9,10,2,1]=>000000000=>111111111=>1
[2,4,6,1,8,3,9,5,10,7]=>000000000=>111111111=>1
[2,4,6,7,8,1,9,3,10,5]=>000000000=>111111111=>1
[2,4,5,6,7,8,9,1,10,3]=>000000000=>111111111=>1
[1,6,2,5,3,4,8,7]=>1000010=>0111101=>2
[1,3,8,2,4,6,5,7]=>1000000=>0111111=>1
[1,7,2,3,6,4,8,5]=>1000000=>0111111=>1
[1,6,8,2,5,3,7,4]=>1000000=>0111111=>1
[1,8,2,5,3,4,7,6]=>1000000=>0111111=>1
[1,8,2,3,6,4,7,5]=>1000000=>0111111=>1
[1,3,5,2,8,4,7,6]=>1000000=>0111111=>1
[1,2,7,3,5,4,6,8]=>1100001=>0011110=>1
[1,8,2,7,3,4,6,5]=>1000000=>0111111=>1
[1,5,8,2,3,7,4,6]=>1000000=>0111111=>1
[1,6,8,2,3,5,4,7]=>1000000=>0111111=>1
[7,1,5,8,4,2,3,6]=>0000000=>1111111=>1
[7,1,4,5,8,2,3,6]=>0000000=>1111111=>1
[2,1,7,5,8,3,4,6]=>0100000=>1011111=>2
[7,1,5,4,8,2,3,6]=>0000000=>1111111=>1
[8,3,7,1,2,4,6,5]=>0000000=>1111111=>1
[8,3,7,5,1,2,4,6]=>0000000=>1111111=>1
[6,7,1,8,4,2,3,5]=>0000000=>1111111=>1
[6,8,1,7,4,2,3,5]=>0000000=>1111111=>1
[7,1,8,4,5,2,3,6]=>0000000=>1111111=>1
[2,1,7,8,5,3,4,6]=>0100000=>1011111=>2
[6,1,2,3,8,7,5,4]=>0000000=>1111111=>1
[6,8,1,4,2,3,7,5]=>0000000=>1111111=>1
[6,8,3,1,2,7,4,5]=>0000000=>1111111=>1
[6,7,3,1,2,8,4,5]=>0000000=>1111111=>1
[6,7,1,4,2,3,8,5]=>0000000=>1111111=>1
[4,3,6,8,5,7,1,2]=>0000000=>1111111=>1
[6,1,2,5,4,8,3,7]=>0000000=>1111111=>1
[7,2,1,5,8,3,4,6]=>0000000=>1111111=>1
[1,3,6,8,7,4,2,5]=>1000000=>0111111=>1
[1,2,8,5,7,3,4,6]=>1100000=>0011111=>1
[2,6,1,5,8,3,4,7]=>0000000=>1111111=>1
[5,7,1,6,8,4,3,2]=>0000000=>1111111=>1
[4,8,1,2,5,7,3,6]=>0000000=>1111111=>1
[8,4,6,2,5,7,3,1]=>0000000=>1111111=>1
[8,3,6,4,7,2,5,1]=>0000000=>1111111=>1
[3,8,1,4,7,2,5,6]=>0000000=>1111111=>1
[1,7,8,4,6,2,5,3]=>1000000=>0111111=>1
[3,7,4,8,5,1,6,2]=>0000000=>1111111=>1
[3,7,1,6,5,4,8,2]=>0000000=>1111111=>1
[2,7,3,1,5,8,4,6]=>0000000=>1111111=>1
[2,7,4,6,8,1,3,5]=>0000000=>1111111=>1
[2,7,5,8,6,4,1,3]=>0000000=>1111111=>1
[8,2,6,7,5,4,3,1]=>0000000=>1111111=>1
[3,8,7,1,6,4,5,2]=>0000000=>1111111=>1
[3,6,8,2,7,4,1,5]=>0000000=>1111111=>1
[1,5,2,8,7,4,6,3]=>1000000=>0111111=>1
[3,4,2,7,8,1,6,5]=>0000000=>1111111=>1
[4,1,3,7,5,6,8,2]=>0000000=>1111111=>1
[6,3,8,1,7,4,2,5]=>0000000=>1111111=>1
[6,5,8,7,1,4,2,3]=>0000000=>1111111=>1
[4,1,7,3,8,5,2,6]=>0000000=>1111111=>1
[3,6,1,4,5,8,2,7]=>0000000=>1111111=>1
[1,6,7,4,5,3,8,2]=>1000000=>0111111=>1
[6,1,7,3,5,4,8,2]=>0000000=>1111111=>1
[6,3,1,2,5,8,4,7]=>0000000=>1111111=>1
[1,4,7,2,8,5,3,6]=>1000000=>0111111=>1
[5,6,8,7,2,4,1,3]=>0000000=>1111111=>1
[6,8,5,7,1,2,4,3]=>0000000=>1111111=>1
[2,8,4,1,7,5,6,3]=>0000000=>1111111=>1
[8,2,4,3,7,5,6,1]=>0000000=>1111111=>1
[6,8,2,1,5,7,3,4]=>0000000=>1111111=>1
[7,2,8,4,1,6,3,5]=>0000000=>1111111=>1
[1,2,4,8,6,5,3,7]=>1100000=>0011111=>1
[7,1,5,6,8,4,3,2]=>0000000=>1111111=>1
[2,7,8,1,4,6,3,5]=>0000000=>1111111=>1
[4,8,2,5,7,1,6,3]=>0000000=>1111111=>1
[4,1,6,8,5,3,7,2]=>0000000=>1111111=>1
[5,2,6,4,8,3,1,7]=>0000000=>1111111=>1
[6,7,1,3,4,5,8,2]=>0000000=>1111111=>1
[1,7,3,2,4,8,5,6]=>1000000=>0111111=>1
[1,3,6,5,2,8,4,7]=>1000000=>0111111=>1
[7,1,6,5,3,4,8,2]=>0000000=>1111111=>1
[6,8,7,4,2,3,5,1]=>0000000=>1111111=>1
[8,6,1,3,5,4,2,7]=>0000000=>1111111=>1
[5,3,8,6,1,2,4,7]=>0000000=>1111111=>1
[3,8,7,2,6,4,5,1]=>0000000=>1111111=>1
[6,3,5,4,8,7,2,1]=>0000000=>1111111=>1
[8,5,2,7,1,4,3,6]=>0000000=>1111111=>1
[5,1,8,6,3,4,2,7]=>0000000=>1111111=>1
[8,2,3,7,6,4,5,1]=>0000000=>1111111=>1
[7,2,5,6,4,8,1,3]=>0000000=>1111111=>1
[1,6,7,4,8,2,3,5]=>1000000=>0111111=>1
[8,2,1,3,5,6,7,4]=>0000000=>1111111=>1
[4,1,3,8,2,6,7,5]=>0000000=>1111111=>1
[3,6,1,4,7,2,8,5]=>0000000=>1111111=>1
[6,2,7,4,5,8,1,3]=>0000000=>1111111=>1
[1,8,5,7,3,2,4,6]=>1000000=>0111111=>1
[2,7,4,1,5,3,8,6]=>0000000=>1111111=>1
[7,4,8,6,2,3,1,5]=>0000000=>1111111=>1
[7,1,3,2,8,5,4,6]=>0000000=>1111111=>1
[5,1,7,4,2,3,8,6]=>0000000=>1111111=>1
[4,1,8,6,5,3,2,7]=>0000000=>1111111=>1
[5,7,4,3,6,2,8,1]=>0000000=>1111111=>1
[6,7,5,1,2,8,3,4]=>0000000=>1111111=>1
[5,2,6,8,3,4,7,1]=>0000000=>1111111=>1
[3,6,8,4,7,2,5,1]=>0000000=>1111111=>1
[6,2,7,5,8,3,1,4]=>0000000=>1111111=>1
[2,1,5,6,8,3,7,4]=>0100000=>1011111=>2
[1,6,8,3,2,7,4,5]=>1000000=>0111111=>1
[6,5,7,2,8,4,1,3]=>0000000=>1111111=>1
[5,7,3,6,4,8,2,1]=>0000000=>1111111=>1
[3,6,1,4,2,7,8,5]=>0000000=>1111111=>1
[1,2,6,3,5,8,7,4]=>1100000=>0011111=>1
[2,3,5,1,8,4,7,6]=>0000000=>1111111=>1
[2,3,6,1,8,5,4,7]=>0000000=>1111111=>1
[3,1,7,5,4,8,6,2]=>0000000=>1111111=>1
[1,2,7,6,4,8,5,3]=>1100000=>0011111=>1
[1,2,7,3,6,8,5,4]=>1100000=>0011111=>1
[2,3,6,1,8,5,7,4]=>0000000=>1111111=>1
[1,2,5,8,4,7,3,6]=>1100000=>0011111=>1
[1,3,6,8,5,2,7,4]=>1000000=>0111111=>1
[1,2,6,8,5,4,3,7]=>1100000=>0011111=>1
[1,3,5,8,2,4,7,6]=>1000000=>0111111=>1
[1,4,6,8,3,2,5,7]=>1000000=>0111111=>1
[1,3,7,5,6,8,2,4]=>1000000=>0111111=>1
[1,2,6,7,3,8,5,4]=>1100000=>0011111=>1
[1,2,5,7,3,8,6,4]=>1100000=>0011111=>1
[2,3,6,5,8,7,1,4]=>0000000=>1111111=>1
[1,2,7,5,6,8,4,3]=>1100000=>0011111=>1
[3,1,6,7,5,8,4,2]=>0000000=>1111111=>1
[4,6,2,7,5,8,3,1]=>0000000=>1111111=>1
[3,5,7,4,8,2,6,1]=>0000000=>1111111=>1
[1,4,6,8,3,5,7,2]=>1000000=>0111111=>1
[1,3,5,8,2,7,4,6]=>1000000=>0111111=>1
[1,2,5,8,4,7,6,3]=>1100000=>0011111=>1
[1,2,5,8,7,4,3,6]=>1100000=>0011111=>1
[1,3,5,8,7,2,4,6]=>1000000=>0111111=>1
[6,4,5,7,2,8,1,3]=>0000000=>1111111=>1
[5,3,4,7,2,8,1,6]=>0000000=>1111111=>1
[3,2,7,4,6,8,1,5]=>0000000=>1111111=>1
[5,3,6,2,7,1,4,8]=>0000001=>1111110=>1
[2,6,3,4,7,1,5,8]=>0000001=>1111110=>1
[2,7,3,4,5,8,1,6]=>0000000=>1111111=>1
[3,7,4,5,6,8,1,2]=>0000000=>1111111=>1
[2,5,7,3,6,8,1,4]=>0000000=>1111111=>1
[4,7,6,2,3,8,1,5]=>0000000=>1111111=>1
[7,3,5,2,4,8,1,6]=>0000000=>1111111=>1
[7,6,2,4,5,8,1,3]=>0000000=>1111111=>1
[6,5,2,3,4,8,1,7]=>0000000=>1111111=>1
[5,3,1,2,8,4,7,6]=>0000000=>1111111=>1
[6,5,2,3,7,1,4,8]=>0000001=>1111110=>1
[5,2,1,7,3,4,6,8]=>0000001=>1111110=>1
[5,2,1,8,3,4,6,7]=>0000000=>1111111=>1
[6,3,2,8,4,5,7,1]=>0000000=>1111111=>1
[7,3,1,2,8,4,6,5]=>0000000=>1111111=>1
[6,4,1,3,8,5,7,2]=>0000000=>1111111=>1
[6,2,3,1,8,4,7,5]=>0000000=>1111111=>1
[8,3,5,2,7,1,4,6]=>0000000=>1111111=>1
[8,6,2,4,7,1,5,3]=>0000000=>1111111=>1
[8,5,2,3,6,1,4,7]=>0000000=>1111111=>1
[8,2,1,7,3,4,5,6]=>0000000=>1111111=>1
[8,6,3,7,2,4,5,1]=>0000000=>1111111=>1
[7,1,6,2,3,4,5,8]=>0000001=>1111110=>1
[8,2,7,3,4,5,6,1]=>0000000=>1111111=>1
[8,1,6,2,3,4,5,7]=>0000000=>1111111=>1
[8,1,7,3,4,5,6,2]=>0000000=>1111111=>1
[8,6,1,7,2,4,5,3]=>0000000=>1111111=>1
[8,1,5,7,2,3,6,4]=>0000000=>1111111=>1
[1,7,5,8,2,3,6,4]=>1000000=>0111111=>1
[7,2,1,8,3,4,5,6]=>0000000=>1111111=>1
[7,3,8,2,4,5,6,1]=>0000000=>1111111=>1
[7,2,8,3,4,5,6,1]=>0000000=>1111111=>1
[1,7,8,3,4,5,6,2]=>1000000=>0111111=>1
[1,4,5,8,3,6,7,2]=>1000000=>0111111=>1
[2,5,7,1,8,3,6,4]=>0000000=>1111111=>1
[6,2,7,1,8,4,5,3]=>0000000=>1111111=>1
[4,7,1,3,8,5,6,2]=>0000000=>1111111=>1
[1,6,2,8,4,5,7,3]=>1000000=>0111111=>1
[4,1,3,6,8,2,7,5]=>0000000=>1111111=>1
[5,3,4,6,8,2,7,1]=>0000000=>1111111=>1
[4,6,3,8,7,1,2,5]=>0000000=>1111111=>1
[6,4,5,8,7,1,2,3]=>0000000=>1111111=>1
[5,3,4,8,7,1,2,6]=>0000000=>1111111=>1
[3,2,8,7,1,4,6,5]=>0000000=>1111111=>1
[3,1,8,7,2,4,6,5]=>0000000=>1111111=>1
[5,3,7,6,1,2,4,8]=>0000001=>1111110=>1
[1,8,3,7,2,4,5,6]=>1000000=>0111111=>1
[3,8,1,7,2,4,5,6]=>0000000=>1111111=>1
[6,8,2,3,5,1,4,7]=>0000000=>1111111=>1
[4,7,8,2,6,1,3,5]=>0000000=>1111111=>1
[6,2,8,7,1,4,5,3]=>0000000=>1111111=>1
[3,8,7,1,4,5,6,2]=>0000000=>1111111=>1
[2,8,6,1,3,4,5,7]=>0000000=>1111111=>1
[2,7,6,1,3,4,5,8]=>0000001=>1111110=>1
[1,7,6,2,3,4,5,8]=>1000001=>0111110=>1
[1,8,6,2,3,4,5,7]=>1000000=>0111111=>1
[2,8,7,3,4,5,6,1]=>0000000=>1111111=>1
[3,8,7,2,4,5,6,1]=>0000000=>1111111=>1
[7,8,3,6,2,4,5,1]=>0000000=>1111111=>1
[1,5,8,7,2,3,6,4]=>1000000=>0111111=>1
[8,7,6,1,3,4,5,2]=>0000000=>1111111=>1
[3,6,2,4,7,1,8,5]=>0000000=>1111111=>1
[3,4,7,2,5,1,8,6]=>0000000=>1111111=>1
[2,1,6,4,8,5,3,7]=>0100000=>1011111=>2
[4,1,8,5,3,2,7,6]=>0000000=>1111111=>1
[3,6,2,5,7,1,4,8]=>0000001=>1111110=>1
[1,2,8,3,7,5,4,6]=>1100000=>0011111=>1
[6,1,3,2,8,5,4,7]=>0000000=>1111111=>1
[5,6,1,2,8,4,3,7]=>0000000=>1111111=>1
[1,6,3,8,7,4,2,5]=>1000000=>0111111=>1
[4,3,8,1,2,6,7,5]=>0000000=>1111111=>1
[7,8,10,9,5,6,3,4,1,2]=>000000000=>111111111=>1
[9,10,5,6,8,7,3,4,1,2]=>000000000=>111111111=>1
[5,8,10,6,9,7,3,4,1,2]=>000000000=>111111111=>1
[5,6,7,10,9,8,3,4,1,2]=>000000000=>111111111=>1
[9,10,7,8,3,4,6,5,1,2]=>000000000=>111111111=>1
[7,8,10,9,3,4,6,5,1,2]=>000000000=>111111111=>1
[9,10,3,6,8,4,7,5,1,2]=>000000000=>111111111=>1
[3,8,10,6,9,4,7,5,1,2]=>000000000=>111111111=>1
[3,6,7,10,9,4,8,5,1,2]=>000000000=>111111111=>1
[9,10,3,4,5,8,7,6,1,2]=>000000000=>111111111=>1
[3,8,10,4,5,9,7,6,1,2]=>000000000=>111111111=>1
[3,4,7,10,5,9,8,6,1,2]=>000000000=>111111111=>1
[3,4,5,6,10,9,8,7,1,2]=>000000000=>111111111=>1
[9,10,7,8,5,6,1,2,4,3]=>000000000=>111111111=>1
[7,8,10,9,5,6,1,2,4,3]=>000000000=>111111111=>1
[9,10,5,6,8,7,1,2,4,3]=>000000000=>111111111=>1
[5,8,10,6,9,7,1,2,4,3]=>000000000=>111111111=>1
[5,6,7,10,9,8,1,2,4,3]=>000000000=>111111111=>1
[9,10,7,8,1,4,6,2,5,3]=>000000000=>111111111=>1
[7,8,10,9,1,4,6,2,5,3]=>000000000=>111111111=>1
[9,10,1,6,8,4,7,2,5,3]=>000000000=>111111111=>1
[1,8,10,6,9,4,7,2,5,3]=>100000000=>011111111=>1
[1,6,7,10,9,4,8,2,5,3]=>100000000=>011111111=>1
[9,10,1,4,5,8,7,2,6,3]=>000000000=>111111111=>1
[1,8,10,4,5,9,7,2,6,3]=>100000000=>011111111=>1
[1,4,7,10,5,9,8,2,6,3]=>100000000=>011111111=>1
[1,4,5,6,10,9,8,2,7,3]=>100000000=>011111111=>1
[9,10,7,8,1,2,3,6,5,4]=>000000000=>111111111=>1
[7,8,10,9,1,2,3,6,5,4]=>000000000=>111111111=>1
[9,10,1,6,8,2,3,7,5,4]=>000000000=>111111111=>1
[1,8,10,6,9,2,3,7,5,4]=>100000000=>011111111=>1
[1,6,7,10,9,2,3,8,5,4]=>100000000=>011111111=>1
[9,10,1,2,5,8,3,7,6,4]=>000000000=>111111111=>1
[1,8,10,2,5,9,3,7,6,4]=>100000000=>011111111=>1
[1,2,7,10,5,9,3,8,6,4]=>110000000=>001111111=>1
[1,2,5,6,10,9,3,8,7,4]=>110000000=>001111111=>1
[9,10,1,2,3,4,8,7,6,5]=>000000000=>111111111=>1
[1,8,10,2,3,4,9,7,6,5]=>100000000=>011111111=>1
[1,2,7,10,3,4,9,8,6,5]=>110000000=>001111111=>1
[1,2,3,6,10,4,9,8,7,5]=>111000000=>000111111=>1
[1,2,3,4,5,10,9,8,7,6]=>111110000=>000001111=>1
[1,10,12,8,11,6,9,4,7,2,5,3]=>10000000000=>01111111111=>1
[1,8,9,12,11,6,10,4,7,2,5,3]=>10000000000=>01111111111=>1
[1,10,12,6,7,11,9,4,8,2,5,3]=>10000000000=>01111111111=>1
[1,6,9,12,7,11,10,4,8,2,5,3]=>10000000000=>01111111111=>1
[1,6,7,8,12,11,10,4,9,2,5,3]=>10000000000=>01111111111=>1
[1,10,12,8,11,4,5,9,7,2,6,3]=>10000000000=>01111111111=>1
[1,8,9,12,11,4,5,10,7,2,6,3]=>10000000000=>01111111111=>1
[1,10,12,4,7,11,5,9,8,2,6,3]=>10000000000=>01111111111=>1
[1,4,9,12,7,11,5,10,8,2,6,3]=>10000000000=>01111111111=>1
[1,4,7,8,12,11,5,10,9,2,6,3]=>10000000000=>01111111111=>1
[1,10,12,4,5,6,11,9,8,2,7,3]=>10000000000=>01111111111=>1
[1,4,9,12,5,6,11,10,8,2,7,3]=>10000000000=>01111111111=>1
[1,4,5,8,12,6,11,10,9,2,7,3]=>10000000000=>01111111111=>1
[1,4,5,6,7,12,11,10,9,2,8,3]=>10000000000=>01111111111=>1
[1,10,12,8,11,6,9,2,3,7,5,4]=>10000000000=>01111111111=>1
[1,8,9,12,11,6,10,2,3,7,5,4]=>10000000000=>01111111111=>1
[1,10,12,6,7,11,9,2,3,8,5,4]=>10000000000=>01111111111=>1
[1,6,9,12,7,11,10,2,3,8,5,4]=>10000000000=>01111111111=>1
[1,6,7,8,12,11,10,2,3,9,5,4]=>10000000000=>01111111111=>1
[1,10,12,8,11,2,5,9,3,7,6,4]=>10000000000=>01111111111=>1
[1,8,9,12,11,2,5,10,3,7,6,4]=>10000000000=>01111111111=>1
[1,10,12,2,7,11,5,9,3,8,6,4]=>10000000000=>01111111111=>1
[1,10,12,2,5,6,11,9,3,8,7,4]=>10000000000=>01111111111=>1
[1,10,12,8,11,2,3,4,9,7,6,5]=>10000000000=>01111111111=>1
[1,8,9,12,11,2,3,4,10,7,6,5]=>10000000000=>01111111111=>1
[1,10,12,2,7,11,3,4,9,8,6,5]=>10000000000=>01111111111=>1
[1,10,12,2,3,6,11,4,9,8,7,5]=>10000000000=>01111111111=>1
[1,10,12,2,3,4,5,11,9,8,7,6]=>10000000000=>01111111111=>1
[3,1,2,4,5,6,7,8,9]=>00111111=>11000000=>1
[2,4,1,3,5,6,7,8,9]=>00011111=>11100000=>1
[2,3,5,1,4,6,7,8,9]=>00001111=>11110000=>1
[2,3,4,6,1,5,7,8,9]=>00000111=>11111000=>1
[2,3,4,5,7,1,6,8,9]=>00000011=>11111100=>1
[2,3,4,5,6,8,1,7,9]=>00000001=>11111110=>1
[3,6,8,7,1,2,5,4]=>0000000=>1111111=>1
[6,5,7,2,4,8,1,3]=>0000000=>1111111=>1
[3,4,1,6,5,8,7,2]=>0000000=>1111111=>1
[3,5,1,2,4,8,7,6]=>0000100=>1111011=>2
[3,7,5,2,1,4,6,8]=>0000001=>1111110=>1
[3,8,5,2,7,4,1,6]=>0000000=>1111111=>1
[5,2,8,4,7,3,1,6]=>0000000=>1111111=>1
[5,2,7,4,1,3,6,8]=>0000001=>1111110=>1
[4,3,5,1,2,8,7,6]=>0000100=>1111011=>2
[3,1,4,6,2,8,7,5]=>0000000=>1111111=>1
[1,4,6,5,2,8,7,3]=>1000000=>0111111=>1
[3,4,5,6,1,8,7,2]=>0000000=>1111111=>1
[3,4,5,8,7,2,1,6]=>0000000=>1111111=>1
[1,4,7,2,6,3,5,8]=>1000001=>0111110=>1
[8,4,7,5,2,1,6,3]=>0000000=>1111111=>1
[8,1,4,7,2,3,6,5]=>0000000=>1111111=>1
[1,8,5,7,3,4,6,2]=>1000000=>0111111=>1
[6,3,5,1,7,4,2,8]=>0000001=>1111110=>1
[6,1,4,8,7,3,2,5]=>0000000=>1111111=>1
[6,4,8,5,7,1,2,3]=>0000000=>1111111=>1
[5,4,8,1,6,3,2,7]=>0000000=>1111111=>1
[1,4,8,6,3,7,2,5]=>1000000=>0111111=>1
[5,4,7,6,3,8,1,2]=>0000000=>1111111=>1
[4,6,3,7,5,8,1,2]=>0000000=>1111111=>1
[4,1,3,5,8,6,2,7]=>0000000=>1111111=>1
[5,7,4,3,8,1,2,6]=>0000000=>1111111=>1
[1,4,8,3,7,6,5,2]=>1000000=>0111111=>1
[4,3,8,2,1,6,5,7]=>0000000=>1111111=>1
[3,8,4,2,7,1,5,6]=>0000000=>1111111=>1
[3,1,2,5,7,6,4,8]=>0010001=>1101110=>2
[1,8,2,7,6,5,4,3]=>1000000=>0111111=>1
[3,8,1,6,7,5,4,2]=>0000000=>1111111=>1
[3,7,2,6,8,5,1,4]=>0000000=>1111111=>1
[7,2,3,8,5,6,1,4]=>0000000=>1111111=>1
[8,2,1,7,5,6,4,3]=>0000000=>1111111=>1
[8,1,3,6,5,7,4,2]=>0000000=>1111111=>1
[8,2,4,3,6,1,5,7]=>0000000=>1111111=>1
[1,7,8,5,4,3,6,2]=>1000000=>0111111=>1
[1,8,4,5,3,2,6,7]=>1000000=>0111111=>1
[7,8,5,4,3,1,6,2]=>0000000=>1111111=>1
[7,1,6,3,4,2,5,8]=>0000001=>1111110=>1
[6,8,7,1,4,2,5,3]=>0000000=>1111111=>1
[3,6,1,4,2,7,5,8]=>0000001=>1111110=>1
[3,4,1,8,5,7,6,2]=>0000000=>1111111=>1
[3,6,5,1,2,8,4,7]=>0000000=>1111111=>1
[3,8,5,6,7,2,1,4]=>0000000=>1111111=>1
[8,1,7,6,2,4,3,5]=>0000000=>1111111=>1
[8,5,6,1,4,2,3,7]=>0000000=>1111111=>1
[8,6,5,4,7,1,3,2]=>0000000=>1111111=>1
[1,6,4,5,7,2,3,8]=>1000001=>0111110=>1
[8,3,6,1,7,2,4,5]=>0000000=>1111111=>1
[1,8,6,5,7,3,4,2]=>1000000=>0111111=>1
[1,7,5,3,6,8,4,2]=>1000000=>0111111=>1
[7,4,1,6,5,8,3,2]=>0000000=>1111111=>1
[4,1,5,8,7,6,3,2]=>0000000=>1111111=>1
[1,2,5,8,6,7,3,4]=>1100000=>0011111=>1
[4,2,1,5,8,7,3,6]=>0000000=>1111111=>1
[5,2,4,6,1,7,3,8]=>0000001=>1111110=>1
[1,5,3,6,8,7,4,2]=>1000000=>0111111=>1
[3,5,4,6,1,8,2,7]=>0000000=>1111111=>1
[3,1,5,7,6,8,2,4]=>0000000=>1111111=>1
[1,4,5,6,8,7,2,3]=>1000000=>0111111=>1
[1,4,6,3,7,2,8,5]=>1000000=>0111111=>1
[1,7,3,6,5,2,8,4]=>1000000=>0111111=>1
[8,6,2,5,4,1,7,3]=>0000000=>1111111=>1
[3,7,2,6,5,4,1,8]=>0000001=>1111110=>1
[7,6,2,5,4,3,1,8]=>0000001=>1111110=>1
[4,7,5,2,6,3,1,8]=>0000001=>1111110=>1
[3,2,6,4,7,5,1,8]=>0000001=>1111110=>1
[6,2,3,7,5,4,1,8]=>0000001=>1111110=>1
[1,3,4,7,6,2,8,5]=>1000000=>0111111=>1
[2,8,3,6,1,7,5,4]=>0000000=>1111111=>1
[8,7,2,5,1,6,4,3]=>0000000=>1111111=>1
[3,8,2,6,5,1,7,4]=>0000000=>1111111=>1
[7,8,2,5,4,1,6,3]=>0000000=>1111111=>1
[4,8,5,2,6,1,7,3]=>0000000=>1111111=>1
[4,5,1,3,7,2,8,6]=>0000000=>1111111=>1
[6,1,3,7,5,2,8,4]=>0000000=>1111111=>1
[7,1,3,6,2,8,5,4]=>0000000=>1111111=>1
[8,1,3,6,2,7,5,4]=>0000000=>1111111=>1
[1,2,4,7,3,8,6,5]=>1100000=>0011111=>1
[7,1,8,2,6,5,4,3]=>0000000=>1111111=>1
[3,1,8,6,2,7,5,4]=>0000000=>1111111=>1
[4,1,7,8,2,6,5,3]=>0000000=>1111111=>1
[5,6,1,8,2,7,4,3]=>0000000=>1111111=>1
[4,2,7,8,1,6,5,3]=>0000000=>1111111=>1
[3,2,8,6,1,7,5,4]=>0000000=>1111111=>1
[7,2,8,1,6,5,4,3]=>0000000=>1111111=>1
[1,8,7,2,6,5,4,3]=>1000000=>0111111=>1
[2,8,7,1,6,5,4,3]=>0000000=>1111111=>1
[3,8,7,1,6,5,4,2]=>0000000=>1111111=>1
[4,8,7,5,1,6,3,2]=>0000000=>1111111=>1
[6,7,8,5,1,4,3,2]=>0000000=>1111111=>1
[5,6,3,8,4,1,7,2]=>0000000=>1111111=>1
[7,3,8,5,4,1,6,2]=>0000000=>1111111=>1
[3,4,8,6,5,1,7,2]=>0000000=>1111111=>1
[8,3,7,5,1,6,4,2]=>0000000=>1111111=>1
[1,4,8,6,2,7,5,3]=>1000000=>0111111=>1
[8,4,6,7,1,5,3,2]=>0000000=>1111111=>1
[5,6,4,7,8,1,3,2]=>0000000=>1111111=>1
[3,4,6,5,1,2,8,7]=>0000010=>1111101=>2
[7,3,5,1,2,8,6,4]=>0000000=>1111111=>1
[1,4,6,2,3,8,7,5]=>1000000=>0111111=>1
[1,3,2,7,4,8,6,5]=>1010000=>0101111=>2
[7,2,1,6,3,8,5,4]=>0000000=>1111111=>1
[2,3,1,7,6,4,8,5]=>0010000=>1101111=>2
[4,5,2,1,7,3,8,6]=>0000000=>1111111=>1
[5,6,7,1,2,8,4,3]=>0000000=>1111111=>1
[4,7,5,1,2,8,6,3]=>0000000=>1111111=>1
[3,7,1,6,2,8,5,4]=>0000000=>1111111=>1
[7,6,1,2,8,5,4,3]=>0000000=>1111111=>1
[2,7,1,3,8,6,5,4]=>0000000=>1111111=>1
[8,6,1,2,7,5,4,3]=>0000000=>1111111=>1
[1,7,2,3,8,6,5,4]=>1000000=>0111111=>1
[8,7,1,2,6,5,4,3]=>0000000=>1111111=>1
[7,8,1,2,6,5,4,3]=>0000000=>1111111=>1
[3,8,1,6,2,7,5,4]=>0000000=>1111111=>1
[4,8,5,1,2,7,6,3]=>0000000=>1111111=>1
[5,6,8,1,2,7,4,3]=>0000000=>1111111=>1
[2,1,3,7,4,8,6,5]=>0110000=>1001111=>2
[4,2,7,3,6,8,1,5]=>0000000=>1111111=>1
[5,3,6,4,2,8,1,7]=>0000000=>1111111=>1
[4,1,5,3,8,2,7,6]=>0000000=>1111111=>1
[5,2,6,4,7,3,1,8]=>0000001=>1111110=>1
[2,6,3,4,7,5,1,8]=>0000001=>1111110=>1
[2,6,3,5,4,8,1,7]=>0000000=>1111111=>1
[2,7,4,3,5,8,1,6]=>0000000=>1111111=>1
[7,3,6,4,2,8,1,5]=>0000000=>1111111=>1
[7,6,4,5,2,8,1,3]=>0000000=>1111111=>1
[5,4,3,1,8,2,7,6]=>0000000=>1111111=>1
[6,5,4,2,7,3,1,8]=>0000001=>1111110=>1
[5,4,1,7,2,6,3,8]=>0000001=>1111110=>1
[5,4,1,8,3,2,6,7]=>0000000=>1111111=>1
[6,5,2,8,3,4,7,1]=>0000000=>1111111=>1
[7,4,2,1,8,3,6,5]=>0000000=>1111111=>1
[6,5,3,4,8,2,7,1]=>0000000=>1111111=>1
[6,1,5,3,8,2,7,4]=>0000000=>1111111=>1
[4,6,3,1,8,2,7,5]=>0000000=>1111111=>1
[5,8,4,2,7,3,1,6]=>0000000=>1111111=>1
[8,2,6,4,7,3,1,5]=>0000000=>1111111=>1
[8,6,2,5,7,4,1,3]=>0000000=>1111111=>1
[8,5,3,2,6,4,1,7]=>0000000=>1111111=>1
[8,3,1,7,2,5,4,6]=>0000000=>1111111=>1
[7,5,2,6,4,3,1,8]=>0000001=>1111110=>1
[7,1,6,2,5,4,3,8]=>0000001=>1111110=>1
[8,1,7,3,5,6,4,2]=>0000000=>1111111=>1
[8,6,1,7,4,5,2,3]=>0000000=>1111111=>1
[8,1,3,7,2,6,5,4]=>0000000=>1111111=>1
[1,7,6,8,3,2,4,5]=>1000000=>0111111=>1
[7,1,5,8,4,2,6,3]=>0000000=>1111111=>1
[7,3,8,4,5,2,6,1]=>0000000=>1111111=>1
[7,2,8,5,3,4,6,1]=>0000000=>1111111=>1
[6,1,8,4,3,2,5,7]=>0000000=>1111111=>1
[6,1,7,4,2,5,3,8]=>0000001=>1111110=>1
[1,2,7,3,4,6,5,8]=>1100001=>0011110=>1
[1,7,8,4,3,5,6,2]=>1000000=>0111111=>1
[1,6,2,8,3,5,7,4]=>1000000=>0111111=>1
[2,6,1,7,3,5,4,8]=>0000001=>1111110=>1
[3,1,5,8,4,2,6,7]=>0000000=>1111111=>1
[4,3,1,6,8,2,7,5]=>0000000=>1111111=>1
[5,7,4,8,3,2,1,6]=>0000000=>1111111=>1
[5,4,8,2,7,3,1,6]=>0000000=>1111111=>1
[5,2,8,7,3,4,1,6]=>0000000=>1111111=>1
[6,4,7,5,3,2,1,8]=>0000001=>1111110=>1
[1,8,3,7,6,2,4,5]=>1000000=>0111111=>1
[5,8,3,2,6,4,1,7]=>0000000=>1111111=>1
[6,8,2,4,7,5,1,3]=>0000000=>1111111=>1
[7,3,8,2,6,4,1,5]=>0000000=>1111111=>1
[4,6,8,2,7,3,1,5]=>0000000=>1111111=>1
[2,6,8,7,3,4,1,5]=>0000000=>1111111=>1
[7,2,8,6,3,5,1,4]=>0000000=>1111111=>1
[6,8,1,7,2,5,4,3]=>0000000=>1111111=>1
[3,8,7,4,5,6,1,2]=>0000000=>1111111=>1
[2,8,6,4,3,5,1,7]=>0000000=>1111111=>1
[2,7,6,3,5,4,1,8]=>0000001=>1111110=>1
[1,7,6,5,2,4,3,8]=>1000001=>0111110=>1
[1,8,6,5,3,2,4,7]=>1000000=>0111111=>1
[3,8,7,4,6,2,5,1]=>0000000=>1111111=>1
[5,8,3,7,6,2,4,1]=>0000000=>1111111=>1
[7,1,8,6,5,2,3,4]=>0000000=>1111111=>1
[8,4,7,5,3,2,1,6]=>0000000=>1111111=>1
[8,7,2,5,4,3,1,6]=>0000000=>1111111=>1
[1,5,7,8,4,3,6,2]=>1000000=>0111111=>1
[6,2,1,8,5,4,7,3]=>0000000=>1111111=>1
[2,6,5,7,4,1,3,8]=>0000001=>1111110=>1
[2,5,6,8,4,3,7,1]=>0000000=>1111111=>1
[5,2,1,8,7,6,4,3]=>0000000=>1111111=>1
[4,8,6,7,5,3,1,2]=>0000000=>1111111=>1
[6,5,4,8,2,1,7,3]=>0000000=>1111111=>1
[5,8,4,7,2,6,3,1]=>0000000=>1111111=>1
[5,8,3,2,7,6,4,1]=>0000000=>1111111=>1
[5,2,1,4,3,6,7,8]=>0000111=>1111000=>1
[3,5,7,4,2,6,1,8]=>0000001=>1111110=>1
[4,2,1,6,5,3,7,8]=>0000011=>1111100=>1
[4,2,1,5,7,6,3,8]=>0000001=>1111110=>1
[3,5,4,7,1,6,2,8]=>0000001=>1111110=>1
[3,4,5,8,6,7,1,2]=>0000000=>1111111=>1
[4,3,5,1,6,8,7,2]=>0000000=>1111111=>1
[4,3,2,1,7,6,5,9,8,10]=>000100101=>111011010=>3
[7,3,2,1,6,5,4,9,8,10]=>000000101=>111111010=>2
[4,3,2,1,9,6,5,8,7,10]=>000100001=>111011110=>2
[6,3,2,1,9,5,4,8,7,10]=>000000001=>111111110=>1
[9,3,2,1,8,5,4,7,6,10]=>000000001=>111111110=>1
[6,5,2,1,9,4,3,8,7,10]=>000000001=>111111110=>1
[9,5,2,1,8,4,3,7,6,10]=>000000001=>111111110=>1
[4,3,2,1,7,6,5,10,8,9]=>000100100=>111011011=>3
[7,3,2,1,6,5,4,10,8,9]=>000000100=>111111011=>2
[4,3,2,1,8,6,5,10,7,9]=>000100000=>111011111=>2
[6,3,2,1,8,5,4,10,7,9]=>000000000=>111111111=>1
[8,3,2,1,7,5,4,10,6,9]=>000000000=>111111111=>1
[6,5,2,1,8,4,3,10,7,9]=>000000000=>111111111=>1
[8,5,2,1,7,4,3,10,6,9]=>000000000=>111111111=>1
[4,3,2,1,10,6,5,9,7,8]=>000100000=>111011111=>2
[6,3,2,1,10,5,4,9,7,8]=>000000000=>111111111=>1
[7,3,2,1,10,5,4,9,6,8]=>000000000=>111111111=>1
[10,3,2,1,9,5,4,8,6,7]=>000000000=>111111111=>1
[6,5,2,1,10,4,3,9,7,8]=>000000000=>111111111=>1
[7,5,2,1,10,4,3,9,6,8]=>000000000=>111111111=>1
[10,5,2,1,9,4,3,8,6,7]=>000000000=>111111111=>1
[4,3,2,1,8,7,5,10,6,9]=>000100000=>111011111=>2
[5,3,2,1,8,7,4,10,6,9]=>000000000=>111111111=>1
[8,3,2,1,7,6,4,10,5,9]=>000000000=>111111111=>1
[5,4,2,1,8,7,3,10,6,9]=>000000000=>111111111=>1
[8,4,2,1,7,6,3,10,5,9]=>000000000=>111111111=>1
[4,3,2,1,10,7,5,9,6,8]=>000100000=>111011111=>2
[5,3,2,1,10,7,4,9,6,8]=>000000000=>111111111=>1
[7,3,2,1,10,6,4,9,5,8]=>000000000=>111111111=>1
[10,3,2,1,9,6,4,8,5,7]=>000000000=>111111111=>1
[5,4,2,1,10,7,3,9,6,8]=>000000000=>111111111=>1
[7,4,2,1,10,6,3,9,5,8]=>000000000=>111111111=>1
[10,4,2,1,9,6,3,8,5,7]=>000000000=>111111111=>1
[7,6,2,1,10,5,3,9,4,8]=>000000000=>111111111=>1
[10,6,2,1,9,5,3,8,4,7]=>000000000=>111111111=>1
[5,4,3,1,8,7,2,10,6,9]=>000000000=>111111111=>1
[8,4,3,1,7,6,2,10,5,9]=>000000000=>111111111=>1
[5,4,3,1,10,7,2,9,6,8]=>000000000=>111111111=>1
[7,4,3,1,10,6,2,9,5,8]=>000000000=>111111111=>1
[10,4,3,1,9,6,2,8,5,7]=>000000000=>111111111=>1
[7,6,3,1,10,5,2,9,4,8]=>000000000=>111111111=>1
[10,6,3,1,9,5,2,8,4,7]=>000000000=>111111111=>1
[10,3,1,5,2,7,4,9,6,8]=>000000000=>111111111=>1
[10,9,4,1,6,2,8,3,5,7]=>000000000=>111111111=>1
[10,9,8,5,1,7,2,3,4,6]=>000000000=>111111111=>1
[7,6,5,4,3,2,9,1,8]=>00000000=>11111111=>1
[6,5,4,3,9,2,8,1,7]=>00000000=>11111111=>1
[6,5,4,3,2,8,1,7,9]=>00000001=>11111110=>1
[5,4,9,3,8,2,7,1,6]=>00000000=>11111111=>1
[5,4,3,8,2,7,1,6,9]=>00000001=>11111110=>1
[5,4,3,2,7,9,1,6,8]=>00000000=>11111111=>1
[5,4,3,2,7,1,6,8,9]=>00000011=>11111100=>1
[4,8,3,7,2,6,1,5,9]=>00000001=>11111110=>1
[4,3,7,2,6,9,1,5,8]=>00000000=>11111111=>1
[4,3,7,2,6,1,5,8,9]=>00000011=>11111100=>1
[4,3,2,6,8,1,5,7,9]=>00000001=>11111110=>1
[4,3,2,6,1,5,7,8,9]=>00000111=>11111000=>1
[3,6,9,2,5,8,1,4,7]=>00000000=>11111111=>1
[3,6,2,5,8,1,4,7,9]=>00000001=>11111110=>1
[3,6,2,5,1,4,7,8,9]=>00000111=>11111000=>1
[3,2,5,7,9,1,4,6,8]=>00000000=>11111111=>1
[3,2,5,7,1,4,6,8,9]=>00000011=>11111100=>1
[3,2,5,1,4,6,7,8,9]=>00001111=>11110000=>1
[2,4,6,8,1,3,5,7,9]=>00000001=>11111110=>1
[2,4,6,1,3,5,7,8,9]=>00000111=>11111000=>1
[8,7,6,5,4,3,2,10,1,9]=>000000000=>111111111=>1
[7,6,5,4,3,10,2,9,1,8]=>000000000=>111111111=>1
[7,6,5,4,3,2,9,1,8,10]=>000000001=>111111110=>1
[6,5,4,10,3,9,2,8,1,7]=>000000000=>111111111=>1
[6,5,4,3,9,2,8,1,7,10]=>000000001=>111111110=>1
[6,5,4,3,2,8,10,1,7,9]=>000000000=>111111111=>1
[6,5,4,3,2,8,1,7,9,10]=>000000011=>111111100=>1
[5,10,4,9,3,8,2,7,1,6]=>000000000=>111111111=>1
[5,4,9,3,8,2,7,1,6,10]=>000000001=>111111110=>1
[5,4,3,8,2,7,10,1,6,9]=>000000000=>111111111=>1
[5,4,3,8,2,7,1,6,9,10]=>000000011=>111111100=>1
[5,4,3,2,7,9,1,6,8,10]=>000000001=>111111110=>1
[5,4,3,2,7,1,6,8,9,10]=>000000111=>111111000=>1
[4,8,3,7,2,6,10,1,5,9]=>000000000=>111111111=>1
[4,8,3,7,2,6,1,5,9,10]=>000000011=>111111100=>1
[4,3,7,10,2,6,9,1,5,8]=>000000000=>111111111=>1
[4,3,7,2,6,9,1,5,8,10]=>000000001=>111111110=>1
[4,3,7,2,6,1,5,8,9,10]=>000000111=>111111000=>1
[4,3,2,6,8,10,1,5,7,9]=>000000000=>111111111=>1
[4,3,2,6,8,1,5,7,9,10]=>000000011=>111111100=>1
[4,3,2,6,1,5,7,8,9,10]=>000001111=>111110000=>1
[3,6,9,2,5,8,1,4,7,10]=>000000001=>111111110=>1
[3,6,2,5,8,10,1,4,7,9]=>000000000=>111111111=>1
[3,6,2,5,8,1,4,7,9,10]=>000000011=>111111100=>1
[3,6,2,5,1,4,7,8,9,10]=>000001111=>111110000=>1
[3,2,5,7,9,1,4,6,8,10]=>000000001=>111111110=>1
[3,2,5,7,1,4,6,8,9,10]=>000000111=>111111000=>1
[3,2,5,1,4,6,7,8,9,10]=>000011111=>111100000=>1
[2,4,6,8,1,3,5,7,9,10]=>000000011=>111111100=>1
[2,4,6,1,3,5,7,8,9,10]=>000001111=>111110000=>1
[2,4,1,3,5,6,7,8,9,10]=>000111111=>111000000=>1
[2,1,7,3,8,4,6,5]=>0100000=>1011111=>2
[4,1,7,2,8,3,6,5]=>0000000=>1111111=>1
[7,1,8,2,4,3,6,5]=>0000000=>1111111=>1
[7,1,5,2,8,3,6,4]=>0000000=>1111111=>1
[5,1,7,2,8,3,6,4]=>0000000=>1111111=>1
[8,1,6,2,5,3,7,4]=>0000000=>1111111=>1
[6,1,7,2,8,3,5,4]=>0000000=>1111111=>1
[1,8,2,7,5,4,6,3]=>1000000=>0111111=>1
[1,8,2,7,4,3,5,6]=>1000000=>0111111=>1
[1,8,6,4,7,2,3,5]=>1000000=>0111111=>1
[1,8,4,2,6,3,5,7]=>1000000=>0111111=>1
[7,4,8,1,5,2,3,6]=>0000000=>1111111=>1
[4,1,7,2,6,3,5,8]=>0000001=>1111110=>1
[5,1,7,4,3,6,2,8]=>0000001=>1111110=>1
[7,5,8,3,2,4,1,6]=>0000000=>1111111=>1
[1,8,5,4,3,6,2,7]=>1000000=>0111111=>1
[1,8,5,4,3,7,2,6]=>1000000=>0111111=>1
[1,8,5,4,7,2,6,3]=>1000000=>0111111=>1
[1,8,4,2,5,3,7,6]=>1000000=>0111111=>1
[1,8,5,4,2,6,7,3]=>1000000=>0111111=>1
[7,4,8,2,1,3,5,6]=>0000000=>1111111=>1
[4,1,7,3,2,5,6,8]=>0000001=>1111110=>1
[7,5,4,8,2,3,6,1]=>0000000=>1111111=>1
[3,1,7,2,6,8,4,5]=>0000000=>1111111=>1
[5,1,7,4,2,6,8,3]=>0000000=>1111111=>1
[4,1,6,3,2,5,8,7]=>0000010=>1111101=>2
[4,3,1,6,2,5,7,8]=>0000011=>1111100=>1
[6,5,4,3,7,1,8,2]=>0000000=>1111111=>1
[6,5,1,7,3,8,2,4]=>0000000=>1111111=>1
[6,3,2,8,5,7,1,4]=>0000000=>1111111=>1
[6,5,4,3,8,2,7,1]=>0000000=>1111111=>1
[6,5,4,3,8,7,1,2]=>0000000=>1111111=>1
[7,6,3,8,5,4,1,2]=>0000000=>1111111=>1
[5,4,8,2,1,7,3,6]=>0000000=>1111111=>1
[7,6,4,8,5,1,2,3]=>0000000=>1111111=>1
[7,2,8,6,3,1,4,5]=>0000000=>1111111=>1
[7,2,8,6,1,5,3,4]=>0000000=>1111111=>1
[2,1,7,8,3,6,4,5]=>0100000=>1011111=>2
[6,4,1,7,8,2,3,5]=>0000000=>1111111=>1
[4,2,1,6,7,3,5,8]=>0000001=>1111110=>1
[4,3,1,5,2,7,6,8]=>0000101=>1111010=>2
[5,4,2,7,3,8,1,6]=>0000000=>1111111=>1
[4,1,5,3,2,8,6,7]=>0000100=>1111011=>2
[3,1,6,2,8,7,4,5]=>0000000=>1111111=>1
[6,5,4,1,7,8,3,2]=>0000000=>1111111=>1
[5,4,3,1,6,7,2,8]=>0000001=>1111110=>1
[6,5,4,2,7,8,3,1]=>0000000=>1111111=>1
[5,4,2,6,3,8,7,1]=>0000000=>1111111=>1
[4,3,1,5,2,6,8,7]=>0000110=>1111001=>2
[5,4,2,1,6,7,8,3]=>0000000=>1111111=>1
[5,4,3,1,6,7,8,2]=>0000000=>1111111=>1
[6,3,8,1,2,5,7,4]=>0000000=>1111111=>1
[3,6,7,1,2,5,8,4]=>0000000=>1111111=>1
[7,8,3,1,2,5,6,4]=>0000000=>1111111=>1
[7,8,1,3,2,4,6,5]=>0000000=>1111111=>1
[7,8,2,1,3,5,4,6]=>0000000=>1111111=>1
[5,2,3,7,1,8,6,4]=>0000000=>1111111=>1
[2,5,3,6,1,8,7,4]=>0000000=>1111111=>1
[2,6,7,3,1,8,4,5]=>0000000=>1111111=>1
[2,6,7,1,3,5,4,8]=>0000001=>1111110=>1
[6,2,8,3,1,7,4,5]=>0000000=>1111111=>1
[3,2,5,7,1,8,4,6]=>0000000=>1111111=>1
[4,3,1,2,7,8,6,5]=>0001000=>1110111=>2
[5,1,2,7,3,6,4,8]=>0000001=>1111110=>1
[5,1,4,7,8,2,3,6]=>0000000=>1111111=>1
[5,3,4,7,8,6,1,2]=>0000000=>1111111=>1
[3,5,4,6,8,7,1,2]=>0000000=>1111111=>1
[1,5,4,6,8,2,3,7]=>1000000=>0111111=>1
[1,6,7,3,2,4,8,5]=>1000000=>0111111=>1
[1,5,3,6,2,7,8,4]=>1000000=>0111111=>1
[5,1,3,7,2,6,8,4]=>0000000=>1111111=>1
[5,2,4,7,8,1,6,3]=>0000000=>1111111=>1
[4,2,5,7,6,1,8,3]=>0000000=>1111111=>1
[4,5,2,8,6,1,7,3]=>0000000=>1111111=>1
[5,3,1,8,2,6,7,4]=>0000000=>1111111=>1
[6,1,8,3,2,4,7,5]=>0000000=>1111111=>1
[4,3,5,7,6,8,1,2]=>0000000=>1111111=>1
[4,1,5,7,6,2,3,8]=>0000001=>1111110=>1
[4,5,1,8,6,2,3,7]=>0000000=>1111111=>1
[5,2,1,8,3,6,4,7]=>0000000=>1111111=>1
[3,4,2,1,8,7,5,6]=>0001000=>1110111=>2
[7,6,5,4,2,1,8,3]=>0000000=>1111111=>1
[7,6,5,4,8,1,3,2]=>0000000=>1111111=>1
[8,7,6,5,4,2,1,9,3]=>00000000=>11111111=>1
[7,6,5,8,2,1,4,3]=>0000000=>1111111=>1
[8,7,6,5,3,2,1,9,4]=>00000000=>11111111=>1
[8,7,6,4,3,2,1,9,5]=>00000000=>11111111=>1
[8,7,5,4,3,2,1,9,6]=>00000000=>11111111=>1
[8,5,4,3,2,1,7,6]=>0000000=>1111111=>1
[8,6,5,4,3,2,1,9,7]=>00000000=>11111111=>1
[7,6,5,4,3,2,1,9,8]=>00000010=>11111101=>2
[7,6,5,4,1,8,3,2]=>0000000=>1111111=>1
[8,7,6,5,4,9,1,3,2]=>00000000=>11111111=>1
[9,8,7,6,5,4,2,1,10,3]=>000000000=>111111111=>1
[7,6,5,2,8,1,4,3]=>0000000=>1111111=>1
[8,7,6,5,9,2,1,4,3]=>00000000=>11111111=>1
[9,8,7,6,5,3,2,1,10,4]=>000000000=>111111111=>1
[7,6,5,8,4,1,3,2]=>0000000=>1111111=>1
[8,7,6,9,3,2,1,5,4]=>00000000=>11111111=>1
[9,8,7,6,4,3,2,1,10,5]=>000000000=>111111111=>1
[7,6,8,5,2,1,4,3]=>0000000=>1111111=>1
[8,7,9,4,3,2,1,6,5]=>00000000=>11111111=>1
[9,8,7,5,4,3,2,1,10,6]=>000000000=>111111111=>1
[7,8,6,3,2,1,5,4]=>0000000=>1111111=>1
[8,9,5,4,3,2,1,7,6]=>00000000=>11111111=>1
[9,8,6,5,4,3,2,1,10,7]=>000000000=>111111111=>1
[8,7,4,3,2,1,6,5]=>0000000=>1111111=>1
[9,6,5,4,3,2,1,8,7]=>00000000=>11111111=>1
[9,7,6,5,4,3,2,1,10,8]=>000000000=>111111111=>1
[7,8,4,5,9,2,3,6,10,1]=>000000000=>111111111=>1
[7,8,2,4,5,1,3,6]=>0000000=>1111111=>1
[4,6,7,2,5,1,3,8]=>0000001=>1111110=>1
[7,8,1,3,2,4,5,6]=>0000000=>1111111=>1
[7,8,4,1,5,2,3,6]=>0000000=>1111111=>1
[3,6,7,2,1,4,5,8]=>0000001=>1111110=>1
[5,2,3,6,1,4,7,8]=>0000011=>1111100=>1
[2,5,3,6,1,4,7,8]=>0000011=>1111100=>1
[2,6,7,3,1,4,5,8]=>0000001=>1111110=>1
[4,6,7,1,5,2,3,8]=>0000001=>1111110=>1
[4,6,7,3,5,8,1,2]=>0000000=>1111111=>1
[6,4,7,1,5,2,3,8]=>0000001=>1111110=>1
[6,2,7,3,1,4,5,8]=>0000001=>1111110=>1
[3,2,5,6,1,4,7,8]=>0000011=>1111100=>1
[3,5,2,6,1,4,7,8]=>0000011=>1111100=>1
[5,1,4,6,7,2,3,8]=>0000001=>1111110=>1
[3,5,4,6,7,8,1,2]=>0000000=>1111111=>1
[1,5,4,6,7,2,3,8]=>1000001=>0111110=>1
[1,6,7,3,2,4,5,8]=>1000001=>0111110=>1
[1,5,3,6,2,4,7,8]=>1000011=>0111100=>1
[5,1,3,6,2,4,7,8]=>0000011=>1111100=>1
[5,2,4,6,7,1,3,8]=>0000001=>1111110=>1
[2,5,4,6,7,1,3,8]=>0000001=>1111110=>1
[2,6,7,4,5,1,3,8]=>0000001=>1111110=>1
[6,2,7,4,5,1,3,8]=>0000001=>1111110=>1
[4,2,5,6,7,1,3,8]=>0000001=>1111110=>1
[4,5,2,6,7,1,3,8]=>0000001=>1111110=>1
[5,3,1,6,2,4,7,8]=>0000011=>1111100=>1
[6,1,7,3,2,4,5,8]=>0000001=>1111110=>1
[6,1,7,4,5,2,3,8]=>0000001=>1111110=>1
[6,3,7,4,5,8,1,2]=>0000000=>1111111=>1
[5,4,1,6,7,2,3,8]=>0000001=>1111110=>1
[5,2,1,6,3,4,7,8]=>0000011=>1111100=>1
[7,3,2,5,4,1,6,8]=>0000001=>1111110=>1
[7,3,5,2,4,1,6,8]=>0000001=>1111110=>1
[7,6,5,2,1,4,3,8]=>0000001=>1111110=>1
[1,3,6,7,5,2,8,4]=>1000000=>0111111=>1
[7,3,2,5,1,6,4,8]=>0000001=>1111110=>1
[1,7,4,6,2,8,5,3]=>1000000=>0111111=>1
[1,3,4,5,8,7,2,6]=>1000000=>0111111=>1
[3,1,2,5,6,8,7,4]=>0010000=>1101111=>2
[3,7,5,4,6,8,1,2]=>0000000=>1111111=>1
[2,3,4,5,8,1,7,6]=>0000000=>1111111=>1
[3,1,4,6,7,8,5,2]=>0000000=>1111111=>1
[7,1,5,2,6,8,3,4]=>0000000=>1111111=>1
[2,3,6,7,5,1,8,4]=>0000000=>1111111=>1
[4,3,2,6,7,1,8,5]=>0000000=>1111111=>1
[7,1,5,4,6,8,3,2]=>0000000=>1111111=>1
[5,7,4,6,1,8,3,2]=>0000000=>1111111=>1
[6,3,4,5,8,1,2,7]=>0000000=>1111111=>1
[7,3,4,5,8,2,1,6]=>0000000=>1111111=>1
[4,8,6,1,7,5,2,3]=>0000000=>1111111=>1
[7,6,4,2,8,3,5,1]=>0000000=>1111111=>1
[8,4,7,3,6,5,1,2]=>0000000=>1111111=>1
[6,4,7,1,8,3,2,5]=>0000000=>1111111=>1
[8,10,7,9,5,6,3,4,1,2]=>000000000=>111111111=>1
[9,10,6,8,5,7,3,4,1,2]=>000000000=>111111111=>1
[8,10,6,9,5,7,3,4,1,2]=>000000000=>111111111=>1
[7,10,6,9,5,8,3,4,1,2]=>000000000=>111111111=>1
[9,10,7,8,4,6,3,5,1,2]=>000000000=>111111111=>1
[8,10,7,9,4,6,3,5,1,2]=>000000000=>111111111=>1
[9,10,6,8,4,7,3,5,1,2]=>000000000=>111111111=>1
[8,10,6,9,4,7,3,5,1,2]=>000000000=>111111111=>1
[7,10,6,9,4,8,3,5,1,2]=>000000000=>111111111=>1
[9,10,5,8,4,7,3,6,1,2]=>000000000=>111111111=>1
[8,10,5,9,4,7,3,6,1,2]=>000000000=>111111111=>1
[7,10,5,9,4,8,3,6,1,2]=>000000000=>111111111=>1
[6,10,5,9,4,8,3,7,1,2]=>000000000=>111111111=>1
[9,10,7,8,5,6,2,4,1,3]=>000000000=>111111111=>1
[8,10,7,9,5,6,2,4,1,3]=>000000000=>111111111=>1
[9,10,6,8,5,7,2,4,1,3]=>000000000=>111111111=>1
[8,10,6,9,5,7,2,4,1,3]=>000000000=>111111111=>1
[7,10,6,9,5,8,2,4,1,3]=>000000000=>111111111=>1
[9,10,7,8,4,6,2,5,1,3]=>000000000=>111111111=>1
[8,10,7,9,4,6,2,5,1,3]=>000000000=>111111111=>1
[9,10,6,8,4,7,2,5,1,3]=>000000000=>111111111=>1
[8,10,6,9,4,7,2,5,1,3]=>000000000=>111111111=>1
[7,10,6,9,4,8,2,5,1,3]=>000000000=>111111111=>1
[9,10,5,8,4,7,2,6,1,3]=>000000000=>111111111=>1
[8,10,5,9,4,7,2,6,1,3]=>000000000=>111111111=>1
[7,10,5,9,4,8,2,6,1,3]=>000000000=>111111111=>1
[6,10,5,9,4,8,2,7,1,3]=>000000000=>111111111=>1
[9,10,7,8,3,6,2,5,1,4]=>000000000=>111111111=>1
[8,10,7,9,3,6,2,5,1,4]=>000000000=>111111111=>1
[9,10,6,8,3,7,2,5,1,4]=>000000000=>111111111=>1
[8,10,6,9,3,7,2,5,1,4]=>000000000=>111111111=>1
[7,10,6,9,3,8,2,5,1,4]=>000000000=>111111111=>1
[9,10,5,8,3,7,2,6,1,4]=>000000000=>111111111=>1
[8,10,5,9,3,7,2,6,1,4]=>000000000=>111111111=>1
[7,10,5,9,3,8,2,6,1,4]=>000000000=>111111111=>1
[6,10,5,9,3,8,2,7,1,4]=>000000000=>111111111=>1
[9,10,4,8,3,7,2,6,1,5]=>000000000=>111111111=>1
[8,10,4,9,3,7,2,6,1,5]=>000000000=>111111111=>1
[7,10,4,9,3,8,2,6,1,5]=>000000000=>111111111=>1
[6,10,4,9,3,8,2,7,1,5]=>000000000=>111111111=>1
[6,2,1,7,3,5,4,8]=>0000001=>1111110=>1
[2,1,8,6,3,5,4,7]=>0100000=>1011111=>2
[2,1,7,3,5,8,6,4]=>0100000=>1011111=>2
[2,7,3,1,5,4,6,8]=>0000001=>1111110=>1
[2,6,3,1,4,8,5,7]=>0000000=>1111111=>1
[4,2,1,8,3,6,7,5]=>0000000=>1111111=>1
[2,1,8,6,3,5,7,4]=>0100000=>1011111=>2
[6,2,1,7,3,5,8,4]=>0000000=>1111111=>1
[2,7,3,1,4,8,5,6]=>0000000=>1111111=>1
[3,2,1,6,4,5,7,8]=>0010011=>1101100=>2
[3,2,1,5,7,8,4,6]=>0010000=>1101111=>2
[2,1,7,3,6,8,4,5]=>0100000=>1011111=>2
[2,7,3,1,5,6,8,4]=>0000000=>1111111=>1
[2,4,7,5,1,6,8,3]=>0000000=>1111111=>1
[4,3,7,5,6,1,8,2]=>0000000=>1111111=>1
[4,3,6,8,5,1,7,2]=>0000000=>1111111=>1
[2,6,1,8,3,5,7,4]=>0000000=>1111111=>1
[2,1,6,8,3,7,4,5]=>0100000=>1011111=>2
[2,1,8,3,5,7,4,6]=>0100000=>1011111=>2
[3,2,1,5,6,8,4,7]=>0010000=>1101111=>2
[3,2,1,5,7,4,6,8]=>0010001=>1101110=>2
[2,1,7,3,6,4,5,8]=>0100001=>1011110=>2
[2,1,6,3,5,8,4,7]=>0100000=>1011111=>2
[8,2,4,1,7,5,6,3]=>0000000=>1111111=>1
[3,8,4,7,5,1,6,2]=>0000000=>1111111=>1
[8,4,3,6,1,7,5,2]=>0000000=>1111111=>1
[8,2,1,7,3,5,4,6]=>0000000=>1111111=>1
[2,6,1,8,3,5,4,7]=>0000000=>1111111=>1
[2,7,3,1,5,6,4,8]=>0000001=>1111110=>1
[2,4,7,5,1,6,3,8]=>0000001=>1111110=>1
[8,2,4,1,7,5,3,6]=>0000000=>1111111=>1
[5,8,6,3,1,7,4,2]=>0000000=>1111111=>1
[2,4,7,1,8,5,3,6]=>0000000=>1111111=>1
[2,4,8,5,1,6,3,7]=>0000000=>1111111=>1
[6,2,1,7,3,4,8,5]=>0000000=>1111111=>1
[6,2,1,7,8,3,5,4]=>0000000=>1111111=>1
[2,7,1,8,3,5,6,4]=>0000000=>1111111=>1
[2,1,8,3,6,4,5,7]=>0100000=>1011111=>2
[3,2,1,6,7,4,5,8]=>0010001=>1101110=>2
[3,2,1,7,4,5,6,8]=>0010001=>1101110=>2
[3,2,1,6,8,4,5,7]=>0010000=>1101111=>2
[2,1,8,3,7,4,5,6]=>0100000=>1011111=>2
[2,1,8,3,6,7,4,5]=>0100000=>1011111=>2
[2,4,8,5,1,6,7,3]=>0000000=>1111111=>1
[4,3,8,5,6,1,7,2]=>0000000=>1111111=>1
[3,2,1,8,4,5,6,7]=>0010000=>1101111=>2
[1,6,8,3,7,2,4,5]=>1000000=>0111111=>1
[3,8,1,5,7,2,4,6]=>0000000=>1111111=>1
[1,2,6,8,4,7,3,5]=>1100000=>0011111=>1
[6,1,5,8,2,4,7,3]=>0000000=>1111111=>1
[1,2,4,8,3,6,7,5]=>1100000=>0011111=>1
[4,1,2,7,8,3,6,5]=>0000000=>1111111=>1
[3,5,7,4,8,6,1,2]=>0000000=>1111111=>1
[5,3,8,4,7,6,1,2]=>0000000=>1111111=>1
[8,7,1,2,5,4,6,3]=>0000000=>1111111=>1
[5,8,1,2,3,7,6,4]=>0000000=>1111111=>1
[1,2,8,4,3,5,7,6]=>1100000=>0011111=>1
[1,2,5,3,7,6,4,8]=>1100001=>0011110=>1
[6,1,2,8,7,4,5,3]=>0000000=>1111111=>1
[7,1,6,2,8,4,5,3]=>0000000=>1111111=>1
[1,2,6,3,8,5,4,7]=>1100000=>0011111=>1
[1,2,8,5,3,6,4,7]=>1100000=>0011111=>1
[1,2,7,3,8,5,4,6]=>1100000=>0011111=>1
[4,1,2,7,8,6,3,5]=>0000000=>1111111=>1
[1,6,2,8,4,3,5,7]=>1000000=>0111111=>1
[1,6,4,2,7,3,5,8]=>1000001=>0111110=>1
[1,8,6,3,2,4,5,7]=>1000000=>0111111=>1
[1,7,3,2,8,4,5,6]=>1000000=>0111111=>1
[3,1,7,8,6,2,4,5]=>0000000=>1111111=>1
[1,8,7,2,4,5,6,3]=>1000000=>0111111=>1
[1,8,7,3,5,6,2,4]=>1000000=>0111111=>1
[1,3,2,8,7,4,5,6]=>1010000=>0101111=>2
[1,8,3,2,6,4,5,7]=>1000000=>0111111=>1
[1,7,6,3,2,4,5,8]=>1000001=>0111110=>1
[1,2,8,4,3,7,5,6]=>1100000=>0011111=>1
[8,5,1,7,2,4,6,3]=>0000000=>1111111=>1
[5,3,8,7,4,6,1,2]=>0000000=>1111111=>1
[3,8,6,4,7,5,1,2]=>0000000=>1111111=>1
[6,1,8,2,7,4,5,3]=>0000000=>1111111=>1
[1,2,5,3,8,6,4,7]=>1100000=>0011111=>1
[1,2,7,5,3,6,4,8]=>1100001=>0011110=>1
[1,2,6,3,7,5,4,8]=>1100001=>0011110=>1
[1,2,3,7,5,4,8,6]=>1110000=>0001111=>1
[3,7,4,8,6,5,1,2]=>0000000=>1111111=>1
[1,8,2,7,6,4,5,3]=>1000000=>0111111=>1
[2,9,8,7,6,5,4,1,3]=>00000000=>11111111=>1
[2,8,7,6,5,1,4,3]=>0000000=>1111111=>1
[7,4,2,1,6,5,3,8]=>0000001=>1111110=>1
[7,4,1,3,5,2,6,8]=>0000001=>1111110=>1
[4,3,2,7,1,5,8,6]=>0000000=>1111111=>1
[5,6,8,7,4,3,1,2]=>0000000=>1111111=>1
[1,8,2,7,4,3,6,5]=>1000000=>0111111=>1
[2,4,8,1,6,3,7,5]=>0000000=>1111111=>1
[5,3,2,6,4,8,1,7]=>0000000=>1111111=>1
[2,4,5,3,8,6,1,7]=>0000000=>1111111=>1
[1,8,4,5,2,6,7,3]=>1000000=>0111111=>1
[1,8,4,3,6,2,7,5]=>1000000=>0111111=>1
[5,6,7,3,2,8,1,4]=>0000000=>1111111=>1
[5,3,2,1,4,8,6,7]=>0000100=>1111011=>2
[3,4,7,8,1,2,6,5]=>0000000=>1111111=>1
[3,6,7,8,1,4,5,2]=>0000000=>1111111=>1
[2,3,6,8,5,1,4,7]=>0000000=>1111111=>1
[3,1,6,4,8,2,5,7]=>0000000=>1111111=>1
[7,3,2,6,8,5,1,4]=>0000000=>1111111=>1
[1,8,4,2,3,5,7,6]=>1000000=>0111111=>1
[6,4,2,8,3,5,1,7]=>0000000=>1111111=>1
[7,5,4,8,3,6,2,1]=>0000000=>1111111=>1
[8,4,6,3,7,2,5,1]=>0000000=>1111111=>1
[7,4,6,3,8,5,1,2]=>0000000=>1111111=>1
[2,5,6,8,3,4,1,7]=>0000000=>1111111=>1
[8,4,6,2,7,5,3,1]=>0000000=>1111111=>1
[8,5,6,7,2,4,3,1]=>0000000=>1111111=>1
[2,5,6,8,4,3,1,7]=>0000000=>1111111=>1
[2,5,7,8,4,1,3,6]=>0000000=>1111111=>1
[6,5,7,8,4,1,3,2]=>0000000=>1111111=>1
[7,5,6,8,2,4,1,3]=>0000000=>1111111=>1
[7,4,6,2,8,5,1,3]=>0000000=>1111111=>1
[4,3,2,6,8,5,1,7]=>0000000=>1111111=>1
[3,5,6,8,2,4,1,7]=>0000000=>1111111=>1
[3,5,6,8,4,2,1,7]=>0000000=>1111111=>1
[2,6,7,8,1,4,5,3]=>0000000=>1111111=>1
[3,6,7,8,1,4,2,5]=>0000000=>1111111=>1
[3,5,7,8,2,1,4,6]=>0000000=>1111111=>1
[2,6,7,8,1,4,3,5]=>0000000=>1111111=>1
[6,5,7,8,3,1,4,2]=>0000000=>1111111=>1
[2,5,7,8,3,1,4,6]=>0000000=>1111111=>1
[2,4,7,3,8,1,5,6]=>0000000=>1111111=>1
[6,4,7,3,8,1,5,2]=>0000000=>1111111=>1
[6,4,7,3,8,1,2,5]=>0000000=>1111111=>1
[7,4,6,3,8,2,1,5]=>0000000=>1111111=>1
[6,3,2,5,4,8,1,7]=>0000000=>1111111=>1
[6,4,5,2,3,8,1,7]=>0000000=>1111111=>1
[6,4,5,3,2,8,1,7]=>0000000=>1111111=>1
[5,4,6,3,8,2,1,7]=>0000000=>1111111=>1
[5,4,7,3,8,1,6,2]=>0000000=>1111111=>1
[2,5,7,8,3,1,6,4]=>0000000=>1111111=>1
[4,5,7,8,3,1,2,6]=>0000000=>1111111=>1
[4,5,6,8,2,3,1,7]=>0000000=>1111111=>1
[5,4,6,2,8,3,1,7]=>0000000=>1111111=>1
[5,3,2,6,8,4,1,7]=>0000000=>1111111=>1
[5,4,7,2,8,1,3,6]=>0000000=>1111111=>1
[4,5,7,8,2,1,3,6]=>0000000=>1111111=>1
[4,6,7,8,1,3,2,5]=>0000000=>1111111=>1
[4,6,7,8,1,3,5,2]=>0000000=>1111111=>1
[2,6,7,8,1,3,5,4]=>0000000=>1111111=>1
[2,6,7,8,1,5,3,4]=>0000000=>1111111=>1
[4,6,7,8,1,5,2,3]=>0000000=>1111111=>1
[4,6,7,8,1,2,5,3]=>0000000=>1111111=>1
[4,5,7,8,2,1,6,3]=>0000000=>1111111=>1
[5,4,7,2,8,1,6,3]=>0000000=>1111111=>1
[5,3,2,7,8,1,6,4]=>0000000=>1111111=>1
[4,3,2,7,8,1,6,5]=>0000000=>1111111=>1
[3,5,7,8,2,1,6,4]=>0000000=>1111111=>1
[3,6,7,8,1,2,5,4]=>0000000=>1111111=>1
[3,6,7,8,1,5,2,4]=>0000000=>1111111=>1
[3,6,7,8,1,5,4,2]=>0000000=>1111111=>1
[2,6,7,8,1,5,4,3]=>0000000=>1111111=>1
[2,3,4,5,6,7,8,9,10,1,11]=>0000000001=>1111111110=>1
[3,4,5,6,7,8,9,1,2,10]=>000000001=>111111110=>1
[1,4,5,6,7,8,2,9,3]=>10000000=>01111111=>1
[1,4,5,6,7,8,9,10,2,3]=>100000000=>011111111=>1
[1,3,4,5,6,7,8,9,10,11,2]=>1000000000=>0111111111=>1
[4,2,7,1,5,3,8,6]=>0000000=>1111111=>1
[4,2,8,6,1,5,3,7]=>0000000=>1111111=>1
[3,2,6,7,5,1,4,8]=>0000001=>1111110=>1
[2,7,1,3,5,4,8,6]=>0000000=>1111111=>1
[4,7,2,1,5,8,6,3]=>0000000=>1111111=>1
[7,2,1,3,5,8,6,4]=>0000000=>1111111=>1
[2,3,6,4,7,1,5,8]=>0000001=>1111110=>1
[1,3,4,8,2,7,5,6]=>1000000=>0111111=>1
[3,1,4,8,2,6,7,5]=>0000000=>1111111=>1
[8,3,1,6,2,5,7,4]=>0000000=>1111111=>1
[4,8,6,2,1,5,7,3]=>0000000=>1111111=>1
[4,8,3,6,5,1,7,2]=>0000000=>1111111=>1
[6,4,7,3,5,1,8,2]=>0000000=>1111111=>1
[6,4,7,5,1,8,2,3]=>0000000=>1111111=>1
[3,6,1,7,5,8,2,4]=>0000000=>1111111=>1
[7,3,5,1,6,8,2,4]=>0000000=>1111111=>1
[4,7,3,5,6,1,8,2]=>0000000=>1111111=>1
[3,4,6,8,5,1,7,2]=>0000000=>1111111=>1
[4,6,8,2,1,5,7,3]=>0000000=>1111111=>1
[6,8,2,1,3,5,7,4]=>0000000=>1111111=>1
[1,8,2,3,5,7,4,6]=>1000000=>0111111=>1
[2,7,3,6,1,4,5,8]=>0000001=>1111110=>1
[2,6,1,3,5,8,4,7]=>0000000=>1111111=>1
[7,3,2,5,6,1,4,8]=>0000001=>1111110=>1
[4,7,5,2,6,1,3,8]=>0000001=>1111110=>1
[4,6,2,8,1,5,3,7]=>0000000=>1111111=>1
[8,4,1,2,7,5,3,6]=>0000000=>1111111=>1
[4,5,6,2,7,1,3,8]=>0000001=>1111110=>1
[8,5,1,2,6,3,4,7]=>0000000=>1111111=>1
[1,6,2,7,4,8,3,5]=>1000000=>0111111=>1
[6,2,1,7,8,5,3,4]=>0000000=>1111111=>1
[6,7,3,8,4,1,5,2]=>0000000=>1111111=>1
[2,7,8,4,1,5,6,3]=>0000000=>1111111=>1
[2,7,1,8,5,6,3,4]=>0000000=>1111111=>1
[8,2,5,1,6,7,3,4]=>0000000=>1111111=>1
[8,2,4,5,1,6,7,3]=>0000000=>1111111=>1
[3,8,4,5,6,1,7,2]=>0000000=>1111111=>1
[4,5,8,3,6,7,1,2]=>0000000=>1111111=>1
[4,5,8,3,7,6,1,2]=>0000000=>1111111=>1
[4,2,8,3,7,1,6,5]=>0000000=>1111111=>1
[7,2,3,4,8,1,6,5]=>0000000=>1111111=>1
[7,2,3,4,8,1,5,6]=>0000000=>1111111=>1
[7,6,3,4,8,5,1,2]=>0000000=>1111111=>1
[7,6,3,5,8,4,1,2]=>0000000=>1111111=>1
[7,6,3,8,4,5,1,2]=>0000000=>1111111=>1
[7,2,3,8,5,1,4,6]=>0000000=>1111111=>1
[7,2,3,8,5,1,6,4]=>0000000=>1111111=>1
[2,6,4,8,1,5,7,3]=>0000000=>1111111=>1
[7,2,3,8,4,1,5,6]=>0000000=>1111111=>1
[7,2,3,5,8,1,4,6]=>0000000=>1111111=>1
[7,8,2,3,6,1,4,5]=>0000000=>1111111=>1
[7,8,2,3,6,1,5,4]=>0000000=>1111111=>1
[4,2,6,3,7,1,5,8]=>0000001=>1111110=>1
[7,2,3,5,8,1,6,4]=>0000000=>1111111=>1
[7,2,3,8,4,1,6,5]=>0000000=>1111111=>1
[2,6,4,8,1,3,7,5]=>0000000=>1111111=>1
[3,6,4,8,1,7,5,2]=>0000000=>1111111=>1
[7,6,5,1,2,3,8,4]=>0000000=>1111111=>1
[7,6,5,1,4,2,8,3]=>0000000=>1111111=>1
[2,6,4,5,1,8,7,3]=>0000000=>1111111=>1
[3,5,6,4,1,2,7,8]=>0000011=>1111100=>1
[7,8,5,4,1,2,6,3]=>0000000=>1111111=>1
[3,5,6,4,1,2,8,7]=>0000010=>1111101=>2
[7,6,5,1,4,2,3,8]=>0000001=>1111110=>1
[7,6,5,1,2,4,3,8]=>0000001=>1111110=>1
[7,6,5,1,2,4,8,3]=>0000000=>1111111=>1
[7,6,5,1,3,2,8,4]=>0000000=>1111111=>1
[7,6,5,1,3,2,4,8]=>0000001=>1111110=>1
[7,6,5,1,3,4,2,8]=>0000001=>1111110=>1
[7,2,3,4,5,1,8,6]=>0000000=>1111111=>1
[2,6,4,3,1,5,8,7]=>0000010=>1111101=>2
[2,6,4,3,1,8,5,7]=>0000000=>1111111=>1
[2,6,4,3,1,8,7,5]=>0000000=>1111111=>1
[3,5,8,4,1,2,7,6]=>0000000=>1111111=>1
[3,5,8,4,1,2,6,7]=>0000000=>1111111=>1
[3,5,8,4,1,6,2,7]=>0000000=>1111111=>1
[4,2,8,3,6,1,7,5]=>0000000=>1111111=>1
[3,5,8,4,1,6,7,2]=>0000000=>1111111=>1
[2,5,8,4,1,7,3,6]=>0000000=>1111111=>1
[3,6,4,2,1,7,8,5]=>0000000=>1111111=>1
[3,6,4,2,1,7,5,8]=>0000001=>1111110=>1
[3,5,6,4,1,8,7,2]=>0000000=>1111111=>1
[2,6,4,5,1,3,7,8]=>0000011=>1111100=>1
[7,6,5,1,4,3,8,2]=>0000000=>1111111=>1
[7,6,5,1,2,8,4,3]=>0000000=>1111111=>1
[7,6,5,1,2,8,3,4]=>0000000=>1111111=>1
[7,6,5,1,8,2,4,3]=>0000000=>1111111=>1
[7,6,5,1,8,2,3,4]=>0000000=>1111111=>1
[7,6,5,1,8,3,2,4]=>0000000=>1111111=>1
[7,6,5,1,4,8,2,3]=>0000000=>1111111=>1
[3,6,4,5,1,7,2,8]=>0000001=>1111110=>1
[2,5,6,4,1,7,8,3]=>0000000=>1111111=>1
[7,8,5,4,1,6,3,2]=>0000000=>1111111=>1
[2,5,6,4,1,7,3,8]=>0000001=>1111110=>1
[3,6,4,5,1,7,8,2]=>0000000=>1111111=>1
[7,6,5,1,4,8,3,2]=>0000000=>1111111=>1
[7,6,5,1,8,3,4,2]=>0000000=>1111111=>1
[7,6,5,1,8,4,2,3]=>0000000=>1111111=>1
[7,8,6,2,1,3,5,4]=>0000000=>1111111=>1
[6,1,3,4,2,8,7,5]=>0000000=>1111111=>1
[6,8,2,7,4,3,5,1]=>0000000=>1111111=>1
[6,2,3,8,4,7,5,1]=>0000000=>1111111=>1
[7,1,3,8,6,4,5,2]=>0000000=>1111111=>1
[7,4,2,1,8,6,5,3]=>0000000=>1111111=>1
[6,2,1,3,4,8,7,5]=>0000000=>1111111=>1
[8,1,3,2,5,6,7,4]=>0000000=>1111111=>1
[3,2,8,7,4,5,1,6]=>0000000=>1111111=>1
[2,1,4,8,7,5,3,6]=>0100000=>1011111=>2
[3,6,8,2,4,1,5,7]=>0000000=>1111111=>1
[6,2,8,1,7,5,4,3]=>0000000=>1111111=>1
[4,2,8,1,5,3,6,7]=>0000000=>1111111=>1
[7,4,8,6,2,1,3,5]=>0000000=>1111111=>1
[7,8,5,6,4,1,3,2]=>0000000=>1111111=>1
[3,8,1,4,5,6,2,7]=>0000000=>1111111=>1
[9,7,8,5,6,3,1,4,2]=>00000000=>11111111=>1
[9,7,8,5,3,6,1,4,2]=>00000000=>11111111=>1
[9,7,5,8,3,6,1,4,2]=>00000000=>11111111=>1
[7,9,5,8,3,6,1,4,2]=>00000000=>11111111=>1
[7,6,8,3,5,1,4,2]=>0000000=>1111111=>1
[8,9,5,7,3,6,1,4,2]=>00000000=>11111111=>1
[8,9,6,7,3,5,1,4,2]=>00000000=>11111111=>1
[8,9,6,7,4,5,1,3,2]=>00000000=>11111111=>1
[8,9,6,7,4,5,2,3,1]=>00000000=>11111111=>1
[9,10,7,8,5,6,3,1,4,2]=>000000000=>111111111=>1
[9,7,8,5,3,1,6,4,2]=>00000000=>11111111=>1
[9,10,7,8,5,3,6,1,4,2]=>000000000=>111111111=>1
[9,7,5,3,8,6,1,4,2]=>00000000=>11111111=>1
[9,10,7,5,8,3,6,1,4,2]=>000000000=>111111111=>1
[7,5,9,8,3,6,1,4,2]=>00000000=>11111111=>1
[9,7,10,5,8,3,6,1,4,2]=>000000000=>111111111=>1
[7,8,6,3,5,1,4,2]=>0000000=>1111111=>1
[5,3,8,7,6,1,4,2]=>0000000=>1111111=>1
[9,8,5,7,3,6,1,4,2]=>00000000=>11111111=>1
[10,7,9,5,8,3,6,1,4,2]=>000000000=>111111111=>1
[7,9,6,8,3,5,1,4,2]=>00000000=>11111111=>1
[10,8,9,5,7,3,6,1,4,2]=>000000000=>111111111=>1
[6,5,8,4,7,1,3,2]=>0000000=>1111111=>1
[8,9,5,7,4,6,1,3,2]=>00000000=>11111111=>1
[10,8,9,6,7,3,5,1,4,2]=>000000000=>111111111=>1
[8,9,6,7,3,5,2,4,1]=>00000000=>11111111=>1
[10,8,9,6,7,4,5,1,3,2]=>000000000=>111111111=>1
[6,7,4,2,5,3,1,8]=>0000001=>1111110=>1
[7,6,4,8,3,1,5,2]=>0000000=>1111111=>1
[7,4,8,5,6,1,3,2]=>0000000=>1111111=>1
[7,4,2,5,6,3,1,8]=>0000001=>1111110=>1
[4,2,7,5,6,3,1,8]=>0000001=>1111110=>1
[3,4,7,5,6,2,1,8]=>0000001=>1111110=>1
[4,7,3,5,6,2,1,8]=>0000001=>1111110=>1
[3,7,2,5,6,4,1,8]=>0000001=>1111110=>1
[7,8,3,5,6,1,4,2]=>0000000=>1111111=>1
[1,6,8,5,2,7,4,3]=>1000000=>0111111=>1
[6,2,8,5,1,7,4,3]=>0000000=>1111111=>1
[6,7,4,8,2,1,5,3]=>0000000=>1111111=>1
[3,2,7,8,6,1,5,4]=>0000000=>1111111=>1
[6,8,4,1,2,3,7,5]=>0000000=>1111111=>1
[4,1,8,5,6,3,2,7]=>0000000=>1111111=>1
[1,8,2,5,6,4,3,7]=>1000000=>0111111=>1
[6,1,8,5,3,7,4,2]=>0000000=>1111111=>1
[3,8,1,5,2,7,6,4]=>0000000=>1111111=>1
[8,2,1,5,3,7,6,4]=>0000000=>1111111=>1
[1,5,2,4,6,7,8,3]=>1000000=>0111111=>1
[4,1,5,3,6,7,8,2]=>0000000=>1111111=>1
[8,1,6,5,3,7,2,4]=>0000000=>1111111=>1
[7,1,4,6,3,2,8,5]=>0000000=>1111111=>1
[3,2,6,4,1,7,8,5]=>0000000=>1111111=>1
[7,6,4,3,1,2,8,5]=>0000000=>1111111=>1
[8,6,3,5,1,7,2,4]=>0000000=>1111111=>1
[4,5,3,1,6,7,8,2]=>0000000=>1111111=>1
[3,5,2,1,6,7,8,4]=>0000000=>1111111=>1
[5,2,3,1,6,7,8,4]=>0000000=>1111111=>1
[1,5,3,2,6,7,8,4]=>1000000=>0111111=>1
[8,4,6,5,1,7,2,3]=>0000000=>1111111=>1
[7,5,4,6,1,2,8,3]=>0000000=>1111111=>1
[3,2,5,6,1,7,8,4]=>0000000=>1111111=>1
[3,2,8,7,6,1,4,5]=>0000000=>1111111=>1
[6,8,4,7,2,1,3,5]=>0000000=>1111111=>1
[3,8,7,5,6,1,2,4]=>0000000=>1111111=>1
[8,2,7,5,6,1,3,4]=>0000000=>1111111=>1
[4,8,6,5,1,7,3,2]=>0000000=>1111111=>1
[1,7,4,6,2,3,8,5]=>1000000=>0111111=>1
[7,6,4,2,1,5,8,3]=>0000000=>1111111=>1
[5,7,4,6,1,3,8,2]=>0000000=>1111111=>1
[8,6,4,7,3,1,2,5]=>0000000=>1111111=>1
[5,2,4,3,7,1,8,6]=>0000000=>1111111=>1
[3,5,4,2,7,1,8,6]=>0000000=>1111111=>1
[8,6,4,1,3,5,2,7]=>0000000=>1111111=>1
[6,7,4,1,5,3,8,2]=>0000000=>1111111=>1
[7,5,4,1,2,6,8,3]=>0000000=>1111111=>1
[1,7,4,2,3,6,8,5]=>1000000=>0111111=>1
[1,8,2,5,3,7,6,4]=>1000000=>0111111=>1
[6,8,1,5,4,7,3,2]=>0000000=>1111111=>1
[8,2,1,5,6,4,3,7]=>0000000=>1111111=>1
[3,8,1,5,6,4,2,7]=>0000000=>1111111=>1
[6,8,4,1,2,5,3,7]=>0000000=>1111111=>1
[3,2,8,1,6,5,4,7]=>0000000=>1111111=>1
[3,2,6,1,5,7,8,4]=>0000000=>1111111=>1
[7,6,4,1,5,2,8,3]=>0000000=>1111111=>1
[8,6,1,5,4,7,2,3]=>0000000=>1111111=>1
[3,5,1,4,6,7,8,2]=>0000000=>1111111=>1
[5,2,1,4,6,7,8,3]=>0000000=>1111111=>1
[5,4,1,3,6,7,8,2]=>0000000=>1111111=>1
[8,4,1,5,3,7,2,6]=>0000000=>1111111=>1
[7,5,4,1,3,2,8,6]=>0000000=>1111111=>1
[3,2,5,1,4,7,8,6]=>0000100=>1111011=>2
[7,1,4,3,5,2,8,6]=>0000000=>1111111=>1
[8,1,3,5,4,7,2,6]=>0000000=>1111111=>1
[5,1,3,4,6,7,8,2]=>0000000=>1111111=>1
[3,1,8,2,5,7,4,6]=>0000000=>1111111=>1
[8,3,2,6,1,4,7,5]=>0000000=>1111111=>1
[2,8,1,6,4,3,7,5]=>0000000=>1111111=>1
[2,6,1,3,8,7,5,4]=>0000000=>1111111=>1
[2,5,7,1,3,8,6,4]=>0000000=>1111111=>1
[2,6,8,1,5,7,4,3]=>0000000=>1111111=>1
[2,7,1,5,8,4,6,3]=>0000000=>1111111=>1
[2,7,1,6,4,8,3,5]=>0000000=>1111111=>1
[2,7,1,6,5,3,8,4]=>0000000=>1111111=>1
[2,8,1,7,6,5,4,3]=>0000000=>1111111=>1
[8,3,2,7,1,6,5,4]=>0000000=>1111111=>1
[4,1,8,7,3,2,6,5]=>0000000=>1111111=>1
[4,1,7,2,8,6,5,3]=>0000000=>1111111=>1
[3,7,1,8,6,5,4,2]=>0000000=>1111111=>1
[3,7,6,1,4,2,5,8]=>0000001=>1111110=>1
[3,7,5,1,4,6,8,2]=>0000000=>1111111=>1
[3,6,8,5,1,4,7,2]=>0000000=>1111111=>1
[7,3,5,8,2,1,4,6]=>0000000=>1111111=>1
[7,3,6,2,1,4,5,8]=>0000001=>1111110=>1
[7,3,6,2,1,5,4,8]=>0000001=>1111110=>1
[7,4,2,8,1,6,5,3]=>0000000=>1111111=>1
[8,7,5,3,2,1,6,4]=>0000000=>1111111=>1
[7,5,2,6,3,1,4,8]=>0000001=>1111110=>1
[7,4,6,2,1,8,3,5]=>0000000=>1111111=>1
[6,8,4,5,2,1,7,3]=>0000000=>1111111=>1
[4,6,8,5,1,7,3,2]=>0000000=>1111111=>1
[4,7,5,1,3,8,6,2]=>0000000=>1111111=>1
[4,7,6,1,5,3,2,8]=>0000001=>1111110=>1
[5,1,7,6,3,8,2,4]=>0000000=>1111111=>1
[5,1,7,6,4,2,8,3]=>0000000=>1111111=>1
[5,1,8,7,6,4,3,2]=>0000000=>1111111=>1
[8,5,2,1,7,6,4,3]=>0000000=>1111111=>1
[8,5,2,1,6,3,7,4]=>0000000=>1111111=>1
[5,1,8,6,3,2,7,4]=>0000000=>1111111=>1
[3,6,1,7,4,8,2,5]=>0000000=>1111111=>1
[4,1,8,6,3,7,2,5]=>0000000=>1111111=>1
[8,4,2,5,7,3,1,6]=>0000000=>1111111=>1
[3,4,6,8,5,7,1,2]=>0000000=>1111111=>1
[5,4,8,2,7,3,6,1]=>0000000=>1111111=>1
[5,4,8,7,3,6,1,2]=>0000000=>1111111=>1
[8,5,4,7,3,6,2,1]=>0000000=>1111111=>1
[6,4,3,8,7,1,2,5]=>0000000=>1111111=>1
[6,3,7,2,4,8,1,5]=>0000000=>1111111=>1
[5,6,8,4,2,7,3,1]=>0000000=>1111111=>1
[5,7,4,2,8,1,3,6]=>0000000=>1111111=>1
[6,5,2,7,1,3,8,4]=>0000000=>1111111=>1
[8,6,5,4,2,1,7,3]=>0000000=>1111111=>1
[6,4,7,3,1,8,2,5]=>0000000=>1111111=>1
[5,7,4,3,8,6,1,2]=>0000000=>1111111=>1
[7,5,8,4,6,3,2,1]=>0000000=>1111111=>1
[7,6,4,8,3,5,2,1]=>0000000=>1111111=>1
[7,6,5,3,8,2,4,1]=>0000000=>1111111=>1
[6,5,4,3,2,1,9,8,7]=>00000100=>11111011=>2
[6,5,4,3,2,1,8,7,9]=>00000101=>11111010=>2
[5,4,3,2,1,9,8,7,6]=>00001000=>11110111=>2
[5,4,3,2,1,8,7,6,9]=>00001001=>11110110=>2
[5,4,3,2,1,7,6,9,8]=>00001010=>11110101=>3
[5,4,3,2,1,7,6,8,9]=>00001011=>11110100=>2
[4,3,2,1,8,7,6,5,9]=>00010001=>11101110=>2
[4,3,2,1,7,6,5,9,8]=>00010010=>11101101=>3
[4,3,2,1,7,6,5,8,9]=>00010011=>11101100=>2
[4,3,2,1,6,5,8,7,9]=>00010101=>11101010=>3
[4,3,2,1,6,5,7,8,9]=>00010111=>11101000=>2
[3,2,1,6,5,4,8,7,9]=>00100101=>11011010=>3
[3,2,1,6,5,4,7,8,9]=>00100111=>11011000=>2
[3,2,1,5,4,7,6,9,8]=>00101010=>11010101=>4
[3,2,1,5,4,7,6,8,9]=>00101011=>11010100=>3
[3,2,1,5,4,6,7,8,9]=>00101111=>11010000=>2
[2,1,4,3,6,5,7,8,9]=>01010111=>10101000=>3
[2,1,4,3,5,6,7,8,9]=>01011111=>10100000=>2
[7,6,5,4,3,2,1,10,9,8]=>000000100=>111111011=>2
[7,6,5,4,3,2,1,9,8,10]=>000000101=>111111010=>2
[6,5,4,3,2,1,9,8,7,10]=>000001001=>111110110=>2
[6,5,4,3,2,1,8,7,9,10]=>000001011=>111110100=>2
[5,4,3,2,1,9,8,7,6,10]=>000010001=>111101110=>2
[5,4,3,2,1,8,7,6,10,9]=>000010010=>111101101=>3
[5,4,3,2,1,8,7,6,9,10]=>000010011=>111101100=>2
[5,4,3,2,1,7,6,9,8,10]=>000010101=>111101010=>3
[5,4,3,2,1,7,6,8,9,10]=>000010111=>111101000=>2
[4,3,2,1,8,7,6,5,9,10]=>000100011=>111011100=>2
[4,3,2,1,7,6,5,10,9,8]=>000100100=>111011011=>3
[4,3,2,1,7,6,5,8,9,10]=>000100111=>111011000=>2
[4,3,2,1,6,5,8,7,9,10]=>000101011=>111010100=>3
[4,3,2,1,6,5,7,8,9,10]=>000101111=>111010000=>2
[3,2,1,6,5,4,9,8,7,10]=>001001001=>110110110=>3
[3,2,1,6,5,4,8,7,10,9]=>001001010=>110110101=>4
[3,2,1,6,5,4,8,7,9,10]=>001001011=>110110100=>3
[3,2,1,6,5,4,7,8,9,10]=>001001111=>110110000=>2
[3,2,1,5,4,7,6,9,8,10]=>001010101=>110101010=>4
[3,2,1,5,4,7,6,8,9,10]=>001010111=>110101000=>3
[3,2,1,5,4,6,7,8,9,10]=>001011111=>110100000=>2
[2,1,4,3,6,5,8,7,9,10]=>010101011=>101010100=>4
[2,1,4,3,6,5,7,8,9,10]=>010101111=>101010000=>3
[2,1,4,3,5,6,7,8,9,10]=>010111111=>101000000=>2
[5,6,3,7,4,2,1,8]=>0000001=>1111110=>1
[7,6,3,8,5,1,4,2]=>0000000=>1111111=>1
[6,4,8,1,3,2,5,7]=>0000000=>1111111=>1
[7,4,8,6,3,1,5,2]=>0000000=>1111111=>1
[4,2,7,6,5,3,1,8]=>0000001=>1111110=>1
[3,7,2,4,6,5,1,8]=>0000001=>1111110=>1
[8,1,3,4,5,2,6,7]=>0000000=>1111111=>1
[1,6,8,4,2,5,3,7]=>1000000=>0111111=>1
[6,2,8,4,1,5,7,3]=>0000000=>1111111=>1
[6,7,4,8,5,1,2,3]=>0000000=>1111111=>1
[3,2,7,8,5,1,6,4]=>0000000=>1111111=>1
[3,2,8,1,5,4,6,7]=>0000000=>1111111=>1
[6,1,4,8,5,3,7,2]=>0000000=>1111111=>1
[1,4,8,5,2,6,7,3]=>1000000=>0111111=>1
[6,1,8,4,3,7,2,5]=>0000000=>1111111=>1
[3,7,1,4,2,5,8,6]=>0000000=>1111111=>1
[7,2,1,4,3,5,6,8]=>0000001=>1111110=>1
[4,1,5,3,6,8,2,7]=>0000000=>1111111=>1
[6,1,8,5,3,2,7,4]=>0000000=>1111111=>1
[7,1,4,6,3,8,5,2]=>0000000=>1111111=>1
[3,2,6,4,1,8,7,5]=>0000000=>1111111=>1
[7,6,4,3,1,8,2,5]=>0000000=>1111111=>1
[3,5,2,1,8,7,6,4]=>0000000=>1111111=>1
[1,5,3,2,8,6,4,7]=>1000000=>0111111=>1
[5,4,2,1,7,8,6,3]=>0000000=>1111111=>1
[8,2,7,6,5,1,3,4]=>0000000=>1111111=>1
[8,6,2,7,1,4,5,3]=>0000000=>1111111=>1
[1,7,3,6,2,8,5,4]=>1000000=>0111111=>1
[7,6,3,2,1,8,5,4]=>0000000=>1111111=>1
[8,6,3,7,4,1,2,5]=>0000000=>1111111=>1
[5,2,3,4,7,1,8,6]=>0000000=>1111111=>1
[8,6,3,1,4,5,7,2]=>0000000=>1111111=>1
[6,7,3,1,5,4,2,8]=>0000001=>1111110=>1
[5,8,3,1,2,4,7,6]=>0000000=>1111111=>1
[8,1,3,2,4,5,6,7]=>0000000=>1111111=>1
[8,4,1,7,2,3,6,5]=>0000000=>1111111=>1
[8,2,1,6,5,4,7,3]=>0000000=>1111111=>1
[3,8,1,5,6,4,7,2]=>0000000=>1111111=>1
[6,8,4,1,2,5,7,3]=>0000000=>1111111=>1
[3,2,8,1,6,5,7,4]=>0000000=>1111111=>1
[7,6,4,1,5,2,3,8]=>0000001=>1111110=>1
[8,6,1,5,4,7,3,2]=>0000000=>1111111=>1
[3,5,1,4,6,7,2,8]=>0000001=>1111110=>1
[5,2,1,4,7,6,3,8]=>0000001=>1111110=>1
[4,5,8,2,1,3,7,6]=>0000000=>1111111=>1
[5,8,2,3,1,4,6,7]=>0000000=>1111111=>1
[4,2,1,3,5,8,7,6]=>0001100=>1110011=>2
[5,4,1,3,6,2,8,7]=>0000010=>1111101=>2
[8,5,4,1,3,6,2,7]=>0000000=>1111111=>1
[3,2,5,1,4,6,8,7]=>0000110=>1111001=>2
[8,1,4,3,5,6,7,2]=>0000000=>1111111=>1
[7,1,3,5,4,6,2,8]=>0000001=>1111110=>1
[5,1,3,4,6,2,7,8]=>0000011=>1111100=>1
[4,1,3,2,5,7,6,8]=>0001101=>1110010=>2
[3,1,4,2,6,5,8,7,9]=>00010101=>11101010=>3
[3,1,5,2,6,4,8,7,9]=>00000101=>11111010=>2
[3,1,5,2,4,7,6,9,8]=>00001010=>11110101=>3
[3,1,2,5,4,7,6,9,8]=>00101010=>11010101=>4
[3,1,4,2,6,5,8,7,10,9]=>000101010=>111010101=>4
[4,1,5,2,6,3,8,7,9]=>00000101=>11111010=>2
[3,1,5,2,6,4,8,7,10,9]=>000001010=>111110101=>3
[3,1,6,2,7,4,8,5,9]=>00000001=>11111110=>1
[3,1,5,2,7,4,8,6,10,9]=>000000010=>111111101=>2
[3,1,5,2,7,4,9,6,10,8]=>000000000=>111111111=>1
[1,3,5,2,4,7,6,9,8]=>10001010=>01110101=>3
[3,1,2,5,4,7,6,9,8,10]=>001010101=>110101010=>4
[4,6,7,3,1,5,2,8]=>0000001=>1111110=>1
[4,1,8,3,5,7,2,6]=>0000000=>1111111=>1
[4,5,7,2,3,6,8,1]=>0000000=>1111111=>1
[2,6,3,4,7,5,8,1]=>0000000=>1111111=>1
[4,5,2,7,1,6,8,3]=>0000000=>1111111=>1
[3,4,1,6,5,8,2,7]=>0000000=>1111111=>1
[6,4,2,8,7,1,5,3]=>0000000=>1111111=>1
[7,2,4,8,1,5,3,6]=>0000000=>1111111=>1
[4,6,3,1,7,8,5,2]=>0000000=>1111111=>1
[5,3,1,6,7,8,4,2]=>0000000=>1111111=>1
[2,1,3,4,8,7,5,6]=>0111000=>1000111=>2
[4,5,6,7,8,9,1,2,3]=>00000000=>11111111=>1
[4,5,6,7,8,9,2,3,1]=>00000000=>11111111=>1
[5,6,7,8,9,1,2,3,4]=>00000000=>11111111=>1
[6,7,8,9,2,3,4,5,1]=>00000000=>11111111=>1
[8,9,6,7,5,4,3,2,1]=>00000000=>11111111=>1
[4,5,6,7,8,9,10,1,2,3]=>000000000=>111111111=>1
[4,5,6,7,8,9,10,2,3,1]=>000000000=>111111111=>1
[5,6,7,8,9,10,1,2,3,4]=>000000000=>111111111=>1
[5,6,7,8,9,10,3,4,1,2]=>000000000=>111111111=>1
[7,8,9,10,3,4,5,6,1,2]=>000000000=>111111111=>1
[7,8,9,10,5,6,3,4,1,2]=>000000000=>111111111=>1
[8,9,10,5,6,7,2,3,4,1]=>000000000=>111111111=>1
[4,8,3,7,6,5,1,2]=>0000000=>1111111=>1
[6,3,8,7,5,4,1,2]=>0000000=>1111111=>1
[5,3,8,7,6,4,1,2]=>0000000=>1111111=>1
[2,8,7,6,1,5,4,3]=>0000000=>1111111=>1
[5,2,8,7,6,1,4,3]=>0000000=>1111111=>1
[6,2,8,7,5,1,4,3]=>0000000=>1111111=>1
[7,8,2,6,5,1,4,3]=>0000000=>1111111=>1
[6,1,8,7,5,4,3,2]=>0000000=>1111111=>1
[3,1,8,7,6,5,4,2]=>0000000=>1111111=>1
[7,8,2,6,1,5,4,3]=>0000000=>1111111=>1
[6,2,8,7,1,5,4,3]=>0000000=>1111111=>1
[4,2,8,1,7,6,5,3]=>0000000=>1111111=>1
[4,8,2,7,6,1,5,3]=>0000000=>1111111=>1
[3,8,7,2,1,6,5,4]=>0000000=>1111111=>1
[6,5,8,7,1,4,3,2]=>0000000=>1111111=>1
[4,8,1,7,6,5,3,2]=>0000000=>1111111=>1
[5,4,1,8,7,6,3,2]=>0000000=>1111111=>1
[6,4,8,1,7,5,3,2]=>0000000=>1111111=>1
[7,8,4,1,6,5,3,2]=>0000000=>1111111=>1
[7,8,3,1,6,5,4,2]=>0000000=>1111111=>1
[6,3,8,1,7,5,4,2]=>0000000=>1111111=>1
[5,3,1,8,7,6,4,2]=>0000000=>1111111=>1
[7,8,2,1,6,5,4,3]=>0000000=>1111111=>1
[6,5,3,1,8,7,4,2]=>0000000=>1111111=>1
[6,4,3,1,8,7,5,2]=>0000000=>1111111=>1
[5,4,3,1,8,7,6,2]=>0000000=>1111111=>1
[7,5,2,1,8,6,4,3]=>0000000=>1111111=>1
[5,4,2,1,8,7,6,3]=>0000000=>1111111=>1
[7,3,2,1,8,6,5,4]=>0000000=>1111111=>1
[6,3,2,1,8,7,5,4]=>0000000=>1111111=>1
[9,7,5,3,1,10,8,6,4,2]=>000000000=>111111111=>1
[8,7,5,3,1,10,9,6,4,2]=>000000000=>111111111=>1
[9,6,5,3,1,10,8,7,4,2]=>000000000=>111111111=>1
[8,6,5,3,1,10,9,7,4,2]=>000000000=>111111111=>1
[7,6,5,3,1,10,9,8,4,2]=>000000000=>111111111=>1
[9,7,4,3,1,10,8,6,5,2]=>000000000=>111111111=>1
[8,7,4,3,1,10,9,6,5,2]=>000000000=>111111111=>1
[9,6,4,3,1,10,8,7,5,2]=>000000000=>111111111=>1
[8,6,4,3,1,10,9,7,5,2]=>000000000=>111111111=>1
[7,6,4,3,1,10,9,8,5,2]=>000000000=>111111111=>1
[9,5,4,3,1,10,8,7,6,2]=>000000000=>111111111=>1
[8,5,4,3,1,10,9,7,6,2]=>000000000=>111111111=>1
[7,5,4,3,1,10,9,8,6,2]=>000000000=>111111111=>1
[6,5,4,3,1,10,9,8,7,2]=>000000000=>111111111=>1
[9,7,5,2,1,10,8,6,4,3]=>000000000=>111111111=>1
[8,7,5,2,1,10,9,6,4,3]=>000000000=>111111111=>1
[9,6,5,2,1,10,8,7,4,3]=>000000000=>111111111=>1
[8,6,5,2,1,10,9,7,4,3]=>000000000=>111111111=>1
[7,6,5,2,1,10,9,8,4,3]=>000000000=>111111111=>1
[9,7,4,2,1,10,8,6,5,3]=>000000000=>111111111=>1
[8,7,4,2,1,10,9,6,5,3]=>000000000=>111111111=>1
[9,6,4,2,1,10,8,7,5,3]=>000000000=>111111111=>1
[8,6,4,2,1,10,9,7,5,3]=>000000000=>111111111=>1
[7,6,4,2,1,10,9,8,5,3]=>000000000=>111111111=>1
[9,5,4,2,1,10,8,7,6,3]=>000000000=>111111111=>1
[8,5,4,2,1,10,9,7,6,3]=>000000000=>111111111=>1
[7,5,4,2,1,10,9,8,6,3]=>000000000=>111111111=>1
[6,5,4,2,1,10,9,8,7,3]=>000000000=>111111111=>1
[9,7,3,2,1,10,8,6,5,4]=>000000000=>111111111=>1
[8,7,3,2,1,10,9,6,5,4]=>000000000=>111111111=>1
[9,6,3,2,1,10,8,7,5,4]=>000000000=>111111111=>1
[8,6,3,2,1,10,9,7,5,4]=>000000000=>111111111=>1
[7,6,3,2,1,10,9,8,5,4]=>000000000=>111111111=>1
[9,5,3,2,1,10,8,7,6,4]=>000000000=>111111111=>1
[8,5,3,2,1,10,9,7,6,4]=>000000000=>111111111=>1
[7,5,3,2,1,10,9,8,6,4]=>000000000=>111111111=>1
[6,5,3,2,1,10,9,8,7,4]=>000000000=>111111111=>1
[9,4,3,2,1,10,8,7,6,5]=>000000000=>111111111=>1
[8,4,3,2,1,10,9,7,6,5]=>000000000=>111111111=>1
[7,4,3,2,1,10,9,8,6,5]=>000000000=>111111111=>1
[6,4,3,2,1,10,9,8,7,5]=>000000000=>111111111=>1
[6,1,4,2,3,5,8,7]=>0000010=>1111101=>2
[8,6,1,4,2,3,5,7]=>0000000=>1111111=>1
[6,8,1,4,2,3,5,7]=>0000000=>1111111=>1
[8,1,4,2,3,6,5,7]=>0000000=>1111111=>1
[6,2,3,8,1,4,5,7]=>0000000=>1111111=>1
[4,6,2,3,8,1,5,7]=>0000000=>1111111=>1
[8,4,3,6,2,1,5,7]=>0000000=>1111111=>1
[6,4,2,3,8,1,5,7]=>0000000=>1111111=>1
[2,8,4,3,6,1,5,7]=>0000000=>1111111=>1
[2,8,3,6,1,4,5,7]=>0000000=>1111111=>1
[8,3,6,4,2,1,5,7]=>0000000=>1111111=>1
[8,3,6,2,4,1,5,7]=>0000000=>1111111=>1
[8,3,6,2,1,4,5,7]=>0000000=>1111111=>1
[3,6,4,7,8,5,1,2]=>0000000=>1111111=>1
[1,6,4,2,7,5,8,3]=>1000000=>0111111=>1
[3,6,4,2,7,1,5,8]=>0000001=>1111110=>1
[1,4,7,2,5,6,8,3]=>1000000=>0111111=>1
[6,4,8,5,3,7,1,2]=>0000000=>1111111=>1
[1,6,5,4,2,7,8,3]=>1000000=>0111111=>1
[4,2,5,3,6,1,7,8]=>0000011=>1111100=>1
[7,1,5,3,6,2,8,4]=>0000000=>1111111=>1
[1,6,5,2,4,8,7,3]=>1000000=>0111111=>1
[1,4,6,2,8,5,7,3]=>1000000=>0111111=>1
[7,8,1,4,2,5,6,3]=>0000000=>1111111=>1
[3,4,8,5,2,1,6,7]=>0000000=>1111111=>1
[4,8,5,3,1,6,2,7]=>0000000=>1111111=>1
[6,1,3,5,8,2,7,4]=>0000000=>1111111=>1
[6,1,8,7,4,2,3,5]=>0000000=>1111111=>1
[1,2,8,5,7,3,6,4]=>1100000=>0011111=>1
[1,3,6,8,7,5,2,4]=>1000000=>0111111=>1
[1,8,2,5,4,7,6,3]=>1000000=>0111111=>1
[7,1,2,4,5,8,6,3]=>0000000=>1111111=>1
[1,2,7,3,5,8,6,4]=>1100000=>0011111=>1
[6,1,3,2,5,7,8,4]=>0000000=>1111111=>1
[4,6,2,1,7,5,3,8]=>0000001=>1111110=>1
[1,6,3,7,8,5,2,4]=>1000000=>0111111=>1
[4,6,2,3,7,8,1,5]=>0000000=>1111111=>1
[4,6,3,7,1,2,8,5]=>0000000=>1111111=>1
[4,2,1,3,5,7,8,6]=>0001100=>1110011=>2
[7,3,2,4,5,1,8,6]=>0000000=>1111111=>1
[3,8,2,5,4,1,7,6]=>0000000=>1111111=>1
[7,8,4,2,6,3,1,5]=>0000000=>1111111=>1
[4,2,6,3,8,7,1,5]=>0000000=>1111111=>1
[5,8,2,7,4,3,1,6]=>0000000=>1111111=>1
[4,3,8,5,1,7,2,6]=>0000000=>1111111=>1
[4,3,6,8,1,2,7,5]=>0000000=>1111111=>1
[6,4,3,5,2,8,1,7]=>0000000=>1111111=>1
[6,5,3,8,4,2,1,7]=>0000000=>1111111=>1
[6,1,7,2,8,3,9,4,10,5]=>000000000=>111111111=>1
[1,8,6,7,5,3,4,2]=>1000000=>0111111=>1
[1,5,8,7,2,6,4,3]=>1000000=>0111111=>1
[4,1,3,6,5,8,7,2]=>0000000=>1111111=>1
[2,1,6,3,5,8,7,4]=>0100000=>1011111=>2
[2,4,1,3,8,5,7,6]=>0001000=>1110111=>2
[2,4,1,3,5,8,7,6]=>0001100=>1110011=>2
[2,6,1,3,5,8,7,4]=>0000000=>1111111=>1
[4,6,1,3,5,8,7,2]=>0000000=>1111111=>1
[6,1,4,3,5,8,7,2]=>0000000=>1111111=>1
[6,4,1,3,5,8,7,2]=>0000000=>1111111=>1
[6,2,1,3,5,8,7,4]=>0000000=>1111111=>1
[4,2,1,3,6,5,7,8]=>0001011=>1110100=>2
[4,2,1,6,3,5,7,8]=>0000011=>1111100=>1
[6,2,1,8,3,5,7,4]=>0000000=>1111111=>1
[6,2,1,3,8,5,7,4]=>0000000=>1111111=>1
[6,1,4,3,8,5,7,2]=>0000000=>1111111=>1
[1,6,4,3,8,5,7,2]=>1000000=>0111111=>1
[8,1,4,3,6,5,7,2]=>0000000=>1111111=>1
[8,4,1,3,6,5,7,2]=>0000000=>1111111=>1
[8,2,1,3,6,5,7,4]=>0000000=>1111111=>1
[8,2,1,6,3,5,7,4]=>0000000=>1111111=>1
[8,2,1,4,3,5,7,6]=>0000000=>1111111=>1
[6,2,1,4,3,5,7,8]=>0000011=>1111100=>1
[8,2,4,1,3,5,7,6]=>0000000=>1111111=>1
[8,2,6,1,3,5,7,4]=>0000000=>1111111=>1
[8,4,6,1,3,5,7,2]=>0000000=>1111111=>1
[8,4,1,6,3,5,7,2]=>0000000=>1111111=>1
[8,1,4,6,3,5,7,2]=>0000000=>1111111=>1
[1,8,4,6,3,5,7,2]=>1000000=>0111111=>1
[1,6,4,8,3,5,7,2]=>1000000=>0111111=>1
[6,4,1,8,3,5,7,2]=>0000000=>1111111=>1
[6,4,8,1,3,5,7,2]=>0000000=>1111111=>1
[6,2,8,1,3,5,7,4]=>0000000=>1111111=>1
[4,2,8,1,3,5,7,6]=>0000000=>1111111=>1
[2,6,8,1,3,5,7,4]=>0000000=>1111111=>1
[4,6,8,1,3,5,7,2]=>0000000=>1111111=>1
[4,6,1,8,3,5,7,2]=>0000000=>1111111=>1
[4,1,6,8,3,5,7,2]=>0000000=>1111111=>1
[1,4,6,3,8,5,7,2]=>1000000=>0111111=>1
[4,6,1,3,8,5,7,2]=>0000000=>1111111=>1
[2,4,1,8,3,5,7,6]=>0000000=>1111111=>1
[2,1,6,8,3,5,7,4]=>0100000=>1011111=>2
[4,1,3,6,8,5,7,2]=>0000000=>1111111=>1
[1,4,3,6,8,5,7,2]=>1000000=>0111111=>1
[4,1,3,8,6,5,7,2]=>0000000=>1111111=>1
[2,1,8,3,6,5,7,4]=>0100000=>1011111=>2
[2,1,6,4,3,5,7,8]=>0100011=>1011100=>2
[2,6,1,4,3,5,7,8]=>0000011=>1111100=>1
[2,8,1,4,3,5,7,6]=>0000000=>1111111=>1
[2,8,1,6,3,5,7,4]=>0000000=>1111111=>1
[4,8,1,3,6,5,7,2]=>0000000=>1111111=>1
[1,4,8,3,6,5,7,2]=>1000000=>0111111=>1
[1,4,8,6,3,5,7,2]=>1000000=>0111111=>1
[4,1,8,6,3,5,7,2]=>0000000=>1111111=>1
[4,8,1,6,3,5,7,2]=>0000000=>1111111=>1
[4,8,6,1,3,5,7,2]=>0000000=>1111111=>1
[2,8,6,1,3,5,7,4]=>0000000=>1111111=>1
[2,8,4,1,3,5,7,6]=>0000000=>1111111=>1
[2,6,4,1,3,5,7,8]=>0000011=>1111100=>1
[4,6,2,1,3,5,7,8]=>0000011=>1111100=>1
[6,8,1,4,3,5,7,2]=>0000000=>1111111=>1
[6,1,8,4,3,5,7,2]=>0000000=>1111111=>1
[1,6,8,4,3,5,7,2]=>1000000=>0111111=>1
[1,8,6,4,3,5,7,2]=>1000000=>0111111=>1
[8,1,6,4,3,5,7,2]=>0000000=>1111111=>1
[8,6,1,4,3,5,7,2]=>0000000=>1111111=>1
[8,6,4,1,3,5,7,2]=>0000000=>1111111=>1
[8,6,2,1,3,5,7,4]=>0000000=>1111111=>1
[8,4,2,1,3,5,7,6]=>0000000=>1111111=>1
[7,8,6,5,2,1,4,3]=>0000000=>1111111=>1
[5,7,4,1,8,6,3,2]=>0000000=>1111111=>1
[3,6,7,4,5,8,2,1]=>0000000=>1111111=>1
[5,4,6,1,7,8,3,2]=>0000000=>1111111=>1
[6,8,1,4,5,3,7,2]=>0000000=>1111111=>1
[6,7,1,4,5,3,2,8]=>0000001=>1111110=>1
[3,7,1,5,4,6,8,2]=>0000000=>1111111=>1
[6,7,1,4,5,3,8,2]=>0000000=>1111111=>1
[5,6,4,2,7,3,8,1]=>0000000=>1111111=>1
[5,4,7,2,8,3,1,6]=>0000000=>1111111=>1
[5,4,7,2,8,3,6,1]=>0000000=>1111111=>1
[3,8,1,5,4,6,2,7]=>0000000=>1111111=>1
[3,6,1,5,4,2,7,8]=>0000011=>1111100=>1
[3,6,1,5,4,8,2,7]=>0000000=>1111111=>1
[6,7,3,1,4,2,8,5]=>0000000=>1111111=>1
[3,4,1,2,6,8,7,5]=>0001000=>1110111=>2
[6,4,7,2,8,5,1,3]=>0000000=>1111111=>1
[3,8,1,5,4,7,2,6]=>0000000=>1111111=>1
[7,8,3,1,4,6,2,5]=>0000000=>1111111=>1
[6,5,8,7,3,4,2,1]=>0000000=>1111111=>1
[3,7,1,5,4,2,6,8]=>0000001=>1111110=>1
[3,8,1,5,4,2,7,6]=>0000000=>1111111=>1
[6,8,4,2,7,5,3,1]=>0000000=>1111111=>1
[6,8,3,1,4,7,5,2]=>0000000=>1111111=>1
[3,7,1,5,4,8,6,2]=>0000000=>1111111=>1
[3,4,1,2,8,5,7,6]=>0001000=>1110111=>2
[6,7,3,1,4,5,8,2]=>0000000=>1111111=>1
[9,8,7,6,5,4,2,1,3]=>00000000=>11111111=>1
[9,8,7,6,5,3,2,1,4]=>00000000=>11111111=>1
[8,7,6,3,5,2,1,4]=>0000000=>1111111=>1
[9,8,7,6,4,3,2,1,5]=>00000000=>11111111=>1
[8,7,4,6,3,2,1,5]=>0000000=>1111111=>1
[9,8,7,5,4,3,2,1,6]=>00000000=>11111111=>1
[8,5,7,4,3,2,1,6]=>0000000=>1111111=>1
[9,8,6,5,4,3,2,1,7]=>00000000=>11111111=>1
[9,7,6,5,4,3,2,1,8]=>00000000=>11111111=>1
[9,8,7,6,5,4,1,3,2]=>00000000=>11111111=>1
[10,9,8,7,6,5,4,2,1,3]=>000000000=>111111111=>1
[9,8,7,6,5,2,4,1,3]=>00000000=>11111111=>1
[10,9,8,7,6,5,3,2,1,4]=>000000000=>111111111=>1
[9,8,7,6,3,5,2,1,4]=>00000000=>11111111=>1
[10,9,8,7,6,4,3,2,1,5]=>000000000=>111111111=>1
[8,7,6,2,5,4,1,3]=>0000000=>1111111=>1
[9,8,7,4,6,3,2,1,5]=>00000000=>11111111=>1
[10,9,8,7,5,4,3,2,1,6]=>000000000=>111111111=>1
[8,5,4,7,3,2,1,6]=>0000000=>1111111=>1
[8,7,3,6,5,2,1,4]=>0000000=>1111111=>1
[9,8,5,7,4,3,2,1,6]=>00000000=>11111111=>1
[10,9,8,6,5,4,3,2,1,7]=>000000000=>111111111=>1
[6,5,8,4,3,2,1,7]=>0000000=>1111111=>1
[8,4,7,6,3,2,1,5]=>0000000=>1111111=>1
[9,6,8,5,4,3,2,1,7]=>00000000=>11111111=>1
[10,9,7,6,5,4,3,2,1,8]=>000000000=>111111111=>1
[5,8,7,4,3,2,1,6]=>0000000=>1111111=>1
[10,8,7,6,5,4,3,2,1,9]=>000000000=>111111111=>1
[4,5,2,7,3,1,8,6]=>0000000=>1111111=>1
[4,8,2,6,3,5,7,1]=>0000000=>1111111=>1
[4,1,7,2,5,8,6,3]=>0000000=>1111111=>1
[7,8,2,1,5,6,4,3]=>0000000=>1111111=>1
[1,6,2,5,8,4,3,7]=>1000000=>0111111=>1
[7,3,1,6,8,5,2,4]=>0000000=>1111111=>1
[5,2,7,1,8,6,3,4]=>0000000=>1111111=>1
[6,5,2,8,1,7,3,4]=>0000000=>1111111=>1
[2,8,3,5,1,7,4,6]=>0000000=>1111111=>1
[5,4,3,8,7,1,6,2]=>0000000=>1111111=>1
[8,5,4,3,7,2,6,1]=>0000000=>1111111=>1
[8,3,7,4,2,6,5,1]=>0000000=>1111111=>1
[2,8,6,5,1,7,4,3]=>0000000=>1111111=>1
[6,3,2,8,4,1,7,5]=>0000000=>1111111=>1
[2,8,3,4,1,7,5,6]=>0000000=>1111111=>1
[5,4,2,8,3,1,7,6]=>0000000=>1111111=>1
[2,8,4,3,1,7,6,5]=>0000000=>1111111=>1
[2,8,5,3,1,7,6,4]=>0000000=>1111111=>1
[2,8,6,4,1,7,5,3]=>0000000=>1111111=>1
[3,8,7,5,1,6,4,2]=>0000000=>1111111=>1
[8,3,7,5,2,6,4,1]=>0000000=>1111111=>1
[8,4,7,6,2,5,3,1]=>0000000=>1111111=>1
[4,8,7,6,1,5,3,2]=>0000000=>1111111=>1
[7,4,8,6,2,1,5,3]=>0000000=>1111111=>1
[7,3,8,5,2,1,6,4]=>0000000=>1111111=>1
[7,3,8,4,2,1,6,5]=>0000000=>1111111=>1
[7,5,4,3,8,2,1,6]=>0000000=>1111111=>1
[3,7,8,4,1,2,6,5]=>0000000=>1111111=>1
[3,7,8,5,1,2,6,4]=>0000000=>1111111=>1
[4,7,8,6,1,2,5,3]=>0000000=>1111111=>1
[8,7,4,6,3,5,2,1]=>0000000=>1111111=>1
[5,7,8,6,1,2,4,3]=>0000000=>1111111=>1
[6,4,7,8,3,1,2,5]=>0000000=>1111111=>1
[7,3,4,8,2,1,5,6]=>0000000=>1111111=>1
[7,6,4,8,3,2,1,5]=>0000000=>1111111=>1
[7,5,8,6,2,1,4,3]=>0000000=>1111111=>1
[6,5,8,7,3,1,4,2]=>0000000=>1111111=>1
[2,4,8,3,1,5,7,6]=>0000000=>1111111=>1
[6,3,2,4,8,1,5,7]=>0000000=>1111111=>1
[2,3,8,4,1,6,7,5]=>0000000=>1111111=>1
[2,3,8,5,1,6,7,4]=>0000000=>1111111=>1
[6,4,8,7,3,1,5,2]=>0000000=>1111111=>1
[8,6,4,7,3,2,5,1]=>0000000=>1111111=>1
[8,3,4,7,2,5,6,1]=>0000000=>1111111=>1
[3,4,8,7,1,5,6,2]=>0000000=>1111111=>1
[2,4,8,6,1,5,7,3]=>0000000=>1111111=>1
[2,5,8,6,1,4,7,3]=>0000000=>1111111=>1
[8,3,5,7,2,4,6,1]=>0000000=>1111111=>1
[8,4,6,7,2,3,5,1]=>0000000=>1111111=>1
[4,6,8,7,1,3,5,2]=>0000000=>1111111=>1
[2,6,8,5,1,3,7,4]=>0000000=>1111111=>1
[2,6,8,4,1,3,7,5]=>0000000=>1111111=>1
[2,5,8,3,1,4,7,6]=>0000000=>1111111=>1
[5,6,8,7,1,3,4,2]=>0000000=>1111111=>1
[7,4,6,8,2,1,3,5]=>0000000=>1111111=>1
[5,4,8,6,2,1,3,7]=>0000000=>1111111=>1
[2,5,6,1,4,7,8,3]=>0000000=>1111111=>1
[1,8,7,6,3,2,5,4]=>1000000=>0111111=>1
[1,8,7,6,3,2,4,5]=>1000000=>0111111=>1
[1,8,4,5,2,7,3,6]=>1000000=>0111111=>1
[1,8,4,5,2,7,6,3]=>1000000=>0111111=>1
[6,3,5,4,7,1,8,2]=>0000000=>1111111=>1
[1,8,4,3,6,2,5,7]=>1000000=>0111111=>1
[2,7,6,4,8,5,3,1]=>0000000=>1111111=>1
[1,8,4,5,2,6,3,7]=>1000000=>0111111=>1
[7,3,5,8,4,6,2,1]=>0000000=>1111111=>1
[2,3,4,6,5,8,1,7]=>0000000=>1111111=>1
[2,3,4,7,5,1,8,6]=>0000000=>1111111=>1
[7,4,8,5,3,2,1,6]=>0000000=>1111111=>1
[8,1,6,2,4,3,5,7]=>0000000=>1111111=>1
[1,7,6,2,4,3,5,8]=>1000001=>0111110=>1
[8,7,3,2,4,6,5,1]=>0000000=>1111111=>1
[1,7,2,5,4,3,6,8]=>1000001=>0111110=>1
[8,7,1,3,4,5,2,6]=>0000000=>1111111=>1
[8,1,2,5,4,3,6,7]=>0000000=>1111111=>1
[8,6,1,2,4,3,5,7]=>0000000=>1111111=>1
[5,1,8,6,2,3,4,7]=>0000000=>1111111=>1
[3,7,6,1,8,2,5,4]=>0000000=>1111111=>1
[7,6,3,1,8,2,4,5]=>0000000=>1111111=>1
[8,2,1,3,5,7,4,6]=>0000000=>1111111=>1
[7,5,4,1,3,8,2,6]=>0000000=>1111111=>1
[7,3,8,5,4,1,2,6]=>0000000=>1111111=>1
[1,7,2,3,5,8,4,6]=>1000000=>0111111=>1
[3,5,2,6,7,1,8,4]=>0000000=>1111111=>1
[3,2,8,4,7,5,1,6]=>0000000=>1111111=>1
[3,8,1,6,5,2,7,4]=>0000000=>1111111=>1
[6,8,3,1,7,2,4,5]=>0000000=>1111111=>1
[2,7,5,3,8,4,1,6]=>0000000=>1111111=>1
[8,3,2,1,5,7,4,6]=>0000000=>1111111=>1
[8,3,6,4,7,1,2,5]=>0000000=>1111111=>1
[1,2,8,3,5,7,4,6]=>1100000=>0011111=>1
[6,5,1,7,4,2,8,3]=>0000000=>1111111=>1
[7,3,6,4,8,2,1,5]=>0000000=>1111111=>1
[4,6,1,7,3,5,2,8]=>0000001=>1111110=>1
[5,6,1,7,3,4,2,8]=>0000001=>1111110=>1
[6,1,7,3,4,2,8,5]=>0000000=>1111111=>1
[7,3,8,1,6,5,2,4]=>0000000=>1111111=>1
[8,3,7,1,6,5,2,4]=>0000000=>1111111=>1
[5,1,7,4,2,8,6,3]=>0000000=>1111111=>1
[2,8,1,7,6,5,3,4]=>0000000=>1111111=>1
[4,2,8,6,5,1,7,3]=>0000000=>1111111=>1
[6,4,2,8,5,1,7,3]=>0000000=>1111111=>1
[8,6,4,7,1,5,2,3]=>0000000=>1111111=>1
[7,6,4,8,1,5,2,3]=>0000000=>1111111=>1
[5,1,6,4,2,3,8,7]=>0000010=>1111101=>2
[4,2,3,8,7,5,1,6]=>0000000=>1111111=>1
[3,8,7,1,6,5,2,4]=>0000000=>1111111=>1
[2,4,3,8,1,6,7,5]=>0000000=>1111111=>1
[2,4,3,7,1,6,8,5]=>0000000=>1111111=>1
[4,2,3,7,8,5,1,6]=>0000000=>1111111=>1
[5,1,6,4,2,3,7,8]=>0000011=>1111100=>1
[6,4,7,8,1,5,2,3]=>0000000=>1111111=>1
[8,7,4,6,1,5,2,3]=>0000000=>1111111=>1
[6,5,7,8,1,4,2,3]=>0000000=>1111111=>1
[4,7,8,6,1,5,2,3]=>0000000=>1111111=>1
[3,2,4,7,8,1,5,6]=>0000000=>1111111=>1
[3,2,4,8,7,1,5,6]=>0000000=>1111111=>1
[4,8,7,6,1,5,2,3]=>0000000=>1111111=>1
[5,8,7,6,1,4,2,3]=>0000000=>1111111=>1
[8,6,5,7,1,4,2,3]=>0000000=>1111111=>1
[5,1,6,7,4,2,3,8]=>0000001=>1111110=>1
[6,7,4,8,1,5,2,3]=>0000000=>1111111=>1
[8,4,7,6,1,5,2,3]=>0000000=>1111111=>1
[8,3,2,4,7,1,5,6]=>0000000=>1111111=>1
[7,3,2,4,8,1,5,6]=>0000000=>1111111=>1
[2,5,3,7,1,6,4,8]=>0000001=>1111110=>1
[8,4,6,7,1,5,2,3]=>0000000=>1111111=>1
[7,4,6,8,1,5,2,3]=>0000000=>1111111=>1
[5,1,6,8,4,2,3,7]=>0000000=>1111111=>1
[4,2,3,7,5,1,6,8]=>0000001=>1111110=>1
[3,7,5,8,1,6,2,4]=>0000000=>1111111=>1
[2,4,3,7,1,6,5,8]=>0000001=>1111110=>1
[2,4,7,1,5,8,6,3]=>0000000=>1111111=>1
[3,2,4,7,6,1,5,8]=>0000001=>1111110=>1
[4,7,6,8,1,5,2,3]=>0000000=>1111111=>1
[8,5,6,7,1,4,2,3]=>0000000=>1111111=>1
[8,6,7,5,1,4,2,3]=>0000000=>1111111=>1
[7,6,8,5,1,4,2,3]=>0000000=>1111111=>1
[6,8,7,5,1,4,2,3]=>0000000=>1111111=>1
[5,6,8,7,1,4,2,3]=>0000000=>1111111=>1
[4,6,8,7,1,5,2,3]=>0000000=>1111111=>1
[2,4,6,7,1,5,8,3]=>0000000=>1111111=>1
[3,2,4,6,1,5,7,8]=>0000011=>1111100=>1
[6,7,8,5,1,4,2,3]=>0000000=>1111111=>1
[7,8,6,5,1,4,2,3]=>0000000=>1111111=>1
[3,1,7,5,4,2,8,6]=>0000000=>1111111=>1
[2,1,8,5,4,6,3,7]=>0100000=>1011111=>2
[4,1,8,5,2,3,6,7]=>0000000=>1111111=>1
[5,4,1,3,6,7,2,8]=>0000001=>1111110=>1
[8,4,1,2,6,3,7,5]=>0000000=>1111111=>1
[8,2,7,1,5,3,4,6]=>0000000=>1111111=>1
[3,2,7,1,5,8,4,6]=>0000000=>1111111=>1
[6,3,7,1,5,4,2,8]=>0000001=>1111110=>1
[7,3,8,1,5,4,2,6]=>0000000=>1111111=>1
[7,1,5,3,8,4,2,6]=>0000000=>1111111=>1
[4,5,1,3,6,8,2,7]=>0000000=>1111111=>1
[3,6,8,1,5,4,2,7]=>0000000=>1111111=>1
[6,8,3,1,5,4,2,7]=>0000000=>1111111=>1
[7,6,3,1,5,4,2,8]=>0000001=>1111110=>1
[3,6,2,1,5,8,4,7]=>0000000=>1111111=>1
[8,6,2,1,5,3,4,7]=>0000000=>1111111=>1
[4,8,2,1,7,5,3,6]=>0000000=>1111111=>1
[2,3,8,1,5,7,4,6]=>0000000=>1111111=>1
[7,1,3,2,8,6,4,5]=>0000000=>1111111=>1
[7,1,6,2,8,3,4,5]=>0000000=>1111111=>1
[4,7,1,2,6,3,8,5]=>0000000=>1111111=>1
[2,7,8,1,5,3,4,6]=>0000000=>1111111=>1
[6,7,2,1,5,3,4,8]=>0000001=>1111110=>1
[4,7,2,1,8,5,3,6]=>0000000=>1111111=>1
[8,7,2,1,4,5,3,6]=>0000000=>1111111=>1
[8,7,5,6,1,4,3,2]=>0000000=>1111111=>1
[5,7,8,6,1,4,3,2]=>0000000=>1111111=>1
[2,7,4,1,6,5,3,8]=>0000001=>1111110=>1
[3,7,1,4,5,6,8,2]=>0000000=>1111111=>1
[7,1,6,4,5,8,3,2]=>0000000=>1111111=>1
[3,5,1,4,7,6,8,2]=>0000000=>1111111=>1
[2,6,4,1,7,5,3,8]=>0000001=>1111110=>1
[5,6,8,7,1,4,3,2]=>0000000=>1111111=>1
[6,8,5,7,1,4,3,2]=>0000000=>1111111=>1
[8,6,5,7,1,4,3,2]=>0000000=>1111111=>1
[8,5,7,6,1,4,3,2]=>0000000=>1111111=>1
[6,5,7,8,1,4,3,2]=>0000000=>1111111=>1
[7,2,3,1,5,6,4,8]=>0000001=>1111110=>1
[4,2,8,1,6,5,3,7]=>0000000=>1111111=>1
[6,2,4,1,8,5,3,7]=>0000000=>1111111=>1
[8,3,1,4,5,6,7,2]=>0000000=>1111111=>1
[5,3,1,4,8,6,7,2]=>0000000=>1111111=>1
[7,5,1,6,3,4,8,2]=>0000000=>1111111=>1
[7,1,5,8,4,3,6,2]=>0000000=>1111111=>1
[5,8,1,6,4,3,7,2]=>0000000=>1111111=>1
[5,3,1,8,4,6,7,2]=>0000000=>1111111=>1
[8,3,1,5,4,6,7,2]=>0000000=>1111111=>1
[8,2,6,1,4,5,3,7]=>0000000=>1111111=>1
[6,2,8,1,4,5,3,7]=>0000000=>1111111=>1
[7,2,6,1,5,3,4,8]=>0000001=>1111110=>1
[2,8,6,1,5,3,4,7]=>0000000=>1111111=>1
[4,2,1,5,6,3,8,7]=>0000010=>1111101=>2
[7,1,2,5,8,3,4,6]=>0000000=>1111111=>1
[7,1,4,5,6,8,3,2]=>0000000=>1111111=>1
[8,5,6,7,1,4,3,2]=>0000000=>1111111=>1
[7,6,8,5,1,4,3,2]=>0000000=>1111111=>1
[6,8,7,5,1,4,3,2]=>0000000=>1111111=>1
[2,6,7,1,4,5,3,8]=>0000001=>1111110=>1
[3,5,1,7,4,6,8,2]=>0000000=>1111111=>1
[7,1,5,6,4,8,3,2]=>0000000=>1111111=>1
[7,1,6,5,4,8,3,2]=>0000000=>1111111=>1
[2,7,6,1,4,5,3,8]=>0000001=>1111110=>1
[5,7,6,8,1,4,3,2]=>0000000=>1111111=>1
[7,8,6,5,1,4,3,2]=>0000000=>1111111=>1
[4,3,1,6,5,8,7,2]=>0000000=>1111111=>1
[5,3,1,2,4,8,7,6]=>0000100=>1111011=>2
[5,3,6,2,1,8,7,4]=>0000000=>1111111=>1
[5,3,7,2,1,4,6,8]=>0000001=>1111110=>1
[5,3,7,2,8,4,1,6]=>0000000=>1111111=>1
[7,2,4,5,8,3,1,6]=>0000000=>1111111=>1
[7,2,4,5,1,3,6,8]=>0000001=>1111110=>1
[6,2,4,5,1,8,7,3]=>0000000=>1111111=>1
[3,1,4,5,2,8,7,6]=>0000100=>1111011=>2
[1,6,4,5,2,8,7,3]=>1000000=>0111111=>1
[3,7,4,5,1,2,6,8]=>0000001=>1111110=>1
[3,7,4,5,8,2,1,6]=>0000000=>1111111=>1
[1,7,4,2,6,3,5,8]=>1000001=>0111110=>1
[8,7,4,5,2,1,6,3]=>0000000=>1111111=>1
[6,3,7,1,8,4,2,5]=>0000000=>1111111=>1
[5,7,4,1,6,3,2,8]=>0000001=>1111110=>1
[1,7,4,8,6,3,2,5]=>1000000=>0111111=>1
[5,7,4,8,6,3,1,2]=>0000000=>1111111=>1
[4,8,3,5,6,7,1,2]=>0000000=>1111111=>1
[1,8,3,5,6,7,2,4]=>1000000=>0111111=>1
[4,8,1,5,6,7,2,3]=>0000000=>1111111=>1
[4,1,3,5,6,7,2,8]=>0000001=>1111110=>1
[5,8,4,3,6,1,2,7]=>0000000=>1111111=>1
[5,3,8,4,1,7,2,6]=>0000000=>1111111=>1
[1,5,8,4,6,7,3,2]=>1000000=>0111111=>1
[1,4,8,3,6,7,5,2]=>1000000=>0111111=>1
[4,3,8,2,1,7,5,6]=>0000000=>1111111=>1
[3,8,4,2,6,1,5,7]=>0000000=>1111111=>1
[1,8,2,5,6,7,4,3]=>1000000=>0111111=>1
[3,8,1,5,6,7,4,2]=>0000000=>1111111=>1
[3,8,2,5,6,7,1,4]=>0000000=>1111111=>1
[8,2,1,5,6,7,4,3]=>0000000=>1111111=>1
[8,1,3,5,6,7,4,2]=>0000000=>1111111=>1
[7,1,4,3,6,2,5,8]=>0000001=>1111110=>1
[7,8,4,3,6,2,1,5]=>0000000=>1111111=>1
[4,3,1,8,5,7,6,2]=>0000000=>1111111=>1
[4,3,1,6,8,7,5,2]=>0000000=>1111111=>1
[6,3,1,8,2,7,4,5]=>0000000=>1111111=>1
[6,3,5,8,2,7,1,4]=>0000000=>1111111=>1
[7,5,4,8,6,2,1,3]=>0000000=>1111111=>1
[7,1,4,8,6,2,3,5]=>0000000=>1111111=>1
[7,5,4,1,6,2,3,8]=>0000001=>1111110=>1
[7,6,4,5,8,1,3,2]=>0000000=>1111111=>1
[1,6,4,5,8,2,3,7]=>1000000=>0111111=>1
[7,3,6,1,8,2,4,5]=>0000000=>1111111=>1
[1,7,6,5,8,3,4,2]=>1000000=>0111111=>1
[1,8,5,3,6,7,4,2]=>1000000=>0111111=>1
[8,3,5,2,1,7,4,6]=>0000000=>1111111=>1
[8,4,1,5,6,7,3,2]=>0000000=>1111111=>1
[8,4,2,5,6,7,1,3]=>0000000=>1111111=>1
[4,1,8,5,6,7,3,2]=>0000000=>1111111=>1
[1,2,8,5,6,7,3,4]=>1100000=>0011111=>1
[4,2,1,5,6,7,3,8]=>0000001=>1111110=>1
[1,5,3,8,6,7,4,2]=>1000000=>0111111=>1
[1,4,5,8,6,7,3,2]=>1000000=>0111111=>1
[4,3,5,8,1,7,2,6]=>0000000=>1111111=>1
[3,5,4,8,6,1,2,7]=>0000000=>1111111=>1
[1,4,8,5,6,7,2,3]=>1000000=>0111111=>1
[3,4,8,5,6,7,1,2]=>0000000=>1111111=>1
[2,7,1,5,6,3,4,8]=>0000001=>1111110=>1
[2,7,1,4,3,6,5,8]=>0000001=>1111110=>1
[4,3,7,2,5,6,8,1]=>0000000=>1111111=>1
[2,6,3,1,4,5,8,7]=>0000010=>1111101=>2
[3,7,1,4,2,6,8,5]=>0000000=>1111111=>1
[3,7,1,5,6,2,8,4]=>0000000=>1111111=>1
[4,7,1,5,6,8,2,3]=>0000000=>1111111=>1
[8,5,2,6,7,3,1,4]=>0000000=>1111111=>1
[8,4,2,6,3,7,1,5]=>0000000=>1111111=>1
[8,4,2,3,5,7,1,6]=>0000000=>1111111=>1
[4,7,3,2,5,6,1,8]=>0000001=>1111110=>1
[5,3,4,6,2,8,1,7]=>0000000=>1111111=>1
[5,3,7,4,2,8,1,6]=>0000000=>1111111=>1
[6,4,7,2,3,8,1,5]=>0000000=>1111111=>1
[6,5,7,2,8,3,1,4]=>0000000=>1111111=>1
[5,3,7,2,4,8,6,1]=>0000000=>1111111=>1
[2,6,5,1,8,3,4,7]=>0000000=>1111111=>1
[8,7,6,1,4,5,2,3]=>0000000=>1111111=>1
[8,7,6,1,3,2,5,4]=>0000000=>1111111=>1
[8,7,2,4,3,1,6,5]=>0000000=>1111111=>1
[8,7,4,5,1,6,2,3]=>0000000=>1111111=>1
[8,5,6,4,1,7,2,3]=>0000000=>1111111=>1
[8,5,6,3,1,2,7,4]=>0000000=>1111111=>1
[8,4,6,2,3,1,7,5]=>0000000=>1111111=>1
[8,3,5,4,2,1,7,6]=>0000000=>1111111=>1
[5,7,3,4,2,1,8,6]=>0000000=>1111111=>1
[6,7,4,2,3,1,8,5]=>0000000=>1111111=>1
[6,7,5,3,1,2,8,4]=>0000000=>1111111=>1
[6,7,5,4,1,8,2,3]=>0000000=>1111111=>1
[8,10,1,2,3,4,5,6,7,9]=>000000000=>111111111=>1
[7,3,5,4,1,8,6,2]=>0000000=>1111111=>1
[2,6,5,7,3,1,8,4]=>0000000=>1111111=>1
[6,3,2,4,7,5,1,8]=>0000001=>1111110=>1
[4,2,1,6,3,7,5,8]=>0000001=>1111110=>1
[4,2,1,6,3,7,8,5]=>0000000=>1111111=>1
[4,2,1,3,7,8,6,5]=>0001000=>1110111=>2
[5,8,1,7,4,3,2,6]=>0000000=>1111111=>1
[7,3,4,2,6,8,1,5]=>0000000=>1111111=>1
[3,6,7,5,2,4,8,1]=>0000000=>1111111=>1
[4,2,1,7,3,6,5,8]=>0000001=>1111110=>1
[3,7,8,6,2,4,5,1]=>0000000=>1111111=>1
[4,2,1,3,5,8,6,7]=>0001100=>1110011=>2
[4,8,1,7,3,6,5,2]=>0000000=>1111111=>1
[4,2,1,8,3,7,6,5]=>0000000=>1111111=>1
[2,6,1,5,4,7,8,3]=>0000000=>1111111=>1
[4,6,3,5,8,7,1,2]=>0000000=>1111111=>1
[3,5,6,1,4,8,7,2]=>0000000=>1111111=>1
[4,7,5,2,1,3,6,8]=>0000001=>1111110=>1
[3,5,6,2,4,1,7,8]=>0000011=>1111100=>1
[2,5,6,1,4,8,3,7]=>0000000=>1111111=>1
[6,7,8,4,1,5,3,2]=>0000000=>1111111=>1
[7,1,6,8,4,5,3,2]=>0000000=>1111111=>1
[7,4,6,5,2,8,1,3]=>0000000=>1111111=>1
[7,1,5,6,4,2,3,8]=>0000001=>1111110=>1
[5,7,4,6,8,1,3,2]=>0000000=>1111111=>1
[5,7,8,1,4,6,3,2]=>0000000=>1111111=>1
[8,1,5,7,4,6,3,2]=>0000000=>1111111=>1
[1,8,4,6,7,5,3,2]=>1000000=>0111111=>1
[6,1,8,4,7,5,3,2]=>0000000=>1111111=>1
[4,5,8,6,1,7,3,2]=>0000000=>1111111=>1
[4,8,5,1,6,7,3,2]=>0000000=>1111111=>1
[8,1,4,5,6,7,3,2]=>0000000=>1111111=>1
[5,6,7,1,4,2,3,8]=>0000001=>1111110=>1
[8,4,2,6,1,5,7,3]=>0000000=>1111111=>1
[4,8,5,2,1,6,7,3]=>0000000=>1111111=>1
[5,1,8,4,2,6,3,7]=>0000000=>1111111=>1
[1,8,4,6,2,5,3,7]=>1000000=>0111111=>1
[6,1,5,2,3,4,7,8]=>0000011=>1111100=>1
[8,3,1,4,6,2,5,7]=>0000000=>1111111=>1
[3,1,8,2,5,6,4,7]=>0000000=>1111111=>1
[3,5,1,8,2,6,4,7]=>0000000=>1111111=>1
[3,5,1,2,8,4,7,6]=>0000000=>1111111=>1
[2,3,5,8,6,1,7,4]=>0000000=>1111111=>1
[8,2,4,3,6,7,1,5]=>0000000=>1111111=>1
[3,2,8,5,7,1,6,4]=>0000000=>1111111=>1
[3,6,2,8,5,1,7,4]=>0000000=>1111111=>1
[6,2,1,8,4,7,5,3]=>0000000=>1111111=>1
[2,8,7,1,4,6,5,3]=>0000000=>1111111=>1
[8,2,7,1,5,4,6,3]=>0000000=>1111111=>1
[7,2,5,3,6,8,1,4]=>0000000=>1111111=>1
[7,3,1,5,6,2,4,8]=>0000001=>1111110=>1
[3,7,5,1,6,2,4,8]=>0000001=>1111110=>1
[2,7,3,6,5,8,1,4]=>0000000=>1111111=>1
[8,7,2,4,1,6,5,3]=>0000000=>1111111=>1
[1,8,7,2,3,6,5,4]=>1000000=>0111111=>1
[1,7,8,2,6,4,3,5]=>1000000=>0111111=>1
[1,7,3,8,2,6,4,5]=>1000000=>0111111=>1
[1,2,7,3,6,4,5,8]=>1100001=>0011110=>1
[7,1,5,8,3,2,4,6]=>0000000=>1111111=>1
[1,6,2,8,4,3,7,5]=>1000000=>0111111=>1
[1,3,8,7,2,4,6,5]=>1000000=>0111111=>1
[1,8,3,7,2,5,4,6]=>1000000=>0111111=>1
[8,1,4,7,3,2,5,6]=>0000000=>1111111=>1
[4,7,8,1,3,2,5,6]=>0000000=>1111111=>1
[7,1,4,2,3,5,6,8]=>0000001=>1111110=>1
[8,2,1,4,7,3,5,6]=>0000000=>1111111=>1
[2,1,3,8,4,6,7,5]=>0110000=>1001111=>2
[1,2,3,4,8,5,7,6]=>1111000=>0000111=>1
[2,4,7,5,6,8,3,1]=>0000000=>1111111=>1
[2,8,5,7,3,6,4,1]=>0000000=>1111111=>1
[3,1,8,5,2,7,6,4]=>0000000=>1111111=>1
[2,5,7,3,4,8,6,1]=>0000000=>1111111=>1
[7,3,8,5,1,6,4,2]=>0000000=>1111111=>1
[4,8,1,5,2,7,3,6]=>0000000=>1111111=>1
[4,1,2,5,3,8,7,6]=>0000100=>1111011=>2
[4,3,6,8,7,5,1,2]=>0000000=>1111111=>1
[5,4,1,8,2,7,6,3]=>0000000=>1111111=>1
[6,4,8,1,2,5,3,7]=>0000000=>1111111=>1
[5,4,1,6,8,2,7,3]=>0000000=>1111111=>1
[6,5,1,2,3,7,8,4]=>0000000=>1111111=>1
[6,5,1,2,3,4,8,7]=>0000010=>1111101=>2
[6,7,4,1,2,5,3,8]=>0000001=>1111110=>1
[2,4,6,3,5,7,1,8]=>0000001=>1111110=>1
[1,4,6,3,7,2,5,8]=>1000001=>0111110=>1
[8,6,2,5,3,1,7,4]=>0000000=>1111111=>1
[8,2,3,4,5,1,7,6]=>0000000=>1111111=>1
[1,8,3,4,2,7,5,6]=>1000000=>0111111=>1
[2,8,3,4,1,6,7,5]=>0000000=>1111111=>1
[8,7,2,3,1,6,5,4]=>0000000=>1111111=>1
[3,8,2,4,6,1,7,5]=>0000000=>1111111=>1
[7,8,2,4,3,1,6,5]=>0000000=>1111111=>1
[4,5,8,2,3,1,7,6]=>0000000=>1111111=>1
[5,1,4,3,7,2,6,8]=>0000001=>1111110=>1
[6,1,3,5,7,2,4,8]=>0000001=>1111110=>1
[2,1,4,7,5,3,6,8]=>0100001=>1011110=>2
[7,1,3,6,2,5,4,8]=>0000001=>1111110=>1
[8,1,3,6,2,4,7,5]=>0000000=>1111111=>1
[2,1,8,3,7,5,4,6]=>0100000=>1011111=>2
[7,1,8,2,5,6,3,4]=>0000000=>1111111=>1
[6,1,5,8,2,7,3,4]=>0000000=>1111111=>1
[4,5,2,8,1,6,7,3]=>0000000=>1111111=>1
[6,2,5,8,1,4,7,3]=>0000000=>1111111=>1
[3,2,8,5,1,6,7,4]=>0000000=>1111111=>1
[8,2,7,1,4,6,5,3]=>0000000=>1111111=>1
[1,3,8,2,5,7,4,6]=>1000000=>0111111=>1
[2,8,7,1,6,4,5,3]=>0000000=>1111111=>1
[3,8,7,1,5,6,4,2]=>0000000=>1111111=>1
[3,4,8,5,6,1,7,2]=>0000000=>1111111=>1
[8,3,7,4,1,6,5,2]=>0000000=>1111111=>1
[1,4,8,6,2,7,3,5]=>1000000=>0111111=>1
[8,4,5,7,1,6,3,2]=>0000000=>1111111=>1
[3,5,6,8,4,1,7,2]=>0000000=>1111111=>1
[6,2,3,1,5,4,7,8]=>0000011=>1111100=>1
[7,2,3,1,4,6,5,8]=>0000001=>1111110=>1
[8,2,3,1,4,5,7,6]=>0000000=>1111111=>1
[8,5,1,3,2,4,7,6]=>0000000=>1111111=>1
[7,5,1,3,2,6,4,8]=>0000001=>1111110=>1
[2,6,1,4,5,3,7,8]=>0000011=>1111100=>1
[3,6,4,1,5,2,7,8]=>0000011=>1111100=>1
[4,5,6,1,3,2,7,8]=>0000011=>1111100=>1
[4,5,7,1,2,6,3,8]=>0000001=>1111110=>1
[3,7,4,1,2,6,5,8]=>0000001=>1111110=>1
[6,7,1,4,2,5,3,8]=>0000001=>1111110=>1
[2,7,1,3,5,6,4,8]=>0000001=>1111110=>1
[8,6,1,2,4,3,7,5]=>0000000=>1111111=>1
[2,8,1,3,4,6,7,5]=>0000000=>1111111=>1
[7,8,1,2,5,3,6,4]=>0000000=>1111111=>1
[3,8,4,1,2,5,7,6]=>0000000=>1111111=>1
[1,2,6,7,5,3,8,4]=>1100000=>0011111=>1
[1,7,5,3,2,8,4,6]=>1000000=>0111111=>1
[1,6,7,5,3,8,4,2]=>1000000=>0111111=>1
[1,6,5,7,2,3,8,4]=>1000000=>0111111=>1
[1,3,8,2,6,5,7,4]=>1000000=>0111111=>1
[1,2,5,7,6,3,4,8]=>1100001=>0011110=>1
[1,3,4,8,2,5,7,6]=>1000000=>0111111=>1
[1,5,7,6,2,3,4,8]=>1000001=>0111110=>1
[1,5,3,8,2,6,4,7]=>1000000=>0111111=>1
[1,4,8,3,2,5,7,6]=>1000000=>0111111=>1
[1,4,8,3,5,7,6,2]=>1000000=>0111111=>1
[1,2,4,8,3,5,7,6]=>1100000=>0011111=>1
[1,3,8,4,2,6,7,5]=>1000000=>0111111=>1
[1,4,8,2,3,5,7,6]=>1000000=>0111111=>1
[6,5,7,3,8,2,4,1]=>0000000=>1111111=>1
[4,2,6,7,5,8,3,1]=>0000000=>1111111=>1
[6,7,5,2,1,8,4,3]=>0000000=>1111111=>1
[3,4,8,7,5,2,1,6]=>0000000=>1111111=>1
[1,7,5,2,8,4,6,3]=>1000000=>0111111=>1
[5,6,8,3,1,7,2,4]=>0000000=>1111111=>1
[6,1,4,8,3,2,7,5]=>0000000=>1111111=>1
[3,4,7,1,8,6,2,5]=>0000000=>1111111=>1
[3,4,6,8,2,1,5,7]=>0000000=>1111111=>1
[3,8,2,5,6,1,4,7]=>0000000=>1111111=>1
[3,5,2,8,6,4,1,7]=>0000000=>1111111=>1
[4,2,5,7,3,8,6,1]=>0000000=>1111111=>1
[7,4,2,5,3,8,1,6]=>0000000=>1111111=>1
[3,1,2,8,5,6,4,7]=>0010000=>1101111=>2
[5,2,1,6,8,3,4,7]=>0000000=>1111111=>1
[5,2,6,8,4,1,3,7]=>0000000=>1111111=>1
[1,5,6,8,3,4,2,7]=>1000000=>0111111=>1
[4,5,8,1,6,3,2,7]=>0000000=>1111111=>1
[4,5,1,6,8,3,2,7]=>0000000=>1111111=>1
[4,5,7,3,8,2,6,1]=>0000000=>1111111=>1
[6,4,3,7,8,2,5,1]=>0000000=>1111111=>1
[6,4,3,1,7,8,2,5]=>0000000=>1111111=>1
[4,5,3,1,7,8,2,6]=>0000000=>1111111=>1
[7,1,3,5,4,8,2,6]=>0000000=>1111111=>1
[7,5,2,8,1,4,3,6]=>0000000=>1111111=>1
[5,7,3,8,4,6,1,2]=>0000000=>1111111=>1
[1,4,5,7,3,8,6,2]=>1000000=>0111111=>1
[4,6,3,7,8,5,2,1]=>0000000=>1111111=>1
[5,3,6,7,8,4,2,1]=>0000000=>1111111=>1
[1,5,3,6,7,8,4,2]=>1000000=>0111111=>1
[4,6,1,7,3,8,5,2]=>0000000=>1111111=>1
[6,3,7,1,8,4,5,2]=>0000000=>1111111=>1
[6,7,2,4,8,1,5,3]=>0000000=>1111111=>1
[2,6,1,4,7,3,8,5]=>0000000=>1111111=>1
[3,2,5,6,7,8,1,4]=>0000000=>1111111=>1
[5,2,3,6,7,8,4,1]=>0000000=>1111111=>1
[6,7,1,3,2,8,4,5]=>0000000=>1111111=>1
[6,2,7,1,3,4,8,5]=>0000000=>1111111=>1
[5,2,1,7,3,8,4,6]=>0000000=>1111111=>1
[6,4,2,7,1,8,3,5]=>0000000=>1111111=>1
[4,2,6,3,7,8,1,5]=>0000000=>1111111=>1
[4,2,6,3,7,8,5,1]=>0000000=>1111111=>1
[6,7,3,8,2,4,5,1]=>0000000=>1111111=>1
[3,6,2,7,4,1,8,5]=>0000000=>1111111=>1
[6,7,3,2,1,4,8,5]=>0000000=>1111111=>1
[7,1,8,3,4,2,5,6]=>0000000=>1111111=>1
[7,2,4,1,8,3,5,6]=>0000000=>1111111=>1
[7,2,4,8,6,1,3,5]=>0000000=>1111111=>1
[7,3,4,8,6,2,1,5]=>0000000=>1111111=>1
[3,5,7,2,1,8,6,4]=>0000000=>1111111=>1
[6,7,8,3,2,5,1,4]=>0000000=>1111111=>1
[6,3,7,8,2,5,4,1]=>0000000=>1111111=>1
[2,6,7,4,8,5,3,1]=>0000000=>1111111=>1
[6,2,4,7,1,8,5,3]=>0000000=>1111111=>1
[4,6,2,7,1,8,5,3]=>0000000=>1111111=>1
[1,7,4,8,5,2,6,3]=>1000000=>0111111=>1
[1,3,7,8,5,2,6,4]=>1000000=>0111111=>1
[2,5,7,8,1,6,3,4]=>0000000=>1111111=>1
[6,3,7,1,8,2,5,4]=>0000000=>1111111=>1
[1,6,4,7,8,2,5,3]=>1000000=>0111111=>1
[2,5,6,1,7,8,4,3]=>0000000=>1111111=>1
[5,6,1,2,7,8,4,3]=>0000000=>1111111=>1
[6,7,2,1,8,5,3,4]=>0000000=>1111111=>1
[6,7,2,8,5,4,1,3]=>0000000=>1111111=>1
[1,6,7,4,8,5,3,2]=>1000000=>0111111=>1
[1,8,2,4,6,3,5,7]=>1000000=>0111111=>1
[1,5,7,4,3,6,2,8]=>1000001=>0111110=>1
[1,8,4,5,3,6,2,7]=>1000000=>0111111=>1
[1,8,5,3,4,7,2,6]=>1000000=>0111111=>1
[1,8,2,4,6,3,7,5]=>1000000=>0111111=>1
[1,8,2,5,4,6,7,3]=>1000000=>0111111=>1
[3,6,2,7,1,4,5,8]=>0000001=>1111110=>1
[1,4,7,5,2,6,8,3]=>1000000=>0111111=>1
[4,6,5,3,7,1,8,2]=>0000000=>1111111=>1
[5,2,4,8,1,3,7,6]=>0000000=>1111111=>1
[6,4,3,5,8,2,7,1]=>0000000=>1111111=>1
[5,2,3,4,8,1,6,7]=>0000000=>1111111=>1
[3,5,2,4,7,1,6,8]=>0000001=>1111110=>1
[4,5,3,7,1,6,2,8]=>0000001=>1111110=>1
[7,6,3,8,5,1,2,4]=>0000000=>1111111=>1
[4,2,6,7,3,8,1,5]=>0000000=>1111111=>1
[1,5,7,4,2,8,6,3]=>1000000=>0111111=>1
[1,3,7,2,8,6,4,5]=>1000000=>0111111=>1
[1,4,3,7,8,6,2,5]=>1000000=>0111111=>1
[1,5,3,6,8,2,7,4]=>1000000=>0111111=>1
[4,3,6,5,7,8,1,2]=>0000000=>1111111=>1
[4,2,3,5,6,8,1,7]=>0000000=>1111111=>1
[5,2,6,4,7,8,3,1]=>0000000=>1111111=>1
[3,2,5,6,8,1,7,4]=>0000000=>1111111=>1
[6,4,5,2,3,8,7,1]=>0000000=>1111111=>1
[6,4,2,5,3,8,7,1]=>0000000=>1111111=>1
[8,6,4,7,5,2,3,1]=>0000000=>1111111=>1
[6,4,2,5,8,7,3,1]=>0000000=>1111111=>1
[4,6,2,5,3,8,7,1]=>0000000=>1111111=>1
[2,6,4,5,8,7,3,1]=>0000000=>1111111=>1
[2,6,4,8,7,5,3,1]=>0000000=>1111111=>1
[8,2,4,6,7,5,3,1]=>0000000=>1111111=>1
[4,2,6,8,7,5,3,1]=>0000000=>1111111=>1
[4,2,6,5,8,7,3,1]=>0000000=>1111111=>1
[6,4,8,7,2,5,3,1]=>0000000=>1111111=>1
[6,4,8,7,5,2,3,1]=>0000000=>1111111=>1
[4,6,5,8,7,2,3,1]=>0000000=>1111111=>1
[4,6,5,8,2,7,3,1]=>0000000=>1111111=>1
[6,8,7,4,2,5,3,1]=>0000000=>1111111=>1
[9,8,7,3,6,2,5,1,4]=>00000000=>11111111=>1
[9,8,7,6,3,5,1,2,4]=>00000000=>11111111=>1
[9,4,8,3,7,2,6,1,5]=>00000000=>11111111=>1
[9,8,4,7,3,6,1,2,5]=>00000000=>11111111=>1
[9,8,7,2,4,6,1,3,5]=>00000000=>11111111=>1
[9,8,7,4,6,1,2,3,5]=>00000000=>11111111=>1
[5,9,4,8,3,7,1,2,6]=>00000000=>11111111=>1
[9,5,8,2,4,7,1,3,6]=>00000000=>11111111=>1
[9,5,8,4,7,1,2,3,6]=>00000000=>11111111=>1
[9,8,3,5,7,1,2,4,6]=>00000000=>11111111=>1
[9,8,5,7,1,2,3,4,6]=>00000000=>11111111=>1
[6,9,3,5,8,1,2,4,7]=>00000000=>11111111=>1
[6,9,5,8,1,2,3,4,7]=>00000000=>11111111=>1
[9,2,4,6,8,1,3,5,7]=>00000000=>11111111=>1
[9,4,6,8,1,2,3,5,7]=>00000000=>11111111=>1
[9,6,8,1,2,3,4,5,7]=>00000000=>11111111=>1
[3,5,7,9,1,2,4,6,8]=>00000000=>11111111=>1
[5,7,9,1,2,3,4,6,8]=>00000000=>11111111=>1
[7,9,1,2,3,4,5,6,8]=>00000000=>11111111=>1
[10,9,8,7,6,5,2,4,1,3]=>000000000=>111111111=>1
[10,9,8,7,3,6,2,5,1,4]=>000000000=>111111111=>1
[10,9,8,7,6,3,5,1,2,4]=>000000000=>111111111=>1
[10,9,4,8,3,7,2,6,1,5]=>000000000=>111111111=>1
[10,9,8,4,7,3,6,1,2,5]=>000000000=>111111111=>1
[10,9,8,7,2,4,6,1,3,5]=>000000000=>111111111=>1
[10,9,8,7,4,6,1,2,3,5]=>000000000=>111111111=>1
[10,5,9,4,8,3,7,1,2,6]=>000000000=>111111111=>1
[10,9,5,8,2,4,7,1,3,6]=>000000000=>111111111=>1
[10,9,5,8,4,7,1,2,3,6]=>000000000=>111111111=>1
[10,9,8,3,5,7,1,2,4,6]=>000000000=>111111111=>1
[10,9,8,5,7,1,2,3,4,6]=>000000000=>111111111=>1
[6,10,5,9,2,4,8,1,3,7]=>000000000=>111111111=>1
[6,10,5,9,4,8,1,2,3,7]=>000000000=>111111111=>1
[10,3,6,9,2,5,8,1,4,7]=>000000000=>111111111=>1
[10,6,9,3,5,8,1,2,4,7]=>000000000=>111111111=>1
[10,6,9,5,8,1,2,3,4,7]=>000000000=>111111111=>1
[10,9,2,4,6,8,1,3,5,7]=>000000000=>111111111=>1
[10,9,4,6,8,1,2,3,5,7]=>000000000=>111111111=>1
[10,9,6,8,1,2,3,4,5,7]=>000000000=>111111111=>1
[4,7,10,3,6,9,1,2,5,8]=>000000000=>111111111=>1
[7,10,2,4,6,9,1,3,5,8]=>000000000=>111111111=>1
[7,10,4,6,9,1,2,3,5,8]=>000000000=>111111111=>1
[7,10,6,9,1,2,3,4,5,8]=>000000000=>111111111=>1
[10,3,5,7,9,1,2,4,6,8]=>000000000=>111111111=>1
[10,5,7,9,1,2,3,4,6,8]=>000000000=>111111111=>1
[10,7,9,1,2,3,4,5,6,8]=>000000000=>111111111=>1
[4,6,8,10,1,2,3,5,7,9]=>000000000=>111111111=>1
[6,8,10,1,2,3,4,5,7,9]=>000000000=>111111111=>1
[4,2,5,6,3,8,1,7]=>0000000=>1111111=>1
[6,2,5,7,4,8,3,1]=>0000000=>1111111=>1
[8,5,2,1,4,7,6,3]=>0000000=>1111111=>1
[6,7,3,2,5,8,4,1]=>0000000=>1111111=>1
[3,2,6,4,8,1,5,7]=>0000000=>1111111=>1
[2,3,6,4,7,8,5,1]=>0000000=>1111111=>1
[7,5,1,8,3,4,6,2]=>0000000=>1111111=>1
[5,7,8,2,6,3,4,1]=>0000000=>1111111=>1
[7,1,6,3,5,8,4,2]=>0000000=>1111111=>1
[6,3,1,7,8,4,5,2]=>0000000=>1111111=>1
[5,3,6,7,4,1,8,2]=>0000000=>1111111=>1
[7,3,1,2,5,8,6,4]=>0000000=>1111111=>1
[1,6,3,5,2,4,8,7]=>1000010=>0111101=>2
[3,4,8,2,7,5,1,6]=>0000000=>1111111=>1
[6,3,2,8,5,7,4,1]=>0000000=>1111111=>1
[3,8,4,7,2,5,6,1]=>0000000=>1111111=>1
[2,4,8,1,5,3,7,6]=>0000000=>1111111=>1
[3,4,8,1,6,2,7,5]=>0000000=>1111111=>1
[1,8,4,6,7,3,5,2]=>1000000=>0111111=>1
[8,1,6,3,4,5,7,2]=>0000000=>1111111=>1
[7,6,5,4,1,2,8,3]=>0000000=>1111111=>1
[5,7,6,8,3,4,2,1]=>0000000=>1111111=>1
[2,8,1,6,5,7,4,3]=>0000000=>1111111=>1
[4,6,8,2,5,3,7,1]=>0000000=>1111111=>1
[5,2,3,7,6,1,8,4]=>0000000=>1111111=>1
[8,1,2,4,6,7,3,5]=>0000000=>1111111=>1
[5,2,3,7,4,8,6,1]=>0000000=>1111111=>1
[5,2,6,8,4,3,1,7]=>0000000=>1111111=>1
[7,8,1,5,4,3,6,2]=>0000000=>1111111=>1
[7,2,4,8,5,3,6,1]=>0000000=>1111111=>1
[3,7,5,1,8,4,6,2]=>0000000=>1111111=>1
[2,7,8,5,4,6,1,3]=>0000000=>1111111=>1
[5,7,4,3,8,6,2,1]=>0000000=>1111111=>1
[4,8,1,6,3,5,2,7]=>0000000=>1111111=>1
[8,3,1,7,4,2,5,6]=>0000000=>1111111=>1
[3,1,8,2,4,5,7,6]=>0000000=>1111111=>1
[8,1,3,7,6,2,4,5]=>0000000=>1111111=>1
[2,3,6,8,7,1,4,5]=>0000000=>1111111=>1
[4,3,2,8,5,7,1,6]=>0000000=>1111111=>1
[3,6,4,2,8,5,7,1]=>0000000=>1111111=>1
[4,7,3,2,5,1,8,6]=>0000000=>1111111=>1
[3,2,4,7,5,8,6,1]=>0000000=>1111111=>1
[4,2,3,8,6,5,1,7]=>0000000=>1111111=>1
[2,4,3,5,1,8,6,7]=>0000100=>1111011=>2
[3,2,8,1,4,6,5,7]=>0000000=>1111111=>1
[4,7,8,3,1,2,6,5]=>0000000=>1111111=>1
[4,7,8,2,1,3,6,5]=>0000000=>1111111=>1
[4,1,6,8,2,3,7,5]=>0000000=>1111111=>1
[4,5,1,2,8,3,7,6]=>0000000=>1111111=>1
[3,6,2,8,4,7,1,5]=>0000000=>1111111=>1
[3,2,6,8,4,7,1,5]=>0000000=>1111111=>1
[4,2,6,8,3,1,7,5]=>0000000=>1111111=>1
[4,2,5,1,8,3,7,6]=>0000000=>1111111=>1
[4,1,2,5,8,3,7,6]=>0000000=>1111111=>1
[4,2,5,3,8,1,7,6]=>0000000=>1111111=>1
[3,2,5,4,8,7,1,6]=>0000000=>1111111=>1
[5,4,1,3,2,8,7,6]=>0000100=>1111011=>2
[5,4,3,1,2,8,7,6]=>0000100=>1111011=>2
[3,5,1,4,8,7,2,6]=>0000000=>1111111=>1
[3,4,5,1,8,7,2,6]=>0000000=>1111111=>1
[2,4,6,8,3,7,5,1]=>0000000=>1111111=>1
[3,4,5,2,8,7,1,6]=>0000000=>1111111=>1
[5,3,1,4,2,8,7,6]=>0000100=>1111011=>2
[5,3,2,1,4,8,7,6]=>0000100=>1111011=>2
[4,3,2,5,8,1,7,6]=>0000000=>1111111=>1
[3,2,4,5,8,7,1,6]=>0000000=>1111111=>1
[5,2,1,3,4,8,7,6]=>0000100=>1111011=>2
[8,6,2,5,4,1,3,7]=>0000000=>1111111=>1
[6,5,7,4,2,8,3,1]=>0000000=>1111111=>1
[6,7,5,3,8,2,4,1]=>0000000=>1111111=>1
[8,2,1,6,3,4,5,7]=>0000000=>1111111=>1
[8,3,5,6,2,4,1,7]=>0000000=>1111111=>1
[8,6,2,1,3,5,4,7]=>0000000=>1111111=>1
[8,1,2,3,4,6,5,7]=>0000000=>1111111=>1
[6,2,3,7,8,4,5,1]=>0000000=>1111111=>1
[7,5,8,2,6,3,4,1]=>0000000=>1111111=>1
[7,3,1,6,5,8,4,2]=>0000000=>1111111=>1
[1,5,6,7,3,4,8,2]=>1000000=>0111111=>1
[6,7,8,2,1,4,5,3]=>0000000=>1111111=>1
[8,4,7,6,2,1,3,5]=>0000000=>1111111=>1
[5,3,8,4,7,2,6,1]=>0000000=>1111111=>1
[8,1,3,7,6,4,2,5]=>0000000=>1111111=>1
[5,3,1,7,8,6,2,4]=>0000000=>1111111=>1
[3,5,8,2,7,1,6,4]=>0000000=>1111111=>1
[6,2,8,5,3,1,7,4]=>0000000=>1111111=>1
[8,2,6,4,7,1,3,5]=>0000000=>1111111=>1
[3,4,2,8,5,1,7,6]=>0000000=>1111111=>1
[3,8,6,5,2,1,7,4]=>0000000=>1111111=>1
[8,3,7,4,2,5,6,1]=>0000000=>1111111=>1
[4,8,5,7,2,1,3,6]=>0000000=>1111111=>1
[3,4,1,8,2,6,7,5]=>0000000=>1111111=>1
[8,4,6,3,7,1,5,2]=>0000000=>1111111=>1
[6,8,3,4,1,5,7,2]=>0000000=>1111111=>1
[5,1,7,6,2,8,4,3]=>0000000=>1111111=>1
[6,8,2,5,7,4,1,3]=>0000000=>1111111=>1
[2,8,5,6,7,1,3,4]=>0000000=>1111111=>1
[2,5,7,6,3,1,8,4]=>0000000=>1111111=>1
[4,2,8,3,1,5,6,7]=>0000000=>1111111=>1
[2,5,7,3,8,4,6,1]=>0000000=>1111111=>1
[4,2,7,1,8,5,3,6]=>0000000=>1111111=>1
[4,2,1,8,7,5,6,3]=>0000000=>1111111=>1
[8,3,6,7,1,5,4,2]=>0000000=>1111111=>1
[1,3,7,5,8,6,4,2]=>1000000=>0111111=>1
[5,7,8,4,3,1,6,2]=>0000000=>1111111=>1
[2,7,4,5,8,3,6,1]=>0000000=>1111111=>1
[3,5,7,1,4,8,6,2]=>0000000=>1111111=>1
[7,2,8,5,1,4,6,3]=>0000000=>1111111=>1
[1,6,5,3,8,4,2,7]=>1000000=>0111111=>1
[5,7,4,8,3,6,2,1]=>0000000=>1111111=>1
[4,8,6,1,3,5,2,7]=>0000000=>1111111=>1
[1,8,3,2,4,7,5,6]=>1000000=>0111111=>1
[8,4,3,2,5,7,1,6]=>0000000=>1111111=>1
[3,6,4,8,2,5,7,1]=>0000000=>1111111=>1
[4,3,7,2,5,8,1,6]=>0000000=>1111111=>1
[3,2,4,7,8,5,6,1]=>0000000=>1111111=>1
[2,6,4,3,8,5,1,7]=>0000000=>1111111=>1
[3,8,2,1,6,4,5,7]=>0000000=>1111111=>1
[8,2,1,3,4,5,7,6]=>0000000=>1111111=>1
[4,6,8,3,2,1,5,7]=>0000000=>1111111=>1
[3,2,6,8,5,4,1,7]=>0000000=>1111111=>1
[7,3,8,2,5,4,1,6]=>0000000=>1111111=>1
[4,2,5,3,8,7,6,1]=>0000000=>1111111=>1
[4,8,2,6,5,3,1,7]=>0000000=>1111111=>1
[2,6,8,5,4,1,3,7]=>0000000=>1111111=>1
[3,1,8,6,5,4,2,7]=>0000000=>1111111=>1
[5,4,8,7,3,2,6,1]=>0000000=>1111111=>1
[6,4,8,3,7,2,5,1]=>0000000=>1111111=>1
[4,7,3,6,2,1,8,5]=>0000000=>1111111=>1
[5,4,3,7,1,8,2,6]=>0000000=>1111111=>1
[7,3,8,5,1,4,2,6]=>0000000=>1111111=>1
[5,4,8,7,6,2,1,3]=>0000000=>1111111=>1
[3,8,1,5,7,4,6,2]=>0000000=>1111111=>1
[4,8,5,7,3,1,6,2]=>0000000=>1111111=>1
[1,5,4,8,3,7,6,2]=>1000000=>0111111=>1
[4,8,3,6,7,1,5,2]=>0000000=>1111111=>1
[4,7,8,3,1,6,5,2]=>0000000=>1111111=>1
[8,7,5,3,6,4,2,1]=>0000000=>1111111=>1
[4,6,1,3,8,7,5,2]=>0000000=>1111111=>1
[6,8,2,1,7,4,5,3]=>0000000=>1111111=>1
[3,7,1,6,4,2,8,5]=>0000000=>1111111=>1
[3,1,2,7,5,6,8,4]=>0010000=>1101111=>2
[3,6,1,2,7,5,8,4]=>0000000=>1111111=>1
[3,7,6,2,5,8,1,4]=>0000000=>1111111=>1
[3,6,2,5,8,7,4,1]=>0000000=>1111111=>1
[8,5,2,3,6,7,4,1]=>0000000=>1111111=>1
[4,7,2,6,3,8,1,5]=>0000000=>1111111=>1
[6,3,2,4,8,7,5,1]=>0000000=>1111111=>1
[3,7,2,4,6,1,8,5]=>0000000=>1111111=>1
[5,3,7,2,8,1,4,6]=>0000000=>1111111=>1
[6,3,2,8,7,5,1,4]=>0000000=>1111111=>1
[7,3,8,2,6,5,1,4]=>0000000=>1111111=>1
[6,4,8,7,2,5,1,3]=>0000000=>1111111=>1
[2,5,4,8,1,7,6,3]=>0000000=>1111111=>1
[5,2,8,1,7,6,3,4]=>0000000=>1111111=>1
[6,2,1,3,8,7,5,4]=>0000000=>1111111=>1
[3,6,1,8,7,5,2,4]=>0000000=>1111111=>1
[5,6,1,2,8,7,4,3]=>0000000=>1111111=>1
[7,5,2,8,1,6,4,3]=>0000000=>1111111=>1
[2,7,6,8,1,5,4,3]=>0000000=>1111111=>1
[7,8,5,1,6,2,4,3]=>0000000=>1111111=>1
[7,4,8,6,1,2,5,3]=>0000000=>1111111=>1
[7,2,1,8,3,6,5,4]=>0000000=>1111111=>1
[5,8,7,1,6,4,3,2]=>0000000=>1111111=>1
[7,6,5,4,3,2,9,8,1]=>00000000=>11111111=>1
[10,7,6,5,4,3,2,1,9,8]=>000000000=>111111111=>1
[9,6,5,4,3,2,8,1,7]=>00000000=>11111111=>1
[9,7,5,4,3,2,1,8,6]=>00000000=>11111111=>1
[8,5,4,3,7,2,1,6]=>0000000=>1111111=>1
[6,5,4,8,3,2,7,1]=>0000000=>1111111=>1
[7,6,5,4,3,9,2,8,1]=>00000000=>11111111=>1
[7,6,4,3,2,8,5,1]=>0000000=>1111111=>1
[8,6,5,4,3,2,9,7,1]=>00000000=>11111111=>1
[8,7,6,5,4,3,2,10,9,1]=>000000000=>111111111=>1
[7,3,1,4,8,2,5,6]=>0000000=>1111111=>1
[7,4,1,2,5,8,3,6]=>0000000=>1111111=>1
[6,7,4,2,5,1,3,8]=>0000001=>1111110=>1
[5,7,2,4,6,8,1,3]=>0000000=>1111111=>1
[4,7,5,1,6,2,8,3]=>0000000=>1111111=>1
[5,7,4,6,3,1,8,2]=>0000000=>1111111=>1
[7,5,1,4,3,2,8,6]=>0000000=>1111111=>1
[8,6,4,2,3,7,5,1]=>0000000=>1111111=>1
[6,4,7,1,3,8,5,2]=>0000000=>1111111=>1
[5,4,2,7,3,1,6,8]=>0000001=>1111110=>1
[4,5,1,2,7,6,8,3]=>0000000=>1111111=>1
[5,4,6,8,3,1,2,7]=>0000000=>1111111=>1
[6,4,8,1,3,7,2,5]=>0000000=>1111111=>1
[4,6,1,3,8,5,2,7]=>0000000=>1111111=>1
[1,3,8,4,5,7,2,6]=>1000000=>0111111=>1
[2,6,7,4,5,3,1,8]=>0000001=>1111110=>1
[2,6,8,4,3,5,1,7]=>0000000=>1111111=>1
[1,3,7,4,2,8,5,6]=>1000000=>0111111=>1
[4,6,1,3,7,2,5,8]=>0000001=>1111110=>1
[7,5,8,6,2,1,3,4]=>0000000=>1111111=>1
[2,8,1,3,6,5,4,7]=>0000000=>1111111=>1
[2,8,7,3,5,4,1,6]=>0000000=>1111111=>1
[3,4,2,6,8,7,1,5]=>0000000=>1111111=>1
[7,4,2,3,6,1,8,5]=>0000000=>1111111=>1
[8,4,2,3,6,5,7,1]=>0000000=>1111111=>1
[7,3,8,4,1,2,6,5]=>0000000=>1111111=>1
[6,8,3,2,7,1,5,4]=>0000000=>1111111=>1
[2,8,5,6,3,7,1,4]=>0000000=>1111111=>1
[7,4,2,5,8,1,6,3]=>0000000=>1111111=>1
[2,7,8,3,4,5,1,6]=>0000000=>1111111=>1
[3,7,1,2,4,6,5,8]=>0000001=>1111110=>1
[7,5,6,8,2,1,4,3]=>0000000=>1111111=>1
[3,1,6,5,2,7,4,8]=>0000001=>1111110=>1
[2,8,6,5,3,4,1,7]=>0000000=>1111111=>1
[1,7,2,3,5,6,8,4]=>1000000=>0111111=>1
[3,7,4,2,1,5,6,8]=>0000001=>1111110=>1
[3,4,6,2,8,5,7,1]=>0000000=>1111111=>1
[4,2,1,7,5,8,3,6]=>0000000=>1111111=>1
[4,7,2,6,5,1,3,8]=>0000001=>1111110=>1
[3,7,4,1,2,5,8,6]=>0000000=>1111111=>1
[4,7,1,6,5,2,8,3]=>0000000=>1111111=>1
[4,7,3,6,5,1,8,2]=>0000000=>1111111=>1
[4,3,7,1,6,8,5,2]=>0000000=>1111111=>1
[4,2,1,7,5,6,8,3]=>0000000=>1111111=>1
[3,2,4,8,6,7,1,5]=>0000000=>1111111=>1
[4,2,6,8,7,3,1,5]=>0000000=>1111111=>1
[3,4,6,1,8,5,2,7]=>0000000=>1111111=>1
[4,1,6,7,5,8,2,3]=>0000000=>1111111=>1
[4,3,6,7,5,1,2,8]=>0000001=>1111110=>1
[4,3,7,1,6,8,2,5]=>0000000=>1111111=>1
[4,3,7,5,6,8,2,1]=>0000000=>1111111=>1
[4,1,7,3,6,5,2,8]=>0000001=>1111110=>1
[2,8,7,4,5,3,1,6]=>0000000=>1111111=>1
[2,8,7,4,3,5,1,6]=>0000000=>1111111=>1
[3,8,1,4,2,6,5,7]=>0000000=>1111111=>1
[4,1,7,3,6,2,5,8]=>0000001=>1111110=>1
[5,8,7,6,1,2,4,3]=>0000000=>1111111=>1
[5,8,7,6,2,1,3,4]=>0000000=>1111111=>1
[4,1,7,2,6,8,5,3]=>0000000=>1111111=>1
[4,2,7,3,6,1,8,5]=>0000000=>1111111=>1
[4,2,7,3,6,5,8,1]=>0000000=>1111111=>1
[3,8,2,4,5,6,7,1]=>0000000=>1111111=>1
[3,8,2,4,1,6,7,5]=>0000000=>1111111=>1
[3,8,5,6,2,4,1,7]=>0000000=>1111111=>1
[2,8,6,5,3,7,1,4]=>0000000=>1111111=>1
[3,8,6,5,1,4,7,2]=>0000000=>1111111=>1
[3,8,2,1,4,6,7,5]=>0000000=>1111111=>1
[3,8,2,5,4,6,7,1]=>0000000=>1111111=>1
[4,2,7,5,6,3,8,1]=>0000000=>1111111=>1
[4,2,7,5,6,1,8,3]=>0000000=>1111111=>1
[4,2,6,7,5,3,1,8]=>0000001=>1111110=>1
[3,2,6,1,4,5,8,7]=>0000010=>1111101=>2
[2,8,7,3,4,5,1,6]=>0000000=>1111111=>1
[3,8,1,2,4,6,5,7]=>0000000=>1111111=>1
[5,8,7,6,1,3,4,2]=>0000000=>1111111=>1
[5,8,7,6,2,3,4,1]=>0000000=>1111111=>1
[4,1,7,5,6,2,3,8]=>0000001=>1111110=>1
[3,8,1,5,2,6,4,7]=>0000000=>1111111=>1
[2,8,7,5,3,4,1,6]=>0000000=>1111111=>1
[2,8,7,5,4,3,1,6]=>0000000=>1111111=>1
[4,1,7,5,6,3,2,8]=>0000001=>1111110=>1
[5,8,7,6,1,3,2,4]=>0000000=>1111111=>1
[5,8,7,6,4,1,2,3]=>0000000=>1111111=>1
[7,4,3,5,2,8,1,6]=>0000000=>1111111=>1
[5,4,1,7,3,6,8,2]=>0000000=>1111111=>1
[3,4,7,6,2,5,8,1]=>0000000=>1111111=>1
[5,7,6,4,3,1,8,2]=>0000000=>1111111=>1
[5,7,6,3,1,4,8,2]=>0000000=>1111111=>1
[3,2,8,6,7,1,4,5]=>0000000=>1111111=>1
[4,8,3,6,5,2,1,7]=>0000000=>1111111=>1
[1,8,7,2,3,5,4,6]=>1000000=>0111111=>1
[1,8,7,2,5,3,4,6]=>1000000=>0111111=>1
[3,6,8,5,1,2,4,7]=>0000000=>1111111=>1
[7,1,2,8,3,5,6,4]=>0000000=>1111111=>1
[5,6,8,4,7,3,2,1]=>0000000=>1111111=>1
[6,4,7,8,5,2,1,3]=>0000000=>1111111=>1
[7,4,3,8,2,6,5,1]=>0000000=>1111111=>1
[8,7,1,3,5,4,6,2]=>0000000=>1111111=>1
[5,8,2,6,3,1,4,7]=>0000000=>1111111=>1
[8,1,7,2,4,5,3,6]=>0000000=>1111111=>1
[8,1,3,6,2,5,4,7]=>0000000=>1111111=>1
[7,2,1,6,3,5,4,8]=>0000001=>1111110=>1
[2,7,1,6,3,5,4,8]=>0000001=>1111110=>1
[2,7,1,5,4,3,6,8]=>0000001=>1111110=>1
[7,2,1,5,4,3,6,8]=>0000001=>1111110=>1
[8,1,3,5,4,2,6,7]=>0000000=>1111111=>1
[8,1,5,3,4,2,6,7]=>0000000=>1111111=>1
[8,1,5,6,2,3,7,4]=>0000000=>1111111=>1
[8,1,4,5,3,2,6,7]=>0000000=>1111111=>1
[8,1,4,3,5,2,6,7]=>0000000=>1111111=>1
[7,2,1,4,5,3,6,8]=>0000001=>1111110=>1
[2,7,1,4,5,3,6,8]=>0000001=>1111110=>1
[2,6,3,1,5,4,7,8]=>0000011=>1111100=>1
[6,3,2,1,5,4,7,8]=>0000011=>1111100=>1
[7,3,1,4,5,2,6,8]=>0000001=>1111110=>1
[7,3,1,5,4,2,6,8]=>0000001=>1111110=>1
[7,3,1,6,2,5,4,8]=>0000001=>1111110=>1
[3,7,1,6,2,5,4,8]=>0000001=>1111110=>1
[3,7,1,4,5,2,6,8]=>0000001=>1111110=>1
[3,6,2,1,5,4,7,8]=>0000011=>1111100=>1
[2,3,6,1,5,4,7,8]=>0000011=>1111100=>1
[3,5,2,4,1,6,7,8]=>0000111=>1111000=>1
[6,3,4,1,5,2,7,8]=>0000011=>1111100=>1
[6,2,4,1,5,3,7,8]=>0000011=>1111100=>1
[2,6,4,1,5,3,7,8]=>0000011=>1111100=>1
[2,6,5,1,3,7,4,8]=>0000001=>1111110=>1
[6,2,5,1,3,7,4,8]=>0000001=>1111110=>1
[6,5,2,1,3,7,4,8]=>0000001=>1111110=>1
[7,6,1,2,4,5,3,8]=>0000001=>1111110=>1
[6,7,1,2,8,3,5,4]=>0000000=>1111111=>1
[6,7,1,2,5,4,3,8]=>0000001=>1111110=>1
[5,6,2,1,3,7,4,8]=>0000001=>1111110=>1
[5,2,6,1,3,7,4,8]=>0000001=>1111110=>1
[2,4,6,1,5,3,7,8]=>0000011=>1111100=>1
[4,7,1,3,5,2,6,8]=>0000001=>1111110=>1
[4,7,1,5,3,2,6,8]=>0000001=>1111110=>1
[5,7,1,4,2,6,3,8]=>0000001=>1111110=>1
[5,7,1,6,2,3,8,4]=>0000000=>1111111=>1
[5,6,3,1,2,7,4,8]=>0000001=>1111110=>1
[4,2,5,3,1,6,7,8]=>0000111=>1111000=>1
[5,3,6,1,2,7,4,8]=>0000001=>1111110=>1
[3,4,6,1,5,2,7,8]=>0000011=>1111100=>1
[6,5,1,8,7,3,4,2]=>0000000=>1111111=>1
[8,2,7,5,4,1,3,6]=>0000000=>1111111=>1
[8,5,6,2,7,1,4,3]=>0000000=>1111111=>1
[7,6,1,5,3,8,4,2]=>0000000=>1111111=>1
[5,8,6,1,7,2,4,3]=>0000000=>1111111=>1
[5,8,7,3,2,6,4,1]=>0000000=>1111111=>1
[8,1,7,2,5,6,3,4]=>0000000=>1111111=>1
[4,8,1,5,2,6,7,3]=>0000000=>1111111=>1
[7,1,2,8,5,6,3,4]=>0000000=>1111111=>1
[8,7,2,1,5,6,3,4]=>0000000=>1111111=>1
[8,6,7,1,5,2,3,4]=>0000000=>1111111=>1
[6,1,7,8,5,2,3,4]=>0000000=>1111111=>1
[7,5,6,2,1,8,4,3]=>0000000=>1111111=>1
[8,7,5,2,1,6,4,3]=>0000000=>1111111=>1
[4,6,7,8,5,1,3,2]=>0000000=>1111111=>1
[4,6,8,1,5,3,7,2]=>0000000=>1111111=>1
[6,5,8,1,3,4,7,2]=>0000000=>1111111=>1
[5,6,8,3,1,2,7,4]=>0000000=>1111111=>1
[8,7,1,3,5,6,2,4]=>0000000=>1111111=>1
[6,7,8,3,5,1,2,4]=>0000000=>1111111=>1
[3,4,8,1,2,6,7,5]=>0000000=>1111111=>1
[5,8,2,4,3,6,7,1]=>0000000=>1111111=>1
[3,4,6,5,1,8,2,7]=>0000000=>1111111=>1
[2,6,3,5,1,8,7,4]=>0000000=>1111111=>1
[3,2,8,7,5,1,6,4]=>0000000=>1111111=>1
[3,8,5,1,6,7,2,4]=>0000000=>1111111=>1
[5,6,7,2,8,1,3,4]=>0000000=>1111111=>1
[6,2,1,5,3,8,7,4]=>0000000=>1111111=>1
[8,7,6,2,5,3,1,4]=>0000000=>1111111=>1
[4,7,6,8,3,2,5,1]=>0000000=>1111111=>1
[7,6,2,8,5,1,4,3]=>0000000=>1111111=>1
[8,1,3,7,5,2,6,4]=>0000000=>1111111=>1
[3,4,8,7,5,1,6,2]=>0000000=>1111111=>1
[6,3,8,5,7,4,1,2]=>0000000=>1111111=>1
[7,1,5,8,2,6,4,3]=>0000000=>1111111=>1
[3,6,8,2,4,1,7,5]=>0000000=>1111111=>1
[2,5,8,4,6,7,3,1]=>0000000=>1111111=>1
[2,8,5,7,4,1,3,6]=>0000000=>1111111=>1
[5,8,4,1,6,7,2,3]=>0000000=>1111111=>1
[6,2,7,3,8,4,1,5]=>0000000=>1111111=>1
[7,4,3,2,8,5,1,6]=>0000000=>1111111=>1
[5,3,2,8,4,6,1,7]=>0000000=>1111111=>1
[8,4,2,6,5,3,1,7]=>0000000=>1111111=>1
[7,4,2,5,3,1,6,8]=>0000001=>1111110=>1
[8,3,6,2,5,4,1,7]=>0000000=>1111111=>1
[5,4,8,3,2,6,1,7]=>0000000=>1111111=>1
[3,5,8,2,4,6,1,7]=>0000000=>1111111=>1
[6,4,7,8,2,3,1,5]=>0000000=>1111111=>1
[5,8,3,6,4,2,1,7]=>0000000=>1111111=>1
[4,8,6,2,5,3,1,7]=>0000000=>1111111=>1
[1,6,4,3,2,8,7,5]=>1000000=>0111111=>1
[1,5,3,2,8,4,7,6]=>1000000=>0111111=>1
[5,7,4,3,1,2,6,8]=>0000001=>1111110=>1
[2,8,7,3,5,1,4,6]=>0000000=>1111111=>1
[7,3,8,6,4,1,2,5]=>0000000=>1111111=>1
[6,1,2,7,3,8,5,4]=>0000000=>1111111=>1
[2,1,7,4,3,8,6,5]=>0100000=>1011111=>2
[6,1,4,3,8,2,7,5]=>0000000=>1111111=>1
[5,1,3,2,8,7,4,6]=>0000000=>1111111=>1
[1,8,4,2,7,6,5,3]=>1000000=>0111111=>1
[1,8,3,7,2,6,5,4]=>1000000=>0111111=>1
[5,1,4,8,3,7,2,6]=>0000000=>1111111=>1
[2,1,6,8,5,4,7,3]=>0100000=>1011111=>2
[6,1,5,7,8,2,4,3]=>0000000=>1111111=>1
[8,3,1,6,7,2,5,4]=>0000000=>1111111=>1
[7,4,8,6,1,3,2,5]=>0000000=>1111111=>1
[4,7,6,1,2,5,3,8]=>0000001=>1111110=>1
[3,7,6,1,5,2,4,8]=>0000001=>1111110=>1
[1,5,4,8,3,2,7,6]=>1000000=>0111111=>1
[7,3,6,1,2,5,4,8]=>0000001=>1111110=>1
[5,4,7,1,3,2,6,8]=>0000001=>1111110=>1
[5,7,4,8,2,1,3,6]=>0000000=>1111111=>1
[4,6,8,2,5,1,3,7]=>0000000=>1111111=>1
[7,4,6,2,1,5,3,8]=>0000001=>1111110=>1
[1,2,6,3,8,5,7,4]=>1100000=>0011111=>1
[1,5,2,6,8,4,7,3]=>1000000=>0111111=>1
[5,7,2,3,8,1,4,6]=>0000000=>1111111=>1
[6,4,7,5,8,1,2,3]=>0000000=>1111111=>1
[7,4,8,5,1,6,3,2]=>0000000=>1111111=>1
[5,8,3,6,1,7,4,2]=>0000000=>1111111=>1
[8,6,4,2,1,7,5,3]=>0000000=>1111111=>1
[7,4,2,1,5,8,6,3]=>0000000=>1111111=>1
[7,6,4,1,8,5,2,3]=>0000000=>1111111=>1
[1,6,4,8,7,5,3,2]=>1000000=>0111111=>1
[6,3,1,2,8,4,7,5]=>0000000=>1111111=>1
[7,5,1,3,2,8,6,4]=>0000000=>1111111=>1
[4,7,1,2,5,8,6,3]=>0000000=>1111111=>1
[6,8,4,1,2,7,5,3]=>0000000=>1111111=>1
[7,5,8,1,2,6,4,3]=>0000000=>1111111=>1
[7,4,8,1,6,3,5,2]=>0000000=>1111111=>1
[5,8,2,1,7,3,6,4]=>0000000=>1111111=>1
[3,6,1,8,2,4,7,5]=>0000000=>1111111=>1
[1,3,8,7,6,2,5,4]=>1000000=>0111111=>1
[5,4,1,8,7,3,2,6]=>0000000=>1111111=>1
[3,5,1,8,7,2,4,6]=>0000000=>1111111=>1
[4,6,1,8,3,7,2,5]=>0000000=>1111111=>1
[4,7,1,2,8,6,3,5]=>0000000=>1111111=>1
[5,8,4,1,7,6,2,3]=>0000000=>1111111=>1
[7,6,8,1,5,4,2,3]=>0000000=>1111111=>1
[8,6,1,7,5,4,3,2]=>0000000=>1111111=>1
[7,1,5,8,6,4,3,2]=>0000000=>1111111=>1
[5,1,8,7,3,6,4,2]=>0000000=>1111111=>1
[4,1,8,7,6,2,5,3]=>0000000=>1111111=>1
[3,1,8,7,6,5,2,4]=>0000000=>1111111=>1
[1,6,4,5,2,3,7,8]=>1000011=>0111100=>1
[1,7,4,5,2,3,6,8]=>1000001=>0111110=>1
[1,7,3,5,2,4,6,8]=>1000001=>0111110=>1
[1,6,3,5,2,4,7,8]=>1000011=>0111100=>1
[1,6,3,4,2,5,7,8]=>1000011=>0111100=>1
[1,7,3,4,2,5,6,8]=>1000001=>0111110=>1
[1,8,6,7,3,4,2,5]=>1000000=>0111111=>1
[1,8,5,7,3,4,2,6]=>1000000=>0111111=>1
[1,7,3,4,2,6,5,8]=>1000001=>0111110=>1
[1,5,2,8,4,7,3,6]=>1000000=>0111111=>1
[1,4,2,8,5,7,3,6]=>1000000=>0111111=>1
[1,7,3,5,2,6,4,8]=>1000001=>0111110=>1
[1,8,4,7,3,5,2,6]=>1000000=>0111111=>1
[1,7,3,6,2,5,4,8]=>1000001=>0111110=>1
[1,7,3,6,2,4,5,8]=>1000001=>0111110=>1
[1,7,4,6,2,3,5,8]=>1000001=>0111110=>1
[1,8,5,6,2,3,4,7]=>1000000=>0111111=>1
[1,8,5,6,2,4,3,7]=>1000000=>0111111=>1
[1,3,2,8,5,6,4,7]=>1010000=>0101111=>2
[1,4,2,8,5,6,3,7]=>1000000=>0111111=>1
[1,5,2,8,4,6,3,7]=>1000000=>0111111=>1
[1,6,2,8,4,5,3,7]=>1000000=>0111111=>1
[9,1,2,3,5,4,6,7,8]=>00000000=>11111111=>1
[8,1,2,4,5,3,6,7]=>0000000=>1111111=>1
[2,3,4,6,5,7,8,9,1]=>00000000=>11111111=>1
[10,1,2,3,4,6,5,7,8,9]=>000000000=>111111111=>1
[9,1,2,3,5,6,4,7,8]=>00000000=>11111111=>1
[2,3,4,7,5,6,8,9,1]=>00000000=>11111111=>1
[2,3,4,6,7,5,8,9,1]=>00000000=>11111111=>1
[2,3,4,5,7,6,8,9,10,1]=>000000000=>111111111=>1
[9,10,5,6,7,8,3,4,1,2]=>000000000=>111111111=>1
[5,8,9,6,7,10,3,4,1,2]=>000000000=>111111111=>1
[9,10,7,8,3,4,5,6,1,2]=>000000000=>111111111=>1
[9,10,3,6,7,4,5,8,1,2]=>000000000=>111111111=>1
[3,8,9,6,7,4,5,10,1,2]=>000000000=>111111111=>1
[3,6,7,8,9,4,5,10,1,2]=>000000000=>111111111=>1
[9,10,3,4,5,6,7,8,1,2]=>000000000=>111111111=>1
[3,8,9,4,5,6,7,10,1,2]=>000000000=>111111111=>1
[3,4,7,8,5,6,9,10,1,2]=>000000000=>111111111=>1
[7,8,9,10,5,6,1,2,3,4]=>000000000=>111111111=>1
[5,8,9,6,7,10,1,2,3,4]=>000000000=>111111111=>1
[9,10,7,8,1,4,5,2,3,6]=>000000000=>111111111=>1
[7,8,9,10,1,4,5,2,3,6]=>000000000=>111111111=>1
[9,10,1,6,7,4,5,2,3,8]=>000000000=>111111111=>1
[1,8,9,6,7,4,5,2,3,10]=>100000001=>011111110=>1
[1,6,7,8,9,4,5,2,3,10]=>100000001=>011111110=>1
[9,10,1,4,5,6,7,2,3,8]=>000000000=>111111111=>1
[1,8,9,4,5,6,7,2,3,10]=>100000001=>011111110=>1
[1,4,7,8,5,6,9,2,3,10]=>100000001=>011111110=>1
[1,4,5,6,7,8,9,2,3,10]=>100000001=>011111110=>1
[9,10,1,6,7,2,3,4,5,8]=>000000000=>111111111=>1
[1,8,9,6,7,2,3,4,5,10]=>100000001=>011111110=>1
[1,6,7,8,9,2,3,4,5,10]=>100000001=>011111110=>1
[9,10,1,2,5,6,3,4,7,8]=>000000000=>111111111=>1
[1,8,9,2,5,6,3,4,7,10]=>100000001=>011111110=>1
[1,2,7,8,5,6,3,4,9,10]=>110000011=>001111100=>1
[1,2,5,6,7,8,3,4,9,10]=>110000011=>001111100=>1
[1,8,9,2,3,4,5,6,7,10]=>100000001=>011111110=>1
[1,2,7,8,3,4,5,6,9,10]=>110000011=>001111100=>1
[1,2,3,6,7,4,5,8,9,10]=>111000111=>000111000=>1
[8,6,4,7,2,1,3,5]=>0000000=>1111111=>1
[1,6,4,7,2,8,3,5]=>1000000=>0111111=>1
[1,4,7,3,5,8,2,6]=>1000000=>0111111=>1
[8,4,6,2,3,5,1,7]=>0000000=>1111111=>1
[5,4,8,2,3,6,1,7]=>0000000=>1111111=>1
[7,4,8,5,2,3,1,6]=>0000000=>1111111=>1
[3,8,6,2,4,5,1,7]=>0000000=>1111111=>1
[4,8,6,2,3,5,1,7]=>0000000=>1111111=>1
[1,7,5,3,4,8,2,6]=>1000000=>0111111=>1
[1,7,6,4,8,2,3,5]=>1000000=>0111111=>1
[5,8,7,4,1,2,3,6]=>0000000=>1111111=>1
[6,8,5,3,4,1,2,7]=>0000000=>1111111=>1
[6,8,3,7,2,1,4,5]=>0000000=>1111111=>1
[8,5,1,6,3,7,2,4]=>0000000=>1111111=>1
[6,1,3,7,4,8,2,5]=>0000000=>1111111=>1
[4,1,7,3,5,8,2,6]=>0000000=>1111111=>1
[7,1,6,4,8,2,3,5]=>0000000=>1111111=>1
[1,8,5,7,2,3,4,6]=>1000000=>0111111=>1
[6,1,5,8,2,3,4,7]=>0000000=>1111111=>1
[5,1,7,3,8,2,4,6]=>0000000=>1111111=>1
[6,1,5,7,8,2,3,4]=>0000000=>1111111=>1
[7,4,8,6,1,2,3,5]=>0000000=>1111111=>1
[3,8,7,5,1,2,4,6]=>0000000=>1111111=>1
[3,7,6,1,2,4,5,8]=>0000001=>1111110=>1
[4,7,6,1,2,3,5,8]=>0000001=>1111110=>1
[1,6,5,8,2,3,4,7]=>1000000=>0111111=>1
[6,5,8,4,1,2,3,7]=>0000000=>1111111=>1
[8,5,7,4,1,2,3,6]=>0000000=>1111111=>1
[1,5,7,4,8,2,3,6]=>1000000=>0111111=>1
[7,6,4,8,2,1,3,5]=>0000000=>1111111=>1
[7,6,2,3,8,1,4,5]=>0000000=>1111111=>1
[7,4,8,5,1,6,2,3]=>0000000=>1111111=>1
[8,6,2,3,1,7,4,5]=>0000000=>1111111=>1
[8,6,4,1,2,7,3,5]=>0000000=>1111111=>1
[1,7,2,8,6,3,4,5]=>1000000=>0111111=>1
[7,6,1,3,8,2,4,5]=>0000000=>1111111=>1
[7,5,8,1,3,6,2,4]=>0000000=>1111111=>1
[5,4,1,8,2,3,6,7]=>0000000=>1111111=>1
[1,4,8,7,2,3,5,6]=>1000000=>0111111=>1
[1,5,8,7,2,3,4,6]=>1000000=>0111111=>1
[6,5,1,8,2,3,4,7]=>0000000=>1111111=>1
[5,7,1,3,8,2,4,6]=>0000000=>1111111=>1
[7,6,8,1,5,2,3,4]=>0000000=>1111111=>1
[7,1,5,8,6,2,3,4]=>0000000=>1111111=>1
[6,1,8,2,7,3,4,5]=>0000000=>1111111=>1
[4,1,8,7,2,3,5,6]=>0000000=>1111111=>1
[5,1,8,7,2,3,4,6]=>0000000=>1111111=>1
[1,8,7,6,4,5,3,2]=>1000000=>0111111=>1
[9,8,7,6,4,5,3,2,1,10]=>000000001=>111111110=>1
[1,8,7,3,6,5,4,2]=>1000000=>0111111=>1
[7,1,5,8,3,4,2,6]=>0000000=>1111111=>1
[7,1,4,3,2,5,6,8]=>0000001=>1111110=>1
[6,4,2,3,8,5,7,1]=>0000000=>1111111=>1
[6,4,2,7,5,8,3,1]=>0000000=>1111111=>1
[2,4,1,7,5,8,3,6]=>0000000=>1111111=>1
[7,1,4,6,5,2,3,8]=>0000001=>1111110=>1
[7,1,4,6,5,8,2,3]=>0000000=>1111111=>1
[7,1,4,6,3,8,2,5]=>0000000=>1111111=>1
[7,1,4,3,2,5,8,6]=>0000000=>1111111=>1
[7,1,4,6,5,2,8,3]=>0000000=>1111111=>1
[7,1,4,6,5,3,8,2]=>0000000=>1111111=>1
[7,1,4,6,5,3,2,8]=>0000001=>1111110=>1
[6,4,2,7,5,3,8,1]=>0000000=>1111111=>1
[3,4,7,2,6,8,5,1]=>0000000=>1111111=>1
[3,4,7,1,6,8,2,5]=>0000000=>1111111=>1
[3,4,7,1,6,8,5,2]=>0000000=>1111111=>1
[2,4,1,7,5,3,6,8]=>0000001=>1111110=>1
[3,4,1,7,8,6,2,5]=>0000000=>1111111=>1
[6,4,2,3,8,5,1,7]=>0000000=>1111111=>1
[6,4,2,7,5,8,1,3]=>0000000=>1111111=>1
[6,4,2,7,5,3,1,8]=>0000001=>1111110=>1
[3,4,7,2,6,8,1,5]=>0000000=>1111111=>1
[5,4,7,3,6,8,2,1]=>0000000=>1111111=>1
[3,4,7,2,6,5,1,8]=>0000001=>1111110=>1
[4,8,3,2,5,6,1,7]=>0000000=>1111111=>1
[4,8,7,3,5,1,2,6]=>0000000=>1111111=>1
[4,8,7,1,3,5,2,6]=>0000000=>1111111=>1
[4,8,3,1,2,6,5,7]=>0000000=>1111111=>1
[3,4,7,1,6,2,5,8]=>0000001=>1111110=>1
[3,4,7,1,6,2,8,5]=>0000000=>1111111=>1
[3,4,7,2,6,5,8,1]=>0000000=>1111111=>1
[4,8,3,1,2,6,7,5]=>0000000=>1111111=>1
[5,8,1,6,3,4,2,7]=>0000000=>1111111=>1
[6,8,5,1,3,7,2,4]=>0000000=>1111111=>1
[6,8,5,1,3,4,7,2]=>0000000=>1111111=>1
[5,8,3,4,2,6,7,1]=>0000000=>1111111=>1
[5,4,7,3,6,2,8,1]=>0000000=>1111111=>1
[5,4,7,2,6,1,8,3]=>0000000=>1111111=>1
[6,4,3,7,5,1,2,8]=>0000001=>1111110=>1
[6,4,3,7,5,1,8,2]=>0000000=>1111111=>1
[6,2,4,3,1,5,8,7]=>0000010=>1111101=>2
[3,8,7,4,1,5,2,6]=>0000000=>1111111=>1
[2,4,7,3,6,1,5,8]=>0000001=>1111110=>1
[5,8,3,2,1,6,4,7]=>0000000=>1111111=>1
[5,8,7,4,3,1,2,6]=>0000000=>1111111=>1
[5,4,7,3,6,2,1,8]=>0000001=>1111110=>1
[7,3,8,2,1,6,5,4]=>0000000=>1111111=>1
[7,4,3,8,5,2,1,6]=>0000000=>1111111=>1
[6,5,2,8,4,3,1,7]=>0000000=>1111111=>1
[4,3,2,8,6,5,1,7]=>0000000=>1111111=>1
[4,3,8,7,5,1,6,2]=>0000000=>1111111=>1
[3,2,5,8,6,1,4,7]=>0000000=>1111111=>1
[8,4,3,7,5,2,6,1]=>0000000=>1111111=>1
[4,3,7,8,5,1,2,6]=>0000000=>1111111=>1
[5,3,7,8,4,1,2,6]=>0000000=>1111111=>1
[6,2,5,8,3,1,4,7]=>0000000=>1111111=>1
[6,2,4,8,3,1,5,7]=>0000000=>1111111=>1
[5,2,3,8,4,1,6,7]=>0000000=>1111111=>1
[5,3,8,7,4,1,6,2]=>0000000=>1111111=>1
[5,3,2,8,6,4,1,7]=>0000000=>1111111=>1
[7,5,3,8,4,2,1,6]=>0000000=>1111111=>1
[7,5,4,3,8,2,6,1]=>0000000=>1111111=>1
[6,4,5,3,8,2,7,1]=>0000000=>1111111=>1
[6,5,8,3,4,2,7,1]=>0000000=>1111111=>1
[7,5,8,4,6,2,3,1]=>0000000=>1111111=>1
[7,4,8,3,6,2,5,1]=>0000000=>1111111=>1
[7,4,8,3,5,2,6,1]=>0000000=>1111111=>1
[6,4,8,3,5,2,7,1]=>0000000=>1111111=>1
[5,4,8,3,7,2,6,1]=>0000000=>1111111=>1
[5,4,6,3,8,2,7,1]=>0000000=>1111111=>1
[5,3,6,2,4,7,8,1]=>0000000=>1111111=>1
[5,3,7,2,4,6,8,1]=>0000000=>1111111=>1
[4,2,1,5,8,6,3,7]=>0000000=>1111111=>1
[3,2,1,8,5,4,6,7]=>0010000=>1101111=>2
[6,7,2,1,8,4,5,3]=>0000000=>1111111=>1
[4,3,1,6,7,8,5,2]=>0000000=>1111111=>1
[4,2,1,6,8,7,5,3]=>0000000=>1111111=>1
[4,2,1,6,8,5,3,7]=>0000000=>1111111=>1
[5,2,6,1,8,3,4,7]=>0000000=>1111111=>1
[4,2,1,7,8,6,3,5]=>0000000=>1111111=>1
[3,2,1,8,6,4,7,5]=>0010000=>1101111=>2
[3,2,1,8,6,4,5,7]=>0010000=>1101111=>2
[3,2,1,8,4,6,5,7]=>0010000=>1101111=>2
[3,2,1,8,4,6,7,5]=>0010000=>1101111=>2
[3,2,1,8,7,4,6,5]=>0010000=>1101111=>2
[4,2,1,7,8,3,5,6]=>0000000=>1111111=>1
[3,2,1,8,4,5,7,6]=>0010000=>1101111=>2
[7,5,2,8,6,3,4,1]=>0000000=>1111111=>1
[7,4,8,6,2,5,3,1]=>0000000=>1111111=>1
[7,3,8,6,2,4,5,1]=>0000000=>1111111=>1
[7,4,3,1,8,2,5,6]=>0000000=>1111111=>1
[7,4,2,8,5,6,1,3]=>0000000=>1111111=>1
[7,3,8,5,2,4,6,1]=>0000000=>1111111=>1
[7,3,8,4,5,6,2,1]=>0000000=>1111111=>1
[6,3,8,2,4,5,1,7]=>0000000=>1111111=>1
[6,3,8,2,5,7,4,1]=>0000000=>1111111=>1
[6,4,3,8,1,5,2,7]=>0000000=>1111111=>1
[6,3,7,8,2,4,1,5]=>0000000=>1111111=>1
[5,6,7,3,8,2,4,1]=>0000000=>1111111=>1
[5,4,7,2,6,8,1,3]=>0000000=>1111111=>1
[5,3,8,2,4,6,7,1]=>0000000=>1111111=>1
[6,3,8,2,4,7,5,1]=>0000000=>1111111=>1
[5,7,4,2,6,8,1,3]=>0000000=>1111111=>1
[6,4,8,2,7,5,1,3]=>0000000=>1111111=>1
[6,5,3,1,4,2,7,8]=>0000011=>1111100=>1
[5,7,4,2,6,1,3,8]=>0000001=>1111110=>1
[5,6,4,2,3,8,1,7]=>0000000=>1111111=>1
[5,6,3,7,8,2,4,1]=>0000000=>1111111=>1
[5,6,3,8,2,4,7,1]=>0000000=>1111111=>1
[6,3,7,2,4,5,1,8]=>0000001=>1111110=>1
[6,3,7,2,5,8,4,1]=>0000000=>1111111=>1
[5,3,6,8,2,4,7,1]=>0000000=>1111111=>1
[5,4,6,2,3,8,1,7]=>0000000=>1111111=>1
[5,3,6,7,8,2,4,1]=>0000000=>1111111=>1
[5,6,3,4,2,1,8,7]=>0000010=>1111101=>2
[5,6,4,2,1,3,8,7]=>0000010=>1111101=>2
[2,5,4,1,7,8,6,3]=>0000000=>1111111=>1
[2,8,6,3,5,4,1,7]=>0000000=>1111111=>1
[5,8,6,4,2,1,3,7]=>0000000=>1111111=>1
[4,3,8,5,7,6,2,1]=>0000000=>1111111=>1
[7,6,2,1,8,4,3,5]=>0000000=>1111111=>1
[8,4,2,1,5,6,3,7]=>0000000=>1111111=>1
[3,8,5,6,4,2,1,7]=>0000000=>1111111=>1
[3,8,6,4,2,1,5,7]=>0000000=>1111111=>1
[6,4,2,1,3,7,8,5]=>0000000=>1111111=>1
[6,3,7,8,4,2,1,5]=>0000000=>1111111=>1
[7,8,4,2,1,6,3,5]=>0000000=>1111111=>1
[8,5,7,6,2,1,4,3]=>0000000=>1111111=>1
[4,8,5,7,6,2,1,3]=>0000000=>1111111=>1
[2,7,5,8,4,3,6,1]=>0000000=>1111111=>1
[6,4,7,8,3,2,1,5]=>0000000=>1111111=>1
[7,6,5,8,4,3,2,1,9]=>00000001=>11111110=>1
[7,6,5,4,9,3,2,1,8]=>00000000=>11111111=>1
[7,6,5,4,3,8,2,1,9]=>00000001=>11111110=>1
[7,6,5,4,3,2,8,1,9]=>00000001=>11111110=>1
[6,9,8,5,4,3,2,1,7]=>00000000=>11111111=>1
[8,7,9,6,5,4,3,2,1,10]=>000000001=>111111110=>1
[7,5,8,9,4,3,2,1,6]=>00000000=>11111111=>1
[8,7,6,9,5,4,3,2,1,10]=>000000001=>111111110=>1
[6,4,3,7,5,2,1,8]=>0000001=>1111110=>1
[7,6,4,8,9,3,2,1,5]=>00000000=>11111111=>1
[8,7,6,5,10,4,3,2,1,9]=>000000000=>111111111=>1
[6,5,3,2,8,4,1,7]=>0000000=>1111111=>1
[7,6,5,3,9,8,2,1,4]=>00000000=>11111111=>1
[8,7,6,5,4,9,3,2,1,10]=>000000001=>111111110=>1
[6,5,2,7,8,4,1,3]=>0000000=>1111111=>1
[7,6,5,4,2,8,9,1,3]=>00000000=>11111111=>1
[8,7,6,5,4,3,9,2,1,10]=>000000001=>111111110=>1
[7,6,5,4,3,1,8,9,2]=>00000000=>11111111=>1
[7,10,9,6,5,4,3,2,1,8]=>000000000=>111111111=>1
[9,8,10,7,6,5,4,3,2,1,11]=>0000000001=>1111111110=>1
[6,5,8,7,4,3,2,1,9]=>00000001=>11111110=>1
[8,6,9,10,5,4,3,2,1,7]=>000000000=>111111111=>1
[9,8,7,10,6,5,4,3,2,1,11]=>0000000001=>1111111110=>1
[7,5,4,8,6,3,2,1,9]=>00000001=>11111110=>1
[5,9,8,7,4,3,2,1,6]=>00000000=>11111111=>1
[8,7,5,9,10,4,3,2,1,6]=>000000000=>111111111=>1
[6,4,3,2,5,8,1,7]=>0000000=>1111111=>1
[7,6,4,3,9,5,2,1,8]=>00000000=>11111111=>1
[7,4,8,9,6,3,2,1,5]=>00000000=>11111111=>1
[8,7,6,4,10,9,3,2,1,5]=>000000000=>111111111=>1
[9,8,7,6,5,10,4,3,2,1,11]=>0000000001=>1111111110=>1
[6,3,7,2,5,4,1,8]=>0000001=>1111110=>1
[7,6,5,3,2,8,4,1,9]=>00000001=>11111110=>1
[7,6,3,8,9,5,2,1,4]=>00000000=>11111111=>1
[8,7,6,5,3,9,10,2,1,4]=>000000000=>111111111=>1
[9,8,7,6,5,4,10,3,2,1,11]=>0000000001=>1111111110=>1
[7,6,5,4,2,1,8,3,9]=>00000001=>11111110=>1
[6,3,2,7,5,4,1,8]=>0000001=>1111110=>1
[7,6,5,2,9,8,4,1,3]=>00000000=>11111111=>1
[8,7,6,5,4,2,9,10,1,3]=>000000000=>111111111=>1
[7,6,5,4,1,8,9,3,2]=>00000000=>11111111=>1
[8,7,6,5,4,3,1,10,9,2]=>000000000=>111111111=>1
[9,8,7,6,5,4,3,2,10,1,11]=>0000000001=>1111111110=>1
[8,4,2,6,3,1,7,5]=>0000000=>1111111=>1
[1,5,3,7,4,2,8,6]=>1000000=>0111111=>1
[1,6,7,3,4,2,8,5]=>1000000=>0111111=>1
[8,6,5,2,3,1,7,4]=>0000000=>1111111=>1
[1,7,6,3,4,2,8,5]=>1000000=>0111111=>1
[1,8,6,3,2,5,7,4]=>1000000=>0111111=>1
[8,7,5,2,1,4,6,3]=>0000000=>1111111=>1
[7,8,5,2,1,4,6,3]=>0000000=>1111111=>1
[6,8,5,2,3,1,7,4]=>0000000=>1111111=>1
[5,8,6,2,3,1,7,4]=>0000000=>1111111=>1
[4,8,2,6,3,1,7,5]=>0000000=>1111111=>1
[3,2,8,6,4,1,7,5]=>0000000=>1111111=>1
[3,2,1,7,5,4,8,6]=>0010000=>1101111=>2
[4,1,3,7,5,2,8,6]=>0000000=>1111111=>1
[5,1,7,3,4,2,8,6]=>0000000=>1111111=>1
[7,1,6,3,2,5,8,4]=>0000000=>1111111=>1
[1,2,7,4,3,6,8,5]=>1100000=>0011111=>1
[6,1,8,2,4,5,7,3]=>0000000=>1111111=>1
[5,1,8,3,2,6,7,4]=>0000000=>1111111=>1
[3,2,8,7,1,5,6,4]=>0000000=>1111111=>1
[4,8,2,7,1,5,6,3]=>0000000=>1111111=>1
[5,8,7,2,1,4,6,3]=>0000000=>1111111=>1
[6,8,7,1,3,4,5,2]=>0000000=>1111111=>1
[7,8,6,1,3,4,5,2]=>0000000=>1111111=>1
[1,7,8,2,4,5,6,3]=>1000000=>0111111=>1
[8,6,7,1,3,4,5,2]=>0000000=>1111111=>1
[7,6,8,1,3,4,5,2]=>0000000=>1111111=>1
[6,5,8,2,3,1,7,4]=>0000000=>1111111=>1
[1,6,8,3,2,5,7,4]=>1000000=>0111111=>1
[1,5,3,8,2,6,7,4]=>1000000=>0111111=>1
[8,4,2,7,1,5,6,3]=>0000000=>1111111=>1
[7,4,2,8,1,5,6,3]=>0000000=>1111111=>1
[6,4,2,8,3,1,7,5]=>0000000=>1111111=>1
[5,4,2,3,8,1,7,6]=>0000000=>1111111=>1
[4,5,2,3,1,6,8,7]=>0000110=>1111001=>2
[7,4,2,1,3,6,8,5]=>0000000=>1111111=>1
[8,4,2,1,3,6,7,5]=>0000000=>1111111=>1
[1,5,3,2,4,7,8,6]=>1000100=>0111011=>2
[8,5,1,3,2,6,7,4]=>0000000=>1111111=>1
[5,6,1,3,4,2,8,7]=>0000010=>1111101=>2
[4,6,2,1,5,3,8,7]=>0000010=>1111101=>2
[4,7,2,1,3,6,8,5]=>0000000=>1111111=>1
[5,7,1,3,2,6,8,4]=>0000000=>1111111=>1
[6,7,1,2,4,5,8,3]=>0000000=>1111111=>1
[8,6,1,2,4,5,7,3]=>0000000=>1111111=>1
[1,8,2,3,5,6,7,4]=>1000000=>0111111=>1
[8,7,1,2,4,5,6,3]=>0000000=>1111111=>1
[7,8,1,2,4,5,6,3]=>0000000=>1111111=>1
[5,8,1,3,2,6,7,4]=>0000000=>1111111=>1
[4,8,2,1,3,6,7,5]=>0000000=>1111111=>1
[4,1,3,2,5,7,8,6]=>0001100=>1110011=>2
[5,1,2,4,3,7,8,6]=>0000100=>1111011=>2
[5,4,8,1,2,3,7,6]=>0000000=>1111111=>1
[1,4,7,6,3,2,5,8]=>1000001=>0111110=>1
[4,8,3,2,7,6,1,5]=>0000000=>1111111=>1
[4,3,8,2,7,1,6,5]=>0000000=>1111111=>1
[4,3,2,8,1,7,6,5]=>0000000=>1111111=>1
[4,1,8,7,3,2,5,6]=>0000000=>1111111=>1
[4,7,8,1,2,5,3,6]=>0000000=>1111111=>1
[2,3,6,7,4,1,8,5]=>0000000=>1111111=>1
[2,6,3,4,7,8,1,5]=>0000000=>1111111=>1
[3,1,7,8,4,2,5,6]=>0000000=>1111111=>1
[3,7,8,2,6,4,1,5]=>0000000=>1111111=>1
[3,7,2,4,8,6,1,5]=>0000000=>1111111=>1
[1,3,6,4,7,2,5,8]=>1000001=>0111110=>1
[4,7,1,5,8,2,3,6]=>0000000=>1111111=>1
[2,6,7,3,8,4,1,5]=>0000000=>1111111=>1
[3,4,6,7,8,5,1,2]=>0000000=>1111111=>1
[1,2,6,4,7,5,8,3]=>1100000=>0011111=>1
[3,1,7,5,4,2,6,8]=>0000001=>1111110=>1
[6,3,8,5,4,7,1,2]=>0000000=>1111111=>1
[1,6,2,5,4,7,8,3]=>1000000=>0111111=>1
[1,8,2,5,6,3,7,4]=>1000000=>0111111=>1
[1,2,6,4,8,5,7,3]=>1100000=>0011111=>1
[7,8,3,1,4,2,5,6]=>0000000=>1111111=>1
[4,8,1,5,2,3,6,7]=>0000000=>1111111=>1
[7,4,1,5,2,3,6,8]=>0000001=>1111110=>1
[5,6,1,8,4,3,2,7]=>0000000=>1111111=>1
[5,1,8,6,4,3,2,7]=>0000000=>1111111=>1
[5,1,6,3,8,7,2,4]=>0000000=>1111111=>1
[6,1,2,5,8,3,7,4]=>0000000=>1111111=>1
[6,1,8,7,4,3,2,5]=>0000000=>1111111=>1
[7,1,2,5,4,8,6,3]=>0000000=>1111111=>1
[1,2,7,5,8,3,6,4]=>1100000=>0011111=>1
[4,1,6,3,7,5,2,8]=>0000001=>1111110=>1
[1,3,6,7,8,5,2,4]=>1000000=>0111111=>1
[1,2,6,4,7,8,5,3]=>1100000=>0011111=>1
[4,1,6,3,7,8,2,5]=>0000000=>1111111=>1
[3,1,6,4,8,2,7,5]=>0000000=>1111111=>1
[7,8,4,1,6,3,2,5]=>0000000=>1111111=>1
[4,1,6,3,8,7,2,5]=>0000000=>1111111=>1
[7,5,1,8,4,3,2,6]=>0000000=>1111111=>1
[6,5,1,7,4,3,2,8]=>0000001=>1111110=>1
[4,1,8,5,2,3,7,6]=>0000000=>1111111=>1
[4,1,6,8,3,7,2,5]=>0000000=>1111111=>1
[5,4,6,1,3,8,2,7]=>0000000=>1111111=>1
[6,5,8,1,4,3,2,7]=>0000000=>1111111=>1
[1,3,5,7,4,6,8,2]=>1000000=>0111111=>1
[1,3,5,4,7,2,6,8]=>1000001=>0111110=>1
[1,3,5,4,7,8,2,6]=>1000000=>0111111=>1
[1,3,5,4,7,2,8,6]=>1000000=>0111111=>1
[1,3,5,7,8,4,2,6]=>1000000=>0111111=>1
[1,6,3,2,7,4,8,5]=>1000000=>0111111=>1
[3,5,1,6,2,8,7,4]=>0000000=>1111111=>1
[1,3,7,2,5,4,8,6]=>1000000=>0111111=>1
[1,3,7,5,2,4,8,6]=>1000000=>0111111=>1
[2,5,7,4,3,8,1,6]=>0000000=>1111111=>1
[2,5,3,7,4,8,1,6]=>0000000=>1111111=>1
[3,2,6,7,8,1,5,4]=>0000000=>1111111=>1
[3,5,2,7,8,4,1,6]=>0000000=>1111111=>1
[1,5,7,4,8,3,2,6]=>1000000=>0111111=>1
[3,5,2,6,8,4,7,1]=>0000000=>1111111=>1
[2,5,7,4,3,8,6,1]=>0000000=>1111111=>1
[1,5,7,2,4,8,6,3]=>1000000=>0111111=>1
[4,6,3,7,2,8,5,1]=>0000000=>1111111=>1
[1,4,7,3,8,6,2,5]=>1000000=>0111111=>1
[5,1,6,8,2,4,3,7]=>0000000=>1111111=>1
[5,3,7,8,2,4,1,6]=>0000000=>1111111=>1
[8,5,3,7,2,4,1,6]=>0000000=>1111111=>1
[8,2,4,7,3,1,5,6]=>0000000=>1111111=>1
[2,4,7,8,3,1,5,6]=>0000000=>1111111=>1
[6,3,1,5,8,2,4,7]=>0000000=>1111111=>1
[6,5,3,4,2,8,1,7]=>0000000=>1111111=>1
[5,2,4,3,8,1,6,7]=>0000000=>1111111=>1
[3,2,4,8,1,5,6,7]=>0000000=>1111111=>1
[3,2,4,6,8,1,5,7]=>0000000=>1111111=>1
[8,1,5,7,3,2,4,6]=>0000000=>1111111=>1
[8,4,6,7,2,3,1,5]=>0000000=>1111111=>1
[4,6,7,8,2,3,1,5]=>0000000=>1111111=>1
[7,4,6,8,2,3,1,5]=>0000000=>1111111=>1
[7,2,4,8,3,1,5,6]=>0000000=>1111111=>1
[5,3,8,7,2,4,1,6]=>0000000=>1111111=>1
[2,4,8,7,3,1,5,6]=>0000000=>1111111=>1
[4,6,8,7,2,3,1,5]=>0000000=>1111111=>1
[8,7,4,6,2,3,1,5]=>0000000=>1111111=>1
[5,6,8,7,2,3,1,4]=>0000000=>1111111=>1
[6,4,8,7,2,3,1,5]=>0000000=>1111111=>1
[3,1,7,4,2,8,6,5]=>0000000=>1111111=>1
[3,2,8,4,1,7,6,5]=>0000000=>1111111=>1
[7,6,4,8,2,3,1,5]=>0000000=>1111111=>1
[5,7,6,8,2,3,1,4]=>0000000=>1111111=>1
[4,7,6,8,2,3,1,5]=>0000000=>1111111=>1
[8,6,4,7,2,3,1,5]=>0000000=>1111111=>1
[8,2,3,7,4,1,6,5]=>0000000=>1111111=>1
[2,3,7,8,4,1,6,5]=>0000000=>1111111=>1
[3,7,4,8,2,5,1,6]=>0000000=>1111111=>1
[2,3,7,4,1,6,8,5]=>0000000=>1111111=>1
[8,1,6,4,2,3,7,5]=>0000000=>1111111=>1
[4,7,8,6,2,3,1,5]=>0000000=>1111111=>1
[2,4,7,3,1,5,8,6]=>0000000=>1111111=>1
[6,3,1,7,4,2,8,5]=>0000000=>1111111=>1
[8,5,7,6,2,3,1,4]=>0000000=>1111111=>1
[7,5,8,6,2,3,1,4]=>0000000=>1111111=>1
[7,1,6,4,2,3,8,5]=>0000000=>1111111=>1
[3,1,7,6,4,2,8,5]=>0000000=>1111111=>1
[4,8,7,6,2,3,1,5]=>0000000=>1111111=>1
[6,8,7,5,2,3,1,4]=>0000000=>1111111=>1
[4,3,6,1,5,8,7,2]=>0000000=>1111111=>1
[4,3,6,5,1,8,7,2]=>0000000=>1111111=>1
[4,6,3,5,1,8,7,2]=>0000000=>1111111=>1
[4,6,3,1,5,8,7,2]=>0000000=>1111111=>1
[4,1,6,5,3,8,7,2]=>0000000=>1111111=>1
[4,6,1,5,3,8,7,2]=>0000000=>1111111=>1
[2,6,5,3,1,8,7,4]=>0000000=>1111111=>1
[2,6,5,1,8,7,3,4]=>0000000=>1111111=>1
[2,6,5,8,1,7,3,4]=>0000000=>1111111=>1
[2,6,5,8,1,3,7,4]=>0000000=>1111111=>1
[2,6,5,8,3,1,7,4]=>0000000=>1111111=>1
[2,6,5,3,8,1,7,4]=>0000000=>1111111=>1
[4,6,1,5,8,3,7,2]=>0000000=>1111111=>1
[4,1,6,5,8,3,7,2]=>0000000=>1111111=>1
[1,4,6,5,8,3,7,2]=>1000000=>0111111=>1
[4,1,6,5,8,7,3,2]=>0000000=>1111111=>1
[2,6,5,3,8,7,1,4]=>0000000=>1111111=>1
[6,4,3,8,7,1,5,2]=>0000000=>1111111=>1
[6,4,8,3,7,1,5,2]=>0000000=>1111111=>1
[2,6,8,5,3,7,1,4]=>0000000=>1111111=>1
[4,6,8,1,5,7,3,2]=>0000000=>1111111=>1
[4,6,1,8,5,7,3,2]=>0000000=>1111111=>1
[4,1,6,8,5,7,3,2]=>0000000=>1111111=>1
[1,4,6,8,5,7,3,2]=>1000000=>0111111=>1
[1,4,6,8,5,3,7,2]=>1000000=>0111111=>1
[4,6,1,8,5,3,7,2]=>0000000=>1111111=>1
[2,6,8,5,3,1,7,4]=>0000000=>1111111=>1
[2,6,8,5,1,7,3,4]=>0000000=>1111111=>1
[4,6,8,3,5,1,7,2]=>0000000=>1111111=>1
[4,6,8,3,1,5,7,2]=>0000000=>1111111=>1
[4,6,3,1,8,5,7,2]=>0000000=>1111111=>1
[4,6,3,8,1,5,7,2]=>0000000=>1111111=>1
[4,6,3,8,5,7,1,2]=>0000000=>1111111=>1
[4,3,6,8,1,5,7,2]=>0000000=>1111111=>1
[4,3,6,1,8,5,7,2]=>0000000=>1111111=>1
[4,3,1,6,8,5,7,2]=>0000000=>1111111=>1
[4,1,3,6,8,7,5,2]=>0000000=>1111111=>1
[4,3,6,1,8,7,5,2]=>0000000=>1111111=>1
[4,3,6,8,1,7,5,2]=>0000000=>1111111=>1
[6,5,2,8,7,3,1,4]=>0000000=>1111111=>1
[6,5,2,8,7,1,3,4]=>0000000=>1111111=>1
[6,2,5,8,7,1,3,4]=>0000000=>1111111=>1
[6,2,5,8,7,3,1,4]=>0000000=>1111111=>1
[4,6,3,8,1,7,5,2]=>0000000=>1111111=>1
[4,6,3,1,8,7,5,2]=>0000000=>1111111=>1
[4,1,6,3,8,7,5,2]=>0000000=>1111111=>1
[1,4,6,3,8,7,5,2]=>1000000=>0111111=>1
[4,1,6,8,3,7,5,2]=>0000000=>1111111=>1
[4,6,1,8,3,7,5,2]=>0000000=>1111111=>1
[4,6,8,1,3,7,5,2]=>0000000=>1111111=>1
[6,2,8,5,7,3,1,4]=>0000000=>1111111=>1
[6,2,8,5,7,1,3,4]=>0000000=>1111111=>1
[2,4,8,7,1,5,3,6]=>0000000=>1111111=>1
[4,2,8,7,5,3,1,6]=>0000000=>1111111=>1
[6,4,1,8,7,5,3,2]=>0000000=>1111111=>1
[6,1,4,8,7,5,3,2]=>0000000=>1111111=>1
[1,6,4,8,7,3,5,2]=>1000000=>0111111=>1
[6,4,1,8,7,3,5,2]=>0000000=>1111111=>1
[4,2,8,7,5,1,3,6]=>0000000=>1111111=>1
[2,4,8,7,3,5,1,6]=>0000000=>1111111=>1
[2,3,4,5,6,8,9,7,1]=>00000000=>11111111=>1
[2,3,4,7,8,5,6,1]=>0000000=>1111111=>1
[2,3,7,1,4,8,6,5]=>0000000=>1111111=>1
[1,5,3,2,6,4,7,8]=>1000011=>0111100=>1
[1,7,3,2,8,5,4,6]=>1000000=>0111111=>1
[1,3,2,7,5,4,8,6]=>1010000=>0101111=>2
[1,6,2,8,5,3,4,7]=>1000000=>0111111=>1
[5,3,2,7,4,6,1,8]=>0000001=>1111110=>1
[1,5,2,6,8,4,3,7]=>1000000=>0111111=>1
[1,5,7,2,8,4,3,6]=>1000000=>0111111=>1
[2,3,1,8,4,5,7,6]=>0010000=>1101111=>2
[7,8,1,4,3,5,2,6]=>0000000=>1111111=>1
[6,1,2,3,4,8,7,5]=>0000000=>1111111=>1
[8,3,2,1,4,5,7,6]=>0000000=>1111111=>1
[8,4,2,5,3,1,6,7]=>0000000=>1111111=>1
[2,4,7,8,1,5,3,6]=>0000000=>1111111=>1
[6,1,2,8,5,3,4,7]=>0000000=>1111111=>1
[7,1,8,3,5,4,2,6]=>0000000=>1111111=>1
[6,8,1,3,4,7,2,5]=>0000000=>1111111=>1
[1,6,2,3,4,8,7,5]=>1000000=>0111111=>1
[7,6,2,3,4,1,8,5]=>0000000=>1111111=>1
[8,1,7,3,5,4,2,6]=>0000000=>1111111=>1
[6,7,2,3,4,1,8,5]=>0000000=>1111111=>1
[7,6,2,3,4,8,1,5]=>0000000=>1111111=>1
[6,3,4,8,7,5,1,2]=>0000000=>1111111=>1
[4,8,7,3,5,6,1,2]=>0000000=>1111111=>1
[4,8,7,5,3,6,1,2]=>0000000=>1111111=>1
[5,8,7,3,4,6,1,2]=>0000000=>1111111=>1
[5,8,4,2,1,6,7,3]=>0000000=>1111111=>1
[5,8,4,1,2,6,7,3]=>0000000=>1111111=>1
[5,3,7,2,6,1,8,4]=>0000000=>1111111=>1
[5,2,8,1,6,3,7,4]=>0000000=>1111111=>1
[5,8,2,1,4,7,6,3]=>0000000=>1111111=>1
[4,8,2,5,1,7,6,3]=>0000000=>1111111=>1
[7,8,4,1,2,6,5,3]=>0000000=>1111111=>1
[4,8,1,5,2,7,6,3]=>0000000=>1111111=>1
[5,8,1,2,4,7,6,3]=>0000000=>1111111=>1
[5,2,8,3,6,7,1,4]=>0000000=>1111111=>1
[3,8,7,6,2,4,1,5]=>0000000=>1111111=>1
[2,8,7,6,4,1,3,5]=>0000000=>1111111=>1
[7,8,2,6,5,1,3,4]=>0000000=>1111111=>1
[1,8,7,6,4,2,3,5]=>1000000=>0111111=>1
[2,8,7,6,3,1,4,5]=>0000000=>1111111=>1
[1,8,7,6,2,4,3,5]=>1000000=>0111111=>1
[1,8,7,6,3,4,2,5]=>1000000=>0111111=>1
[2,8,1,4,5,6,7,3]=>0000000=>1111111=>1
[2,1,7,3,6,5,8,4]=>0100000=>1011111=>2
[3,1,7,2,6,5,8,4]=>0000000=>1111111=>1
[3,2,7,1,6,5,8,4]=>0000000=>1111111=>1
[6,1,2,8,5,7,3,4]=>0000000=>1111111=>1
[6,2,1,8,5,7,3,4]=>0000000=>1111111=>1
[6,3,1,8,5,7,2,4]=>0000000=>1111111=>1
[6,4,2,1,7,5,8,3]=>0000000=>1111111=>1
[6,1,3,8,5,2,7,4]=>0000000=>1111111=>1
[2,3,7,1,6,8,5,4]=>0000000=>1111111=>1
[1,3,7,2,6,8,5,4]=>1000000=>0111111=>1
[7,8,2,6,5,3,1,4]=>0000000=>1111111=>1
[3,2,6,7,5,8,1,4]=>0000000=>1111111=>1
[1,2,7,5,6,3,8,4]=>1100000=>0011111=>1
[2,8,7,6,4,3,1,5]=>0000000=>1111111=>1
[3,8,7,6,1,2,5,4]=>0000000=>1111111=>1
[3,8,7,6,2,1,5,4]=>0000000=>1111111=>1
[4,8,7,6,2,1,3,5]=>0000000=>1111111=>1
[4,8,7,6,1,3,2,5]=>0000000=>1111111=>1
[3,8,7,6,4,1,2,5]=>0000000=>1111111=>1
[7,8,3,6,5,1,2,4]=>0000000=>1111111=>1
[2,3,7,5,6,8,1,4]=>0000000=>1111111=>1
[3,8,7,6,4,2,1,5]=>0000000=>1111111=>1
[4,6,1,2,5,8,3,7]=>0000000=>1111111=>1
[1,3,6,5,7,8,2,4]=>1000000=>0111111=>1
[7,4,8,5,3,1,6,2]=>0000000=>1111111=>1
[7,1,4,2,3,6,8,5]=>0000000=>1111111=>1
[6,1,2,7,5,3,8,4]=>0000000=>1111111=>1
[7,3,2,8,6,4,1,5]=>0000000=>1111111=>1
[2,7,8,4,6,3,1,5]=>0000000=>1111111=>1
[8,1,6,3,5,7,2,4]=>0000000=>1111111=>1
[8,3,2,6,4,7,1,5]=>0000000=>1111111=>1
[2,3,8,7,6,5,1,4]=>0000000=>1111111=>1
[1,2,8,7,3,6,5,4]=>1100000=>0011111=>1
[4,2,8,7,3,6,1,5]=>0000000=>1111111=>1
[4,5,8,7,1,2,6,3]=>0000000=>1111111=>1
[1,5,8,7,3,2,6,4]=>1000000=>0111111=>1
[4,5,8,7,3,2,1,6]=>0000000=>1111111=>1
[2,6,8,1,7,5,4,3]=>0000000=>1111111=>1
[3,6,8,4,7,2,1,5]=>0000000=>1111111=>1
[2,5,8,3,7,6,1,4]=>0000000=>1111111=>1
[3,2,8,4,7,6,1,5]=>0000000=>1111111=>1
[1,5,8,3,7,2,6,4]=>1000000=>0111111=>1
[3,5,8,4,7,2,1,6]=>0000000=>1111111=>1
[5,6,8,2,3,7,1,4]=>0000000=>1111111=>1
[1,6,8,4,2,7,5,3]=>1000000=>0111111=>1
[1,5,8,4,2,7,6,3]=>1000000=>0111111=>1
[1,5,8,2,3,7,6,4]=>1000000=>0111111=>1
[2,1,8,4,3,7,6,5]=>0100000=>1011111=>2
[2,5,8,4,3,7,1,6]=>0000000=>1111111=>1
[5,6,8,4,1,2,7,3]=>0000000=>1111111=>1
[5,6,8,1,3,2,7,4]=>0000000=>1111111=>1
[1,6,8,4,3,2,7,5]=>1000000=>0111111=>1
[5,6,8,4,3,2,1,7]=>0000000=>1111111=>1
[7,1,2,8,6,5,4,3]=>0000000=>1111111=>1
[7,1,4,8,6,2,5,3]=>0000000=>1111111=>1
[7,3,1,8,6,2,5,4]=>0000000=>1111111=>1
[7,2,4,8,3,6,1,5]=>0000000=>1111111=>1
[7,1,4,8,3,2,6,5]=>0000000=>1111111=>1
[7,4,5,8,3,2,1,6]=>0000000=>1111111=>1
[1,6,2,8,7,5,4,3]=>1000000=>0111111=>1
[1,6,4,8,7,2,5,3]=>1000000=>0111111=>1
[3,6,4,8,7,2,1,5]=>0000000=>1111111=>1
[3,2,5,8,7,6,1,4]=>0000000=>1111111=>1
[3,2,4,8,7,6,1,5]=>0000000=>1111111=>1
[3,1,5,8,7,2,6,4]=>0000000=>1111111=>1
[3,1,4,8,7,2,6,5]=>0000000=>1111111=>1
[1,6,4,8,2,7,5,3]=>1000000=>0111111=>1
[1,4,5,8,2,7,6,3]=>1000000=>0111111=>1
[2,4,5,8,3,7,1,6]=>0000000=>1111111=>1
[4,6,5,8,1,2,7,3]=>0000000=>1111111=>1
[1,6,4,8,3,2,7,5]=>1000000=>0111111=>1
[1,4,5,8,3,2,7,6]=>1000000=>0111111=>1
[7,6,1,4,8,2,5,3]=>0000000=>1111111=>1
[7,6,1,3,8,2,5,4]=>0000000=>1111111=>1
[7,6,3,4,8,2,1,5]=>0000000=>1111111=>1
[7,2,5,1,8,6,4,3]=>0000000=>1111111=>1
[7,2,5,3,8,6,1,4]=>0000000=>1111111=>1
[7,2,1,4,8,6,5,3]=>0000000=>1111111=>1
[7,2,1,3,8,6,5,4]=>0000000=>1111111=>1
[7,2,3,4,8,6,1,5]=>0000000=>1111111=>1
[7,3,5,4,8,2,1,6]=>0000000=>1111111=>1
[2,6,5,1,8,7,4,3]=>0000000=>1111111=>1
[2,3,5,4,8,7,1,6]=>0000000=>1111111=>1
[1,6,5,4,8,2,7,3]=>1000000=>0111111=>1
[1,6,5,3,8,2,7,4]=>1000000=>0111111=>1
[1,6,3,4,8,2,7,5]=>1000000=>0111111=>1
[1,3,5,4,8,2,7,6]=>1000000=>0111111=>1
[3,6,5,4,8,2,1,7]=>0000000=>1111111=>1
[7,6,5,2,3,8,1,4]=>0000000=>1111111=>1
[7,6,1,4,2,8,5,3]=>0000000=>1111111=>1
[7,6,1,2,3,8,5,4]=>0000000=>1111111=>1
[7,6,2,4,3,8,1,5]=>0000000=>1111111=>1
[7,1,5,4,2,8,6,3]=>0000000=>1111111=>1
[7,1,5,2,3,8,6,4]=>0000000=>1111111=>1
[7,1,2,4,3,8,6,5]=>0000000=>1111111=>1
[2,6,5,4,3,8,1,7]=>0000000=>1111111=>1
[7,6,1,4,3,2,8,5]=>0000000=>1111111=>1
[7,1,5,4,3,2,8,6]=>0000000=>1111111=>1
[3,4,2,6,7,8,1,5]=>0000000=>1111111=>1
[3,1,4,2,6,8,7,5]=>0001000=>1110111=>2
[8,3,4,2,6,1,7,5]=>0000000=>1111111=>1
[2,6,7,3,5,4,1,8]=>0000001=>1111110=>1
[2,7,8,3,5,4,1,6]=>0000000=>1111111=>1
[2,6,8,3,5,4,1,7]=>0000000=>1111111=>1
[4,7,1,2,8,5,3,6]=>0000000=>1111111=>1
[4,8,1,2,7,5,3,6]=>0000000=>1111111=>1
[2,1,6,3,7,5,4,8]=>0100001=>1011110=>2
[2,7,1,3,6,8,4,5]=>0000000=>1111111=>1
[6,7,3,2,8,1,4,5]=>0000000=>1111111=>1
[7,3,4,2,6,1,8,5]=>0000000=>1111111=>1
[7,4,1,2,8,5,3,6]=>0000000=>1111111=>1
[8,7,4,2,1,5,3,6]=>0000000=>1111111=>1
[7,4,1,2,6,5,3,8]=>0000001=>1111110=>1
[7,4,3,1,5,6,8,2]=>0000000=>1111111=>1
[6,7,4,1,5,8,3,2]=>0000000=>1111111=>1
[4,7,5,1,6,8,3,2]=>0000000=>1111111=>1
[4,5,3,1,7,6,8,2]=>0000000=>1111111=>1
[4,6,1,2,7,5,3,8]=>0000001=>1111110=>1
[2,7,1,3,6,5,4,8]=>0000001=>1111110=>1
[4,1,8,2,6,5,3,7]=>0000000=>1111111=>1
[4,6,1,2,8,5,3,7]=>0000000=>1111111=>1
[8,4,3,1,5,6,7,2]=>0000000=>1111111=>1
[4,5,3,1,8,6,7,2]=>0000000=>1111111=>1
[4,8,5,6,3,1,7,2]=>0000000=>1111111=>1
[5,1,3,4,8,6,7,2]=>0000000=>1111111=>1
[5,4,3,8,1,6,7,2]=>0000000=>1111111=>1
[8,5,3,4,1,6,7,2]=>0000000=>1111111=>1
[6,4,8,2,1,5,3,7]=>0000000=>1111111=>1
[6,7,3,2,5,1,4,8]=>0000001=>1111110=>1
[6,8,3,2,5,1,4,7]=>0000000=>1111111=>1
[5,7,1,4,6,8,3,2]=>0000000=>1111111=>1
[5,1,3,4,7,6,8,2]=>0000000=>1111111=>1
[6,1,4,2,7,5,3,8]=>0000001=>1111110=>1
[5,4,3,7,1,6,8,2]=>0000000=>1111111=>1
[6,7,5,4,1,8,3,2]=>0000000=>1111111=>1
[7,6,4,2,1,5,3,8]=>0000001=>1111110=>1
[8,2,7,6,5,4,1,3]=>0000000=>1111111=>1
[7,2,8,6,5,4,3,1]=>0000000=>1111111=>1
[8,1,9,7,6,5,4,3,2]=>00000000=>11111111=>1
[2,10,9,8,7,6,5,4,1,3]=>000000000=>111111111=>1
[9,2,8,7,6,5,4,1,3]=>00000000=>11111111=>1
[3,9,8,7,6,5,4,1,2]=>00000000=>11111111=>1
[8,7,2,6,5,4,1,3]=>0000000=>1111111=>1
[3,2,8,7,6,5,1,4]=>0000000=>1111111=>1
[4,8,7,6,5,3,1,2]=>0000000=>1111111=>1
[7,8,6,1,5,4,3,2]=>0000000=>1111111=>1
[8,9,1,7,6,5,4,3,2]=>00000000=>11111111=>1
[7,3,8,6,5,4,2,1]=>0000000=>1111111=>1
[8,2,9,7,6,5,4,3,1]=>00000000=>11111111=>1
[9,1,10,8,7,6,5,4,3,2]=>000000000=>111111111=>1
[4,8,5,7,6,3,2,1]=>0000000=>1111111=>1
[8,5,6,1,3,2,4,7]=>0000000=>1111111=>1
[8,6,1,5,3,2,4,7]=>0000000=>1111111=>1
[7,8,1,5,3,2,4,6]=>0000000=>1111111=>1
[8,1,7,5,3,2,4,6]=>0000000=>1111111=>1
[8,6,1,4,5,2,3,7]=>0000000=>1111111=>1
[8,6,3,1,5,2,4,7]=>0000000=>1111111=>1
[8,4,6,1,5,2,3,7]=>0000000=>1111111=>1
[8,6,2,1,5,4,3,7]=>0000000=>1111111=>1
[8,5,2,6,1,4,3,7]=>0000000=>1111111=>1
[8,5,2,1,7,4,3,6]=>0000000=>1111111=>1
[7,8,2,1,5,4,3,6]=>0000000=>1111111=>1
[7,8,3,1,5,2,4,6]=>0000000=>1111111=>1
[8,2,7,5,1,3,4,6]=>0000000=>1111111=>1
[8,4,1,7,5,2,3,6]=>0000000=>1111111=>1
[8,2,7,1,5,4,3,6]=>0000000=>1111111=>1
[8,2,6,1,7,4,3,5]=>0000000=>1111111=>1
[8,1,7,4,3,2,6,5]=>0000000=>1111111=>1
[8,1,5,7,3,2,6,4]=>0000000=>1111111=>1
[5,7,8,1,3,2,6,4]=>0000000=>1111111=>1
[8,2,6,1,5,7,3,4]=>0000000=>1111111=>1
[5,8,1,6,7,2,3,4]=>0000000=>1111111=>1
[5,7,6,1,8,2,3,4]=>0000000=>1111111=>1
[6,7,2,5,1,8,3,4]=>0000000=>1111111=>1
[7,5,1,6,8,2,3,4]=>0000000=>1111111=>1
[6,5,7,1,8,2,3,4]=>0000000=>1111111=>1
[6,7,3,8,1,2,4,5]=>0000000=>1111111=>1
[7,5,4,1,8,2,3,6]=>0000000=>1111111=>1
[7,6,1,4,8,2,3,5]=>0000000=>1111111=>1
[8,1,6,4,7,2,3,5]=>0000000=>1111111=>1
[7,5,8,1,3,2,4,6]=>0000000=>1111111=>1
[7,8,4,1,3,2,5,6]=>0000000=>1111111=>1
[8,3,7,4,1,2,5,6]=>0000000=>1111111=>1
[8,5,1,7,3,2,4,6]=>0000000=>1111111=>1
[6,8,1,7,3,2,4,5]=>0000000=>1111111=>1
[7,1,8,4,3,6,2,5]=>0000000=>1111111=>1
[7,3,1,8,6,4,2,5]=>0000000=>1111111=>1
[8,3,1,7,4,6,2,5]=>0000000=>1111111=>1
[8,4,5,1,7,2,3,6]=>0000000=>1111111=>1
[5,6,8,1,7,2,3,4]=>0000000=>1111111=>1
[6,5,8,1,2,7,3,4]=>0000000=>1111111=>1
[7,3,1,8,5,6,2,4]=>0000000=>1111111=>1
[6,2,7,8,3,1,5,4]=>0000000=>1111111=>1
[5,8,1,7,3,2,6,4]=>0000000=>1111111=>1
[8,4,1,7,3,2,6,5]=>0000000=>1111111=>1
[8,3,4,7,1,2,6,5]=>0000000=>1111111=>1
[8,2,7,4,1,3,6,5]=>0000000=>1111111=>1
[7,4,8,2,1,3,6,5]=>0000000=>1111111=>1
[7,4,3,8,1,2,6,5]=>0000000=>1111111=>1
[8,2,3,6,7,1,5,4]=>0000000=>1111111=>1
[6,8,5,2,3,4,7,1]=>0000000=>1111111=>1
[3,5,2,6,8,1,4,7]=>0000000=>1111111=>1
[3,5,2,4,6,8,1,7]=>0000000=>1111111=>1
[2,4,5,7,3,6,8,1]=>0000000=>1111111=>1
[2,4,5,3,6,8,1,7]=>0000000=>1111111=>1
[5,2,4,6,8,1,3,7]=>0000000=>1111111=>1
[5,1,3,4,6,8,2,7]=>0000000=>1111111=>1
[4,3,5,2,6,8,1,7]=>0000000=>1111111=>1
[4,3,5,7,2,8,1,6]=>0000000=>1111111=>1
[4,3,5,7,2,6,8,1]=>0000000=>1111111=>1
[4,6,3,7,2,5,8,1]=>0000000=>1111111=>1
[4,6,3,1,7,8,2,5]=>0000000=>1111111=>1
[4,3,5,1,7,8,2,6]=>0000000=>1111111=>1
[5,7,1,3,4,8,2,6]=>0000000=>1111111=>1
[5,7,1,3,4,6,8,2]=>0000000=>1111111=>1
[4,5,7,1,3,6,8,2]=>0000000=>1111111=>1
[4,3,6,7,1,5,8,2]=>0000000=>1111111=>1
[4,6,3,5,1,7,8,2]=>0000000=>1111111=>1
[4,6,3,5,7,2,8,1]=>0000000=>1111111=>1
[3,5,6,4,1,7,8,2]=>0000000=>1111111=>1
[3,1,5,6,7,4,8,2]=>0000000=>1111111=>1
[5,1,6,7,3,4,8,2]=>0000000=>1111111=>1
[6,4,7,1,3,5,8,2]=>0000000=>1111111=>1
[1,6,7,3,4,5,8,2]=>1000000=>0111111=>1
[2,6,7,4,5,8,1,3]=>0000000=>1111111=>1
[2,6,7,4,8,1,3,5]=>0000000=>1111111=>1
[5,3,6,1,2,7,8,4]=>0000000=>1111111=>1
[3,5,2,6,1,7,8,4]=>0000000=>1111111=>1
[3,5,2,6,7,4,8,1]=>0000000=>1111111=>1
[5,2,3,6,7,4,8,1]=>0000000=>1111111=>1
[5,2,3,6,1,7,8,4]=>0000000=>1111111=>1
[5,2,6,1,3,7,8,4]=>0000000=>1111111=>1
[4,2,6,7,3,5,8,1]=>0000000=>1111111=>1
[6,3,7,2,4,5,8,1]=>0000000=>1111111=>1
[3,5,7,2,8,1,4,6]=>0000000=>1111111=>1
[3,7,2,4,8,1,5,6]=>0000000=>1111111=>1
[7,2,4,6,8,1,3,5]=>0000000=>1111111=>1
[7,1,3,4,6,8,2,5]=>0000000=>1111111=>1
[3,7,2,4,6,8,1,5]=>0000000=>1111111=>1
[3,5,7,2,6,8,1,4]=>0000000=>1111111=>1
[6,3,7,2,5,8,1,4]=>0000000=>1111111=>1
[6,3,5,7,2,8,1,4]=>0000000=>1111111=>1
[6,3,5,7,2,4,8,1]=>0000000=>1111111=>1
[6,2,4,5,7,3,8,1]=>0000000=>1111111=>1
[6,2,4,5,1,7,8,3]=>0000000=>1111111=>1
[4,7,1,2,5,6,8,3]=>0000000=>1111111=>1
[2,6,7,5,8,1,3,4]=>0000000=>1111111=>1
[4,6,7,1,2,5,8,3]=>0000000=>1111111=>1
[5,6,2,4,7,3,8,1]=>0000000=>1111111=>1
[5,4,2,6,7,3,8,1]=>0000000=>1111111=>1
[5,4,2,6,1,7,8,3]=>0000000=>1111111=>1
[1,5,4,6,2,7,8,3]=>1000000=>0111111=>1
[5,6,4,1,2,7,8,3]=>0000000=>1111111=>1
[6,4,5,1,2,7,8,3]=>0000000=>1111111=>1
[6,3,5,1,7,8,2,4]=>0000000=>1111111=>1
[6,5,7,2,8,1,3,4]=>0000000=>1111111=>1
[6,5,7,1,3,4,8,2]=>0000000=>1111111=>1
[5,6,4,7,1,3,8,2]=>0000000=>1111111=>1
[5,4,6,3,1,7,8,2]=>0000000=>1111111=>1
[7,5,3,2,4,8,1,6]=>0000000=>1111111=>1
[8,4,5,2,6,1,3,7]=>0000000=>1111111=>1
[8,5,4,2,1,6,3,7]=>0000000=>1111111=>1
[8,5,3,4,1,6,2,7]=>0000000=>1111111=>1
[8,4,5,3,1,6,2,7]=>0000000=>1111111=>1
[7,5,4,2,1,8,3,6]=>0000000=>1111111=>1
[7,5,4,2,1,6,8,3]=>0000000=>1111111=>1
[7,4,5,3,1,6,8,2]=>0000000=>1111111=>1
[7,4,3,5,6,1,8,2]=>0000000=>1111111=>1
[5,6,3,7,4,1,8,2]=>0000000=>1111111=>1
[5,6,7,3,1,4,8,2]=>0000000=>1111111=>1
[6,7,3,4,1,5,8,2]=>0000000=>1111111=>1
[6,7,4,2,1,5,8,3]=>0000000=>1111111=>1
[5,6,7,3,1,8,2,4]=>0000000=>1111111=>1
[5,6,3,7,8,1,2,4]=>0000000=>1111111=>1
[5,6,3,7,2,4,8,1]=>0000000=>1111111=>1
[5,6,7,2,3,8,1,4]=>0000000=>1111111=>1
[7,4,5,2,8,1,3,6]=>0000000=>1111111=>1
[6,7,3,2,4,8,1,5]=>0000000=>1111111=>1
[7,6,4,2,1,3,8,5]=>0000000=>1111111=>1
[7,6,3,4,1,2,8,5]=>0000000=>1111111=>1
[7,6,3,2,4,1,8,5]=>0000000=>1111111=>1
[6,7,3,2,5,1,8,4]=>0000000=>1111111=>1
[6,5,3,2,7,8,1,4]=>0000000=>1111111=>1
[6,5,3,2,7,4,8,1]=>0000000=>1111111=>1
[6,4,5,2,7,3,8,1]=>0000000=>1111111=>1
[6,4,5,2,7,8,1,3]=>0000000=>1111111=>1
[7,4,5,2,6,1,8,3]=>0000000=>1111111=>1
[7,4,5,6,1,2,8,3]=>0000000=>1111111=>1
[7,5,6,2,1,3,8,4]=>0000000=>1111111=>1
[6,7,3,5,1,2,8,4]=>0000000=>1111111=>1
[5,6,7,4,1,2,8,3]=>0000000=>1111111=>1
[5,6,7,2,4,1,8,3]=>0000000=>1111111=>1
[5,6,4,2,7,8,1,3]=>0000000=>1111111=>1
[6,5,7,2,1,8,3,4]=>0000000=>1111111=>1
[6,5,7,2,1,4,8,3]=>0000000=>1111111=>1
[5,4,6,7,3,1,8,2]=>0000000=>1111111=>1
[3,7,8,5,6,1,4,2]=>0000000=>1111111=>1
[1,7,8,5,6,3,4,2]=>1000000=>0111111=>1
[1,7,5,8,6,3,4,2]=>1000000=>0111111=>1
[3,7,5,8,6,1,4,2]=>0000000=>1111111=>1
[5,7,3,8,6,4,1,2]=>0000000=>1111111=>1
[1,5,7,8,6,3,4,2]=>1000000=>0111111=>1
[1,5,7,8,3,6,4,2]=>1000000=>0111111=>1
[5,3,7,8,1,6,4,2]=>0000000=>1111111=>1
[7,8,1,5,6,3,4,2]=>0000000=>1111111=>1
[7,1,8,5,6,3,4,2]=>0000000=>1111111=>1
[7,1,5,8,6,3,4,2]=>0000000=>1111111=>1
[5,1,7,8,3,6,4,2]=>0000000=>1111111=>1
[3,1,7,8,5,6,4,2]=>0000000=>1111111=>1
[1,3,7,8,5,6,4,2]=>1000000=>0111111=>1
[3,1,7,5,8,6,4,2]=>0000000=>1111111=>1
[5,1,7,3,8,6,4,2]=>0000000=>1111111=>1
[7,1,5,3,8,6,4,2]=>0000000=>1111111=>1
[7,1,5,8,3,6,4,2]=>0000000=>1111111=>1
[7,3,5,8,1,6,4,2]=>0000000=>1111111=>1
[5,3,7,1,8,6,4,2]=>0000000=>1111111=>1
[3,5,7,1,8,6,4,2]=>0000000=>1111111=>1
[1,7,5,3,8,6,4,2]=>1000000=>0111111=>1
[5,7,3,1,8,6,4,2]=>0000000=>1111111=>1
[5,7,3,8,6,1,4,2]=>0000000=>1111111=>1
[3,7,5,8,1,6,4,2]=>0000000=>1111111=>1
[1,7,5,8,3,6,4,2]=>1000000=>0111111=>1
[1,7,8,5,3,6,4,2]=>1000000=>0111111=>1
[5,7,8,6,3,1,4,2]=>0000000=>1111111=>1
[7,5,8,6,1,3,4,2]=>0000000=>1111111=>1
[5,7,8,1,6,3,4,2]=>0000000=>1111111=>1
[3,7,8,1,5,6,4,2]=>0000000=>1111111=>1
[1,7,8,3,5,6,4,2]=>1000000=>0111111=>1
[1,7,3,8,5,6,4,2]=>1000000=>0111111=>1
[3,7,1,8,5,6,4,2]=>0000000=>1111111=>1
[5,7,1,8,3,6,4,2]=>0000000=>1111111=>1
[5,7,1,8,6,3,4,2]=>0000000=>1111111=>1
[7,5,1,8,6,3,4,2]=>0000000=>1111111=>1
[7,5,8,1,6,3,4,2]=>0000000=>1111111=>1
[7,8,5,1,6,3,4,2]=>0000000=>1111111=>1
[7,5,8,1,3,6,4,2]=>0000000=>1111111=>1
[7,5,1,8,3,6,4,2]=>0000000=>1111111=>1
[7,5,1,3,8,6,4,2]=>0000000=>1111111=>1
[5,7,1,3,8,6,4,2]=>0000000=>1111111=>1
[3,7,1,5,8,6,4,2]=>0000000=>1111111=>1
[1,7,3,5,8,6,4,2]=>1000000=>0111111=>1
[1,5,3,7,8,6,4,2]=>1000000=>0111111=>1
[3,5,1,7,8,6,4,2]=>0000000=>1111111=>1
[5,3,1,7,8,6,4,2]=>0000000=>1111111=>1
[7,3,1,5,8,6,4,2]=>0000000=>1111111=>1
[7,3,1,8,5,6,4,2]=>0000000=>1111111=>1
[7,8,3,1,5,6,4,2]=>0000000=>1111111=>1
[7,1,8,3,5,6,4,2]=>0000000=>1111111=>1
[7,1,3,8,5,6,4,2]=>0000000=>1111111=>1
[7,1,3,5,8,6,4,2]=>0000000=>1111111=>1
[3,1,5,7,8,6,4,2]=>0000000=>1111111=>1
[5,7,3,4,8,6,1,2]=>0000000=>1111111=>1
[5,7,3,4,8,1,6,2]=>0000000=>1111111=>1
[5,7,3,1,4,6,2,8]=>0000001=>1111110=>1
[5,7,3,1,4,8,6,2]=>0000000=>1111111=>1
[5,3,7,1,4,2,6,8]=>0000001=>1111110=>1
[5,3,7,1,4,2,8,6]=>0000000=>1111111=>1
[3,7,5,1,2,8,6,4]=>0000000=>1111111=>1
[7,3,5,8,1,2,6,4]=>0000000=>1111111=>1
[3,7,5,1,2,6,8,4]=>0000000=>1111111=>1
[3,5,6,2,4,1,8,7]=>0000010=>1111101=>2
[6,2,7,8,3,4,1,5]=>0000000=>1111111=>1
[2,5,3,4,8,1,7,6]=>0000000=>1111111=>1
[5,1,8,2,3,4,7,6]=>0000000=>1111111=>1
[5,4,7,6,2,8,1,3]=>0000000=>1111111=>1
[3,8,1,5,6,7,2,4]=>0000000=>1111111=>1
[2,8,3,6,7,5,1,4]=>0000000=>1111111=>1
[8,2,1,7,6,3,5,4]=>0000000=>1111111=>1
[6,4,7,5,2,3,8,1]=>0000000=>1111111=>1
[4,8,7,2,3,1,5,6]=>0000000=>1111111=>1
[4,2,3,1,8,7,5,6]=>0001000=>1110111=>2
[7,6,8,1,3,5,2,4]=>0000000=>1111111=>1
[8,7,2,6,4,1,5,3]=>0000000=>1111111=>1
[7,4,8,1,2,5,6,3]=>0000000=>1111111=>1
[6,1,7,4,3,2,8,5]=>0000000=>1111111=>1
[6,8,3,4,2,1,7,5]=>0000000=>1111111=>1
[4,2,6,1,5,7,8,3]=>0000000=>1111111=>1
[2,4,6,7,3,5,8,1]=>0000000=>1111111=>1
[7,1,4,8,3,5,6,2]=>0000000=>1111111=>1
[3,4,8,2,5,7,6,1]=>0000000=>1111111=>1
[2,5,7,4,8,6,1,3]=>0000000=>1111111=>1
[2,6,3,7,5,1,8,4]=>0000000=>1111111=>1
[6,3,7,2,8,5,1,4]=>0000000=>1111111=>1
[3,6,2,5,8,7,1,4]=>0000000=>1111111=>1
[5,2,8,4,7,6,1,3]=>0000000=>1111111=>1
[7,2,4,8,6,5,1,3]=>0000000=>1111111=>1
[2,5,1,4,7,3,8,6]=>0000000=>1111111=>1
[3,1,5,6,2,8,7,4]=>0000000=>1111111=>1
[1,2,4,6,3,8,7,5]=>1100000=>0011111=>1
[4,1,5,2,8,7,6,3]=>0000000=>1111111=>1
[7,2,3,5,1,8,6,4]=>0000000=>1111111=>1
[1,4,5,2,8,7,6,3]=>1000000=>0111111=>1
[1,6,4,2,8,7,5,3]=>1000000=>0111111=>1
[7,4,2,5,1,8,6,3]=>0000000=>1111111=>1
[4,6,2,7,5,1,8,3]=>0000000=>1111111=>1
[1,5,3,6,2,8,7,4]=>1000000=>0111111=>1
[4,5,8,2,1,7,6,3]=>0000000=>1111111=>1
[3,5,2,1,7,4,8,6]=>0000000=>1111111=>1
[6,3,1,7,2,8,5,4]=>0000000=>1111111=>1
[7,5,1,2,8,6,4,3]=>0000000=>1111111=>1
[4,5,1,2,8,7,6,3]=>0000000=>1111111=>1
[6,4,1,2,8,7,5,3]=>0000000=>1111111=>1
[5,2,8,1,3,7,6,4]=>0000000=>1111111=>1
[4,7,5,6,8,3,1,2]=>0000000=>1111111=>1
[8,6,4,7,5,3,1,2]=>0000000=>1111111=>1
[7,5,2,6,4,1,3,8]=>0000001=>1111110=>1
[1,6,3,7,5,8,4,2]=>1000000=>0111111=>1
[1,3,7,4,5,8,6,2]=>1000000=>0111111=>1
[7,2,6,3,4,1,5,8]=>0000001=>1111110=>1
[8,3,7,4,6,5,1,2]=>0000000=>1111111=>1
[6,8,4,7,5,3,1,2]=>0000000=>1111111=>1
[4,8,7,5,6,3,1,2]=>0000000=>1111111=>1
[3,8,7,6,4,5,1,2]=>0000000=>1111111=>1
[1,6,5,2,8,3,7,4]=>1000000=>0111111=>1
[8,6,5,2,1,4,3,7]=>0000000=>1111111=>1
[2,7,6,3,1,4,5,8]=>0000001=>1111110=>1
[6,8,5,3,2,1,4,7]=>0000000=>1111111=>1
[2,7,6,4,5,1,3,8]=>0000001=>1111110=>1
[5,7,2,6,4,1,3,8]=>0000001=>1111110=>1
[6,1,3,7,5,8,4,2]=>0000000=>1111111=>1
[4,1,7,3,6,8,5,2]=>0000000=>1111111=>1
[8,1,6,4,3,7,5,2]=>0000000=>1111111=>1
[2,1,7,4,8,6,3,5]=>0100000=>1011111=>2
[1,8,6,3,7,5,4,2]=>1000000=>0111111=>1
[1,8,2,7,3,6,5,4]=>1000000=>0111111=>1
[2,1,3,8,4,7,5,6]=>0110000=>1001111=>2
[8,1,2,7,4,3,6,5]=>0000000=>1111111=>1
[5,3,1,6,8,4,7,2]=>0000000=>1111111=>1
[6,2,8,7,1,4,3,5]=>0000000=>1111111=>1
[8,7,2,1,5,4,3,6]=>0000000=>1111111=>1
[8,2,3,1,4,6,5,7]=>0000000=>1111111=>1
[2,4,8,3,1,5,6,7]=>0000000=>1111111=>1
[3,4,2,7,1,5,6,8]=>0000001=>1111110=>1
[4,7,3,8,2,1,5,6]=>0000000=>1111111=>1
[5,2,7,3,1,4,6,8]=>0000001=>1111110=>1
[8,3,7,2,1,5,4,6]=>0000000=>1111111=>1
[1,3,7,2,8,4,6,5]=>1000000=>0111111=>1
[1,4,2,5,8,6,7,3]=>1000000=>0111111=>1
[6,5,3,8,2,1,4,7]=>0000000=>1111111=>1
[2,6,4,5,7,1,3,8]=>0000001=>1111110=>1
[5,4,6,2,7,1,3,8]=>0000001=>1111110=>1
[7,6,3,1,8,4,5,2]=>0000000=>1111111=>1
[7,6,2,1,8,5,3,4]=>0000000=>1111111=>1
[1,7,5,8,6,4,3,2]=>1000000=>0111111=>1
[6,5,1,2,8,3,7,4]=>0000000=>1111111=>1
[8,6,1,4,3,7,5,2]=>0000000=>1111111=>1
[6,8,4,1,3,7,5,2]=>0000000=>1111111=>1
[6,5,7,1,3,8,4,2]=>0000000=>1111111=>1
[5,8,3,1,7,4,6,2]=>0000000=>1111111=>1
[8,3,1,7,5,4,6,2]=>0000000=>1111111=>1
[1,3,8,7,4,6,5,2]=>1000000=>0111111=>1
[1,2,8,7,6,3,5,4]=>1100000=>0011111=>1
[8,2,1,7,6,4,3,5]=>0000000=>1111111=>1
[2,3,1,8,7,4,5,6]=>0010000=>1101111=>2
[2,4,1,8,5,7,3,6]=>0000000=>1111111=>1
[5,8,2,1,7,6,3,4]=>0000000=>1111111=>1
[6,2,7,1,8,5,3,4]=>0000000=>1111111=>1
[8,7,1,6,5,4,3,2]=>0000000=>1111111=>1
[7,1,8,3,6,5,4,2]=>0000000=>1111111=>1
[4,1,8,7,5,6,3,2]=>0000000=>1111111=>1
[8,1,2,3,4,5,9,6,7]=>00000000=>11111111=>1
[8,1,2,3,4,9,5,6,7]=>00000000=>11111111=>1
[8,1,2,9,3,4,5,6,7]=>00000000=>11111111=>1
[8,1,9,2,3,4,5,6,7]=>00000000=>11111111=>1
[9,1,2,3,4,5,6,10,7,8]=>000000000=>111111111=>1
[2,1,8,9,3,4,5,6,7]=>01000000=>10111111=>2
[3,5,8,7,2,6,4,1]=>0000000=>1111111=>1
[5,8,2,7,1,6,4,3]=>0000000=>1111111=>1
[2,1,6,4,5,8,3,7]=>0100000=>1011111=>2
[8,6,3,7,5,2,1,4]=>0000000=>1111111=>1
[4,6,3,8,5,2,1,7]=>0000000=>1111111=>1
[4,6,3,7,5,2,8,1]=>0000000=>1111111=>1
[3,5,7,8,2,6,1,4]=>0000000=>1111111=>1
[8,2,3,4,6,1,5,7]=>0000000=>1111111=>1
[4,8,3,7,5,1,6,2]=>0000000=>1111111=>1
[5,2,3,4,8,7,1,6]=>0000000=>1111111=>1
[4,2,8,5,7,6,1,3]=>0000000=>1111111=>1
[4,8,3,7,5,2,1,6]=>0000000=>1111111=>1
[4,2,7,5,8,6,3,1]=>0000000=>1111111=>1
[5,2,7,8,4,6,3,1]=>0000000=>1111111=>1
[5,2,8,3,7,6,1,4]=>0000000=>1111111=>1
[8,2,7,3,1,6,4,5]=>0000000=>1111111=>1
[6,2,3,4,8,5,1,7]=>0000000=>1111111=>1
[7,2,3,4,1,8,6,5]=>0000000=>1111111=>1
[1,2,3,4,8,7,5,6]=>1111000=>0000111=>1
[1,2,8,5,3,4,6,7]=>1100000=>0011111=>1
[1,8,4,2,3,5,6,7]=>1000000=>0111111=>1
[8,6,7,4,1,5,3,2]=>0000000=>1111111=>1
[4,8,6,7,5,1,3,2]=>0000000=>1111111=>1
[7,1,8,4,6,5,2,3]=>0000000=>1111111=>1
[8,7,1,5,4,6,2,3]=>0000000=>1111111=>1
[8,5,7,1,4,6,3,2]=>0000000=>1111111=>1
[6,4,8,5,1,7,3,2]=>0000000=>1111111=>1
[4,8,5,7,1,6,3,2]=>0000000=>1111111=>1
[8,4,7,1,5,6,3,2]=>0000000=>1111111=>1
[8,7,1,4,5,6,3,2]=>0000000=>1111111=>1
[8,7,4,5,6,1,3,2]=>0000000=>1111111=>1
[8,7,5,1,4,6,2,3]=>0000000=>1111111=>1
[8,7,2,5,1,4,6,3]=>0000000=>1111111=>1
[4,8,7,2,5,1,6,3]=>0000000=>1111111=>1
[1,6,4,8,5,2,7,3]=>1000000=>0111111=>1
[8,7,1,4,2,5,6,3]=>0000000=>1111111=>1
[8,7,5,1,2,4,6,3]=>0000000=>1111111=>1
[7,1,8,5,6,2,3,4]=>0000000=>1111111=>1
[3,8,7,1,2,5,6,4]=>0000000=>1111111=>1
[3,5,8,7,1,2,6,4]=>0000000=>1111111=>1
[2,3,8,5,7,1,6,4]=>0000000=>1111111=>1
[3,8,7,1,5,6,2,4]=>0000000=>1111111=>1
[3,5,8,7,1,6,2,4]=>0000000=>1111111=>1
[2,3,8,6,7,5,1,4]=>0000000=>1111111=>1
[3,2,8,6,7,5,1,4]=>0000000=>1111111=>1
[4,1,8,6,2,7,5,3]=>0000000=>1111111=>1
[8,7,4,1,2,6,5,3]=>0000000=>1111111=>1
[1,3,8,6,7,5,2,4]=>1000000=>0111111=>1
[5,7,1,8,2,6,3,4]=>0000000=>1111111=>1
[2,8,7,1,5,6,3,4]=>0000000=>1111111=>1
[8,7,1,5,2,4,6,3]=>0000000=>1111111=>1
[7,1,8,2,4,6,5,3]=>0000000=>1111111=>1
[1,6,2,8,4,7,5,3]=>1000000=>0111111=>1
[1,3,8,5,7,2,6,4]=>1000000=>0111111=>1
[1,8,3,7,2,5,6,4]=>1000000=>0111111=>1
[2,8,7,1,3,5,6,4]=>0000000=>1111111=>1
[5,7,1,8,2,3,6,4]=>0000000=>1111111=>1
[7,1,8,2,3,5,6,4]=>0000000=>1111111=>1
[8,6,3,7,4,1,5,2]=>0000000=>1111111=>1
[4,2,8,6,7,5,1,3]=>0000000=>1111111=>1
[8,4,2,7,5,6,1,3]=>0000000=>1111111=>1
[4,8,3,6,1,7,5,2]=>0000000=>1111111=>1
[8,3,4,7,5,1,6,2]=>0000000=>1111111=>1
[8,3,7,4,5,1,6,2]=>0000000=>1111111=>1
[8,7,4,2,5,6,1,3]=>0000000=>1111111=>1
[8,7,5,1,6,2,3,4]=>0000000=>1111111=>1
[8,7,2,4,1,5,6,3]=>0000000=>1111111=>1
[4,8,6,1,7,2,5,3]=>0000000=>1111111=>1
[4,7,1,8,2,6,5,3]=>0000000=>1111111=>1
[4,2,8,6,7,1,5,3]=>0000000=>1111111=>1
[8,7,4,1,2,5,6,3]=>0000000=>1111111=>1
[8,2,7,1,6,3,4,5]=>0000000=>1111111=>1
[8,2,7,1,3,6,4,5]=>0000000=>1111111=>1
[2,8,3,6,7,1,5,4]=>0000000=>1111111=>1
[8,7,2,1,3,5,6,4]=>0000000=>1111111=>1
[1,8,7,2,3,6,4,5]=>1000000=>0111111=>1
[1,8,7,2,6,3,4,5]=>1000000=>0111111=>1
[8,2,7,3,6,1,4,5]=>0000000=>1111111=>1
[1,8,7,3,6,2,4,5]=>1000000=>0111111=>1
[1,8,2,7,6,3,4,5]=>1000000=>0111111=>1
[8,2,7,4,1,5,6,3]=>0000000=>1111111=>1
[8,2,1,7,5,6,3,4]=>0000000=>1111111=>1
[8,7,3,1,5,6,2,4]=>0000000=>1111111=>1
[2,8,7,3,5,6,1,4]=>0000000=>1111111=>1
[8,3,1,6,7,5,2,4]=>0000000=>1111111=>1
[8,5,2,1,6,7,4,3]=>0000000=>1111111=>1
[1,5,2,8,6,7,4,3]=>1000000=>0111111=>1
[1,2,8,6,7,5,3,4]=>1100000=>0011111=>1
[1,8,3,6,7,5,2,4]=>1000000=>0111111=>1
[8,2,3,6,7,5,1,4]=>0000000=>1111111=>1
[8,3,7,2,5,6,1,4]=>0000000=>1111111=>1
[8,1,3,7,5,6,2,4]=>0000000=>1111111=>1
[8,4,1,2,7,5,6,3]=>0000000=>1111111=>1
[8,1,4,2,6,7,5,3]=>0000000=>1111111=>1
[1,2,8,6,7,3,5,4]=>1100000=>0011111=>1
[8,1,2,7,3,6,4,5]=>0000000=>1111111=>1
[8,1,7,3,6,2,4,5]=>0000000=>1111111=>1
[8,1,7,2,6,3,4,5]=>0000000=>1111111=>1
[8,1,7,2,3,6,4,5]=>0000000=>1111111=>1
[8,1,3,7,2,5,6,4]=>0000000=>1111111=>1
[1,8,3,6,7,2,5,4]=>1000000=>0111111=>1
[1,7,8,2,3,6,5,4]=>1000000=>0111111=>1
[8,3,7,1,2,5,6,4]=>0000000=>1111111=>1
[8,7,1,2,3,6,4,5]=>0000000=>1111111=>1
[2,8,5,7,4,6,3,1]=>0000000=>1111111=>1
[3,1,8,5,7,4,2,6]=>0000000=>1111111=>1
[8,3,5,7,4,2,6,1]=>0000000=>1111111=>1
[8,3,6,2,4,5,7,1]=>0000000=>1111111=>1
[2,8,6,4,3,5,7,1]=>0000000=>1111111=>1
[2,6,8,3,5,4,7,1]=>0000000=>1111111=>1
[2,7,5,8,4,6,3,1]=>0000000=>1111111=>1
[8,4,2,7,6,1,3,5]=>0000000=>1111111=>1
[4,8,1,7,6,3,2,5]=>0000000=>1111111=>1
[4,1,7,6,2,3,5,8]=>0000001=>1111110=>1
[3,7,1,8,6,2,5,4]=>0000000=>1111111=>1
[3,1,7,6,4,5,2,8]=>0000001=>1111110=>1
[3,1,7,5,8,4,2,6]=>0000000=>1111111=>1
[3,1,6,8,7,5,2,4]=>0000000=>1111111=>1
[6,3,8,7,5,2,4,1]=>0000000=>1111111=>1
[7,3,5,8,4,2,6,1]=>0000000=>1111111=>1
[7,3,6,4,2,8,5,1]=>0000000=>1111111=>1
[7,8,3,6,2,5,4,1]=>0000000=>1111111=>1
[7,4,8,2,1,6,3,5]=>0000000=>1111111=>1
[8,7,4,6,3,2,5,1]=>0000000=>1111111=>1
[7,8,5,2,1,4,3,6]=>0000000=>1111111=>1
[7,5,2,3,1,4,8,6]=>0000000=>1111111=>1
[7,4,6,2,3,8,1,5]=>0000000=>1111111=>1
[6,4,2,5,8,3,7,1]=>0000000=>1111111=>1
[4,6,5,8,1,3,2,7]=>0000000=>1111111=>1
[4,7,1,5,3,8,2,6]=>0000000=>1111111=>1
[4,7,8,1,3,6,2,5]=>0000000=>1111111=>1
[5,7,1,3,4,6,2,8]=>0000001=>1111110=>1
[5,7,1,4,2,3,6,8]=>0000001=>1111110=>1
[5,8,1,3,2,4,6,7]=>0000000=>1111111=>1
[4,8,6,1,3,2,7,5]=>0000000=>1111111=>1
[8,4,6,2,1,3,7,5]=>0000000=>1111111=>1
[5,4,8,7,2,3,6,1]=>0000000=>1111111=>1
[5,4,8,7,3,1,2,6]=>0000000=>1111111=>1
[6,8,3,7,2,5,4,1]=>0000000=>1111111=>1
[5,4,6,8,2,3,7,1]=>0000000=>1111111=>1
[5,7,4,2,8,3,6,1]=>0000000=>1111111=>1
[6,4,7,2,1,8,3,5]=>0000000=>1111111=>1
[6,5,3,4,1,2,8,7]=>0000010=>1111101=>2
[6,8,5,4,1,3,2,7]=>0000000=>1111111=>1
[6,4,3,7,1,5,2,8]=>0000001=>1111110=>1
[9,8,7,6,5,2,3,1,4]=>00000000=>11111111=>1
[9,8,7,6,3,4,2,1,5]=>00000000=>11111111=>1
[9,8,7,4,5,3,2,1,6]=>00000000=>11111111=>1
[9,8,5,6,4,3,2,1,7]=>00000000=>11111111=>1
[9,6,7,5,4,3,2,1,8]=>00000000=>11111111=>1
[7,4,2,6,1,5,3,8]=>0000001=>1111110=>1
[7,4,2,5,6,1,3,8]=>0000001=>1111110=>1
[6,4,2,8,1,5,7,3]=>0000000=>1111111=>1
[6,3,7,8,2,5,1,4]=>0000000=>1111111=>1
[7,3,5,6,4,2,1,8]=>0000001=>1111110=>1
[7,4,3,1,5,6,2,8]=>0000001=>1111110=>1
[7,4,5,2,6,1,3,8]=>0000001=>1111110=>1
[5,3,7,2,8,6,4,1]=>0000000=>1111111=>1
[5,3,8,2,6,7,4,1]=>0000000=>1111111=>1
[6,3,8,2,5,4,7,1]=>0000000=>1111111=>1
[6,4,8,2,1,5,7,3]=>0000000=>1111111=>1
[6,4,3,1,8,2,7,5]=>0000000=>1111111=>1
[5,3,7,8,2,6,4,1]=>0000000=>1111111=>1
[4,7,8,5,6,3,2,1]=>0000000=>1111111=>1
[5,3,7,6,8,2,4,1]=>0000000=>1111111=>1
[5,7,8,4,6,2,1,3]=>0000000=>1111111=>1
[5,8,4,3,6,7,1,2]=>0000000=>1111111=>1
[5,8,6,4,7,2,1,3]=>0000000=>1111111=>1
[5,3,8,6,2,7,4,1]=>0000000=>1111111=>1
[4,7,5,8,6,3,2,1]=>0000000=>1111111=>1
[4,8,6,7,5,3,2,1]=>0000000=>1111111=>1
[6,3,8,7,2,4,1,5]=>0000000=>1111111=>1
[5,3,8,7,2,6,4,1]=>0000000=>1111111=>1
[5,3,8,6,7,2,4,1]=>0000000=>1111111=>1
[5,3,7,8,6,2,4,1]=>0000000=>1111111=>1
[5,7,6,4,8,2,1,3]=>0000000=>1111111=>1
[5,8,4,6,7,2,1,3]=>0000000=>1111111=>1
[6,4,2,8,1,7,3,5]=>0000000=>1111111=>1
[6,5,2,4,3,7,8,1]=>0000000=>1111111=>1
[5,4,6,2,8,7,1,3]=>0000000=>1111111=>1
[5,6,3,8,7,2,4,1]=>0000000=>1111111=>1
[6,7,4,3,1,8,2,5]=>0000000=>1111111=>1
[5,7,4,3,6,8,1,2]=>0000000=>1111111=>1
[5,7,3,8,6,2,4,1]=>0000000=>1111111=>1
[4,5,8,6,7,3,2,1]=>0000000=>1111111=>1
[4,6,8,5,7,3,2,1]=>0000000=>1111111=>1
[5,6,8,3,7,2,4,1]=>0000000=>1111111=>1
[5,4,6,8,2,7,1,3]=>0000000=>1111111=>1
[5,7,8,2,6,4,1,3]=>0000000=>1111111=>1
[3,6,8,5,7,1,4,2]=>0000000=>1111111=>1
[1,7,4,8,6,2,3,5]=>1000000=>0111111=>1
[4,2,5,6,7,1,8,3]=>0000000=>1111111=>1
[8,1,3,6,7,2,4,5]=>0000000=>1111111=>1
[6,1,3,8,2,7,4,5]=>0000000=>1111111=>1
[1,7,5,2,8,6,3,4]=>1000000=>0111111=>1
[1,5,8,4,2,6,3,7]=>1000000=>0111111=>1
[3,5,7,4,1,6,8,2]=>0000000=>1111111=>1
[3,5,7,1,2,6,4,8]=>0000001=>1111110=>1
[4,5,1,8,2,3,7,6]=>0000000=>1111111=>1
[4,7,1,8,2,6,3,5]=>0000000=>1111111=>1
[5,2,6,1,3,4,8,7]=>0000010=>1111101=>2
[7,8,4,5,1,3,2,6]=>0000000=>1111111=>1
[6,7,1,3,2,5,4,8]=>0000001=>1111110=>1
[6,7,1,4,3,5,2,8]=>0000001=>1111110=>1
[7,8,2,3,1,5,4,6]=>0000000=>1111111=>1
[7,8,2,4,3,5,1,6]=>0000000=>1111111=>1
[7,8,2,4,1,5,3,6]=>0000000=>1111111=>1
[1,4,2,6,5,7,3,8]=>1000001=>0111110=>1
[5,6,1,4,2,7,3,8]=>0000001=>1111110=>1
[6,7,2,4,1,5,3,8]=>0000001=>1111110=>1
[6,7,2,4,3,5,1,8]=>0000001=>1111110=>1
[6,7,2,3,1,5,4,8]=>0000001=>1111110=>1
[6,7,3,5,4,8,1,2]=>0000000=>1111111=>1
[2,4,1,6,5,7,3,8]=>0000001=>1111110=>1
[1,5,2,6,4,7,3,8]=>1000001=>0111110=>1
[2,5,1,6,4,7,3,8]=>0000001=>1111110=>1
[3,6,5,7,4,8,1,2]=>0000000=>1111111=>1
[5,6,2,4,3,7,1,8]=>0000001=>1111110=>1
[4,5,2,6,1,7,3,8]=>0000001=>1111110=>1
[4,5,1,6,3,7,2,8]=>0000001=>1111110=>1
[4,5,3,6,1,7,2,8]=>0000001=>1111110=>1
[5,6,3,4,1,7,2,8]=>0000001=>1111110=>1
[5,6,1,4,3,7,2,8]=>0000001=>1111110=>1
[5,6,1,3,2,7,4,8]=>0000001=>1111110=>1
[5,6,4,7,1,3,2,8]=>0000001=>1111110=>1
[6,7,4,5,1,3,2,8]=>0000001=>1111110=>1
[6,7,5,8,1,3,2,4]=>0000000=>1111111=>1
[4,5,1,3,2,7,6,8]=>0000101=>1111010=>2
[4,6,5,7,1,3,2,8]=>0000001=>1111110=>1
[4,6,1,3,2,7,5,8]=>0000001=>1111110=>1
[1,4,3,6,2,7,5,8]=>1000001=>0111110=>1
[3,4,1,6,5,7,2,8]=>0000001=>1111110=>1
[4,5,2,3,1,7,6,8]=>0000101=>1111010=>2
[4,5,3,7,6,8,1,2]=>0000000=>1111111=>1
[4,6,5,7,3,8,1,2]=>0000000=>1111111=>1
[4,6,5,7,2,3,1,8]=>0000001=>1111110=>1
[3,5,4,6,1,7,2,8]=>0000001=>1111110=>1
[3,5,1,6,4,7,2,8]=>0000001=>1111110=>1
[1,5,3,6,4,7,2,8]=>1000001=>0111110=>1
[1,5,3,6,2,7,4,8]=>1000001=>0111110=>1
[3,5,2,6,1,7,4,8]=>0000001=>1111110=>1
[3,5,2,6,4,7,1,8]=>0000001=>1111110=>1
[3,4,2,6,1,7,5,8]=>0000001=>1111110=>1
[4,6,2,3,1,7,5,8]=>0000001=>1111110=>1
[2,4,3,6,1,7,5,8]=>0000001=>1111110=>1
[2,5,3,6,4,7,1,8]=>0000001=>1111110=>1
[2,5,3,6,1,7,4,8]=>0000001=>1111110=>1
[3,6,2,7,5,4,8,1]=>0000000=>1111111=>1
[5,2,6,7,4,3,8,1]=>0000000=>1111111=>1
[3,5,2,7,6,4,8,1]=>0000000=>1111111=>1
[2,5,7,3,1,8,4,6]=>0000000=>1111111=>1
[2,1,5,6,8,4,3,7]=>0100000=>1011111=>2
[1,3,7,2,8,5,4,6]=>1000000=>0111111=>1
[4,6,2,7,1,8,3,5]=>0000000=>1111111=>1
[1,5,4,3,6,8,2,7]=>1000000=>0111111=>1
[1,6,4,5,7,8,3,2]=>1000000=>0111111=>1
[2,1,5,6,8,4,7,3]=>0100000=>1011111=>2
[2,1,5,6,8,7,3,4]=>0100000=>1011111=>2
[3,6,5,2,7,8,4,1]=>0000000=>1111111=>1
[6,2,4,7,5,8,3,1]=>0000000=>1111111=>1
[1,5,7,8,4,2,6,3]=>1000000=>0111111=>1
[3,7,4,1,8,6,2,5]=>0000000=>1111111=>1
[3,4,6,8,5,7,2,1]=>0000000=>1111111=>1
[4,2,5,7,3,1,8,6]=>0000000=>1111111=>1
[4,5,6,2,8,7,3,1]=>0000000=>1111111=>1
[2,5,6,8,1,7,4,3]=>0000000=>1111111=>1
[4,5,6,1,8,7,3,2]=>0000000=>1111111=>1
[4,5,6,3,1,8,7,2]=>0000000=>1111111=>1
[4,3,6,2,1,7,5,8]=>0000001=>1111110=>1
[4,6,3,2,1,7,5,8]=>0000001=>1111110=>1
[4,6,3,1,7,5,2,8]=>0000001=>1111110=>1
[4,5,3,7,6,1,8,2]=>0000000=>1111111=>1
[4,5,1,7,3,8,6,2]=>0000000=>1111111=>1
[2,5,7,1,4,3,8,6]=>0000000=>1111111=>1
[4,3,5,7,6,1,8,2]=>0000000=>1111111=>1
[4,3,6,1,7,5,2,8]=>0000001=>1111110=>1
[4,3,2,6,1,7,5,8]=>0000001=>1111110=>1
[5,3,2,1,6,4,7,8]=>0000011=>1111100=>1
[5,3,1,6,2,7,4,8]=>0000001=>1111110=>1
[5,1,6,3,2,7,4,8]=>0000001=>1111110=>1
[2,6,1,4,7,5,3,8]=>0000001=>1111110=>1
[3,6,1,7,4,2,5,8]=>0000001=>1111110=>1
[4,6,1,7,5,3,2,8]=>0000001=>1111110=>1
[5,1,6,3,7,4,2,8]=>0000001=>1111110=>1
[5,3,6,4,2,1,7,8]=>0000011=>1111100=>1
[5,3,2,6,4,1,7,8]=>0000011=>1111100=>1
[5,2,1,6,3,7,4,8]=>0000001=>1111110=>1
[5,2,6,3,1,7,4,8]=>0000001=>1111110=>1
[4,2,6,3,1,7,8,5]=>0000000=>1111111=>1
[3,6,2,1,7,4,5,8]=>0000001=>1111110=>1
[3,6,2,7,4,1,5,8]=>0000001=>1111110=>1
[3,5,7,2,8,6,4,1]=>0000000=>1111111=>1
[2,4,7,1,3,6,5,8]=>0000001=>1111110=>1
[2,6,1,3,7,5,4,8]=>0000001=>1111110=>1
[3,6,1,7,5,2,4,8]=>0000001=>1111110=>1
[5,1,6,2,7,4,3,8]=>0000001=>1111110=>1
[5,2,6,4,3,1,7,8]=>0000011=>1111100=>1
[5,2,1,6,4,3,7,8]=>0000011=>1111100=>1
[5,4,2,1,6,3,7,8]=>0000011=>1111100=>1
[5,4,2,6,3,1,7,8]=>0000011=>1111100=>1
[5,4,1,6,2,7,3,8]=>0000001=>1111110=>1
[5,1,6,4,2,7,3,8]=>0000001=>1111110=>1
[3,6,1,7,5,4,8,2]=>0000000=>1111111=>1
[2,6,1,5,4,3,7,8]=>0000011=>1111100=>1
[3,1,6,2,5,4,7,8]=>0000011=>1111100=>1
[5,1,6,4,3,2,7,8]=>0000011=>1111100=>1
[5,4,1,6,3,2,7,8]=>0000011=>1111100=>1
[5,4,3,1,6,2,7,8]=>0000011=>1111100=>1
[8,2,1,7,6,5,4,3,9]=>00000001=>11111110=>1
[7,3,1,6,5,4,8,2]=>0000000=>1111111=>1
[7,2,8,1,5,4,3,6]=>0000000=>1111111=>1
[4,2,7,6,5,8,1,3]=>0000000=>1111111=>1
[3,8,2,6,5,4,1,7]=>0000000=>1111111=>1
[3,2,8,7,6,5,4,1,9]=>00000001=>11111110=>1
[9,2,1,8,7,6,5,4,3,10]=>000000001=>111111110=>1
[8,3,1,7,6,5,4,9,2]=>00000000=>11111111=>1
[8,2,9,1,6,5,4,3,7]=>00000000=>11111111=>1
[7,3,2,1,5,4,6,8]=>0000001=>1111110=>1
[7,2,8,6,1,4,3,5]=>0000000=>1111111=>1
[5,2,7,6,8,4,1,3]=>0000000=>1111111=>1
[4,2,8,7,6,5,9,1,3]=>00000000=>11111111=>1
[3,8,7,2,5,4,1,6]=>0000000=>1111111=>1
[3,9,2,7,6,5,4,1,8]=>00000000=>11111111=>1
[3,2,9,8,7,6,5,4,1,10]=>000000001=>111111110=>1
[10,2,1,9,8,7,6,5,4,3,11]=>0000000001=>1111111110=>1
[9,3,1,8,7,6,5,4,10,2]=>000000000=>111111111=>1
[9,2,10,1,7,6,5,4,3,8]=>000000000=>111111111=>1
[8,4,1,7,6,5,9,3,2]=>00000000=>11111111=>1
[8,3,2,1,6,5,4,7,9]=>00000001=>11111110=>1
[8,2,9,7,1,5,4,3,6]=>00000000=>11111111=>1
[7,5,1,6,8,4,3,2]=>0000000=>1111111=>1
[7,4,2,1,5,6,3,8]=>0000001=>1111110=>1
[7,2,8,6,5,1,3,4]=>0000000=>1111111=>1
[5,3,2,6,7,4,1,8]=>0000001=>1111110=>1
[5,2,8,7,6,9,4,1,3]=>00000000=>11111111=>1
[4,3,7,2,5,6,1,8]=>0000001=>1111110=>1
[4,3,2,7,6,5,8,1,9]=>00000001=>11111110=>1
[4,2,9,8,7,6,5,10,1,3]=>000000000=>111111111=>1
[3,9,8,2,6,5,4,1,7]=>00000000=>11111111=>1
[3,10,2,8,7,6,5,4,1,9]=>000000000=>111111111=>1
[3,2,10,9,8,7,6,5,4,1,11]=>0000000001=>1111111110=>1
[3,5,8,7,2,4,6,1]=>0000000=>1111111=>1
[1,4,8,2,7,6,3,5]=>1000000=>0111111=>1
[5,4,2,1,7,8,3,6]=>0000000=>1111111=>1
[4,7,8,3,5,2,1,6]=>0000000=>1111111=>1
[6,3,7,2,8,5,4,1]=>0000000=>1111111=>1
[1,7,5,3,8,2,6,4]=>1000000=>0111111=>1
[1,7,6,4,3,8,2,5]=>1000000=>0111111=>1
[5,1,4,3,2,7,8,6]=>0000100=>1111011=>2
[3,7,8,5,2,4,1,6]=>0000000=>1111111=>1
[3,7,6,2,4,1,8,5]=>0000000=>1111111=>1
[5,2,7,8,4,3,1,6]=>0000000=>1111111=>1
[5,3,1,7,8,4,2,6]=>0000000=>1111111=>1
[6,3,1,7,5,2,8,4]=>0000000=>1111111=>1
[6,7,1,8,3,4,2,5]=>0000000=>1111111=>1
[7,8,3,5,1,4,2,6]=>0000000=>1111111=>1
[5,6,2,7,1,8,3,4]=>0000000=>1111111=>1
[6,7,2,4,3,8,1,5]=>0000000=>1111111=>1
[2,4,3,8,6,7,1,5]=>0000000=>1111111=>1
[1,8,2,7,4,5,3,6]=>1000000=>0111111=>1
[2,5,4,8,3,6,1,7]=>0000000=>1111111=>1
[2,3,1,8,5,6,4,7]=>0010000=>1101111=>2
[3,8,5,6,4,7,1,2]=>0000000=>1111111=>1
[5,7,3,6,4,8,1,2]=>0000000=>1111111=>1
[5,7,2,3,1,6,4,8]=>0000001=>1111110=>1
[5,7,2,4,3,6,1,8]=>0000001=>1111110=>1
[4,6,2,7,1,5,3,8]=>0000001=>1111110=>1
[4,7,1,6,2,5,3,8]=>0000001=>1111110=>1
[4,7,1,5,3,6,2,8]=>0000001=>1111110=>1
[4,6,3,5,1,7,2,8]=>0000001=>1111110=>1
[6,7,3,5,1,4,2,8]=>0000001=>1111110=>1
[5,6,3,7,1,4,2,8]=>0000001=>1111110=>1
[5,7,1,6,3,4,2,8]=>0000001=>1111110=>1
[1,8,5,6,3,4,2,7]=>1000000=>0111111=>1
[1,8,5,6,4,7,2,3]=>1000000=>0111111=>1
[5,7,1,6,4,8,2,3]=>0000000=>1111111=>1
[4,6,5,8,1,7,2,3]=>0000000=>1111111=>1
[3,7,1,4,2,8,5,6]=>0000000=>1111111=>1
[3,5,1,4,2,8,6,7]=>0000100=>1111011=>2
[4,6,5,8,3,7,1,2]=>0000000=>1111111=>1
[4,6,5,8,2,3,1,7]=>0000000=>1111111=>1
[3,4,2,6,5,8,1,7]=>0000000=>1111111=>1
[3,5,4,6,2,8,1,7]=>0000000=>1111111=>1
[1,8,3,5,4,7,2,6]=>1000000=>0111111=>1
[3,4,2,7,1,8,5,6]=>0000000=>1111111=>1
[4,7,2,3,1,8,5,6]=>0000000=>1111111=>1
[2,4,3,8,1,7,5,6]=>0000000=>1111111=>1
[2,5,3,8,4,7,1,6]=>0000000=>1111111=>1
[2,6,3,8,1,7,4,5]=>0000000=>1111111=>1
[2,7,1,8,3,6,4,5]=>0000000=>1111111=>1
[4,5,1,8,7,6,2,3]=>0000000=>1111111=>1
[4,5,7,8,2,6,3,1]=>0000000=>1111111=>1
[3,1,6,8,7,4,5,2]=>0000000=>1111111=>1
[6,1,4,8,7,2,5,3]=>0000000=>1111111=>1
[6,1,8,4,7,3,5,2]=>0000000=>1111111=>1
[6,8,3,5,7,1,4,2]=>0000000=>1111111=>1
[6,7,4,2,8,5,3,1]=>0000000=>1111111=>1
[2,7,5,3,8,6,4,1]=>0000000=>1111111=>1
[1,5,8,2,7,3,6,4]=>1000000=>0111111=>1
[6,7,4,8,1,5,3,2]=>0000000=>1111111=>1
[1,7,4,8,6,2,5,3]=>1000000=>0111111=>1
[6,8,5,3,7,2,4,1]=>0000000=>1111111=>1
[6,8,5,2,3,7,4,1]=>0000000=>1111111=>1
[7,5,3,8,2,6,4,1]=>0000000=>1111111=>1
[3,6,4,7,8,5,2,1]=>0000000=>1111111=>1
[6,3,4,7,8,5,2,1]=>0000000=>1111111=>1
[2,5,8,3,4,1,6,7]=>0000000=>1111111=>1
[4,6,7,3,2,5,8,1]=>0000000=>1111111=>1
[2,6,7,3,8,5,4,1]=>0000000=>1111111=>1
[2,6,1,8,4,5,3,7]=>0000000=>1111111=>1
[3,6,8,4,5,7,1,2]=>0000000=>1111111=>1
[1,6,8,4,7,2,3,5]=>1000000=>0111111=>1
[1,4,5,7,8,2,6,3]=>1000000=>0111111=>1
[3,4,5,7,8,6,1,2]=>0000000=>1111111=>1
[3,4,5,7,6,8,1,2]=>0000000=>1111111=>1
[3,6,7,4,8,5,1,2]=>0000000=>1111111=>1
[3,4,5,6,8,7,1,2]=>0000000=>1111111=>1
[1,4,5,8,7,2,3,6]=>1000000=>0111111=>1
[1,2,5,8,3,6,4,7]=>1100000=>0011111=>1
[1,4,5,8,6,2,3,7]=>1000000=>0111111=>1
[7,8,1,4,6,2,3,5]=>0000000=>1111111=>1
[1,6,7,4,8,2,5,3]=>1000000=>0111111=>1
[1,4,5,6,8,2,7,3]=>1000000=>0111111=>1
[1,4,5,8,6,2,7,3]=>1000000=>0111111=>1
[1,2,5,8,3,4,7,6]=>1100000=>0011111=>1
[1,6,7,2,3,5,8,4]=>1000000=>0111111=>1
[7,8,1,2,3,5,4,6]=>0000000=>1111111=>1
[1,6,7,2,3,5,4,8]=>1000001=>0111110=>1
[1,4,5,7,6,2,3,8]=>1000001=>0111110=>1
[1,2,5,7,3,6,4,8]=>1100001=>0011110=>1
[1,2,5,7,3,6,8,4]=>1100000=>0011111=>1
[1,6,8,2,3,5,7,4]=>1000000=>0111111=>1
[1,6,8,4,5,2,3,7]=>1000000=>0111111=>1
[1,6,8,4,5,2,7,3]=>1000000=>0111111=>1
[1,6,8,2,3,4,7,5]=>1000000=>0111111=>1
[1,6,8,2,3,7,4,5]=>1000000=>0111111=>1
[1,4,5,7,6,2,8,3]=>1000000=>0111111=>1
[7,8,1,4,5,2,6,3]=>0000000=>1111111=>1
[7,8,1,2,3,4,6,5]=>0000000=>1111111=>1
[7,8,1,2,3,6,4,5]=>0000000=>1111111=>1
[1,6,7,2,3,8,5,4]=>1000000=>0111111=>1
[1,2,5,6,3,8,7,4]=>1100000=>0011111=>1
[4,2,1,6,5,3,8,7]=>0000010=>1111101=>2
[8,6,2,4,3,1,5,7]=>0000000=>1111111=>1
[4,6,5,2,8,3,7,1]=>0000000=>1111111=>1
[2,6,4,5,8,3,7,1]=>0000000=>1111111=>1
[4,2,6,3,5,8,7,1]=>0000000=>1111111=>1
[8,2,4,3,6,5,1,7]=>0000000=>1111111=>1
[6,2,1,8,4,3,7,5]=>0000000=>1111111=>1
[4,6,8,7,5,2,1,3]=>0000000=>1111111=>1
[4,2,8,6,5,7,1,3]=>0000000=>1111111=>1
[8,2,6,4,5,1,3,7]=>0000000=>1111111=>1
[2,8,5,3,1,4,6,7]=>0000000=>1111111=>1
[2,7,4,8,3,5,1,6]=>0000000=>1111111=>1
[2,7,4,8,3,5,6,1]=>0000000=>1111111=>1
[7,2,8,4,3,5,1,6]=>0000000=>1111111=>1
[8,4,2,1,5,3,6,7]=>0000000=>1111111=>1
[8,5,1,4,2,3,6,7]=>0000000=>1111111=>1
[8,4,1,5,3,2,6,7]=>0000000=>1111111=>1
[6,7,3,8,4,2,5,1]=>0000000=>1111111=>1
[6,7,3,8,4,2,1,5]=>0000000=>1111111=>1
[7,1,8,4,3,5,2,6]=>0000000=>1111111=>1
[1,7,8,4,3,5,2,6]=>1000000=>0111111=>1
[7,1,4,8,3,5,2,6]=>0000000=>1111111=>1
[7,4,8,1,5,6,2,3]=>0000000=>1111111=>1
[7,1,8,4,3,5,6,2]=>0000000=>1111111=>1
[6,7,3,1,8,4,5,2]=>0000000=>1111111=>1
[6,7,3,8,4,5,2,1]=>0000000=>1111111=>1
[6,7,1,4,8,3,5,2]=>0000000=>1111111=>1
[6,7,4,1,3,8,2,5]=>0000000=>1111111=>1
[1,6,7,8,4,3,2,5]=>1000000=>0111111=>1
[7,2,1,8,4,5,3,6]=>0000000=>1111111=>1
[6,2,7,1,8,4,3,5]=>0000000=>1111111=>1
[6,2,7,8,4,3,1,5]=>0000000=>1111111=>1
[6,2,7,8,4,3,5,1]=>0000000=>1111111=>1
[2,6,7,4,8,3,5,1]=>0000000=>1111111=>1
[2,6,7,4,8,3,1,5]=>0000000=>1111111=>1
[7,8,1,3,6,2,4,5]=>0000000=>1111111=>1
[1,2,7,8,6,3,4,5]=>1100000=>0011111=>1
[2,6,7,1,8,5,3,4]=>0000000=>1111111=>1
[2,6,7,8,5,3,1,4]=>0000000=>1111111=>1
[2,6,7,8,5,3,4,1]=>0000000=>1111111=>1
[6,2,7,8,4,5,3,1]=>0000000=>1111111=>1
[7,2,1,8,4,5,6,3]=>0000000=>1111111=>1
[1,7,2,8,4,5,6,3]=>1000000=>0111111=>1
[3,7,8,1,5,6,2,4]=>0000000=>1111111=>1
[6,3,7,8,1,5,2,4]=>0000000=>1111111=>1
[6,7,1,2,8,5,3,4]=>0000000=>1111111=>1
[1,6,7,8,4,2,5,3]=>1000000=>0111111=>1
[4,1,5,7,3,2,6,8]=>0000001=>1111110=>1
[4,6,1,7,3,2,5,8]=>0000001=>1111110=>1
[1,6,5,8,7,3,4,2]=>1000000=>0111111=>1
[1,5,7,3,4,8,6,2]=>1000000=>0111111=>1
[3,8,1,2,4,5,7,6]=>0000000=>1111111=>1
[7,6,2,4,3,1,5,8]=>0000001=>1111110=>1
[8,1,7,4,6,3,2,5]=>0000000=>1111111=>1
[7,4,5,2,3,8,6,1]=>0000000=>1111111=>1
[7,2,3,4,5,8,6,1]=>0000000=>1111111=>1
[8,2,3,4,5,7,1,6]=>0000000=>1111111=>1
[4,7,3,2,8,6,1,5]=>0000000=>1111111=>1
[4,8,1,5,6,7,3,2]=>0000000=>1111111=>1
[3,7,6,1,8,5,2,4]=>0000000=>1111111=>1
[7,6,1,4,8,5,2,3]=>0000000=>1111111=>1
[5,4,8,3,6,7,1,2]=>0000000=>1111111=>1
[4,6,8,3,5,2,7,1]=>0000000=>1111111=>1
[5,7,8,3,2,4,1,6]=>0000000=>1111111=>1
[6,8,2,3,1,4,5,7]=>0000000=>1111111=>1
[5,2,7,4,8,3,1,6]=>0000000=>1111111=>1
[3,7,8,2,1,4,6,5]=>0000000=>1111111=>1
[3,7,5,2,8,4,1,6]=>0000000=>1111111=>1
[6,3,2,4,1,8,7,5]=>0000000=>1111111=>1
[7,2,3,4,8,5,1,6]=>0000000=>1111111=>1
[5,7,3,1,4,2,6,8]=>0000001=>1111110=>1
[3,7,4,1,8,2,5,6]=>0000000=>1111111=>1
[6,3,7,4,8,1,2,5]=>0000000=>1111111=>1
[8,3,7,4,2,6,1,5]=>0000000=>1111111=>1
[3,7,4,1,5,6,2,8]=>0000001=>1111110=>1
[1,8,3,2,4,5,7,6]=>1000000=>0111111=>1
[8,4,1,6,3,7,5,2]=>0000000=>1111111=>1
[8,7,4,2,1,6,3,5]=>0000000=>1111111=>1
[8,3,5,2,7,4,1,6]=>0000000=>1111111=>1
[1,5,3,8,7,6,4,2]=>1000000=>0111111=>1
[7,2,4,8,1,3,6,5]=>0000000=>1111111=>1
[1,2,8,7,5,6,3,4]=>1100000=>0011111=>1
[3,1,8,6,7,5,2,4]=>0000000=>1111111=>1
[1,4,8,6,5,7,2,3]=>1000000=>0111111=>1
[1,6,5,4,8,2,3,7]=>1000000=>0111111=>1
[5,1,6,8,3,4,2,7]=>0000000=>1111111=>1
[6,2,5,1,7,4,3,8]=>0000001=>1111110=>1
[5,2,1,8,7,4,3,6]=>0000000=>1111111=>1
[5,2,6,3,8,1,4,7]=>0000000=>1111111=>1
[5,2,8,3,4,6,1,7]=>0000000=>1111111=>1
[6,2,8,4,3,1,7,5]=>0000000=>1111111=>1
[7,2,8,1,3,6,5,4]=>0000000=>1111111=>1
[7,3,8,1,4,6,2,5]=>0000000=>1111111=>1
[1,7,8,5,4,6,3,2]=>1000000=>0111111=>1
[1,5,8,4,6,3,7,2]=>1000000=>0111111=>1
[5,3,8,4,1,2,7,6]=>0000000=>1111111=>1
[5,8,4,3,6,2,1,7]=>0000000=>1111111=>1
[1,8,3,6,5,2,7,4]=>1000000=>0111111=>1
[1,8,2,4,7,6,5,3]=>1000000=>0111111=>1
[3,8,1,4,6,7,5,2]=>0000000=>1111111=>1
[3,8,2,5,1,7,6,4]=>0000000=>1111111=>1
[4,3,8,2,5,1,6,7]=>0000000=>1111111=>1
[8,2,4,3,5,1,7,6]=>0000000=>1111111=>1
[8,2,1,4,6,5,7,3]=>0000000=>1111111=>1
[8,1,3,4,5,7,6,2]=>0000000=>1111111=>1
[6,1,5,2,4,7,8,3]=>0000000=>1111111=>1
[4,1,8,5,2,7,6,3]=>0000000=>1111111=>1
[4,1,8,2,3,7,5,6]=>0000000=>1111111=>1
[6,7,3,5,1,4,8,2]=>0000000=>1111111=>1
[6,4,7,5,8,2,3,1]=>0000000=>1111111=>1
[5,7,8,4,2,6,3,1]=>0000000=>1111111=>1
[5,4,7,6,2,8,3,1]=>0000000=>1111111=>1
[5,7,4,1,6,8,3,2]=>0000000=>1111111=>1
[6,8,4,5,7,1,3,2]=>0000000=>1111111=>1
[5,8,4,6,1,7,3,2]=>0000000=>1111111=>1
[5,6,1,4,7,8,3,2]=>0000000=>1111111=>1
[5,6,7,2,4,8,3,1]=>0000000=>1111111=>1
[5,6,3,7,4,8,2,1]=>0000000=>1111111=>1
[5,3,6,7,4,8,2,1]=>0000000=>1111111=>1
[5,3,2,8,6,7,4,1]=>0000000=>1111111=>1
[5,4,8,2,6,7,3,1]=>0000000=>1111111=>1
[5,4,8,6,2,7,3,1]=>0000000=>1111111=>1
[6,4,8,5,7,2,3,1]=>0000000=>1111111=>1
[7,4,8,5,6,2,1,3]=>0000000=>1111111=>1
[4,6,8,5,7,2,3,1]=>0000000=>1111111=>1
[5,6,8,2,4,7,3,1]=>0000000=>1111111=>1
[5,6,3,8,4,7,2,1]=>0000000=>1111111=>1
[4,6,3,5,8,7,2,1]=>0000000=>1111111=>1
[4,6,3,2,8,7,5,1]=>0000000=>1111111=>1
[5,6,3,8,2,7,4,1]=>0000000=>1111111=>1
[3,6,5,8,7,2,4,1]=>0000000=>1111111=>1
[5,3,6,8,2,7,4,1]=>0000000=>1111111=>1
[4,3,7,2,8,6,5,1]=>0000000=>1111111=>1
[5,4,7,2,6,8,3,1]=>0000000=>1111111=>1
[5,3,2,7,6,8,4,1]=>0000000=>1111111=>1
[6,7,3,8,5,2,4,1]=>0000000=>1111111=>1
[6,3,2,7,5,4,8,1]=>0000000=>1111111=>1
[6,4,7,2,5,3,8,1]=>0000000=>1111111=>1
[6,2,7,5,1,4,8,3]=>0000000=>1111111=>1
[2,7,8,5,3,6,1,4]=>0000000=>1111111=>1
[6,3,7,8,4,2,5,1]=>0000000=>1111111=>1
[3,5,7,8,4,6,2,1]=>0000000=>1111111=>1
[5,3,7,8,4,6,2,1]=>0000000=>1111111=>1
[5,7,8,2,4,6,3,1]=>0000000=>1111111=>1
[2,5,8,4,3,7,6,1]=>0000000=>1111111=>1
[2,6,8,4,7,3,5,1]=>0000000=>1111111=>1
[3,7,4,8,6,2,1,5]=>0000000=>1111111=>1
[3,6,4,8,7,2,5,1]=>0000000=>1111111=>1
[3,5,4,8,2,7,6,1]=>0000000=>1111111=>1
[4,3,7,5,8,6,2,1]=>0000000=>1111111=>1
[4,5,7,3,8,6,2,1]=>0000000=>1111111=>1
[3,5,6,8,4,7,2,1]=>0000000=>1111111=>1
[6,3,1,8,7,5,4,2]=>0000000=>1111111=>1
[5,4,8,1,7,6,3,2]=>0000000=>1111111=>1
[8,5,4,1,7,6,3,2]=>0000000=>1111111=>1
[1,8,2,5,6,3,4,7]=>1000000=>0111111=>1
[7,2,8,4,5,1,3,6]=>0000000=>1111111=>1
[1,3,7,5,6,2,4,8]=>1000001=>0111110=>1
[1,6,7,4,3,5,2,8]=>1000001=>0111110=>1
[1,8,5,2,3,7,4,6]=>1000000=>0111111=>1
[1,8,2,5,3,6,7,4]=>1000000=>0111111=>1
[2,6,8,4,3,5,7,1]=>0000000=>1111111=>1
[7,5,8,3,2,1,6,4]=>0000000=>1111111=>1
[7,2,8,4,1,5,6,3]=>0000000=>1111111=>1
[7,5,8,1,2,6,3,4]=>0000000=>1111111=>1
[1,6,7,4,3,2,8,5]=>1000000=>0111111=>1
[1,5,2,6,4,7,8,3]=>1000000=>0111111=>1
[1,5,4,6,2,3,7,8]=>1000011=>0111100=>1
[6,2,5,7,1,4,8,3]=>0000000=>1111111=>1
[6,5,4,3,8,1,7,2]=>0000000=>1111111=>1
[7,3,6,8,5,2,4,1]=>0000000=>1111111=>1
[2,7,8,3,6,5,1,4]=>0000000=>1111111=>1
[2,7,8,5,4,6,3,1]=>0000000=>1111111=>1
[2,6,5,8,3,4,1,7]=>0000000=>1111111=>1
[2,6,5,7,3,4,1,8]=>0000001=>1111110=>1
[6,2,5,7,4,1,3,8]=>0000001=>1111110=>1
[6,2,5,8,4,1,3,7]=>0000000=>1111111=>1
[2,7,8,4,6,1,3,5]=>0000000=>1111111=>1
[6,1,2,8,3,7,4,5]=>0000000=>1111111=>1
[6,1,2,8,5,4,7,3]=>0000000=>1111111=>1
[6,2,5,7,8,1,3,4]=>0000000=>1111111=>1
[1,5,4,2,6,7,3,8]=>1000001=>0111110=>1
[2,6,5,7,3,8,1,4]=>0000000=>1111111=>1
[1,6,2,7,5,8,4,3]=>1000000=>0111111=>1
[1,3,2,7,8,5,6,4]=>1010000=>0101111=>2
[1,6,2,4,8,7,3,5]=>1000000=>0111111=>1
[6,5,2,1,8,7,3,4]=>0000000=>1111111=>1
[2,6,5,3,7,8,4,1]=>0000000=>1111111=>1
[6,2,5,3,8,4,7,1]=>0000000=>1111111=>1
[6,5,2,3,8,7,1,4]=>0000000=>1111111=>1
[5,4,1,2,3,8,6,7]=>0000100=>1111011=>2
[5,1,4,2,3,7,8,6]=>0000100=>1111011=>2
[1,5,4,2,6,3,8,7]=>1000010=>0111101=>2
[9,8,7,6,5,4,3,1,2,10]=>000000001=>111111110=>1
[8,7,6,5,4,2,1,3,9]=>00000001=>11111110=>1
[1,9,8,7,6,5,3,2,4]=>10000000=>01111111=>1
[1,8,7,6,2,5,4,3]=>1000000=>0111111=>1
[1,9,8,7,6,5,2,4,3]=>10000000=>01111111=>1
[1,10,9,8,7,6,5,4,2,3]=>100000000=>011111111=>1
[2,1,9,8,7,6,5,4,3]=>01000000=>10111111=>2
[1,2,9,8,7,6,5,4,3]=>11000000=>00111111=>1
[3,2,1,9,8,7,6,5,4]=>00100000=>11011111=>2
[1,3,2,9,8,7,6,5,4]=>10100000=>01011111=>2
[1,2,3,9,8,7,6,5,4]=>11100000=>00011111=>1
[4,3,2,1,9,8,7,6,5]=>00010000=>11101111=>2
[1,4,3,2,9,8,7,6,5]=>10010000=>01101111=>2
[2,1,4,3,9,8,7,6,5]=>01010000=>10101111=>3
[1,2,4,3,9,8,7,6,5]=>11010000=>00101111=>2
[1,2,3,4,9,8,7,6,5]=>11110000=>00001111=>1
[1,5,4,3,2,9,8,7,6]=>10001000=>01110111=>2
[2,1,5,4,3,9,8,7,6]=>01001000=>10110111=>3
[1,2,5,4,3,9,8,7,6]=>11001000=>00110111=>2
[1,3,2,5,4,9,8,7,6]=>10101000=>01010111=>3
[1,2,3,5,4,9,8,7,6]=>11101000=>00010111=>2
[1,2,3,4,5,9,8,7,6]=>11111000=>00000111=>1
[1,3,2,6,5,4,9,8,7]=>10100100=>01011011=>3
[1,2,3,6,5,4,9,8,7]=>11100100=>00011011=>2
[2,1,4,3,6,5,9,8,7]=>01010100=>10101011=>4
[1,2,4,3,6,5,9,8,7]=>11010100=>00101011=>3
[1,2,3,4,6,5,9,8,7]=>11110100=>00001011=>2
[1,2,3,5,4,7,6,9,8]=>11101010=>00010101=>3
[1,2,3,4,5,7,6,9,8]=>11111010=>00000101=>2
[1,2,10,9,8,7,6,5,4,3]=>110000000=>001111111=>1
[3,2,1,10,9,8,7,6,5,4]=>001000000=>110111111=>2
[1,3,2,10,9,8,7,6,5,4]=>101000000=>010111111=>2
[1,2,3,10,9,8,7,6,5,4]=>111000000=>000111111=>1
[1,4,3,2,10,9,8,7,6,5]=>100100000=>011011111=>2
[1,2,4,3,10,9,8,7,6,5]=>110100000=>001011111=>2
[1,2,3,4,10,9,8,7,6,5]=>111100000=>000011111=>1
[1,5,4,3,2,10,9,8,7,6]=>100010000=>011101111=>2
[2,1,5,4,3,10,9,8,7,6]=>010010000=>101101111=>3
[1,2,5,4,3,10,9,8,7,6]=>110010000=>001101111=>2
[1,3,2,5,4,10,9,8,7,6]=>101010000=>010101111=>3
[1,2,3,5,4,10,9,8,7,6]=>111010000=>000101111=>2
[1,2,6,5,4,3,10,9,8,7]=>110001000=>001110111=>2
[3,2,1,6,5,4,10,9,8,7]=>001001000=>110110111=>3
[1,3,2,6,5,4,10,9,8,7]=>101001000=>010110111=>3
[1,2,3,6,5,4,10,9,8,7]=>111001000=>000110111=>2
[1,2,4,3,6,5,10,9,8,7]=>110101000=>001010111=>3
[1,2,3,4,6,5,10,9,8,7]=>111101000=>000010111=>2
[1,2,3,4,5,6,10,9,8,7]=>111111000=>000000111=>1
[1,4,3,2,7,6,5,10,9,8]=>100100100=>011011011=>3
[2,1,4,3,7,6,5,10,9,8]=>010100100=>101011011=>4
[1,2,4,3,7,6,5,10,9,8]=>110100100=>001011011=>3
[1,2,3,4,7,6,5,10,9,8]=>111100100=>000011011=>2
[1,3,2,5,4,7,6,10,9,8]=>101010100=>010101011=>4
[1,2,3,5,4,7,6,10,9,8]=>111010100=>000101011=>3
[1,2,3,4,5,7,6,10,9,8]=>111110100=>000001011=>2
[1,2,3,4,5,6,7,10,9,8]=>111111100=>000000011=>1
[1,2,4,3,6,5,8,7,10,9]=>110101010=>001010101=>4
[1,2,3,4,6,5,8,7,10,9]=>111101010=>000010101=>3
[1,2,3,4,5,6,8,7,10,9]=>111111010=>000000101=>2
[5,2,7,4,1,6,3,8]=>0000001=>1111110=>1
[4,7,3,1,5,6,2,8]=>0000001=>1111110=>1
[5,8,3,4,1,6,7,2]=>0000000=>1111111=>1
[1,7,8,4,5,6,2,3]=>1000000=>0111111=>1
[1,5,8,4,2,6,7,3]=>1000000=>0111111=>1
[1,6,3,8,5,2,7,4]=>1000000=>0111111=>1
[5,2,3,7,1,6,4,8]=>0000001=>1111110=>1
[6,2,3,7,5,1,4,8]=>0000001=>1111110=>1
[1,7,3,4,8,6,2,5]=>1000000=>0111111=>1
[6,2,3,4,8,1,7,5]=>0000000=>1111111=>1
[8,7,3,2,1,6,5,4]=>0000000=>1111111=>1
[8,7,6,3,1,5,2,4]=>0000000=>1111111=>1
[8,5,1,7,2,3,4,6]=>0000000=>1111111=>1
[9,8,7,6,5,2,1,4,3]=>00000000=>11111111=>1
[9,8,7,3,2,1,6,5,4]=>00000000=>11111111=>1
[9,8,7,6,3,1,5,2,4]=>00000000=>11111111=>1
[9,4,3,2,1,8,7,6,5]=>00000000=>11111111=>1
[9,8,4,3,1,7,6,2,5]=>00000000=>11111111=>1
[9,8,7,2,1,4,3,6,5]=>00000000=>11111111=>1
[9,8,7,4,1,6,2,3,5]=>00000000=>11111111=>1
[5,4,3,1,9,8,7,2,6]=>00000000=>11111111=>1
[9,5,2,1,8,4,3,7,6]=>00000000=>11111111=>1
[9,8,3,1,5,2,7,4,6]=>00000000=>11111111=>1
[6,3,1,9,5,2,8,4,7]=>00000000=>11111111=>1
[6,5,1,9,8,2,3,4,7]=>00000000=>11111111=>1
[9,2,1,4,3,6,5,8,7]=>00000000=>11111111=>1
[9,6,1,8,2,3,4,5,7]=>00000000=>11111111=>1
[5,1,7,2,9,3,4,6,8]=>00000000=>11111111=>1
[7,1,9,2,3,4,5,6,8]=>00000000=>11111111=>1
[10,9,8,7,6,5,2,1,4,3]=>000000000=>111111111=>1
[10,9,8,7,3,2,1,6,5,4]=>000000000=>111111111=>1
[10,9,8,7,6,3,1,5,2,4]=>000000000=>111111111=>1
[10,9,4,3,2,1,8,7,6,5]=>000000000=>111111111=>1
[10,9,8,4,3,1,7,6,2,5]=>000000000=>111111111=>1
[10,9,8,7,2,1,4,3,6,5]=>000000000=>111111111=>1
[10,9,8,7,4,1,6,2,3,5]=>000000000=>111111111=>1
[10,5,4,3,1,9,8,7,2,6]=>000000000=>111111111=>1
[10,9,5,2,1,8,4,3,7,6]=>000000000=>111111111=>1
[10,9,5,4,1,8,7,2,3,6]=>000000000=>111111111=>1
[10,9,8,3,1,5,2,7,4,6]=>000000000=>111111111=>1
[6,5,2,1,10,9,4,3,8,7]=>000000000=>111111111=>1
[6,5,4,1,10,9,8,2,3,7]=>000000000=>111111111=>1
[10,3,2,1,6,5,4,9,8,7]=>000000000=>111111111=>1
[10,6,5,1,9,8,2,3,4,7]=>000000000=>111111111=>1
[10,9,2,1,4,3,6,5,8,7]=>000000000=>111111111=>1
[10,9,6,1,8,2,3,4,5,7]=>000000000=>111111111=>1
[4,3,1,7,6,2,10,9,5,8]=>000000000=>111111111=>1
[7,2,1,10,4,3,6,5,9,8]=>000000000=>111111111=>1
[7,4,1,10,6,2,9,3,5,8]=>000000000=>111111111=>1
[7,6,1,10,9,2,3,4,5,8]=>000000000=>111111111=>1
[10,5,1,7,2,9,3,4,6,8]=>000000000=>111111111=>1
[10,7,1,9,2,3,4,5,6,8]=>000000000=>111111111=>1
[4,1,6,2,8,3,10,5,7,9]=>000000000=>111111111=>1
[6,1,8,2,10,3,4,5,7,9]=>000000000=>111111111=>1
[8,1,10,2,3,4,5,6,7,9]=>000000000=>111111111=>1
[2,4,8,5,3,7,1,6]=>0000000=>1111111=>1
[2,4,1,8,5,3,7,6]=>0000000=>1111111=>1
[2,4,8,6,3,1,7,5]=>0000000=>1111111=>1
[3,4,6,8,2,1,7,5]=>0000000=>1111111=>1
[3,4,1,5,8,2,7,6]=>0000000=>1111111=>1
[8,1,4,5,3,2,7,6]=>0000000=>1111111=>1
[3,4,1,5,2,8,7,6]=>0000100=>1111011=>2
[3,4,6,2,1,8,7,5]=>0000000=>1111111=>1
[3,5,6,2,1,7,8,4]=>0000000=>1111111=>1
[3,4,6,2,7,8,1,5]=>0000000=>1111111=>1
[8,1,4,6,3,7,2,5]=>0000000=>1111111=>1
[8,1,4,6,3,7,5,2]=>0000000=>1111111=>1
[3,5,6,2,1,7,4,8]=>0000001=>1111110=>1
[8,1,5,6,7,3,4,2]=>0000000=>1111111=>1
[8,1,5,6,7,3,2,4]=>0000000=>1111111=>1
[3,4,1,6,8,7,2,5]=>0000000=>1111111=>1
[3,5,6,1,8,7,2,4]=>0000000=>1111111=>1
[2,1,3,8,6,7,4,5]=>0110000=>1001111=>2
[8,1,3,2,6,7,5,4]=>0000000=>1111111=>1
[2,3,8,6,7,1,5,4]=>0000000=>1111111=>1
[2,4,1,8,6,7,5,3]=>0000000=>1111111=>1
[2,5,8,6,1,7,4,3]=>0000000=>1111111=>1
[3,5,6,1,8,7,4,2]=>0000000=>1111111=>1
[3,4,1,6,8,7,5,2]=>0000000=>1111111=>1
[3,4,6,8,7,1,5,2]=>0000000=>1111111=>1
[8,1,4,6,2,7,5,3]=>0000000=>1111111=>1
[3,5,1,6,7,8,4,2]=>0000000=>1111111=>1
[4,5,6,1,7,8,3,2]=>0000000=>1111111=>1
[4,5,6,1,7,3,8,2]=>0000000=>1111111=>1
[3,5,1,6,7,4,8,2]=>0000000=>1111111=>1
[8,1,5,6,7,4,2,3]=>0000000=>1111111=>1
[8,1,5,6,7,4,3,2]=>0000000=>1111111=>1
[3,5,1,6,7,4,2,8]=>0000001=>1111110=>1
[4,5,6,1,7,3,2,8]=>0000001=>1111110=>1
[6,5,8,7,4,3,1,2]=>0000000=>1111111=>1
[6,1,4,8,7,5,2,3]=>0000000=>1111111=>1
[7,6,2,1,4,8,3,5]=>0000000=>1111111=>1
[8,1,6,3,4,7,2,5]=>0000000=>1111111=>1
[1,2,7,5,4,8,3,6]=>1100000=>0011111=>1
[3,2,7,5,4,8,1,6]=>0000000=>1111111=>1
[6,8,3,2,4,7,1,5]=>0000000=>1111111=>1
[3,7,2,5,4,8,1,6]=>0000000=>1111111=>1
[1,3,7,5,4,8,2,6]=>1000000=>0111111=>1
[8,7,5,6,2,1,4,3]=>0000000=>1111111=>1
[2,7,3,5,4,8,1,6]=>0000000=>1111111=>1
[8,2,5,4,7,3,1,6]=>0000000=>1111111=>1
[8,1,7,6,4,3,5,2]=>0000000=>1111111=>1
[7,1,8,6,4,3,5,2]=>0000000=>1111111=>1
[7,3,6,5,2,1,4,8]=>0000001=>1111110=>1
[6,4,2,5,1,8,3,7]=>0000000=>1111111=>1
[6,3,5,2,1,4,7,8]=>0000011=>1111100=>1
[2,3,5,8,1,4,7,6]=>0000000=>1111111=>1
[6,3,8,5,2,7,1,4]=>0000000=>1111111=>1
[7,3,5,2,1,4,6,8]=>0000001=>1111110=>1
[8,4,2,5,1,3,7,6]=>0000000=>1111111=>1
[2,3,6,8,1,4,7,5]=>0000000=>1111111=>1
[7,3,8,5,2,1,4,6]=>0000000=>1111111=>1
[2,3,6,1,8,4,7,5]=>0000000=>1111111=>1
[2,4,8,1,3,7,5,6]=>0000000=>1111111=>1
[2,5,8,1,7,3,6,4]=>0000000=>1111111=>1
[2,8,1,5,7,3,6,4]=>0000000=>1111111=>1
[2,6,8,1,5,7,3,4]=>0000000=>1111111=>1
[2,7,1,5,8,3,4,6]=>0000000=>1111111=>1
[3,7,5,8,1,2,6,4]=>0000000=>1111111=>1
[7,3,6,1,2,8,4,5]=>0000000=>1111111=>1
[6,8,4,5,1,7,2,3]=>0000000=>1111111=>1
[5,1,8,7,6,2,3,4]=>0000000=>1111111=>1
[8,5,1,6,2,7,3,4]=>0000000=>1111111=>1
[4,6,1,8,7,5,2,3]=>0000000=>1111111=>1
[4,5,1,8,7,2,3,6]=>0000000=>1111111=>1
[3,4,8,7,1,2,5,6]=>0000000=>1111111=>1
[5,6,8,3,7,1,4,2]=>0000000=>1111111=>1
[6,4,7,1,2,8,5,3]=>0000000=>1111111=>1
[6,5,1,2,7,3,8,4]=>0000000=>1111111=>1
[6,5,1,8,2,7,3,4]=>0000000=>1111111=>1
[6,5,1,8,7,2,3,4]=>0000000=>1111111=>1
[6,5,1,7,2,8,3,4]=>0000000=>1111111=>1
[6,5,1,7,2,3,8,4]=>0000000=>1111111=>1
[5,6,8,7,4,1,2,3]=>0000000=>1111111=>1
[6,8,5,7,4,1,2,3]=>0000000=>1111111=>1
[7,3,8,1,5,2,4,6]=>0000000=>1111111=>1
[4,1,7,5,3,6,2,8]=>0000001=>1111110=>1
[1,8,4,2,3,6,7,5]=>1000000=>0111111=>1
[2,5,8,3,4,6,7,1]=>0000000=>1111111=>1
[4,1,7,2,3,6,8,5]=>0000000=>1111111=>1
[4,6,2,1,5,7,8,3]=>0000000=>1111111=>1
[4,5,2,3,1,7,8,6]=>0000100=>1111011=>2
[3,2,6,7,4,1,8,5]=>0000000=>1111111=>1
[5,6,2,7,1,4,8,3]=>0000000=>1111111=>1
[6,2,3,8,1,7,4,5]=>0000000=>1111111=>1
[2,6,8,3,4,7,1,5]=>0000000=>1111111=>1
[4,6,2,7,5,1,3,8]=>0000001=>1111110=>1
[2,6,3,1,8,4,5,7]=>0000000=>1111111=>1
[2,4,3,7,8,1,5,6]=>0000000=>1111111=>1
[5,3,2,7,4,8,1,6]=>0000000=>1111111=>1
[5,1,2,7,6,8,4,3]=>0000000=>1111111=>1
[2,6,3,1,8,7,4,5]=>0000000=>1111111=>1
[3,5,6,4,7,8,1,2]=>0000000=>1111111=>1
[5,3,6,4,2,8,7,1]=>0000000=>1111111=>1
[5,4,2,3,7,8,6,1]=>0000000=>1111111=>1
[4,1,8,2,5,7,3,6]=>0000000=>1111111=>1
[3,1,8,4,7,2,5,6]=>0000000=>1111111=>1
[6,2,3,8,4,1,7,5]=>0000000=>1111111=>1
[2,6,4,1,5,3,8,7]=>0000010=>1111101=>2
[3,2,7,6,4,1,8,5]=>0000000=>1111111=>1
[2,5,4,1,7,6,8,3]=>0000000=>1111111=>1
[6,2,1,4,7,8,3,5]=>0000000=>1111111=>1
[2,6,5,1,7,8,3,4]=>0000000=>1111111=>1
[4,7,5,2,1,6,3,8]=>0000001=>1111110=>1
[4,2,3,7,8,1,6,5]=>0000000=>1111111=>1
[6,8,3,1,5,2,4,7]=>0000000=>1111111=>1
[6,8,3,2,5,1,7,4]=>0000000=>1111111=>1
[6,8,4,3,1,5,7,2]=>0000000=>1111111=>1
[6,8,4,2,1,5,7,3]=>0000000=>1111111=>1
[5,1,7,3,2,4,6,8]=>0000001=>1111110=>1
[4,3,8,1,6,2,7,5]=>0000000=>1111111=>1
[4,2,1,8,5,7,3,6]=>0000000=>1111111=>1
[6,3,2,1,7,4,5,8]=>0000001=>1111110=>1
[6,4,2,1,7,5,3,8]=>0000001=>1111110=>1
[6,3,2,8,7,1,4,5]=>0000000=>1111111=>1
[4,2,8,1,7,3,5,6]=>0000000=>1111111=>1
[4,3,8,7,2,1,5,6]=>0000000=>1111111=>1
[4,3,1,6,2,7,5,8]=>0000001=>1111110=>1
[5,4,1,7,2,8,6,3]=>0000000=>1111111=>1
[6,5,3,1,7,8,4,2]=>0000000=>1111111=>1
[5,4,2,1,6,7,3,8]=>0000001=>1111110=>1
[6,4,2,1,7,8,5,3]=>0000000=>1111111=>1
[5,3,2,1,6,7,8,4]=>0000000=>1111111=>1
[8,6,1,4,5,7,2,3]=>0000000=>1111111=>1
[5,2,8,3,7,4,6,1]=>0000000=>1111111=>1
[6,2,8,5,4,7,3,1]=>0000000=>1111111=>1
[1,8,6,3,7,4,2,5]=>1000000=>0111111=>1
[1,8,6,5,7,2,3,4]=>1000000=>0111111=>1
[5,2,8,4,3,6,7,1]=>0000000=>1111111=>1
[5,4,2,7,3,6,1,8]=>0000001=>1111110=>1
[5,4,2,8,3,6,1,7]=>0000000=>1111111=>1
[6,5,3,8,4,7,2,1]=>0000000=>1111111=>1
[5,2,8,4,3,7,1,6]=>0000000=>1111111=>1
[6,2,8,3,7,4,1,5]=>0000000=>1111111=>1
[5,4,2,7,3,1,8,6]=>0000000=>1111111=>1
[6,4,3,7,1,2,8,5]=>0000000=>1111111=>1
[6,4,3,8,1,2,7,5]=>0000000=>1111111=>1
[7,6,3,8,4,2,1,5]=>0000000=>1111111=>1
[7,2,8,5,1,6,3,4]=>0000000=>1111111=>1
[7,2,8,4,3,1,5,6]=>0000000=>1111111=>1
[7,5,3,8,4,2,6,1]=>0000000=>1111111=>1
[6,4,2,7,3,1,5,8]=>0000001=>1111110=>1
[7,6,4,8,2,3,5,1]=>0000000=>1111111=>1
[7,6,8,1,2,5,3,4]=>0000000=>1111111=>1
[5,3,1,7,8,4,6,2]=>0000000=>1111111=>1
[5,3,2,7,8,4,6,1]=>0000000=>1111111=>1
[5,4,1,6,3,8,7,2]=>0000000=>1111111=>1
[6,5,1,7,8,2,3,4]=>0000000=>1111111=>1
[6,3,1,7,8,4,2,5]=>0000000=>1111111=>1
[5,4,1,7,3,8,2,6]=>0000000=>1111111=>1
[6,3,2,7,8,4,1,5]=>0000000=>1111111=>1
[8,7,6,1,3,5,2,4]=>0000000=>1111111=>1
[8,4,1,5,7,6,2,3]=>0000000=>1111111=>1
[8,4,7,6,3,1,5,2]=>0000000=>1111111=>1
[5,4,1,7,6,2,8,3]=>0000000=>1111111=>1
[3,5,6,7,1,4,8,2]=>0000000=>1111111=>1
[5,7,2,1,6,3,8,4]=>0000000=>1111111=>1
[6,8,7,1,3,2,5,4]=>0000000=>1111111=>1
[6,4,8,1,3,2,7,5]=>0000000=>1111111=>1
[1,4,5,2,8,6,7,3]=>1000000=>0111111=>1
[2,3,1,7,8,6,4,5]=>0010000=>1101111=>2
[4,5,6,1,2,8,7,3]=>0000000=>1111111=>1
[5,1,3,2,7,8,4,6]=>0000000=>1111111=>1
[1,5,4,2,7,8,3,6]=>1000000=>0111111=>1
[5,3,8,1,7,2,4,6]=>0000000=>1111111=>1
[3,6,7,8,4,2,1,5]=>0000000=>1111111=>1
[2,5,8,3,1,6,7,4]=>0000000=>1111111=>1
[1,5,8,3,2,6,7,4]=>1000000=>0111111=>1
[1,3,8,6,2,4,7,5]=>1000000=>0111111=>1
[4,8,7,2,1,6,3,5]=>0000000=>1111111=>1
[8,3,4,2,1,6,5,7]=>0000000=>1111111=>1
[2,4,5,8,3,6,1,7]=>0000000=>1111111=>1
[3,5,8,1,2,6,4,7]=>0000000=>1111111=>1
[2,6,4,3,7,8,5,1]=>0000000=>1111111=>1
[7,4,1,8,3,2,5,6]=>0000000=>1111111=>1
[5,6,1,7,4,2,8,3]=>0000000=>1111111=>1
[3,6,5,7,1,8,4,2]=>0000000=>1111111=>1
[6,7,3,8,4,1,2,5]=>0000000=>1111111=>1
[4,7,5,8,3,1,2,6]=>0000000=>1111111=>1
[3,6,7,4,8,1,2,5]=>0000000=>1111111=>1
[5,7,3,1,6,8,4,2]=>0000000=>1111111=>1
[8,7,6,4,1,2,5,3]=>0000000=>1111111=>1
[8,5,3,2,7,6,1,4]=>0000000=>1111111=>1
[2,5,1,3,6,8,7,4]=>0000000=>1111111=>1
[8,7,5,4,2,1,6,3]=>0000000=>1111111=>1
[6,7,2,5,1,8,4,3]=>0000000=>1111111=>1
[3,6,1,2,5,8,4,7]=>0000000=>1111111=>1
[1,4,5,8,2,3,7,6]=>1000000=>0111111=>1
[1,2,6,4,5,8,3,7]=>1100000=>0011111=>1
[1,5,2,4,6,8,3,7]=>1000000=>0111111=>1
[3,6,1,5,8,2,4,7]=>0000000=>1111111=>1
[2,6,5,1,4,8,3,7]=>0000000=>1111111=>1
[5,2,6,1,4,8,3,7]=>0000000=>1111111=>1
[2,5,1,8,4,7,3,6]=>0000000=>1111111=>1
[2,7,1,4,3,6,8,5]=>0000000=>1111111=>1
[1,3,7,5,8,2,4,6]=>1000000=>0111111=>1
[8,2,1,5,7,3,4,6]=>0000000=>1111111=>1
[2,5,4,8,1,3,7,6]=>0000000=>1111111=>1
[2,4,1,3,8,6,7,5]=>0001000=>1110111=>2
[8,4,3,7,1,2,6,5]=>0000000=>1111111=>1
[1,7,3,5,8,2,6,4]=>1000000=>0111111=>1
[1,8,4,2,6,7,3,5]=>1000000=>0111111=>1
[3,1,6,8,7,2,4,5]=>0000000=>1111111=>1
[7,2,1,6,8,3,4,5]=>0000000=>1111111=>1
[3,1,7,6,8,2,4,5]=>0000000=>1111111=>1
[4,1,7,2,6,8,3,5]=>0000000=>1111111=>1
[5,1,7,2,3,6,8,4]=>0000000=>1111111=>1
[7,2,1,6,3,5,8,4]=>0000000=>1111111=>1
[2,6,1,7,3,5,8,4]=>0000000=>1111111=>1
[7,1,2,5,3,6,8,4]=>0000000=>1111111=>1
[5,4,1,2,7,8,3,6]=>0000000=>1111111=>1
[8,1,3,2,4,6,7,5]=>0000000=>1111111=>1
[7,3,1,2,4,6,8,5]=>0000000=>1111111=>1
[1,8,3,4,7,2,5,6]=>1000000=>0111111=>1
[3,5,8,1,2,7,4,6]=>0000000=>1111111=>1
[3,6,8,1,2,4,7,5]=>0000000=>1111111=>1
[4,1,3,8,7,2,6,5]=>0000000=>1111111=>1
[1,3,7,4,8,2,6,5]=>1000000=>0111111=>1
[1,4,6,8,2,3,7,5]=>1000000=>0111111=>1
[3,5,8,1,7,2,4,6]=>0000000=>1111111=>1
[2,6,8,1,7,3,4,5]=>0000000=>1111111=>1
[6,1,5,8,2,3,7,4]=>0000000=>1111111=>1
[1,8,3,2,7,5,6,4]=>1000000=>0111111=>1
[3,1,7,2,8,5,6,4]=>0000000=>1111111=>1
[2,6,7,3,8,1,5,4]=>0000000=>1111111=>1
[8,4,1,7,3,6,2,5]=>0000000=>1111111=>1
[3,7,2,8,6,1,5,4]=>0000000=>1111111=>1
[6,2,3,8,7,1,5,4]=>0000000=>1111111=>1
[6,8,2,4,3,7,5,1]=>0000000=>1111111=>1
[6,8,2,7,3,5,4,1]=>0000000=>1111111=>1
[3,7,8,2,4,1,5,6]=>0000000=>1111111=>1
[8,6,1,7,2,5,4,3]=>0000000=>1111111=>1
[8,7,6,1,2,3,5,4]=>0000000=>1111111=>1
[8,3,4,7,1,6,2,5]=>0000000=>1111111=>1
[2,8,6,7,5,3,4,1]=>0000000=>1111111=>1
[2,1,8,7,3,6,4,5]=>0100000=>1011111=>2
[4,6,5,2,7,3,8,1]=>0000000=>1111111=>1
[6,3,8,7,4,5,1,2]=>0000000=>1111111=>1
[8,5,7,4,6,2,1,3]=>0000000=>1111111=>1
[5,8,3,2,4,6,1,7]=>0000000=>1111111=>1
[2,1,8,6,4,3,7,5]=>0100000=>1011111=>2
[7,5,4,3,1,8,6,2]=>0000000=>1111111=>1
[4,1,3,6,7,5,8,2]=>0000000=>1111111=>1
[1,7,2,4,5,8,3,6]=>1000000=>0111111=>1
[1,7,4,5,8,3,2,6]=>1000000=>0111111=>1
[2,6,4,7,8,3,5,1]=>0000000=>1111111=>1
[1,2,6,4,7,8,3,5]=>1100000=>0011111=>1
[6,1,4,7,8,3,5,2]=>0000000=>1111111=>1
[3,6,4,7,8,1,2,5]=>0000000=>1111111=>1
[4,7,2,1,5,3,8,6]=>0000000=>1111111=>1
[1,3,6,4,7,2,8,5]=>1000000=>0111111=>1
[3,6,4,7,2,8,5,1]=>0000000=>1111111=>1
[5,1,3,4,2,7,8,6]=>0000100=>1111011=>2
[1,6,7,3,8,2,5,4]=>1000000=>0111111=>1
[6,1,4,7,8,5,2,3]=>0000000=>1111111=>1
[8,6,5,1,3,2,4,7]=>0000000=>1111111=>1
[5,8,6,4,1,3,2,7]=>0000000=>1111111=>1
[6,8,5,7,4,2,3,1]=>0000000=>1111111=>1
[2,3,8,7,1,6,4,5]=>0000000=>1111111=>1
[3,5,8,7,4,1,2,6]=>0000000=>1111111=>1
[4,8,1,2,7,3,5,6]=>0000000=>1111111=>1
[6,8,1,2,7,4,5,3]=>0000000=>1111111=>1
[2,4,8,7,5,6,1,3]=>0000000=>1111111=>1
[6,4,8,7,5,1,2,3]=>0000000=>1111111=>1
[6,3,8,7,2,1,4,5]=>0000000=>1111111=>1
[3,7,6,8,5,1,2,4]=>0000000=>1111111=>1
[2,6,7,8,5,1,3,4]=>0000000=>1111111=>1
[2,8,3,4,1,5,7,6]=>0000000=>1111111=>1
[6,8,7,1,5,2,3,4]=>0000000=>1111111=>1
[5,8,3,2,7,6,1,4]=>0000000=>1111111=>1
[4,5,3,2,8,6,7,1]=>0000000=>1111111=>1
[3,5,8,6,1,4,7,2]=>0000000=>1111111=>1
[2,6,4,8,5,1,7,3]=>0000000=>1111111=>1
[7,6,4,8,5,2,1,3]=>0000000=>1111111=>1
[3,4,8,7,5,6,2,1]=>0000000=>1111111=>1
[7,5,3,2,8,6,1,4]=>0000000=>1111111=>1
[4,5,1,2,8,6,7,3]=>0000000=>1111111=>1
[6,1,5,7,2,4,8,3]=>0000000=>1111111=>1
[7,4,5,1,2,3,8,6]=>0000000=>1111111=>1
[8,4,7,6,2,1,5,3]=>0000000=>1111111=>1
[3,5,7,6,4,1,8,2]=>0000000=>1111111=>1
[5,7,2,3,6,4,8,1]=>0000000=>1111111=>1
[4,8,7,6,1,2,5,3]=>0000000=>1111111=>1
[6,8,3,1,2,4,5,7]=>0000000=>1111111=>1
[6,2,7,4,8,1,3,5]=>0000000=>1111111=>1
[4,3,2,6,8,1,7,5]=>0000000=>1111111=>1
[3,5,4,2,8,1,6,7]=>0000000=>1111111=>1
[1,5,8,3,7,4,2,6]=>1000000=>0111111=>1
[3,6,8,5,2,7,4,1]=>0000000=>1111111=>1
[2,1,6,5,4,8,3,7]=>0100000=>1011111=>2
[2,1,7,8,4,6,5,3]=>0100000=>1011111=>2
[7,6,3,8,1,5,4,2]=>0000000=>1111111=>1
[7,2,4,1,6,3,8,5]=>0000000=>1111111=>1
[8,4,3,1,7,5,2,6]=>0000000=>1111111=>1
[4,3,8,7,1,6,5,2]=>0000000=>1111111=>1
[5,2,4,3,6,8,1,7]=>0000000=>1111111=>1
[4,2,7,5,8,3,6,1]=>0000000=>1111111=>1
[5,8,2,7,3,4,6,1]=>0000000=>1111111=>1
[6,7,2,4,5,3,8,1]=>0000000=>1111111=>1
[6,3,2,1,4,8,5,7]=>0000000=>1111111=>1
[8,7,3,5,4,2,1,6]=>0000000=>1111111=>1
[8,4,6,5,3,2,1,7]=>0000000=>1111111=>1
[9,1,8,7,6,5,4,3,2]=>00000000=>11111111=>1
[7,6,8,1,5,4,3,2]=>0000000=>1111111=>1
[7,1,9,8,6,5,4,3,2]=>00000000=>11111111=>1
[6,1,9,8,7,5,4,3,2]=>00000000=>11111111=>1
[5,4,8,7,6,1,3,2]=>0000000=>1111111=>1
[5,1,9,8,7,6,4,3,2]=>00000000=>11111111=>1
[4,1,9,8,7,6,5,3,2]=>00000000=>11111111=>1
[3,1,9,8,7,6,5,4,2]=>00000000=>11111111=>1
[10,1,9,8,7,6,5,4,3,2]=>000000000=>111111111=>1
[9,8,1,7,6,5,4,3,2]=>00000000=>11111111=>1
[7,6,1,8,5,4,3,2]=>0000000=>1111111=>1
[8,7,9,1,6,5,4,3,2]=>00000000=>11111111=>1
[8,1,10,9,7,6,5,4,3,2]=>000000000=>111111111=>1
[6,5,8,1,7,4,3,2]=>0000000=>1111111=>1
[7,6,9,8,1,5,4,3,2]=>00000000=>11111111=>1
[7,1,10,9,8,6,5,4,3,2]=>000000000=>111111111=>1
[6,5,9,8,7,1,4,3,2]=>00000000=>11111111=>1
[6,1,10,9,8,7,5,4,3,2]=>000000000=>111111111=>1
[6,5,8,7,4,1,3,2]=>0000000=>1111111=>1
[5,4,9,8,7,6,1,3,2]=>00000000=>11111111=>1
[5,1,10,9,8,7,6,4,3,2]=>000000000=>111111111=>1
[4,3,9,8,7,6,5,1,2]=>00000000=>11111111=>1
[4,1,10,9,8,7,6,5,3,2]=>000000000=>111111111=>1
[3,2,9,8,7,6,5,4,1]=>00000000=>11111111=>1
[3,1,10,9,8,7,6,5,4,2]=>000000000=>111111111=>1
[1,6,4,8,3,2,5,7]=>1000000=>0111111=>1
[1,8,3,5,6,2,4,7]=>1000000=>0111111=>1
[1,4,8,5,6,2,3,7]=>1000000=>0111111=>1
[1,2,8,5,3,7,4,6]=>1100000=>0011111=>1
[6,1,4,8,2,3,5,7]=>0000000=>1111111=>1
[8,7,2,5,6,1,4,3]=>0000000=>1111111=>1
[1,8,2,5,4,7,3,6]=>1000000=>0111111=>1
[5,7,4,1,2,3,8,6]=>0000000=>1111111=>1
[1,7,4,2,5,3,8,6]=>1000000=>0111111=>1
[6,7,4,2,1,3,8,5]=>0000000=>1111111=>1
[6,4,3,8,5,7,1,2]=>0000000=>1111111=>1
[7,4,3,6,2,1,5,8]=>0000001=>1111110=>1
[7,2,5,3,4,1,6,8]=>0000001=>1111110=>1
[8,3,7,4,5,6,1,2]=>0000000=>1111111=>1
[2,7,4,3,1,5,6,8]=>0000001=>1111110=>1
[6,8,4,2,3,1,5,7]=>0000000=>1111111=>1
[3,7,5,2,4,1,6,8]=>0000001=>1111110=>1
[7,1,3,2,8,4,5,6]=>0000000=>1111111=>1
[2,1,7,4,8,3,5,6]=>0100000=>1011111=>2
[5,2,8,6,1,3,4,7]=>0000000=>1111111=>1
[2,8,3,1,4,5,6,7]=>0000000=>1111111=>1
[7,4,8,2,3,1,5,6]=>0000000=>1111111=>1
[4,2,7,3,1,5,6,8]=>0000001=>1111110=>1
[8,3,7,2,1,4,5,6]=>0000000=>1111111=>1
[6,5,2,4,7,1,3,8]=>0000001=>1111110=>1
[6,5,7,4,1,8,2,3]=>0000000=>1111111=>1
[7,6,4,5,1,8,2,3]=>0000000=>1111111=>1
[8,6,4,1,3,7,2,5]=>0000000=>1111111=>1
[6,4,3,1,8,2,5,7]=>0000000=>1111111=>1
[7,4,1,2,8,3,5,6]=>0000000=>1111111=>1
[4,8,1,3,5,7,2,6]=>0000000=>1111111=>1
[7,8,4,1,3,6,2,5]=>0000000=>1111111=>1
[6,5,8,1,3,7,2,4]=>0000000=>1111111=>1
[5,3,6,1,8,2,4,7]=>0000000=>1111111=>1
[4,7,3,1,8,2,5,6]=>0000000=>1111111=>1
[8,3,1,7,2,4,5,6]=>0000000=>1111111=>1
[2,8,1,4,7,3,5,6]=>0000000=>1111111=>1
[3,1,8,5,4,7,6,2]=>0000000=>1111111=>1
[4,1,5,8,3,7,6,2]=>0000000=>1111111=>1
[4,1,5,3,8,7,6,2]=>0000000=>1111111=>1
[4,5,1,8,2,7,6,3]=>0000000=>1111111=>1
[4,8,5,3,1,7,6,2]=>0000000=>1111111=>1
[4,5,2,8,1,7,6,3]=>0000000=>1111111=>1
[4,5,2,1,8,7,6,3]=>0000000=>1111111=>1
[5,6,2,7,8,1,4,3]=>0000000=>1111111=>1
[4,6,2,8,7,1,5,3]=>0000000=>1111111=>1
[4,8,6,3,7,1,5,2]=>0000000=>1111111=>1
[4,8,6,3,7,5,1,2]=>0000000=>1111111=>1
[4,6,8,2,7,5,1,3]=>0000000=>1111111=>1
[4,6,2,8,7,5,1,3]=>0000000=>1111111=>1
[5,6,2,7,4,1,8,3]=>0000000=>1111111=>1
[5,6,7,2,3,1,8,4]=>0000000=>1111111=>1
[5,6,7,2,8,3,1,4]=>0000000=>1111111=>1
[5,6,7,2,1,8,3,4]=>0000000=>1111111=>1
[5,6,7,2,1,3,8,4]=>0000000=>1111111=>1
[5,6,1,7,8,2,4,3]=>0000000=>1111111=>1
[5,6,1,7,2,4,8,3]=>0000000=>1111111=>1
[5,1,6,7,8,3,4,2]=>0000000=>1111111=>1
[4,1,6,8,7,3,5,2]=>0000000=>1111111=>1
[3,1,8,6,7,5,4,2]=>0000000=>1111111=>1
[4,1,6,8,7,5,3,2]=>0000000=>1111111=>1
[5,1,6,7,4,8,3,2]=>0000000=>1111111=>1
[5,6,1,7,8,4,2,3]=>0000000=>1111111=>1
[4,6,8,1,7,5,2,3]=>0000000=>1111111=>1
[4,8,6,1,7,5,3,2]=>0000000=>1111111=>1
[5,6,7,1,8,3,2,4]=>0000000=>1111111=>1
[5,6,7,1,3,8,2,4]=>0000000=>1111111=>1
[5,6,7,1,3,2,8,4]=>0000000=>1111111=>1
[5,6,7,3,1,2,8,4]=>0000000=>1111111=>1
[5,6,7,3,8,1,2,4]=>0000000=>1111111=>1
[5,6,8,7,4,2,1,3]=>0000000=>1111111=>1
[5,6,7,3,8,2,1,4]=>0000000=>1111111=>1
[7,4,6,2,3,5,1,8]=>0000001=>1111110=>1
[1,4,8,6,3,2,5,7]=>1000000=>0111111=>1
[7,4,1,6,3,8,5,2]=>0000000=>1111111=>1
[7,6,3,1,5,8,4,2]=>0000000=>1111111=>1
[6,4,2,5,7,3,1,8]=>0000001=>1111110=>1
[4,2,5,7,6,3,1,8]=>0000001=>1111110=>1
[7,4,5,6,1,8,3,2]=>0000000=>1111111=>1
[4,1,5,8,6,3,2,7]=>0000000=>1111111=>1
[3,2,7,6,1,8,5,4]=>0000000=>1111111=>1
[4,7,5,1,6,8,2,3]=>0000000=>1111111=>1
[8,6,5,1,2,7,4,3]=>0000000=>1111111=>1
[3,2,5,1,4,8,7,6]=>0000100=>1111011=>2
[8,5,4,1,3,2,7,6]=>0000000=>1111111=>1
[1,4,2,3,6,8,7,5]=>1001000=>0110111=>2
[5,4,8,3,7,1,6,2]=>0000000=>1111111=>1
[4,7,1,8,2,5,3,6]=>0000000=>1111111=>1
[6,4,1,8,5,3,7,2]=>0000000=>1111111=>1
[8,4,6,1,3,5,2,7]=>0000000=>1111111=>1
[3,2,5,4,7,8,1,6]=>0000000=>1111111=>1
[5,2,4,3,7,8,1,6]=>0000000=>1111111=>1
[8,1,6,7,2,5,3,4]=>0000000=>1111111=>1
[3,1,7,6,5,8,2,4]=>0000000=>1111111=>1
[1,2,7,5,6,8,3,4]=>1100000=>0011111=>1
[6,1,4,7,2,8,3,5]=>0000000=>1111111=>1
[3,2,1,7,6,8,4,5]=>0010000=>1101111=>2
[3,2,8,6,4,7,1,5]=>0000000=>1111111=>1
[7,8,4,6,3,2,1,5]=>0000000=>1111111=>1
[1,8,6,5,3,7,2,4]=>1000000=>0111111=>1
[8,2,5,3,6,7,1,4]=>0000000=>1111111=>1
[3,8,5,2,7,6,1,4]=>0000000=>1111111=>1
[4,7,5,3,1,8,6,2]=>0000000=>1111111=>1
[4,5,3,6,8,1,7,2]=>0000000=>1111111=>1
[3,5,2,6,1,8,7,4]=>0000000=>1111111=>1
[1,6,3,5,7,2,8,4]=>1000000=>0111111=>1
[1,5,4,6,7,8,2,3]=>1000000=>0111111=>1
[8,4,6,5,7,2,1,3]=>0000000=>1111111=>1
[7,4,5,2,6,8,1,3]=>0000000=>1111111=>1
[5,4,2,6,8,7,1,3]=>0000000=>1111111=>1
[6,5,1,4,3,2,8,7]=>0000010=>1111101=>2
[7,5,4,2,3,8,1,6]=>0000000=>1111111=>1
[1,7,8,3,5,6,2,4]=>1000000=>0111111=>1
[1,3,7,5,8,2,6,4]=>1000000=>0111111=>1
[3,1,7,5,8,2,6,4]=>0000000=>1111111=>1
[3,5,7,1,8,4,6,2]=>0000000=>1111111=>1
[3,5,7,8,1,4,6,2]=>0000000=>1111111=>1
[5,3,7,1,8,4,6,2]=>0000000=>1111111=>1
[5,1,3,7,8,4,2,6]=>0000000=>1111111=>1
[5,2,8,1,7,3,4,6]=>0000000=>1111111=>1
[5,8,3,2,7,1,4,6]=>0000000=>1111111=>1
[2,6,8,3,7,1,4,5]=>0000000=>1111111=>1
[5,1,8,3,7,2,4,6]=>0000000=>1111111=>1
[5,1,8,4,6,2,3,7]=>0000000=>1111111=>1
[3,1,8,4,2,5,6,7]=>0000000=>1111111=>1
[4,8,5,2,6,1,3,7]=>0000000=>1111111=>1
[4,1,7,5,6,2,8,3]=>0000000=>1111111=>1
[5,7,4,3,8,1,6,2]=>0000000=>1111111=>1
[5,7,4,3,8,2,6,1]=>0000000=>1111111=>1
[3,8,4,2,6,7,5,1]=>0000000=>1111111=>1
[3,8,4,1,6,7,5,2]=>0000000=>1111111=>1
[6,1,7,5,2,8,4,3]=>0000000=>1111111=>1
[5,6,4,3,2,8,1,7]=>0000000=>1111111=>1
[2,6,7,5,3,8,4,1]=>0000000=>1111111=>1
[6,7,4,8,2,5,3,1]=>0000000=>1111111=>1
[2,1,6,7,5,3,8,4]=>0100000=>1011111=>2
[3,8,4,2,1,6,7,5]=>0000000=>1111111=>1
[5,7,4,3,8,2,1,6]=>0000000=>1111111=>1
[6,7,4,8,1,2,5,3]=>0000000=>1111111=>1
[6,7,5,8,1,2,4,3]=>0000000=>1111111=>1
[6,7,4,8,3,1,2,5]=>0000000=>1111111=>1
[3,4,8,1,2,5,7,6]=>0000000=>1111111=>1
[6,1,3,4,8,2,5,7]=>0000000=>1111111=>1
[6,2,3,4,8,1,5,7]=>0000000=>1111111=>1
[3,4,8,2,1,5,7,6]=>0000000=>1111111=>1
[6,7,5,8,2,4,3,1]=>0000000=>1111111=>1
[6,7,5,8,3,1,4,2]=>0000000=>1111111=>1
[3,4,8,1,5,7,6,2]=>0000000=>1111111=>1
[2,5,7,6,1,4,8,3]=>0000000=>1111111=>1
[6,7,4,8,2,3,5,1]=>0000000=>1111111=>1
[6,7,4,8,1,3,5,2]=>0000000=>1111111=>1
[2,6,7,5,1,3,8,4]=>0000000=>1111111=>1
[6,3,1,4,8,2,5,7]=>0000000=>1111111=>1
[6,7,4,8,1,3,2,5]=>0000000=>1111111=>1
[6,7,5,8,4,1,3,2]=>0000000=>1111111=>1
[6,7,4,8,2,1,3,5]=>0000000=>1111111=>1
[6,7,4,8,1,2,3,5]=>0000000=>1111111=>1
[1,5,6,3,4,8,2,7]=>1000000=>0111111=>1
[1,4,3,6,5,8,2,7]=>1000000=>0111111=>1
[1,8,3,4,7,6,2,5]=>1000000=>0111111=>1
[3,8,1,7,5,2,6,4]=>0000000=>1111111=>1
[2,1,3,8,4,6,5,7]=>0110000=>1001111=>2
[8,3,1,5,7,2,6,4]=>0000000=>1111111=>1
[1,4,8,5,7,6,2,3]=>1000000=>0111111=>1
[2,4,8,5,7,3,6,1]=>0000000=>1111111=>1
[4,2,8,6,7,3,5,1]=>0000000=>1111111=>1
[3,2,8,7,5,4,6,1]=>0000000=>1111111=>1
[3,1,8,7,5,6,2,4]=>0000000=>1111111=>1
[5,1,7,8,6,4,2,3]=>0000000=>1111111=>1
[7,8,3,2,6,1,4,5]=>0000000=>1111111=>1
[3,4,8,2,6,1,7,5]=>0000000=>1111111=>1
[7,8,4,1,5,6,3,2]=>0000000=>1111111=>1
[7,8,1,4,5,6,3,2]=>0000000=>1111111=>1
[7,8,1,2,6,3,4,5]=>0000000=>1111111=>1
[7,8,5,1,4,6,3,2]=>0000000=>1111111=>1
[7,8,4,5,1,6,3,2]=>0000000=>1111111=>1
[5,3,8,4,1,6,7,2]=>0000000=>1111111=>1
[6,2,4,8,1,5,3,7]=>0000000=>1111111=>1
[3,4,8,5,1,6,7,2]=>0000000=>1111111=>1
[3,5,8,1,4,6,7,2]=>0000000=>1111111=>1
[1,4,8,2,6,3,7,5]=>1000000=>0111111=>1
[5,3,8,1,4,6,7,2]=>0000000=>1111111=>1
[4,2,6,8,1,5,3,7]=>0000000=>1111111=>1
[7,4,2,8,1,5,3,6]=>0000000=>1111111=>1
[6,1,7,5,8,4,3,2]=>0000000=>1111111=>1
[6,2,1,8,4,5,3,7]=>0000000=>1111111=>1
[1,2,7,8,5,3,4,6]=>1100000=>0011111=>1
[6,3,7,8,5,4,1,2]=>0000000=>1111111=>1
[6,1,5,7,8,4,3,2]=>0000000=>1111111=>1
[1,7,5,6,8,4,3,2]=>1000000=>0111111=>1
[3,1,8,4,5,6,7,2]=>0000000=>1111111=>1
[2,1,4,8,6,5,3,7]=>0100000=>1011111=>2
[2,4,1,8,6,5,3,7]=>0000000=>1111111=>1
[4,2,1,8,6,5,3,7]=>0000000=>1111111=>1
[3,2,7,8,5,1,4,6]=>0000000=>1111111=>1
[2,3,7,8,5,1,4,6]=>0000000=>1111111=>1
[2,7,3,8,5,1,4,6]=>0000000=>1111111=>1
[3,6,2,8,5,1,4,7]=>0000000=>1111111=>1
[4,1,2,8,7,5,3,6]=>0000000=>1111111=>1
[1,4,2,8,7,5,3,6]=>1000000=>0111111=>1
[7,3,6,8,5,4,1,2]=>0000000=>1111111=>1
[7,2,1,8,5,3,4,6]=>0000000=>1111111=>1
[1,2,6,8,4,5,3,7]=>1100000=>0011111=>1
[7,1,6,5,8,4,3,2]=>0000000=>1111111=>1
[6,5,7,1,8,4,3,2]=>0000000=>1111111=>1
[5,7,6,1,8,4,3,2]=>0000000=>1111111=>1
[6,7,1,5,8,4,3,2]=>0000000=>1111111=>1
[6,7,3,8,5,4,1,2]=>0000000=>1111111=>1
[7,1,2,8,4,5,3,6]=>0000000=>1111111=>1
[7,6,1,5,8,4,3,2]=>0000000=>1111111=>1
[7,5,6,1,8,4,3,2]=>0000000=>1111111=>1
[9,10,7,8,5,6,2,1,3,4]=>000000000=>111111111=>1
[9,10,7,8,4,3,5,6,1,2]=>000000000=>111111111=>1
[9,10,7,8,4,2,5,1,3,6]=>000000000=>111111111=>1
[9,10,7,8,3,2,1,4,5,6]=>000000000=>111111111=>1
[9,10,6,5,7,8,3,4,1,2]=>000000000=>111111111=>1
[9,10,6,5,7,8,2,1,3,4]=>000000000=>111111111=>1
[9,10,6,4,7,3,5,8,1,2]=>000000000=>111111111=>1
[9,10,6,4,7,2,5,1,3,8]=>000000000=>111111111=>1
[9,10,6,3,7,2,1,4,5,8]=>000000000=>111111111=>1
[9,10,5,4,3,6,7,8,1,2]=>000000000=>111111111=>1
[9,10,5,4,2,6,7,1,3,8]=>000000000=>111111111=>1
[9,10,5,3,2,6,1,4,7,8]=>000000000=>111111111=>1
[9,10,4,3,2,1,5,6,7,8]=>000000000=>111111111=>1
[8,7,9,10,5,6,3,4,1,2]=>000000000=>111111111=>1
[8,7,9,10,5,6,2,1,3,4]=>000000000=>111111111=>1
[8,7,9,10,4,3,5,6,1,2]=>000000000=>111111111=>1
[8,7,9,10,4,2,5,1,3,6]=>000000000=>111111111=>1
[8,7,9,10,3,2,1,4,5,6]=>000000000=>111111111=>1
[8,6,9,5,7,10,3,4,1,2]=>000000000=>111111111=>1
[8,6,9,5,7,10,2,1,3,4]=>000000000=>111111111=>1
[8,6,9,4,7,3,5,10,1,2]=>000000000=>111111111=>1
[8,6,9,3,7,2,1,4,5,10]=>000000001=>111111110=>1
[8,5,9,4,3,6,7,10,1,2]=>000000000=>111111111=>1
[8,5,9,4,2,6,7,1,3,10]=>000000001=>111111110=>1
[8,5,9,3,2,6,1,4,7,10]=>000000001=>111111110=>1
[8,4,9,3,2,1,5,6,7,10]=>000000001=>111111110=>1
[7,6,5,8,9,10,3,4,1,2]=>000000000=>111111111=>1
[7,6,5,8,9,10,2,1,3,4]=>000000000=>111111111=>1
[7,6,4,8,9,3,5,10,1,2]=>000000000=>111111111=>1
[7,6,4,8,9,2,5,1,3,10]=>000000001=>111111110=>1
[7,6,3,8,9,2,1,4,5,10]=>000000001=>111111110=>1
[7,5,4,8,3,6,9,10,1,2]=>000000000=>111111111=>1
[7,5,4,8,2,6,9,1,3,10]=>000000001=>111111110=>1
[7,4,3,8,2,1,5,6,9,10]=>000000011=>111111100=>1
[6,5,4,3,7,8,9,10,1,2]=>000000000=>111111111=>1
[6,5,4,2,7,8,9,1,3,10]=>000000001=>111111110=>1
[6,5,3,2,7,8,1,4,9,10]=>000000011=>111111100=>1
[10,8,11,6,9,4,7,2,5,1,3,12]=>00000000001=>11111111110=>1
[10,8,11,6,9,3,7,2,1,4,5,12]=>00000000001=>11111111110=>1
[10,8,11,5,9,4,2,6,7,1,3,12]=>00000000001=>11111111110=>1
[10,8,11,5,9,3,2,6,1,4,7,12]=>00000000001=>11111111110=>1
[10,8,11,4,9,3,2,1,5,6,7,12]=>00000000001=>11111111110=>1
[10,7,11,6,4,8,9,2,5,1,3,12]=>00000000001=>11111111110=>1
[10,7,11,6,3,8,9,2,1,4,5,12]=>00000000001=>11111111110=>1
[10,7,11,5,4,8,2,6,9,1,3,12]=>00000000001=>11111111110=>1
[10,7,11,5,3,8,2,6,1,4,9,12]=>00000000001=>11111111110=>1
[10,7,11,4,3,8,2,1,5,6,9,12]=>00000000001=>11111111110=>1
[10,6,11,5,4,2,7,8,9,1,3,12]=>00000000001=>11111111110=>1
[10,6,11,5,3,2,7,8,1,4,9,12]=>00000000001=>11111111110=>1
[10,6,11,4,3,2,7,1,5,8,9,12]=>00000000001=>11111111110=>1
[10,5,11,4,3,2,1,6,7,8,9,12]=>00000000001=>11111111110=>1
[9,8,6,10,11,4,7,2,5,1,3,12]=>00000000001=>11111111110=>1
[9,8,6,10,11,3,7,2,1,4,5,12]=>00000000001=>11111111110=>1
[9,8,5,10,11,4,2,6,7,1,3,12]=>00000000001=>11111111110=>1
[9,8,5,10,11,3,2,6,1,4,7,12]=>00000000001=>11111111110=>1
[9,8,4,10,11,3,2,1,5,6,7,12]=>00000000001=>11111111110=>1
[9,7,6,10,4,8,11,2,5,1,3,12]=>00000000001=>11111111110=>1
[9,7,6,10,3,8,11,2,1,4,5,12]=>00000000001=>11111111110=>1
[9,7,5,10,4,8,2,6,11,1,3,12]=>00000000001=>11111111110=>1
[9,6,5,10,4,2,7,8,11,1,3,12]=>00000000001=>11111111110=>1
[8,7,6,4,9,10,11,2,5,1,3,12]=>00000000001=>11111111110=>1
[8,7,6,3,9,10,11,2,1,4,5,12]=>00000000001=>11111111110=>1
[8,7,5,4,9,10,2,6,11,1,3,12]=>00000000001=>11111111110=>1
[8,6,5,4,9,2,7,10,11,1,3,12]=>00000000001=>11111111110=>1
[7,6,5,4,2,8,9,10,11,1,3,12]=>00000000001=>11111111110=>1
[1,8,7,5,3,2,4,6]=>1000000=>0111111=>1
[1,8,7,4,2,5,3,6]=>1000000=>0111111=>1
[5,3,7,1,6,4,2,8]=>0000001=>1111110=>1
[1,5,3,8,7,4,2,6]=>1000000=>0111111=>1
[1,8,6,3,5,7,4,2]=>1000000=>0111111=>1
[6,3,8,5,2,1,7,4]=>0000000=>1111111=>1
[6,3,7,4,1,8,5,2]=>0000000=>1111111=>1
[6,1,8,7,4,2,5,3]=>0000000=>1111111=>1
[1,8,6,3,2,4,7,5]=>1000000=>0111111=>1
[4,3,2,8,7,6,1,5]=>0000000=>1111111=>1
[1,7,5,8,6,3,2,4]=>1000000=>0111111=>1
[1,7,4,2,5,8,6,3]=>1000000=>0111111=>1
[8,6,3,1,7,4,2,5]=>0000000=>1111111=>1
[8,7,4,2,5,3,1,6]=>0000000=>1111111=>1
[1,8,5,2,7,4,6,3]=>1000000=>0111111=>1
[7,4,8,5,2,1,6,3]=>0000000=>1111111=>1
[1,7,4,6,3,8,5,2]=>1000000=>0111111=>1
[4,1,8,5,7,3,2,6]=>0000000=>1111111=>1
[2,1,5,7,8,4,3,6]=>0100000=>1011111=>2
[5,1,7,4,8,3,2,6]=>0000000=>1111111=>1
[4,7,2,8,3,6,1,5]=>0000000=>1111111=>1
[1,3,2,7,6,5,10,9,8,4]=>101000000=>010111111=>2
[1,4,3,6,5,2,10,9,8,7]=>100001000=>011110111=>2
[1,4,3,7,6,2,10,9,8,5]=>100000000=>011111111=>1
[1,5,4,7,6,3,10,9,8,2]=>100000000=>011111111=>1
[1,4,3,8,7,2,10,9,6,5]=>100000000=>011111111=>1
[1,5,4,8,7,3,10,9,6,2]=>100000000=>011111111=>1
[2,3,1,6,5,4,10,9,8,7]=>001001000=>110110111=>3
[2,3,1,7,6,5,10,9,8,4]=>001000000=>110111111=>2
[2,4,1,6,5,3,10,9,8,7]=>000001000=>111110111=>2
[2,4,1,7,6,3,10,9,8,5]=>000000000=>111111111=>1
[2,5,1,7,6,4,10,9,8,3]=>000000000=>111111111=>1
[2,4,1,8,7,3,10,9,6,5]=>000000000=>111111111=>1
[2,5,1,8,7,4,10,9,6,3]=>000000000=>111111111=>1
[3,4,2,6,5,1,10,9,8,7]=>000001000=>111110111=>2
[3,4,2,7,6,1,10,9,8,5]=>000000000=>111111111=>1
[3,5,2,7,6,1,10,9,8,4]=>000000000=>111111111=>1
[4,5,3,7,6,2,10,9,8,1]=>000000000=>111111111=>1
[3,4,2,8,7,1,10,9,6,5]=>000000000=>111111111=>1
[3,5,2,8,7,1,10,9,6,4]=>000000000=>111111111=>1
[4,5,3,8,7,2,10,9,6,1]=>000000000=>111111111=>1
[2,5,1,6,4,3,10,9,8,7]=>000001000=>111110111=>2
[2,5,1,7,4,3,10,9,8,6]=>000000000=>111111111=>1
[2,6,1,7,5,4,10,9,8,3]=>000000000=>111111111=>1
[2,5,1,8,4,3,10,9,7,6]=>000000000=>111111111=>1
[2,6,1,8,5,4,10,9,7,3]=>000000000=>111111111=>1
[3,5,2,6,4,1,10,9,8,7]=>000001000=>111110111=>2
[3,5,2,7,4,1,10,9,8,6]=>000000000=>111111111=>1
[3,6,2,7,5,1,10,9,8,4]=>000000000=>111111111=>1
[4,6,3,7,5,2,10,9,8,1]=>000000000=>111111111=>1
[3,5,2,8,4,1,10,9,7,6]=>000000000=>111111111=>1
[3,6,2,8,5,1,10,9,7,4]=>000000000=>111111111=>1
[4,6,3,8,5,2,10,9,7,1]=>000000000=>111111111=>1
[3,7,2,8,6,1,10,9,5,4]=>000000000=>111111111=>1
[4,7,3,8,6,2,10,9,5,1]=>000000000=>111111111=>1
[2,5,1,9,4,3,10,8,7,6]=>000000000=>111111111=>1
[2,6,1,9,5,4,10,8,7,3]=>000000000=>111111111=>1
[3,5,2,9,4,1,10,8,7,6]=>000000000=>111111111=>1
[3,6,2,9,5,1,10,8,7,4]=>000000000=>111111111=>1
[4,6,3,9,5,2,10,8,7,1]=>000000000=>111111111=>1
[3,7,2,9,6,1,10,8,5,4]=>000000000=>111111111=>1
[6,2,8,4,1,7,3,5]=>0000000=>1111111=>1
[1,8,5,4,2,3,7,6]=>1000000=>0111111=>1
[3,5,4,8,1,2,7,6]=>0000000=>1111111=>1
[5,6,3,8,7,1,2,4]=>0000000=>1111111=>1
[2,6,8,4,1,7,3,5]=>0000000=>1111111=>1
[1,8,7,4,2,6,3,5]=>1000000=>0111111=>1
[6,3,5,8,7,1,2,4]=>0000000=>1111111=>1
[5,2,8,6,7,1,3,4]=>0000000=>1111111=>1
[6,2,8,7,5,1,3,4]=>0000000=>1111111=>1
[1,8,5,7,6,2,3,4]=>1000000=>0111111=>1
[3,6,7,8,5,1,2,4]=>0000000=>1111111=>1
[1,8,6,7,5,2,3,4]=>1000000=>0111111=>1
[5,4,2,7,6,8,1,3]=>0000000=>1111111=>1
[4,2,1,8,7,3,5,6]=>0000000=>1111111=>1
[5,1,6,3,2,8,7,4]=>0000000=>1111111=>1
[4,3,5,2,8,7,1,6]=>0000000=>1111111=>1
[2,8,6,1,7,3,5,4]=>0000000=>1111111=>1
[3,7,5,1,6,8,2,4]=>0000000=>1111111=>1
[3,6,7,4,1,8,2,5]=>0000000=>1111111=>1
[2,7,1,6,5,4,8,3]=>0000000=>1111111=>1
[7,3,2,6,1,8,5,4]=>0000000=>1111111=>1
[8,4,1,6,3,2,5,7]=>0000000=>1111111=>1
[4,7,3,8,5,2,1,6]=>0000000=>1111111=>1
[4,7,5,1,8,6,3,2]=>0000000=>1111111=>1
[6,1,5,7,3,8,4,2]=>0000000=>1111111=>1
[7,2,6,5,8,4,1,3]=>0000000=>1111111=>1
[2,5,8,1,6,4,7,3]=>0000000=>1111111=>1
[3,6,5,8,4,1,7,2]=>0000000=>1111111=>1
[5,7,3,1,6,4,8,2]=>0000000=>1111111=>1
[8,7,2,5,4,1,3,6]=>0000000=>1111111=>1
[8,7,2,5,3,1,4,6]=>0000000=>1111111=>1
[5,2,8,7,1,4,3,6]=>0000000=>1111111=>1
[8,1,6,2,7,5,3,4]=>0000000=>1111111=>1
[6,3,4,1,7,2,8,5]=>0000000=>1111111=>1
[5,1,7,4,3,8,2,6]=>0000000=>1111111=>1
[6,1,7,3,2,8,5,4]=>0000000=>1111111=>1
[4,7,2,1,6,3,8,5]=>0000000=>1111111=>1
[6,2,1,5,3,8,4,7]=>0000000=>1111111=>1
[8,5,1,3,7,4,2,6]=>0000000=>1111111=>1
[6,1,8,3,7,5,2,4]=>0000000=>1111111=>1
[7,4,1,5,8,3,2,6]=>0000000=>1111111=>1
[6,1,8,4,5,2,7,3]=>0000000=>1111111=>1
[3,5,2,7,1,6,8,4]=>0000000=>1111111=>1
[6,1,3,7,4,8,5,2]=>0000000=>1111111=>1
[3,2,1,7,4,8,5,6]=>0010000=>1101111=>2
[4,1,5,2,7,6,3,8]=>0000001=>1111110=>1
[2,5,1,3,7,6,4,8]=>0000001=>1111110=>1
[2,5,1,4,3,8,6,7]=>0000100=>1111011=>2
[3,7,2,1,5,8,6,4]=>0000000=>1111111=>1
[6,2,7,1,4,8,5,3]=>0000000=>1111111=>1
[3,7,4,2,1,8,5,6]=>0000000=>1111111=>1
[7,2,5,3,1,8,6,4]=>0000000=>1111111=>1
[7,5,1,4,2,8,6,3]=>0000000=>1111111=>1
[7,5,4,1,3,8,6,2]=>0000000=>1111111=>1
[5,3,2,1,7,6,4,8]=>0000001=>1111110=>1
[6,3,2,8,1,5,7,4]=>0000000=>1111111=>1
[7,4,3,2,8,1,6,5]=>0000000=>1111111=>1
[7,6,2,4,8,3,5,1]=>0000000=>1111111=>1
[7,3,6,4,8,1,5,2]=>0000000=>1111111=>1
[2,7,5,3,8,1,4,6]=>0000000=>1111111=>1
[1,8,5,3,6,4,2,7]=>1000000=>0111111=>1
[8,6,2,3,7,5,4,1]=>0000000=>1111111=>1
[8,6,3,2,7,5,4,1]=>0000000=>1111111=>1
[8,3,2,7,1,6,4,5]=>0000000=>1111111=>1
[7,2,6,1,5,4,3,8]=>0000001=>1111110=>1
[8,5,7,4,3,6,2,1]=>0000000=>1111111=>1
[8,5,7,2,4,6,3,1]=>0000000=>1111111=>1
[8,4,6,7,1,3,2,5]=>0000000=>1111111=>1
[2,8,5,6,1,4,3,7]=>0000000=>1111111=>1
[7,2,6,8,4,1,5,3]=>0000000=>1111111=>1
[7,6,4,8,3,2,5,1]=>0000000=>1111111=>1
[6,5,8,1,4,2,7,3]=>0000000=>1111111=>1
[6,5,8,4,1,3,7,2]=>0000000=>1111111=>1
[5,4,8,3,2,1,7,6]=>0000000=>1111111=>1
[4,3,7,2,1,6,5,8]=>0000001=>1111110=>1
[2,5,8,1,4,3,7,6]=>0000000=>1111111=>1
[3,6,8,2,1,5,7,4]=>0000000=>1111111=>1
[5,7,4,8,1,3,6,2]=>0000000=>1111111=>1
[5,7,1,4,8,2,6,3]=>0000000=>1111111=>1
[2,7,4,1,8,3,6,5]=>0000000=>1111111=>1
[3,5,1,8,4,2,7,6]=>0000000=>1111111=>1
[4,1,5,7,3,6,2,8]=>0000001=>1111110=>1
[4,2,5,8,3,1,7,6]=>0000000=>1111111=>1
[6,1,2,7,8,3,5,4]=>0000000=>1111111=>1
[5,3,1,8,6,4,2,7]=>0000000=>1111111=>1
[3,1,8,4,7,5,2,6]=>0000000=>1111111=>1
[4,2,8,7,3,5,1,6]=>0000000=>1111111=>1
[4,8,1,7,6,2,3,5]=>0000000=>1111111=>1
[6,8,1,4,7,5,2,3]=>0000000=>1111111=>1
[7,3,8,1,6,4,2,5]=>0000000=>1111111=>1
[4,7,8,1,5,3,2,6]=>0000000=>1111111=>1
[7,1,8,6,2,5,3,4]=>0000000=>1111111=>1
[5,8,7,1,3,6,4,2]=>0000000=>1111111=>1
[3,8,7,2,1,6,4,5]=>0000000=>1111111=>1
[2,8,7,1,6,3,5,4]=>0000000=>1111111=>1
[3,7,6,1,5,4,2,8]=>0000001=>1111110=>1
[4,8,7,6,1,3,5,2]=>0000000=>1111111=>1
[5,8,7,2,6,1,4,3]=>0000000=>1111111=>1
[6,8,1,7,5,2,4,3]=>0000000=>1111111=>1
[7,3,8,6,5,1,2,4]=>0000000=>1111111=>1
[5,7,8,4,3,1,2,6]=>0000000=>1111111=>1
[5,8,6,4,3,2,1,7]=>0000000=>1111111=>1
[8,7,3,6,4,2,1,5]=>0000000=>1111111=>1
[6,1,4,2,5,3,7,8]=>0000011=>1111100=>1
[1,3,7,5,4,2,8,6]=>1000000=>0111111=>1
[6,1,3,5,4,2,7,8]=>0000011=>1111100=>1
[6,1,2,5,4,7,3,8]=>0000001=>1111110=>1
[5,1,6,3,4,7,8,2]=>0000000=>1111111=>1
[5,2,6,3,4,7,1,8]=>0000001=>1111110=>1
[3,4,7,5,8,6,1,2]=>0000000=>1111111=>1
[2,4,7,1,5,3,8,6]=>0000000=>1111111=>1
[2,3,6,7,4,8,1,5]=>0000000=>1111111=>1
[1,3,6,7,4,8,5,2]=>1000000=>0111111=>1
[2,7,6,5,3,1,8,4]=>0000000=>1111111=>1
[5,2,6,1,4,7,8,3]=>0000000=>1111111=>1
[4,7,6,5,2,1,8,3]=>0000000=>1111111=>1
[5,3,6,2,4,1,7,8]=>0000011=>1111100=>1
[5,7,4,2,1,3,6,8]=>0000001=>1111110=>1
[6,3,1,5,4,7,8,2]=>0000000=>1111111=>1
[5,3,6,1,4,2,7,8]=>0000011=>1111100=>1
[1,7,4,2,6,3,8,5]=>1000000=>0111111=>1
[5,7,4,1,2,3,6,8]=>0000001=>1111110=>1
[6,4,1,2,5,3,7,8]=>0000011=>1111100=>1
[4,7,6,3,8,5,1,2]=>0000000=>1111111=>1
[3,7,6,5,2,8,1,4]=>0000000=>1111111=>1
[3,7,6,5,1,2,8,4]=>0000000=>1111111=>1
[4,7,2,6,1,3,8,5]=>0000000=>1111111=>1
[2,7,1,6,8,3,5,4]=>0000000=>1111111=>1
[2,7,6,5,8,1,4,3]=>0000000=>1111111=>1
[2,3,4,5,6,9,7,8,1]=>00000000=>11111111=>1
[2,3,4,5,6,7,8,10,9,1]=>000000000=>111111111=>1
[9,2,1,8,7,6,5,4,3]=>00000000=>11111111=>1
[3,2,10,9,8,7,6,5,4,1]=>000000000=>111111111=>1
[3,9,2,8,7,6,5,4,1]=>00000000=>11111111=>1
[4,2,9,8,7,6,5,3,1]=>00000000=>11111111=>1
[5,2,8,7,6,4,3,1]=>0000000=>1111111=>1
[8,2,7,6,1,5,4,3]=>0000000=>1111111=>1
[9,2,8,1,7,6,5,4,3]=>00000000=>11111111=>1
[8,4,1,7,6,5,3,2]=>0000000=>1111111=>1
[9,3,1,8,7,6,5,4,2]=>00000000=>11111111=>1
[10,2,1,9,8,7,6,5,4,3]=>000000000=>111111111=>1
[4,5,6,2,3,8,1,7]=>0000000=>1111111=>1
[3,2,7,4,5,8,1,6]=>0000000=>1111111=>1
[6,3,4,7,8,2,5,1]=>0000000=>1111111=>1
[5,3,7,4,8,6,1,2]=>0000000=>1111111=>1
[5,4,3,1,7,8,2,6]=>0000000=>1111111=>1
[5,7,6,2,8,4,1,3]=>0000000=>1111111=>1
[6,8,5,1,7,2,4,3]=>0000000=>1111111=>1
[8,1,7,4,2,3,6,5]=>0000000=>1111111=>1
[2,8,3,1,6,7,5,4]=>0000000=>1111111=>1
[3,8,4,1,2,7,6,5]=>0000000=>1111111=>1
[6,4,1,3,2,7,8,5]=>0000000=>1111111=>1
[6,5,7,3,8,2,1,4]=>0000000=>1111111=>1
[8,1,4,7,2,5,6,3]=>0000000=>1111111=>1
[4,2,6,8,3,1,5,7]=>0000000=>1111111=>1
[3,7,6,2,4,5,1,8]=>0000001=>1111110=>1
[2,3,6,5,8,1,4,7]=>0000000=>1111111=>1
[2,3,5,8,6,1,4,7]=>0000000=>1111111=>1
[4,2,3,8,6,1,5,7]=>0000000=>1111111=>1
[6,4,1,2,8,3,5,7]=>0000000=>1111111=>1
[1,2,3,7,4,6,8,5]=>1110000=>0001111=>1
[3,2,7,1,4,5,8,6]=>0000000=>1111111=>1
[2,1,5,3,8,7,4,6]=>0100000=>1011111=>2
[5,8,3,2,4,1,6,7]=>0000000=>1111111=>1
[4,2,7,1,8,3,5,6]=>0000000=>1111111=>1
[4,1,8,2,7,3,5,6]=>0000000=>1111111=>1
[1,2,7,5,3,8,4,6]=>1100000=>0011111=>1
[3,2,7,1,4,8,5,6]=>0000000=>1111111=>1
[1,2,3,7,6,8,4,5]=>1110000=>0001111=>1
[1,2,3,6,8,7,4,5]=>1110000=>0001111=>1
[1,2,3,7,8,4,6,5]=>1110000=>0001111=>1
[1,2,3,6,8,4,7,5]=>1110000=>0001111=>1
[1,2,3,7,8,6,4,5]=>1110000=>0001111=>1
[6,2,8,3,7,5,1,4]=>0000000=>1111111=>1
[4,2,8,3,7,5,6,1]=>0000000=>1111111=>1
[7,3,4,8,6,5,1,2]=>0000000=>1111111=>1
[5,3,4,8,7,2,6,1]=>0000000=>1111111=>1
[4,3,5,8,7,2,6,1]=>0000000=>1111111=>1
[4,6,3,8,5,7,2,1]=>0000000=>1111111=>1
[7,5,3,8,6,2,4,1]=>0000000=>1111111=>1
[2,6,8,3,7,4,5,1]=>0000000=>1111111=>1
[1,8,4,3,7,5,6,2]=>1000000=>0111111=>1
[2,5,8,3,7,4,6,1]=>0000000=>1111111=>1
[7,4,3,8,6,2,5,1]=>0000000=>1111111=>1
[3,5,4,8,7,2,6,1]=>0000000=>1111111=>1
[4,5,3,8,6,7,2,1]=>0000000=>1111111=>1
[3,6,7,8,4,5,2,1]=>0000000=>1111111=>1
[2,6,8,5,4,7,3,1]=>0000000=>1111111=>1
[1,8,5,6,4,7,3,2]=>1000000=>0111111=>1
[2,5,8,6,4,7,3,1]=>0000000=>1111111=>1
[7,4,6,5,8,3,2,1]=>0000000=>1111111=>1
[6,3,7,8,4,5,2,1]=>0000000=>1111111=>1
[4,3,7,8,5,6,2,1]=>0000000=>1111111=>1
[5,2,8,6,4,7,3,1]=>0000000=>1111111=>1
[4,2,8,6,5,7,3,1]=>0000000=>1111111=>1
[3,2,8,6,7,4,5,1]=>0000000=>1111111=>1
[2,3,8,7,5,4,6,1]=>0000000=>1111111=>1
[1,8,2,7,4,5,6,3]=>1000000=>0111111=>1
[7,2,8,6,3,4,5,1]=>0000000=>1111111=>1
[6,2,8,4,5,7,3,1]=>0000000=>1111111=>1
[5,2,8,4,6,7,3,1]=>0000000=>1111111=>1
[4,2,8,5,6,7,3,1]=>0000000=>1111111=>1
[4,3,6,8,5,7,2,1]=>0000000=>1111111=>1
[3,4,6,8,7,2,5,1]=>0000000=>1111111=>1
[7,3,5,8,6,2,4,1]=>0000000=>1111111=>1
[1,8,3,5,7,4,6,2]=>1000000=>0111111=>1
[2,7,8,4,5,6,3,1]=>0000000=>1111111=>1
[3,7,5,8,4,6,2,1]=>0000000=>1111111=>1
[5,7,4,6,8,3,2,1]=>0000000=>1111111=>1
[3,6,5,8,4,7,2,1]=>0000000=>1111111=>1
[2,6,8,4,5,7,3,1]=>0000000=>1111111=>1
[4,2,7,1,3,8,5,6]=>0000000=>1111111=>1
[4,2,5,1,3,8,6,7]=>0000100=>1111011=>2
[5,3,6,1,7,2,4,8]=>0000001=>1111110=>1
[3,7,1,2,5,8,6,4]=>0000000=>1111111=>1
[3,7,4,1,2,8,5,6]=>0000000=>1111111=>1
[7,5,1,3,4,8,6,2]=>0000000=>1111111=>1
[7,5,1,2,4,8,6,3]=>0000000=>1111111=>1
[6,4,2,3,7,1,5,8]=>0000001=>1111110=>1
[7,6,3,8,1,2,5,4]=>0000000=>1111111=>1
[7,4,2,3,8,1,6,5]=>0000000=>1111111=>1
[4,7,5,2,8,1,3,6]=>0000000=>1111111=>1
[8,2,6,3,7,1,4,5]=>0000000=>1111111=>1
[8,6,1,2,7,4,5,3]=>0000000=>1111111=>1
[8,4,7,1,2,3,6,5]=>0000000=>1111111=>1
[8,5,7,1,2,4,6,3]=>0000000=>1111111=>1
[8,5,7,1,3,4,6,2]=>0000000=>1111111=>1
[8,6,2,7,1,3,5,4]=>0000000=>1111111=>1
[3,8,5,6,1,2,4,7]=>0000000=>1111111=>1
[3,7,5,8,1,2,4,6]=>0000000=>1111111=>1
[7,6,4,8,1,3,5,2]=>0000000=>1111111=>1
[6,5,8,1,2,4,7,3]=>0000000=>1111111=>1
[3,6,8,1,2,5,7,4]=>0000000=>1111111=>1
[3,7,2,4,8,1,6,5]=>0000000=>1111111=>1
[4,6,3,8,1,2,5,7]=>0000000=>1111111=>1
[4,6,3,7,1,2,5,8]=>0000001=>1111110=>1
[4,1,7,8,2,3,6,5]=>0000000=>1111111=>1
[5,1,2,8,6,3,4,7]=>0000000=>1111111=>1
[5,3,8,1,6,2,4,7]=>0000000=>1111111=>1
[6,1,8,5,2,3,4,7]=>0000000=>1111111=>1
[6,1,7,5,2,3,4,8]=>0000001=>1111110=>1
[6,8,1,3,7,4,5,2]=>0000000=>1111111=>1
[7,2,8,1,6,3,4,5]=>0000000=>1111111=>1
[4,7,8,2,5,1,3,6]=>0000000=>1111111=>1
[6,8,2,7,1,4,5,3]=>0000000=>1111111=>1
[4,8,7,1,3,5,6,2]=>0000000=>1111111=>1
[3,8,7,1,2,4,6,5]=>0000000=>1111111=>1
[4,8,7,1,2,3,6,5]=>0000000=>1111111=>1
[5,8,7,1,2,4,6,3]=>0000000=>1111111=>1
[5,8,7,1,3,4,6,2]=>0000000=>1111111=>1
[7,1,8,6,2,3,5,4]=>0000000=>1111111=>1
[5,8,6,4,1,2,3,7]=>0000000=>1111111=>1
[7,8,4,1,2,5,3,6]=>0000000=>1111111=>1
[7,8,1,2,6,5,3,4]=>0000000=>1111111=>1
[1,4,8,2,7,5,3,6]=>1000000=>0111111=>1
[6,1,3,4,7,2,5,8]=>0000001=>1111110=>1
[7,8,2,1,6,3,5,4]=>0000000=>1111111=>1
[6,1,2,7,5,4,3,8]=>0000001=>1111110=>1
[1,2,8,7,5,4,3,6]=>1100000=>0011111=>1
[5,1,7,3,6,4,8,2]=>0000000=>1111111=>1
[6,2,1,5,7,4,3,8]=>0000001=>1111110=>1
[6,2,3,7,4,1,5,8]=>0000001=>1111110=>1
[3,4,8,7,5,6,1,2]=>0000000=>1111111=>1
[2,3,8,7,4,1,5,6]=>0000000=>1111111=>1
[2,7,3,8,6,4,1,5]=>0000000=>1111111=>1
[1,8,3,7,6,4,5,2]=>1000000=>0111111=>1
[5,2,7,1,4,6,8,3]=>0000000=>1111111=>1
[4,6,7,5,2,1,8,3]=>0000000=>1111111=>1
[6,3,1,4,5,7,8,2]=>0000000=>1111111=>1
[5,3,1,4,6,2,7,8]=>0000011=>1111100=>1
[5,1,2,4,7,6,8,3]=>0000000=>1111111=>1
[5,7,4,1,2,6,3,8]=>0000001=>1111110=>1
[4,8,1,2,6,7,3,5]=>0000000=>1111111=>1
[4,1,7,8,2,6,3,5]=>0000000=>1111111=>1
[1,2,8,7,6,5,3,4]=>1100000=>0011111=>1
[3,1,2,4,6,8,7,5]=>0011000=>1100111=>2
[3,1,8,4,5,7,6,2]=>0000000=>1111111=>1
[3,2,8,5,4,7,1,6]=>0000000=>1111111=>1
[4,2,8,1,5,3,7,6]=>0000000=>1111111=>1
[4,3,8,5,7,6,1,2]=>0000000=>1111111=>1
[4,8,2,1,6,3,7,5]=>0000000=>1111111=>1
[3,8,6,5,2,7,1,4]=>0000000=>1111111=>1
[3,8,5,6,1,7,4,2]=>0000000=>1111111=>1
[3,5,7,8,1,2,6,4]=>0000000=>1111111=>1
[3,7,8,5,2,1,6,4]=>0000000=>1111111=>1
[3,7,2,8,4,1,6,5]=>0000000=>1111111=>1
[2,8,1,7,4,6,5,3]=>0000000=>1111111=>1
[2,8,7,5,1,6,4,3]=>0000000=>1111111=>1
[2,8,6,7,5,1,4,3]=>0000000=>1111111=>1
[5,1,3,4,6,7,2,8]=>0000001=>1111110=>1
[1,3,4,8,7,5,2,6]=>1000000=>0111111=>1
[8,2,4,1,7,3,5,6]=>0000000=>1111111=>1
[8,6,1,4,2,3,7,5]=>0000000=>1111111=>1
[3,6,1,4,2,8,7,5]=>0000000=>1111111=>1
[1,6,8,4,3,7,2,5]=>1000000=>0111111=>1
[3,1,4,7,8,5,2,6]=>0000000=>1111111=>1
[6,1,7,4,3,8,2,5]=>0000000=>1111111=>1
[1,8,7,4,3,6,2,5]=>1000000=>0111111=>1
[7,4,1,3,8,2,6,5]=>0000000=>1111111=>1
[4,8,2,3,1,5,7,6]=>0000000=>1111111=>1
[4,8,6,2,1,3,7,5]=>0000000=>1111111=>1
[2,7,4,1,8,3,5,6]=>0000000=>1111111=>1
[1,7,8,4,2,3,6,5]=>1000000=>0111111=>1
[4,7,1,3,8,2,6,5]=>0000000=>1111111=>1
[8,7,1,3,4,2,6,5]=>0000000=>1111111=>1
[1,7,4,3,6,2,8,5]=>1000000=>0111111=>1
[3,8,6,4,5,2,1,7]=>0000000=>1111111=>1
[3,8,4,6,5,2,1,7]=>0000000=>1111111=>1
[2,4,3,7,5,8,1,6]=>0000000=>1111111=>1
[1,4,7,3,6,2,8,5]=>1000000=>0111111=>1
[1,8,3,4,2,6,7,5]=>1000000=>0111111=>1
[6,4,1,3,7,2,8,5]=>0000000=>1111111=>1
[8,1,4,3,6,2,7,5]=>0000000=>1111111=>1
[4,2,3,8,5,7,1,6]=>0000000=>1111111=>1
[2,8,5,7,3,4,1,6]=>0000000=>1111111=>1
[5,8,2,6,4,3,1,7]=>0000000=>1111111=>1
[7,2,5,8,4,3,1,6]=>0000000=>1111111=>1
[4,2,3,5,8,7,1,6]=>0000000=>1111111=>1
[8,2,3,5,4,7,1,6]=>0000000=>1111111=>1
[6,1,8,3,4,2,7,5]=>0000000=>1111111=>1
[1,8,6,4,2,3,7,5]=>1000000=>0111111=>1
[3,8,4,5,6,2,1,7]=>0000000=>1111111=>1
[2,4,3,5,7,8,1,6]=>0000000=>1111111=>1
[3,8,6,5,4,2,1,7]=>0000000=>1111111=>1
[6,3,1,4,2,8,7,5]=>0000000=>1111111=>1
[7,3,8,1,2,6,4,5]=>0000000=>1111111=>1
[7,1,4,5,3,2,6,8]=>0000001=>1111110=>1
[1,8,4,2,6,5,3,7]=>1000000=>0111111=>1
[5,1,4,8,6,3,2,7]=>0000000=>1111111=>1
[5,3,1,8,4,7,2,6]=>0000000=>1111111=>1
[4,3,8,1,5,7,2,6]=>0000000=>1111111=>1
[6,3,1,2,5,7,4,8]=>0000001=>1111110=>1
[7,1,4,2,6,5,3,8]=>0000001=>1111110=>1
[3,8,4,1,6,5,2,7]=>0000000=>1111111=>1
[7,3,6,4,5,8,2,1]=>0000000=>1111111=>1
[8,7,2,4,5,1,6,3]=>0000000=>1111111=>1
[7,1,5,4,8,6,3,2]=>0000000=>1111111=>1
[5,7,1,4,8,6,3,2]=>0000000=>1111111=>1
[6,5,3,7,4,8,2,1]=>0000000=>1111111=>1
[7,5,8,4,1,6,3,2]=>0000000=>1111111=>1
[2,7,8,4,5,1,6,3]=>0000000=>1111111=>1
[5,7,3,8,4,1,6,2]=>0000000=>1111111=>1
[5,6,3,8,1,4,7,2]=>0000000=>1111111=>1
[3,7,8,4,1,6,5,2]=>0000000=>1111111=>1
[8,7,3,1,5,4,2,6]=>0000000=>1111111=>1
[6,8,2,7,4,3,1,5]=>0000000=>1111111=>1
[6,8,2,3,7,5,1,4]=>0000000=>1111111=>1
[5,2,7,3,8,6,1,4]=>0000000=>1111111=>1
[4,8,3,2,1,7,6,5]=>0000000=>1111111=>1
[6,8,3,7,2,1,5,4]=>0000000=>1111111=>1
[2,7,6,3,8,1,4,5]=>0000000=>1111111=>1
[2,1,5,4,8,7,3,6]=>0100000=>1011111=>2
[3,2,8,7,5,4,1,6]=>0000000=>1111111=>1
[5,4,2,6,3,1,8,7]=>0000010=>1111101=>2
[7,6,2,3,4,8,5,1]=>0000000=>1111111=>1
[2,1,8,7,4,3,5,6]=>0100000=>1011111=>2
[3,8,7,4,2,1,5,6]=>0000000=>1111111=>1
[8,5,2,6,1,7,3,4]=>0000000=>1111111=>1
[5,4,2,6,8,3,7,1]=>0000000=>1111111=>1
[8,1,2,4,3,5,6,7]=>0000000=>1111111=>1
[2,3,4,6,5,7,8,9,10,1]=>000000000=>111111111=>1
[2,3,5,6,4,7,8,9,1]=>00000000=>11111111=>1
[2,3,6,4,5,7,8,9,1]=>00000000=>11111111=>1
[9,1,2,4,5,3,6,7,8]=>00000000=>11111111=>1
[10,1,2,3,5,4,6,7,8,9]=>000000000=>111111111=>1
[5,8,7,4,6,3,2,1]=>0000000=>1111111=>1
[4,8,7,6,3,5,2,1]=>0000000=>1111111=>1
[3,8,7,6,5,2,4,1]=>0000000=>1111111=>1
[7,9,6,8,5,4,3,2,1]=>00000000=>11111111=>1
[5,8,4,7,6,3,2,1]=>0000000=>1111111=>1
[6,9,8,5,7,4,3,2,1]=>00000000=>11111111=>1
[6,8,5,4,7,3,2,1]=>0000000=>1111111=>1
[5,9,8,7,4,6,3,2,1]=>00000000=>11111111=>1
[3,8,7,6,2,5,4,1]=>0000000=>1111111=>1
[4,9,8,7,6,3,5,2,1]=>00000000=>11111111=>1
[4,8,7,6,3,2,5,1]=>0000000=>1111111=>1
[3,9,8,7,6,5,2,4,1]=>00000000=>11111111=>1
[3,8,7,6,5,2,1,4]=>0000000=>1111111=>1
[8,6,9,7,4,5,2,3,1]=>00000000=>11111111=>1
[8,6,9,4,7,5,2,3,1]=>00000000=>11111111=>1
[8,6,9,4,7,2,5,3,1]=>00000000=>11111111=>1
[8,6,9,4,7,3,5,1,2]=>00000000=>11111111=>1
[8,6,9,5,7,3,4,1,2]=>00000000=>11111111=>1
[8,7,9,5,6,3,4,1,2]=>00000000=>11111111=>1
[9,7,10,8,5,6,3,4,1,2]=>000000000=>111111111=>1
[8,6,4,9,7,5,2,3,1]=>00000000=>11111111=>1
[9,7,10,5,8,6,3,4,1,2]=>000000000=>111111111=>1
[8,6,9,4,2,7,5,3,1]=>00000000=>11111111=>1
[9,7,10,5,8,3,6,4,1,2]=>000000000=>111111111=>1
[8,6,9,4,7,2,1,5,3]=>00000000=>11111111=>1
[7,5,8,4,6,3,1,2]=>0000000=>1111111=>1
[8,6,9,4,7,3,5,2,1]=>00000000=>11111111=>1
[9,7,10,5,8,3,6,2,4,1]=>000000000=>111111111=>1
[8,6,9,5,7,2,4,1,3]=>00000000=>11111111=>1
[9,7,10,5,8,4,6,2,3,1]=>000000000=>111111111=>1
[7,6,8,2,5,1,4,3]=>0000000=>1111111=>1
[8,7,9,4,6,3,5,1,2]=>00000000=>11111111=>1
[9,7,10,6,8,4,5,2,3,1]=>000000000=>111111111=>1
[9,6,8,5,7,3,4,1,2]=>00000000=>11111111=>1
[9,8,10,6,7,4,5,2,3,1]=>000000000=>111111111=>1
[3,5,2,4,7,6,1,8]=>0000001=>1111110=>1
[3,5,4,7,2,6,1,8]=>0000001=>1111110=>1
[3,5,4,7,6,1,2,8]=>0000001=>1111110=>1
[3,5,4,7,6,1,8,2]=>0000000=>1111111=>1
[3,5,7,4,6,1,8,2]=>0000000=>1111111=>1
[3,5,7,4,6,1,2,8]=>0000001=>1111110=>1
[3,5,7,4,6,2,1,8]=>0000001=>1111110=>1
[3,2,5,7,4,6,1,8]=>0000001=>1111110=>1
[3,5,2,7,6,4,1,8]=>0000001=>1111110=>1
[3,5,7,2,6,4,1,8]=>0000001=>1111110=>1
[5,3,7,6,2,4,1,8]=>0000001=>1111110=>1
[5,3,7,6,1,2,8,4]=>0000000=>1111111=>1
[5,3,7,6,1,4,2,8]=>0000001=>1111110=>1
[5,3,7,6,4,1,2,8]=>0000001=>1111110=>1
[3,5,7,2,6,1,4,8]=>0000001=>1111110=>1
[3,5,2,7,6,1,4,8]=>0000001=>1111110=>1
[5,3,7,6,4,1,8,2]=>0000000=>1111111=>1
[3,7,5,4,1,8,2,6]=>0000000=>1111111=>1
[3,7,5,4,1,8,6,2]=>0000000=>1111111=>1
[3,7,5,1,4,8,6,2]=>0000000=>1111111=>1
[3,7,5,1,4,8,2,6]=>0000000=>1111111=>1
[3,5,7,1,2,6,8,4]=>0000000=>1111111=>1
[3,5,7,2,1,6,8,4]=>0000000=>1111111=>1
[3,5,2,7,1,6,4,8]=>0000001=>1111110=>1
[3,5,7,2,1,6,4,8]=>0000001=>1111110=>1
[5,3,7,1,6,2,4,8]=>0000001=>1111110=>1
[3,5,7,1,4,6,8,2]=>0000000=>1111111=>1
[3,5,7,1,4,6,2,8]=>0000001=>1111110=>1
[3,5,7,1,4,2,6,8]=>0000001=>1111110=>1
[3,5,7,2,1,4,6,8]=>0000001=>1111110=>1
[3,5,2,7,1,4,6,8]=>0000001=>1111110=>1
[3,2,5,7,4,1,6,8]=>0000001=>1111110=>1
[3,5,2,7,4,1,6,8]=>0000001=>1111110=>1
[3,5,7,4,2,1,6,8]=>0000001=>1111110=>1
[3,5,7,4,1,2,6,8]=>0000001=>1111110=>1
[3,5,4,7,1,6,8,2]=>0000000=>1111111=>1
[3,5,4,7,1,2,6,8]=>0000001=>1111110=>1
[3,5,4,7,2,1,6,8]=>0000001=>1111110=>1
[3,5,4,2,7,1,6,8]=>0000001=>1111110=>1
[3,2,5,4,7,1,6,8]=>0000001=>1111110=>1
[3,5,4,7,2,1,8,6]=>0000000=>1111111=>1
[3,5,4,7,1,2,8,6]=>0000000=>1111111=>1
[5,7,6,3,1,8,4,2]=>0000000=>1111111=>1
[5,7,6,3,1,8,2,4]=>0000000=>1111111=>1
[3,5,7,4,1,2,8,6]=>0000000=>1111111=>1
[3,5,7,4,2,1,8,6]=>0000000=>1111111=>1
[3,2,5,7,4,1,8,6]=>0000000=>1111111=>1
[3,2,5,7,1,4,8,6]=>0000000=>1111111=>1
[3,5,2,7,1,4,8,6]=>0000000=>1111111=>1
[3,5,7,2,1,4,8,6]=>0000000=>1111111=>1
[3,5,7,1,4,2,8,6]=>0000000=>1111111=>1
[3,7,5,2,1,8,6,4]=>0000000=>1111111=>1
[3,7,2,5,1,8,6,4]=>0000000=>1111111=>1
[3,2,7,5,1,8,6,4]=>0000000=>1111111=>1
[3,2,7,5,1,8,4,6]=>0000000=>1111111=>1
[3,7,2,5,1,8,4,6]=>0000000=>1111111=>1
[3,7,5,2,1,8,4,6]=>0000000=>1111111=>1
[2,1,7,5,8,4,6,3]=>0100000=>1011111=>2
[1,3,4,5,6,7,9,2,8]=>10000000=>01111111=>1
[2,3,4,5,6,7,1,9,8]=>00000010=>11111101=>2
[2,1,4,5,6,7,8,9,3]=>01000000=>10111111=>2
[3,1,4,5,6,7,8,2,9]=>00000001=>11111110=>1
[3,8,6,4,1,7,5,2]=>0000000=>1111111=>1
[3,8,4,1,7,6,5,2]=>0000000=>1111111=>1
[3,2,8,7,6,1,5,4]=>0000000=>1111111=>1
[4,2,5,8,1,7,3,6]=>0000000=>1111111=>1
[5,8,2,4,1,6,3,7]=>0000000=>1111111=>1
[8,4,2,6,5,1,3,7]=>0000000=>1111111=>1
[3,2,6,8,1,5,4,7]=>0000000=>1111111=>1
[3,2,6,8,7,1,5,4]=>0000000=>1111111=>1
[8,7,3,2,5,6,1,4]=>0000000=>1111111=>1
[7,2,4,1,8,3,6,5]=>0000000=>1111111=>1
[3,2,8,5,7,1,4,6]=>0000000=>1111111=>1
[2,6,5,7,1,8,3,4]=>0000000=>1111111=>1
[2,5,1,8,7,4,3,6]=>0000000=>1111111=>1
[8,1,4,6,3,5,2,7]=>0000000=>1111111=>1
[8,3,5,4,1,6,2,7]=>0000000=>1111111=>1
[8,6,3,4,1,5,2,7]=>0000000=>1111111=>1
[5,4,7,6,8,2,3,1]=>0000000=>1111111=>1
[4,1,8,2,3,7,6,5]=>0000000=>1111111=>1
[2,1,8,5,3,4,7,6]=>0100000=>1011111=>2
[5,2,4,6,8,7,3,1]=>0000000=>1111111=>1
[1,6,8,3,4,5,7,2]=>1000000=>0111111=>1
[5,7,4,8,6,1,3,2]=>0000000=>1111111=>1
[5,4,2,6,7,8,1,3]=>0000000=>1111111=>1
[6,4,2,7,3,5,8,1]=>0000000=>1111111=>1
[7,4,1,8,3,5,6,2]=>0000000=>1111111=>1
[6,5,4,8,7,3,1,2]=>0000000=>1111111=>1
[8,7,4,2,1,3,6,5]=>0000000=>1111111=>1
[8,7,1,3,2,5,6,4]=>0000000=>1111111=>1
[6,8,2,3,1,7,5,4]=>0000000=>1111111=>1
[7,4,3,2,6,8,5,1]=>0000000=>1111111=>1
[2,7,4,3,8,5,6,1]=>0000000=>1111111=>1
[8,3,7,2,1,5,6,4]=>0000000=>1111111=>1
[5,7,8,2,4,3,1,6]=>0000000=>1111111=>1
[8,4,7,3,2,6,1,5]=>0000000=>1111111=>1
[8,3,1,6,7,4,2,5]=>0000000=>1111111=>1
[3,2,5,7,4,8,1,6]=>0000000=>1111111=>1
[8,2,7,3,4,1,5,6]=>0000000=>1111111=>1
[7,1,6,3,5,8,2,4]=>0000000=>1111111=>1
[2,8,5,6,7,1,4,3]=>0000000=>1111111=>1
[1,5,2,7,8,6,4,3]=>1000000=>0111111=>1
[2,6,8,5,1,4,7,3]=>0000000=>1111111=>1
[1,4,2,8,6,5,7,3]=>1000000=>0111111=>1
[3,5,1,6,8,7,2,4]=>0000000=>1111111=>1
[5,7,6,2,1,3,8,4]=>0000000=>1111111=>1
[2,5,8,7,4,1,6,3]=>0000000=>1111111=>1
[4,1,7,5,2,6,8,3]=>0000000=>1111111=>1
[7,6,2,4,5,1,8,3]=>0000000=>1111111=>1
[7,3,4,2,5,8,6,1]=>0000000=>1111111=>1
[8,7,4,2,5,1,6,3]=>0000000=>1111111=>1
[8,1,4,5,2,6,7,3]=>0000000=>1111111=>1
[5,2,4,8,6,7,1,3]=>0000000=>1111111=>1
[8,5,6,2,1,3,7,4]=>0000000=>1111111=>1
[4,2,1,5,6,7,8,3]=>0000000=>1111111=>1
[3,4,6,5,1,7,8,2]=>0000000=>1111111=>1
[7,3,5,2,4,6,1,8]=>0000001=>1111110=>1
[5,3,7,2,4,6,1,8]=>0000001=>1111110=>1
[3,7,5,2,4,6,1,8]=>0000001=>1111110=>1
[5,7,3,2,4,6,1,8]=>0000001=>1111110=>1
[1,5,3,2,4,7,6,8]=>1000101=>0111010=>2
[1,5,3,2,7,4,6,8]=>1000001=>0111110=>1
[5,7,3,2,1,4,6,8]=>0000001=>1111110=>1
[5,7,3,2,4,1,6,8]=>0000001=>1111110=>1
[3,7,2,5,4,1,6,8]=>0000001=>1111110=>1
[5,1,3,2,4,7,6,8]=>0000101=>1111010=>2
[5,1,3,2,7,4,6,8]=>0000001=>1111110=>1
[7,1,3,2,5,4,6,8]=>0000001=>1111110=>1
[1,7,3,2,5,4,6,8]=>1000001=>0111110=>1
[7,1,3,5,2,4,6,8]=>0000001=>1111110=>1
[5,1,3,7,2,4,6,8]=>0000001=>1111110=>1
[3,2,7,5,1,4,6,8]=>0000001=>1111110=>1
[3,7,5,1,2,4,6,8]=>0000001=>1111110=>1
[5,7,3,1,2,4,6,8]=>0000001=>1111110=>1
[1,5,3,7,2,4,6,8]=>1000001=>0111110=>1
[5,3,2,7,4,1,6,8]=>0000001=>1111110=>1
[5,3,2,4,7,1,6,8]=>0000001=>1111110=>1
[5,3,2,1,4,7,6,8]=>0000101=>1111010=>2
[5,3,2,1,7,4,6,8]=>0000001=>1111110=>1
[1,3,2,7,5,4,6,8]=>1010001=>0101110=>2
[1,3,7,2,5,4,6,8]=>1000001=>0111110=>1
[7,3,1,2,5,4,6,8]=>0000001=>1111110=>1
[5,3,1,2,7,4,6,8]=>0000001=>1111110=>1
[5,3,1,2,4,7,6,8]=>0000101=>1111010=>2
[3,2,5,1,4,7,6,8]=>0000101=>1111010=>2
[7,3,1,5,2,4,6,8]=>0000001=>1111110=>1
[1,3,7,5,2,4,6,8]=>1000001=>0111110=>1
[7,5,1,3,2,4,6,8]=>0000001=>1111110=>1
[5,7,1,3,2,4,6,8]=>0000001=>1111110=>1
[3,7,1,5,2,4,6,8]=>0000001=>1111110=>1
[3,7,1,2,5,4,6,8]=>0000001=>1111110=>1
[3,7,2,1,5,4,6,8]=>0000001=>1111110=>1
[3,2,1,7,5,4,6,8]=>0010001=>1101110=>2
[3,1,2,7,5,4,6,8]=>0010001=>1101110=>2
[3,1,7,2,5,4,6,8]=>0000001=>1111110=>1
[3,1,7,5,2,4,6,8]=>0000001=>1111110=>1
[7,1,5,3,2,4,6,8]=>0000001=>1111110=>1
[1,7,5,3,2,4,6,8]=>1000001=>0111110=>1
[1,2,3,4,5,7,9,6,8]=>11111000=>00000111=>1
[1,2,3,5,9,4,6,7,8]=>11100000=>00011111=>1
[1,9,8,7,6,2,5,4,3]=>10000000=>01111111=>1
[2,9,8,7,1,6,5,4,3]=>00000000=>11111111=>1
[1,9,8,2,7,6,5,4,3]=>10000000=>01111111=>1
[1,9,2,8,7,6,5,4,3]=>10000000=>01111111=>1
[3,9,8,7,6,5,2,1,4]=>00000000=>11111111=>1
[1,10,9,8,7,6,5,2,4,3]=>100000000=>011111111=>1
[4,9,8,7,6,1,2,5,3]=>00000000=>11111111=>1
[1,10,9,8,7,6,2,5,4,3]=>100000000=>011111111=>1
[1,8,7,4,2,6,5,3]=>1000000=>0111111=>1
[5,9,8,7,1,2,6,4,3]=>00000000=>11111111=>1
[2,10,9,8,7,1,6,5,4,3]=>000000000=>111111111=>1
[2,8,5,1,7,6,4,3]=>0000000=>1111111=>1
[6,9,8,2,1,7,5,4,3]=>00000000=>11111111=>1
[1,10,9,8,2,7,6,5,4,3]=>100000000=>011111111=>1
[6,8,5,1,2,7,4,3]=>0000000=>1111111=>1
[7,9,1,2,8,6,5,4,3]=>00000000=>11111111=>1
[1,10,9,2,8,7,6,5,4,3]=>100000000=>011111111=>1
[8,1,2,9,7,6,5,4,3]=>00000000=>11111111=>1
[2,10,1,9,8,7,6,5,4,3]=>000000000=>111111111=>1
[3,10,9,8,7,6,5,2,1,4]=>000000000=>111111111=>1
[1,11,10,9,8,7,6,5,2,4,3]=>1000000000=>0111111111=>1
[1,9,8,7,6,3,2,5,4]=>10000000=>01111111=>1
[4,10,9,8,7,6,1,2,5,3]=>000000000=>111111111=>1
[1,11,10,9,8,7,6,2,5,4,3]=>1000000000=>0111111111=>1
[1,9,8,7,4,2,6,5,3]=>10000000=>01111111=>1
[4,9,8,7,6,3,2,1,5]=>00000000=>11111111=>1
[5,10,9,8,7,1,2,6,4,3]=>000000000=>111111111=>1
[2,8,1,4,7,6,5,3]=>0000000=>1111111=>1
[2,9,8,5,1,7,6,4,3]=>00000000=>11111111=>1
[5,9,8,7,4,1,2,6,3]=>00000000=>11111111=>1
[6,10,9,8,2,1,7,5,4,3]=>000000000=>111111111=>1
[1,11,10,9,8,2,7,6,5,4,3]=>1000000000=>0111111111=>1
[1,9,6,2,8,7,5,4,3]=>10000000=>01111111=>1
[1,8,7,4,3,2,6,5]=>1000000=>0111111=>1
[6,9,8,5,1,2,7,4,3]=>00000000=>11111111=>1
[7,10,9,1,2,8,6,5,4,3]=>000000000=>111111111=>1
[1,11,10,9,2,8,7,6,5,4,3]=>1000000000=>0111111111=>1
[1,7,2,9,8,6,5,4,3]=>10000000=>01111111=>1
[1,8,5,4,2,7,6,3]=>1000000=>0111111=>1
[7,9,6,2,1,8,5,4,3]=>00000000=>11111111=>1
[8,10,1,2,9,7,6,5,4,3]=>000000000=>111111111=>1
[8,7,1,2,9,6,5,4,3]=>00000000=>11111111=>1
[9,2,1,10,8,7,6,5,4,3]=>000000000=>111111111=>1
[1,11,2,10,9,8,7,6,5,4,3]=>1000000000=>0111111111=>1
[1,7,2,3,6,8,5,4]=>1000000=>0111111=>1
[3,5,6,4,8,2,7,1]=>0000000=>1111111=>1
[3,5,1,4,8,2,7,6]=>0000000=>1111111=>1
[1,7,5,4,8,2,6,3]=>1000000=>0111111=>1
[3,7,5,1,6,4,8,2]=>0000000=>1111111=>1
[2,7,5,4,8,1,3,6]=>0000000=>1111111=>1
[2,7,5,4,8,6,1,3]=>0000000=>1111111=>1
[1,7,5,4,8,6,3,2]=>1000000=>0111111=>1
[2,5,1,4,8,7,3,6]=>0000000=>1111111=>1
[3,6,4,2,8,7,1,5]=>0000000=>1111111=>1
[3,5,2,4,8,1,6,7]=>0000000=>1111111=>1
[3,5,6,4,8,1,2,7]=>0000000=>1111111=>1
[1,5,6,4,8,7,2,3]=>1000000=>0111111=>1
[3,6,4,1,8,7,2,5]=>0000000=>1111111=>1
[3,6,4,5,8,7,2,1]=>0000000=>1111111=>1
[1,6,4,3,8,5,2,7]=>1000000=>0111111=>1
[7,1,3,4,5,8,2,6]=>0000000=>1111111=>1
[7,6,1,4,5,3,8,2]=>0000000=>1111111=>1
[7,6,1,3,5,4,8,2]=>0000000=>1111111=>1
[7,1,3,2,5,8,4,6]=>0000000=>1111111=>1
[1,6,4,2,8,5,3,7]=>1000000=>0111111=>1
[7,6,5,8,2,4,3,1]=>0000000=>1111111=>1
[7,6,5,8,3,1,4,2]=>0000000=>1111111=>1
[2,6,4,3,8,1,7,5]=>0000000=>1111111=>1
[2,6,4,3,8,5,7,1]=>0000000=>1111111=>1
[7,2,3,1,5,8,6,4]=>0000000=>1111111=>1
[7,1,5,6,3,8,4,2]=>0000000=>1111111=>1
[7,3,6,5,1,4,8,2]=>0000000=>1111111=>1
[7,2,6,5,3,8,1,4]=>0000000=>1111111=>1
[7,2,3,1,4,8,6,5]=>0000000=>1111111=>1
[7,2,3,5,4,8,6,1]=>0000000=>1111111=>1
[2,6,4,5,8,1,7,3]=>0000000=>1111111=>1
[1,5,6,4,8,3,7,2]=>1000000=>0111111=>1
[2,5,6,4,8,3,1,7]=>0000000=>1111111=>1
[3,5,6,1,4,7,8,2]=>0000000=>1111111=>1
[7,6,1,3,4,5,8,2]=>0000000=>1111111=>1
[7,1,3,2,4,8,5,6]=>0000000=>1111111=>1
[7,6,1,5,3,4,8,2]=>0000000=>1111111=>1
[7,6,1,5,4,3,8,2]=>0000000=>1111111=>1
[1,6,4,5,8,3,2,7]=>1000000=>0111111=>1
[7,6,5,8,1,3,2,4]=>0000000=>1111111=>1
[3,4,6,8,7,2,1,5]=>0000000=>1111111=>1
[3,5,6,8,2,1,7,4]=>0000000=>1111111=>1
[4,2,1,5,3,7,8,6]=>0000100=>1111011=>2
[4,2,5,6,3,1,8,7]=>0000010=>1111101=>2
[3,5,6,8,1,7,2,4]=>0000000=>1111111=>1
[4,1,5,6,3,2,8,7]=>0000010=>1111101=>2
[4,5,3,1,7,2,8,6]=>0000000=>1111111=>1
[4,1,3,5,2,7,8,6]=>0000100=>1111011=>2
[2,5,4,7,3,8,6,1]=>0000000=>1111111=>1
[3,5,7,1,8,4,2,6]=>0000000=>1111111=>1
[4,1,5,3,2,7,8,6]=>0000100=>1111011=>2
[4,5,3,7,1,2,8,6]=>0000000=>1111111=>1
[4,3,6,1,2,7,5,8]=>0000001=>1111110=>1
[5,1,3,2,4,6,7,8]=>0000111=>1111000=>1
[3,6,1,7,4,5,2,8]=>0000001=>1111110=>1
[5,1,3,4,2,6,7,8]=>0000111=>1111000=>1
[5,3,1,4,2,6,7,8]=>0000111=>1111000=>1
[4,5,2,3,7,1,8,6]=>0000000=>1111111=>1
[4,2,6,1,3,7,5,8]=>0000001=>1111110=>1
[4,6,2,1,3,7,5,8]=>0000001=>1111110=>1
[3,6,2,1,7,4,8,5]=>0000000=>1111111=>1
[3,1,4,7,6,5,2,8]=>0000001=>1111110=>1
[3,6,2,7,1,5,8,4]=>0000000=>1111111=>1
[4,6,2,7,1,3,5,8]=>0000001=>1111110=>1
[3,5,7,1,8,2,6,4]=>0000000=>1111111=>1
[5,1,4,2,3,6,7,8]=>0000111=>1111000=>1
[3,6,1,7,2,5,8,4]=>0000000=>1111111=>1
[2,6,5,3,4,7,8,1]=>0000000=>1111111=>1
[3,6,1,7,5,4,2,8]=>0000001=>1111110=>1
[5,1,4,3,2,6,7,8]=>0000111=>1111000=>1
[5,4,1,3,2,6,7,8]=>0000111=>1111000=>1
[6,2,4,5,1,8,3,7]=>0000000=>1111111=>1
[7,6,4,5,1,3,8,2]=>0000000=>1111111=>1
[1,6,7,5,3,4,8,2]=>1000000=>0111111=>1
[7,6,2,3,8,4,1,5]=>0000000=>1111111=>1
[1,6,7,5,8,2,3,4]=>1000000=>0111111=>1
[6,2,5,8,3,4,7,1]=>0000000=>1111111=>1
[6,2,3,8,7,4,1,5]=>0000000=>1111111=>1
[2,4,7,3,5,8,6,1]=>0000000=>1111111=>1
[2,5,3,7,1,8,4,6]=>0000000=>1111111=>1
[5,2,8,3,1,4,6,7]=>0000000=>1111111=>1
[4,8,2,3,6,5,7,1]=>0000000=>1111111=>1
[5,8,1,3,6,4,7,2]=>0000000=>1111111=>1
[5,8,1,4,3,6,2,7]=>0000000=>1111111=>1
[5,8,4,1,3,7,6,2]=>0000000=>1111111=>1
[6,4,5,3,8,1,7,2]=>0000000=>1111111=>1
[4,6,5,3,7,1,2,8]=>0000001=>1111110=>1
[4,5,1,3,6,2,8,7]=>0000010=>1111101=>2
[4,2,6,5,1,7,3,8]=>0000001=>1111110=>1
[4,3,5,7,2,1,6,8]=>0000001=>1111110=>1
[3,4,7,6,8,1,2,5]=>0000000=>1111111=>1
[3,4,6,2,5,8,7,1]=>0000000=>1111111=>1
[3,5,2,4,6,1,8,7]=>0000010=>1111101=>2
[4,2,5,1,6,8,3,7]=>0000000=>1111111=>1
[1,8,2,3,6,5,7,4]=>1000000=>0111111=>1
[4,2,8,3,5,7,1,6]=>0000000=>1111111=>1
[4,3,8,6,5,7,1,2]=>0000000=>1111111=>1
[1,3,7,2,6,5,8,4]=>1000000=>0111111=>1
[1,3,6,4,2,5,8,7]=>1000010=>0111101=>2
[1,5,4,7,3,6,8,2]=>1000000=>0111111=>1
[5,2,3,8,4,1,7,6]=>0000000=>1111111=>1
[7,5,3,4,8,2,1,6]=>0000000=>1111111=>1
[7,2,8,3,4,1,5,6]=>0000000=>1111111=>1
[7,4,3,8,5,2,6,1]=>0000000=>1111111=>1
[4,6,2,7,3,1,5,8]=>0000001=>1111110=>1
[7,6,3,8,2,4,5,1]=>0000000=>1111111=>1
[7,2,8,5,1,3,4,6]=>0000000=>1111111=>1
[1,5,3,7,6,8,4,2]=>1000000=>0111111=>1
[1,6,3,7,8,2,4,5]=>1000000=>0111111=>1
[1,4,3,7,8,5,2,6]=>1000000=>0111111=>1
[4,2,6,5,7,8,3,1]=>0000000=>1111111=>1
[4,2,6,7,5,8,1,3]=>0000000=>1111111=>1
[3,2,4,7,8,5,1,6]=>0000000=>1111111=>1
[3,2,6,7,8,1,4,5]=>0000000=>1111111=>1
[3,8,5,6,1,7,2,4]=>0000000=>1111111=>1
[3,4,8,1,7,6,2,5]=>0000000=>1111111=>1
[6,7,4,8,5,1,3,2]=>0000000=>1111111=>1
[3,6,5,8,7,1,4,2]=>0000000=>1111111=>1
[5,6,8,3,1,7,4,2]=>0000000=>1111111=>1
[5,3,8,1,7,2,6,4]=>0000000=>1111111=>1
[6,5,3,8,2,7,4,1]=>0000000=>1111111=>1
[6,4,8,1,3,7,5,2]=>0000000=>1111111=>1
[7,6,3,1,4,2,5,8]=>0000001=>1111110=>1
[1,5,4,3,7,8,2,6]=>1000000=>0111111=>1
[4,2,8,7,6,3,1,5]=>0000000=>1111111=>1
[6,3,1,8,7,5,2,4]=>0000000=>1111111=>1
[7,6,3,1,8,4,2,5]=>0000000=>1111111=>1
[7,6,4,2,1,8,3,5]=>0000000=>1111111=>1
[8,3,5,7,6,4,2,1]=>0000000=>1111111=>1
[1,8,2,7,5,3,6,4]=>1000000=>0111111=>1
[7,5,2,1,8,3,6,4]=>0000000=>1111111=>1
[5,2,7,4,1,8,6,3]=>0000000=>1111111=>1
[8,7,4,1,5,2,6,3]=>0000000=>1111111=>1
[8,7,5,2,6,3,1,4]=>0000000=>1111111=>1
[1,3,7,6,5,8,2,4]=>1000000=>0111111=>1
[8,6,4,7,5,2,1,3]=>0000000=>1111111=>1
[6,3,1,4,7,5,2,8]=>0000001=>1111110=>1
[8,6,3,1,4,7,5,2]=>0000000=>1111111=>1
[1,8,2,6,4,7,5,3]=>1000000=>0111111=>1
[7,5,2,1,6,4,8,3]=>0000000=>1111111=>1
[1,4,7,3,5,2,6,8]=>1000001=>0111110=>1
[5,7,4,2,6,3,1,8]=>0000001=>1111110=>1
[4,2,6,3,5,7,1,8]=>0000001=>1111110=>1
[6,1,3,7,4,2,5,8]=>0000001=>1111110=>1
[3,2,6,8,1,5,7,4]=>0000000=>1111111=>1
[8,6,2,7,1,5,4,3]=>0000000=>1111111=>1
[6,3,7,2,8,1,5,4]=>0000000=>1111111=>1
[7,5,2,8,6,1,4,3]=>0000000=>1111111=>1
[1,6,8,5,2,4,3,7]=>1000000=>0111111=>1
[4,5,7,2,8,1,6,3]=>0000000=>1111111=>1
[4,5,3,1,7,2,6,8]=>0000001=>1111110=>1
[6,1,3,4,2,8,5,7]=>0000000=>1111111=>1
[1,7,4,3,6,8,2,5]=>1000000=>0111111=>1
[8,7,1,3,6,5,4,2]=>0000000=>1111111=>1
[4,7,5,3,8,2,1,6]=>0000000=>1111111=>1
[6,3,5,8,7,4,1,2]=>0000000=>1111111=>1
[4,7,2,8,5,6,3,1]=>0000000=>1111111=>1
[1,4,8,7,3,5,6,2]=>1000000=>0111111=>1
[8,1,7,6,3,5,4,2]=>0000000=>1111111=>1
[3,6,8,5,7,4,1,2]=>0000000=>1111111=>1
[3,8,7,5,6,4,2,1]=>0000000=>1111111=>1
[2,8,7,6,4,5,3,1]=>0000000=>1111111=>1
[1,8,7,6,5,3,4,2]=>1000000=>0111111=>1
[4,6,7,2,5,3,1,8]=>0000001=>1111110=>1
[4,2,6,8,7,1,5,3]=>0000000=>1111111=>1
[2,7,3,8,1,6,5,4]=>0000000=>1111111=>1
[2,6,8,4,1,7,5,3]=>0000000=>1111111=>1
[3,6,1,8,2,7,5,4]=>0000000=>1111111=>1
[6,3,7,1,2,8,5,4]=>0000000=>1111111=>1
[1,7,8,5,4,3,2,6]=>1000000=>0111111=>1
[1,2,6,7,8,4,3,5]=>1100000=>0011111=>1
[4,7,1,3,6,8,2,5]=>0000000=>1111111=>1
[3,7,6,4,8,1,2,5]=>0000000=>1111111=>1
[1,3,6,7,4,2,8,5]=>1000000=>0111111=>1
[3,6,4,8,2,7,5,1]=>0000000=>1111111=>1
[8,1,6,7,5,3,2,4]=>0000000=>1111111=>1
[8,7,2,4,6,5,3,1]=>0000000=>1111111=>1
[1,7,8,2,6,4,5,3]=>1000000=>0111111=>1
[8,7,2,5,4,6,1,3]=>0000000=>1111111=>1
[8,7,3,2,1,5,6,4]=>0000000=>1111111=>1
[8,7,6,1,4,5,3,2]=>0000000=>1111111=>1
[4,8,1,2,3,7,5,6]=>0000000=>1111111=>1
[1,8,2,3,6,5,4,7]=>1000000=>0111111=>1
[3,5,8,4,7,2,6,1]=>0000000=>1111111=>1
[1,8,5,4,6,2,3,7]=>1000000=>0111111=>1
[3,8,5,4,6,1,2,7]=>0000000=>1111111=>1
[3,8,5,1,6,4,2,7]=>0000000=>1111111=>1
[2,8,5,4,6,1,3,7]=>0000000=>1111111=>1
[2,8,5,4,6,3,1,7]=>0000000=>1111111=>1
[1,8,5,4,6,3,2,7]=>1000000=>0111111=>1
[2,5,8,4,7,3,6,1]=>0000000=>1111111=>1
[3,6,4,2,7,8,5,1]=>0000000=>1111111=>1
[3,5,4,1,6,2,7,8]=>0000011=>1111100=>1
[4,5,8,1,7,6,2,3]=>0000000=>1111111=>1
[3,5,8,4,7,1,6,2]=>0000000=>1111111=>1
[1,5,8,4,7,3,6,2]=>1000000=>0111111=>1
[3,6,4,1,7,8,5,2]=>0000000=>1111111=>1
[3,6,4,8,7,5,2,1]=>0000000=>1111111=>1
[1,6,4,3,7,8,5,2]=>1000000=>0111111=>1
[7,1,3,4,8,6,5,2]=>0000000=>1111111=>1
[7,6,1,3,8,4,2,5]=>0000000=>1111111=>1
[1,6,4,2,7,8,3,5]=>1000000=>0111111=>1
[2,6,4,3,7,1,8,5]=>0000000=>1111111=>1
[2,6,4,1,7,8,3,5]=>0000000=>1111111=>1
[7,2,3,4,8,6,5,1]=>0000000=>1111111=>1
[7,2,3,1,8,6,4,5]=>0000000=>1111111=>1
[7,2,3,4,1,6,8,5]=>0000000=>1111111=>1
[1,2,4,3,8,5,7,6]=>1101000=>0010111=>2
[7,3,8,6,1,4,2,5]=>0000000=>1111111=>1
[7,2,8,6,3,4,1,5]=>0000000=>1111111=>1
[7,2,3,1,5,6,8,4]=>0000000=>1111111=>1
[7,2,3,8,1,6,5,4]=>0000000=>1111111=>1
[7,2,3,8,5,6,4,1]=>0000000=>1111111=>1
[2,6,4,8,7,1,5,3]=>0000000=>1111111=>1
[1,5,8,4,7,6,2,3]=>1000000=>0111111=>1
[3,5,8,1,6,7,2,4]=>0000000=>1111111=>1
[7,6,1,3,5,8,2,4]=>0000000=>1111111=>1
[7,1,3,2,5,6,8,4]=>0000000=>1111111=>1
[7,1,3,8,2,6,5,4]=>0000000=>1111111=>1
[7,6,1,8,5,4,2,3]=>0000000=>1111111=>1
[4,3,7,1,6,5,8,2]=>0000000=>1111111=>1
[5,2,6,4,8,1,7,3]=>0000000=>1111111=>1
[5,3,7,4,8,1,6,2]=>0000000=>1111111=>1
[4,3,7,1,5,2,8,6]=>0000000=>1111111=>1
[4,3,7,1,6,2,8,5]=>0000000=>1111111=>1
[5,4,8,1,6,3,7,2]=>0000000=>1111111=>1
[4,1,7,8,6,3,2,5]=>0000000=>1111111=>1
[1,2,6,8,3,7,4,5]=>1100000=>0011111=>1
[7,5,8,4,3,1,6,2]=>0000000=>1111111=>1
[6,8,2,4,1,3,7,5]=>0000000=>1111111=>1
[6,1,2,7,5,8,4,3]=>0000000=>1111111=>1
[4,5,2,6,8,3,7,1]=>0000000=>1111111=>1
[6,8,4,1,5,3,7,2]=>0000000=>1111111=>1
[6,8,3,5,1,4,7,2]=>0000000=>1111111=>1
[8,1,3,4,2,6,5,7]=>0000000=>1111111=>1
[8,1,3,2,5,6,4,7]=>0000000=>1111111=>1
[8,1,2,4,5,3,7,6]=>0000000=>1111111=>1
[7,4,5,1,6,2,8,3]=>0000000=>1111111=>1
[8,3,6,1,5,7,4,2]=>0000000=>1111111=>1
[3,2,7,5,8,6,1,4]=>0000000=>1111111=>1
[2,4,6,7,8,1,5,3]=>0000000=>1111111=>1
[2,4,6,8,1,7,5,3]=>0000000=>1111111=>1
[7,4,3,8,6,2,1,5]=>0000000=>1111111=>1
[4,3,6,2,1,8,5,7]=>0000000=>1111111=>1
[4,6,2,3,7,5,8,1]=>0000000=>1111111=>1
[8,4,5,3,2,1,7,6]=>0000000=>1111111=>1
[5,8,3,4,2,1,7,6]=>0000000=>1111111=>1
[6,4,8,3,2,7,1,5]=>0000000=>1111111=>1
[5,8,3,7,2,1,6,4]=>0000000=>1111111=>1
[6,4,7,3,8,2,1,5]=>0000000=>1111111=>1
[6,7,4,3,2,1,8,5]=>0000000=>1111111=>1
[8,4,3,7,2,1,5,6]=>0000000=>1111111=>1
[1,2,6,5,8,7,3,4]=>1100000=>0011111=>1
[1,5,2,8,4,6,7,3]=>1000000=>0111111=>1
[1,5,2,7,4,6,8,3]=>1000000=>0111111=>1
[5,1,2,7,3,6,8,4]=>0000000=>1111111=>1
[5,6,3,4,8,7,2,1]=>0000000=>1111111=>1
[6,5,3,4,8,7,2,1]=>0000000=>1111111=>1
[4,1,2,8,3,6,7,5]=>0000000=>1111111=>1
[4,1,2,7,3,6,8,5]=>0000000=>1111111=>1
[7,5,3,8,4,6,2,1]=>0000000=>1111111=>1
[8,5,3,7,4,6,2,1]=>0000000=>1111111=>1
[5,8,1,2,3,4,7,6]=>0000000=>1111111=>1
[7,1,2,8,3,6,4,5]=>0000000=>1111111=>1
[1,6,8,2,4,5,7,3]=>1000000=>0111111=>1
[4,3,8,7,5,6,2,1]=>0000000=>1111111=>1
[1,8,2,7,4,6,5,3]=>1000000=>0111111=>1
[5,8,3,7,4,6,2,1]=>0000000=>1111111=>1
[6,8,7,3,4,5,2,1]=>0000000=>1111111=>1
[1,8,7,2,4,5,3,6]=>1000000=>0111111=>1
[8,1,6,2,3,5,4,7]=>0000000=>1111111=>1
[1,7,6,2,4,5,3,8]=>1000001=>0111110=>1
[1,8,7,4,6,3,5,2]=>1000000=>0111111=>1
[1,8,3,5,7,2,6,4]=>1000000=>0111111=>1
[2,3,4,6,8,5,7,1]=>0000000=>1111111=>1
[2,4,6,3,7,8,5,1]=>0000000=>1111111=>1
[2,5,7,1,8,6,3,4]=>0000000=>1111111=>1
[8,2,4,5,1,3,7,6]=>0000000=>1111111=>1
[1,6,2,7,8,5,3,4]=>1000000=>0111111=>1
[3,5,2,6,7,8,4,1]=>0000000=>1111111=>1
[4,5,1,6,7,3,8,2]=>0000000=>1111111=>1
[2,8,4,1,7,5,3,6]=>0000000=>1111111=>1
[8,5,3,1,7,4,2,6]=>0000000=>1111111=>1
[3,1,6,7,8,4,2,5]=>0000000=>1111111=>1
[1,6,7,8,9,2,3,4,5]=>10000000=>01111111=>1
[1,7,8,9,2,3,4,5,6]=>10000000=>01111111=>1
[1,7,8,9,10,2,3,4,5,6]=>100000000=>011111111=>1
[8,6,2,3,5,1,4,7]=>0000000=>1111111=>1
[8,2,4,5,7,3,1,6]=>0000000=>1111111=>1
[2,6,3,8,7,5,4,1]=>0000000=>1111111=>1
[8,2,3,7,5,4,1,6]=>0000000=>1111111=>1
[8,2,6,3,5,4,1,7]=>0000000=>1111111=>1
[8,6,1,5,2,4,3,7]=>0000000=>1111111=>1
[8,6,2,4,1,5,3,7]=>0000000=>1111111=>1
[8,4,1,6,5,3,2,7]=>0000000=>1111111=>1
[8,3,6,1,5,4,2,7]=>0000000=>1111111=>1
[8,3,2,6,5,4,1,7]=>0000000=>1111111=>1
[8,3,2,5,7,4,1,6]=>0000000=>1111111=>1
[8,3,1,7,5,4,2,6]=>0000000=>1111111=>1
[8,2,7,4,1,5,3,6]=>0000000=>1111111=>1
[6,1,3,8,7,5,4,2]=>0000000=>1111111=>1
[3,6,1,8,7,5,4,2]=>0000000=>1111111=>1
[3,8,1,5,7,6,4,2]=>0000000=>1111111=>1
[3,5,2,8,7,6,4,1]=>0000000=>1111111=>1
[3,4,8,2,7,6,5,1]=>0000000=>1111111=>1
[3,4,8,7,1,6,5,2]=>0000000=>1111111=>1
[8,1,3,5,7,6,4,2]=>0000000=>1111111=>1
[4,1,8,5,7,6,3,2]=>0000000=>1111111=>1
[8,2,7,1,4,5,6,3]=>0000000=>1111111=>1
[8,1,7,3,4,6,2,5]=>0000000=>1111111=>1
[8,3,1,7,2,6,5,4]=>0000000=>1111111=>1
[3,8,2,4,7,6,5,1]=>0000000=>1111111=>1
[2,8,3,7,4,6,5,1]=>0000000=>1111111=>1
[8,2,3,7,1,6,5,4]=>0000000=>1111111=>1
[8,2,7,1,3,6,5,4]=>0000000=>1111111=>1
[8,1,7,2,6,4,3,5]=>0000000=>1111111=>1
[8,1,7,5,2,4,3,6]=>0000000=>1111111=>1
[8,2,3,7,4,6,1,5]=>0000000=>1111111=>1
[2,4,8,5,7,6,3,1]=>0000000=>1111111=>1
[8,2,4,3,7,6,1,5]=>0000000=>1111111=>1
[8,2,7,3,5,1,4,6]=>0000000=>1111111=>1
[8,2,7,4,3,1,5,6]=>0000000=>1111111=>1
[8,2,7,3,1,5,6,4]=>0000000=>1111111=>1
[8,2,1,5,7,6,4,3]=>0000000=>1111111=>1
[6,2,1,8,7,5,4,3]=>0000000=>1111111=>1
[6,1,8,2,7,5,4,3]=>0000000=>1111111=>1
[8,1,7,3,5,2,6,4]=>0000000=>1111111=>1
[8,1,5,2,7,6,4,3]=>0000000=>1111111=>1
[8,1,7,2,4,6,5,3]=>0000000=>1111111=>1
[8,2,4,1,7,6,5,3]=>0000000=>1111111=>1
[4,2,8,3,7,6,5,1]=>0000000=>1111111=>1
[4,8,2,1,7,6,5,3]=>0000000=>1111111=>1
[5,1,8,7,2,6,4,3]=>0000000=>1111111=>1
[5,8,1,3,7,6,2,4]=>0000000=>1111111=>1
[8,2,5,4,1,7,6,3]=>0000000=>1111111=>1
[5,1,4,8,7,6,3,2]=>0000000=>1111111=>1
[8,1,4,3,7,6,5,2]=>0000000=>1111111=>1
[4,8,1,3,7,6,5,2]=>0000000=>1111111=>1
[4,3,8,1,7,6,5,2]=>0000000=>1111111=>1
[5,7,6,3,2,4,1,8]=>0000001=>1111110=>1
[6,5,7,2,4,3,1,8]=>0000001=>1111110=>1
[5,7,1,3,2,8,6,4]=>0000000=>1111111=>1
[5,8,1,3,2,7,4,6]=>0000000=>1111111=>1
[8,5,1,3,2,4,6,7]=>0000000=>1111111=>1
[7,5,8,2,1,4,3,6]=>0000000=>1111111=>1
[8,1,6,4,2,3,5,7]=>0000000=>1111111=>1
[1,7,8,2,3,5,6,4]=>1000000=>0111111=>1
[7,4,1,2,6,8,3,5]=>0000000=>1111111=>1
[6,2,8,1,5,7,3,4]=>0000000=>1111111=>1
[7,3,5,4,2,1,8,6]=>0000000=>1111111=>1
[7,3,2,8,5,6,1,4]=>0000000=>1111111=>1
[4,7,6,5,1,3,8,2]=>0000000=>1111111=>1
[6,7,4,2,1,8,5,3]=>0000000=>1111111=>1
[1,7,6,3,2,8,4,5]=>1000000=>0111111=>1
[5,4,2,1,7,3,6,8]=>0000001=>1111110=>1
[3,5,8,2,6,1,7,4]=>0000000=>1111111=>1
[3,7,6,1,5,2,8,4]=>0000000=>1111111=>1
[1,7,6,2,5,8,4,3]=>1000000=>0111111=>1
[3,7,6,5,8,1,2,4]=>0000000=>1111111=>1
[3,7,6,2,8,4,5,1]=>0000000=>1111111=>1
[4,3,6,8,5,1,2,7]=>0000000=>1111111=>1
[2,7,1,5,8,4,3,6]=>0000000=>1111111=>1
[7,1,2,6,3,5,4,8]=>0000001=>1111110=>1
[6,7,8,4,2,5,3,1]=>0000000=>1111111=>1
[6,1,2,5,7,8,4,3]=>0000000=>1111111=>1
[4,7,3,1,2,6,8,5]=>0000000=>1111111=>1
[3,7,6,1,5,8,2,4]=>0000000=>1111111=>1
[3,8,5,6,4,2,7,1]=>0000000=>1111111=>1
[3,2,6,4,7,8,5,1]=>0000000=>1111111=>1
[4,2,7,5,8,3,1,6]=>0000000=>1111111=>1
[4,2,7,1,3,8,6,5]=>0000000=>1111111=>1
[5,2,1,4,7,8,3,6]=>0000000=>1111111=>1
[5,6,2,7,3,4,8,1]=>0000000=>1111111=>1
[2,7,6,8,5,3,1,4]=>0000000=>1111111=>1
[1,5,8,6,4,2,3,7]=>1000000=>0111111=>1
[1,6,2,3,5,8,7,4]=>1000000=>0111111=>1
[7,4,6,2,8,3,5,1]=>0000000=>1111111=>1
[7,5,4,3,8,6,2,1]=>0000000=>1111111=>1
[4,3,8,2,5,7,1,6]=>0000000=>1111111=>1
[6,7,2,3,1,5,8,4]=>0000000=>1111111=>1
[4,5,1,7,6,3,8,2]=>0000000=>1111111=>1
[8,6,3,1,4,2,5,7]=>0000000=>1111111=>1
[4,5,1,6,2,8,7,3]=>0000000=>1111111=>1
[4,8,3,6,1,7,2,5]=>0000000=>1111111=>1
[6,2,7,8,3,4,5,1]=>0000000=>1111111=>1
[9,2,3,4,5,6,7,8,1]=>00000000=>11111111=>1
[8,2,3,4,5,6,7,1,9]=>00000001=>11111110=>1
[7,2,3,4,5,6,1,8,9]=>00000011=>11111100=>1
[6,2,3,4,5,1,7,8,9]=>00000111=>11111000=>1
[5,2,3,4,1,6,7,8,9]=>00001111=>11110000=>1
[4,2,3,1,5,6,7,8,9]=>00011111=>11100000=>1
[1,2,4,3,5,6,7,8,9]=>11011111=>00100000=>1
[1,2,4,6,8,9,7,5,3]=>11000000=>00111111=>1
[1,2,4,5,3,6,7,8,9]=>11001111=>00110000=>1
[1,2,4,3,5,6,7,8,9,10]=>110111111=>001000000=>1
[1,2,4,6,8,10,9,7,5,3]=>110000000=>001111111=>1
[1,2,4,6,8,5,7,3]=>1100000=>0011111=>1
[7,3,8,4,6,5,1,2]=>0000000=>1111111=>1
[7,4,3,6,5,8,1,2]=>0000000=>1111111=>1
[4,5,8,7,2,6,1,3]=>0000000=>1111111=>1
[3,8,6,7,5,1,4,2]=>0000000=>1111111=>1
[4,6,7,8,5,2,3,1]=>0000000=>1111111=>1
[6,3,8,7,5,1,4,2]=>0000000=>1111111=>1
[3,2,4,5,1,8,6,7]=>0000100=>1111011=>2
[4,2,5,1,7,8,3,6]=>0000000=>1111111=>1
[2,5,4,1,3,8,6,7]=>0000100=>1111011=>2
[1,4,5,3,8,2,6,7]=>1000000=>0111111=>1
[5,1,8,2,4,3,6,7]=>0000000=>1111111=>1
[3,6,2,4,8,7,1,5]=>0000000=>1111111=>1
[7,3,4,6,8,1,2,5]=>0000000=>1111111=>1
[1,5,6,8,3,7,2,4]=>1000000=>0111111=>1
[6,1,5,8,3,4,7,2]=>0000000=>1111111=>1
[5,6,8,1,3,4,7,2]=>0000000=>1111111=>1
[3,1,7,8,5,4,6,2]=>0000000=>1111111=>1
[1,6,2,7,4,8,5,3]=>1000000=>0111111=>1
[2,7,1,8,4,3,5,6]=>0000000=>1111111=>1
[6,7,1,8,3,2,4,5]=>0000000=>1111111=>1
[6,7,2,8,1,3,4,5]=>0000000=>1111111=>1
[5,1,6,8,7,2,3,4]=>0000000=>1111111=>1
[1,5,7,6,8,2,3,4]=>1000000=>0111111=>1
[7,4,6,8,5,3,1,2]=>0000000=>1111111=>1
[4,7,5,8,6,3,1,2]=>0000000=>1111111=>1
[2,6,8,1,5,4,7,3]=>0000000=>1111111=>1
[1,5,4,7,6,2,8,3]=>1000000=>0111111=>1
[2,3,7,6,5,1,8,4]=>0000000=>1111111=>1
[6,1,5,8,3,2,7,4]=>0000000=>1111111=>1
[3,1,2,4,8,5,7,6]=>0011000=>1100111=>2
[7,1,5,4,8,3,2,6]=>0000000=>1111111=>1
[6,4,1,7,5,3,2,8]=>0000001=>1111110=>1
[1,7,2,5,3,8,6,4]=>1000000=>0111111=>1
[2,4,1,3,6,8,5,7,9]=>00010001=>11101110=>2
[7,3,2,5,8,1,6,4]=>0000000=>1111111=>1
[5,3,8,4,1,2,6,7]=>0000000=>1111111=>1
[2,4,8,3,7,1,5,6]=>0000000=>1111111=>1
[5,2,8,4,1,6,3,7]=>0000000=>1111111=>1
[7,6,5,2,1,8,4,3]=>0000000=>1111111=>1
[2,7,5,1,8,3,6,4]=>0000000=>1111111=>1
[5,7,1,3,2,4,8,6]=>0000000=>1111111=>1
[4,2,7,6,3,5,8,1]=>0000000=>1111111=>1
[8,1,7,4,2,3,5,6]=>0000000=>1111111=>1
[4,7,8,3,2,5,1,6]=>0000000=>1111111=>1
[8,6,5,1,7,4,3,2]=>0000000=>1111111=>1
[7,6,4,1,3,5,8,2]=>0000000=>1111111=>1
[8,2,3,7,1,4,5,6]=>0000000=>1111111=>1
[5,6,2,7,4,3,1,8]=>0000001=>1111110=>1
[8,6,2,7,4,1,3,5]=>0000000=>1111111=>1
[6,8,4,7,3,1,5,2]=>0000000=>1111111=>1
[4,8,6,5,1,2,7,3]=>0000000=>1111111=>1
[4,8,6,5,1,2,3,7]=>0000000=>1111111=>1
[3,4,5,1,7,6,8,2]=>0000000=>1111111=>1
[5,8,2,6,1,4,7,3]=>0000000=>1111111=>1
[3,8,7,5,6,1,4,2]=>0000000=>1111111=>1
[6,8,4,7,2,1,5,3]=>0000000=>1111111=>1
[7,4,6,5,1,3,8,2]=>0000000=>1111111=>1
[1,7,3,4,5,2,8,6]=>1000000=>0111111=>1
[4,8,2,1,3,5,6,7]=>0000000=>1111111=>1
[1,7,2,5,4,3,8,6]=>1000000=>0111111=>1
[2,6,7,3,4,8,1,5]=>0000000=>1111111=>1
[2,1,5,7,4,3,8,6]=>0100000=>1011111=>2
[4,1,8,7,5,6,2,3]=>0000000=>1111111=>1
[1,5,8,7,4,3,6,2]=>1000000=>0111111=>1
[6,4,1,3,8,7,5,2]=>0000000=>1111111=>1
[2,1,7,4,6,8,3,5]=>0100000=>1011111=>2
[1,7,2,4,6,8,3,5]=>1000000=>0111111=>1
[8,6,4,2,7,3,5,1]=>0000000=>1111111=>1
[7,4,6,1,2,3,8,5]=>0000000=>1111111=>1
[1,8,6,2,7,3,5,4]=>1000000=>0111111=>1
[1,7,8,6,2,3,5,4]=>1000000=>0111111=>1
[2,1,8,3,5,7,6,4]=>0100000=>1011111=>2
[3,5,8,1,7,6,2,4]=>0000000=>1111111=>1
[2,8,1,3,6,7,5,4]=>0000000=>1111111=>1
[7,2,4,8,6,1,5,3]=>0000000=>1111111=>1
[2,3,4,5,6,8,1,9,10,7]=>000000000=>111111111=>1
[4,1,2,5,6,7,8,9,10,3]=>000000000=>111111111=>1
[8,2,1,3,4,5,6,7,9]=>00000001=>11111110=>1
[3,2,4,5,6,7,8,1,9]=>00000001=>11111110=>1
[9,2,1,3,4,5,6,7,8,10]=>000000001=>111111110=>1
[8,3,1,2,4,5,6,7,9]=>00000001=>11111110=>1
[8,2,3,1,4,5,6,7,9]=>00000001=>11111110=>1
[4,2,3,5,6,7,8,1,9]=>00000001=>11111110=>1
[8,7,2,4,6,10,1,3,5,9]=>000000000=>111111111=>1
[2,10,7,9,4,6,8,1,3,5]=>000000000=>111111111=>1
[6,5,2,4,8,10,1,3,7,9]=>000000000=>111111111=>1
[2,8,5,7,4,6,10,1,3,9]=>000000000=>111111111=>1
[10,5,2,4,7,9,6,8,1,3]=>000000000=>111111111=>1
[10,9,2,8,5,7,4,6,1,3]=>000000000=>111111111=>1
[8,7,6,5,2,4,10,1,3,9]=>000000000=>111111111=>1
[10,7,2,6,5,9,4,8,1,3]=>000000000=>111111111=>1
[6,10,5,9,8,7,2,4,1,3]=>000000000=>111111111=>1
[4,10,3,9,2,6,8,1,5,7]=>000000000=>111111111=>1
[4,3,10,7,9,2,6,8,1,5]=>000000000=>111111111=>1
[3,6,2,5,4,8,10,1,7,9]=>000000000=>111111111=>1
[3,6,10,2,5,9,4,8,1,7]=>000000000=>111111111=>1
[3,5,8,2,4,7,6,10,1,9]=>000000000=>111111111=>1
[3,5,7,10,2,4,6,9,8,1]=>000000000=>111111111=>1
[10,9,3,5,8,2,4,7,6,1]=>000000000=>111111111=>1
[8,7,3,6,2,5,4,10,1,9]=>000000000=>111111111=>1
[7,6,3,5,10,2,4,9,8,1]=>000000000=>111111111=>1
[3,6,10,9,8,2,5,7,4,1]=>000000000=>111111111=>1
[10,9,8,7,3,6,2,5,4,1]=>000000000=>111111111=>1
[5,4,3,8,2,7,6,10,1,9]=>000000000=>111111111=>1
[5,4,3,7,10,2,6,9,8,1]=>000000000=>111111111=>1
[5,10,4,9,3,8,2,7,6,1]=>000000000=>111111111=>1
[4,8,3,7,6,5,2,10,1,9]=>000000000=>111111111=>1
[4,7,3,6,5,10,2,9,8,1]=>000000000=>111111111=>1
[4,6,10,3,5,9,8,7,2,1]=>000000000=>111111111=>1
[10,9,4,8,3,7,6,5,2,1]=>000000000=>111111111=>1
[7,6,5,4,3,10,2,9,8,1]=>000000000=>111111111=>1
[6,5,4,10,3,9,8,7,2,1]=>000000000=>111111111=>1
[5,10,4,9,8,7,6,3,2,1]=>000000000=>111111111=>1
[5,4,7,3,2,6,8,1]=>0000000=>1111111=>1
[4,8,1,7,5,3,2,6]=>0000000=>1111111=>1
[5,4,3,7,2,8,6,1]=>0000000=>1111111=>1
[2,6,5,8,7,3,1,4]=>0000000=>1111111=>1
[6,3,8,4,1,7,2,5]=>0000000=>1111111=>1
[7,2,8,1,6,4,3,5]=>0000000=>1111111=>1
[5,4,2,8,6,3,7,1]=>0000000=>1111111=>1
[2,4,7,8,5,3,1,6]=>0000000=>1111111=>1
[6,5,8,7,3,2,4,1]=>0000000=>1111111=>1
[8,3,1,6,5,7,4,2]=>0000000=>1111111=>1
[8,5,6,7,3,1,4,2]=>0000000=>1111111=>1
[8,7,5,3,2,6,4,1]=>0000000=>1111111=>1
[8,5,3,1,4,6,7,2]=>0000000=>1111111=>1
[8,5,1,6,4,3,7,2]=>0000000=>1111111=>1
[6,1,4,3,7,8,2,5]=>0000000=>1111111=>1
[6,1,2,7,5,8,3,4]=>0000000=>1111111=>1
[2,7,3,1,4,6,8,5]=>0000000=>1111111=>1
[3,8,5,6,7,1,2,4]=>0000000=>1111111=>1
[6,5,1,2,8,4,7,3]=>0000000=>1111111=>1
[2,5,8,1,4,6,7,3]=>0000000=>1111111=>1
[2,1,8,7,5,4,6,3]=>0100000=>1011111=>2
[7,8,3,4,1,6,5,2]=>0000000=>1111111=>1
[6,4,7,5,2,8,3,1]=>0000000=>1111111=>1
[4,6,3,8,7,5,1,2]=>0000000=>1111111=>1
[2,8,4,1,5,7,6,3]=>0000000=>1111111=>1
[1,8,4,2,5,7,6,3]=>1000000=>0111111=>1
[2,8,5,4,1,7,6,3]=>0000000=>1111111=>1
[2,5,8,3,7,1,6,4]=>0000000=>1111111=>1
[1,8,5,2,4,7,6,3]=>1000000=>0111111=>1
[1,4,6,2,8,7,5,3]=>1000000=>0111111=>1
[7,8,2,4,1,6,5,3]=>0000000=>1111111=>1
[2,4,6,1,8,7,5,3]=>0000000=>1111111=>1
[2,8,4,5,1,7,6,3]=>0000000=>1111111=>1
[3,5,8,2,7,6,1,4]=>0000000=>1111111=>1
[2,1,6,8,7,5,3,4]=>0100000=>1011111=>2
[1,8,2,4,5,7,6,3]=>1000000=>0111111=>1
[1,2,8,3,5,7,6,4]=>1100000=>0011111=>1
[1,3,8,2,5,7,6,4]=>1000000=>0111111=>1
[2,3,8,1,5,7,6,4]=>0000000=>1111111=>1
[2,6,1,8,7,5,3,4]=>0000000=>1111111=>1
[1,6,2,8,7,5,3,4]=>1000000=>0111111=>1
[1,6,3,8,7,5,2,4]=>1000000=>0111111=>1
[2,6,3,8,7,5,1,4]=>0000000=>1111111=>1
[3,2,8,1,5,7,6,4]=>0000000=>1111111=>1
[3,1,8,2,5,7,6,4]=>0000000=>1111111=>1
[2,8,1,4,5,7,6,3]=>0000000=>1111111=>1
[7,8,2,1,4,6,5,3]=>0000000=>1111111=>1
[2,3,6,8,7,5,1,4]=>0000000=>1111111=>1
[3,1,6,8,7,2,5,4]=>0000000=>1111111=>1
[3,8,4,5,1,6,2,7]=>0000000=>1111111=>1
[6,1,4,5,7,2,3,8]=>0000001=>1111110=>1
[8,1,4,7,6,3,2,5]=>0000000=>1111111=>1
[8,3,1,6,4,7,2,5]=>0000000=>1111111=>1
[5,3,8,6,2,7,1,4]=>0000000=>1111111=>1
[8,3,6,1,5,7,2,4]=>0000000=>1111111=>1
[8,4,6,3,1,2,5,7]=>0000000=>1111111=>1
[6,8,1,4,5,2,3,7]=>0000000=>1111111=>1
[1,5,8,4,6,2,3,7]=>1000000=>0111111=>1
[2,1,6,5,3,8,4,7]=>0100000=>1011111=>2
[5,6,8,1,4,2,3,7]=>0000000=>1111111=>1
[5,7,4,8,1,2,3,6]=>0000000=>1111111=>1
[8,2,1,5,3,7,4,6]=>0000000=>1111111=>1
[4,7,8,1,2,6,3,5]=>0000000=>1111111=>1
[8,7,1,5,6,2,3,4]=>0000000=>1111111=>1
[1,6,5,8,7,2,3,4]=>1000000=>0111111=>1
[3,7,1,6,2,4,8,5]=>0000000=>1111111=>1
[5,1,2,7,6,8,3,4]=>0000000=>1111111=>1
[6,1,7,2,5,8,3,4]=>0000000=>1111111=>1
[1,7,6,5,8,2,3,4]=>1000000=>0111111=>1
[1,6,8,5,7,2,3,4]=>1000000=>0111111=>1
[7,5,1,2,6,8,3,4]=>0000000=>1111111=>1
[6,1,5,2,7,8,3,4]=>0000000=>1111111=>1
[1,6,3,8,7,2,4,5]=>1000000=>0111111=>1
[1,7,3,2,4,6,8,5]=>1000000=>0111111=>1
[8,3,1,4,2,5,7,6]=>0000000=>1111111=>1
[3,1,2,7,8,4,6,5]=>0010000=>1101111=>2
[5,1,2,6,8,7,3,4]=>0000000=>1111111=>1
[1,8,6,2,5,7,3,4]=>1000000=>0111111=>1
[5,7,8,1,2,6,3,4]=>0000000=>1111111=>1
[8,1,5,7,6,2,3,4]=>0000000=>1111111=>1
[7,1,6,8,5,2,3,4]=>0000000=>1111111=>1
[3,7,1,2,8,4,6,5]=>0000000=>1111111=>1
[8,3,1,2,7,6,4,5]=>0000000=>1111111=>1
[1,5,8,7,6,2,3,4]=>1000000=>0111111=>1
[7,8,6,1,5,2,3,4]=>0000000=>1111111=>1
[1,9,3,4,5,6,7,8,2]=>10000000=>01111111=>1
[1,9,8,4,5,6,7,3,2]=>10000000=>01111111=>1
[1,10,3,4,5,6,7,8,9,2]=>100000000=>011111111=>1
[1,10,9,4,5,6,7,8,3,2]=>100000000=>011111111=>1
[1,7,4,8,2,5,3,6]=>1000000=>0111111=>1
[6,4,7,3,2,5,1,8]=>0000001=>1111110=>1
[3,1,2,7,6,8,5,4]=>0010000=>1101111=>2
[6,3,2,8,4,5,1,7]=>0000000=>1111111=>1
[3,8,5,2,4,6,1,7]=>0000000=>1111111=>1
[5,7,8,4,6,3,2,1]=>0000000=>1111111=>1
[5,3,2,8,6,4,7,1]=>0000000=>1111111=>1
[3,1,6,4,7,5,2,8]=>0000001=>1111110=>1
[2,6,4,7,5,3,8,1]=>0000000=>1111111=>1
[4,7,6,2,3,1,8,5]=>0000000=>1111111=>1
[2,6,8,7,5,3,1,4]=>0000000=>1111111=>1
[6,4,1,7,5,2,8,3]=>0000000=>1111111=>1
[8,6,2,1,5,7,4,3]=>0000000=>1111111=>1
[1,3,8,5,2,7,4,6]=>1000000=>0111111=>1
[1,3,8,6,7,2,4,5]=>1000000=>0111111=>1
[2,8,3,7,6,1,4,5]=>0000000=>1111111=>1
[1,3,8,7,6,2,4,5]=>1000000=>0111111=>1
[4,5,6,8,1,2,7,3]=>0000000=>1111111=>1
[3,5,8,6,1,2,7,4]=>0000000=>1111111=>1
[4,2,6,8,7,1,3,5]=>0000000=>1111111=>1
[1,4,6,8,7,2,3,5]=>1000000=>0111111=>1
[3,5,8,4,1,7,2,6]=>0000000=>1111111=>1
[7,6,4,8,5,1,3,2]=>0000000=>1111111=>1
[6,3,7,5,2,4,8,1]=>0000000=>1111111=>1
[8,2,7,3,1,5,4,6]=>0000000=>1111111=>1
[2,6,4,8,3,1,7,5]=>0000000=>1111111=>1
[4,1,6,5,7,8,2,3]=>0000000=>1111111=>1
[6,1,3,7,4,2,8,5]=>0000000=>1111111=>1
[1,3,8,2,5,6,7,4]=>1000000=>0111111=>1
[1,8,6,7,2,5,4,3]=>1000000=>0111111=>1
[7,6,8,3,5,4,2,1]=>0000000=>1111111=>1
[1,6,7,3,8,5,4,2]=>1000000=>0111111=>1
[7,8,6,5,2,4,3,1]=>0000000=>1111111=>1
[5,4,6,7,8,1,3,2]=>0000000=>1111111=>1
[5,3,6,7,8,1,4,2]=>0000000=>1111111=>1
[5,3,7,6,8,4,1,2]=>0000000=>1111111=>1
[2,5,4,7,8,1,3,6]=>0000000=>1111111=>1
[5,3,7,4,6,2,8,1]=>0000000=>1111111=>1
[4,5,6,2,7,3,8,1]=>0000000=>1111111=>1
[5,4,6,2,8,3,7,1]=>0000000=>1111111=>1
[8,4,6,1,7,2,5,3]=>0000000=>1111111=>1
[5,2,1,6,3,8,7,4]=>0000000=>1111111=>1
[6,3,2,8,5,4,1,7]=>0000000=>1111111=>1
[4,3,1,5,2,8,6,7]=>0000100=>1111011=>2
[8,5,4,1,3,2,6,7]=>0000000=>1111111=>1
[4,3,5,1,2,7,6,8]=>0000101=>1111010=>2
[4,2,1,8,6,3,7,5]=>0000000=>1111111=>1
[7,3,2,1,6,4,5,8]=>0000001=>1111110=>1
[2,8,6,1,7,4,3,5]=>0000000=>1111111=>1
[2,5,4,6,1,3,7,8]=>0000011=>1111100=>1
[2,5,6,4,1,3,7,8]=>0000011=>1111100=>1
[8,5,2,6,1,3,7,4]=>0000000=>1111111=>1
[7,1,5,6,3,2,4,8]=>0000001=>1111110=>1
[4,1,2,7,5,6,3,8]=>0000001=>1111110=>1
[7,1,2,6,5,4,3,8]=>0000001=>1111110=>1
[8,2,1,5,6,3,7,4]=>0000000=>1111111=>1
[2,8,5,1,6,4,7,3]=>0000000=>1111111=>1
[6,1,4,5,3,2,7,8]=>0000011=>1111100=>1
[3,1,6,5,4,2,7,8]=>0000011=>1111100=>1
[2,1,8,6,3,7,5,4]=>0100000=>1011111=>2
[5,8,3,1,7,6,4,2]=>0000000=>1111111=>1
[5,6,3,8,7,4,1,2]=>0000000=>1111111=>1
[5,2,6,8,7,4,1,3]=>0000000=>1111111=>1
[4,3,8,5,7,2,6,1]=>0000000=>1111111=>1
[6,3,8,4,5,1,2,7]=>0000000=>1111111=>1
[5,2,3,1,4,8,6,7]=>0000100=>1111011=>2
[5,4,1,3,2,8,6,7]=>0000100=>1111011=>2
[5,1,3,4,2,8,6,7]=>0000100=>1111011=>2
[4,2,7,3,8,5,1,6]=>0000000=>1111111=>1
[5,4,3,1,2,8,6,7]=>0000100=>1111011=>2
[5,1,7,3,4,6,8,2]=>0000000=>1111111=>1
[5,8,7,4,3,1,6,2]=>0000000=>1111111=>1
[6,8,1,3,4,5,7,2]=>0000000=>1111111=>1
[3,1,7,8,2,5,4,6]=>0000000=>1111111=>1
[6,2,3,7,4,1,8,5]=>0000000=>1111111=>1
[6,3,7,4,1,2,5,8]=>0000001=>1111110=>1
[7,2,6,8,4,3,1,5]=>0000000=>1111111=>1
[3,6,7,5,1,2,4,8]=>0000001=>1111110=>1
[2,1,4,8,3,7,5,6]=>0100000=>1011111=>2
[1,2,7,8,4,3,6,5]=>1100000=>0011111=>1
[5,3,7,8,4,2,6,1]=>0000000=>1111111=>1
[6,3,7,8,2,4,5,1]=>0000000=>1111111=>1
[8,5,2,4,3,1,7,6]=>0000000=>1111111=>1
[7,5,4,2,3,1,8,6]=>0000000=>1111111=>1
[1,4,2,6,5,8,7,3]=>1000000=>0111111=>1
[1,3,2,6,4,8,7,5]=>1010000=>0101111=>2
[1,4,2,5,3,8,7,6]=>1000100=>0111011=>2
[1,5,2,6,4,8,7,3]=>1000000=>0111111=>1
[1,6,2,5,3,8,7,4]=>1000000=>0111111=>1
[1,7,3,5,4,8,6,2]=>1000000=>0111111=>1
[1,8,2,6,3,7,5,4]=>1000000=>0111111=>1
[1,8,3,6,4,7,5,2]=>1000000=>0111111=>1
[1,7,2,6,4,8,5,3]=>1000000=>0111111=>1
[1,7,2,6,3,8,5,4]=>1000000=>0111111=>1
[1,5,2,7,4,8,6,3]=>1000000=>0111111=>1
[1,4,2,8,5,7,6,3]=>1000000=>0111111=>1
[4,8,1,3,2,6,5,7]=>0000000=>1111111=>1
[1,5,3,8,4,7,6,2]=>1000000=>0111111=>1
[1,8,4,7,3,6,5,2]=>1000000=>0111111=>1
[8,3,5,7,4,1,2,6]=>0000000=>1111111=>1
[6,8,7,3,1,5,4,2]=>0000000=>1111111=>1
[2,5,8,7,4,6,3,1]=>0000000=>1111111=>1
[4,8,7,6,5,1,3,2]=>0000000=>1111111=>1
[6,8,4,1,5,2,7,3]=>0000000=>1111111=>1
[6,8,2,1,7,5,3,4]=>0000000=>1111111=>1
[4,8,7,6,5,2,1,3]=>0000000=>1111111=>1
[4,8,7,5,1,6,2,3]=>0000000=>1111111=>1
[4,5,2,1,8,6,7,3]=>0000000=>1111111=>1
[4,5,8,3,1,6,7,2]=>0000000=>1111111=>1
[5,7,2,8,4,6,1,3]=>0000000=>1111111=>1
[6,7,3,2,4,8,5,1]=>0000000=>1111111=>1
[7,2,8,6,4,5,1,3]=>0000000=>1111111=>1
[8,7,2,6,5,1,3,4]=>0000000=>1111111=>1
[5,2,7,8,4,1,3,6]=>0000000=>1111111=>1
[2,7,8,6,4,1,3,5]=>0000000=>1111111=>1
[7,6,3,5,2,8,4,1]=>0000000=>1111111=>1
[6,2,7,4,8,5,3,1]=>0000000=>1111111=>1
[8,6,5,1,7,2,4,3]=>0000000=>1111111=>1
[6,8,5,1,7,3,2,4]=>0000000=>1111111=>1
[1,6,8,3,7,4,2,5]=>1000000=>0111111=>1
[5,1,6,3,4,8,2,7]=>0000000=>1111111=>1
[3,5,2,6,4,8,1,7]=>0000000=>1111111=>1
[3,5,2,4,8,1,7,6]=>0000000=>1111111=>1
[6,3,8,2,4,1,7,5]=>0000000=>1111111=>1
[4,6,3,8,7,5,2,1]=>0000000=>1111111=>1
[6,3,8,7,5,4,2,1]=>0000000=>1111111=>1
[6,8,4,2,1,7,5,3]=>0000000=>1111111=>1
[5,2,6,4,3,8,1,7]=>0000000=>1111111=>1
[6,5,3,1,4,8,2,7]=>0000000=>1111111=>1
[3,1,7,8,6,4,2,5]=>0000000=>1111111=>1
[3,8,1,7,6,2,5,4]=>0000000=>1111111=>1
[8,1,7,6,4,2,5,3]=>0000000=>1111111=>1
[7,2,6,3,8,5,4,1]=>0000000=>1111111=>1
[7,3,8,6,4,1,5,2]=>0000000=>1111111=>1
[1,7,5,8,2,4,3,6]=>1000000=>0111111=>1
[6,1,5,2,4,8,3,7]=>0000000=>1111111=>1
[1,5,6,3,8,2,4,7]=>1000000=>0111111=>1
[8,7,1,3,6,5,2,4]=>0000000=>1111111=>1
[2,6,7,4,3,8,5,1]=>0000000=>1111111=>1
[5,2,4,7,3,8,6,1]=>0000000=>1111111=>1
[1,5,8,7,2,4,6,3]=>1000000=>0111111=>1
[1,4,8,7,3,6,5,2]=>1000000=>0111111=>1
[8,3,7,2,5,1,6,4]=>0000000=>1111111=>1
[3,7,2,8,1,5,4,6]=>0000000=>1111111=>1
[3,2,6,1,5,8,4,7]=>0000000=>1111111=>1
[7,2,1,5,8,4,3,6]=>0000000=>1111111=>1
[7,2,8,1,4,3,6,5]=>0000000=>1111111=>1
[1,7,8,3,2,6,5,4]=>1000000=>0111111=>1
[1,7,4,8,3,2,6,5]=>1000000=>0111111=>1
[1,7,5,4,8,3,2,6]=>1000000=>0111111=>1
[6,1,5,4,3,8,2,7]=>0000000=>1111111=>1
[1,6,4,2,3,5,7,8]=>1000011=>0111100=>1
[1,8,7,2,3,4,5,6]=>1000000=>0111111=>1
[1,5,8,6,2,3,4,7]=>1000000=>0111111=>1
[1,2,3,7,6,4,5,8]=>1110001=>0001110=>1
[1,5,4,2,3,8,6,7]=>1000100=>0111011=>2
[1,7,5,8,2,3,4,6]=>1000000=>0111111=>1
[1,8,7,5,2,3,4,6]=>1000000=>0111111=>1
[2,1,5,8,6,3,7,4]=>0100000=>1011111=>2
[2,5,8,4,6,1,7,3]=>0000000=>1111111=>1
[5,8,4,6,1,3,7,2]=>0000000=>1111111=>1
[8,3,5,7,2,6,4,1]=>0000000=>1111111=>1
[2,4,6,8,5,3,7,1]=>0000000=>1111111=>1
[2,4,8,1,7,6,5,3]=>0000000=>1111111=>1
[4,3,8,1,5,7,6,2]=>0000000=>1111111=>1
[4,3,6,8,5,2,7,1]=>0000000=>1111111=>1
[8,5,4,7,2,6,3,1]=>0000000=>1111111=>1
[3,6,8,5,4,2,7,1]=>0000000=>1111111=>1
[3,6,4,1,8,2,7,5]=>0000000=>1111111=>1
[4,8,6,5,1,3,7,2]=>0000000=>1111111=>1
[2,3,7,4,6,1,8,5]=>0000000=>1111111=>1
[2,6,7,4,1,3,8,5]=>0000000=>1111111=>1
[2,4,6,3,5,7,8,1]=>0000000=>1111111=>1
[2,3,6,1,5,7,8,4]=>0000000=>1111111=>1
[4,7,3,1,8,6,5,2]=>0000000=>1111111=>1
[5,6,4,2,7,1,8,3]=>0000000=>1111111=>1
[4,2,7,5,3,1,8,6]=>0000000=>1111111=>1
[5,3,6,4,8,2,1,7]=>0000000=>1111111=>1
[7,3,2,5,4,1,8,6]=>0000000=>1111111=>1
[7,3,2,5,1,8,6,4]=>0000000=>1111111=>1
[4,6,3,8,7,2,1,5]=>0000000=>1111111=>1
[4,7,3,8,6,2,1,5]=>0000000=>1111111=>1
[5,7,3,2,6,1,8,4]=>0000000=>1111111=>1
[5,7,3,2,6,4,1,8]=>0000001=>1111110=>1
[2,7,5,3,1,8,6,4]=>0000000=>1111111=>1
[7,5,2,8,4,3,1,6]=>0000000=>1111111=>1
[4,3,7,5,8,2,1,6]=>0000000=>1111111=>1
[4,3,7,5,2,6,1,8]=>0000001=>1111110=>1
[4,3,5,2,8,6,1,7]=>0000000=>1111111=>1
[1,2,8,6,4,5,7,3]=>1100000=>0011111=>1
[1,9,4,3,5,6,7,8,2]=>10000000=>01111111=>1
[9,3,2,4,5,6,7,8,1]=>00000000=>11111111=>1
[10,2,3,4,5,6,7,8,9,1]=>000000000=>111111111=>1
[1,2,3,5,7,4,6,9,8]=>11100010=>00011101=>2
[1,2,3,6,4,7,5,9,8]=>11100010=>00011101=>2
[1,2,3,4,6,8,5,7,10,9]=>111100010=>000011101=>2
[1,2,3,4,6,8,5,7,9]=>11110001=>00001110=>1
[1,2,3,4,7,5,8,6,9]=>11110001=>00001110=>1
[1,2,3,4,7,5,8,6,10,9]=>111100010=>000011101=>2
[1,2,3,4,6,8,5,7,10,9,11]=>1111000101=>0000111010=>2
[1,2,3,5,7,4,6,9,8,10]=>111000101=>000111010=>2
[1,2,5,7,3,4,6,9,8]=>11000010=>00111101=>2
[1,2,4,5,7,3,6,9,8]=>11000010=>00111101=>2
[1,2,6,3,4,7,5,9,8]=>11000010=>00111101=>2
[1,2,5,6,3,7,4,9,8]=>11000010=>00111101=>2
[1,2,3,6,4,7,5,9,8,10]=>111000101=>000111010=>2
[1,2,3,4,7,5,8,6,10,9,11]=>1111000101=>0000111010=>2
[3,2,6,4,1,8,5,7]=>0000000=>1111111=>1
[5,4,8,6,2,3,1,7]=>0000000=>1111111=>1
[4,8,7,5,2,3,1,6]=>0000000=>1111111=>1
[6,4,1,8,7,3,2,5]=>0000000=>1111111=>1
[1,8,5,4,2,7,3,6]=>1000000=>0111111=>1
[3,7,6,1,5,8,4,2]=>0000000=>1111111=>1
[3,6,5,8,2,7,4,1]=>0000000=>1111111=>1
[8,3,2,7,4,6,5,1]=>0000000=>1111111=>1
[7,5,8,4,1,3,6,2]=>0000000=>1111111=>1
[7,1,6,2,3,8,4,5]=>0000000=>1111111=>1
[6,4,7,1,3,2,8,5]=>0000000=>1111111=>1
[5,1,3,8,7,2,6,4]=>0000000=>1111111=>1
[8,7,1,6,2,5,3,4]=>0000000=>1111111=>1
[3,8,5,2,4,7,6,1]=>0000000=>1111111=>1
[7,1,5,2,4,8,3,6]=>0000000=>1111111=>1
[3,8,5,1,4,7,2,6]=>0000000=>1111111=>1
[7,2,5,4,1,3,8,6]=>0000000=>1111111=>1
[4,9,1,2,3,5,6,7,8]=>00000000=>11111111=>1
[3,9,1,2,4,5,6,7,8]=>00000000=>11111111=>1
[1,8,2,3,4,5,6,7,9]=>10000001=>01111110=>1
[7,4,6,1,3,2,5,8]=>0000001=>1111110=>1
[1,4,5,8,6,3,2,7]=>1000000=>0111111=>1
[5,2,6,3,1,7,8,4]=>0000000=>1111111=>1
[4,3,5,1,6,7,8,2]=>0000000=>1111111=>1
[5,7,6,1,2,3,8,4]=>0000000=>1111111=>1
[3,6,7,5,1,2,8,4]=>0000000=>1111111=>1
[1,7,6,8,5,2,4,3]=>1000000=>0111111=>1
[9,8,7,5,6,4,3,2,1]=>00000000=>11111111=>1
[2,1,9,8,6,7,5,4,3]=>01000000=>10111111=>2
[10,9,8,7,5,6,4,3,2,1]=>000000000=>111111111=>1
[9,8,7,5,4,6,3,2,1]=>00000000=>11111111=>1
[9,8,7,4,6,5,3,2,1]=>00000000=>11111111=>1
[2,1,9,8,6,5,7,4,3]=>01000000=>10111111=>2
[2,1,9,8,5,7,6,4,3]=>01000000=>10111111=>2
[2,1,10,9,8,6,7,5,4,3]=>010000000=>101111111=>2
[1,8,7,6,5,4,3,2,9]=>10000001=>01111110=>1
[1,9,8,7,6,5,4,3,2,10]=>100000001=>011111110=>1
[2,1,8,7,6,5,4,3,9]=>01000001=>10111110=>2
[6,5,8,3,7,2,1,4]=>0000000=>1111111=>1
[1,8,4,3,2,6,7,5]=>1000000=>0111111=>1
[5,4,3,8,2,1,7,6]=>0000000=>1111111=>1
[6,4,8,3,2,1,7,5]=>0000000=>1111111=>1
[5,4,3,8,2,1,6,7]=>0000000=>1111111=>1
[1,8,4,3,2,5,7,6]=>1000000=>0111111=>1
[4,5,6,7,8,1,2,9,3]=>00000000=>11111111=>1
[4,5,6,7,1,2,8,9,3]=>00000000=>11111111=>1
[4,5,6,1,2,7,8,9,3]=>00000000=>11111111=>1
[4,5,1,2,6,7,8,9,3]=>00000000=>11111111=>1
[7,2,3,4,5,8,1,6]=>0000000=>1111111=>1
[7,3,6,2,8,1,5,4]=>0000000=>1111111=>1
[8,1,5,2,3,7,6,4]=>0000000=>1111111=>1
[4,3,6,2,1,8,7,5]=>0000000=>1111111=>1
[3,7,4,5,1,6,2,8]=>0000001=>1111110=>1
[3,6,4,5,8,2,1,7]=>0000000=>1111111=>1
[6,1,4,5,2,8,7,3]=>0000000=>1111111=>1
[7,2,4,5,1,6,3,8]=>0000001=>1111110=>1
[7,5,4,1,6,3,2,8]=>0000001=>1111110=>1
[1,5,4,8,6,3,2,7]=>1000000=>0111111=>1
[7,5,4,8,6,3,1,2]=>0000000=>1111111=>1
[1,8,7,5,3,6,4,2]=>1000000=>0111111=>1
[8,3,7,4,1,6,2,5]=>0000000=>1111111=>1
[8,5,4,1,6,3,2,7]=>0000000=>1111111=>1
[1,7,4,2,6,5,3,8]=>1000001=>0111110=>1
[8,2,1,5,6,7,3,4]=>0000000=>1111111=>1
[6,3,1,8,4,7,2,5]=>0000000=>1111111=>1
[7,1,4,8,6,3,2,5]=>0000000=>1111111=>1
[4,1,8,5,6,7,2,3]=>0000000=>1111111=>1
[5,7,4,8,6,2,1,3]=>0000000=>1111111=>1
[5,3,6,8,2,7,1,4]=>0000000=>1111111=>1
[6,3,7,4,8,2,1,5]=>0000000=>1111111=>1
[5,3,6,1,4,7,2,8]=>0000001=>1111110=>1
[4,3,6,8,2,7,1,5]=>0000000=>1111111=>1
[5,3,7,4,8,2,1,6]=>0000000=>1111111=>1
[5,3,8,4,1,6,2,7]=>0000000=>1111111=>1
[5,3,8,1,4,7,2,6]=>0000000=>1111111=>1
[5,8,4,1,6,3,2,7]=>0000000=>1111111=>1
[7,3,8,4,1,6,2,5]=>0000000=>1111111=>1
[1,5,8,3,6,7,4,2]=>1000000=>0111111=>1
[1,8,2,5,6,7,3,4]=>1000000=>0111111=>1
[7,8,4,1,6,5,2,3]=>0000000=>1111111=>1
[6,3,8,1,5,7,2,4]=>0000000=>1111111=>1
[8,3,1,2,5,7,4,6]=>0000000=>1111111=>1
[8,1,4,2,6,5,3,7]=>0000000=>1111111=>1
[7,8,1,2,3,4,5,9,6]=>00000000=>11111111=>1
[2,8,9,1,3,4,5,6,7]=>00000000=>11111111=>1
[2,8,9,10,1,3,4,5,6,7]=>000000000=>111111111=>1
[7,1,8,2,9,3,4,5,6]=>00000000=>11111111=>1
[6,1,7,2,8,3,9,4,5]=>00000000=>11111111=>1
[5,1,6,2,7,3,8,4,9]=>00000001=>11111110=>1
[8,1,9,2,10,3,4,5,6,7]=>000000000=>111111111=>1
[7,1,8,2,3,9,4,5,6]=>00000000=>11111111=>1
[7,1,8,2,9,3,10,4,5,6]=>000000000=>111111111=>1
[6,1,7,2,8,3,4,9,5]=>00000000=>11111111=>1
[5,1,6,2,7,3,9,4,8]=>00000000=>11111111=>1
[5,1,6,2,7,3,8,4,10,9]=>000000010=>111111101=>2
[4,1,5,2,7,3,8,6,9]=>00000001=>11111110=>1
[4,1,5,2,6,3,8,7,10,9]=>000001010=>111110101=>3
[5,1,3,7,4,8,2,6]=>0000000=>1111111=>1
[5,1,3,4,7,8,2,6]=>0000000=>1111111=>1
[2,5,8,7,4,3,6,1]=>0000000=>1111111=>1
[5,1,7,8,3,4,2,6]=>0000000=>1111111=>1
[2,5,4,8,3,7,6,1]=>0000000=>1111111=>1
[5,6,8,2,3,4,1,7]=>0000000=>1111111=>1
[4,5,2,3,8,6,1,7]=>0000000=>1111111=>1
[5,8,2,1,6,3,4,7]=>0000000=>1111111=>1
[2,4,7,8,5,3,6,1]=>0000000=>1111111=>1
[5,3,1,4,7,2,8,6]=>0000000=>1111111=>1
[2,4,7,5,8,3,6,1]=>0000000=>1111111=>1
[4,3,5,8,2,1,7,6]=>0000000=>1111111=>1
[4,8,5,3,7,1,2,6]=>0000000=>1111111=>1
[4,8,5,7,3,1,2,6]=>0000000=>1111111=>1
[4,8,7,5,1,3,2,6]=>0000000=>1111111=>1
[1,8,5,7,2,4,3,6]=>1000000=>0111111=>1
[1,8,5,4,2,3,6,7]=>1000000=>0111111=>1
[1,3,6,8,5,4,2,7]=>1000000=>0111111=>1
[1,6,3,8,2,7,4,5]=>1000000=>0111111=>1
[1,4,2,7,5,8,3,6]=>1000000=>0111111=>1
[1,8,2,3,6,7,5,4]=>1000000=>0111111=>1
[1,3,6,8,2,7,5,4]=>1000000=>0111111=>1
[1,6,5,4,3,8,2,7]=>1000000=>0111111=>1
[1,8,3,4,5,6,2,7]=>1000000=>0111111=>1
[1,8,3,6,2,4,5,7]=>1000000=>0111111=>1
[1,4,5,8,3,6,2,7]=>1000000=>0111111=>1
[6,2,8,7,5,4,1,3]=>0000000=>1111111=>1
[6,2,8,4,3,7,1,5]=>0000000=>1111111=>1
[5,2,8,4,3,1,7,6]=>0000000=>1111111=>1
[1,2,5,4,8,3,7,6]=>1100000=>0011111=>1
[1,4,3,6,8,7,2,5]=>1000000=>0111111=>1
[5,3,2,6,8,4,7,1]=>0000000=>1111111=>1
[3,1,8,6,4,7,2,5]=>0000000=>1111111=>1
[3,1,6,8,5,4,2,7]=>0000000=>1111111=>1
[5,3,8,2,7,6,1,4]=>0000000=>1111111=>1
[6,5,4,8,3,7,2,1]=>0000000=>1111111=>1
[4,8,5,1,3,7,2,6]=>0000000=>1111111=>1
[4,3,8,7,2,6,5,1]=>0000000=>1111111=>1
[2,7,5,1,8,4,6,3]=>0000000=>1111111=>1
[7,8,5,2,1,6,4,3]=>0000000=>1111111=>1
[7,6,4,8,1,2,5,3]=>0000000=>1111111=>1
[7,5,4,8,3,2,6,1]=>0000000=>1111111=>1
[3,8,5,6,2,7,1,4]=>0000000=>1111111=>1
[2,4,5,8,7,3,1,6]=>0000000=>1111111=>1
[4,3,7,5,6,2,8,1]=>0000000=>1111111=>1
[4,5,1,8,6,7,3,2]=>0000000=>1111111=>1
[3,4,5,8,6,7,2,1]=>0000000=>1111111=>1
[2,1,5,8,6,7,4,3]=>0100000=>1011111=>2
[3,4,5,8,7,1,2,6]=>0000000=>1111111=>1
[6,5,4,7,1,3,8,2]=>0000000=>1111111=>1
[6,1,4,7,2,3,8,5]=>0000000=>1111111=>1
[2,1,3,4,5,6,8,9,7]=>01111100=>10000011=>2
[2,1,3,4,5,6,7,9,8]=>01111110=>10000001=>2
[1,2,3,4,5,6,7,8,10,11,9]=>1111111100=>0000000011=>1
[2,1,3,4,5,6,7,9,10,8]=>011111100=>100000011=>2
[2,3,1,4,5,6,8,9,7]=>00111100=>11000011=>2
[1,3,2,4,5,6,8,9,7]=>10111100=>01000011=>2
[2,3,1,4,5,6,7,9,8]=>00111110=>11000001=>2
[1,3,2,4,5,6,7,9,8]=>10111110=>01000001=>2
[2,1,3,4,5,6,7,8,10,9]=>011111110=>100000001=>2
[1,6,2,5,4,8,3,7]=>1000000=>0111111=>1
[4,1,2,7,5,8,3,6]=>0000000=>1111111=>1
[6,1,3,5,8,2,4,7]=>0000000=>1111111=>1
[5,6,4,3,1,8,2,7]=>0000000=>1111111=>1
[6,2,3,5,8,1,4,7]=>0000000=>1111111=>1
[6,7,2,3,8,4,5,1]=>0000000=>1111111=>1
[6,7,2,1,3,8,4,5]=>0000000=>1111111=>1
[5,7,4,1,8,3,2,6]=>0000000=>1111111=>1
[4,1,7,5,8,3,6,2]=>0000000=>1111111=>1
[6,7,1,3,8,4,5,2]=>0000000=>1111111=>1
[1,6,7,4,3,8,5,2]=>1000000=>0111111=>1
[6,1,7,4,2,8,5,3]=>0000000=>1111111=>1
[2,1,6,7,4,3,8,5]=>0100000=>1011111=>2
[6,7,3,2,1,8,4,5]=>0000000=>1111111=>1
[2,5,7,3,1,4,8,6]=>0000000=>1111111=>1
[6,7,3,2,8,4,5,1]=>0000000=>1111111=>1
[1,2,6,7,4,3,8,5]=>1100000=>0011111=>1
[2,7,1,8,4,6,3,5]=>0000000=>1111111=>1
[2,7,5,8,1,6,3,4]=>0000000=>1111111=>1
[6,7,1,8,4,5,3,2]=>0000000=>1111111=>1
[8,3,5,7,6,1,4,2]=>0000000=>1111111=>1
[8,7,3,6,2,1,5,4]=>0000000=>1111111=>1
[8,6,2,4,7,3,1,5]=>0000000=>1111111=>1
[8,6,1,5,4,3,2,7]=>0000000=>1111111=>1
[2,4,5,8,3,1,6,7]=>0000000=>1111111=>1
[7,8,3,2,5,4,6,1]=>0000000=>1111111=>1
[1,5,6,7,3,8,2,4]=>1000000=>0111111=>1
[1,6,5,4,8,3,2,7]=>1000000=>0111111=>1
[7,2,1,6,4,8,5,3]=>0000000=>1111111=>1
[1,3,7,6,4,8,5,2]=>1000000=>0111111=>1
[3,1,8,7,6,4,2,5]=>0000000=>1111111=>1
[3,1,8,7,5,4,2,6]=>0000000=>1111111=>1
[3,1,7,6,5,4,2,8]=>0000001=>1111110=>1
[4,7,1,6,5,3,2,8]=>0000001=>1111110=>1
[4,8,1,6,5,3,2,7]=>0000000=>1111111=>1
[8,4,1,7,6,3,2,5]=>0000000=>1111111=>1
[5,4,1,8,6,3,2,7]=>0000000=>1111111=>1
[5,4,1,7,6,3,2,8]=>0000001=>1111110=>1
[6,4,1,8,5,3,2,7]=>0000000=>1111111=>1
[8,4,1,7,5,3,2,6]=>0000000=>1111111=>1
[7,4,1,6,5,3,2,8]=>0000001=>1111110=>1
[7,5,6,1,4,3,2,8]=>0000001=>1111110=>1
[8,5,6,1,4,3,2,7]=>0000000=>1111111=>1
[8,5,7,1,4,3,2,6]=>0000000=>1111111=>1
[5,7,6,1,4,3,2,8]=>0000001=>1111110=>1
[5,8,6,1,4,3,2,7]=>0000000=>1111111=>1
[6,7,5,1,4,3,2,8]=>0000001=>1111110=>1
[8,7,5,1,4,3,2,6]=>0000000=>1111111=>1
[8,6,5,1,4,3,2,7]=>0000000=>1111111=>1
[1,8,6,3,4,2,5,7]=>1000000=>0111111=>1
[3,1,6,4,5,8,7,2]=>0000000=>1111111=>1
[3,1,6,4,5,8,2,7]=>0000000=>1111111=>1
[4,6,8,7,2,5,1,3]=>0000000=>1111111=>1
[7,6,3,8,4,5,2,1]=>0000000=>1111111=>1
[8,2,7,6,1,4,3,5]=>0000000=>1111111=>1
[5,2,7,8,1,4,3,6]=>0000000=>1111111=>1
[5,6,3,8,4,1,2,7]=>0000000=>1111111=>1
[5,2,3,4,7,1,6,8]=>0000001=>1111110=>1
[5,2,3,7,1,6,8,4]=>0000000=>1111111=>1
[8,7,5,3,1,6,4,2]=>0000000=>1111111=>1
[1,4,7,8,5,2,3,6]=>1000000=>0111111=>1
[3,2,6,7,4,1,5,8]=>0000001=>1111110=>1
[5,8,3,7,6,4,1,2]=>0000000=>1111111=>1
[4,7,5,8,2,1,3,6]=>0000000=>1111111=>1
[8,1,2,7,5,4,3,6]=>0000000=>1111111=>1
[6,5,1,8,3,7,2,4]=>0000000=>1111111=>1
[7,6,3,1,2,8,5,4]=>0000000=>1111111=>1
[6,3,5,7,1,4,2,8]=>0000001=>1111110=>1
[1,7,5,2,6,4,8,3]=>1000000=>0111111=>1
[7,1,3,6,8,2,4,5]=>0000000=>1111111=>1
[1,2,5,7,8,4,6,3]=>1100000=>0011111=>1
[3,1,2,7,5,4,8,6]=>0010000=>1101111=>2
[6,7,4,1,3,2,8,5]=>0000000=>1111111=>1
[1,7,2,8,4,3,5,6]=>1000000=>0111111=>1
[1,6,3,5,7,8,2,4]=>1000000=>0111111=>1
[8,6,1,7,5,2,4,3]=>0000000=>1111111=>1
[7,6,4,1,8,3,2,5]=>0000000=>1111111=>1
[8,4,1,6,5,2,7,3]=>0000000=>1111111=>1
[1,5,3,4,7,8,2,6]=>1000000=>0111111=>1
[4,2,1,5,7,8,3,6]=>0000000=>1111111=>1
[5,4,1,6,7,8,2,3]=>0000000=>1111111=>1
[5,1,4,6,7,8,2,3]=>0000000=>1111111=>1
[4,1,5,3,7,8,2,6]=>0000000=>1111111=>1
[8,1,4,6,5,2,7,3]=>0000000=>1111111=>1
[7,1,5,4,6,3,2,8]=>0000001=>1111110=>1
[8,2,1,6,7,5,4,3]=>0000000=>1111111=>1
[1,2,4,7,6,3,8,5]=>1100000=>0011111=>1
[6,7,4,1,8,5,2,3]=>0000000=>1111111=>1
[8,6,4,1,5,7,3,2]=>0000000=>1111111=>1
[5,2,4,3,7,1,6,8]=>0000001=>1111110=>1
[6,1,5,4,8,3,2,7]=>0000000=>1111111=>1
[1,2,8,7,4,3,6,5]=>1100000=>0011111=>1
[3,2,1,7,5,8,4,6]=>0010000=>1101111=>2
[1,3,6,4,7,8,2,5]=>1000000=>0111111=>1
[4,5,1,3,7,8,2,6]=>0000000=>1111111=>1
[5,2,3,1,7,8,4,6]=>0000000=>1111111=>1
[1,6,4,3,7,8,2,5]=>1000000=>0111111=>1
[7,6,4,3,1,5,2,8]=>0000001=>1111110=>1
[7,5,4,6,1,3,2,8]=>0000001=>1111110=>1
[8,4,6,5,1,2,7,3]=>0000000=>1111111=>1
[1,5,6,3,7,8,2,4]=>1000000=>0111111=>1
[7,1,2,3,4,5,8,9,10,6]=>000000000=>111111111=>1
[6,7,1,2,3,4,8,9,5]=>00000000=>11111111=>1
[6,1,2,3,4,7,8,9,10,5]=>000000000=>111111111=>1
[5,1,2,3,6,7,8,9,10,4]=>000000000=>111111111=>1
[1,5,2,4,3,8,7,6]=>1000100=>0111011=>2
[8,6,5,7,2,1,4,3]=>0000000=>1111111=>1
[1,6,3,8,4,5,7,2]=>1000000=>0111111=>1
[7,5,4,2,6,3,8,1]=>0000000=>1111111=>1
[7,8,6,5,4,3,2,9,1]=>00000000=>11111111=>1
[9,7,6,5,4,3,1,2,8]=>00000000=>11111111=>1
[2,4,3,5,6,7,8,9,1]=>00000000=>11111111=>1
[4,3,7,8,6,2,5,1]=>0000000=>1111111=>1
[2,4,7,8,6,1,5,3]=>0000000=>1111111=>1
[2,4,8,5,1,7,3,6]=>0000000=>1111111=>1
[2,8,3,5,1,6,4,7]=>0000000=>1111111=>1
[8,2,4,6,3,7,5,1]=>0000000=>1111111=>1
[4,5,3,8,2,1,7,6]=>0000000=>1111111=>1
[4,5,6,7,8,9,2,1,3]=>00000000=>11111111=>1
[5,6,7,8,9,2,1,3,4]=>00000000=>11111111=>1
[6,7,8,9,2,1,3,4,5]=>00000000=>11111111=>1
[7,8,9,2,1,3,4,5,6]=>00000000=>11111111=>1
[8,9,2,1,3,4,5,6,7]=>00000000=>11111111=>1
[8,2,1,4,5,6,7,3]=>0000000=>1111111=>1
[7,8,2,1,5,4,6,3]=>0000000=>1111111=>1
[1,4,8,5,2,6,3,7]=>1000000=>0111111=>1
[1,2,8,4,3,6,7,5]=>1100000=>0011111=>1
[1,2,7,5,3,4,6,8]=>1100001=>0011110=>1
[1,7,3,2,6,8,4,5]=>1000000=>0111111=>1
[7,2,1,3,6,8,4,5]=>0000000=>1111111=>1
[4,7,8,1,6,5,3,2]=>0000000=>1111111=>1
[1,8,4,2,7,6,3,5]=>1000000=>0111111=>1
[7,3,8,1,6,5,4,2]=>0000000=>1111111=>1
[7,1,3,8,6,5,4,2]=>0000000=>1111111=>1
[8,1,3,7,6,5,4,2]=>0000000=>1111111=>1
[2,4,1,8,7,3,6,5]=>0000000=>1111111=>1
[7,3,8,6,1,5,4,2]=>0000000=>1111111=>1
[3,5,1,7,8,2,6,4]=>0000000=>1111111=>1
[5,4,7,8,2,1,6,3]=>0000000=>1111111=>1
[6,4,7,1,5,3,2,8]=>0000001=>1111110=>1
[3,4,6,2,1,8,5,7]=>0000000=>1111111=>1
[4,5,7,2,1,6,3,8]=>0000001=>1111110=>1
[5,6,4,8,3,2,1,7]=>0000000=>1111111=>1
[5,7,4,8,2,1,6,3]=>0000000=>1111111=>1
[4,7,5,8,2,1,6,3]=>0000000=>1111111=>1
[5,7,4,2,6,3,8,1]=>0000000=>1111111=>1
[8,5,6,1,7,3,2,4]=>0000000=>1111111=>1
[4,5,1,6,7,8,3,2]=>0000000=>1111111=>1
[8,4,6,7,2,5,1,3]=>0000000=>1111111=>1
[7,1,4,6,8,3,5,2]=>0000000=>1111111=>1
[6,7,1,2,4,8,5,3]=>0000000=>1111111=>1
[1,6,3,4,7,8,5,2]=>1000000=>0111111=>1
[7,8,1,3,4,5,6,2]=>0000000=>1111111=>1
[1,8,2,6,7,3,4,5]=>1000000=>0111111=>1
[4,7,3,2,8,1,5,6]=>0000000=>1111111=>1
[7,1,2,6,3,8,5,4]=>0000000=>1111111=>1
[8,1,2,6,3,7,5,4]=>0000000=>1111111=>1
[8,1,2,7,6,3,5,4]=>0000000=>1111111=>1
[4,8,7,3,1,6,2,5]=>0000000=>1111111=>1
[4,7,8,3,1,6,2,5]=>0000000=>1111111=>1
[7,4,3,1,6,2,8,5]=>0000000=>1111111=>1
[3,7,6,2,4,8,1,5]=>0000000=>1111111=>1
[4,3,7,2,8,6,1,5]=>0000000=>1111111=>1
[6,1,2,7,4,3,8,5]=>0000000=>1111111=>1
[5,1,2,7,3,8,6,4]=>0000000=>1111111=>1
[6,1,2,7,3,5,8,4]=>0000000=>1111111=>1
[7,5,3,2,1,8,6,4]=>0000000=>1111111=>1
[4,2,1,5,3,6,7,8]=>0000111=>1111000=>1
[8,6,4,3,2,1,9,7,5]=>00000000=>11111111=>1
[7,5,4,3,2,1,8,6,9]=>00000001=>11111110=>1
[8,6,4,2,1,9,7,5,3]=>00000000=>11111111=>1
[7,5,3,2,1,8,6,4,9]=>00000001=>11111110=>1
[7,4,3,2,1,8,5,9,6]=>00000000=>11111111=>1
[6,4,3,2,1,7,5,8,9]=>00000011=>11111100=>1
[7,5,3,1,8,6,4,2,9]=>00000001=>11111110=>1
[7,4,2,1,8,5,3,9,6]=>00000000=>11111111=>1
[6,4,2,1,7,5,3,8,9]=>00000011=>11111100=>1
[6,3,2,1,7,4,8,5,9]=>00000001=>11111110=>1
[5,3,2,1,6,4,7,8,9]=>00000111=>11111000=>1
[7,4,1,8,5,2,9,6,3]=>00000000=>11111111=>1
[6,3,1,7,4,2,8,5,9]=>00000001=>11111110=>1
[5,3,1,6,4,2,7,8,9]=>00000111=>11111000=>1
[6,2,1,7,3,8,4,9,5]=>00000000=>11111111=>1
[5,2,1,6,3,7,4,8,9]=>00000011=>11111100=>1
[4,2,1,5,3,6,7,8,9]=>00001111=>11110000=>1
[4,1,5,2,6,3,7,8,9]=>00000111=>11111000=>1
[3,1,4,2,5,6,7,8,9]=>00011111=>11100000=>1
[9,7,5,4,3,2,1,10,8,6]=>000000000=>111111111=>1
[8,6,5,4,3,2,1,9,7,10]=>000000001=>111111110=>1
[9,7,5,3,2,1,10,8,6,4]=>000000000=>111111111=>1
[8,6,4,3,2,1,9,7,5,10]=>000000001=>111111110=>1
[8,5,4,3,2,1,9,6,10,7]=>000000000=>111111111=>1
[7,5,4,3,2,1,8,6,9,10]=>000000011=>111111100=>1
[8,6,4,2,1,9,7,5,3,10]=>000000001=>111111110=>1
[8,5,3,2,1,9,6,4,10,7]=>000000000=>111111111=>1
[7,5,3,2,1,8,6,4,9,10]=>000000011=>111111100=>1
[7,4,3,2,1,8,5,9,6,10]=>000000001=>111111110=>1
[6,4,3,2,1,7,5,8,9,10]=>000000111=>111111000=>1
[8,5,3,1,9,6,4,2,10,7]=>000000000=>111111111=>1
[7,5,3,1,8,6,4,2,9,10]=>000000011=>111111100=>1
[8,5,2,1,9,6,3,10,7,4]=>000000000=>111111111=>1
[7,4,2,1,8,5,3,9,6,10]=>000000001=>111111110=>1
[6,4,2,1,7,5,3,8,9,10]=>000000111=>111111000=>1
[7,3,2,1,8,4,9,5,10,6]=>000000000=>111111111=>1
[6,3,2,1,7,4,8,5,9,10]=>000000011=>111111100=>1
[5,3,2,1,6,4,7,8,9,10]=>000001111=>111110000=>1
[7,4,1,8,5,2,9,6,3,10]=>000000001=>111111110=>1
[7,3,1,8,4,2,9,5,10,6]=>000000000=>111111111=>1
[6,3,1,7,4,2,8,5,9,10]=>000000011=>111111100=>1
[5,3,1,6,4,2,7,8,9,10]=>000001111=>111110000=>1
[6,2,1,7,3,8,4,9,5,10]=>000000001=>111111110=>1
[5,2,1,6,3,7,4,8,9,10]=>000000111=>111111000=>1
[4,2,1,5,3,6,7,8,9,10]=>000011111=>111100000=>1
[5,1,6,2,7,3,8,4,9,10]=>000000011=>111111100=>1
[4,1,5,2,6,3,7,8,9,10]=>000001111=>111110000=>1
[3,1,4,2,5,6,7,8,9,10]=>000111111=>111000000=>1
[6,2,5,4,1,8,7,3]=>0000000=>1111111=>1
[4,6,3,2,1,8,7,5]=>0000000=>1111111=>1
[6,5,3,2,1,8,7,4]=>0000000=>1111111=>1
[8,4,3,2,7,6,1,5]=>0000000=>1111111=>1
[1,5,8,4,7,6,3,2]=>1000000=>0111111=>1
[3,2,7,4,8,6,1,5]=>0000000=>1111111=>1
[7,4,3,2,8,6,1,5]=>0000000=>1111111=>1
[6,8,3,7,5,2,1,4]=>0000000=>1111111=>1
[5,7,8,4,3,2,1,6]=>0000000=>1111111=>1
[6,4,3,8,5,2,1,7]=>0000000=>1111111=>1
[8,2,5,4,7,6,1,3]=>0000000=>1111111=>1
[7,2,5,4,8,6,1,3]=>0000000=>1111111=>1
[4,5,3,2,8,6,1,7]=>0000000=>1111111=>1
[3,2,5,4,8,6,1,7]=>0000000=>1111111=>1
[3,2,8,6,5,4,1,7]=>0000000=>1111111=>1
[8,4,3,6,5,2,1,7]=>0000000=>1111111=>1
[8,4,3,7,5,2,1,6]=>0000000=>1111111=>1
[3,2,7,8,5,4,1,6]=>0000000=>1111111=>1
[6,8,7,4,3,2,1,5]=>0000000=>1111111=>1
[3,6,1,4,8,7,2,5]=>0000000=>1111111=>1
[5,8,1,3,7,2,6,4]=>0000000=>1111111=>1
[4,7,5,1,8,2,6,3]=>0000000=>1111111=>1
[6,3,2,1,8,7,4,5]=>0000000=>1111111=>1
[6,2,3,1,8,7,4,5]=>0000000=>1111111=>1
[3,4,8,1,7,5,6,2]=>0000000=>1111111=>1
[7,2,1,5,8,4,6,3]=>0000000=>1111111=>1
[4,2,8,1,7,5,6,3]=>0000000=>1111111=>1
[3,7,4,1,5,8,6,2]=>0000000=>1111111=>1
[5,8,6,1,2,7,4,3]=>0000000=>1111111=>1
[6,7,1,4,3,8,5,2]=>0000000=>1111111=>1
[6,8,1,2,4,7,5,3]=>0000000=>1111111=>1
[8,6,4,1,3,7,5,2]=>0000000=>1111111=>1
[8,5,3,6,1,7,4,2]=>0000000=>1111111=>1
[7,2,1,4,5,8,6,3]=>0000000=>1111111=>1
[8,5,6,1,2,7,4,3]=>0000000=>1111111=>1
[2,8,4,1,3,6,7,5]=>0000000=>1111111=>1
[8,1,2,4,5,6,7,3]=>0000000=>1111111=>1
[1,8,3,6,7,2,4,5]=>1000000=>0111111=>1
[1,2,8,3,7,4,6,5]=>1100000=>0011111=>1
[1,9,2,3,4,5,6,7,8,10]=>100000001=>011111110=>1
[1,7,2,3,4,5,6,8,9]=>10000011=>01111100=>1
[8,2,6,5,4,3,1,7]=>0000000=>1111111=>1
[8,2,7,6,4,5,3,1]=>0000000=>1111111=>1
[8,7,3,5,4,2,6,1]=>0000000=>1111111=>1
[3,7,8,4,5,1,6,2]=>0000000=>1111111=>1
[3,6,1,5,7,8,2,4]=>0000000=>1111111=>1
[3,7,8,5,4,1,6,2]=>0000000=>1111111=>1
[4,6,5,2,7,8,1,3]=>0000000=>1111111=>1
[1,6,5,2,3,4,8,7]=>1000010=>0111101=>2
[4,6,5,1,7,3,8,2]=>0000000=>1111111=>1
[5,7,3,1,2,4,8,6]=>0000000=>1111111=>1
[6,3,2,5,1,7,4,8]=>0000001=>1111110=>1
[6,3,1,7,2,5,8,4]=>0000000=>1111111=>1
[1,2,3,4,5,6,8,7,9]=>11111101=>00000010=>1
[1,2,3,4,5,6,7,9,8,10]=>111111101=>000000010=>1
[1,2,3,4,5,7,6,8,9]=>11111011=>00000100=>1
[9,2,3,4,5,6,7,1,8]=>00000000=>11111111=>1
[1,3,5,8,6,4,7,2]=>1000000=>0111111=>1
[1,3,5,8,6,7,2,4]=>1000000=>0111111=>1
[6,1,7,4,8,5,3,2]=>0000000=>1111111=>1
[7,4,3,1,6,5,8,2]=>0000000=>1111111=>1
[8,6,1,7,5,3,2,4]=>0000000=>1111111=>1
[7,8,1,4,6,5,3,2]=>0000000=>1111111=>1
[7,8,6,1,4,5,3,2]=>0000000=>1111111=>1
[6,2,7,3,8,5,4,1]=>0000000=>1111111=>1
[1,2,7,5,3,4,8,6]=>1100000=>0011111=>1
[6,2,7,8,3,1,4,5]=>0000000=>1111111=>1
[1,2,8,7,3,4,6,5]=>1100000=>0011111=>1
[8,2,7,4,5,1,6,3]=>0000000=>1111111=>1
[3,8,1,5,7,2,6,4]=>0000000=>1111111=>1
[7,5,4,8,6,1,2,3]=>0000000=>1111111=>1
[7,1,8,6,4,5,2,3]=>0000000=>1111111=>1
[6,8,4,3,1,7,2,5]=>0000000=>1111111=>1
[4,8,1,3,7,5,6,2]=>0000000=>1111111=>1
[2,1,6,8,5,3,4,7]=>0100000=>1011111=>2
[4,5,1,3,8,6,7,2]=>0000000=>1111111=>1
[1,2,6,8,5,3,4,7]=>1100000=>0011111=>1
[6,8,5,7,3,1,2,4]=>0000000=>1111111=>1
[5,1,4,2,6,8,7,3]=>0000000=>1111111=>1
[6,3,2,4,7,1,8,5]=>0000000=>1111111=>1
[5,1,8,6,2,4,3,7]=>0000000=>1111111=>1
[5,7,6,3,8,1,2,4]=>0000000=>1111111=>1
[1,2,5,3,6,8,7,4]=>1100000=>0011111=>1
[6,8,7,2,1,5,3,4]=>0000000=>1111111=>1
[7,8,1,6,5,3,4,2]=>0000000=>1111111=>1
[8,7,3,2,1,4,6,5]=>0000000=>1111111=>1
[5,8,2,6,4,3,7,1]=>0000000=>1111111=>1
[1,7,2,3,5,8,6,4]=>1000000=>0111111=>1
[6,4,8,7,2,1,5,3]=>0000000=>1111111=>1
[1,6,7,8,2,4,3,5]=>1000000=>0111111=>1
[1,8,5,6,4,3,2,7]=>1000000=>0111111=>1
[7,6,8,3,2,5,1,4]=>0000000=>1111111=>1
[2,7,1,4,5,3,8,6]=>0000000=>1111111=>1
[1,5,2,7,4,3,6,8]=>1000001=>0111110=>1
[5,1,3,8,4,6,2,7]=>0000000=>1111111=>1
[6,5,8,7,1,3,2,4]=>0000000=>1111111=>1
[2,7,3,5,1,6,8,4]=>0000000=>1111111=>1
[5,7,6,8,2,1,4,3]=>0000000=>1111111=>1
[1,3,6,5,2,7,4,8]=>1000001=>0111110=>1
[1,2,6,5,3,4,7,8]=>1100011=>0011100=>1
[1,7,2,5,6,8,3,4]=>1000000=>0111111=>1
[1,7,2,4,8,3,5,6]=>1000000=>0111111=>1
[1,6,2,4,5,3,7,8]=>1000011=>0111100=>1
[1,3,2,8,4,5,7,6]=>1010000=>0101111=>2
[1,6,8,2,4,3,5,7]=>1000000=>0111111=>1
[1,6,7,2,5,3,4,8]=>1000001=>0111110=>1
[1,2,8,3,6,7,4,5]=>1100000=>0011111=>1
[1,7,2,5,3,4,8,6]=>1000000=>0111111=>1
[7,1,5,6,2,3,8,4]=>0000000=>1111111=>1
[8,2,1,4,6,7,3,5]=>0000000=>1111111=>1
[7,2,6,1,3,4,8,5]=>0000000=>1111111=>1
[4,1,3,7,2,5,8,6]=>0000000=>1111111=>1
[6,2,7,5,1,3,8,4]=>0000000=>1111111=>1
[1,7,5,6,2,3,8,4]=>1000000=>0111111=>1
[3,7,6,1,2,4,8,5]=>0000000=>1111111=>1
[8,6,1,3,5,7,2,4]=>0000000=>1111111=>1
[1,7,4,3,8,2,5,6]=>1000000=>0111111=>1
[6,1,5,3,4,8,2,7]=>0000000=>1111111=>1
[3,6,7,5,2,8,1,4]=>0000000=>1111111=>1
[7,8,4,1,5,6,2,3]=>0000000=>1111111=>1
[5,8,1,3,6,7,2,4]=>0000000=>1111111=>1
[2,8,4,3,7,1,5,6]=>0000000=>1111111=>1
[3,8,4,6,7,1,2,5]=>0000000=>1111111=>1
[6,3,8,4,7,1,2,5]=>0000000=>1111111=>1
[1,2,5,4,8,3,6,7]=>1100000=>0011111=>1
[7,1,3,8,2,4,5,6]=>0000000=>1111111=>1
[8,1,3,7,2,4,5,6]=>0000000=>1111111=>1
[3,5,4,7,8,1,2,6]=>0000000=>1111111=>1
[8,3,1,4,7,2,5,6]=>0000000=>1111111=>1
[1,6,4,7,8,2,3,5]=>1000000=>0111111=>1
[5,2,3,6,7,8,1,4]=>0000000=>1111111=>1
[6,2,7,3,8,5,1,4]=>0000000=>1111111=>1
[1,3,7,8,5,6,2,4]=>1000000=>0111111=>1
[8,2,6,7,5,1,3,4]=>0000000=>1111111=>1
[8,1,7,4,6,2,3,5]=>0000000=>1111111=>1
[2,5,8,4,7,1,3,6]=>0000000=>1111111=>1
[4,5,8,7,1,2,3,6]=>0000000=>1111111=>1
[4,1,8,5,7,2,3,6]=>0000000=>1111111=>1
[1,8,7,4,6,2,3,5]=>1000000=>0111111=>1
[2,6,5,4,1,8,3,7]=>0000000=>1111111=>1
[8,5,4,1,3,6,7,2]=>0000000=>1111111=>1
[8,4,7,6,5,3,1,2]=>0000000=>1111111=>1
[1,8,4,2,3,7,6,5]=>1000000=>0111111=>1
[2,3,1,8,7,6,4,5]=>0010000=>1101111=>2
[8,2,7,5,6,4,1,3]=>0000000=>1111111=>1
[6,8,5,4,1,7,2,3]=>0000000=>1111111=>1
[8,4,7,2,1,6,5,3]=>0000000=>1111111=>1
[1,8,4,7,6,5,2,3]=>1000000=>0111111=>1
[8,2,3,4,5,6,9,1,7]=>00000000=>11111111=>1
[8,2,3,9,5,6,7,1,4]=>00000000=>11111111=>1
[8,2,9,4,5,6,7,1,3]=>00000000=>11111111=>1
[8,9,3,4,5,6,7,1,2]=>00000000=>11111111=>1
[9,2,3,4,5,6,7,10,1,8]=>000000000=>111111111=>1
[4,2,3,1,9,8,7,6,5]=>00010000=>11101111=>2
[9,2,10,4,5,6,7,8,1,3]=>000000000=>111111111=>1
[3,8,1,2,5,6,4,7]=>0000000=>1111111=>1
[3,7,1,2,5,6,4,8]=>0000001=>1111110=>1
[8,5,2,1,4,6,7,3]=>0000000=>1111111=>1
[4,2,6,3,8,5,7,1]=>0000000=>1111111=>1
[8,3,5,4,2,7,1,6]=>0000000=>1111111=>1
[3,1,8,6,5,2,7,4]=>0000000=>1111111=>1
[3,8,2,4,1,5,7,6]=>0000000=>1111111=>1
[5,8,3,2,4,1,7,6]=>0000000=>1111111=>1
[7,2,6,8,4,3,5,1]=>0000000=>1111111=>1
[6,5,3,2,4,8,1,7]=>0000000=>1111111=>1
[5,2,4,6,1,3,8,7]=>0000010=>1111101=>2
[3,7,5,2,8,6,1,4]=>0000000=>1111111=>1
[2,1,7,5,8,3,6,4]=>0100000=>1011111=>2
[6,1,5,8,3,7,4,2]=>0000000=>1111111=>1
[2,6,3,5,8,7,4,1]=>0000000=>1111111=>1
[8,6,5,3,7,2,1,4]=>0000000=>1111111=>1
[7,4,8,6,5,3,2,1]=>0000000=>1111111=>1
[5,1,6,3,8,2,4,7]=>0000000=>1111111=>1
[3,6,5,1,4,8,7,2]=>0000000=>1111111=>1
[7,3,6,2,8,4,1,5]=>0000000=>1111111=>1
[7,5,4,8,1,6,2,3]=>0000000=>1111111=>1
[4,3,5,8,7,1,2,6]=>0000000=>1111111=>1
[4,3,5,8,2,1,6,7]=>0000000=>1111111=>1
[7,8,6,3,1,4,2,5]=>0000000=>1111111=>1
[6,1,8,4,7,2,3,5]=>0000000=>1111111=>1
[5,6,4,3,7,1,8,2]=>0000000=>1111111=>1
[6,5,3,7,2,4,8,1]=>0000000=>1111111=>1
[5,6,2,8,4,3,7,1]=>0000000=>1111111=>1
[5,7,4,3,6,8,2,1]=>0000000=>1111111=>1
[4,6,2,7,8,3,5,1]=>0000000=>1111111=>1
[4,6,3,5,2,8,7,1]=>0000000=>1111111=>1
[5,6,3,4,8,2,7,1]=>0000000=>1111111=>1
[5,2,6,4,1,7,8,3]=>0000000=>1111111=>1
[5,8,4,6,3,2,7,1]=>0000000=>1111111=>1
[5,4,3,8,6,2,7,1]=>0000000=>1111111=>1
[5,7,8,2,4,3,6,1]=>0000000=>1111111=>1
[5,6,2,4,8,3,7,1]=>0000000=>1111111=>1
[6,4,7,8,2,3,5,1]=>0000000=>1111111=>1
[3,7,5,2,4,8,1,6]=>0000000=>1111111=>1
[4,7,5,2,3,8,6,1]=>0000000=>1111111=>1
[6,4,7,3,2,5,8,1]=>0000000=>1111111=>1
[5,7,3,2,8,4,6,1]=>0000000=>1111111=>1
[5,3,7,2,8,4,6,1]=>0000000=>1111111=>1
[4,3,7,2,5,8,6,1]=>0000000=>1111111=>1
[4,7,3,2,5,8,6,1]=>0000000=>1111111=>1
[4,7,3,2,6,8,5,1]=>0000000=>1111111=>1
[7,5,3,2,6,4,8,1]=>0000000=>1111111=>1
[8,5,2,6,7,3,4,1]=>0000000=>1111111=>1
[8,4,2,6,3,7,5,1]=>0000000=>1111111=>1
[7,4,6,2,3,8,5,1]=>0000000=>1111111=>1
[7,5,6,2,8,3,4,1]=>0000000=>1111111=>1
[5,7,6,2,8,3,4,1]=>0000000=>1111111=>1
[4,7,6,2,3,8,5,1]=>0000000=>1111111=>1
[7,6,3,2,5,8,1,4]=>0000000=>1111111=>1
[7,6,4,2,5,8,3,1]=>0000000=>1111111=>1
[1,3,2,4,5,6,7,8,9]=>10111111=>01000000=>1
[1,4,2,3,5,6,7,8,9]=>10011111=>01100000=>1
[1,3,2,4,5,6,7,8,9,10]=>101111111=>010000000=>1
[2,4,6,3,8,7,5,1]=>0000000=>1111111=>1
[2,4,3,6,8,7,1,5]=>0000000=>1111111=>1
[2,4,6,3,8,7,1,5]=>0000000=>1111111=>1
[2,4,6,5,8,7,1,3]=>0000000=>1111111=>1
[2,4,6,8,5,7,3,1]=>0000000=>1111111=>1
[2,4,6,8,5,7,1,3]=>0000000=>1111111=>1
[2,4,6,8,3,7,1,5]=>0000000=>1111111=>1
[2,4,6,8,1,7,3,5]=>0000000=>1111111=>1
[2,4,6,5,8,3,7,1]=>0000000=>1111111=>1
[2,4,6,5,8,1,7,3]=>0000000=>1111111=>1
[2,4,6,8,5,1,7,3]=>0000000=>1111111=>1
[2,4,6,8,7,3,5,1]=>0000000=>1111111=>1
[2,4,6,8,7,1,5,3]=>0000000=>1111111=>1
[2,4,6,8,7,1,3,5]=>0000000=>1111111=>1
[2,4,6,8,5,1,3,7]=>0000000=>1111111=>1
[2,4,6,5,3,8,1,7]=>0000000=>1111111=>1
[2,4,6,5,8,3,1,7]=>0000000=>1111111=>1
[2,4,6,8,5,3,1,7]=>0000000=>1111111=>1
[2,4,6,8,7,3,1,5]=>0000000=>1111111=>1
[2,4,6,8,7,5,1,3]=>0000000=>1111111=>1
[4,8,7,5,2,1,3,6]=>0000000=>1111111=>1
[6,1,4,7,5,8,2,3]=>0000000=>1111111=>1
[1,8,6,5,3,2,7,4]=>1000000=>0111111=>1
[1,6,3,5,8,2,4,7]=>1000000=>0111111=>1
[4,6,1,7,8,5,3,2]=>0000000=>1111111=>1
[6,1,2,7,8,4,5,3]=>0000000=>1111111=>1
[6,1,3,2,7,8,5,4]=>0000000=>1111111=>1
[5,6,3,1,7,4,8,2]=>0000000=>1111111=>1
[4,8,3,7,1,6,5,2]=>0000000=>1111111=>1
[8,7,2,6,5,1,4,3]=>0000000=>1111111=>1
[5,8,3,2,1,7,6,4]=>0000000=>1111111=>1
[5,4,3,8,1,7,6,2]=>0000000=>1111111=>1
[6,5,3,8,7,1,4,2]=>0000000=>1111111=>1
[4,3,8,2,7,6,5,1]=>0000000=>1111111=>1
[4,8,2,7,6,5,3,1]=>0000000=>1111111=>1
[7,8,2,6,5,4,1,3]=>0000000=>1111111=>1
[3,8,7,6,2,5,1,4]=>0000000=>1111111=>1
[4,8,3,7,2,1,6,5]=>0000000=>1111111=>1
[8,6,3,1,7,5,4,2]=>0000000=>1111111=>1
[8,6,3,7,1,5,4,2]=>0000000=>1111111=>1
[4,8,3,7,6,2,5,1]=>0000000=>1111111=>1
[5,8,2,7,6,4,1,3]=>0000000=>1111111=>1
[8,4,2,1,7,6,5,3]=>0000000=>1111111=>1
[1,6,4,2,5,3,7,8]=>1000011=>0111100=>1
[1,8,6,2,7,3,4,5]=>1000000=>0111111=>1
[1,6,3,2,4,5,7,8]=>1000011=>0111100=>1
[1,5,2,6,4,3,7,8]=>1000011=>0111100=>1
[1,5,2,4,6,3,7,8]=>1000011=>0111100=>1
[1,8,6,2,3,7,4,5]=>1000000=>0111111=>1
[1,5,2,8,6,3,4,7]=>1000000=>0111111=>1
[1,3,6,8,2,7,4,5]=>1000000=>0111111=>1
[1,4,3,8,2,5,6,7]=>1000000=>0111111=>1
[1,7,2,3,8,5,4,6]=>1000000=>0111111=>1
[1,3,8,4,2,5,6,7]=>1000000=>0111111=>1
[1,6,2,8,5,4,3,7]=>1000000=>0111111=>1
[1,7,2,3,8,6,4,5]=>1000000=>0111111=>1
[1,5,3,8,2,7,4,6]=>1000000=>0111111=>1
[1,4,8,2,5,6,3,7]=>1000000=>0111111=>1
[1,5,7,3,2,8,4,6]=>1000000=>0111111=>1
[1,2,7,3,6,8,4,5]=>1100000=>0011111=>1
[1,7,2,3,6,8,4,5]=>1000000=>0111111=>1
[1,4,8,3,2,5,6,7]=>1000000=>0111111=>1
[1,7,2,5,8,3,4,6]=>1000000=>0111111=>1
[8,2,3,4,5,6,7,9,1]=>00000000=>11111111=>1
[2,9,3,4,5,6,7,8,1]=>00000000=>11111111=>1
[2,10,3,4,5,6,7,8,9,1]=>000000000=>111111111=>1
[1,3,6,7,4,5,8,2]=>1000000=>0111111=>1
[1,5,6,3,4,2,7,8]=>1000011=>0111100=>1
[1,5,3,6,4,2,7,8]=>1000011=>0111100=>1
[1,5,3,7,4,6,2,8]=>1000001=>0111110=>1
[2,5,7,4,1,3,8,6]=>0000000=>1111111=>1
[4,6,3,5,8,2,1,7]=>0000000=>1111111=>1
[7,2,4,8,6,3,1,5]=>0000000=>1111111=>1
[7,4,5,2,1,8,6,3]=>0000000=>1111111=>1
[8,5,3,6,2,1,7,4]=>0000000=>1111111=>1
[4,5,7,3,1,2,8,6]=>0000000=>1111111=>1
[4,5,1,8,3,2,7,6]=>0000000=>1111111=>1
[2,5,3,8,4,1,7,6]=>0000000=>1111111=>1
[6,3,1,2,4,8,7,5]=>0000000=>1111111=>1
[4,7,5,2,3,6,1,8]=>0000001=>1111110=>1
[7,2,6,5,3,4,1,8]=>0000001=>1111110=>1
[8,2,6,5,4,1,3,7]=>0000000=>1111111=>1
[6,2,8,4,5,1,3,7]=>0000000=>1111111=>1
[4,5,3,8,2,1,6,7]=>0000000=>1111111=>1
[3,7,2,1,8,4,6,5]=>0000000=>1111111=>1
[1,2,6,4,7,5,3,8]=>1100001=>0011110=>1
[2,6,8,4,7,5,1,3]=>0000000=>1111111=>1
[1,6,5,7,3,8,4,2]=>1000000=>0111111=>1
[7,8,6,1,4,3,2,5]=>0000000=>1111111=>1
[2,4,7,8,6,1,3,5]=>0000000=>1111111=>1
[4,6,2,5,3,1,7,8]=>0000011=>1111100=>1
[4,1,5,6,3,2,7,8]=>0000011=>1111100=>1
[6,8,5,3,7,2,1,4]=>0000000=>1111111=>1
[4,7,1,5,8,2,6,3]=>0000000=>1111111=>1
[7,3,4,8,5,2,1,6]=>0000000=>1111111=>1
[4,5,2,3,8,6,7,1]=>0000000=>1111111=>1
[6,7,4,8,5,3,2,1]=>0000000=>1111111=>1
[4,1,2,8,5,7,6,3]=>0000000=>1111111=>1
[3,1,4,6,7,5,8,2]=>0000000=>1111111=>1
[2,6,4,5,8,1,3,7]=>0000000=>1111111=>1
[6,4,1,3,5,8,2,7]=>0000000=>1111111=>1
[3,4,1,7,2,6,8,5]=>0000000=>1111111=>1
[2,4,7,5,8,1,3,6]=>0000000=>1111111=>1
[3,1,6,4,8,7,5,2]=>0000000=>1111111=>1
[4,2,6,1,3,7,8,5]=>0000000=>1111111=>1
[8,5,4,2,7,6,3,1]=>0000000=>1111111=>1
[2,8,4,6,7,1,3,5]=>0000000=>1111111=>1
[5,8,2,1,4,6,7,3]=>0000000=>1111111=>1
[2,6,7,1,3,5,8,4]=>0000000=>1111111=>1
[3,6,7,1,8,2,5,4]=>0000000=>1111111=>1
[3,1,5,7,2,8,6,4]=>0000000=>1111111=>1
[3,8,1,4,7,2,6,5]=>0000000=>1111111=>1
[4,8,1,3,2,7,6,5]=>0000000=>1111111=>1
[4,1,8,3,2,7,6,5]=>0000000=>1111111=>1
[4,3,8,1,2,7,6,5]=>0000000=>1111111=>1
[3,8,4,2,7,1,6,5]=>0000000=>1111111=>1
[2,8,4,3,7,6,1,5]=>0000000=>1111111=>1
[3,8,2,4,7,1,6,5]=>0000000=>1111111=>1
[3,2,4,8,7,1,6,5]=>0000000=>1111111=>1
[3,2,5,7,1,8,6,4]=>0000000=>1111111=>1
[4,2,8,3,1,7,6,5]=>0000000=>1111111=>1
[4,8,2,1,3,7,6,5]=>0000000=>1111111=>1
[4,2,8,1,3,7,6,5]=>0000000=>1111111=>1
[2,3,4,6,8,7,1,5]=>0000000=>1111111=>1
[4,5,1,7,6,8,2,3]=>0000000=>1111111=>1
[6,7,2,8,3,1,4,5]=>0000000=>1111111=>1
[6,2,7,8,4,1,3,5]=>0000000=>1111111=>1
[6,3,7,8,4,1,2,5]=>0000000=>1111111=>1
[7,6,2,3,1,8,4,5]=>0000000=>1111111=>1
[3,4,1,7,8,5,2,6]=>0000000=>1111111=>1
[4,5,1,3,2,7,8,6]=>0000100=>1111011=>2
[2,3,7,8,5,4,1,6]=>0000000=>1111111=>1
[8,3,5,6,1,7,2,4]=>0000000=>1111111=>1
[4,5,8,1,2,6,7,3]=>0000000=>1111111=>1
[5,3,6,7,8,2,1,4]=>0000000=>1111111=>1
[1,3,4,8,6,2,7,5]=>1000000=>0111111=>1
[4,6,8,2,3,7,5,1]=>0000000=>1111111=>1
[4,5,7,2,3,6,1,8]=>0000001=>1111110=>1
[2,7,3,4,1,5,6,8]=>0000001=>1111110=>1
[4,2,6,3,5,7,8,1]=>0000000=>1111111=>1
[2,3,4,5,6,1,8,7,9]=>00000101=>11111010=>2
[2,3,4,5,1,7,6,8,9]=>00001011=>11110100=>2
[2,3,4,1,6,5,7,8,9]=>00010111=>11101000=>2
[2,3,1,5,4,6,7,8,9]=>00101111=>11010000=>2
[1,4,8,5,6,2,7,3]=>1000000=>0111111=>1
[2,8,7,4,5,1,6,3]=>0000000=>1111111=>1
[1,3,8,5,2,6,7,4]=>1000000=>0111111=>1
[7,2,8,4,5,1,6,3]=>0000000=>1111111=>1
[8,6,2,4,1,5,7,3]=>0000000=>1111111=>1
[1,6,4,3,2,7,8,5]=>1000000=>0111111=>1
[8,5,3,2,1,6,7,4]=>0000000=>1111111=>1
[7,1,5,2,3,6,8,4]=>0000000=>1111111=>1
[8,1,2,5,3,6,7,4]=>0000000=>1111111=>1
[8,4,1,6,3,7,2,5]=>0000000=>1111111=>1
[5,2,6,8,3,7,1,4]=>0000000=>1111111=>1
[4,2,5,8,6,7,1,3]=>0000000=>1111111=>1
[3,7,2,4,1,8,6,5]=>0000000=>1111111=>1
[2,4,7,8,5,1,3,6]=>0000000=>1111111=>1
[3,1,7,4,5,6,2,8]=>0000001=>1111110=>1
[2,4,8,3,5,7,1,6]=>0000000=>1111111=>1
[8,1,7,2,4,3,5,6]=>0000000=>1111111=>1
[1,3,8,2,4,7,5,6]=>1000000=>0111111=>1
[1,3,7,2,4,6,5,8]=>1000001=>0111110=>1
[1,7,3,2,4,6,5,8]=>1000001=>0111110=>1
[1,8,3,7,4,2,5,6]=>1000000=>0111111=>1
[8,7,3,1,4,2,5,6]=>0000000=>1111111=>1
[2,8,4,3,5,7,1,6]=>0000000=>1111111=>1
[3,2,8,7,4,1,5,6]=>0000000=>1111111=>1
[3,2,1,7,4,6,5,8]=>0010001=>1101110=>2
[3,2,6,5,1,7,8,4]=>0000000=>1111111=>1
[5,3,2,6,7,1,8,4]=>0000000=>1111111=>1
[3,2,8,6,7,4,1,5]=>0000000=>1111111=>1
[8,4,6,2,7,3,1,5]=>0000000=>1111111=>1
[4,3,8,6,7,2,1,5]=>0000000=>1111111=>1
[4,3,6,2,8,7,1,5]=>0000000=>1111111=>1
[3,8,4,7,6,5,1,2]=>0000000=>1111111=>1
[7,8,4,2,6,3,5,1]=>0000000=>1111111=>1
[3,2,7,8,6,4,5,1]=>0000000=>1111111=>1
[3,2,7,5,6,8,4,1]=>0000000=>1111111=>1
[5,7,8,6,3,2,4,1]=>0000000=>1111111=>1
[6,5,4,2,1,7,8,3]=>0000000=>1111111=>1
[5,4,2,1,7,6,3,8]=>0000001=>1111110=>1
[4,1,6,5,2,7,8,3]=>0000000=>1111111=>1
[5,4,1,6,7,2,8,3]=>0000000=>1111111=>1
[6,8,5,3,1,7,2,4]=>0000000=>1111111=>1
[5,2,6,3,8,7,1,4]=>0000000=>1111111=>1
[8,6,1,7,3,4,2,5]=>0000000=>1111111=>1
[1,8,3,6,7,4,2,5]=>1000000=>0111111=>1
[1,6,3,5,2,7,8,4]=>1000000=>0111111=>1
[1,5,7,3,2,6,4,8]=>1000001=>0111110=>1
[5,1,3,7,2,6,4,8]=>0000001=>1111110=>1
[8,1,6,7,2,4,3,5]=>0000000=>1111111=>1
[6,1,4,8,2,7,3,5]=>0000000=>1111111=>1
[6,2,4,8,3,7,1,5]=>0000000=>1111111=>1
[8,7,2,6,3,5,1,4]=>0000000=>1111111=>1
[8,1,7,6,5,2,3,4]=>0000000=>1111111=>1
[7,1,5,6,8,2,4,3]=>0000000=>1111111=>1
[6,7,1,5,2,4,8,3]=>0000000=>1111111=>1
[7,6,1,5,2,4,3,8]=>0000001=>1111110=>1
[7,1,6,3,5,4,2,8]=>0000001=>1111110=>1
[1,6,7,3,5,4,8,2]=>1000000=>0111111=>1
[1,7,3,5,6,8,4,2]=>1000000=>0111111=>1
[1,7,8,3,6,4,5,2]=>1000000=>0111111=>1
[1,8,7,6,4,5,2,3]=>1000000=>0111111=>1
[8,2,7,4,6,5,1,3]=>0000000=>1111111=>1
[2,8,5,7,6,4,1,3]=>0000000=>1111111=>1
[7,4,5,1,6,8,3,2]=>0000000=>1111111=>1
[4,1,7,5,6,8,3,2]=>0000000=>1111111=>1
[5,6,7,4,3,1,8,2]=>0000000=>1111111=>1
[6,7,8,5,3,1,4,2]=>0000000=>1111111=>1
[1,4,6,2,5,3,7,8]=>1000011=>0111100=>1
[1,6,3,2,5,4,7,8]=>1000011=>0111100=>1
[1,6,8,2,5,4,7,3]=>1000000=>0111111=>1
[1,5,4,2,6,3,7,8]=>1000011=>0111100=>1
[1,2,6,4,3,5,7,8]=>1100011=>0011100=>1
[1,6,8,2,7,5,4,3]=>1000000=>0111111=>1
[1,7,4,3,2,6,8,5]=>1000000=>0111111=>1
[1,5,4,7,2,6,8,3]=>1000000=>0111111=>1
[1,3,7,6,2,8,5,4]=>1000000=>0111111=>1
[1,7,6,2,8,4,3,5]=>1000000=>0111111=>1
[1,5,2,8,4,3,7,6]=>1000000=>0111111=>1
[1,2,8,4,3,6,5,7]=>1100000=>0011111=>1
[1,2,8,5,6,3,4,7]=>1100000=>0011111=>1
[1,7,3,5,2,8,6,4]=>1000000=>0111111=>1
[1,6,7,2,5,8,4,3]=>1000000=>0111111=>1
[1,5,8,3,2,7,4,6]=>1000000=>0111111=>1
[1,4,5,8,2,6,3,7]=>1000000=>0111111=>1
[1,7,6,4,8,2,5,3]=>1000000=>0111111=>1
[1,4,8,6,5,2,7,3]=>1000000=>0111111=>1
[1,3,8,2,6,5,4,7]=>1000000=>0111111=>1
[1,7,6,3,8,2,4,5]=>1000000=>0111111=>1
[1,5,2,7,6,4,8,3]=>1000000=>0111111=>1
[1,2,4,3,8,7,5,6]=>1101000=>0010111=>2
[1,4,3,8,7,2,5,6]=>1000000=>0111111=>1
[1,3,8,6,2,4,5,7]=>1000000=>0111111=>1
[1,3,8,5,4,2,6,7]=>1000000=>0111111=>1
[1,7,2,4,8,6,5,3]=>1000000=>0111111=>1
[1,6,5,3,2,8,7,4]=>1000000=>0111111=>1
[1,3,2,8,7,5,4,6]=>1010000=>0101111=>2
[1,2,8,6,5,4,3,7]=>1100000=>0011111=>1
[8,5,3,2,1,6,4,7]=>0000000=>1111111=>1
[7,6,8,4,1,3,2,5]=>0000000=>1111111=>1
[8,7,6,1,5,2,3,4]=>0000000=>1111111=>1
[8,7,5,1,3,6,2,4]=>0000000=>1111111=>1
[7,4,8,2,6,3,1,5]=>0000000=>1111111=>1
[8,7,3,1,6,4,5,2]=>0000000=>1111111=>1
[8,7,3,1,4,6,5,2]=>0000000=>1111111=>1
[8,7,3,1,6,2,5,4]=>0000000=>1111111=>1
[7,8,2,4,6,5,1,3]=>0000000=>1111111=>1
[8,7,3,2,6,1,5,4]=>0000000=>1111111=>1
[1,8,6,4,2,9,7,5,3]=>10000000=>01111111=>1
[8,4,6,7,5,3,2,1]=>0000000=>1111111=>1
[1,4,8,6,7,5,3,2]=>1000000=>0111111=>1
[7,1,3,6,8,5,4,2]=>0000000=>1111111=>1
[1,8,3,6,7,5,4,2]=>1000000=>0111111=>1
[8,1,7,6,4,5,3,2]=>0000000=>1111111=>1
[1,6,2,7,4,5,3,8]=>1000001=>0111110=>1
[1,8,2,6,4,3,5,7]=>1000000=>0111111=>1
[1,7,2,6,4,3,5,8]=>1000001=>0111110=>1
[1,7,2,5,4,6,3,8]=>1000001=>0111110=>1
[6,7,2,5,8,1,4,3]=>0000000=>1111111=>1
[6,5,7,3,8,1,4,2]=>0000000=>1111111=>1
[6,3,7,4,8,2,5,1]=>0000000=>1111111=>1
[6,3,7,4,8,1,5,2]=>0000000=>1111111=>1
[6,2,7,4,8,1,5,3]=>0000000=>1111111=>1
[7,2,1,5,3,8,6,4]=>0000000=>1111111=>1
[5,8,2,7,6,1,3,4]=>0000000=>1111111=>1
[8,2,3,6,7,1,4,5]=>0000000=>1111111=>1
[4,2,3,1,5,8,6,7]=>0001100=>1110011=>2
[8,6,5,4,3,2,1,7,9]=>00000001=>11111110=>1
[3,1,2,4,5,6,7,8,9,10]=>001111111=>110000000=>1
[9,7,6,5,4,3,2,1,8,10]=>000000001=>111111110=>1
[2,4,8,7,5,3,1,6]=>0000000=>1111111=>1
[4,6,8,7,5,3,1,2]=>0000000=>1111111=>1
[4,8,7,3,1,2,6,5]=>0000000=>1111111=>1
[8,7,3,2,6,5,1,4]=>0000000=>1111111=>1
[2,8,7,1,6,5,3,4]=>0000000=>1111111=>1
[2,8,7,1,4,3,6,5]=>0000000=>1111111=>1
[2,4,3,1,8,7,5,6]=>0001000=>1110111=>2
[4,3,1,2,6,8,7,5]=>0001000=>1110111=>2
[2,6,8,7,5,1,4,3]=>0000000=>1111111=>1
[2,4,8,7,3,6,5,1]=>0000000=>1111111=>1
[8,7,2,4,3,6,5,1]=>0000000=>1111111=>1
[1,9,2,3,4,5,6,8,7]=>10000000=>01111111=>1
[7,1,2,6,4,5,3,8]=>0000001=>1111110=>1
[1,10,2,3,4,5,6,7,9,8]=>100000000=>011111111=>1
[4,7,3,6,5,1,2,8]=>0000001=>1111110=>1
[7,5,4,2,8,3,1,6]=>0000000=>1111111=>1
[8,3,6,1,5,2,4,7]=>0000000=>1111111=>1
[3,1,6,8,5,7,2,4]=>0000000=>1111111=>1
[7,2,8,6,4,3,1,5]=>0000000=>1111111=>1
[6,3,8,7,4,2,1,5]=>0000000=>1111111=>1
[7,6,3,2,8,4,1,5]=>0000000=>1111111=>1
[5,8,3,7,4,2,1,6]=>0000000=>1111111=>1
[4,1,7,3,5,8,6,2]=>0000000=>1111111=>1
[8,4,7,3,5,2,1,6]=>0000000=>1111111=>1
[5,4,8,1,3,2,6,7]=>0000000=>1111111=>1
[4,5,8,2,1,3,6,7]=>0000000=>1111111=>1
[1,8,3,5,7,2,4,6]=>1000000=>0111111=>1
[1,3,4,5,6,7,8,2,9]=>10000001=>01111110=>1
[1,3,4,5,6,7,8,10,2,9]=>100000000=>011111111=>1
[2,1,4,5,6,7,9,3,8]=>01000000=>10111111=>2
[2,1,4,5,6,7,8,3,9]=>01000001=>10111110=>2
[1,3,4,5,6,7,8,9,2,10]=>100000001=>011111110=>1
[1,2,4,7,8,5,3,6]=>1100000=>0011111=>1
[5,1,7,3,6,8,2,4]=>0000000=>1111111=>1
[5,8,6,1,7,3,2,4]=>0000000=>1111111=>1
[2,1,3,8,6,5,4,7]=>0110000=>1001111=>2
[1,3,2,8,6,5,4,7]=>1010000=>0101111=>2
[2,5,7,1,8,4,3,6]=>0000000=>1111111=>1
[3,5,7,1,6,8,2,4]=>0000000=>1111111=>1
[5,4,7,6,8,3,1,2]=>0000000=>1111111=>1
[1,3,9,8,7,6,5,4,2]=>10000000=>01111111=>1
[1,5,8,4,3,7,6,2]=>1000000=>0111111=>1
[8,1,7,2,5,6,4,3]=>0000000=>1111111=>1
[8,1,3,5,2,7,6,4]=>0000000=>1111111=>1
[2,7,1,5,4,8,6,3]=>0000000=>1111111=>1
[8,6,2,4,3,7,5,1]=>0000000=>1111111=>1
[2,4,1,6,7,5,8,3]=>0000000=>1111111=>1
[8,1,4,5,6,3,7,2]=>0000000=>1111111=>1
[8,1,4,5,6,2,7,3]=>0000000=>1111111=>1
[8,1,4,7,6,2,5,3]=>0000000=>1111111=>1
[2,5,1,7,8,6,4,3]=>0000000=>1111111=>1
[3,5,6,2,8,7,4,1]=>0000000=>1111111=>1
[2,4,5,1,7,6,3,8]=>0000001=>1111110=>1
[7,3,1,5,6,4,2,8]=>0000001=>1111110=>1
[8,3,2,5,6,7,1,4]=>0000000=>1111111=>1
[8,4,5,3,7,6,2,1]=>0000000=>1111111=>1
[3,4,5,6,2,8,1,7]=>0000000=>1111111=>1
[3,7,4,2,8,5,1,6]=>0000000=>1111111=>1
[7,3,4,1,6,8,2,5]=>0000000=>1111111=>1
[2,6,3,1,4,7,5,8]=>0000001=>1111110=>1
[7,2,1,6,3,4,8,5]=>0000000=>1111111=>1
[7,3,4,1,6,5,8,2]=>0000000=>1111111=>1
[3,7,4,2,5,8,6,1]=>0000000=>1111111=>1
[2,3,5,1,4,8,7,6]=>0000100=>1111011=>2
[2,7,1,3,6,8,5,4]=>0000000=>1111111=>1
[2,7,1,3,8,4,6,5]=>0000000=>1111111=>1
[3,8,7,1,6,2,5,4]=>0000000=>1111111=>1
[3,8,7,1,4,5,2,6]=>0000000=>1111111=>1
[3,7,4,2,1,8,6,5]=>0000000=>1111111=>1
[4,8,5,7,2,6,3,1]=>0000000=>1111111=>1
[8,4,5,7,3,2,6,1]=>0000000=>1111111=>1
[8,3,7,2,4,1,5,6]=>0000000=>1111111=>1
[8,6,7,2,1,4,3,5]=>0000000=>1111111=>1
[8,3,7,5,1,2,6,4]=>0000000=>1111111=>1
[7,3,4,6,2,1,5,8]=>0000001=>1111110=>1
[3,7,4,6,1,5,2,8]=>0000001=>1111110=>1
[3,4,7,6,1,2,8,5]=>0000000=>1111111=>1
[4,5,8,7,6,1,3,2]=>0000000=>1111111=>1
[8,7,3,5,6,1,4,2]=>0000000=>1111111=>1
[8,5,2,7,6,1,3,4]=>0000000=>1111111=>1
[6,4,7,2,1,5,8,3]=>0000000=>1111111=>1
[8,5,3,1,6,4,7,2]=>0000000=>1111111=>1
[8,6,4,1,7,5,2,3]=>0000000=>1111111=>1
[8,5,3,7,1,6,4,2]=>0000000=>1111111=>1
[7,6,3,8,1,4,2,5]=>0000000=>1111111=>1
[7,4,8,2,6,1,5,3]=>0000000=>1111111=>1
[6,4,7,3,1,5,2,8]=>0000001=>1111110=>1
[8,5,3,1,6,4,2,7]=>0000000=>1111111=>1
[8,7,4,1,2,5,3,6]=>0000000=>1111111=>1
[6,5,3,7,4,2,1,8]=>0000001=>1111110=>1
[1,6,3,8,4,2,5,7]=>1000000=>0111111=>1
[4,7,2,5,3,6,1,8]=>0000001=>1111110=>1
[1,8,3,4,5,2,6,7]=>1000000=>0111111=>1
[1,8,6,4,2,5,3,7]=>1000000=>0111111=>1
[8,2,6,4,1,5,7,3]=>0000000=>1111111=>1
[7,8,3,4,6,1,5,2]=>0000000=>1111111=>1
[4,8,7,5,3,1,6,2]=>0000000=>1111111=>1
[6,1,4,8,3,2,5,7]=>0000000=>1111111=>1
[4,1,8,5,3,2,6,7]=>0000000=>1111111=>1
[8,1,6,4,2,7,3,5]=>0000000=>1111111=>1
[3,1,7,4,2,5,8,6]=>0000000=>1111111=>1
[1,2,7,4,3,5,6,8]=>1100001=>0011110=>1
[6,1,8,5,2,4,3,7]=>0000000=>1111111=>1
[6,8,2,5,1,4,7,3]=>0000000=>1111111=>1
[4,5,2,1,6,8,7,3]=>0000000=>1111111=>1
[7,2,8,6,5,1,4,3]=>0000000=>1111111=>1
[7,4,8,6,1,5,3,2]=>0000000=>1111111=>1
[8,7,2,6,1,4,5,3]=>0000000=>1111111=>1
[1,7,8,6,2,4,3,5]=>1000000=>0111111=>1
[7,6,3,1,2,5,4,8]=>0000001=>1111110=>1
[8,5,3,1,2,4,7,6]=>0000000=>1111111=>1
[8,2,1,6,5,3,4,7]=>0000000=>1111111=>1
[3,8,1,5,6,2,4,7]=>0000000=>1111111=>1
[6,8,4,1,5,2,3,7]=>0000000=>1111111=>1
[3,2,8,1,6,4,5,7]=>0000000=>1111111=>1
[5,2,1,3,7,6,4,8]=>0000001=>1111110=>1
[5,4,1,2,8,3,7,6]=>0000000=>1111111=>1
[5,8,4,1,2,3,7,6]=>0000000=>1111111=>1
[7,1,2,5,3,4,6,8]=>0000001=>1111110=>1
[1,6,7,3,2,8,4,5]=>1000000=>0111111=>1
[1,4,6,2,8,5,3,7]=>1000000=>0111111=>1
[1,5,6,2,8,4,3,7]=>1000000=>0111111=>1
[3,4,8,6,5,7,2,1]=>0000000=>1111111=>1
[1,2,5,7,4,6,8,3]=>1100000=>0011111=>1
[1,2,4,7,6,8,3,5]=>1100000=>0011111=>1
[3,5,8,6,1,7,2,4]=>0000000=>1111111=>1
[3,2,1,6,8,4,7,5]=>0010000=>1101111=>2
[1,6,8,5,4,2,7,3]=>1000000=>0111111=>1
[6,5,8,4,2,1,7,3]=>0000000=>1111111=>1
[1,7,8,6,5,4,2,3]=>1000000=>0111111=>1
[6,8,7,4,5,1,3,2]=>0000000=>1111111=>1
[5,7,1,2,3,8,6,4]=>0000000=>1111111=>1
[7,4,6,2,8,1,5,3]=>0000000=>1111111=>1
[7,6,4,8,2,1,5,3]=>0000000=>1111111=>1
[6,1,8,4,2,3,5,7]=>0000000=>1111111=>1
[7,3,6,2,1,8,5,4]=>0000000=>1111111=>1
[5,6,2,1,8,4,7,3]=>0000000=>1111111=>1
[2,8,1,6,5,7,3,4]=>0000000=>1111111=>1
[5,1,6,4,3,8,7,2]=>0000000=>1111111=>1
[5,4,6,8,1,3,7,2]=>0000000=>1111111=>1
[3,5,2,1,4,6,7,8]=>0000111=>1111000=>1
[1,3,8,7,5,4,6,2]=>1000000=>0111111=>1
[1,2,3,4,5,7,9,8,6]=>11111000=>00000111=>1
[1,2,3,4,6,7,9,8,5]=>11110000=>00001111=>1
[1,2,3,4,6,8,9,7,5]=>11110000=>00001111=>1
[1,2,3,4,6,9,8,7,5]=>11110000=>00001111=>1
[1,2,3,5,6,7,9,8,4]=>11100000=>00011111=>1
[1,2,3,5,6,8,9,7,4]=>11100000=>00011111=>1
[1,2,3,5,6,9,8,7,4]=>11100000=>00011111=>1
[1,2,3,5,7,9,8,6,4]=>11100000=>00011111=>1
[1,2,3,5,9,8,7,6,4]=>11100000=>00011111=>1
[1,2,4,5,7,8,9,6,3]=>11000000=>00111111=>1
[1,2,4,5,7,9,8,6,3]=>11000000=>00111111=>1
[1,2,4,5,9,8,7,6,3]=>11000000=>00111111=>1
[1,2,4,6,9,8,7,5,3]=>11000000=>00111111=>1
[1,2,4,9,8,7,6,5,3]=>11000000=>00111111=>1
[1,3,5,7,9,8,6,4,2]=>10000000=>01111111=>1
[1,3,5,9,8,7,6,4,2]=>10000000=>01111111=>1
[1,2,3,4,5,6,8,10,9,7]=>111111000=>000000111=>1
[1,2,3,4,5,7,8,10,9,6]=>111110000=>000001111=>1
[1,2,3,4,5,7,9,10,8,6]=>111110000=>000001111=>1
[1,2,3,4,5,7,10,9,8,6]=>111110000=>000001111=>1
[1,2,3,4,6,7,8,10,9,5]=>111100000=>000011111=>1
[1,2,3,4,6,7,9,10,8,5]=>111100000=>000011111=>1
[1,2,3,4,6,7,10,9,8,5]=>111100000=>000011111=>1
[1,2,3,4,6,8,10,9,7,5]=>111100000=>000011111=>1
[1,2,3,4,6,10,9,8,7,5]=>111100000=>000011111=>1
[1,2,3,5,6,7,9,10,8,4]=>111000000=>000111111=>1
[1,2,3,5,6,7,10,9,8,4]=>111000000=>000111111=>1
[1,2,3,5,6,8,9,10,7,4]=>111000000=>000111111=>1
[1,2,3,5,6,8,10,9,7,4]=>111000000=>000111111=>1
[1,2,3,5,6,10,9,8,7,4]=>111000000=>000111111=>1
[1,2,3,5,7,9,10,8,6,4]=>111000000=>000111111=>1
[1,2,3,5,7,10,9,8,6,4]=>111000000=>000111111=>1
[1,2,3,5,10,9,8,7,6,4]=>111000000=>000111111=>1
[1,2,4,5,7,8,10,9,6,3]=>110000000=>001111111=>1
[1,2,4,5,7,9,10,8,6,3]=>110000000=>001111111=>1
[1,2,4,5,7,10,9,8,6,3]=>110000000=>001111111=>1
[1,2,4,5,10,9,8,7,6,3]=>110000000=>001111111=>1
[1,2,4,6,10,9,8,7,5,3]=>110000000=>001111111=>1
[1,2,4,10,9,8,7,6,5,3]=>110000000=>001111111=>1
[1,3,5,7,9,10,8,6,4,2]=>100000000=>011111111=>1
[1,3,5,7,10,9,8,6,4,2]=>100000000=>011111111=>1
[1,3,5,10,9,8,7,6,4,2]=>100000000=>011111111=>1
[1,3,10,9,8,7,6,5,4,2]=>100000000=>011111111=>1
[6,7,3,4,8,5,1,2]=>0000000=>1111111=>1
[7,3,1,6,2,8,5,4]=>0000000=>1111111=>1
[4,8,2,5,3,1,6,7]=>0000000=>1111111=>1
[5,1,3,4,8,2,6,7]=>0000000=>1111111=>1
[6,3,4,7,1,8,5,2]=>0000000=>1111111=>1
[7,8,5,1,3,4,6,2]=>0000000=>1111111=>1
[1,8,3,5,6,2,7,4]=>1000000=>0111111=>1
[4,2,5,1,6,8,7,3]=>0000000=>1111111=>1
[5,4,2,7,8,6,1,3]=>0000000=>1111111=>1
[6,8,7,2,1,3,4,5]=>0000000=>1111111=>1
[3,7,6,8,5,2,4,1]=>0000000=>1111111=>1
[1,7,8,5,2,6,3,4]=>1000000=>0111111=>1
[7,6,1,2,5,3,8,4]=>0000000=>1111111=>1
[7,6,2,4,8,1,5,3]=>0000000=>1111111=>1
[1,5,7,3,8,6,2,4]=>1000000=>0111111=>1
[4,3,2,8,7,1,6,5]=>0000000=>1111111=>1
[4,8,3,1,7,6,5,2]=>0000000=>1111111=>1
[5,3,8,7,1,6,4,2]=>0000000=>1111111=>1
[5,8,7,3,1,6,4,2]=>0000000=>1111111=>1
[5,3,8,2,1,7,6,4]=>0000000=>1111111=>1
[3,8,7,2,6,5,1,4]=>0000000=>1111111=>1
[7,4,1,8,6,5,3,2]=>0000000=>1111111=>1
[5,4,2,8,1,7,6,3]=>0000000=>1111111=>1
[5,8,4,2,1,7,6,3]=>0000000=>1111111=>1
[5,8,4,7,1,6,3,2]=>0000000=>1111111=>1
[5,4,8,3,1,7,6,2]=>0000000=>1111111=>1
[8,5,6,1,4,7,2,3]=>0000000=>1111111=>1
[6,7,4,1,2,5,8,3]=>0000000=>1111111=>1
[1,6,7,4,2,5,8,3]=>1000000=>0111111=>1
[3,6,7,5,8,1,2,4]=>0000000=>1111111=>1
[3,8,6,5,7,4,1,2]=>0000000=>1111111=>1
[6,5,8,7,4,2,3,1]=>0000000=>1111111=>1
[6,8,5,7,4,2,1,3]=>0000000=>1111111=>1
[4,7,5,3,6,1,2,8]=>0000001=>1111110=>1
[4,7,5,3,1,6,2,8]=>0000001=>1111110=>1
[2,7,5,3,6,4,8,1]=>0000000=>1111111=>1
[4,7,5,3,8,1,6,2]=>0000000=>1111111=>1
[2,7,5,8,6,3,4,1]=>0000000=>1111111=>1
[2,7,5,6,8,3,4,1]=>0000000=>1111111=>1
[2,7,5,6,8,3,1,4]=>0000000=>1111111=>1
[4,7,5,3,6,8,1,2]=>0000000=>1111111=>1
[8,7,5,3,1,4,6,2]=>0000000=>1111111=>1
[5,7,6,1,8,3,2,4]=>0000000=>1111111=>1
[6,1,7,2,8,4,3,5]=>0000000=>1111111=>1
[6,1,7,3,8,5,2,4]=>0000000=>1111111=>1
[7,1,8,3,2,5,4,6]=>0000000=>1111111=>1
[2,4,6,7,8,5,1,3]=>0000000=>1111111=>1
[2,4,6,7,8,3,1,5]=>0000000=>1111111=>1
[4,6,5,8,7,3,1,2]=>0000000=>1111111=>1
[4,5,1,2,8,7,3,6]=>0000000=>1111111=>1
[5,8,7,1,6,2,4,3]=>0000000=>1111111=>1
[8,4,5,1,7,6,2,3]=>0000000=>1111111=>1
[6,3,1,4,8,2,7,5]=>0000000=>1111111=>1
[8,5,6,1,7,2,4,3]=>0000000=>1111111=>1
[7,5,6,1,3,8,4,2]=>0000000=>1111111=>1
[5,7,6,1,3,8,4,2]=>0000000=>1111111=>1
[6,7,1,4,2,8,5,3]=>0000000=>1111111=>1
[2,1,6,4,8,3,7,5]=>0100000=>1011111=>2
[7,4,5,1,3,8,6,2]=>0000000=>1111111=>1
[1,5,7,8,4,2,3,6]=>1000000=>0111111=>1
[1,3,6,4,2,5,7,8]=>1000011=>0111100=>1
[1,4,5,7,8,3,6,2]=>1000000=>0111111=>1
[1,5,7,8,3,6,2,4]=>1000000=>0111111=>1
[1,5,7,8,2,4,3,6]=>1000000=>0111111=>1
[6,8,4,7,3,2,1,5]=>0000000=>1111111=>1
[6,8,5,4,2,7,1,3]=>0000000=>1111111=>1
[1,8,4,6,3,2,7,5]=>1000000=>0111111=>1
[3,5,6,1,4,2,7,8]=>0000011=>1111100=>1
[1,6,3,8,4,2,7,5]=>1000000=>0111111=>1
[2,6,5,7,8,3,1,4]=>0000000=>1111111=>1
[4,1,8,2,6,7,5,3]=>0000000=>1111111=>1
[3,6,7,8,2,1,4,5]=>0000000=>1111111=>1
[2,5,7,1,6,3,4,8]=>0000001=>1111110=>1
[4,2,8,3,6,5,1,7]=>0000000=>1111111=>1
[6,3,8,7,2,4,5,1]=>0000000=>1111111=>1
[2,4,5,7,1,8,6,3]=>0000000=>1111111=>1
[8,1,6,2,3,4,7,5]=>0000000=>1111111=>1
[6,1,4,2,5,7,8,3]=>0000000=>1111111=>1
[6,5,1,2,3,7,8,9,4]=>00000000=>11111111=>1
[1,8,3,4,5,2,7,6]=>1000000=>0111111=>1
[1,8,3,6,4,7,2,5]=>1000000=>0111111=>1
[1,4,7,2,5,6,3,8]=>1000001=>0111110=>1
[7,3,5,8,2,6,1,4]=>0000000=>1111111=>1
[3,4,8,6,7,2,1,5]=>0000000=>1111111=>1
[3,4,8,2,5,1,7,6]=>0000000=>1111111=>1
[1,7,2,5,8,4,3,6]=>1000000=>0111111=>1
[1,4,6,7,8,3,5,2]=>1000000=>0111111=>1
[4,1,5,3,6,8,7,2]=>0000000=>1111111=>1
[5,8,7,4,6,2,3,1]=>0000000=>1111111=>1
[6,4,8,1,5,7,3,2]=>0000000=>1111111=>1
[1,6,8,3,5,2,7,4]=>1000000=>0111111=>1
[7,2,1,8,6,4,5,3]=>0000000=>1111111=>1
[2,4,7,8,5,6,1,3]=>0000000=>1111111=>1
[2,8,5,4,1,3,7,6]=>0000000=>1111111=>1
[5,4,6,3,1,7,2,8]=>0000001=>1111110=>1
[1,5,6,8,7,3,2,4]=>1000000=>0111111=>1
[1,4,8,3,6,5,2,7]=>1000000=>0111111=>1
[1,2,8,6,4,3,7,5]=>1100000=>0011111=>1
[1,8,4,7,6,2,3,5]=>1000000=>0111111=>1
[6,5,1,8,7,2,4,3]=>0000000=>1111111=>1
[6,1,2,8,7,3,4,5]=>0000000=>1111111=>1
[6,5,1,8,7,4,3,2]=>0000000=>1111111=>1
[7,5,1,8,6,4,3,2]=>0000000=>1111111=>1
[8,5,1,7,6,4,3,2]=>0000000=>1111111=>1
[8,5,3,7,6,1,4,2]=>0000000=>1111111=>1
[3,8,7,6,1,5,4,2]=>0000000=>1111111=>1
[8,3,7,5,4,1,6,2]=>0000000=>1111111=>1
[1,5,8,6,2,7,4,3]=>1000000=>0111111=>1
[3,1,8,5,7,2,6,4]=>0000000=>1111111=>1
[8,5,2,6,1,4,7,3]=>0000000=>1111111=>1
[2,7,5,8,1,4,6,3]=>0000000=>1111111=>1
[3,2,6,7,1,8,5,4]=>0000000=>1111111=>1
[3,4,6,7,8,2,1,5]=>0000000=>1111111=>1
[6,2,7,4,8,5,1,3]=>0000000=>1111111=>1
[6,7,1,3,8,5,4,2]=>0000000=>1111111=>1
[1,2,6,7,8,5,3,4]=>1100000=>0011111=>1
[1,6,7,4,8,3,2,5]=>1000000=>0111111=>1
[1,4,6,7,8,3,2,5]=>1000000=>0111111=>1
[3,5,7,9,1,2,4,6,8,10]=>000000001=>111111110=>1
[4,1,2,3,5,6,7,8,9,10]=>000111111=>111000000=>1
[5,1,2,3,4,6,7,8,9,10]=>000011111=>111100000=>1
[8,1,2,3,4,5,6,7,9,10]=>000000011=>111111100=>1
[7,1,2,3,4,5,6,8,9,10]=>000000111=>111111000=>1
[6,1,2,3,4,5,7,8,9,10]=>000001111=>111110000=>1
[3,2,6,4,8,7,5,1]=>0000000=>1111111=>1
[4,7,2,8,6,5,1,3]=>0000000=>1111111=>1
[4,7,1,8,6,5,3,2]=>0000000=>1111111=>1
[2,7,4,8,3,6,1,5]=>0000000=>1111111=>1
[4,7,3,8,6,1,5,2]=>0000000=>1111111=>1
[4,3,6,8,7,2,5,1]=>0000000=>1111111=>1
[4,3,8,2,5,7,6,1]=>0000000=>1111111=>1
[4,1,2,6,8,7,5,3]=>0000000=>1111111=>1
[3,1,6,4,8,7,2,5]=>0000000=>1111111=>1
[4,1,6,8,7,5,2,3]=>0000000=>1111111=>1
[3,8,1,4,5,7,2,6]=>0000000=>1111111=>1
[3,8,1,4,2,5,7,6]=>0000000=>1111111=>1
[4,1,8,3,5,2,7,6]=>0000000=>1111111=>1
[3,8,1,2,5,4,7,6]=>0000000=>1111111=>1
[4,2,3,6,8,7,1,5]=>0000000=>1111111=>1
[4,2,8,3,5,1,7,6]=>0000000=>1111111=>1
[4,2,8,3,5,7,6,1]=>0000000=>1111111=>1
[3,8,2,4,5,7,6,1]=>0000000=>1111111=>1
[3,8,2,5,1,4,7,6]=>0000000=>1111111=>1
[4,2,8,5,7,1,3,6]=>0000000=>1111111=>1
[3,8,1,5,2,4,7,6]=>0000000=>1111111=>1
[7,3,2,1,4,6,5,8]=>0000001=>1111110=>1
[2,7,1,3,5,6,8,4]=>0000000=>1111111=>1
[2,3,6,1,5,8,7,4]=>0000000=>1111111=>1
[4,8,5,3,2,6,7,1]=>0000000=>1111111=>1
[6,4,1,8,5,2,7,3]=>0000000=>1111111=>1
[2,6,1,8,5,4,7,3]=>0000000=>1111111=>1
[3,7,6,4,8,5,2,1]=>0000000=>1111111=>1
[3,1,6,8,5,4,7,2]=>0000000=>1111111=>1
[2,3,5,8,4,6,7,1]=>0000000=>1111111=>1
[6,2,1,7,8,5,4,3]=>0000000=>1111111=>1
[7,5,6,1,2,3,8,4]=>0000000=>1111111=>1
[1,5,7,6,3,2,8,4]=>1000000=>0111111=>1
[8,4,6,2,3,1,5,7]=>0000000=>1111111=>1
[7,5,2,1,4,3,8,6]=>0000000=>1111111=>1
[3,1,7,8,5,4,2,6]=>0000000=>1111111=>1
[7,6,4,8,3,1,2,5]=>0000000=>1111111=>1
[7,4,8,5,6,1,2,3]=>0000000=>1111111=>1
[6,2,8,5,1,3,4,7]=>0000000=>1111111=>1
[3,2,7,8,6,1,4,5]=>0000000=>1111111=>1
[6,8,2,5,1,3,7,4]=>0000000=>1111111=>1
[6,7,4,2,1,5,3,8]=>0000001=>1111110=>1
[5,7,4,1,3,6,2,8]=>0000001=>1111110=>1
[4,2,7,5,1,8,3,6]=>0000000=>1111111=>1
[4,1,6,5,3,8,2,7]=>0000000=>1111111=>1
[1,5,4,6,3,8,2,7]=>1000000=>0111111=>1
[1,8,6,4,7,3,2,5]=>1000000=>0111111=>1
[4,7,1,8,6,3,5,2]=>0000000=>1111111=>1
[5,4,8,1,7,3,6,2]=>0000000=>1111111=>1
[4,3,8,6,2,1,7,5]=>0000000=>1111111=>1
[8,3,6,2,4,1,7,5]=>0000000=>1111111=>1
[7,8,3,2,4,6,5,1]=>0000000=>1111111=>1
[7,2,8,5,3,1,6,4]=>0000000=>1111111=>1
[2,5,4,8,7,3,6,1]=>0000000=>1111111=>1
[6,4,2,8,7,3,1,5]=>0000000=>1111111=>1
[3,6,8,1,7,4,2,5]=>0000000=>1111111=>1
[7,8,6,3,1,4,5,2]=>0000000=>1111111=>1
[3,8,6,1,7,5,2,4]=>0000000=>1111111=>1
[2,7,5,4,8,3,1,6]=>0000000=>1111111=>1
[6,8,7,5,2,1,3,4]=>0000000=>1111111=>1
[7,6,2,8,5,1,3,4]=>0000000=>1111111=>1
[1,5,7,6,2,8,4,3]=>1000000=>0111111=>1
[1,6,5,2,7,8,4,3]=>1000000=>0111111=>1
[2,7,8,5,6,1,4,3]=>0000000=>1111111=>1
[6,7,8,4,2,1,5,3]=>0000000=>1111111=>1
[8,6,4,1,2,5,7,3]=>0000000=>1111111=>1
[6,1,4,7,2,5,8,3]=>0000000=>1111111=>1
[6,7,8,3,5,4,2,1]=>0000000=>1111111=>1
[6,7,8,2,1,5,3,4]=>0000000=>1111111=>1
[5,6,3,2,7,4,1,8]=>0000001=>1111110=>1
[2,6,4,3,7,5,8,1]=>0000000=>1111111=>1
[7,6,2,3,5,4,8,1]=>0000000=>1111111=>1
[8,5,2,4,3,6,1,7]=>0000000=>1111111=>1
[7,4,8,2,1,5,6,3]=>0000000=>1111111=>1
[8,3,7,1,6,4,2,5]=>0000000=>1111111=>1
[8,2,1,7,6,5,3,4]=>0000000=>1111111=>1
[5,7,4,1,6,8,2,3]=>0000000=>1111111=>1
[6,5,1,2,8,3,4,7]=>0000000=>1111111=>1
[5,6,8,1,3,7,2,4]=>0000000=>1111111=>1
[3,7,4,8,6,1,2,5]=>0000000=>1111111=>1
[1,6,8,5,3,2,4,7]=>1000000=>0111111=>1
[5,8,1,6,7,4,2,3]=>0000000=>1111111=>1
[7,2,8,4,6,1,3,5]=>0000000=>1111111=>1
[6,2,7,4,3,8,1,5]=>0000000=>1111111=>1
[1,7,8,4,6,2,3,5]=>1000000=>0111111=>1
[8,1,6,5,4,7,2,3]=>0000000=>1111111=>1
[4,1,6,8,7,3,2,5]=>0000000=>1111111=>1
[5,1,4,6,7,3,8,2]=>0000000=>1111111=>1
[7,1,3,4,6,2,8,5]=>0000000=>1111111=>1
[3,4,1,6,2,5,8,7,9]=>00000101=>11111010=>2
[3,4,1,2,6,5,8,7,9]=>00010101=>11101010=>3
[3,4,1,6,2,5,8,7,10,9]=>000001010=>111110101=>3
[3,5,1,6,2,4,8,7,9]=>00000101=>11111010=>2
[2,5,1,6,3,4,8,7,9]=>00000101=>11111010=>2
[3,5,1,2,6,4,8,7,9]=>00000101=>11111010=>2
[2,5,1,3,6,4,8,7,9]=>00000101=>11111010=>2
[1,4,7,5,8,6,3,2]=>1000000=>0111111=>1
[1,8,6,3,5,2,7,4]=>1000000=>0111111=>1
[4,7,1,6,8,3,5,2]=>0000000=>1111111=>1
[3,6,5,2,8,4,1,7]=>0000000=>1111111=>1
[7,1,8,4,2,5,3,6]=>0000000=>1111111=>1
[1,4,8,7,5,2,6,3]=>1000000=>0111111=>1
[1,5,6,4,2,3,7,8]=>1000011=>0111100=>1
[5,7,3,6,8,4,2,1]=>0000000=>1111111=>1
[5,8,7,4,2,1,3,6]=>0000000=>1111111=>1
[1,8,7,3,2,5,4,6]=>1000000=>0111111=>1
[1,2,5,4,8,7,3,6]=>1100000=>0011111=>1
[1,2,4,8,6,3,5,7]=>1100000=>0011111=>1
[1,5,2,4,7,3,8,6]=>1000000=>0111111=>1
[1,2,7,6,8,4,3,5]=>1100000=>0011111=>1
[1,6,3,2,5,7,8,4]=>1000000=>0111111=>1
[1,7,3,4,2,6,8,5]=>1000000=>0111111=>1
[1,6,3,5,8,4,2,7]=>1000000=>0111111=>1
[1,5,3,2,7,8,4,6]=>1000000=>0111111=>1
[1,7,6,4,3,8,5,2]=>1000000=>0111111=>1
[1,8,5,7,6,3,2,4]=>1000000=>0111111=>1
[1,6,3,5,7,8,4,2]=>1000000=>0111111=>1
[6,8,5,2,1,7,4,3]=>0000000=>1111111=>1
[1,2,6,8,4,3,7,5]=>1100000=>0011111=>1
[5,3,7,2,6,4,1,8]=>0000001=>1111110=>1
[7,6,2,5,3,4,1,8]=>0000001=>1111110=>1
[7,6,2,4,5,3,1,8]=>0000001=>1111110=>1
[7,6,2,4,3,5,1,8]=>0000001=>1111110=>1
[7,6,2,3,5,4,1,8]=>0000001=>1111110=>1
[8,4,2,7,1,6,3,5]=>0000000=>1111111=>1
[8,7,6,1,5,3,2,4]=>0000000=>1111111=>1
[8,7,6,1,4,3,5,2]=>0000000=>1111111=>1
[8,7,6,1,3,5,4,2]=>0000000=>1111111=>1
[8,7,6,1,5,4,2,3]=>0000000=>1111111=>1
[8,6,2,7,1,5,3,4]=>0000000=>1111111=>1
[8,7,6,1,2,5,3,4]=>0000000=>1111111=>1
[8,7,6,1,2,5,4,3]=>0000000=>1111111=>1
[8,7,6,1,4,2,5,3]=>0000000=>1111111=>1
[6,5,7,3,8,4,1,2]=>0000000=>1111111=>1
[5,7,1,3,4,2,8,6]=>0000000=>1111111=>1
[1,5,3,7,8,4,6,2]=>1000000=>0111111=>1
[1,3,7,5,8,6,2,4]=>1000000=>0111111=>1
[5,3,7,6,8,1,2,4]=>0000000=>1111111=>1
[3,1,2,7,5,8,4,6]=>0010000=>1101111=>2
[6,1,4,8,5,2,7,3]=>0000000=>1111111=>1
[3,4,5,8,1,6,7,2]=>0000000=>1111111=>1
[3,1,6,8,5,2,7,4]=>0000000=>1111111=>1
[5,4,8,1,2,6,7,3]=>0000000=>1111111=>1
[5,2,3,8,1,7,4,6]=>0000000=>1111111=>1
[1,5,3,8,2,4,6,7]=>1000000=>0111111=>1
[8,6,2,7,5,1,4,3]=>0000000=>1111111=>1
[2,7,1,8,6,3,5,4]=>0000000=>1111111=>1
[5,7,6,1,3,2,8,4]=>0000000=>1111111=>1
[3,5,4,6,1,7,8,2]=>0000000=>1111111=>1
[8,1,5,4,6,3,7,2]=>0000000=>1111111=>1
[2,7,1,5,6,4,3,8]=>0000001=>1111110=>1
[8,4,6,3,1,7,2,5]=>0000000=>1111111=>1
[8,4,2,5,6,3,7,1]=>0000000=>1111111=>1
[5,4,7,2,8,6,1,3]=>0000000=>1111111=>1
[3,5,6,4,1,7,2,8]=>0000001=>1111110=>1
[2,5,6,1,7,4,3,8]=>0000001=>1111110=>1
[2,7,1,8,6,5,4,3]=>0000000=>1111111=>1
[3,7,6,1,8,5,4,2]=>0000000=>1111111=>1
[8,6,4,2,1,3,5,7,9]=>00000001=>11111110=>1
[8,6,2,1,4,3,5,7,9]=>00000001=>11111110=>1
[8,4,2,1,6,3,5,7,9]=>00000001=>11111110=>1
[6,4,2,1,8,3,5,7,9]=>00000001=>11111110=>1
[8,6,4,2,9,1,3,5,7]=>00000000=>11111111=>1
[9,6,4,2,7,1,3,5,8]=>00000000=>11111111=>1
[9,7,4,2,5,1,3,6,8]=>00000000=>11111111=>1
[9,7,5,2,3,1,4,6,8]=>00000000=>11111111=>1
[9,7,5,3,1,2,4,6,8]=>00000000=>11111111=>1
[10,8,6,4,2,1,3,5,7,9]=>000000000=>111111111=>1
[10,8,6,2,1,4,3,5,7,9]=>000000000=>111111111=>1
[8,2,1,4,3,6,5,7,9]=>00000001=>11111110=>1
[10,8,4,2,1,6,3,5,7,9]=>000000000=>111111111=>1
[4,2,1,6,3,5,8,7,9]=>00000101=>11111010=>2
[10,6,4,2,1,8,3,5,7,9]=>000000000=>111111111=>1
[6,4,2,1,8,3,5,9,7]=>00000000=>11111111=>1
[8,6,4,2,1,10,3,5,7,9]=>000000000=>111111111=>1
[6,4,2,7,1,3,5,8,9]=>00000011=>11111100=>1
[8,6,4,2,9,1,3,5,7,10]=>000000001=>111111110=>1
[6,2,8,3,1,4,5,7]=>0000000=>1111111=>1
[8,9,4,2,5,1,3,6,7]=>00000000=>11111111=>1
[9,6,4,2,7,1,3,5,8,10]=>000000001=>111111110=>1
[2,7,8,3,1,4,5,6]=>0000000=>1111111=>1
[9,6,7,2,3,1,4,5,8]=>00000000=>11111111=>1
[9,7,4,2,5,1,3,6,8,10]=>000000001=>111111110=>1
[9,7,4,5,1,2,3,6,8]=>00000000=>11111111=>1
[9,7,5,2,3,1,4,6,8,10]=>000000001=>111111110=>1
[9,7,5,3,1,2,4,6,8,10]=>000000001=>111111110=>1
[1,8,5,3,2,6,7,4]=>1000000=>0111111=>1
[1,5,6,7,3,2,8,4]=>1000000=>0111111=>1
[1,7,5,2,3,4,8,6]=>1000000=>0111111=>1
[1,7,5,2,4,8,6,3]=>1000000=>0111111=>1
[1,4,8,6,2,3,5,7]=>1000000=>0111111=>1
[1,2,8,6,3,5,7,4]=>1100000=>0011111=>1
[1,8,6,7,4,2,3,5]=>1000000=>0111111=>1
[1,6,7,8,4,2,3,5]=>1000000=>0111111=>1
[1,7,8,4,2,3,5,6]=>1000000=>0111111=>1
[1,7,3,5,6,2,8,4]=>1000000=>0111111=>1
[1,7,8,3,4,2,5,6]=>1000000=>0111111=>1
[1,2,3,7,8,5,4,6]=>1110000=>0001111=>1
[1,2,7,4,6,3,8,5]=>1100000=>0011111=>1
[1,7,8,4,5,2,3,6]=>1000000=>0111111=>1
[1,2,8,4,5,6,3,7]=>1100000=>0011111=>1
[5,8,2,7,3,4,1,6]=>0000000=>1111111=>1
[6,8,7,2,3,4,1,5]=>0000000=>1111111=>1
[5,3,8,1,6,7,4,2]=>0000000=>1111111=>1
[5,1,8,3,6,7,4,2]=>0000000=>1111111=>1
[3,1,8,4,6,2,7,5]=>0000000=>1111111=>1
[8,4,1,6,5,2,3,7]=>0000000=>1111111=>1
[1,8,7,6,4,3,5,2]=>1000000=>0111111=>1
[6,8,7,3,2,4,1,5]=>0000000=>1111111=>1
[2,3,7,5,6,8,4,1]=>0000000=>1111111=>1
[3,2,4,7,5,8,1,6]=>0000000=>1111111=>1
[2,8,7,6,4,5,1,3]=>0000000=>1111111=>1
[4,8,7,6,3,1,5,2]=>0000000=>1111111=>1
[3,5,2,4,7,6,8,1]=>0000000=>1111111=>1
[5,3,2,7,6,4,8,1]=>0000000=>1111111=>1
[3,5,2,7,4,6,8,1]=>0000000=>1111111=>1
[3,4,7,6,8,2,5,1]=>0000000=>1111111=>1
[5,2,8,4,1,3,6,7]=>0000000=>1111111=>1
[3,8,5,2,1,4,6,7]=>0000000=>1111111=>1
[7,6,4,1,8,2,5,3]=>0000000=>1111111=>1
[7,5,4,2,1,6,3,8]=>0000001=>1111110=>1
[8,1,6,7,3,4,2,5]=>0000000=>1111111=>1
[8,2,1,6,7,4,3,5]=>0000000=>1111111=>1
[5,2,8,6,3,7,1,4]=>0000000=>1111111=>1
[7,6,8,1,2,5,4,3]=>0000000=>1111111=>1
[1,2,9,3,4,5,6,8,7]=>11000000=>00111111=>1
[1,2,3,8,4,5,9,6,7]=>11100000=>00011111=>1
[1,2,3,4,9,5,6,8,7]=>11110000=>00001111=>1
[2,1,3,4,8,5,7,6]=>0111000=>1000111=>2
[1,2,3,4,5,9,6,8,7]=>11111000=>00000111=>1
[7,1,2,3,4,8,5,9,6]=>00000000=>11111111=>1
[6,9,1,2,3,4,8,5,7]=>00000000=>11111111=>1
[1,2,10,3,4,5,6,7,9,8]=>110000000=>001111111=>1
[5,1,9,2,3,4,8,6,7]=>00000000=>11111111=>1
[1,2,3,9,4,5,6,10,7,8]=>111000000=>000111111=>1
[4,1,2,3,5,8,6,9,7]=>00011000=>11100111=>2
[1,2,3,4,10,5,6,7,9,8]=>111100000=>000011111=>1
[3,1,2,4,9,5,8,6,7]=>00110000=>11001111=>2
[1,2,3,4,5,10,6,7,9,8]=>111110000=>000001111=>1
[2,1,3,4,5,9,6,8,7]=>01111000=>10000111=>2
[1,2,3,4,5,6,9,10,7,8]=>111111000=>000000111=>1
[8,1,2,3,4,5,9,6,10,7]=>000000000=>111111111=>1
[1,11,2,3,4,5,6,7,8,10,9]=>1000000000=>0111111111=>1
[1,7,2,3,4,5,9,8,6]=>10000000=>01111111=>1
[7,10,1,2,3,4,5,9,6,8]=>000000000=>111111111=>1
[1,6,2,3,4,5,9,8,7]=>10000100=>01111011=>2
[6,1,2,3,7,4,8,9,5]=>00000000=>11111111=>1
[6,1,10,2,3,4,5,9,7,8]=>000000000=>111111111=>1
[1,2,3,10,4,5,6,7,11,8,9]=>1110000000=>0001111111=>1
[5,7,1,2,6,8,3,4]=>0000000=>1111111=>1
[1,2,3,8,5,4,6,9,7]=>11100000=>00011111=>1
[5,9,1,2,6,3,4,8,7]=>00000000=>11111111=>1
[5,1,2,3,4,6,9,7,10,8]=>000011000=>111100111=>2
[1,2,3,4,11,5,6,7,8,10,9]=>1111000000=>0000111111=>1
[1,4,2,3,5,6,9,8,7]=>10011100=>01100011=>2
[1,5,2,3,6,8,7,4]=>1000000=>0111111=>1
[4,1,9,5,2,3,6,8,7]=>00000000=>11111111=>1
[4,1,2,3,10,5,6,9,7,8]=>000100000=>111011111=>2
[1,2,3,4,5,11,6,7,8,10,9]=>1111100000=>0000011111=>1
[1,3,2,4,5,6,9,8,7]=>10111100=>01000011=>2
[3,4,1,2,5,6,8,9,7]=>00011100=>11100011=>2
[3,1,2,4,5,10,6,9,7,8]=>001110000=>110001111=>2
[1,2,3,4,5,6,10,7,11,8,9]=>1111110000=>0000001111=>1
[2,3,1,4,9,5,6,8,7]=>00110000=>11001111=>2
[1,2,3,4,5,6,7,11,8,10,9]=>1111111000=>0000000111=>1
[1,2,3,4,5,6,7,8,11,10,9]=>1111111100=>0000000011=>1
[8,6,4,7,5,1,2,3]=>0000000=>1111111=>1
[8,6,4,1,2,5,3,7]=>0000000=>1111111=>1
[2,8,4,3,1,6,5,7]=>0000000=>1111111=>1
[8,3,5,6,1,4,7,2]=>0000000=>1111111=>1
[6,8,7,3,5,4,2,1]=>0000000=>1111111=>1
[3,1,2,8,5,7,4,6]=>0010000=>1101111=>2
[2,1,4,7,6,3,5,8]=>0100001=>1011110=>2
[7,2,4,5,3,8,1,6]=>0000000=>1111111=>1
[8,4,2,5,6,7,3,1]=>0000000=>1111111=>1
[5,4,1,6,3,7,8,2]=>0000000=>1111111=>1
[4,5,1,3,6,7,8,2]=>0000000=>1111111=>1
[5,1,7,6,3,4,8,2]=>0000000=>1111111=>1
[6,1,7,5,4,8,2,3]=>0000000=>1111111=>1
[3,7,2,1,6,8,4,5]=>0000000=>1111111=>1
[1,5,8,2,4,7,6,3]=>1000000=>0111111=>1
[5,8,1,6,4,7,3,2]=>0000000=>1111111=>1
[3,8,6,5,7,2,4,1]=>0000000=>1111111=>1
[6,8,1,4,7,3,5,2]=>0000000=>1111111=>1
[1,6,8,2,7,4,5,3]=>1000000=>0111111=>1
[5,7,2,1,8,4,3,6]=>0000000=>1111111=>1
[5,7,1,6,8,3,2,4]=>0000000=>1111111=>1
[5,6,2,1,8,3,4,7]=>0000000=>1111111=>1
[6,4,1,7,3,8,2,5]=>0000000=>1111111=>1
[8,2,5,6,7,1,4,3]=>0000000=>1111111=>1
[7,2,4,6,8,3,1,5]=>0000000=>1111111=>1
[6,2,4,7,8,1,3,5]=>0000000=>1111111=>1
[6,1,4,3,2,8,5,7]=>0000000=>1111111=>1
[2,7,4,8,6,1,5,3]=>0000000=>1111111=>1
[2,4,8,6,5,7,3,1]=>0000000=>1111111=>1
[3,7,8,6,4,2,5,1]=>0000000=>1111111=>1
[6,2,8,4,7,5,1,3]=>0000000=>1111111=>1
[4,2,8,5,1,6,3,7]=>0000000=>1111111=>1
[2,3,8,4,1,6,5,7]=>0000000=>1111111=>1
[4,5,7,3,1,6,2,8]=>0000001=>1111110=>1
[5,1,8,7,4,6,3,2]=>0000000=>1111111=>1
[3,5,7,6,1,8,4,2]=>0000000=>1111111=>1
[3,5,7,6,2,8,4,1]=>0000000=>1111111=>1
[6,1,4,3,8,7,5,2]=>0000000=>1111111=>1
[6,3,1,8,7,4,2,5]=>0000000=>1111111=>1
[5,3,6,2,8,7,4,1]=>0000000=>1111111=>1
[6,2,3,8,7,5,4,1]=>0000000=>1111111=>1
[4,1,3,5,8,7,6,2]=>0000000=>1111111=>1
[2,7,8,3,4,1,5,6]=>0000000=>1111111=>1
[6,8,2,7,4,1,5,3]=>0000000=>1111111=>1
[5,8,3,4,6,1,7,2]=>0000000=>1111111=>1
[5,3,8,2,7,1,6,4]=>0000000=>1111111=>1
[3,7,1,5,2,6,8,4]=>0000000=>1111111=>1
[6,7,1,8,3,4,5,2]=>0000000=>1111111=>1
[3,8,5,2,6,7,1,4]=>0000000=>1111111=>1
[7,1,8,4,6,3,5,2]=>0000000=>1111111=>1
[3,8,6,4,7,1,5,2]=>0000000=>1111111=>1
[3,7,1,4,8,6,5,2]=>0000000=>1111111=>1
[2,3,7,6,5,8,1,4]=>0000000=>1111111=>1
[4,3,5,6,7,8,9,1,2]=>00000000=>11111111=>1
[6,7,8,5,4,3,2,1,9]=>00000001=>11111110=>1
[6,5,7,8,4,3,2,1,9]=>00000001=>11111110=>1
[6,5,4,7,8,3,2,1,9]=>00000001=>11111110=>1
[6,5,4,3,7,8,2,1,9]=>00000001=>11111110=>1
[6,5,4,3,2,7,8,1,9]=>00000001=>11111110=>1
[7,8,9,5,4,3,2,1,6]=>00000000=>11111111=>1
[7,8,9,6,5,4,3,2,1,10]=>000000001=>111111110=>1
[6,7,8,9,4,3,2,1,5]=>00000000=>11111111=>1
[7,6,8,9,5,4,3,2,1,10]=>000000001=>111111110=>1
[6,5,7,8,9,3,2,1,4]=>00000000=>11111111=>1
[7,6,5,8,9,4,3,2,1,10]=>000000001=>111111110=>1
[6,5,4,7,8,9,2,1,3]=>00000000=>11111111=>1
[7,6,5,4,8,9,3,2,1,10]=>000000001=>111111110=>1
[6,5,4,3,7,8,9,1,2]=>00000000=>11111111=>1
[7,6,5,4,3,8,9,2,1,10]=>000000001=>111111110=>1
[6,5,4,3,2,7,8,9,1]=>00000000=>11111111=>1
[7,6,5,4,3,2,8,9,1,10]=>000000001=>111111110=>1
[3,5,7,6,8,2,1,4]=>0000000=>1111111=>1
[4,2,5,3,7,6,1,8]=>0000001=>1111110=>1
[6,2,4,3,7,5,1,8]=>0000001=>1111110=>1
[1,3,6,4,7,5,2,8]=>1000001=>0111110=>1
[8,2,5,3,6,4,1,7]=>0000000=>1111111=>1
[7,2,5,3,6,4,1,8]=>0000001=>1111110=>1
[6,2,5,3,7,4,1,8]=>0000001=>1111110=>1
[4,2,6,3,7,5,1,8]=>0000001=>1111110=>1
[5,2,7,3,6,4,1,8]=>0000001=>1111110=>1
[7,3,6,2,5,4,1,8]=>0000001=>1111110=>1
[6,3,8,2,5,4,1,7]=>0000000=>1111111=>1
[7,3,1,4,6,5,2,8]=>0000001=>1111110=>1
[8,3,7,2,5,4,1,6]=>0000000=>1111111=>1
[5,2,8,3,6,4,1,7]=>0000000=>1111111=>1
[3,2,8,4,6,5,1,7]=>0000000=>1111111=>1
[1,4,7,3,6,5,2,8]=>1000001=>0111110=>1
[8,2,5,4,1,6,3,7]=>0000000=>1111111=>1
[8,2,6,4,1,5,3,7]=>0000000=>1111111=>1
[1,4,8,3,7,5,2,6]=>1000000=>0111111=>1
[6,2,1,4,8,5,3,7]=>0000000=>1111111=>1
[5,2,1,4,8,6,3,7]=>0000000=>1111111=>1
[3,2,1,5,8,6,4,7]=>0010000=>1101111=>2
[4,2,8,3,7,5,1,6]=>0000000=>1111111=>1
[5,2,8,3,7,4,1,6]=>0000000=>1111111=>1
[8,3,7,2,6,4,1,5]=>0000000=>1111111=>1
[7,3,1,4,8,5,2,6]=>0000000=>1111111=>1
[1,3,7,4,8,5,2,6]=>1000000=>0111111=>1
[8,2,6,3,7,4,1,5]=>0000000=>1111111=>1
[7,2,6,3,8,4,1,5]=>0000000=>1111111=>1
[5,2,7,3,8,4,1,6]=>0000000=>1111111=>1
[3,2,7,4,8,5,1,6]=>0000000=>1111111=>1
[5,2,6,3,8,4,1,7]=>0000000=>1111111=>1
[6,2,5,3,8,4,1,7]=>0000000=>1111111=>1
[7,2,5,3,8,4,1,6]=>0000000=>1111111=>1
[8,2,5,3,7,4,1,6]=>0000000=>1111111=>1
[1,3,6,4,8,5,2,7]=>1000000=>0111111=>1
[1,3,5,4,8,6,2,7]=>1000000=>0111111=>1
[8,2,4,3,7,5,1,6]=>0000000=>1111111=>1
[7,2,4,3,8,5,1,6]=>0000000=>1111111=>1
[6,2,4,3,8,5,1,7]=>0000000=>1111111=>1
[5,2,4,3,8,6,1,7]=>0000000=>1111111=>1
[4,2,5,3,8,6,1,7]=>0000000=>1111111=>1
[4,2,5,3,1,7,6,8]=>0000101=>1111010=>2
[6,2,4,3,1,7,5,8]=>0000001=>1111110=>1
[7,2,4,3,1,6,5,8]=>0000001=>1111110=>1
[8,5,1,3,6,4,2,7]=>0000000=>1111111=>1
[8,4,1,3,6,5,2,7]=>0000000=>1111111=>1
[1,5,2,4,7,6,3,8]=>1000001=>0111110=>1
[7,2,5,3,1,6,4,8]=>0000001=>1111110=>1
[6,2,5,3,1,7,4,8]=>0000001=>1111110=>1
[4,2,6,3,1,7,5,8]=>0000001=>1111110=>1
[3,2,6,4,1,7,5,8]=>0000001=>1111110=>1
[3,2,7,4,1,6,5,8]=>0000001=>1111110=>1
[4,2,7,3,1,6,5,8]=>0000001=>1111110=>1
[5,2,7,3,1,6,4,8]=>0000001=>1111110=>1
[6,2,7,3,1,5,4,8]=>0000001=>1111110=>1
[7,2,6,3,1,5,4,8]=>0000001=>1111110=>1
[1,5,2,4,8,6,3,7]=>1000000=>0111111=>1
[8,4,1,3,7,5,2,6]=>0000000=>1111111=>1
[6,2,1,5,3,7,4,8]=>0000001=>1111110=>1
[3,2,1,6,4,7,5,8]=>0010001=>1101110=>2
[3,2,8,5,1,6,4,7]=>0000000=>1111111=>1
[6,2,8,4,1,5,3,7]=>0000000=>1111111=>1
[8,3,7,4,1,5,2,6]=>0000000=>1111111=>1
[7,1,3,2,5,6,4,8]=>0000001=>1111110=>1
[6,3,5,2,4,8,1,7]=>0000000=>1111111=>1
[1,5,2,8,7,4,3,6]=>1000000=>0111111=>1
[5,7,2,8,1,4,3,6]=>0000000=>1111111=>1
[5,8,2,7,1,4,3,6]=>0000000=>1111111=>1
[8,7,6,5,3,2,1,4,9]=>00000001=>11111110=>1
[8,7,6,4,3,2,1,5,9]=>00000001=>11111110=>1
[8,7,5,4,3,2,1,6,9]=>00000001=>11111110=>1
[8,7,6,5,4,1,2,3,9]=>00000001=>11111110=>1
[9,8,7,6,5,4,2,1,3,10]=>000000001=>111111110=>1
[8,7,6,5,2,3,1,4,9]=>00000001=>11111110=>1
[9,8,7,6,5,3,2,1,4,10]=>000000001=>111111110=>1
[8,7,6,3,4,2,1,5,9]=>00000001=>11111110=>1
[9,8,7,6,4,3,2,1,5,10]=>000000001=>111111110=>1
[8,7,4,5,3,2,1,6,9]=>00000001=>11111110=>1
[9,8,7,5,4,3,2,1,6,10]=>000000001=>111111110=>1
[8,5,6,4,3,2,1,7,9]=>00000001=>11111110=>1
[9,8,6,5,4,3,2,1,7,10]=>000000001=>111111110=>1
[6,7,5,4,3,2,1,8,9]=>00000011=>11111100=>1
[8,6,2,3,1,5,7,4]=>0000000=>1111111=>1
[1,4,2,7,3,6,8,5]=>1000000=>0111111=>1
[3,2,1,7,8,5,4,6]=>0010000=>1101111=>2
[1,7,6,3,2,4,8,5]=>1000000=>0111111=>1
[2,1,6,4,7,8,5,3]=>0100000=>1011111=>2
[1,6,3,2,4,7,8,5]=>1000000=>0111111=>1
[1,2,3,7,5,8,4,6]=>1110000=>0001111=>1
[1,8,5,3,2,4,7,6]=>1000000=>0111111=>1
[4,7,8,1,5,6,2,3]=>0000000=>1111111=>1
[3,6,7,1,8,4,2,5]=>0000000=>1111111=>1
[1,3,7,6,2,4,5,8]=>1000001=>0111110=>1
[7,1,4,3,8,5,6,2]=>0000000=>1111111=>1
[5,6,2,7,8,3,4,1]=>0000000=>1111111=>1
[7,2,5,8,1,6,3,4]=>0000000=>1111111=>1
[6,4,8,1,5,7,2,3]=>0000000=>1111111=>1
[2,7,4,1,3,6,8,5]=>0000000=>1111111=>1
[6,2,1,4,7,5,8,3]=>0000000=>1111111=>1
[6,8,7,9,5,4,3,2,1]=>00000000=>11111111=>1
[5,8,7,6,9,4,3,2,1]=>00000000=>11111111=>1
[4,8,7,6,5,9,3,2,1]=>00000000=>11111111=>1
[3,8,7,6,5,4,9,2,1]=>00000000=>11111111=>1
[2,8,7,6,5,4,3,9,1]=>00000000=>11111111=>1
[2,6,1,5,4,7,3,8]=>0000001=>1111110=>1
[2,3,6,8,4,1,7,5]=>0000000=>1111111=>1
[1,7,2,8,6,3,5,4]=>1000000=>0111111=>1
[8,3,2,6,7,4,1,5]=>0000000=>1111111=>1
[5,2,6,8,1,3,7,4]=>0000000=>1111111=>1
[8,3,5,2,6,1,4,7]=>0000000=>1111111=>1
[8,3,2,4,6,7,1,5]=>0000000=>1111111=>1
[4,2,7,6,1,8,5,3]=>0000000=>1111111=>1
[7,3,2,1,8,5,4,6]=>0000000=>1111111=>1
[7,3,2,1,6,4,8,5]=>0000000=>1111111=>1
[3,6,5,2,1,8,4,7]=>0000000=>1111111=>1
[6,7,2,4,3,5,8,1]=>0000000=>1111111=>1
[4,3,8,2,1,5,7,6]=>0000000=>1111111=>1
[4,3,2,8,1,6,7,5]=>0000000=>1111111=>1
[4,5,8,3,2,7,1,6]=>0000000=>1111111=>1
[5,4,7,8,2,3,6,1]=>0000000=>1111111=>1
[4,3,8,2,1,6,7,5]=>0000000=>1111111=>1
[9,1,3,4,5,6,7,8,2]=>00000000=>11111111=>1
[5,3,7,6,2,4,8,1]=>0000000=>1111111=>1
[4,6,7,2,5,3,8,1]=>0000000=>1111111=>1
[6,4,7,8,3,1,5,2]=>0000000=>1111111=>1
[5,8,1,7,6,4,2,3]=>0000000=>1111111=>1
[5,6,7,1,8,3,4,2]=>0000000=>1111111=>1
[7,1,8,6,2,5,4,3]=>0000000=>1111111=>1
[1,5,8,2,6,4,7,3]=>1000000=>0111111=>1
[1,5,7,4,6,8,3,2]=>1000000=>0111111=>1
[5,6,7,4,8,1,3,2]=>0000000=>1111111=>1
[2,6,7,1,5,4,8,3]=>0000000=>1111111=>1
[3,2,7,6,5,8,1,4]=>0000000=>1111111=>1
[1,7,3,4,5,8,2,6]=>1000000=>0111111=>1
[7,1,8,4,5,6,3,2]=>0000000=>1111111=>1
[10,1,3,4,5,6,7,8,9,2]=>000000000=>111111111=>1
[1,2,3,4,5,6,7,8,11,9,10]=>1111111100=>0000000011=>1
[1,8,3,4,5,6,9,2,7]=>10000000=>01111111=>1
[8,2,3,4,5,1,9,7,6]=>00000000=>11111111=>1
[1,2,7,4,5,8,3,6]=>1100000=>0011111=>1
[8,1,9,4,5,6,7,3,2]=>00000000=>11111111=>1
[7,9,3,4,5,6,1,8,2]=>00000000=>11111111=>1
[1,9,3,4,5,6,7,10,2,8]=>100000000=>011111111=>1
[9,2,3,4,5,6,1,10,8,7]=>000000000=>111111111=>1
[1,2,8,4,5,6,9,3,7]=>11000000=>00111111=>1
[7,8,3,4,5,2,9,1,6]=>00000000=>11111111=>1
[8,2,3,4,1,6,9,7,5]=>00000000=>11111111=>1
[6,7,3,2,5,8,1,4]=>0000000=>1111111=>1
[8,1,3,9,5,6,7,4,2]=>00000000=>11111111=>1
[6,1,8,4,5,3,7,2]=>0000000=>1111111=>1
[7,8,9,4,5,6,3,1,2]=>00000000=>11111111=>1
[9,1,10,4,5,6,7,8,3,2]=>000000000=>111111111=>1
[6,9,3,4,5,1,7,8,2]=>00000000=>11111111=>1
[8,10,3,4,5,6,7,1,9,2]=>000000000=>111111111=>1
[5,1,4,6,2,8,7,3]=>0000000=>1111111=>1
[7,3,5,2,1,6,8,4]=>0000000=>1111111=>1
[1,5,8,7,4,6,3,2]=>1000000=>0111111=>1
[5,7,2,1,3,6,8,4]=>0000000=>1111111=>1
[3,7,2,6,8,1,5,4]=>0000000=>1111111=>1
[7,4,8,6,5,1,3,2]=>0000000=>1111111=>1
[1,5,4,7,8,6,2,3]=>1000000=>0111111=>1
[1,5,7,8,6,2,4,3]=>1000000=>0111111=>1
[3,6,2,1,4,7,8,5]=>0000000=>1111111=>1
[6,8,2,7,5,4,3,1]=>0000000=>1111111=>1
[5,8,1,7,6,4,3,2]=>0000000=>1111111=>1
[4,1,5,6,7,8,9,2,3]=>00000000=>11111111=>1
[2,3,6,7,1,8,9,4,5]=>00000000=>11111111=>1
[8,6,3,2,1,5,4,7]=>0000000=>1111111=>1
[8,5,3,2,4,1,7,6]=>0000000=>1111111=>1
[7,5,2,4,3,6,8,1]=>0000000=>1111111=>1
[8,5,1,4,6,3,2,7]=>0000000=>1111111=>1
[8,5,1,6,3,4,2,7]=>0000000=>1111111=>1
[8,4,3,6,1,5,2,7]=>0000000=>1111111=>1
[8,4,3,5,2,1,7,6]=>0000000=>1111111=>1
[6,4,3,2,8,7,1,5]=>0000000=>1111111=>1
[8,5,1,4,3,7,2,6]=>0000000=>1111111=>1
[8,5,4,2,1,3,7,6]=>0000000=>1111111=>1
[4,7,3,6,1,8,5,2]=>0000000=>1111111=>1
[7,6,2,4,1,5,8,3]=>0000000=>1111111=>1
[8,1,6,3,7,4,2,5]=>0000000=>1111111=>1
[5,3,8,2,6,7,1,4]=>0000000=>1111111=>1
[8,2,5,1,7,6,3,4]=>0000000=>1111111=>1
[8,2,4,6,3,7,1,5]=>0000000=>1111111=>1
[7,2,6,4,3,5,8,1]=>0000000=>1111111=>1
[7,3,6,2,4,5,8,1]=>0000000=>1111111=>1
[8,3,7,2,1,4,6,5]=>0000000=>1111111=>1
[7,6,4,1,3,2,8,5]=>0000000=>1111111=>1
[7,3,8,2,1,5,6,4]=>0000000=>1111111=>1
[6,2,5,7,4,3,8,1]=>0000000=>1111111=>1
[6,2,5,4,8,7,1,3]=>0000000=>1111111=>1
[7,2,4,8,5,1,6,3]=>0000000=>1111111=>1
[4,2,7,6,8,5,1,3]=>0000000=>1111111=>1
[7,1,6,2,8,5,4,3]=>0000000=>1111111=>1
[7,1,6,3,8,5,2,4]=>0000000=>1111111=>1
[7,2,6,8,1,3,5,4]=>0000000=>1111111=>1
[7,2,8,5,1,3,6,4]=>0000000=>1111111=>1
[7,1,8,5,3,2,6,4]=>0000000=>1111111=>1
[7,1,8,2,5,6,4,3]=>0000000=>1111111=>1
[6,1,5,8,7,2,4,3]=>0000000=>1111111=>1
[6,1,5,7,4,8,3,2]=>0000000=>1111111=>1
[6,1,5,7,8,3,4,2]=>0000000=>1111111=>1
[4,6,7,3,1,8,5,2]=>0000000=>1111111=>1
[4,2,6,3,1,8,7,5]=>0000000=>1111111=>1
[6,1,4,2,5,8,7,3]=>0000000=>1111111=>1
[1,5,3,8,4,6,2,7]=>1000000=>0111111=>1
[7,2,3,5,8,4,1,6]=>0000000=>1111111=>1
[7,6,4,2,8,5,1,3]=>0000000=>1111111=>1
[1,7,6,4,8,5,3,2]=>1000000=>0111111=>1
[8,7,4,2,1,5,6,3]=>0000000=>1111111=>1
[8,2,3,5,1,4,6,7]=>0000000=>1111111=>1
[8,7,4,1,3,2,6,5]=>0000000=>1111111=>1
[7,1,4,8,3,6,2,5]=>0000000=>1111111=>1
[4,1,8,5,7,6,2,3]=>0000000=>1111111=>1
[3,7,5,8,4,2,1,6]=>0000000=>1111111=>1
[6,1,5,8,3,4,2,7]=>0000000=>1111111=>1
[6,7,5,1,3,2,4,8]=>0000001=>1111110=>1
[5,2,6,1,7,3,4,8]=>0000001=>1111110=>1
[4,2,6,8,3,7,1,5]=>0000000=>1111111=>1
[6,8,5,1,4,2,3,7]=>0000000=>1111111=>1
[7,8,4,5,1,3,6,2]=>0000000=>1111111=>1
[1,7,8,5,3,4,6,2]=>1000000=>0111111=>1
[1,5,8,3,6,4,7,2]=>1000000=>0111111=>1
[6,3,8,1,4,2,7,5]=>0000000=>1111111=>1
[4,8,1,5,6,3,7,2]=>0000000=>1111111=>1
[1,8,2,6,5,3,7,4]=>1000000=>0111111=>1
[3,8,1,7,2,6,5,4]=>0000000=>1111111=>1
[7,3,8,1,2,6,5,4]=>0000000=>1111111=>1
[8,1,4,2,3,5,7,6]=>0000000=>1111111=>1
[8,1,2,4,6,5,7,3]=>0000000=>1111111=>1
[8,4,7,1,5,3,6,2]=>0000000=>1111111=>1
[7,2,5,3,4,6,1,8]=>0000001=>1111110=>1
[7,6,4,2,5,3,1,8]=>0000001=>1111110=>1
[5,8,4,3,6,2,7,1]=>0000000=>1111111=>1
[1,7,2,6,3,4,8,5]=>1000000=>0111111=>1
[7,5,1,6,3,2,4,8]=>0000001=>1111110=>1
[7,1,2,6,3,4,5,8]=>0000001=>1111110=>1
[7,3,1,4,6,2,5,8]=>0000001=>1111110=>1
[7,1,6,5,4,2,3,8]=>0000001=>1111110=>1
[3,6,8,5,2,4,7,1]=>0000000=>1111111=>1
[5,7,8,4,3,2,6,1]=>0000000=>1111111=>1
[1,3,8,4,7,2,6,5]=>1000000=>0111111=>1
[6,7,1,3,2,8,5,4]=>0000000=>1111111=>1
[1,5,3,2,6,8,4,7]=>1000000=>0111111=>1
[5,4,3,1,7,2,8,6]=>0000000=>1111111=>1
[3,7,6,5,8,2,4,1]=>0000000=>1111111=>1
[5,7,4,2,8,6,1,3]=>0000000=>1111111=>1
[3,8,5,7,6,2,4,1]=>0000000=>1111111=>1
[1,3,6,8,7,2,5,4]=>1000000=>0111111=>1
[7,6,8,4,3,1,5,2]=>0000000=>1111111=>1
[1,7,6,5,3,2,4,8]=>1000001=>0111110=>1
[2,7,6,5,4,1,3,8]=>0000001=>1111110=>1
[4,7,6,1,5,8,3,2]=>0000000=>1111111=>1
[6,8,7,1,5,4,3,2]=>0000000=>1111111=>1
[9,10,1,8,7,6,5,4,3,2]=>000000000=>111111111=>1
[3,5,2,4,7,6,9,8,1]=>00000000=>11111111=>1
[2,4,3,6,5,8,7,1,9]=>00000001=>11111110=>1
[3,2,5,4,7,6,9,8,1,10]=>000000001=>111111110=>1
[2,4,3,6,5,8,7,10,9,1]=>000000000=>111111111=>1
[4,7,3,6,8,2,1,5]=>0000000=>1111111=>1
[5,4,7,3,8,2,1,6]=>0000000=>1111111=>1
[4,3,5,7,2,6,1,8]=>0000001=>1111110=>1
[1,7,2,8,5,4,3,6]=>1000000=>0111111=>1
[5,4,8,3,6,2,1,7]=>0000000=>1111111=>1
[5,8,4,2,7,3,6,1]=>0000000=>1111111=>1
[8,6,1,3,4,5,7,2]=>0000000=>1111111=>1
[8,5,1,2,4,6,7,3]=>0000000=>1111111=>1
[2,6,8,7,3,4,5,1]=>0000000=>1111111=>1
[1,7,8,5,6,4,2,3]=>1000000=>0111111=>1
[3,1,7,5,8,2,4,6]=>0000000=>1111111=>1
[8,1,3,2,4,6,5,7]=>0000000=>1111111=>1
[8,1,6,5,4,3,2,7]=>0000000=>1111111=>1
[3,5,8,2,1,4,7,6]=>0000000=>1111111=>1
[4,2,8,5,3,7,6,1]=>0000000=>1111111=>1
[4,2,7,5,3,8,6,1]=>0000000=>1111111=>1
[6,4,5,1,8,3,2,7]=>0000000=>1111111=>1
[5,4,7,8,3,1,2,6]=>0000000=>1111111=>1
[4,5,8,1,3,7,2,6]=>0000000=>1111111=>1
[1,5,3,6,8,7,2,4]=>1000000=>0111111=>1
[7,6,2,8,1,4,3,5]=>0000000=>1111111=>1
[4,7,2,6,8,3,5,1]=>0000000=>1111111=>1
[6,3,2,8,7,4,5,1]=>0000000=>1111111=>1
[7,4,3,8,5,6,2,1]=>0000000=>1111111=>1
[3,1,5,8,7,6,2,4]=>0000000=>1111111=>1
[8,2,1,6,5,7,3,4]=>0000000=>1111111=>1
[3,1,8,6,5,7,2,4]=>0000000=>1111111=>1
[1,2,7,6,4,5,8,3]=>1100000=>0011111=>1
[7,2,6,5,1,8,3,4]=>0000000=>1111111=>1
[4,2,8,5,6,3,1,7]=>0000000=>1111111=>1
[4,7,3,2,5,1,6,8]=>0000001=>1111110=>1
[4,2,5,3,8,7,1,6]=>0000000=>1111111=>1
[7,5,6,1,8,3,2,4]=>0000000=>1111111=>1
[4,5,6,2,7,3,1,8]=>0000001=>1111110=>1
[3,5,1,4,6,8,2,7]=>0000000=>1111111=>1
[8,5,7,4,2,1,3,6]=>0000000=>1111111=>1
[4,6,2,7,5,8,1,3]=>0000000=>1111111=>1
[6,5,2,4,8,7,1,3]=>0000000=>1111111=>1
[8,5,2,4,1,3,7,6]=>0000000=>1111111=>1
[5,1,2,4,3,6,8,7]=>0000110=>1111001=>2
[8,6,2,7,5,3,1,4]=>0000000=>1111111=>1
[3,5,1,2,4,7,6,9,8]=>00001010=>11110101=>3
[7,8,1,6,5,2,4,3]=>0000000=>1111111=>1
[7,4,8,6,5,1,2,3]=>0000000=>1111111=>1
[3,7,8,6,5,1,2,4]=>0000000=>1111111=>1
[4,5,8,2,7,3,1,6]=>0000000=>1111111=>1
[6,5,8,2,7,3,1,4]=>0000000=>1111111=>1
[6,4,8,2,7,3,1,5]=>0000000=>1111111=>1
[7,8,1,3,6,4,2,5]=>0000000=>1111111=>1
[4,5,7,8,3,2,1,6]=>0000000=>1111111=>1
[5,7,3,4,2,6,8,1]=>0000000=>1111111=>1
[5,7,4,2,3,6,8,1]=>0000000=>1111111=>1
[5,4,7,3,2,8,1,6]=>0000000=>1111111=>1
[6,8,3,2,4,5,1,7]=>0000000=>1111111=>1
[5,8,3,4,6,1,2,7]=>0000000=>1111111=>1
[6,4,3,8,5,1,2,7]=>0000000=>1111111=>1
[6,4,8,2,3,5,1,7]=>0000000=>1111111=>1
[5,4,6,8,2,3,1,7]=>0000000=>1111111=>1
[5,6,8,4,1,2,3,7]=>0000000=>1111111=>1
[6,4,8,5,1,2,3,7]=>0000000=>1111111=>1
[7,4,8,3,1,2,5,6]=>0000000=>1111111=>1
[5,7,8,2,3,1,4,6]=>0000000=>1111111=>1
[5,4,7,8,2,1,3,6]=>0000000=>1111111=>1
[5,8,6,3,1,2,4,7]=>0000000=>1111111=>1
[6,8,5,2,1,3,4,7]=>0000000=>1111111=>1
[5,3,7,2,1,8,6,4]=>0000000=>1111111=>1
[6,1,5,4,7,2,8,3]=>0000000=>1111111=>1
[5,4,8,3,2,7,1,6]=>0000000=>1111111=>1
[5,4,3,7,2,1,6,8]=>0000001=>1111110=>1
[5,4,3,7,8,2,1,6]=>0000000=>1111111=>1
[3,4,5,6,7,8,2,9,1]=>00000000=>11111111=>1
[1,4,8,6,3,2,7,5]=>1000000=>0111111=>1
[8,7,6,4,5,3,2,9,1]=>00000000=>11111111=>1
[2,9,8,7,5,6,4,3,1]=>00000000=>11111111=>1
[6,1,3,5,8,7,4,2]=>0000000=>1111111=>1
[3,5,8,7,4,6,2,1]=>0000000=>1111111=>1
[6,8,5,7,3,4,2,1]=>0000000=>1111111=>1
[5,3,6,8,4,2,1,7]=>0000000=>1111111=>1
[5,1,6,8,4,7,3,2]=>0000000=>1111111=>1
[6,2,8,3,4,1,5,7]=>0000000=>1111111=>1
[2,4,1,8,7,6,3,5]=>0000000=>1111111=>1
[1,3,5,8,4,7,2,6]=>1000000=>0111111=>1
[2,3,8,7,5,1,6,4]=>0000000=>1111111=>1
[8,5,4,7,6,1,3,2]=>0000000=>1111111=>1
[5,8,7,2,4,1,3,6]=>0000000=>1111111=>1
[4,1,3,5,6,2,8,7]=>0000010=>1111101=>2
[6,3,8,5,1,7,4,2]=>0000000=>1111111=>1
[8,2,4,6,1,3,7,5]=>0000000=>1111111=>1
[6,4,8,7,3,5,2,1]=>0000000=>1111111=>1
[8,2,3,5,6,1,4,7]=>0000000=>1111111=>1
[4,3,5,6,8,2,7,1]=>0000000=>1111111=>1
[8,2,3,4,6,1,7,5]=>0000000=>1111111=>1
[1,7,4,3,5,2,8,6]=>1000000=>0111111=>1
[2,7,4,3,8,1,5,6]=>0000000=>1111111=>1
[3,8,2,7,6,4,1,5]=>0000000=>1111111=>1
[5,3,6,2,1,8,4,7]=>0000000=>1111111=>1
[4,3,8,6,2,7,1,5]=>0000000=>1111111=>1
[8,2,1,4,6,3,7,5]=>0000000=>1111111=>1
[3,1,6,8,2,7,5,4]=>0000000=>1111111=>1
[5,3,8,6,7,2,1,4]=>0000000=>1111111=>1
[5,8,7,2,4,6,1,3]=>0000000=>1111111=>1
[1,5,2,8,7,6,4,3]=>1000000=>0111111=>1
[2,7,1,4,6,5,3,8]=>0000001=>1111110=>1
[4,7,1,2,6,5,8,3]=>0000000=>1111111=>1
[4,2,5,6,8,7,3,1]=>0000000=>1111111=>1
[6,5,8,3,7,4,2,1]=>0000000=>1111111=>1
[8,2,5,1,6,3,7,4]=>0000000=>1111111=>1
[8,3,4,5,1,6,7,2]=>0000000=>1111111=>1
[7,8,1,3,5,4,6,2]=>0000000=>1111111=>1
[3,5,7,6,4,8,1,2]=>0000000=>1111111=>1
[1,3,7,8,5,4,6,2]=>1000000=>0111111=>1
[1,3,2,7,8,5,4,6]=>1010000=>0101111=>2
[6,5,8,4,3,7,1,2]=>0000000=>1111111=>1
[6,7,3,1,5,2,4,8]=>0000001=>1111110=>1
[5,2,4,1,8,3,6,7]=>0000000=>1111111=>1
[7,2,3,8,5,4,1,6]=>0000000=>1111111=>1
[4,1,5,7,6,3,8,2]=>0000000=>1111111=>1
[3,2,5,4,7,6,9,8,11,10,1,12]=>00000000001=>11111111110=>1
[1,4,8,2,3,6,5,7]=>1000000=>0111111=>1
[1,4,6,7,3,5,2,8]=>1000001=>0111110=>1
[1,4,8,2,6,7,5,3]=>1000000=>0111111=>1
[1,7,3,2,4,5,6,8]=>1000001=>0111110=>1
[1,7,3,2,4,5,8,6]=>1000000=>0111111=>1
[4,2,6,5,3,1,7,8]=>0000011=>1111100=>1
[5,2,1,6,8,7,4,3]=>0000000=>1111111=>1
[1,3,5,8,6,2,7,4]=>1000000=>0111111=>1
[1,3,8,5,7,4,2,6]=>1000000=>0111111=>1
[1,2,3,7,5,4,6,8]=>1110001=>0001110=>1
[1,4,2,8,6,3,5,7]=>1000000=>0111111=>1
[2,8,6,3,5,7,4,1]=>0000000=>1111111=>1
[6,1,8,2,5,3,4,7]=>0000000=>1111111=>1
[1,5,4,2,3,6,8,7]=>1000110=>0111001=>2
[6,1,5,2,3,4,8,7]=>0000010=>1111101=>2
[3,1,2,4,8,6,7,5]=>0011000=>1100111=>2
[3,1,2,5,8,7,4,6]=>0010000=>1101111=>2
[6,5,2,1,8,4,7,3]=>0000000=>1111111=>1
[5,6,2,4,3,8,1,7]=>0000000=>1111111=>1
[3,7,5,2,8,1,4,6]=>0000000=>1111111=>1
[5,1,4,7,3,2,8,6]=>0000000=>1111111=>1
[4,1,5,8,6,2,3,7]=>0000000=>1111111=>1
[5,4,8,6,3,7,1,2]=>0000000=>1111111=>1
[6,5,2,3,1,8,7,4]=>0000000=>1111111=>1
[6,4,7,5,3,8,1,2]=>0000000=>1111111=>1
[5,7,4,8,3,1,6,2]=>0000000=>1111111=>1
[4,3,5,1,8,7,2,6]=>0000000=>1111111=>1
[2,5,3,6,1,8,4,7]=>0000000=>1111111=>1
[1,7,2,4,5,3,6,8]=>1000001=>0111110=>1
[1,7,4,5,3,2,6,8]=>1000001=>0111110=>1
[1,6,4,7,3,5,2,8]=>1000001=>0111110=>1
[3,5,6,4,8,2,1,7]=>0000000=>1111111=>1
[1,6,4,7,5,2,3,8]=>1000001=>0111110=>1
[1,5,2,6,7,4,3,8]=>1000001=>0111110=>1
[8,5,6,1,4,3,7,2]=>0000000=>1111111=>1
[2,5,4,7,8,3,1,6]=>0000000=>1111111=>1
[6,4,5,8,2,3,1,7]=>0000000=>1111111=>1
[8,6,1,3,2,5,7,4]=>0000000=>1111111=>1
[7,5,8,1,4,6,3,2]=>0000000=>1111111=>1
[4,2,6,7,8,1,5,3]=>0000000=>1111111=>1
[3,4,6,7,8,1,5,2]=>0000000=>1111111=>1
[4,7,3,8,5,1,6,2]=>0000000=>1111111=>1
[4,3,2,7,5,8,1,6]=>0000000=>1111111=>1
[4,8,5,3,2,6,1,7]=>0000000=>1111111=>1
[2,8,4,5,3,6,1,7]=>0000000=>1111111=>1
[8,1,5,3,2,4,7,6]=>0000000=>1111111=>1
[7,8,4,1,3,6,5,2]=>0000000=>1111111=>1
[8,6,1,3,2,7,4,5]=>0000000=>1111111=>1
[7,3,8,2,4,1,6,5]=>0000000=>1111111=>1
[6,2,3,7,8,1,5,4]=>0000000=>1111111=>1
[6,3,7,8,1,5,4,2]=>0000000=>1111111=>1
[2,6,3,7,8,1,5,4]=>0000000=>1111111=>1
[7,5,8,1,6,4,2,3]=>0000000=>1111111=>1
[8,1,4,3,7,5,6,2]=>0000000=>1111111=>1
[8,2,7,6,4,1,5,3]=>0000000=>1111111=>1
[2,7,4,3,8,5,1,6]=>0000000=>1111111=>1
[4,1,5,8,3,6,7,2]=>0000000=>1111111=>1
[4,8,5,7,1,3,2,6]=>0000000=>1111111=>1
[4,8,2,7,1,3,6,5]=>0000000=>1111111=>1
[8,2,1,7,4,6,3,5]=>0000000=>1111111=>1
[4,5,2,8,7,3,1,6]=>0000000=>1111111=>1
[4,8,5,3,1,6,7,2]=>0000000=>1111111=>1
[5,2,7,8,4,1,6,3]=>0000000=>1111111=>1
[6,7,8,3,2,5,4,1]=>0000000=>1111111=>1
[6,2,3,7,8,1,4,5]=>0000000=>1111111=>1
[1,7,6,4,2,3,5,8]=>1000001=>0111110=>1
[1,3,2,5,8,6,4,7]=>1010000=>0101111=>2
[6,1,4,7,2,8,5,3]=>0000000=>1111111=>1
[1,6,7,2,4,8,5,3]=>1000000=>0111111=>1
[5,7,2,4,3,6,8,1]=>0000000=>1111111=>1
[5,7,3,4,6,2,8,1]=>0000000=>1111111=>1
[2,8,3,6,1,7,4,5]=>0000000=>1111111=>1
[4,3,1,8,5,2,6,7]=>0000000=>1111111=>1
[1,8,4,5,6,2,7,3]=>1000000=>0111111=>1
[7,3,8,2,1,4,5,6]=>0000000=>1111111=>1
[8,2,5,3,1,7,4,6]=>0000000=>1111111=>1
[6,3,5,8,1,7,4,2]=>0000000=>1111111=>1
[3,5,4,8,6,1,7,2]=>0000000=>1111111=>1
[7,5,2,3,8,4,6,1]=>0000000=>1111111=>1
[2,7,5,1,4,8,3,6]=>0000000=>1111111=>1
[5,7,6,1,2,8,3,4]=>0000000=>1111111=>1
[7,4,6,5,1,8,2,3]=>0000000=>1111111=>1
[7,1,3,2,6,8,4,5]=>0000000=>1111111=>1
[4,3,5,2,8,1,6,7]=>0000000=>1111111=>1
[1,7,3,8,2,4,6,5]=>1000000=>0111111=>1
[2,7,4,8,5,3,1,6]=>0000000=>1111111=>1
[6,1,3,8,4,2,7,5]=>0000000=>1111111=>1
[5,4,1,8,6,2,7,3]=>0000000=>1111111=>1
[5,4,6,8,1,3,2,7]=>0000000=>1111111=>1
[3,6,1,5,8,4,7,2]=>0000000=>1111111=>1
[6,4,8,3,5,7,2,1]=>0000000=>1111111=>1
[3,5,8,2,4,1,7,6]=>0000000=>1111111=>1
[7,2,8,4,1,3,6,5]=>0000000=>1111111=>1
[5,8,1,2,4,3,6,7]=>0000000=>1111111=>1
[4,1,5,2,3,8,7,6]=>0000100=>1111011=>2
[6,3,5,8,2,4,7,1]=>0000000=>1111111=>1
[2,8,7,1,4,6,3,5]=>0000000=>1111111=>1
[7,5,6,2,8,4,3,1]=>0000000=>1111111=>1
[8,6,9,7,5,4,3,2,1]=>00000000=>11111111=>1
[3,2,5,4,7,6,1,10,9,8]=>000000100=>111111011=>2
[3,2,5,4,9,8,7,6,1,10]=>000000001=>111111110=>1
[3,2,5,4,1,8,7,10,9,6]=>000010000=>111101111=>2
[3,2,5,4,1,10,9,8,7,6]=>000010000=>111101111=>2
[3,2,7,6,5,4,9,8,1,10]=>000000001=>111111110=>1
[3,2,7,6,5,4,1,10,9,8]=>000000100=>111111011=>2
[3,2,9,6,5,8,7,4,1,10]=>000000001=>111111110=>1
[3,2,1,6,5,8,7,10,9,4]=>001000000=>110111111=>2
[3,2,1,6,5,10,9,8,7,4]=>001000000=>110111111=>2
[3,2,1,8,7,6,5,10,9,4]=>001000000=>110111111=>2
[3,2,1,10,7,6,9,8,5,4]=>001000000=>110111111=>2
[5,4,3,2,7,6,9,8,1,10]=>000000001=>111111110=>1
[5,4,3,2,7,6,1,10,9,8]=>000000100=>111111011=>2
[5,4,3,2,9,8,7,6,1,10]=>000000001=>111111110=>1
[5,4,3,2,1,8,7,10,9,6]=>000010000=>111101111=>2
[7,4,3,6,5,2,9,8,1,10]=>000000001=>111111110=>1
[7,4,3,6,5,2,1,10,9,8]=>000000100=>111111011=>2
[9,4,3,6,5,8,7,2,1,10]=>000000001=>111111110=>1
[1,4,3,6,5,8,7,10,9,2]=>100000000=>011111111=>1
[1,4,3,6,5,10,9,8,7,2]=>100000000=>011111111=>1
[9,4,3,8,7,6,5,2,1,10]=>000000001=>111111110=>1
[1,4,3,8,7,6,5,10,9,2]=>100000000=>011111111=>1
[1,4,3,10,7,6,9,8,5,2]=>100000000=>011111111=>1
[1,4,3,10,9,8,7,6,5,2]=>100000000=>011111111=>1
[7,6,5,4,3,2,9,8,1,10]=>000000001=>111111110=>1
[9,6,5,4,3,8,7,2,1,10]=>000000001=>111111110=>1
[1,6,5,4,3,8,7,10,9,2]=>100000000=>011111111=>1
[1,6,5,4,3,10,9,8,7,2]=>100000000=>011111111=>1
[9,8,5,4,7,6,3,2,1,10]=>000000001=>111111110=>1
[1,8,5,4,7,6,3,10,9,2]=>100000000=>011111111=>1
[1,10,5,4,7,6,9,8,3,2]=>100000000=>011111111=>1
[1,10,5,4,9,8,7,6,3,2]=>100000000=>011111111=>1
[1,10,7,6,5,4,9,8,3,2]=>100000000=>011111111=>1
[1,10,9,6,5,8,7,4,3,2]=>100000000=>011111111=>1
[3,2,5,4,7,6,11,10,9,8,1,12]=>00000000001=>11111111110=>1
[3,2,5,4,9,8,7,6,11,10,1,12]=>00000000001=>11111111110=>1
[3,2,5,4,11,8,7,10,9,6,1,12]=>00000000001=>11111111110=>1
[3,2,5,4,11,10,9,8,7,6,1,12]=>00000000001=>11111111110=>1
[3,2,7,6,5,4,9,8,11,10,1,12]=>00000000001=>11111111110=>1
[3,2,7,6,5,4,11,10,9,8,1,12]=>00000000001=>11111111110=>1
[3,2,9,6,5,8,7,4,11,10,1,12]=>00000000001=>11111111110=>1
[3,2,11,6,5,8,7,10,9,4,1,12]=>00000000001=>11111111110=>1
[3,2,11,6,5,10,9,8,7,4,1,12]=>00000000001=>11111111110=>1
[3,2,9,8,7,6,5,4,11,10,1,12]=>00000000001=>11111111110=>1
[3,2,11,8,7,6,5,10,9,4,1,12]=>00000000001=>11111111110=>1
[3,2,11,10,7,6,9,8,5,4,1,12]=>00000000001=>11111111110=>1
[3,2,11,10,9,8,7,6,5,4,1,12]=>00000000001=>11111111110=>1
[5,4,3,2,7,6,9,8,11,10,1,12]=>00000000001=>11111111110=>1
[5,4,3,2,7,6,11,10,9,8,1,12]=>00000000001=>11111111110=>1
[5,4,3,2,9,8,7,6,11,10,1,12]=>00000000001=>11111111110=>1
[5,4,3,2,11,8,7,10,9,6,1,12]=>00000000001=>11111111110=>1
[5,4,3,2,11,10,9,8,7,6,1,12]=>00000000001=>11111111110=>1
[7,4,3,6,5,2,9,8,11,10,1,12]=>00000000001=>11111111110=>1
[7,4,3,6,5,2,11,10,9,8,1,12]=>00000000001=>11111111110=>1
[9,4,3,6,5,8,7,2,11,10,1,12]=>00000000001=>11111111110=>1
[11,4,3,6,5,8,7,10,9,2,1,12]=>00000000001=>11111111110=>1
[1,4,3,6,5,8,7,10,9,12,11,2]=>10000000000=>01111111111=>1
[1,4,3,6,5,8,7,12,11,10,9,2]=>10000000000=>01111111111=>1
[11,4,3,6,5,10,9,8,7,2,1,12]=>00000000001=>11111111110=>1
[1,4,3,6,5,10,9,8,7,12,11,2]=>10000000000=>01111111111=>1
[1,4,3,6,5,12,9,8,11,10,7,2]=>10000000000=>01111111111=>1
[1,4,3,6,5,12,11,10,9,8,7,2]=>10000000000=>01111111111=>1
[9,4,3,8,7,6,5,2,11,10,1,12]=>00000000001=>11111111110=>1
[11,4,3,8,7,6,5,10,9,2,1,12]=>00000000001=>11111111110=>1
[1,4,3,8,7,6,5,10,9,12,11,2]=>10000000000=>01111111111=>1
[1,4,3,8,7,6,5,12,11,10,9,2]=>10000000000=>01111111111=>1
[11,4,3,10,7,6,9,8,5,2,1,12]=>00000000001=>11111111110=>1
[1,4,3,10,7,6,9,8,5,12,11,2]=>10000000000=>01111111111=>1
[1,4,3,12,7,6,9,8,11,10,5,2]=>10000000000=>01111111111=>1
[1,4,3,12,7,6,11,10,9,8,5,2]=>10000000000=>01111111111=>1
[11,4,3,10,9,8,7,6,5,2,1,12]=>00000000001=>11111111110=>1
[1,4,3,10,9,8,7,6,5,12,11,2]=>10000000000=>01111111111=>1
[1,4,3,12,9,8,7,6,11,10,5,2]=>10000000000=>01111111111=>1
[1,4,3,12,11,8,7,10,9,6,5,2]=>10000000000=>01111111111=>1
[1,4,3,12,11,10,9,8,7,6,5,2]=>10000000000=>01111111111=>1
[7,6,5,4,3,2,9,8,11,10,1,12]=>00000000001=>11111111110=>1
[7,6,5,4,3,2,11,10,9,8,1,12]=>00000000001=>11111111110=>1
[9,6,5,4,3,8,7,2,11,10,1,12]=>00000000001=>11111111110=>1
[11,6,5,4,3,8,7,10,9,2,1,12]=>00000000001=>11111111110=>1
[1,6,5,4,3,8,7,10,9,12,11,2]=>10000000000=>01111111111=>1
[1,6,5,4,3,8,7,12,11,10,9,2]=>10000000000=>01111111111=>1
[11,6,5,4,3,10,9,8,7,2,1,12]=>00000000001=>11111111110=>1
[1,6,5,4,3,10,9,8,7,12,11,2]=>10000000000=>01111111111=>1
[1,6,5,4,3,12,9,8,11,10,7,2]=>10000000000=>01111111111=>1
[1,6,5,4,3,12,11,10,9,8,7,2]=>10000000000=>01111111111=>1
[9,8,5,4,7,6,3,2,11,10,1,12]=>00000000001=>11111111110=>1
[11,8,5,4,7,6,3,10,9,2,1,12]=>00000000001=>11111111110=>1
[1,8,5,4,7,6,3,10,9,12,11,2]=>10000000000=>01111111111=>1
[1,8,5,4,7,6,3,12,11,10,9,2]=>10000000000=>01111111111=>1
[11,10,5,4,7,6,9,8,3,2,1,12]=>00000000001=>11111111110=>1
[1,10,5,4,7,6,9,8,3,12,11,2]=>10000000000=>01111111111=>1
[1,12,5,4,7,6,9,8,11,10,3,2]=>10000000000=>01111111111=>1
[1,12,5,4,7,6,11,10,9,8,3,2]=>10000000000=>01111111111=>1
[11,10,5,4,9,8,7,6,3,2,1,12]=>00000000001=>11111111110=>1
[1,10,5,4,9,8,7,6,3,12,11,2]=>10000000000=>01111111111=>1
[1,12,5,4,9,8,7,6,11,10,3,2]=>10000000000=>01111111111=>1
[1,12,5,4,11,8,7,10,9,6,3,2]=>10000000000=>01111111111=>1
[1,12,5,4,11,10,9,8,7,6,3,2]=>10000000000=>01111111111=>1
[9,8,7,6,5,4,3,2,11,10,1,12]=>00000000001=>11111111110=>1
[11,8,7,6,5,4,3,10,9,2,1,12]=>00000000001=>11111111110=>1
[1,8,7,6,5,4,3,10,9,12,11,2]=>10000000000=>01111111111=>1
[1,8,7,6,5,4,3,12,11,10,9,2]=>10000000000=>01111111111=>1
[11,10,7,6,5,4,9,8,3,2,1,12]=>00000000001=>11111111110=>1
[1,10,7,6,5,4,9,8,3,12,11,2]=>10000000000=>01111111111=>1
[1,12,7,6,5,4,9,8,11,10,3,2]=>10000000000=>01111111111=>1
[1,12,7,6,5,4,11,10,9,8,3,2]=>10000000000=>01111111111=>1
[11,10,9,6,5,8,7,4,3,2,1,12]=>00000000001=>11111111110=>1
[1,10,9,6,5,8,7,4,3,12,11,2]=>10000000000=>01111111111=>1
[1,12,9,6,5,8,7,4,11,10,3,2]=>10000000000=>01111111111=>1
[1,12,11,6,5,8,7,10,9,4,3,2]=>10000000000=>01111111111=>1
[1,12,11,6,5,10,9,8,7,4,3,2]=>10000000000=>01111111111=>1
[11,10,9,8,7,6,5,4,3,2,1,12]=>00000000001=>11111111110=>1
[1,10,9,8,7,6,5,4,3,12,11,2]=>10000000000=>01111111111=>1
[1,12,9,8,7,6,5,4,11,10,3,2]=>10000000000=>01111111111=>1
[1,12,11,8,7,6,5,10,9,4,3,2]=>10000000000=>01111111111=>1
[1,12,11,10,7,6,9,8,5,4,3,2]=>10000000000=>01111111111=>1
[1,12,11,10,9,8,7,6,5,4,3,2]=>10000000000=>01111111111=>1
[1,5,7,2,4,3,6,8]=>1000001=>0111110=>1
[1,6,5,3,2,4,7,8]=>1000011=>0111100=>1
[1,7,2,4,6,5,3,8]=>1000001=>0111110=>1
[1,4,7,2,6,5,3,8]=>1000001=>0111110=>1
[1,2,6,8,7,4,3,5]=>1100000=>0011111=>1
[1,2,7,4,3,5,8,6]=>1100000=>0011111=>1
[1,6,2,8,7,4,3,5]=>1000000=>0111111=>1
[1,7,4,2,3,5,8,6]=>1000000=>0111111=>1
[1,8,5,2,3,6,4,7]=>1000000=>0111111=>1
[1,7,4,8,5,2,3,6]=>1000000=>0111111=>1
[1,4,7,5,2,8,6,3]=>1000000=>0111111=>1
[1,6,3,7,4,2,8,5]=>1000000=>0111111=>1
[1,8,5,2,7,4,3,6]=>1000000=>0111111=>1
[1,4,8,7,5,3,2,6]=>1000000=>0111111=>1
[1,2,5,8,6,3,7,4]=>1100000=>0011111=>1
[1,2,4,7,5,8,6,3]=>1100000=>0011111=>1
[1,5,8,7,6,2,4,3]=>1000000=>0111111=>1
[1,3,5,8,7,6,2,4]=>1000000=>0111111=>1
[1,5,2,4,3,6,8,7]=>1000110=>0111001=>2
[1,6,8,7,5,3,2,4]=>1000000=>0111111=>1
[1,2,5,7,4,3,8,6]=>1100000=>0011111=>1
[1,5,3,2,6,8,7,4]=>1000000=>0111111=>1
[1,4,2,6,8,7,5,3]=>1000000=>0111111=>1
[1,5,8,6,3,2,7,4]=>1000000=>0111111=>1
[1,8,5,2,6,3,4,7]=>1000000=>0111111=>1
[1,7,4,6,3,2,8,5]=>1000000=>0111111=>1
[1,6,3,2,8,5,4,7]=>1000000=>0111111=>1
[1,3,8,6,4,2,5,7]=>1000000=>0111111=>1
[1,5,7,4,2,3,8,6]=>1000000=>0111111=>1
[6,3,7,5,4,2,8,1]=>0000000=>1111111=>1
[7,5,2,6,3,4,8,1]=>0000000=>1111111=>1
[3,8,2,7,5,4,1,6]=>0000000=>1111111=>1
[5,4,8,6,7,1,2,3]=>0000000=>1111111=>1
[2,7,3,6,8,5,4,1]=>0000000=>1111111=>1
[3,7,2,8,1,6,4,5]=>0000000=>1111111=>1
[2,5,8,7,1,4,3,6]=>0000000=>1111111=>1
[3,4,6,5,8,2,7,1]=>0000000=>1111111=>1
[4,2,7,1,6,8,3,5]=>0000000=>1111111=>1
[5,2,8,6,4,7,1,3]=>0000000=>1111111=>1
[8,4,7,2,5,3,1,6]=>0000000=>1111111=>1
[8,3,4,5,2,1,7,6]=>0000000=>1111111=>1
[8,6,1,4,7,3,5,2]=>0000000=>1111111=>1
[5,3,6,7,2,8,4,1]=>0000000=>1111111=>1
[8,6,1,4,7,5,2,3]=>0000000=>1111111=>1
[1,5,8,2,6,7,4,3]=>1000000=>0111111=>1
[7,1,3,6,5,2,8,4]=>0000000=>1111111=>1
[8,2,1,4,5,7,6,3]=>0000000=>1111111=>1
[1,4,7,5,2,3,8,6]=>1000000=>0111111=>1
[6,1,7,5,4,2,8,3]=>0000000=>1111111=>1
[2,7,3,6,5,1,8,4]=>0000000=>1111111=>1
[8,6,5,1,3,7,4,2]=>0000000=>1111111=>1
[5,7,6,2,4,8,1,3]=>0000000=>1111111=>1
[3,7,5,6,4,8,1,2]=>0000000=>1111111=>1
[7,6,8,1,3,5,4,2]=>0000000=>1111111=>1
[2,8,4,6,1,7,5,3]=>0000000=>1111111=>1
[2,8,6,4,7,3,5,1]=>0000000=>1111111=>1
[8,7,1,4,6,5,3,2]=>0000000=>1111111=>1
[3,5,8,6,7,1,4,2]=>0000000=>1111111=>1
[1,2,4,6,8,5,3,7]=>1100000=>0011111=>1
[3,1,5,8,6,2,4,7]=>0000000=>1111111=>1
[2,5,4,6,8,1,3,7]=>0000000=>1111111=>1
[6,5,2,4,7,8,1,3]=>0000000=>1111111=>1
[7,2,5,8,6,4,1,3]=>0000000=>1111111=>1
[5,2,8,3,4,7,6,1]=>0000000=>1111111=>1
[2,4,3,8,7,1,6,5]=>0000000=>1111111=>1
[1,5,8,7,4,2,6,3]=>1000000=>0111111=>1
[6,8,7,5,4,3,1,2]=>0000000=>1111111=>1
[3,4,5,8,6,2,7,1]=>0000000=>1111111=>1
[5,1,7,4,3,6,8,2]=>0000000=>1111111=>1
[4,3,7,6,8,2,1,5]=>0000000=>1111111=>1
[6,1,8,5,2,7,3,4]=>0000000=>1111111=>1
[8,7,1,6,4,5,2,3]=>0000000=>1111111=>1
[5,4,1,3,7,2,8,6]=>0000000=>1111111=>1
[3,1,8,7,5,2,4,6]=>0000000=>1111111=>1
[6,5,8,7,2,4,3,1]=>0000000=>1111111=>1
[4,3,6,5,8,2,1,7]=>0000000=>1111111=>1
[4,7,3,1,8,5,2,6]=>0000000=>1111111=>1
[7,5,1,4,2,3,6,8]=>0000001=>1111110=>1
[7,8,6,1,2,4,5,3]=>0000000=>1111111=>1
[5,1,7,8,6,2,3,4]=>0000000=>1111111=>1
[8,5,1,6,7,2,3,4]=>0000000=>1111111=>1
[1,8,3,6,4,5,7,2]=>1000000=>0111111=>1
[7,1,6,2,5,3,4,8]=>0000001=>1111110=>1
[8,1,2,7,4,5,6,3]=>0000000=>1111111=>1
[7,1,8,2,5,3,4,6]=>0000000=>1111111=>1
[5,1,7,2,6,3,4,8]=>0000001=>1111110=>1
[1,6,3,7,4,5,8,2]=>1000000=>0111111=>1
[2,4,7,3,5,1,6,8]=>0000001=>1111110=>1
[2,4,8,6,3,5,1,7]=>0000000=>1111111=>1
[2,3,7,5,4,1,6,8]=>0000001=>1111110=>1
[3,4,6,2,1,5,8,7]=>0000010=>1111101=>2
[3,4,7,2,1,6,5,8]=>0000001=>1111110=>1
[2,3,6,1,5,8,4,7]=>0000000=>1111111=>1
[2,3,7,1,6,5,8,4]=>0000000=>1111111=>1
[2,4,7,1,3,6,8,5]=>0000000=>1111111=>1
[5,4,7,8,1,3,2,6]=>0000000=>1111111=>1
[2,5,7,1,4,6,3,8]=>0000001=>1111110=>1
[2,4,7,1,6,3,5,8]=>0000001=>1111110=>1
[2,3,7,1,6,5,4,8]=>0000001=>1111110=>1
[2,5,7,1,4,3,6,8]=>0000001=>1111110=>1
[2,5,7,3,1,4,6,8]=>0000001=>1111110=>1
[3,4,7,2,1,6,8,5]=>0000000=>1111111=>1
[4,6,3,7,1,5,2,8]=>0000001=>1111110=>1
[5,7,3,2,8,1,4,6]=>0000000=>1111111=>1
[2,6,5,7,1,8,4,3]=>0000000=>1111111=>1
[5,4,7,8,1,3,6,2]=>0000000=>1111111=>1
[2,5,7,1,4,6,8,3]=>0000000=>1111111=>1
[2,4,7,1,6,3,8,5]=>0000000=>1111111=>1
[2,4,7,1,6,8,3,5]=>0000000=>1111111=>1
[1,8,3,4,5,6,7,9,2]=>10000000=>01111111=>1
[6,5,1,4,8,3,2,7]=>0000000=>1111111=>1
[8,7,5,1,4,2,3,6]=>0000000=>1111111=>1
[8,7,5,1,4,2,6,3]=>0000000=>1111111=>1
[4,2,5,7,3,1,6,8]=>0000001=>1111110=>1
[8,2,4,5,3,1,6,7]=>0000000=>1111111=>1
[8,4,5,1,3,2,6,7]=>0000000=>1111111=>1
[4,3,7,5,2,1,6,8]=>0000001=>1111110=>1
[1,6,7,4,3,2,5,8]=>1000001=>0111110=>1
[1,4,5,7,3,2,6,8]=>1000001=>0111110=>1
[3,5,1,4,7,2,6,8]=>0000001=>1111110=>1
[2,5,1,4,7,8,3,6]=>0000000=>1111111=>1
[4,3,7,1,5,2,6,8]=>0000001=>1111110=>1
[3,5,1,6,4,2,7,8]=>0000011=>1111100=>1
[6,4,3,1,7,2,5,8]=>0000001=>1111110=>1
[6,2,7,4,3,1,5,8]=>0000001=>1111110=>1
[2,6,4,1,7,3,5,8]=>0000001=>1111110=>1
[6,3,2,7,4,5,1,8]=>0000001=>1111110=>1
[7,2,4,1,3,6,8,5]=>0000000=>1111111=>1
[6,3,2,5,7,1,4,8]=>0000001=>1111110=>1
[3,2,6,5,7,1,4,8]=>0000001=>1111110=>1
[1,7,3,2,5,6,4,8]=>1000001=>0111110=>1
[2,1,7,3,5,6,8,4]=>0100000=>1011111=>2
[2,1,6,3,5,7,8,4]=>0100000=>1011111=>2
[1,6,3,2,5,7,4,8]=>1000001=>0111110=>1
[1,4,6,5,2,7,3,8]=>1000001=>0111110=>1
[5,6,2,1,4,3,7,8]=>0000011=>1111100=>1
[2,5,1,6,4,3,7,8]=>0000011=>1111100=>1
[2,5,4,1,6,3,7,8]=>0000011=>1111100=>1
[4,6,1,5,2,7,3,8]=>0000001=>1111110=>1
[1,6,5,3,7,2,4,8]=>1000001=>0111110=>1
[1,2,5,3,4,8,7,6]=>1100100=>0011011=>2
[5,8,2,6,1,7,4,3]=>0000000=>1111111=>1
[1,5,8,3,6,2,7,4]=>1000000=>0111111=>1
[1,2,6,4,7,3,8,5]=>1100000=>0011111=>1
[1,2,7,8,3,5,6,4]=>1100000=>0011111=>1
[2,6,1,8,5,4,3,7]=>0000000=>1111111=>1
[5,8,6,2,1,4,3,7]=>0000000=>1111111=>1
[4,5,8,6,2,1,3,7]=>0000000=>1111111=>1
[6,4,7,5,8,2,1,3]=>0000000=>1111111=>1
[4,2,8,5,3,6,1,7]=>0000000=>1111111=>1
[8,1,7,4,5,6,2,3]=>0000000=>1111111=>1
[2,1,7,8,4,5,6,3]=>0100000=>1011111=>2
[8,2,1,4,3,7,6,5]=>0000000=>1111111=>1
[7,6,5,3,1,2,8,4]=>0000000=>1111111=>1
[5,4,1,6,2,8,3,7]=>0000000=>1111111=>1
[6,2,3,1,7,8,4,5]=>0000000=>1111111=>1
[3,1,8,6,7,2,4,5]=>0000000=>1111111=>1
[4,5,3,7,1,6,8,2]=>0000000=>1111111=>1
[4,2,8,5,3,6,7,1]=>0000000=>1111111=>1
[3,5,2,8,6,4,7,1]=>0000000=>1111111=>1
[7,3,5,1,6,4,8,2]=>0000000=>1111111=>1
[5,1,4,7,2,6,8,3]=>0000000=>1111111=>1
[2,7,1,4,8,5,6,3]=>0000000=>1111111=>1
[8,3,7,6,2,1,5,4]=>0000000=>1111111=>1
[8,5,2,7,6,1,4,3]=>0000000=>1111111=>1
[5,8,2,7,6,1,4,3]=>0000000=>1111111=>1
[2,6,3,7,5,4,8,1]=>0000000=>1111111=>1
[2,8,5,1,4,7,3,6]=>0000000=>1111111=>1
[7,2,6,5,8,4,3,1]=>0000000=>1111111=>1
[6,1,3,4,2,5,7,8]=>0000011=>1111100=>1
[1,5,6,3,2,4,7,8]=>1000011=>0111100=>1
[6,3,5,2,4,1,7,8]=>0000011=>1111100=>1
[7,8,3,5,2,4,6,1]=>0000000=>1111111=>1
[2,4,5,7,3,6,1,8]=>0000001=>1111110=>1
[2,5,3,1,6,4,7,8]=>0000011=>1111100=>1
[6,5,1,3,4,2,7,8]=>0000011=>1111100=>1
[5,7,4,3,2,6,1,8]=>0000001=>1111110=>1
[6,8,7,4,3,5,1,2]=>0000000=>1111111=>1
[2,6,7,8,4,3,5,1]=>0000000=>1111111=>1
[1,7,8,4,5,3,6,2]=>1000000=>0111111=>1
[7,1,8,5,3,4,6,2]=>0000000=>1111111=>1
[5,7,4,2,1,6,3,8]=>0000001=>1111110=>1
[5,1,4,7,3,6,2,8]=>0000001=>1111110=>1
[7,4,8,6,3,5,2,1]=>0000000=>1111111=>1
[4,7,6,3,5,2,1,8]=>0000001=>1111110=>1
[1,6,5,8,7,4,2,3]=>1000000=>0111111=>1
[6,1,3,8,7,5,2,4]=>0000000=>1111111=>1
[7,6,2,1,8,3,5,4]=>0000000=>1111111=>1
[7,1,3,6,8,2,5,4]=>0000000=>1111111=>1
[1,7,5,6,8,2,4,3]=>1000000=>0111111=>1
[3,6,7,5,8,2,4,1]=>0000000=>1111111=>1
[1,7,4,5,2,8,6,3]=>1000000=>0111111=>1
[7,5,4,2,1,8,6,3]=>0000000=>1111111=>1
[3,6,7,4,2,8,5,1]=>0000000=>1111111=>1
[4,6,3,2,7,8,5,1]=>0000000=>1111111=>1
[7,6,1,3,4,2,5,8]=>0000001=>1111110=>1
[7,8,2,6,4,5,3,1]=>0000000=>1111111=>1
[7,2,5,4,6,1,3,8]=>0000001=>1111110=>1
[7,1,2,4,5,6,3,8]=>0000001=>1111110=>1
[7,3,2,1,5,6,4,8]=>0000001=>1111110=>1
[3,6,2,1,7,5,4,8]=>0000001=>1111110=>1
[2,6,7,3,1,5,4,8]=>0000001=>1111110=>1
[2,1,6,4,7,5,3,8]=>0100001=>1011110=>2
[7,2,8,5,6,4,3,1]=>0000000=>1111111=>1
[7,6,8,5,4,1,3,2]=>0000000=>1111111=>1
[7,1,8,4,6,5,3,2]=>0000000=>1111111=>1
[7,8,6,3,1,5,4,2]=>0000000=>1111111=>1
[7,6,1,4,5,3,2,8]=>0000001=>1111110=>1
[7,1,5,6,4,3,2,8]=>0000001=>1111110=>1
[5,6,3,2,8,1,7,4]=>0000000=>1111111=>1
[8,2,6,3,1,5,7,4]=>0000000=>1111111=>1
[8,2,5,3,4,7,6,1]=>0000000=>1111111=>1
[7,5,3,2,4,1,8,6]=>0000000=>1111111=>1
[7,1,2,3,6,8,4,5]=>0000000=>1111111=>1
[3,1,8,4,6,5,7,2]=>0000000=>1111111=>1
[8,1,6,7,4,2,3,5]=>0000000=>1111111=>1
[8,1,6,4,5,2,3,7]=>0000000=>1111111=>1
[8,6,4,1,2,3,7,5]=>0000000=>1111111=>1
[8,6,1,4,2,5,7,3]=>0000000=>1111111=>1
[8,6,4,1,5,7,2,3]=>0000000=>1111111=>1
[8,6,1,4,7,2,5,3]=>0000000=>1111111=>1
[8,6,4,1,5,2,3,7]=>0000000=>1111111=>1
[8,6,7,1,4,5,2,3]=>0000000=>1111111=>1
[3,4,7,5,8,2,6,1]=>0000000=>1111111=>1
[8,7,1,4,6,5,2,3]=>0000000=>1111111=>1
[8,3,7,6,4,5,1,2]=>0000000=>1111111=>1
[5,3,8,6,4,1,7,2]=>0000000=>1111111=>1
[10,8,1,9,2,3,4,5,6,7]=>000000000=>111111111=>1
[6,1,2,3,4,5,7,8,9]=>00000111=>11111000=>1
[5,1,2,3,4,6,7,8,9]=>00001111=>11110000=>1
[4,1,2,3,5,6,7,8,9]=>00011111=>11100000=>1
[6,4,7,1,8,5,2,3]=>0000000=>1111111=>1
[3,8,2,5,1,7,4,6]=>0000000=>1111111=>1
[4,8,5,2,1,7,3,6]=>0000000=>1111111=>1
[6,8,7,5,2,4,1,3]=>0000000=>1111111=>1
[8,6,4,1,7,3,2,5]=>0000000=>1111111=>1
[8,9,2,3,4,5,6,7,1]=>00000000=>11111111=>1
[9,8,7,6,4,5,3,2,1]=>00000000=>11111111=>1
[5,6,7,8,9,1,4,3,2]=>00000000=>11111111=>1
[3,4,7,8,5,1,2,6]=>0000000=>1111111=>1
[4,7,3,2,5,6,8,1]=>0000000=>1111111=>1
[3,2,7,6,4,5,8,1]=>0000000=>1111111=>1
[1,7,3,6,8,4,2,5]=>1000000=>0111111=>1
[2,3,6,5,1,8,7,4]=>0000000=>1111111=>1
[8,3,1,2,6,4,7,5]=>0000000=>1111111=>1
[1,7,8,2,4,3,5,6]=>1000000=>0111111=>1
[3,6,4,7,1,2,8,5]=>0000000=>1111111=>1
[5,7,4,8,1,3,2,6]=>0000000=>1111111=>1
[4,3,7,8,1,5,2,6]=>0000000=>1111111=>1
[8,5,4,2,6,1,7,3]=>0000000=>1111111=>1
[3,2,6,8,7,4,1,5]=>0000000=>1111111=>1
[2,3,7,5,1,8,6,4]=>0000000=>1111111=>1
[6,3,1,2,8,7,4,5]=>0000000=>1111111=>1
[5,2,1,3,8,7,6,4]=>0000000=>1111111=>1
[7,2,1,5,3,8,4,6]=>0000000=>1111111=>1
[1,5,8,2,4,3,6,7]=>1000000=>0111111=>1
[4,3,6,8,1,5,2,7]=>0000000=>1111111=>1
[5,4,6,8,3,1,7,2]=>0000000=>1111111=>1
[3,6,8,4,5,1,7,2]=>0000000=>1111111=>1
[8,6,1,7,2,4,3,5]=>0000000=>1111111=>1
[7,3,1,2,8,6,4,5]=>0000000=>1111111=>1
[2,3,7,6,1,8,5,4]=>0000000=>1111111=>1
[3,2,7,8,6,4,1,5]=>0000000=>1111111=>1
[6,2,8,3,1,4,7,5]=>0000000=>1111111=>1
[3,1,2,8,7,4,5,6]=>0010000=>1101111=>2
[2,1,3,8,7,4,6,5]=>0110000=>1001111=>2
[2,1,3,8,7,4,5,6]=>0110000=>1001111=>2
[1,6,8,3,2,4,7,5]=>1000000=>0111111=>1
[8,5,1,7,2,4,3,6]=>0000000=>1111111=>1
[8,4,1,7,3,2,5,6]=>0000000=>1111111=>1
[8,3,1,6,2,7,5,4]=>0000000=>1111111=>1
[1,3,2,8,7,6,4,5]=>1010000=>0101111=>2
[2,1,3,8,7,6,4,5]=>0110000=>1001111=>2
[1,6,3,7,2,5,4,8]=>1000001=>0111110=>1
[1,7,2,4,6,3,5,8]=>1000001=>0111110=>1
[3,5,8,4,2,1,6,7]=>0000000=>1111111=>1
[2,5,8,3,1,4,6,7]=>0000000=>1111111=>1
[2,8,1,3,5,7,4,6]=>0000000=>1111111=>1
[3,4,8,5,7,1,2,6]=>0000000=>1111111=>1
[3,6,8,7,2,5,4,1]=>0000000=>1111111=>1
[2,4,6,7,8,3,5,1]=>0000000=>1111111=>1
[1,4,2,5,7,6,3,8]=>1000001=>0111110=>1
[1,4,2,6,8,5,3,7]=>1000000=>0111111=>1
[1,2,6,8,3,5,4,7]=>1100000=>0011111=>1
[1,6,8,3,5,4,2,7]=>1000000=>0111111=>1
[1,5,3,2,4,6,8,7]=>1000110=>0111001=>2
[1,5,8,7,6,3,2,4]=>1000000=>0111111=>1
[1,5,7,6,3,2,4,8]=>1000001=>0111110=>1
[1,6,3,2,4,7,5,8]=>1000001=>0111110=>1
[1,6,3,2,4,8,7,5]=>1000000=>0111111=>1
[1,2,7,6,4,3,5,8]=>1100001=>0011110=>1
[1,8,7,5,2,4,6,3]=>1000000=>0111111=>1
[1,7,5,2,4,6,3,8]=>1000001=>0111110=>1
[1,7,4,2,5,3,6,8]=>1000001=>0111110=>1
[1,8,4,7,5,2,6,3]=>1000000=>0111111=>1
[1,7,5,2,3,6,4,8]=>1000001=>0111110=>1
[1,7,5,2,6,3,4,8]=>1000001=>0111110=>1
[1,6,3,7,4,2,5,8]=>1000001=>0111110=>1
[1,6,3,2,7,5,4,8]=>1000001=>0111110=>1
[1,4,7,5,2,6,3,8]=>1000001=>0111110=>1
[1,3,6,4,8,7,5,2]=>1000000=>0111111=>1
[1,3,7,6,4,2,5,8]=>1000001=>0111110=>1
[1,3,2,4,8,5,7,6]=>1011000=>0100111=>2
[1,3,8,7,5,2,4,6]=>1000000=>0111111=>1
[1,4,6,3,2,7,5,8]=>1000001=>0111110=>1
[1,4,6,3,2,8,7,5]=>1000000=>0111111=>1
[1,5,7,6,4,2,3,8]=>1000001=>0111110=>1
[1,6,3,2,8,4,7,5]=>1000000=>0111111=>1
[1,6,3,5,2,7,4,8]=>1000001=>0111110=>1
[1,6,3,5,2,8,7,4]=>1000000=>0111111=>1
[1,8,3,7,5,2,4,6]=>1000000=>0111111=>1
[7,8,4,9,5,2,10,6,3,1]=>000000000=>111111111=>1
[1,3,4,2,8,5,7,6]=>1001000=>0110111=>2
[3,2,1,4,8,5,7,6]=>0011000=>1100111=>2
[7,4,1,6,2,5,3,8]=>0000001=>1111110=>1
[5,4,1,8,2,6,3,7]=>0000000=>1111111=>1
[6,5,1,4,2,7,3,8]=>0000001=>1111110=>1
[1,8,7,3,4,5,2,6]=>1000000=>0111111=>1
[1,8,9,3,4,5,6,7,2]=>10000000=>01111111=>1
[1,8,7,4,5,2,3,6]=>1000000=>0111111=>1
[1,2,6,8,7,3,4,5]=>1100000=>0011111=>1
[1,3,7,8,4,5,6,2]=>1000000=>0111111=>1
[1,3,4,5,6,7,8,9,10,11,12,2]=>10000000000=>01111111111=>1
[6,4,2,1,8,5,3,7]=>0000000=>1111111=>1
[2,8,6,4,5,1,7,3]=>0000000=>1111111=>1
[2,6,3,1,7,4,8,5]=>0000000=>1111111=>1
[1,8,7,4,5,3,2,6]=>1000000=>0111111=>1
[2,8,3,1,4,5,7,6]=>0000000=>1111111=>1
[6,1,7,2,8,4,5,3]=>0000000=>1111111=>1
[8,3,2,1,5,6,7,4]=>0000000=>1111111=>1
[3,2,6,7,8,4,5,1]=>0000000=>1111111=>1
[4,5,3,1,8,7,6,2]=>0000000=>1111111=>1
[6,3,4,2,7,8,5,1]=>0000000=>1111111=>1
[5,1,8,4,3,7,2,6]=>0000000=>1111111=>1
[7,2,8,1,4,5,6,3]=>0000000=>1111111=>1
[2,3,4,5,10,6,7,8,9,1]=>000000000=>111111111=>1
[8,1,6,7,2,5,4,3]=>0000000=>1111111=>1
[8,1,4,6,5,3,2,7]=>0000000=>1111111=>1
[8,1,4,7,6,5,2,3]=>0000000=>1111111=>1
[8,1,2,7,6,5,4,3]=>0000000=>1111111=>1
[3,2,8,6,1,5,7,4]=>0000000=>1111111=>1
[3,7,2,5,8,4,6,1]=>0000000=>1111111=>1
[6,7,8,4,1,5,2,3]=>0000000=>1111111=>1
[6,2,7,4,5,3,1,8]=>0000001=>1111110=>1
[6,1,8,7,4,5,2,3]=>0000000=>1111111=>1
[1,3,2,6,8,7,4,5]=>1010000=>0101111=>2
[1,3,8,2,5,4,6,7]=>1000000=>0111111=>1
[1,6,2,5,8,7,3,4]=>1000000=>0111111=>1
[1,6,8,7,2,3,5,4]=>1000000=>0111111=>1
[1,6,8,7,2,5,3,4]=>1000000=>0111111=>1
[1,5,2,4,8,3,6,7]=>1000000=>0111111=>1
[1,2,4,5,8,6,3,7]=>1100000=>0011111=>1
[1,2,8,3,5,4,7,6]=>1100000=>0011111=>1
[1,3,8,2,5,4,7,6]=>1000000=>0111111=>1
[1,6,7,5,2,4,8,3]=>1000000=>0111111=>1
[1,5,6,4,7,2,3,8]=>1000001=>0111110=>1
[1,7,4,2,5,8,3,6]=>1000000=>0111111=>1
[1,6,4,3,7,5,2,8]=>1000001=>0111110=>1
[1,6,5,4,7,2,3,8]=>1000001=>0111110=>1
[1,7,3,2,6,4,8,5]=>1000000=>0111111=>1
[1,5,8,2,3,6,7,4]=>1000000=>0111111=>1
[1,3,2,6,8,5,4,7]=>1010000=>0101111=>2
[1,6,3,2,7,4,5,8]=>1000001=>0111110=>1
[1,7,8,5,4,2,3,6]=>1000000=>0111111=>1
[1,8,4,2,3,6,5,7]=>1000000=>0111111=>1
[1,4,2,7,5,3,8,6]=>1000000=>0111111=>1
[1,5,7,6,2,4,3,8]=>1000001=>0111110=>1
[1,8,4,7,3,2,6,5]=>1000000=>0111111=>1
[1,3,8,4,2,6,5,7]=>1000000=>0111111=>1
[1,7,4,2,6,5,8,3]=>1000000=>0111111=>1
[1,6,5,8,3,7,4,2]=>1000000=>0111111=>1
[1,7,4,8,3,2,5,6]=>1000000=>0111111=>1
[1,4,8,3,2,7,5,6]=>1000000=>0111111=>1
[1,8,3,6,4,5,2,7]=>1000000=>0111111=>1
[1,6,4,7,3,2,8,5]=>1000000=>0111111=>1
[7,6,3,2,1,8,4,5]=>0000000=>1111111=>1
[7,1,6,5,4,3,8,2]=>0000000=>1111111=>1
[5,1,7,3,8,6,2,4]=>0000000=>1111111=>1
[3,4,5,6,1,8,9,2,7]=>00000000=>11111111=>1
[3,4,5,6,8,1,9,2,7]=>00000000=>11111111=>1
[3,4,5,6,8,9,1,2,7]=>00000000=>11111111=>1
[2,4,5,1,6,7,8,9,3]=>00000000=>11111111=>1
[2,3,4,1,6,7,8,9,5]=>00010000=>11101111=>2
[2,3,4,5,6,1,8,9,10,7]=>000001000=>111110111=>2
[3,4,5,6,1,2,9,7,8]=>00000100=>11111011=>2
[3,4,5,6,8,1,2,7,9]=>00000001=>11111110=>1
[2,3,4,5,6,8,9,1,10,7]=>000000000=>111111111=>1
[3,4,5,1,6,7,8,2,9]=>00000001=>11111110=>1
[5,6,1,7,8,9,2,3,4]=>00000000=>11111111=>1
[4,5,6,1,7,8,9,10,2,3]=>000000000=>111111111=>1
[1,3,5,2,6,7,8,9,4]=>10000000=>01111111=>1
[3,5,6,1,7,8,9,10,2,4]=>000000000=>111111111=>1
[2,1,4,3,6,7,8,9,5]=>01010000=>10101111=>3
[3,4,6,1,7,8,9,10,2,5]=>000000000=>111111111=>1
[2,3,1,5,6,7,8,9,4]=>00100000=>11011111=>2
[3,4,5,1,7,8,9,10,2,6]=>000000000=>111111111=>1
[3,2,5,8,7,4,1,6]=>0000000=>1111111=>1
[4,2,5,8,7,3,1,6]=>0000000=>1111111=>1
[8,3,4,1,6,5,2,7]=>0000000=>1111111=>1
[3,4,8,5,7,2,1,6]=>0000000=>1111111=>1
[3,6,4,8,5,7,2,1]=>0000000=>1111111=>1
[5,8,4,7,3,6,2,1]=>0000000=>1111111=>1
[4,2,8,7,3,1,6,5]=>0000000=>1111111=>1
[6,5,8,2,1,7,4,3]=>0000000=>1111111=>1
[6,1,4,3,8,7,2,5]=>0000000=>1111111=>1
[5,1,3,2,6,8,7,4]=>0000000=>1111111=>1
[6,1,3,8,7,2,4,5]=>0000000=>1111111=>1
[1,2,8,4,5,7,3,6]=>1100000=>0011111=>1
[4,2,1,8,7,6,3,5]=>0000000=>1111111=>1
[3,2,5,8,7,1,4,6]=>0000000=>1111111=>1
[5,6,3,8,7,2,1,4]=>0000000=>1111111=>1
[2,5,8,4,7,1,6,3]=>0000000=>1111111=>1
[1,6,2,4,8,5,7,3]=>1000000=>0111111=>1
[3,1,6,5,8,7,2,4]=>0000000=>1111111=>1
[4,8,5,3,6,7,1,2]=>0000000=>1111111=>1
[1,8,5,3,4,7,6,2]=>1000000=>0111111=>1
[2,7,1,3,6,4,5,8]=>0000001=>1111110=>1
[3,2,4,8,5,7,1,6]=>0000000=>1111111=>1
[8,1,2,4,7,5,6,3]=>0000000=>1111111=>1
[6,4,5,8,3,1,7,2]=>0000000=>1111111=>1
[4,6,2,8,5,3,7,1]=>0000000=>1111111=>1
[8,7,2,4,1,5,3,6]=>0000000=>1111111=>1
[7,5,3,4,8,6,2,1]=>0000000=>1111111=>1
[4,3,6,5,1,2,7,8]=>0000011=>1111100=>1
[5,8,3,7,6,4,2,1]=>0000000=>1111111=>1
[1,3,8,7,6,5,2,4]=>1000000=>0111111=>1
[1,8,7,2,6,3,5,4]=>1000000=>0111111=>1
[8,7,2,1,4,3,5,6]=>0000000=>1111111=>1
[2,8,7,1,6,3,4,5]=>0000000=>1111111=>1
[4,2,8,7,6,5,1,3]=>0000000=>1111111=>1
[1,2,5,7,4,8,6,3]=>1100000=>0011111=>1
[6,2,1,8,7,5,3,4]=>0000000=>1111111=>1
[2,8,3,4,1,5,6,7]=>0000000=>1111111=>1
[1,3,7,5,4,8,6,2]=>1000000=>0111111=>1
[1,5,6,3,8,4,2,7]=>1000000=>0111111=>1
[2,6,5,3,8,4,1,7]=>0000000=>1111111=>1
[5,7,3,8,4,2,6,1]=>0000000=>1111111=>1
[5,3,6,2,8,4,1,7]=>0000000=>1111111=>1
[2,3,6,5,4,8,1,7]=>0000000=>1111111=>1
[5,3,7,1,2,8,4,6]=>0000000=>1111111=>1
[6,3,8,7,2,5,4,1]=>0000000=>1111111=>1
[1,2,3,4,6,5,7,8,9]=>11110111=>00001000=>1
[1,2,3,5,4,6,7,8,9]=>11101111=>00010000=>1
[8,1,4,6,7,5,2,3]=>0000000=>1111111=>1
[6,4,8,1,2,7,5,3]=>0000000=>1111111=>1
[8,2,1,6,7,4,5,3]=>0000000=>1111111=>1
[4,2,8,1,6,7,5,3]=>0000000=>1111111=>1
[4,8,2,1,6,7,5,3]=>0000000=>1111111=>1
[8,2,4,6,1,7,5,3]=>0000000=>1111111=>1
[2,1,4,5,6,7,8,9,10,3]=>010000000=>101111111=>2
[2,3,4,1,6,5,8,7,10,9]=>000101010=>111010101=>4
[2,3,4,1,6,7,8,9,10,5]=>000100000=>111011111=>2
[4,3,5,6,7,8,9,10,1,2]=>000000000=>111111111=>1
[2,3,4,5,6,1,8,7,10,9]=>000001010=>111110101=>3
[2,3,4,5,6,7,8,1,10,9]=>000000010=>111111101=>2
[2,3,4,5,6,7,8,9,10,1,12,11]=>00000000010=>11111111101=>2
[4,6,1,3,2,8,7,5]=>0000000=>1111111=>1
[7,1,4,8,2,3,6,5]=>0000000=>1111111=>1
[4,5,3,6,7,1,8,2]=>0000000=>1111111=>1
[1,4,7,8,3,5,2,6]=>1000000=>0111111=>1
[4,6,1,3,5,2,8,7]=>0000010=>1111101=>2
[2,5,1,4,8,3,7,6]=>0000000=>1111111=>1
[6,1,2,5,4,8,7,3]=>0000000=>1111111=>1
[8,4,1,2,5,7,3,6]=>0000000=>1111111=>1
[2,4,5,6,8,3,1,7]=>0000000=>1111111=>1
[3,4,5,8,6,2,1,7]=>0000000=>1111111=>1
[1,8,2,3,4,5,9,6,7]=>10000000=>01111111=>1
[8,3,7,2,1,6,5,4]=>0000000=>1111111=>1
[8,4,7,6,2,5,1,3]=>0000000=>1111111=>1
[8,4,7,3,6,2,1,5]=>0000000=>1111111=>1
[3,8,7,5,6,4,1,2]=>0000000=>1111111=>1
[3,8,7,5,6,2,1,4]=>0000000=>1111111=>1
[3,8,7,5,6,2,4,1]=>0000000=>1111111=>1
[2,8,7,5,6,4,1,3]=>0000000=>1111111=>1
[4,5,2,3,6,7,8,9,1]=>00000000=>11111111=>1
[4,3,2,5,6,7,8,9,1]=>00000000=>11111111=>1
[5,6,7,2,3,4,8,9,1]=>00000000=>11111111=>1
[5,3,6,2,4,7,8,9,1]=>00000000=>11111111=>1
[5,4,3,2,6,7,8,9,1]=>00000000=>11111111=>1
[6,3,7,8,2,4,5,9,1]=>00000000=>11111111=>1
[6,7,4,5,2,3,8,9,1]=>00000000=>11111111=>1
[6,4,3,7,2,5,8,9,1]=>00000000=>11111111=>1
[7,8,4,5,9,2,3,6,1]=>00000000=>11111111=>1
[7,4,3,8,9,2,5,6,1]=>00000000=>11111111=>1
[7,5,8,3,6,2,4,9,1]=>00000000=>11111111=>1
[7,5,4,3,8,2,6,9,1]=>00000000=>11111111=>1
[7,6,5,4,3,2,8,9,1]=>00000000=>11111111=>1
[8,6,4,9,3,7,2,5,1]=>00000000=>11111111=>1
[8,6,5,4,3,9,2,7,1]=>00000000=>11111111=>1
[4,5,2,3,6,7,8,9,10,1]=>000000000=>111111111=>1
[4,3,2,5,6,7,8,9,10,1]=>000000000=>111111111=>1
[5,6,7,2,3,4,8,9,10,1]=>000000000=>111111111=>1
[5,3,6,2,4,7,8,9,10,1]=>000000000=>111111111=>1
[5,4,3,2,6,7,8,9,10,1]=>000000000=>111111111=>1
[6,7,8,9,2,3,4,5,10,1]=>000000000=>111111111=>1
[6,3,7,8,2,4,5,9,10,1]=>000000000=>111111111=>1
[6,7,4,5,2,3,8,9,10,1]=>000000000=>111111111=>1
[6,4,3,7,2,5,8,9,10,1]=>000000000=>111111111=>1
[6,5,4,3,2,7,8,9,10,1]=>000000000=>111111111=>1
[7,8,9,10,1,3,4,5,6,2]=>000000000=>111111111=>1
[7,3,8,9,10,2,4,5,6,1]=>000000000=>111111111=>1
[7,4,3,8,9,2,5,6,10,1]=>000000000=>111111111=>1
[7,5,8,3,6,2,4,9,10,1]=>000000000=>111111111=>1
[7,5,4,3,8,2,6,9,10,1]=>000000000=>111111111=>1
[7,6,5,4,3,2,8,9,10,1]=>000000000=>111111111=>1
[8,5,9,3,6,10,2,4,7,1]=>000000000=>111111111=>1
[8,5,4,3,9,10,2,6,7,1]=>000000000=>111111111=>1
[8,9,6,7,4,5,2,3,10,1]=>000000000=>111111111=>1
[8,6,4,9,3,7,2,5,10,1]=>000000000=>111111111=>1
[8,6,5,4,3,9,2,7,10,1]=>000000000=>111111111=>1
[8,7,6,5,4,3,2,9,10,1]=>000000000=>111111111=>1
[9,7,5,4,10,3,8,2,6,1]=>000000000=>111111111=>1
[9,7,6,5,4,3,10,2,8,1]=>000000000=>111111111=>1
[1,5,6,3,8,2,7,4]=>1000000=>0111111=>1
[2,6,3,8,4,7,1,5]=>0000000=>1111111=>1
[2,6,3,5,7,8,1,4]=>0000000=>1111111=>1
[1,5,6,3,7,2,8,4]=>1000000=>0111111=>1
[1,7,5,3,6,2,8,4]=>1000000=>0111111=>1
[1,5,7,3,4,2,8,6]=>1000000=>0111111=>1
[1,5,8,3,4,2,7,6]=>1000000=>0111111=>1
[1,4,5,3,7,2,8,6]=>1000000=>0111111=>1
[1,4,5,3,8,2,7,6]=>1000000=>0111111=>1
[6,5,1,4,2,7,8,3]=>0000000=>1111111=>1
[6,5,1,4,2,8,7,3]=>0000000=>1111111=>1
[1,7,5,4,2,8,6,3]=>1000000=>0111111=>1
[1,2,3,4,5,6,7,8,9,10,11]=>1111111111=>0000000000=>0
[2,4,1,5,3,6,7,8,9]=>00001111=>11110000=>1
[1,4,8,2,6,5,3,7]=>1000000=>0111111=>1
[7,5,1,8,3,4,2,6]=>0000000=>1111111=>1
[1,2,5,6,8,7,3,4]=>1100000=>0011111=>1
[2,6,7,3,4,1,8,5]=>0000000=>1111111=>1
[1,6,5,7,8,2,4,3]=>1000000=>0111111=>1
[1,3,7,2,6,4,8,5]=>1000000=>0111111=>1
[1,6,5,8,7,2,4,3]=>1000000=>0111111=>1
[3,6,5,8,1,2,7,4]=>0000000=>1111111=>1
[5,4,7,8,1,6,3,2]=>0000000=>1111111=>1
[2,5,6,8,1,3,7,4]=>0000000=>1111111=>1
[5,3,6,8,1,2,7,4]=>0000000=>1111111=>1
[4,6,5,8,3,2,7,1]=>0000000=>1111111=>1
[4,5,6,8,2,3,7,1]=>0000000=>1111111=>1
[2,5,8,7,1,6,4,3]=>0000000=>1111111=>1
[4,7,5,8,3,6,2,1]=>0000000=>1111111=>1
[7,3,6,8,5,2,1,4]=>0000000=>1111111=>1
[8,3,6,7,5,2,4,1]=>0000000=>1111111=>1
[8,4,5,7,3,6,2,1]=>0000000=>1111111=>1
[2,4,7,8,5,6,3,1]=>0000000=>1111111=>1
[3,6,8,7,5,2,4,1]=>0000000=>1111111=>1
[6,4,7,8,5,1,3,2]=>0000000=>1111111=>1
[7,8,4,6,5,3,1,2]=>0000000=>1111111=>1
[6,8,4,7,5,1,3,2]=>0000000=>1111111=>1
[8,9,2,3,4,5,1,6,7]=>00000000=>11111111=>1
[6,5,7,8,9,1,2,3,4]=>00000000=>11111111=>1
[7,6,1,2,3,5,4,8]=>0000001=>1111110=>1
[2,8,7,5,1,6,3,4]=>0000000=>1111111=>1
[8,7,6,4,2,1,5,3]=>0000000=>1111111=>1
[3,8,7,5,2,6,4,1]=>0000000=>1111111=>1
[3,8,7,5,1,2,6,4]=>0000000=>1111111=>1
[5,3,8,2,4,6,1,7]=>0000000=>1111111=>1
[4,5,8,3,2,6,1,7]=>0000000=>1111111=>1
[5,8,2,1,4,6,3,7]=>0000000=>1111111=>1
[4,1,5,8,3,6,2,7]=>0000000=>1111111=>1
[4,5,8,3,6,1,2,7]=>0000000=>1111111=>1
[3,2,7,1,8,5,4,6]=>0000000=>1111111=>1
[4,7,8,5,2,3,1,6]=>0000000=>1111111=>1
[6,2,7,8,1,5,3,4]=>0000000=>1111111=>1
[2,6,7,8,4,1,3,5]=>0000000=>1111111=>1
[2,6,7,8,4,3,1,5]=>0000000=>1111111=>1
[7,1,2,3,4,5,8,6,9]=>00000001=>11111110=>1
[6,1,2,3,4,7,5,8,9]=>00000011=>11111100=>1
[5,1,2,3,6,4,7,8,9]=>00000111=>11111000=>1
[4,1,2,5,3,6,7,8,9]=>00001111=>11110000=>1
[8,1,2,6,5,3,7,4]=>0000000=>1111111=>1
[8,5,4,6,1,2,7,3]=>0000000=>1111111=>1
[7,4,1,8,2,5,3,6]=>0000000=>1111111=>1
[8,4,5,3,1,6,7,2]=>0000000=>1111111=>1
[8,2,3,1,6,7,4,5]=>0000000=>1111111=>1
[8,2,1,7,4,3,5,6]=>0000000=>1111111=>1
[3,7,5,8,2,4,6,1]=>0000000=>1111111=>1
[3,5,6,8,4,7,1,2]=>0000000=>1111111=>1
[6,2,8,4,5,3,7,1]=>0000000=>1111111=>1
[4,7,3,1,8,6,2,5]=>0000000=>1111111=>1
[7,2,5,8,1,3,6,4]=>0000000=>1111111=>1
[6,1,2,4,5,7,8,3]=>0000000=>1111111=>1
[3,6,4,5,2,8,1,7]=>0000000=>1111111=>1
[8,1,5,4,7,3,6,2]=>0000000=>1111111=>1
[7,6,5,4,1,8,2,3]=>0000000=>1111111=>1
[8,1,5,4,7,6,3,2]=>0000000=>1111111=>1
[2,5,1,4,6,7,3,8]=>0000001=>1111110=>1
[7,6,5,2,8,4,1,3]=>0000000=>1111111=>1
[3,1,6,5,2,8,7,4]=>0000000=>1111111=>1
[1,7,2,4,3,5,8,6]=>1000000=>0111111=>1
[3,8,1,7,4,2,6,5]=>0000000=>1111111=>1
[8,1,7,4,3,5,6,2]=>0000000=>1111111=>1
[6,8,2,4,5,3,7,1]=>0000000=>1111111=>1
[4,8,5,3,6,1,7,2]=>0000000=>1111111=>1
[2,7,3,1,8,4,5,6]=>0000000=>1111111=>1
[1,2,8,3,5,6,4,7]=>1100000=>0011111=>1
[3,5,7,4,8,1,6,2]=>0000000=>1111111=>1
[1,5,2,8,6,4,3,7]=>1000000=>0111111=>1
[7,4,8,6,3,1,2,5]=>0000000=>1111111=>1
[3,6,8,4,1,2,5,7]=>0000000=>1111111=>1
[4,7,8,5,2,1,3,6]=>0000000=>1111111=>1
[6,1,5,2,8,7,3,4]=>0000000=>1111111=>1
[8,1,3,5,7,4,2,6]=>0000000=>1111111=>1
[3,1,8,5,4,7,2,6]=>0000000=>1111111=>1
[3,1,6,4,8,5,2,7]=>0000000=>1111111=>1
[5,1,3,4,2,6,8,7]=>0000110=>1111001=>2
[3,2,6,4,1,5,7,8]=>0000011=>1111100=>1
[5,4,2,1,8,3,6,7]=>0000000=>1111111=>1
[4,2,5,1,8,7,3,6]=>0000000=>1111111=>1
[6,8,2,7,1,4,3,5]=>0000000=>1111111=>1
[1,8,4,7,3,2,5,6]=>1000000=>0111111=>1
[8,6,3,1,5,7,2,4]=>0000000=>1111111=>1
[5,8,3,1,4,7,6,2]=>0000000=>1111111=>1
[1,2,5,4,7,8,3,6]=>1100000=>0011111=>1
[1,8,3,2,6,4,7,5]=>1000000=>0111111=>1
[4,7,1,2,5,3,6,8]=>0000001=>1111110=>1
[6,8,4,1,3,7,2,5]=>0000000=>1111111=>1
[3,2,6,1,7,8,5,4]=>0000000=>1111111=>1
[7,6,4,1,8,3,5,2]=>0000000=>1111111=>1
[5,4,1,6,7,3,2,8]=>0000001=>1111110=>1
[7,4,1,6,5,8,2,3]=>0000000=>1111111=>1
[8,5,4,1,6,7,3,2]=>0000000=>1111111=>1
[1,3,4,8,5,2,6,7]=>1000000=>0111111=>1
[7,3,1,4,2,5,8,6]=>0000000=>1111111=>1
[3,2,5,7,8,4,1,6]=>0000000=>1111111=>1
[8,6,3,5,4,1,2,7]=>0000000=>1111111=>1
[8,3,2,6,1,5,4,7]=>0000000=>1111111=>1
[8,5,1,7,4,6,2,3]=>0000000=>1111111=>1
[4,8,1,7,6,3,5,2]=>0000000=>1111111=>1
[8,5,1,7,4,3,6,2]=>0000000=>1111111=>1
[8,5,7,6,2,1,3,4]=>0000000=>1111111=>1
[5,4,8,3,1,7,2,6]=>0000000=>1111111=>1
[5,1,4,8,3,2,7,6]=>0000000=>1111111=>1
[4,8,1,7,6,5,2,3]=>0000000=>1111111=>1
[4,3,8,7,2,6,1,5]=>0000000=>1111111=>1
[3,8,7,2,6,4,1,5]=>0000000=>1111111=>1
[8,2,5,7,4,3,6,1]=>0000000=>1111111=>1
[3,8,7,4,6,1,2,5]=>0000000=>1111111=>1
[8,7,6,3,5,4,1,2]=>0000000=>1111111=>1
[2,8,4,7,6,1,5,3]=>0000000=>1111111=>1
[2,5,4,8,3,1,7,6]=>0000000=>1111111=>1
[5,4,8,2,1,3,7,6]=>0000000=>1111111=>1
[3,8,7,2,6,1,5,4]=>0000000=>1111111=>1
[1,8,4,7,6,3,5,2]=>1000000=>0111111=>1
[1,8,3,7,6,5,2,4]=>1000000=>0111111=>1
[1,4,3,8,7,2,6,5]=>1000000=>0111111=>1
[7,1,5,4,6,2,3,8]=>0000001=>1111110=>1
[7,4,1,3,6,2,5,8]=>0000001=>1111110=>1
[5,4,3,1,7,6,2,8]=>0000001=>1111110=>1
[2,5,4,8,1,7,3,6]=>0000000=>1111111=>1
[7,5,2,4,8,3,6,1]=>0000000=>1111111=>1
[7,8,2,6,3,5,4,1]=>0000000=>1111111=>1
[7,2,6,5,8,3,4,1]=>0000000=>1111111=>1
[5,6,3,1,4,2,7,8]=>0000011=>1111100=>1
[2,6,5,3,4,8,7,1]=>0000000=>1111111=>1
[2,6,1,5,3,4,7,8]=>0000011=>1111100=>1
[3,4,7,8,5,1,6,2]=>0000000=>1111111=>1
[3,6,2,4,7,8,5,1]=>0000000=>1111111=>1
[5,3,6,4,8,7,2,1]=>0000000=>1111111=>1
[1,5,4,8,6,2,7,3]=>1000000=>0111111=>1
[4,5,2,7,6,3,8,1]=>0000000=>1111111=>1
[5,8,3,1,2,7,6,4]=>0000000=>1111111=>1
[8,4,6,1,3,7,2,5]=>0000000=>1111111=>1
[4,8,5,1,2,3,6,7]=>0000000=>1111111=>1
[4,5,1,3,8,6,2,7]=>0000000=>1111111=>1
[7,4,2,3,6,8,5,1]=>0000000=>1111111=>1
[7,8,1,3,6,4,5,2]=>0000000=>1111111=>1
[7,2,6,8,4,5,3,1]=>0000000=>1111111=>1
[7,3,6,8,5,1,4,2]=>0000000=>1111111=>1
[7,5,8,1,6,2,4,3]=>0000000=>1111111=>1
[5,7,8,1,6,3,2,4]=>0000000=>1111111=>1
[7,2,6,8,5,1,4,3]=>0000000=>1111111=>1
[7,5,2,4,8,3,1,6]=>0000000=>1111111=>1
[7,8,3,1,6,2,5,4]=>0000000=>1111111=>1
[6,7,8,4,3,1,5,2]=>0000000=>1111111=>1
[7,8,3,6,4,1,5,2]=>0000000=>1111111=>1
[7,3,8,1,6,4,5,2]=>0000000=>1111111=>1
[1,7,5,8,2,4,6,3]=>1000000=>0111111=>1
[7,5,2,8,1,4,6,3]=>0000000=>1111111=>1
[3,7,8,2,6,5,1,4]=>0000000=>1111111=>1
[3,7,8,2,1,6,4,5]=>0000000=>1111111=>1
[7,8,1,6,3,5,4,2]=>0000000=>1111111=>1
[6,7,8,2,5,4,3,1]=>0000000=>1111111=>1
[6,7,8,3,1,5,4,2]=>0000000=>1111111=>1
[7,8,1,6,2,5,4,3]=>0000000=>1111111=>1
[5,6,1,4,3,8,2,7]=>0000000=>1111111=>1
[5,1,6,8,3,4,7,2]=>0000000=>1111111=>1
[7,1,6,8,5,4,3,2]=>0000000=>1111111=>1
[5,6,8,1,2,3,7,4]=>0000000=>1111111=>1
[4,8,1,2,7,6,5,3]=>0000000=>1111111=>1
[6,4,7,3,5,2,1,8]=>0000001=>1111110=>1
[3,1,6,2,5,7,8,4]=>0000000=>1111111=>1
[1,6,4,5,2,7,3,8]=>1000001=>0111110=>1
[6,2,1,4,5,3,7,8]=>0000011=>1111100=>1
[6,2,1,5,7,3,4,8]=>0000001=>1111110=>1
[1,2,3,4,5,8,9,6,7]=>11111000=>00000111=>1
[1,2,4,6,8,3,7,5]=>1100000=>0011111=>1
[3,9,1,4,5,6,7,8,2]=>00000000=>11111111=>1
[6,1,3,7,2,8,5,4]=>0000000=>1111111=>1
[6,4,5,8,3,7,1,2]=>0000000=>1111111=>1
[2,6,8,4,3,1,7,5]=>0000000=>1111111=>1
[8,1,5,2,6,4,3,7]=>0000000=>1111111=>1
[1,6,7,4,2,8,3,5]=>1000000=>0111111=>1
[1,7,8,4,3,6,2,5]=>1000000=>0111111=>1
[1,4,7,2,3,6,8,5]=>1000000=>0111111=>1
[3,1,2,6,7,8,5,4]=>0010000=>1101111=>2
[1,6,3,4,7,8,2,5]=>1000000=>0111111=>1
[3,1,5,7,6,2,8,4]=>0000000=>1111111=>1
[6,3,1,4,2,7,8,5]=>0000000=>1111111=>1
[2,4,3,7,6,1,8,5]=>0000000=>1111111=>1
[3,1,7,6,5,2,8,4]=>0000000=>1111111=>1
[1,4,7,6,8,3,2,5]=>1000000=>0111111=>1
[7,2,1,5,6,3,8,4]=>0000000=>1111111=>1
[4,3,1,8,6,2,7,5]=>0000000=>1111111=>1
[3,1,5,2,8,7,6,4]=>0000000=>1111111=>1
[1,2,8,4,3,7,6,5]=>1100000=>0011111=>1
[2,6,1,8,7,4,3,5]=>0000000=>1111111=>1
[7,5,1,8,3,2,6,4]=>0000000=>1111111=>1
[4,7,6,3,1,8,2,5]=>0000000=>1111111=>1
[5,3,1,8,6,2,4,7]=>0000000=>1111111=>1
[5,1,8,6,3,2,4,7]=>0000000=>1111111=>1
[1,5,4,2,8,6,3,7]=>1000000=>0111111=>1
[1,4,2,8,5,3,7,6]=>1000000=>0111111=>1
[8,3,1,6,4,2,5,7]=>0000000=>1111111=>1
[1,7,4,8,3,5,2,6]=>1000000=>0111111=>1
[7,3,2,4,8,5,1,6]=>0000000=>1111111=>1
[5,7,8,1,4,2,6,3]=>0000000=>1111111=>1
[2,6,3,8,1,7,5,4]=>0000000=>1111111=>1
[2,5,1,8,6,3,7,4]=>0000000=>1111111=>1
[2,8,6,4,1,7,3,5]=>0000000=>1111111=>1
[1,8,4,2,7,5,3,6]=>1000000=>0111111=>1
[6,5,1,7,2,8,4,3]=>0000000=>1111111=>1
[2,8,1,7,5,3,6,4]=>0000000=>1111111=>1
[1,2,8,7,6,4,3,5]=>1100000=>0011111=>1
[4,3,5,7,1,6,2,8]=>0000001=>1111110=>1
[4,1,8,5,3,6,2,7]=>0000000=>1111111=>1
[6,4,2,5,3,1,7,8]=>0000011=>1111100=>1
[3,1,5,8,2,7,4,6]=>0000000=>1111111=>1
[6,4,1,5,3,2,7,8]=>0000011=>1111100=>1
[6,2,1,5,4,3,7,8]=>0000011=>1111100=>1
[3,1,8,5,4,6,2,7]=>0000000=>1111111=>1
[6,1,8,4,5,3,2,7]=>0000000=>1111111=>1
[4,5,2,7,1,6,3,8]=>0000001=>1111110=>1
[4,3,5,7,1,6,8,2]=>0000000=>1111111=>1
[4,1,8,5,3,6,7,2]=>0000000=>1111111=>1
[6,3,8,4,5,1,7,2]=>0000000=>1111111=>1
[3,1,6,8,5,7,4,2]=>0000000=>1111111=>1
[2,6,1,8,5,7,4,3]=>0000000=>1111111=>1
[6,3,8,4,5,2,1,7]=>0000000=>1111111=>1
[6,5,8,7,2,3,4,1]=>0000000=>1111111=>1
[6,3,8,4,5,2,7,1]=>0000000=>1111111=>1
[2,1,6,8,5,3,7,4]=>0100000=>1011111=>2
[3,2,6,8,5,4,7,1]=>0000000=>1111111=>1
[4,1,8,5,2,6,3,7]=>0000000=>1111111=>1
[3,1,6,8,5,2,4,7]=>0000000=>1111111=>1
[6,5,8,7,4,1,2,3]=>0000000=>1111111=>1
[6,5,8,7,4,2,1,3]=>0000000=>1111111=>1
[6,5,8,7,2,4,1,3]=>0000000=>1111111=>1
[6,2,8,4,5,7,1,3]=>0000000=>1111111=>1
[6,1,8,4,5,7,3,2]=>0000000=>1111111=>1
[4,2,7,3,5,8,6,1]=>0000000=>1111111=>1
[3,6,2,4,8,5,7,1]=>0000000=>1111111=>1
[3,5,1,8,4,7,6,2]=>0000000=>1111111=>1
[3,6,1,8,5,4,7,2]=>0000000=>1111111=>1
[2,4,8,3,7,6,5,1]=>0000000=>1111111=>1
[3,6,8,2,5,7,4,1]=>0000000=>1111111=>1
[2,6,8,5,4,3,7,1]=>0000000=>1111111=>1
[3,6,8,2,5,4,7,1]=>0000000=>1111111=>1
[4,6,8,3,2,5,7,1]=>0000000=>1111111=>1
[4,6,2,8,3,5,7,1]=>0000000=>1111111=>1
[3,6,1,8,5,7,4,2]=>0000000=>1111111=>1
[5,2,6,8,4,1,7,3]=>0000000=>1111111=>1
[3,5,8,2,7,4,6,1]=>0000000=>1111111=>1
[2,6,8,5,7,4,3,1]=>0000000=>1111111=>1
[2,4,8,7,6,3,5,1]=>0000000=>1111111=>1
[7,5,1,6,3,2,8,4]=>0000000=>1111111=>1
[2,7,6,3,4,1,8,5]=>0000000=>1111111=>1
[4,8,2,1,7,5,6,3]=>0000000=>1111111=>1
[1,5,4,8,6,2,3,7]=>1000000=>0111111=>1
[8,2,1,6,7,3,5,4]=>0000000=>1111111=>1
[6,2,8,1,7,5,3,4]=>0000000=>1111111=>1
[3,5,1,8,7,6,2,4]=>0000000=>1111111=>1
[1,4,2,3,6,5,8,7,9]=>10010101=>01101010=>3
[1,3,4,2,6,5,8,7,9]=>10010101=>01101010=>3
[1,4,2,3,6,5,8,7,10,9]=>100101010=>011010101=>4
[2,3,1,4,6,5,8,7,9]=>00110101=>11001010=>3
[4,6,1,2,3,5,8,7,9]=>00000101=>11111010=>2
[3,4,5,1,6,2,8,7,9]=>00000101=>11111010=>2
[3,1,2,4,6,5,8,7,9]=>00110101=>11001010=>3
[1,3,4,2,6,5,8,7,10,9]=>100101010=>011010101=>4
[5,6,2,7,8,1,3,4]=>0000000=>1111111=>1
[2,1,3,4,5,6,9,7,8]=>01111100=>10000011=>2
[1,2,3,4,5,6,7,8,10,9,11]=>1111111101=>0000000010=>1
[1,2,3,4,5,7,8,6,9]=>11111001=>00000110=>1
[2,1,3,4,5,6,7,10,8,9]=>011111100=>100000011=>2
[3,2,5,6,8,4,7,1]=>0000000=>1111111=>1
[2,5,6,4,8,3,7,1]=>0000000=>1111111=>1
[4,2,5,7,3,8,1,6]=>0000000=>1111111=>1
[4,7,3,1,6,8,2,5]=>0000000=>1111111=>1
[4,2,7,6,8,1,3,5]=>0000000=>1111111=>1
[1,7,4,6,8,3,2,5]=>1000000=>0111111=>1
[4,7,2,5,6,3,1,8]=>0000001=>1111110=>1
[5,4,1,3,7,8,2,6]=>0000000=>1111111=>1
[6,1,5,8,3,7,2,4]=>0000000=>1111111=>1
[4,5,2,1,7,8,3,6]=>0000000=>1111111=>1
[2,3,7,8,5,1,6,4]=>0000000=>1111111=>1
[1,2,6,7,4,3,5,8]=>1100001=>0011110=>1
[10,2,3,4,5,6,7,8,1,9]=>000000000=>111111111=>1
[3,10,1,4,5,6,7,8,9,2]=>000000000=>111111111=>1
[8,7,9,1,2,3,4,5,6]=>00000000=>11111111=>1
[6,8,2,7,5,3,1,4]=>0000000=>1111111=>1
[6,3,2,5,8,4,1,7]=>0000000=>1111111=>1
[5,6,7,2,8,4,1,3]=>0000000=>1111111=>1
[5,8,3,6,4,1,7,2]=>0000000=>1111111=>1
[3,2,5,8,4,7,1,6]=>0000000=>1111111=>1
[2,5,8,1,3,4,7,6]=>0000000=>1111111=>1
[3,5,1,8,7,4,2,6]=>0000000=>1111111=>1
[5,1,7,8,3,2,4,6]=>0000000=>1111111=>1
[3,1,7,6,2,8,5,4]=>0000000=>1111111=>1
[5,3,6,7,4,2,8,1]=>0000000=>1111111=>1
[5,4,2,8,6,7,3,1]=>0000000=>1111111=>1
[6,1,4,2,8,7,3,5]=>0000000=>1111111=>1
[3,7,2,6,8,4,5,1]=>0000000=>1111111=>1
[4,6,5,2,7,8,3,1]=>0000000=>1111111=>1
[5,4,6,2,7,8,3,1]=>0000000=>1111111=>1
[2,1,7,6,8,4,5,3]=>0100000=>1011111=>2
[6,4,7,2,8,3,1,5]=>0000000=>1111111=>1
[4,7,3,1,5,2,8,6]=>0000000=>1111111=>1
[2,4,7,3,8,5,1,6]=>0000000=>1111111=>1
[2,7,3,1,8,5,4,6]=>0000000=>1111111=>1
[7,6,8,9,1,2,3,4,5]=>00000000=>11111111=>1
[5,4,6,7,8,9,1,2,3]=>00000000=>11111111=>1
[1,2,6,8,3,4,7,5]=>1100000=>0011111=>1
[1,6,3,5,7,4,8,2]=>1000000=>0111111=>1
[1,5,4,7,2,8,3,6]=>1000000=>0111111=>1
[3,8,5,2,6,1,7,4]=>0000000=>1111111=>1
[3,7,4,8,5,2,6,1]=>0000000=>1111111=>1
[6,8,7,1,3,4,2,5]=>0000000=>1111111=>1
[3,4,2,8,6,7,5,1]=>0000000=>1111111=>1
[3,6,1,5,2,7,8,4]=>0000000=>1111111=>1
[7,1,6,8,3,4,2,5]=>0000000=>1111111=>1
[6,2,8,4,7,1,3,5]=>0000000=>1111111=>1
[1,4,3,2,5,6,7,8,9]=>10011111=>01100000=>1
[6,8,2,7,5,4,1,3]=>0000000=>1111111=>1
[1,8,4,3,7,6,2,5]=>1000000=>0111111=>1
[4,3,8,7,1,2,6,5]=>0000000=>1111111=>1
[1,8,4,5,7,6,2,3]=>1000000=>0111111=>1
[4,3,8,5,7,1,6,2]=>0000000=>1111111=>1
[6,3,4,8,7,2,1,5]=>0000000=>1111111=>1
[5,3,8,4,7,1,6,2]=>0000000=>1111111=>1
[5,2,8,7,1,4,6,3]=>0000000=>1111111=>1
[3,2,8,7,1,6,4,5]=>0000000=>1111111=>1
[2,7,8,3,1,6,4,5]=>0000000=>1111111=>1
[2,7,8,5,1,4,6,3]=>0000000=>1111111=>1
[3,5,8,7,4,1,6,2]=>0000000=>1111111=>1
[7,4,6,8,3,5,1,2]=>0000000=>1111111=>1
[2,7,8,1,3,6,4,5]=>0000000=>1111111=>1
[2,7,8,1,5,4,6,3]=>0000000=>1111111=>1
[2,7,8,1,4,5,6,3]=>0000000=>1111111=>1
[3,6,7,8,2,4,1,5]=>0000000=>1111111=>1
[4,5,7,8,6,3,1,2]=>0000000=>1111111=>1
[5,4,6,8,7,3,1,2]=>0000000=>1111111=>1
[4,5,8,6,7,1,3,2]=>0000000=>1111111=>1
[5,7,6,8,2,1,3,4]=>0000000=>1111111=>1
[3,7,6,8,2,4,1,5]=>0000000=>1111111=>1
[5,4,7,8,6,3,1,2]=>0000000=>1111111=>1
[4,5,7,8,2,6,1,3]=>0000000=>1111111=>1
[4,5,6,8,7,3,1,2]=>0000000=>1111111=>1
[6,1,5,3,8,4,7,2]=>0000000=>1111111=>1
[1,8,6,2,5,4,7,3]=>1000000=>0111111=>1
[3,8,4,1,7,5,2,6]=>0000000=>1111111=>1
[6,2,7,4,8,3,1,5]=>0000000=>1111111=>1
[2,8,5,1,4,3,7,6]=>0000000=>1111111=>1
[6,8,2,7,5,1,4,3]=>0000000=>1111111=>1
[5,3,6,4,7,2,1,8]=>0000001=>1111110=>1
[4,2,6,5,7,3,1,8]=>0000001=>1111110=>1
[5,4,6,2,7,3,1,8]=>0000001=>1111110=>1
[3,2,6,5,8,4,1,7]=>0000000=>1111111=>1
[3,2,6,5,8,7,1,4]=>0000000=>1111111=>1
[4,2,6,5,8,7,1,3]=>0000000=>1111111=>1
[5,2,6,4,8,7,1,3]=>0000000=>1111111=>1
[5,4,7,6,8,2,1,3]=>0000000=>1111111=>1
[6,4,7,5,8,3,1,2]=>0000000=>1111111=>1
[4,2,7,5,8,6,1,3]=>0000000=>1111111=>1
[3,2,7,5,8,4,1,6]=>0000000=>1111111=>1
[4,3,7,2,8,5,1,6]=>0000000=>1111111=>1
[4,3,6,2,8,5,1,7]=>0000000=>1111111=>1
[4,3,7,6,8,5,1,2]=>0000000=>1111111=>1
[5,3,7,6,8,2,1,4]=>0000000=>1111111=>1
[5,3,7,2,8,6,1,4]=>0000000=>1111111=>1
[3,2,6,4,8,7,1,5]=>0000000=>1111111=>1
[4,2,7,3,8,6,1,5]=>0000000=>1111111=>1
[5,2,7,6,8,3,1,4]=>0000000=>1111111=>1
[3,2,7,6,8,4,1,5]=>0000000=>1111111=>1
[3,2,7,6,8,5,1,4]=>0000000=>1111111=>1
[6,2,7,5,8,4,1,3]=>0000000=>1111111=>1
[6,7,1,3,2,5,8,4]=>0000000=>1111111=>1
[8,7,6,4,1,5,3,2]=>0000000=>1111111=>1
[7,2,5,3,4,8,1,6]=>0000000=>1111111=>1
[5,3,6,2,4,1,8,7]=>0000010=>1111101=>2
[5,8,2,6,3,7,4,1]=>0000000=>1111111=>1
[4,8,2,3,7,5,6,1]=>0000000=>1111111=>1
[4,5,3,7,1,2,6,8]=>0000001=>1111110=>1
[8,5,6,4,1,3,2,7]=>0000000=>1111111=>1
[6,7,2,8,4,3,1,5]=>0000000=>1111111=>1
[6,7,3,2,8,4,1,5]=>0000000=>1111111=>1
[4,7,8,3,1,5,2,6]=>0000000=>1111111=>1
[4,5,8,1,3,2,6,7]=>0000000=>1111111=>1
[4,7,8,1,6,3,2,5]=>0000000=>1111111=>1
[4,7,1,3,8,6,5,2]=>0000000=>1111111=>1
[5,7,2,8,3,4,6,1]=>0000000=>1111111=>1
[3,7,2,8,5,6,4,1]=>0000000=>1111111=>1
[3,1,5,8,6,4,7,2]=>0000000=>1111111=>1
[2,5,6,1,8,7,3,4]=>0000000=>1111111=>1
[3,6,2,8,4,7,5,1]=>0000000=>1111111=>1
[2,3,8,6,7,5,4,1]=>0000000=>1111111=>1
[5,7,8,3,4,6,2,1]=>0000000=>1111111=>1
[3,5,1,8,6,4,2,7]=>0000000=>1111111=>1
[7,5,3,8,6,4,2,1]=>0000000=>1111111=>1
[1,5,8,3,6,4,2,7]=>1000000=>0111111=>1
[1,5,8,6,3,4,2,7]=>1000000=>0111111=>1
[3,7,5,8,2,6,4,1]=>0000000=>1111111=>1
[5,7,8,1,4,6,2,3]=>0000000=>1111111=>1
[1,3,7,8,4,2,6,5]=>1000000=>0111111=>1
[1,4,6,5,7,2,3,8]=>1000001=>0111110=>1
[8,1,6,7,3,5,4,2]=>0000000=>1111111=>1
[7,2,4,1,6,5,3,8]=>0000001=>1111110=>1
[1,3,2,6,8,4,7,5]=>1010000=>0101111=>2
[8,1,7,5,4,2,6,3]=>0000000=>1111111=>1
[1,2,6,4,7,3,5,8]=>1100001=>0011110=>1
[1,6,4,3,7,2,5,8]=>1000001=>0111110=>1
[2,3,4,5,6,9,8,7,1]=>00000000=>11111111=>1
[8,4,5,1,3,7,6,2]=>0000000=>1111111=>1
[8,6,4,3,7,1,5,2]=>0000000=>1111111=>1
[3,4,5,6,7,1,2,8,9]=>00000011=>11111100=>1
[3,1,6,5,7,8,4,2]=>0000000=>1111111=>1
[1,7,2,5,6,8,4,3]=>1000000=>0111111=>1
[4,7,6,8,3,1,5,2]=>0000000=>1111111=>1
[3,5,4,7,1,8,6,2]=>0000000=>1111111=>1
[6,1,3,8,4,5,2,7]=>0000000=>1111111=>1
[4,1,5,7,6,3,2,8]=>0000001=>1111110=>1
[4,5,1,7,6,3,2,8]=>0000001=>1111110=>1
[1,4,2,6,7,8,5,3]=>1000000=>0111111=>1
[1,4,2,5,6,8,7,3]=>1000000=>0111111=>1
[1,8,6,2,4,3,5,7]=>1000000=>0111111=>1
[3,2,4,5,7,8,1,6]=>0000000=>1111111=>1
[6,5,2,8,7,4,3,1]=>0000000=>1111111=>1
[7,8,5,4,2,1,6,3]=>0000000=>1111111=>1
[7,5,2,8,6,4,3,1]=>0000000=>1111111=>1
[7,8,3,2,6,5,4,1]=>0000000=>1111111=>1
[8,6,7,2,5,3,1,4]=>0000000=>1111111=>1
[1,6,2,7,8,4,5,3]=>1000000=>0111111=>1
[1,6,8,2,7,5,3,4]=>1000000=>0111111=>1
[5,1,7,4,3,8,6,2]=>0000000=>1111111=>1
[8,6,3,7,2,4,1,5]=>0000000=>1111111=>1
[1,7,8,6,4,2,3,5]=>1000000=>0111111=>1
[7,2,8,6,4,1,3,5]=>0000000=>1111111=>1
[1,5,3,7,4,2,6,8]=>1000001=>0111110=>1
[1,7,6,4,3,2,8,5]=>1000000=>0111111=>1
[1,5,4,2,3,8,7,6]=>1000100=>0111011=>2
[1,5,4,2,3,7,8,6]=>1000100=>0111011=>2
[1,2,7,6,3,5,8,4]=>1100000=>0011111=>1
[3,2,7,5,6,1,8,4]=>0000000=>1111111=>1
[7,4,5,1,6,3,8,2]=>0000000=>1111111=>1
[3,2,6,4,8,5,7,1]=>0000000=>1111111=>1
[7,2,8,1,6,3,5,4]=>0000000=>1111111=>1
[1,3,5,2,4,7,6,9,8,10]=>100010101=>011101010=>3
[2,3,5,1,4,7,6,9,8]=>00001010=>11110101=>3
[3,4,1,5,2,7,6,9,8]=>00001010=>11110101=>3
[4,1,2,5,3,7,6,9,8]=>00001010=>11110101=>3
[1,4,2,5,3,7,6,9,8,10]=>100010101=>011101010=>3
[8,3,6,5,4,1,2,7]=>0000000=>1111111=>1
[1,7,5,8,4,6,3,2]=>1000000=>0111111=>1
[6,5,7,1,2,8,3,4]=>0000000=>1111111=>1
[7,1,4,2,3,8,6,5]=>0000000=>1111111=>1
[8,1,2,5,3,7,6,4]=>0000000=>1111111=>1
[3,6,5,2,4,1,7,8]=>0000011=>1111100=>1
[6,8,5,2,4,3,1,7]=>0000000=>1111111=>1
[4,6,7,2,5,1,8,3]=>0000000=>1111111=>1
[3,6,2,5,1,7,8,4]=>0000000=>1111111=>1
[5,8,1,4,3,6,7,2]=>0000000=>1111111=>1
[7,2,3,8,6,4,1,5]=>0000000=>1111111=>1
[5,2,3,8,7,4,1,6]=>0000000=>1111111=>1
[4,2,6,8,1,3,5,7,9]=>00000001=>11111110=>1
[4,6,2,8,1,3,5,7,9]=>00000001=>11111110=>1
[4,6,8,2,1,3,5,7,9]=>00000001=>11111110=>1
[4,6,2,7,8,1,3,5]=>0000000=>1111111=>1
[4,6,8,2,9,1,3,5,7]=>00000000=>11111111=>1
[4,6,2,7,9,1,3,5,8]=>00000000=>11111111=>1
[6,2,3,7,1,4,5,8]=>0000001=>1111110=>1
[4,2,5,7,9,1,3,6,8]=>00000000=>11111111=>1
[2,3,5,7,9,1,4,6,8]=>00000000=>11111111=>1
[4,2,6,8,10,1,3,5,7,9]=>000000000=>111111111=>1
[6,4,2,8,1,3,5,7,9]=>00000001=>11111110=>1
[4,6,2,8,10,1,3,5,7,9]=>000000000=>111111111=>1
[8,4,6,2,1,3,5,7,9]=>00000001=>11111110=>1
[4,6,8,2,10,1,3,5,7,9]=>000000000=>111111111=>1
[4,6,8,9,2,1,3,5,7]=>00000000=>11111111=>1
[4,6,8,10,2,1,3,5,7,9]=>000000000=>111111111=>1
[4,6,7,8,2,1,3,5]=>0000000=>1111111=>1
[4,6,2,7,1,3,5,8,9]=>00000011=>11111100=>1
[4,6,8,2,9,1,3,5,7,10]=>000000001=>111111110=>1
[4,8,2,5,9,1,3,6,7]=>00000000=>11111111=>1
[4,6,2,7,9,1,3,5,8,10]=>000000001=>111111110=>1
[6,2,3,7,9,1,4,5,8]=>00000000=>11111111=>1
[4,2,5,7,9,1,3,6,8,10]=>000000001=>111111110=>1
[1,4,5,7,9,2,3,6,8]=>10000000=>01111111=>1
[2,3,5,7,9,1,4,6,8,10]=>000000001=>111111110=>1
[8,6,4,9,7,5,3,2,1]=>00000000=>11111111=>1
[7,8,5,9,6,4,3,2,1]=>00000000=>11111111=>1
[8,6,4,2,9,7,5,3,1]=>00000000=>11111111=>1
[7,8,5,3,9,6,4,2,1]=>00000000=>11111111=>1
[7,4,8,5,9,6,3,2,1]=>00000000=>11111111=>1
[6,7,8,4,9,5,3,2,1]=>00000000=>11111111=>1
[7,8,5,3,1,9,6,4,2]=>00000000=>11111111=>1
[7,4,8,5,2,9,6,3,1]=>00000000=>11111111=>1
[6,7,8,4,2,9,5,3,1]=>00000000=>11111111=>1
[6,7,3,8,4,9,5,2,1]=>00000000=>11111111=>1
[5,6,7,8,3,9,4,2,1]=>00000000=>11111111=>1
[6,7,3,8,4,1,9,5,2]=>00000000=>11111111=>1
[5,6,7,8,3,1,9,4,2]=>00000000=>11111111=>1
[6,2,7,3,8,4,9,5,1]=>00000000=>11111111=>1
[5,6,7,2,8,3,9,4,1]=>00000000=>11111111=>1
[4,5,6,7,8,2,9,3,1]=>00000000=>11111111=>1
[5,6,1,7,2,8,3,9,4]=>00000000=>11111111=>1
[4,5,6,7,1,8,2,9,3]=>00000000=>11111111=>1
[9,7,10,8,6,5,4,3,2,1]=>000000000=>111111111=>1
[9,7,5,10,8,6,4,3,2,1]=>000000000=>111111111=>1
[8,9,6,10,7,5,4,3,2,1]=>000000000=>111111111=>1
[9,7,5,3,10,8,6,4,2,1]=>000000000=>111111111=>1
[8,9,6,4,10,7,5,3,2,1]=>000000000=>111111111=>1
[8,5,9,6,10,7,4,3,2,1]=>000000000=>111111111=>1
[7,8,9,5,10,6,4,3,2,1]=>000000000=>111111111=>1
[8,9,6,4,2,10,7,5,3,1]=>000000000=>111111111=>1
[8,5,9,6,3,10,7,4,2,1]=>000000000=>111111111=>1
[7,8,9,5,3,10,6,4,2,1]=>000000000=>111111111=>1
[7,8,4,9,5,10,6,3,2,1]=>000000000=>111111111=>1
[6,7,8,9,4,10,5,3,2,1]=>000000000=>111111111=>1
[8,5,9,6,3,1,10,7,4,2]=>000000000=>111111111=>1
[7,8,9,5,3,1,10,6,4,2]=>000000000=>111111111=>1
[8,5,2,9,6,3,10,7,4,1]=>000000000=>111111111=>1
[6,7,8,9,4,2,10,5,3,1]=>000000000=>111111111=>1
[7,3,8,4,9,5,10,6,2,1]=>000000000=>111111111=>1
[6,7,8,3,9,4,10,5,2,1]=>000000000=>111111111=>1
[5,6,7,8,9,3,10,4,2,1]=>000000000=>111111111=>1
[7,8,4,1,9,5,2,10,6,3]=>000000000=>111111111=>1
[7,3,8,4,9,5,1,10,6,2]=>000000000=>111111111=>1
[6,7,8,3,9,4,1,10,5,2]=>000000000=>111111111=>1
[5,6,7,8,9,3,1,10,4,2]=>000000000=>111111111=>1
[6,7,2,8,3,9,4,10,5,1]=>000000000=>111111111=>1
[5,6,7,8,2,9,3,10,4,1]=>000000000=>111111111=>1
[4,5,6,7,8,9,2,10,3,1]=>000000000=>111111111=>1
[5,6,7,1,8,2,9,3,10,4]=>000000000=>111111111=>1
[4,5,6,7,8,1,9,2,10,3]=>000000000=>111111111=>1
[6,1,3,4,2,5,8,7]=>0000010=>1111101=>2
[1,5,7,6,8,2,4,3]=>1000000=>0111111=>1
[5,7,1,3,8,4,2,6]=>0000000=>1111111=>1
[2,6,1,4,3,7,8,5]=>0000000=>1111111=>1
[1,6,2,4,3,5,8,7]=>1000010=>0111101=>2
[5,3,7,6,1,8,4,2]=>0000000=>1111111=>1
[1,5,6,3,7,8,4,2]=>1000000=>0111111=>1
[7,3,5,6,1,8,4,2]=>0000000=>1111111=>1
[7,3,6,1,5,8,4,2]=>0000000=>1111111=>1
[1,6,3,7,8,5,4,2]=>1000000=>0111111=>1
[1,7,8,6,3,5,4,2]=>1000000=>0111111=>1
[3,7,5,6,1,8,4,2]=>0000000=>1111111=>1
[7,3,5,4,1,2,6,8]=>0000001=>1111110=>1
[7,8,5,1,3,2,4,6]=>0000000=>1111111=>1
[7,1,3,8,2,5,4,6]=>0000000=>1111111=>1
[3,1,5,4,7,2,6,8]=>0000001=>1111110=>1
[1,6,3,7,2,4,5,8]=>1000001=>0111110=>1
[5,3,2,4,8,1,7,6]=>0000000=>1111111=>1
[6,8,5,3,2,7,1,4]=>0000000=>1111111=>1
[8,3,7,2,6,5,1,4]=>0000000=>1111111=>1
[3,5,1,4,7,2,8,6]=>0000000=>1111111=>1
[6,1,3,4,2,7,8,5]=>0000000=>1111111=>1
[6,5,2,3,7,8,1,4]=>0000000=>1111111=>1
[1,5,3,8,4,2,7,6]=>1000000=>0111111=>1
[5,4,2,1,8,3,7,6]=>0000000=>1111111=>1
[3,1,7,4,2,6,8,5]=>0000000=>1111111=>1
[8,1,7,3,2,5,6,4]=>0000000=>1111111=>1
[3,1,6,8,4,2,7,5]=>0000000=>1111111=>1
[2,3,4,5,9,6,7,8,1]=>00000000=>11111111=>1
[2,3,4,9,5,6,7,8,1]=>00000000=>11111111=>1
[2,3,9,4,5,6,7,8,1]=>00000000=>11111111=>1
[2,3,4,5,6,7,10,8,9,1]=>000000000=>111111111=>1
[2,3,4,5,9,7,6,8,1]=>00000000=>11111111=>1
[2,3,4,5,6,10,7,8,9,1]=>000000000=>111111111=>1
[2,3,4,9,6,5,7,8,1]=>00000000=>11111111=>1
[2,3,9,5,4,6,7,8,1]=>00000000=>11111111=>1
[2,3,4,10,5,6,7,8,9,1]=>000000000=>111111111=>1
[2,9,4,3,5,6,7,8,1]=>00000000=>11111111=>1
[2,3,10,4,5,6,7,8,9,1]=>000000000=>111111111=>1
[4,5,1,2,7,8,6,3]=>0000000=>1111111=>1
[2,8,4,6,3,1,5,7]=>0000000=>1111111=>1
[1,7,8,6,3,4,2,5]=>1000000=>0111111=>1
[1,7,3,8,6,4,2,5]=>1000000=>0111111=>1
[7,8,1,5,6,4,2,3]=>0000000=>1111111=>1
[7,1,5,8,6,4,2,3]=>0000000=>1111111=>1
[8,1,3,5,6,4,2,7]=>0000000=>1111111=>1
[1,3,8,5,6,4,2,7]=>1000000=>0111111=>1
[1,3,5,8,6,4,2,7]=>1000000=>0111111=>1
[1,5,7,8,6,4,2,3]=>1000000=>0111111=>1
[3,2,5,4,7,6,9,8,10,1]=>000000000=>111111111=>1
[8,1,3,5,6,7,2,4]=>0000000=>1111111=>1
[6,8,7,5,2,1,4,3]=>0000000=>1111111=>1
[1,2,8,6,4,5,3,7]=>1100000=>0011111=>1
[1,4,7,8,5,6,3,2]=>1000000=>0111111=>1
[1,6,4,8,5,7,3,2]=>1000000=>0111111=>1
[1,6,8,5,2,7,3,4]=>1000000=>0111111=>1
[1,3,4,8,5,2,7,6]=>1000000=>0111111=>1
[3,5,8,7,6,2,4,1]=>0000000=>1111111=>1
[6,5,3,7,4,1,8,2]=>0000000=>1111111=>1
[3,1,5,4,6,8,7,2]=>0000000=>1111111=>1
[3,1,6,4,2,5,8,7]=>0000010=>1111101=>2
[3,6,1,4,5,7,8,2]=>0000000=>1111111=>1
[1,8,4,7,2,3,6,5]=>1000000=>0111111=>1
[5,7,8,2,4,6,1,3]=>0000000=>1111111=>1
[5,4,2,3,6,8,1,7]=>0000000=>1111111=>1
[3,8,1,6,4,2,5,7]=>0000000=>1111111=>1
[7,3,2,1,8,6,4,5]=>0000000=>1111111=>1
[8,7,2,4,1,3,6,5]=>0000000=>1111111=>1
[8,2,6,3,5,7,1,4]=>0000000=>1111111=>1
[1,8,3,7,4,6,5,2]=>1000000=>0111111=>1
[8,2,3,1,7,4,5,6]=>0000000=>1111111=>1
[3,1,7,8,6,2,5,4]=>0000000=>1111111=>1
[4,8,1,2,6,5,7,3]=>0000000=>1111111=>1
[5,6,1,8,3,7,2,4]=>0000000=>1111111=>1
[2,8,1,6,5,3,7,4]=>0000000=>1111111=>1
[2,1,5,7,6,3,8,4]=>0100000=>1011111=>2
[4,1,2,5,7,6,8,3]=>0000000=>1111111=>1
[4,3,5,1,7,8,6,2]=>0000000=>1111111=>1
[1,8,5,2,3,4,7,6]=>1000000=>0111111=>1
[1,9,6,2,3,4,5,8,7]=>10000000=>01111111=>1
[1,5,8,2,3,4,7,6]=>1000000=>0111111=>1
[1,2,7,8,4,5,6,3]=>1100000=>0011111=>1
[1,2,3,4,5,6,9,7,10,8]=>111111000=>000000111=>1
[4,3,8,7,6,2,5,1]=>0000000=>1111111=>1
[5,4,8,2,7,6,3,1]=>0000000=>1111111=>1
[2,3,6,1,7,5,8,4]=>0000000=>1111111=>1
[4,6,5,2,1,7,8,3]=>0000000=>1111111=>1
[3,5,6,2,1,4,7,8]=>0000011=>1111100=>1
[4,3,6,5,1,7,8,2]=>0000000=>1111111=>1
[4,6,5,3,1,7,8,2]=>0000000=>1111111=>1
[1,2,3,4,5,7,6,8,9,10]=>111110111=>000001000=>1
[1,2,3,5,4,6,7,8,9,10]=>111011111=>000100000=>1
[1,2,3,5,4,7,6,9,8,10]=>111010101=>000101010=>3
[5,8,1,4,2,3,6,7]=>0000000=>1111111=>1
[4,5,8,2,3,1,6,7]=>0000000=>1111111=>1
[3,5,4,8,1,7,2,6]=>0000000=>1111111=>1
[5,3,6,8,1,4,7,2]=>0000000=>1111111=>1
[3,5,1,8,6,4,7,2]=>0000000=>1111111=>1
[4,7,2,8,3,1,6,5]=>0000000=>1111111=>1
[1,2,5,6,8,3,7,4]=>1100000=>0011111=>1
[5,3,8,4,6,2,7,1]=>0000000=>1111111=>1
[7,4,8,1,5,2,6,3]=>0000000=>1111111=>1
[8,3,2,1,6,5,7,4]=>0000000=>1111111=>1
[4,1,5,6,8,7,2,3]=>0000000=>1111111=>1
[1,2,5,6,8,4,7,3]=>1100000=>0011111=>1
[1,5,6,8,4,7,2,3]=>1000000=>0111111=>1
[5,6,8,1,2,4,7,3]=>0000000=>1111111=>1
[6,8,1,4,5,7,2,3]=>0000000=>1111111=>1
[4,3,5,1,8,6,7,2]=>0000000=>1111111=>1
[1,3,5,6,8,4,7,2]=>1000000=>0111111=>1
[5,6,8,2,3,4,7,1]=>0000000=>1111111=>1
[9,8,7,4,5,6,3,2,1]=>00000000=>11111111=>1
[6,5,1,2,4,8,7,3]=>0000000=>1111111=>1
[5,8,7,2,1,3,6,4]=>0000000=>1111111=>1
[5,1,7,2,8,6,3,4]=>0000000=>1111111=>1
[6,1,5,3,4,8,7,2]=>0000000=>1111111=>1
[5,8,6,3,2,1,4,7]=>0000000=>1111111=>1
[8,7,1,6,3,5,4,2]=>0000000=>1111111=>1
[3,2,1,7,8,6,4,5]=>0010000=>1101111=>2
[8,6,7,1,2,5,3,4]=>0000000=>1111111=>1
[1,5,6,4,2,8,7,3]=>1000000=>0111111=>1
[7,5,1,4,8,2,3,6]=>0000000=>1111111=>1
[3,2,8,1,7,5,6,4]=>0000000=>1111111=>1
[8,4,3,1,7,5,6,2]=>0000000=>1111111=>1
[6,1,7,8,4,2,3,5]=>0000000=>1111111=>1
[7,4,3,1,8,5,2,6]=>0000000=>1111111=>1
[7,8,1,6,3,4,5,2]=>0000000=>1111111=>1
[6,8,1,7,3,4,2,5]=>0000000=>1111111=>1
[1,5,6,7,8,9,2,3,4]=>10000000=>01111111=>1
[1,5,6,7,8,9,10,2,3,4]=>100000000=>011111111=>1
[3,4,2,1,5,6,7,8,9]=>00011111=>11100000=>1
[4,3,1,2,5,6,7,8,9]=>00011111=>11100000=>1
[3,4,2,1,5,6,7,8,9,10]=>000111111=>111000000=>1
[4,5,2,1,3,6,7,8,9]=>00001111=>11110000=>1
[3,4,2,5,1,6,7,8,9]=>00001111=>11110000=>1
[5,3,1,2,4,6,7,8,9]=>00001111=>11110000=>1
[4,3,5,1,2,6,7,8,9]=>00001111=>11110000=>1
[4,3,1,2,5,6,7,8,9,10]=>000111111=>111000000=>1
[4,6,5,3,8,2,7,1]=>0000000=>1111111=>1
[6,3,7,5,2,4,1,8]=>0000001=>1111110=>1
[7,8,1,5,6,4,3,2]=>0000000=>1111111=>1
[1,3,8,2,4,6,7,5]=>1000000=>0111111=>1
[6,1,7,3,4,2,5,8]=>0000001=>1111110=>1
[2,8,7,1,5,6,4,3]=>0000000=>1111111=>1
[3,5,6,2,8,1,7,4]=>0000000=>1111111=>1
[4,1,5,7,3,8,2,6]=>0000000=>1111111=>1
[5,4,3,1,2,6,7,8,9]=>00001111=>11110000=>1
[6,5,4,3,1,2,7,8,9]=>00000111=>11111000=>1
[8,5,4,3,9,1,2,6,7]=>00000000=>11111111=>1
[6,5,4,3,1,2,7,8,9,10]=>000001111=>111110000=>1
[7,6,5,4,3,1,2,8,9,10]=>000000111=>111111000=>1
[9,6,5,4,3,10,1,2,7,8]=>000000000=>111111111=>1
[3,8,6,1,4,5,7,2]=>0000000=>1111111=>1
[2,3,1,7,6,8,4,5]=>0010000=>1101111=>2
[5,8,7,2,6,4,1,3]=>0000000=>1111111=>1
[6,8,5,1,7,4,3,2]=>0000000=>1111111=>1
[6,8,5,2,7,4,1,3]=>0000000=>1111111=>1
[7,3,8,6,5,2,1,4]=>0000000=>1111111=>1
[7,5,8,1,6,4,3,2]=>0000000=>1111111=>1
[7,5,8,2,6,4,1,3]=>0000000=>1111111=>1
[6,3,2,8,1,7,5,4]=>0000000=>1111111=>1
[2,1,3,4,5,6,8,7,9]=>01111101=>10000010=>2
[2,3,4,5,6,8,7,9,1]=>00000000=>11111111=>1
[4,5,3,1,2,8,6,7]=>0000100=>1111011=>2
[7,5,4,1,3,2,6,8]=>0000001=>1111110=>1
[5,3,4,8,7,6,2,1]=>0000000=>1111111=>1
[8,3,1,6,7,5,4,2]=>0000000=>1111111=>1
[1,8,2,6,7,4,5,3]=>1000000=>0111111=>1
[8,5,7,2,4,3,6,1]=>0000000=>1111111=>1
[1,2,8,3,4,7,6,5]=>1100000=>0011111=>1
[6,8,5,2,7,1,3,4]=>0000000=>1111111=>1
[8,7,5,1,4,6,3,2]=>0000000=>1111111=>1
[6,3,4,7,2,8,5,1]=>0000000=>1111111=>1
[6,8,4,3,1,5,2,7]=>0000000=>1111111=>1
[1,4,5,8,3,2,6,7]=>1000000=>0111111=>1
[1,5,2,4,7,8,6,3]=>1000000=>0111111=>1
[2,7,6,8,3,5,4,1]=>0000000=>1111111=>1
[6,2,3,7,4,5,8,1]=>0000000=>1111111=>1
[6,4,2,7,1,5,8,3]=>0000000=>1111111=>1
[1,6,5,2,4,7,3,8]=>1000001=>0111110=>1
[1,8,7,2,4,6,3,5]=>1000000=>0111111=>1
[1,8,7,2,5,4,3,6]=>1000000=>0111111=>1
[1,5,4,2,7,3,6,8]=>1000001=>0111110=>1
[1,5,4,2,8,7,3,6]=>1000000=>0111111=>1
[1,6,8,3,5,2,4,7]=>1000000=>0111111=>1
[1,7,6,2,3,5,8,4]=>1000000=>0111111=>1
[1,2,8,3,6,5,4,7]=>1100000=>0011111=>1
[1,3,8,6,5,2,4,7]=>1000000=>0111111=>1
[1,4,7,3,2,8,6,5]=>1000000=>0111111=>1
[1,8,6,5,2,4,7,3]=>1000000=>0111111=>1
[1,6,8,4,3,2,5,7]=>1000000=>0111111=>1
[1,7,5,3,2,6,4,8]=>1000001=>0111110=>1
[1,2,6,5,3,8,4,7]=>1100000=>0011111=>1
[1,7,3,2,8,4,6,5]=>1000000=>0111111=>1
[1,6,5,2,8,4,7,3]=>1000000=>0111111=>1
[1,8,3,7,2,4,6,5]=>1000000=>0111111=>1
[5,4,2,8,7,6,1,3]=>0000000=>1111111=>1
[8,6,3,2,5,7,4,1]=>0000000=>1111111=>1
[7,3,2,1,6,5,8,4]=>0000000=>1111111=>1
[6,8,5,2,7,1,4,3]=>0000000=>1111111=>1
[6,8,2,5,1,7,4,3]=>0000000=>1111111=>1
[6,8,5,7,2,1,4,3]=>0000000=>1111111=>1
[6,5,8,2,7,4,1,3]=>0000000=>1111111=>1
[6,2,1,7,5,8,4,3]=>0000000=>1111111=>1
[1,6,4,8,5,3,7,2]=>1000000=>0111111=>1
[4,2,6,7,8,1,3,5]=>0000000=>1111111=>1
[4,1,7,6,5,8,2,3]=>0000000=>1111111=>1
[2,4,3,6,7,8,1,5]=>0000000=>1111111=>1
[7,2,1,4,3,5,8,6]=>0000000=>1111111=>1
[8,1,5,4,2,3,6,7]=>0000000=>1111111=>1
[6,1,4,8,7,2,3,5]=>0000000=>1111111=>1
[6,1,7,5,8,2,3,4]=>0000000=>1111111=>1
[6,1,4,7,8,2,3,5]=>0000000=>1111111=>1
[6,7,1,4,2,3,5,8]=>0000001=>1111110=>1
[6,1,7,4,8,2,3,5]=>0000000=>1111111=>1
[8,6,5,4,3,2,7,9,1]=>00000000=>11111111=>1
[8,9,5,4,3,2,1,6,7]=>00000000=>11111111=>1
[7,6,5,4,3,8,9,1,2]=>00000000=>11111111=>1
[9,6,5,4,3,2,7,1,8]=>00000000=>11111111=>1
[8,7,6,5,4,3,2,9,1,10]=>000000001=>111111110=>1
[9,2,3,4,5,6,1,7,8]=>00000000=>11111111=>1
[3,1,5,6,7,8,9,2,4]=>00000000=>11111111=>1
[2,1,3,5,6,7,8,9,4]=>01100000=>10011111=>2
[4,3,8,5,6,2,7,1]=>0000000=>1111111=>1
[6,2,5,4,7,1,8,3]=>0000000=>1111111=>1
[8,2,1,6,5,7,4,3]=>0000000=>1111111=>1
[2,7,1,8,5,6,4,3]=>0000000=>1111111=>1
[3,5,8,6,2,1,4,7]=>0000000=>1111111=>1
[8,7,3,6,5,2,4,1]=>0000000=>1111111=>1
[7,3,8,6,2,1,4,5]=>0000000=>1111111=>1
[8,3,5,6,4,7,2,1]=>0000000=>1111111=>1
[8,5,6,2,4,3,7,1]=>0000000=>1111111=>1
[6,5,8,1,3,4,2,7]=>0000000=>1111111=>1
[6,8,4,5,1,3,2,7]=>0000000=>1111111=>1
[6,4,8,7,5,3,2,1]=>0000000=>1111111=>1
[6,7,1,4,3,2,8,5]=>0000000=>1111111=>1
[7,2,5,1,4,8,3,6]=>0000000=>1111111=>1
[5,8,1,3,4,2,7,6]=>0000000=>1111111=>1
[1,5,6,3,2,8,7,4]=>1000000=>0111111=>1
[1,3,7,6,8,4,2,5]=>1000000=>0111111=>1
[1,6,7,3,2,8,5,4]=>1000000=>0111111=>1
[3,2,7,6,8,4,5,1]=>0000000=>1111111=>1
[1,3,8,5,2,7,6,4]=>1000000=>0111111=>1
[6,4,1,5,2,8,7,3]=>0000000=>1111111=>1
[7,6,5,3,1,8,2,4]=>0000000=>1111111=>1
[2,5,1,4,7,3,6,8]=>0000001=>1111110=>1
[3,1,6,5,7,2,4,8]=>0000001=>1111110=>1
[2,6,1,5,7,4,8,3]=>0000000=>1111111=>1
[2,5,7,1,6,3,8,4]=>0000000=>1111111=>1
[2,6,1,5,7,4,3,8]=>0000001=>1111110=>1
[3,1,6,5,2,4,7,8]=>0000011=>1111100=>1
[3,6,5,1,4,2,7,8]=>0000011=>1111100=>1
[3,6,5,1,7,2,4,8]=>0000001=>1111110=>1
[3,6,5,2,1,4,7,8]=>0000011=>1111100=>1
[5,4,3,6,1,7,2,8]=>0000001=>1111110=>1
[4,5,2,7,6,1,3,8]=>0000001=>1111110=>1
[4,6,5,3,1,2,7,8]=>0000011=>1111100=>1
[5,4,1,6,3,7,2,8]=>0000001=>1111110=>1
[5,4,2,6,3,7,8,1]=>0000000=>1111111=>1
[3,6,5,7,1,4,2,8]=>0000001=>1111110=>1
[3,6,5,1,4,7,2,8]=>0000001=>1111110=>1
[4,3,6,5,7,1,2,8]=>0000001=>1111110=>1
[4,2,6,5,1,3,7,8]=>0000011=>1111100=>1
[4,1,6,5,3,7,8,2]=>0000000=>1111111=>1
[4,2,5,7,6,1,3,8]=>0000001=>1111110=>1
[3,4,7,6,1,2,5,8]=>0000001=>1111110=>1
[4,2,5,7,6,3,8,1]=>0000000=>1111111=>1
[4,1,6,5,2,7,3,8]=>0000001=>1111110=>1
[3,6,5,7,2,1,4,8]=>0000001=>1111110=>1
[3,5,7,6,2,4,1,8]=>0000001=>1111110=>1
[5,4,2,6,3,7,1,8]=>0000001=>1111110=>1
[4,6,5,2,7,3,1,8]=>0000001=>1111110=>1
[4,6,5,2,1,7,3,8]=>0000001=>1111110=>1
[3,5,8,2,1,4,6,7]=>0000000=>1111111=>1
[3,5,8,2,4,6,7,1]=>0000000=>1111111=>1
[5,3,8,2,1,4,6,7]=>0000000=>1111111=>1
[5,3,1,8,2,4,6,7]=>0000000=>1111111=>1
[5,1,3,8,2,4,6,7]=>0000000=>1111111=>1
[1,5,8,4,2,3,6,7]=>1000000=>0111111=>1
[5,8,2,1,4,3,6,7]=>0000000=>1111111=>1
[5,8,2,4,1,6,7,3]=>0000000=>1111111=>1
[5,8,2,4,6,3,1,7]=>0000000=>1111111=>1
[5,8,2,4,3,6,1,7]=>0000000=>1111111=>1
[5,8,1,4,6,2,3,7]=>0000000=>1111111=>1
[1,5,8,4,6,7,2,3]=>1000000=>0111111=>1
[5,1,8,4,6,7,2,3]=>0000000=>1111111=>1
[5,8,2,4,6,3,7,1]=>0000000=>1111111=>1
[3,8,4,6,7,2,1,5]=>0000000=>1111111=>1
[3,8,4,6,7,2,5,1]=>0000000=>1111111=>1
[8,4,3,6,7,2,5,1]=>0000000=>1111111=>1
[8,4,3,6,7,2,1,5]=>0000000=>1111111=>1
[8,6,2,4,5,3,7,1]=>0000000=>1111111=>1
[1,8,6,4,5,7,2,3]=>1000000=>0111111=>1
[8,6,2,4,5,3,1,7]=>0000000=>1111111=>1
[1,8,6,4,2,3,5,7]=>1000000=>0111111=>1
[3,8,1,6,2,4,5,7]=>0000000=>1111111=>1
[3,8,6,2,1,4,5,7]=>0000000=>1111111=>1
[3,8,6,2,4,1,5,7]=>0000000=>1111111=>1
[3,8,6,2,4,5,7,1]=>0000000=>1111111=>1
[8,3,6,2,4,5,1,7]=>0000000=>1111111=>1
[8,1,3,6,2,4,5,7]=>0000000=>1111111=>1
[8,3,6,7,2,1,4,5]=>0000000=>1111111=>1
[3,8,6,7,2,1,4,5]=>0000000=>1111111=>1
[8,2,6,4,5,1,7,3]=>0000000=>1111111=>1
[1,8,4,6,7,5,2,3]=>1000000=>0111111=>1
[8,4,6,2,3,7,5,1]=>0000000=>1111111=>1
[8,4,7,2,1,3,6,5]=>0000000=>1111111=>1
[8,4,2,1,5,3,7,6]=>0000000=>1111111=>1
[8,2,1,4,7,3,6,5]=>0000000=>1111111=>1
[1,6,2,5,8,4,7,3]=>1000000=>0111111=>1
[2,1,5,8,7,3,6,4]=>0100000=>1011111=>2
[4,3,1,7,8,5,2,6]=>0000000=>1111111=>1
[2,8,5,3,6,4,7,1]=>0000000=>1111111=>1
[1,2,8,6,4,7,3,5]=>1100000=>0011111=>1
[5,3,2,7,8,6,4,1]=>0000000=>1111111=>1
[4,2,7,8,3,5,6,1]=>0000000=>1111111=>1
[2,8,3,7,1,4,6,5]=>0000000=>1111111=>1
[3,2,4,8,7,5,6,1]=>0000000=>1111111=>1
[3,2,5,6,8,1,4,7]=>0000000=>1111111=>1
[5,7,2,3,1,4,8,6]=>0000000=>1111111=>1
[8,4,2,7,3,5,6,1]=>0000000=>1111111=>1
[1,8,6,4,7,5,3,2]=>1000000=>0111111=>1
[2,8,5,1,7,4,6,3]=>0000000=>1111111=>1
[2,7,4,6,3,8,5,1]=>0000000=>1111111=>1
[1,2,8,6,4,7,5,3]=>1100000=>0011111=>1
[3,4,5,6,7,9,1,2,8]=>00000000=>11111111=>1
[3,4,5,7,8,9,1,2,6]=>00000000=>11111111=>1
[3,5,6,7,8,9,1,2,4]=>00000000=>11111111=>1
[3,4,5,6,8,9,10,1,2,7]=>000000000=>111111111=>1
[3,5,6,7,8,9,10,1,2,4]=>000000000=>111111111=>1
[3,4,5,6,7,8,9,10,1,2,11]=>0000000001=>1111111110=>1
[3,4,5,6,7,8,1,2,9,10]=>000000011=>111111100=>1
[3,4,5,6,9,1,2,7,8]=>00000000=>11111111=>1
[3,4,5,6,1,2,7,8,9]=>00000111=>11111000=>1
[4,1,8,6,3,7,5,2]=>0000000=>1111111=>1
[8,4,3,1,6,2,5,7]=>0000000=>1111111=>1
[7,5,4,3,8,1,6,2]=>0000000=>1111111=>1
[3,5,4,1,7,8,2,6]=>0000000=>1111111=>1
[6,4,2,1,5,7,3,8]=>0000001=>1111110=>1
[3,1,5,8,7,2,4,6]=>0000000=>1111111=>1
[3,2,5,7,8,4,6,1]=>0000000=>1111111=>1
[5,3,7,4,2,6,8,1]=>0000000=>1111111=>1
[5,3,7,4,2,6,1,8]=>0000001=>1111110=>1
[5,3,8,4,2,1,6,7]=>0000000=>1111111=>1
[5,2,8,4,3,1,6,7]=>0000000=>1111111=>1
[5,1,8,4,3,2,6,7]=>0000000=>1111111=>1
[5,2,7,4,3,6,1,8]=>0000001=>1111110=>1
[5,2,7,4,3,6,8,1]=>0000000=>1111111=>1
[5,3,7,4,1,6,8,2]=>0000000=>1111111=>1
[3,1,5,7,8,4,6,2]=>0000000=>1111111=>1
[3,1,5,7,8,4,2,6]=>0000000=>1111111=>1
[5,2,7,4,1,3,8,6]=>0000000=>1111111=>1
[6,2,3,7,4,8,5,1]=>0000000=>1111111=>1
[6,2,3,7,4,8,1,5]=>0000000=>1111111=>1
[6,2,3,7,4,5,1,8]=>0000001=>1111110=>1
[6,1,3,7,4,5,8,2]=>0000000=>1111111=>1
[1,2,8,6,4,3,5,7]=>1100000=>0011111=>1
[6,1,3,7,4,5,2,8]=>0000001=>1111110=>1
[1,8,6,3,5,4,2,7]=>1000000=>0111111=>1
[2,6,1,8,5,3,4,7]=>0000000=>1111111=>1
[4,5,7,8,1,6,3,2]=>0000000=>1111111=>1
[2,5,7,8,4,6,3,1]=>0000000=>1111111=>1
[1,8,2,7,5,3,4,6]=>1000000=>0111111=>1
[2,5,4,1,8,6,7,3]=>0000000=>1111111=>1
[5,6,8,3,4,2,7,1]=>0000000=>1111111=>1
[4,1,5,3,8,6,7,2]=>0000000=>1111111=>1
[7,1,3,2,4,5,6,8]=>0000001=>1111110=>1
[3,8,7,1,4,2,5,6]=>0000000=>1111111=>1
[5,1,7,8,2,4,3,6]=>0000000=>1111111=>1
[5,3,2,1,4,6,8,7]=>0000110=>1111001=>2
[5,3,2,4,8,1,6,7]=>0000000=>1111111=>1
[5,3,2,4,7,1,8,6]=>0000000=>1111111=>1
[8,4,5,3,7,1,2,6]=>0000000=>1111111=>1
[5,3,2,4,6,8,1,7]=>0000000=>1111111=>1
[1,2,4,3,5,7,8,9,6]=>11011000=>00100111=>2
[1,7,6,4,2,5,3,8]=>1000001=>0111110=>1
[7,6,4,2,8,3,1,5]=>0000000=>1111111=>1
[8,5,1,4,3,7,6,2]=>0000000=>1111111=>1
[7,5,4,1,3,6,8,2]=>0000000=>1111111=>1
[3,6,7,2,5,1,8,4]=>0000000=>1111111=>1
[2,6,5,7,1,4,8,3]=>0000000=>1111111=>1
[3,5,1,7,8,4,6,2]=>0000000=>1111111=>1
[1,5,2,4,6,8,7,3]=>1000000=>0111111=>1
[8,1,2,4,7,6,5,3]=>0000000=>1111111=>1
[3,4,1,8,6,7,5,2]=>0000000=>1111111=>1
[4,3,8,5,1,7,6,2]=>0000000=>1111111=>1
[6,1,3,2,8,5,7,4]=>0000000=>1111111=>1
[3,1,2,4,5,6,7,9,8]=>00111110=>11000001=>2
[8,5,2,1,6,4,3,7]=>0000000=>1111111=>1
[4,5,2,1,6,7,8,3]=>0000000=>1111111=>1
[3,5,1,4,2,8,7,6]=>0000100=>1111011=>2
[3,5,1,4,2,6,8,7]=>0000110=>1111001=>2
[3,5,1,4,2,6,7,8]=>0000111=>1111000=>1
[1,3,8,4,6,2,5,7]=>1000000=>0111111=>1
[1,8,4,2,3,7,5,6]=>1000000=>0111111=>1
[1,4,8,3,2,7,6,5]=>1000000=>0111111=>1
[1,2,8,6,7,5,4,3]=>1100000=>0011111=>1
[1,7,5,4,3,2,6,8]=>1000001=>0111110=>1
[8,9,10,1,5,6,7,3,4,2]=>000000000=>111111111=>1
[8,9,10,5,6,7,1,3,4,2]=>000000000=>111111111=>1
[8,9,10,1,5,6,3,4,7,2]=>000000000=>111111111=>1
[8,9,10,5,6,1,3,4,7,2]=>000000000=>111111111=>1
[8,9,10,5,6,3,4,7,1,2]=>000000000=>111111111=>1
[8,9,5,6,10,1,3,4,7,2]=>000000000=>111111111=>1
[8,9,5,6,10,3,4,7,1,2]=>000000000=>111111111=>1
[8,9,10,1,5,6,7,3,2,4]=>000000000=>111111111=>1
[8,9,10,5,6,7,1,3,2,4]=>000000000=>111111111=>1
[8,9,10,1,5,6,3,7,2,4]=>000000000=>111111111=>1
[8,9,10,5,6,1,3,7,2,4]=>000000000=>111111111=>1
[8,9,10,5,6,3,7,1,2,4]=>000000000=>111111111=>1
[8,9,5,6,10,1,3,7,2,4]=>000000000=>111111111=>1
[8,9,5,6,10,3,7,1,2,4]=>000000000=>111111111=>1
[8,9,10,1,5,6,3,2,4,7]=>000000000=>111111111=>1
[8,9,10,5,6,1,3,2,4,7]=>000000000=>111111111=>1
[8,9,10,5,6,3,1,2,4,7]=>000000000=>111111111=>1
[8,9,10,5,6,3,2,4,7,1]=>000000000=>111111111=>1
[8,9,5,6,10,1,3,2,4,7]=>000000000=>111111111=>1
[8,9,5,6,10,3,1,2,4,7]=>000000000=>111111111=>1
[8,9,5,6,10,3,2,4,7,1]=>000000000=>111111111=>1
[8,9,10,1,5,3,6,7,2,4]=>000000000=>111111111=>1
[8,9,10,5,1,3,6,7,2,4]=>000000000=>111111111=>1
[8,9,10,5,3,6,7,1,2,4]=>000000000=>111111111=>1
[8,9,5,10,1,3,6,7,2,4]=>000000000=>111111111=>1
[8,9,5,10,3,6,7,1,2,4]=>000000000=>111111111=>1
[8,9,10,1,5,3,6,2,4,7]=>000000000=>111111111=>1
[8,9,10,5,1,3,6,2,4,7]=>000000000=>111111111=>1
[8,9,10,5,3,6,1,2,4,7]=>000000000=>111111111=>1
[8,9,10,5,3,6,2,4,7,1]=>000000000=>111111111=>1
[8,9,5,10,1,3,6,2,4,7]=>000000000=>111111111=>1
[8,9,5,10,3,6,1,2,4,7]=>000000000=>111111111=>1
[8,9,5,10,3,6,2,4,7,1]=>000000000=>111111111=>1
[8,9,5,3,6,10,1,2,4,7]=>000000000=>111111111=>1
[8,9,5,3,6,10,2,4,7,1]=>000000000=>111111111=>1
[8,5,9,10,1,3,6,7,2,4]=>000000000=>111111111=>1
[8,5,9,10,3,6,7,1,2,4]=>000000000=>111111111=>1
[8,5,9,10,1,3,6,2,4,7]=>000000000=>111111111=>1
[8,5,9,10,3,6,1,2,4,7]=>000000000=>111111111=>1
[8,5,9,10,3,6,2,4,7,1]=>000000000=>111111111=>1
[3,8,5,7,4,6,2,1]=>0000000=>1111111=>1
[6,7,2,4,5,1,8,3]=>0000000=>1111111=>1
[5,2,7,8,3,6,1,4]=>0000000=>1111111=>1
[8,5,1,2,3,7,4,6]=>0000000=>1111111=>1
[5,2,8,3,1,4,7,6]=>0000000=>1111111=>1
[8,3,5,1,2,4,7,6]=>0000000=>1111111=>1
[8,4,1,7,5,2,6,3]=>0000000=>1111111=>1
[8,4,2,7,5,3,1,6]=>0000000=>1111111=>1
[8,3,5,7,6,2,4,1]=>0000000=>1111111=>1
[1,4,6,8,2,5,7,3]=>1000000=>0111111=>1
[3,6,2,4,8,1,7,5]=>0000000=>1111111=>1
[1,5,2,6,8,3,7,4]=>1000000=>0111111=>1
[4,5,3,1,8,2,6,7]=>0000000=>1111111=>1
[7,2,8,4,1,3,5,6]=>0000000=>1111111=>1
[6,1,7,3,2,8,4,5]=>0000000=>1111111=>1
[6,2,1,7,3,8,4,5]=>0000000=>1111111=>1
[5,8,2,1,3,4,6,7]=>0000000=>1111111=>1
[4,2,5,1,8,3,6,7]=>0000000=>1111111=>1
[7,4,2,8,3,1,5,6]=>0000000=>1111111=>1
[6,7,8,5,2,1,4,3]=>0000000=>1111111=>1
[1,6,2,7,8,4,3,5]=>1000000=>0111111=>1
[7,3,4,1,8,6,2,5]=>0000000=>1111111=>1
[4,7,6,3,5,8,2,1]=>0000000=>1111111=>1
[3,7,6,5,2,4,8,1]=>0000000=>1111111=>1
[1,4,7,8,6,2,5,3]=>1000000=>0111111=>1
[1,3,2,7,8,4,6,5]=>1010000=>0101111=>2
[5,7,1,4,6,2,8,3]=>0000000=>1111111=>1
[9,8,7,1,5,6,4,3,2]=>00000000=>11111111=>1
[9,1,7,8,6,5,4,3,2]=>00000000=>11111111=>1
[4,5,7,1,8,6,2,3]=>0000000=>1111111=>1
[4,3,8,6,5,2,7,1]=>0000000=>1111111=>1
[2,3,8,6,5,1,7,4]=>0000000=>1111111=>1
[5,4,7,3,1,2,6,8]=>0000001=>1111110=>1
[7,3,2,6,1,4,8,5]=>0000000=>1111111=>1
[7,2,6,8,5,4,3,1]=>0000000=>1111111=>1
[3,7,5,6,2,4,1,8]=>0000001=>1111110=>1
[1,3,4,5,6,7,2,9,8]=>10000010=>01111101=>2
[3,4,5,6,7,1,9,2,8]=>00000000=>11111111=>1
[5,3,4,2,7,1,8,6]=>0000000=>1111111=>1
[6,5,2,1,3,8,4,7]=>0000000=>1111111=>1
[2,4,3,5,6,8,1,7]=>0000000=>1111111=>1
[6,3,2,4,8,5,1,7]=>0000000=>1111111=>1
[6,3,1,2,7,8,4,5]=>0000000=>1111111=>1
[8,4,7,1,2,5,3,6]=>0000000=>1111111=>1
[7,4,6,1,8,5,2,3]=>0000000=>1111111=>1
[8,5,6,7,2,1,4,3]=>0000000=>1111111=>1
[1,7,6,2,8,3,5,4]=>1000000=>0111111=>1
[8,2,5,6,4,3,1,7]=>0000000=>1111111=>1
[2,4,3,8,6,5,1,7]=>0000000=>1111111=>1
[3,1,4,5,8,6,2,7]=>0000000=>1111111=>1
[5,1,7,3,2,8,4,6]=>0000000=>1111111=>1
[5,7,8,1,3,2,4,6]=>0000000=>1111111=>1
[7,8,6,1,3,5,4,2]=>0000000=>1111111=>1
[1,2,5,7,8,3,6,4]=>1100000=>0011111=>1
[3,4,5,8,1,7,2,6]=>0000000=>1111111=>1
[5,6,3,7,8,2,1,4]=>0000000=>1111111=>1
[4,3,8,6,7,5,1,2]=>0000000=>1111111=>1
[4,5,6,2,7,8,3,1]=>0000000=>1111111=>1
[4,5,6,2,7,1,8,3]=>0000000=>1111111=>1
[4,5,6,2,1,7,8,3]=>0000000=>1111111=>1
[4,5,6,2,1,7,3,8]=>0000001=>1111110=>1
[4,5,1,6,7,3,2,8]=>0000001=>1111110=>1
[2,5,1,8,3,7,4,6]=>0000000=>1111111=>1
[5,7,2,1,3,8,4,6]=>0000000=>1111111=>1
[9,8,7,6,5,4,3,2,1,11,10]=>0000000010=>1111111101=>2
[2,3,4,6,8,1,7,5]=>0000000=>1111111=>1
[2,5,4,8,6,7,3,1]=>0000000=>1111111=>1
[8,5,2,1,7,6,3,4]=>0000000=>1111111=>1
[2,7,3,6,4,1,8,5]=>0000000=>1111111=>1
[7,2,1,8,5,6,4,3]=>0000000=>1111111=>1
[3,6,5,1,4,8,2,7]=>0000000=>1111111=>1
[6,3,5,4,8,1,2,7]=>0000000=>1111111=>1
[2,5,1,4,6,3,8,7]=>0000010=>1111101=>2
[8,5,6,4,3,1,7,2]=>0000000=>1111111=>1
[3,7,6,4,2,8,1,5]=>0000000=>1111111=>1
[8,6,1,4,3,7,2,5]=>0000000=>1111111=>1
[8,4,7,5,1,6,3,2]=>0000000=>1111111=>1
[8,4,1,3,7,6,5,2]=>0000000=>1111111=>1
[5,8,1,4,3,2,6,7]=>0000000=>1111111=>1
[5,6,4,3,8,2,7,1]=>0000000=>1111111=>1
[1,6,4,3,8,2,7,5]=>1000000=>0111111=>1
[7,8,1,4,3,2,5,6]=>0000000=>1111111=>1
[7,1,8,4,5,3,6,2]=>0000000=>1111111=>1
[4,3,1,8,6,5,7,2]=>0000000=>1111111=>1
[4,3,2,7,5,1,8,6]=>0000000=>1111111=>1
[5,2,3,7,4,1,8,6]=>0000000=>1111111=>1
[2,1,7,4,3,6,8,5]=>0100000=>1011111=>2
[7,1,2,4,5,6,8,3]=>0000000=>1111111=>1
[2,8,7,1,4,5,6,3]=>0000000=>1111111=>1
[8,7,1,3,4,5,6,2]=>0000000=>1111111=>1
[5,8,3,1,4,6,7,2]=>0000000=>1111111=>1
[1,7,2,5,4,6,8,3]=>1000000=>0111111=>1
[2,5,3,8,1,6,7,4]=>0000000=>1111111=>1
[1,6,4,2,5,7,8,3]=>1000000=>0111111=>1
[6,5,3,4,1,7,8,2]=>0000000=>1111111=>1
[5,6,3,4,1,7,8,2]=>0000000=>1111111=>1
[2,5,3,1,4,7,8,6]=>0000100=>1111011=>2
[6,8,2,3,1,5,7,4]=>0000000=>1111111=>1
[4,3,1,5,2,7,8,6]=>0000100=>1111011=>2
[5,2,3,1,4,7,8,6]=>0000100=>1111011=>2
[7,2,1,3,5,6,8,4]=>0000000=>1111111=>1
[5,2,4,7,8,6,3,1]=>0000000=>1111111=>1
[5,4,8,7,2,3,1,6]=>0000000=>1111111=>1
[8,1,4,5,3,6,2,7]=>0000000=>1111111=>1
[8,3,5,1,4,6,2,7]=>0000000=>1111111=>1
[5,8,2,1,7,4,3,6]=>0000000=>1111111=>1
[6,5,7,2,1,8,4,3]=>0000000=>1111111=>1
[1,5,4,7,3,8,6,2]=>1000000=>0111111=>1
[7,4,1,3,8,5,6,2]=>0000000=>1111111=>1
[3,6,8,4,1,7,2,5]=>0000000=>1111111=>1
[2,1,8,4,7,6,3,5]=>0100000=>1011111=>2
[2,7,5,6,8,4,3,1]=>0000000=>1111111=>1
[3,5,2,4,7,8,6,1]=>0000000=>1111111=>1
[7,5,6,3,8,2,1,4]=>0000000=>1111111=>1
[1,6,2,7,4,5,8,3]=>1000000=>0111111=>1
[7,4,2,6,1,5,8,3]=>0000000=>1111111=>1
[8,4,1,6,2,5,7,3]=>0000000=>1111111=>1
[7,3,4,5,1,6,8,2]=>0000000=>1111111=>1
[1,3,2,5,4,7,6,9,8,11,10]=>1010101010=>0101010101=>5
[1,4,2,6,3,7,5,9,8]=>10000010=>01111101=>2
[1,3,2,6,4,7,5,9,8]=>10100010=>01011101=>3
[2,1,6,3,7,4,8,5,9]=>01000001=>10111110=>2
[8,4,2,7,6,1,5,3]=>0000000=>1111111=>1
[6,8,7,4,2,5,1,3]=>0000000=>1111111=>1
[6,5,4,3,2,7,1,8,9]=>00000011=>11111100=>1
[5,4,3,2,6,1,7,8,9]=>00000111=>11111000=>1
[4,3,2,5,1,6,7,8,9]=>00001111=>11110000=>1
[3,2,4,1,5,6,7,8,9]=>00011111=>11100000=>1
[3,1,6,5,4,7,2,8]=>0000001=>1111110=>1
[4,1,2,6,5,3,7,8]=>0000011=>1111100=>1
[4,6,1,3,5,2,7,8]=>0000011=>1111100=>1
[4,2,6,3,5,1,7,8]=>0000011=>1111100=>1
[5,8,4,7,1,3,6,2]=>0000000=>1111111=>1
[6,4,7,1,3,5,2,8]=>0000001=>1111110=>1
[6,8,3,1,5,4,7,2]=>0000000=>1111111=>1
[4,2,8,6,7,1,3,5]=>0000000=>1111111=>1
[6,1,2,4,7,3,5,8]=>0000001=>1111110=>1
[5,3,1,6,4,7,2,8]=>0000001=>1111110=>1
[1,3,5,2,7,4,6,9,8]=>10000010=>01111101=>2
[1,2,4,3,6,5,8,7,9]=>11010101=>00101010=>3
[1,3,5,7,2,4,6,9,8]=>10000010=>01111101=>2
[1,3,5,7,2,4,6,9,8,10]=>100000101=>011111010=>2
[1,3,5,7,2,9,4,6,8]=>10000000=>01111111=>1
[3,6,4,1,7,2,8,5]=>0000000=>1111111=>1
[5,6,2,1,3,7,4,8,9]=>00000011=>11111100=>1
[3,2,5,1,6,4,7,8,9]=>00000111=>11111000=>1
[6,7,2,1,8,3,4,9,5]=>00000000=>11111111=>1
[3,6,4,1,7,2,8,5,9]=>00000001=>11111110=>1
[3,6,7,2,1,4,8,5,9]=>00000001=>11111110=>1
[4,2,6,1,7,5,3,8,9]=>00000011=>11111100=>1
[4,3,2,6,1,7,5,8,9]=>00000011=>11111100=>1
[4,7,2,5,1,8,3,9,6]=>00000000=>11111111=>1
[4,3,7,8,2,1,5,9,6]=>00000000=>11111111=>1
[3,5,2,7,1,8,6,4,9]=>00000001=>11111110=>1
[5,4,3,2,7,1,8,6,9]=>00000001=>11111110=>1
[6,4,2,8,1,9,7,5,3]=>00000000=>11111111=>1
[4,3,6,2,8,1,9,7,5]=>00000000=>11111111=>1
[6,5,4,3,2,8,1,9,7]=>00000000=>11111111=>1
[2,4,1,5,3,6,7,8,9,10]=>000011111=>111100000=>1
[5,6,2,1,3,7,4,8,9,10]=>000000111=>111111000=>1
[3,2,5,1,6,4,7,8,9,10]=>000001111=>111110000=>1
[6,7,2,1,8,3,4,9,5,10]=>000000001=>111111110=>1
[3,6,4,1,7,2,8,5,9,10]=>000000011=>111111100=>1
[3,6,7,2,1,4,8,5,9,10]=>000000011=>111111100=>1
[4,2,6,1,7,5,3,8,9,10]=>000000111=>111111000=>1
[4,3,2,6,1,7,5,8,9,10]=>000000111=>111111000=>1
[3,4,7,1,8,2,9,5,10,6]=>000000000=>111111111=>1
[7,8,9,3,2,1,4,5,10,6]=>000000000=>111111111=>1
[4,7,2,5,1,8,3,9,6,10]=>000000001=>111111110=>1
[4,3,7,8,2,1,5,9,6,10]=>000000001=>111111110=>1
[3,5,2,7,1,8,6,4,9,10]=>000000011=>111111100=>1
[5,4,3,2,7,1,8,6,9,10]=>000000011=>111111100=>1
[5,8,9,2,1,6,3,10,7,4]=>000000000=>111111111=>1
[5,3,8,6,4,1,9,2,10,7]=>000000000=>111111111=>1
[3,5,8,2,6,1,9,4,10,7]=>000000000=>111111111=>1
[5,4,3,8,9,2,1,6,10,7]=>000000000=>111111111=>1
[6,4,2,8,1,9,7,5,3,10]=>000000001=>111111110=>1
[4,3,6,2,8,1,9,7,5,10]=>000000001=>111111110=>1
[6,5,4,3,2,8,1,9,7,10]=>000000001=>111111110=>1
[5,3,7,2,9,1,10,8,6,4]=>000000000=>111111111=>1
[5,4,3,7,2,9,1,10,8,6]=>000000000=>111111111=>1
[7,6,5,4,3,2,9,1,10,8]=>000000000=>111111111=>1
[5,2,6,3,7,8,4,1]=>0000000=>1111111=>1
[2,4,1,3,7,8,6,5]=>0001000=>1110111=>2
[2,6,1,5,7,8,4,3]=>0000000=>1111111=>1
[5,1,6,4,7,8,2,3]=>0000000=>1111111=>1
[8,4,6,3,7,5,1,2]=>0000000=>1111111=>1
[4,7,6,8,2,3,5,1]=>0000000=>1111111=>1
[5,7,4,8,1,2,6,3]=>0000000=>1111111=>1
[3,6,7,5,8,1,4,2]=>0000000=>1111111=>1
[3,7,5,6,8,2,4,1]=>0000000=>1111111=>1
[2,7,1,6,8,4,5,3]=>0000000=>1111111=>1
[1,5,4,7,2,6,3,8]=>1000001=>0111110=>1
[2,4,5,8,3,1,7,6]=>0000000=>1111111=>1
[1,4,7,5,8,3,6,2]=>1000000=>0111111=>1
[2,6,8,7,3,5,1,4]=>0000000=>1111111=>1
[4,7,8,6,2,5,1,3]=>0000000=>1111111=>1
[4,8,7,3,5,6,2,1]=>0000000=>1111111=>1
[1,7,6,3,5,4,2,8]=>1000001=>0111110=>1
[4,3,8,1,6,5,7,2]=>0000000=>1111111=>1
[1,3,6,2,5,8,7,4]=>1000000=>0111111=>1
[5,8,7,1,4,6,3,2]=>0000000=>1111111=>1
[6,2,5,1,3,4,8,7]=>0000010=>1111101=>2
[2,6,5,1,3,4,8,7]=>0000010=>1111101=>2
[4,6,5,1,2,7,3,8]=>0000001=>1111110=>1
[5,6,4,1,2,7,3,8]=>0000001=>1111110=>1
[8,1,5,6,2,4,3,7]=>0000000=>1111111=>1
[6,4,5,1,2,7,3,8]=>0000001=>1111110=>1
[5,4,6,1,3,2,7,8]=>0000011=>1111100=>1
[5,7,1,4,3,2,6,8]=>0000001=>1111110=>1
[2,6,4,1,3,7,5,8]=>0000001=>1111110=>1
[7,8,5,3,2,1,6,4]=>0000000=>1111111=>1
[1,2,6,7,8,4,5,3]=>1100000=>0011111=>1
[6,1,4,8,2,7,5,3]=>0000000=>1111111=>1
[5,4,1,7,3,2,8,6]=>0000000=>1111111=>1
[1,5,6,7,4,8,2,3]=>1000000=>0111111=>1
[6,3,2,5,7,4,8,1]=>0000000=>1111111=>1
[4,5,2,7,6,3,1,8]=>0000001=>1111110=>1
[4,5,2,1,7,6,3,8]=>0000001=>1111110=>1
[2,6,7,8,3,1,4,5]=>0000000=>1111111=>1
[6,3,2,5,1,7,8,4]=>0000000=>1111111=>1
[4,6,3,7,8,2,1,5]=>0000000=>1111111=>1
[5,6,7,1,8,4,2,3]=>0000000=>1111111=>1
[1,7,3,2,8,6,5,4]=>1000000=>0111111=>1
[3,7,1,2,8,6,5,4]=>0000000=>1111111=>1
[8,1,5,7,3,4,6,2]=>0000000=>1111111=>1
[5,8,2,7,6,3,1,4]=>0000000=>1111111=>1
[2,8,4,7,6,3,1,5]=>0000000=>1111111=>1
[1,8,2,4,7,6,3,5]=>1000000=>0111111=>1
[1,8,2,4,6,7,5,3]=>1000000=>0111111=>1
[2,5,1,8,4,7,6,3]=>0000000=>1111111=>1
[3,4,2,8,1,7,6,5]=>0000000=>1111111=>1
[2,4,5,8,1,7,6,3]=>0000000=>1111111=>1
[3,1,8,2,6,7,5,4]=>0000000=>1111111=>1
[2,6,8,1,4,3,7,5]=>0000000=>1111111=>1
[1,6,5,2,8,7,3,4]=>1000000=>0111111=>1
[2,6,1,5,8,7,3,4]=>0000000=>1111111=>1
[7,5,8,1,6,2,3,4]=>0000000=>1111111=>1
[6,8,4,5,3,1,7,2]=>0000000=>1111111=>1
[7,6,1,3,5,2,4,8]=>0000001=>1111110=>1
[6,2,4,5,3,8,1,7]=>0000000=>1111111=>1
[6,8,5,4,7,1,3,2]=>0000000=>1111111=>1
[7,5,8,1,3,4,2,6]=>0000000=>1111111=>1
[1,4,2,8,3,5,7,6]=>1000000=>0111111=>1
[1,3,5,4,8,7,2,6]=>1000000=>0111111=>1
[1,6,2,4,8,3,7,5]=>1000000=>0111111=>1
[1,7,8,5,4,2,6,3]=>1000000=>0111111=>1
[1,5,2,8,6,4,7,3]=>1000000=>0111111=>1
[1,6,5,2,7,4,8,3]=>1000000=>0111111=>1
[1,5,4,2,8,6,7,3]=>1000000=>0111111=>1
[1,7,5,4,6,2,8,3]=>1000000=>0111111=>1
[6,4,5,1,7,2,8,3]=>0000000=>1111111=>1
[4,8,1,3,7,6,2,5]=>0000000=>1111111=>1
[4,5,3,1,2,8,7,6]=>0000100=>1111011=>2
[6,4,2,3,1,8,7,5]=>0000000=>1111111=>1
[6,5,2,1,3,8,7,4]=>0000000=>1111111=>1
[7,6,1,8,2,5,3,4]=>0000000=>1111111=>1
[8,4,2,3,7,6,1,5]=>0000000=>1111111=>1
[5,7,8,1,2,4,3,6]=>0000000=>1111111=>1
[1,7,6,8,3,5,4,2]=>1000000=>0111111=>1
[5,7,6,4,2,1,3,8]=>0000001=>1111110=>1
[6,5,7,4,1,3,2,8]=>0000001=>1111110=>1
[4,6,1,8,3,5,2,7]=>0000000=>1111111=>1
[7,1,6,8,2,5,4,3]=>0000000=>1111111=>1
[4,7,1,8,3,2,5,6]=>0000000=>1111111=>1
[4,8,3,6,1,5,2,7]=>0000000=>1111111=>1
[1,7,8,6,4,5,3,2]=>1000000=>0111111=>1
[3,2,8,6,4,5,1,7]=>0000000=>1111111=>1
[8,4,3,6,2,5,1,7]=>0000000=>1111111=>1
[1,6,8,7,4,3,5,2]=>1000000=>0111111=>1
[3,1,2,6,8,7,5,4]=>0010000=>1101111=>2
[7,4,6,3,8,1,5,2]=>0000000=>1111111=>1
[7,4,8,3,6,2,1,5]=>0000000=>1111111=>1
[6,4,8,2,5,7,1,3]=>0000000=>1111111=>1
[6,8,4,2,7,1,3,5]=>0000000=>1111111=>1
[6,8,2,4,1,7,3,5]=>0000000=>1111111=>1
[7,5,1,6,2,4,8,3]=>0000000=>1111111=>1
[4,2,5,7,1,6,8,3]=>0000000=>1111111=>1
[4,5,2,3,8,7,1,6]=>0000000=>1111111=>1
[2,5,4,7,6,1,3,8]=>0000001=>1111110=>1
[5,2,3,7,6,1,4,8]=>0000001=>1111110=>1
[4,2,3,7,6,1,5,8]=>0000001=>1111110=>1
[4,2,7,3,5,1,6,8]=>0000001=>1111110=>1
[5,6,2,3,8,4,7,1]=>0000000=>1111111=>1
[5,6,2,3,1,7,8,4]=>0000000=>1111111=>1
[5,7,2,3,4,1,6,8]=>0000001=>1111110=>1
[6,2,7,3,5,1,4,8]=>0000001=>1111110=>1
[7,2,6,3,5,1,4,8]=>0000001=>1111110=>1
[6,5,2,3,1,7,8,4]=>0000000=>1111111=>1
[6,5,2,3,8,4,7,1]=>0000000=>1111111=>1
[7,5,2,1,4,6,8,3]=>0000000=>1111111=>1
[8,5,2,3,1,6,4,7]=>0000000=>1111111=>1
[8,6,2,3,1,5,4,7]=>0000000=>1111111=>1
[8,2,6,3,1,7,4,5]=>0000000=>1111111=>1
[1,6,3,4,2,7,5,8]=>1000001=>0111110=>1
[8,5,2,7,3,4,6,1]=>0000000=>1111111=>1
[1,7,2,4,5,6,8,3]=>1000000=>0111111=>1
[1,8,3,2,5,6,4,7]=>1000000=>0111111=>1
[7,2,8,1,4,6,3,5]=>0000000=>1111111=>1
[2,7,8,1,5,6,3,4]=>0000000=>1111111=>1
[6,8,2,3,1,5,4,7]=>0000000=>1111111=>1
[5,8,2,3,1,6,4,7]=>0000000=>1111111=>1
[5,7,2,1,4,6,8,3]=>0000000=>1111111=>1
[4,2,7,1,5,6,8,3]=>0000000=>1111111=>1
[4,2,3,8,1,7,5,6]=>0000000=>1111111=>1
[4,2,1,5,3,7,6,8]=>0000101=>1111010=>2
[5,1,3,8,4,6,7,2]=>0000000=>1111111=>1
[5,1,3,2,6,7,8,4]=>0000000=>1111111=>1
[5,1,3,4,2,7,6,8]=>0000101=>1111010=>2
[6,1,3,4,2,7,5,8]=>0000001=>1111110=>1
[7,2,1,3,5,8,4,6]=>0000000=>1111111=>1
[6,8,7,2,3,4,5,1]=>0000000=>1111111=>1
[2,8,7,5,1,3,4,6]=>0000000=>1111111=>1
[2,1,10,3,4,5,6,7,8,9]=>010000000=>101111111=>2
[9,7,5,3,1,8,6,4,2]=>00000000=>11111111=>1
[9,5,1,6,2,7,3,8,4]=>00000000=>11111111=>1
[10,7,4,1,8,5,2,9,6,3]=>000000000=>111111111=>1
[5,2,1,3,6,7,8,4]=>0000000=>1111111=>1
[8,3,7,5,1,4,2,6]=>0000000=>1111111=>1
[4,3,7,5,1,6,2,8]=>0000001=>1111110=>1
[5,2,6,1,4,3,7,8]=>0000011=>1111100=>1
[3,5,2,8,6,7,4,1]=>0000000=>1111111=>1
[5,3,7,4,2,8,6,1]=>0000000=>1111111=>1
[7,4,8,2,3,5,6,1]=>0000000=>1111111=>1
[5,6,2,8,7,1,4,3]=>0000000=>1111111=>1
[4,6,3,5,2,7,8,1]=>0000000=>1111111=>1
[4,1,6,3,5,7,2,8]=>0000001=>1111110=>1
[3,1,5,7,4,6,8,2]=>0000000=>1111111=>1
[7,2,5,8,6,1,4,3]=>0000000=>1111111=>1
[4,3,6,1,5,7,8,2]=>0000000=>1111111=>1
[3,5,4,1,2,6,7,8]=>0000111=>1111000=>1
[5,3,1,4,6,7,8,2]=>0000000=>1111111=>1
[4,6,7,1,3,5,8,2]=>0000000=>1111111=>1
[5,6,1,3,4,7,2,8]=>0000001=>1111110=>1
[2,5,3,7,8,4,6,1]=>0000000=>1111111=>1
[4,6,2,1,3,7,8,5]=>0000000=>1111111=>1
[3,6,2,4,1,7,5,8]=>0000001=>1111110=>1
[3,2,6,7,4,8,5,1]=>0000000=>1111111=>1
[7,1,3,8,4,5,2,6]=>0000000=>1111111=>1
[7,1,8,3,4,6,2,5]=>0000000=>1111111=>1
[6,3,2,7,5,8,4,1]=>0000000=>1111111=>1
[6,2,7,1,4,5,3,8]=>0000001=>1111110=>1
[4,2,6,1,5,7,3,8]=>0000001=>1111110=>1
[2,5,4,1,3,6,7,8]=>0000111=>1111000=>1
[5,4,1,2,6,7,3,8]=>0000001=>1111110=>1
[6,5,2,7,4,1,3,8]=>0000001=>1111110=>1
[6,5,7,3,1,4,2,8]=>0000001=>1111110=>1
[6,7,4,3,1,5,8,2]=>0000000=>1111111=>1
[4,2,5,6,7,8,9,1,3]=>00000000=>11111111=>1
[3,1,6,7,8,4,5,2]=>0000000=>1111111=>1
[6,4,5,2,7,1,8,3]=>0000000=>1111111=>1
[3,7,5,6,2,1,8,4]=>0000000=>1111111=>1
[6,4,1,2,7,8,3,5]=>0000000=>1111111=>1
[6,5,4,7,2,8,3,1]=>0000000=>1111111=>1
[3,2,4,6,5,8,1,7]=>0000000=>1111111=>1
[3,5,4,8,7,1,6,2]=>0000000=>1111111=>1
[7,5,2,1,6,3,4,8]=>0000001=>1111110=>1
[6,3,1,7,4,2,5,8]=>0000001=>1111110=>1
[8,7,2,1,5,3,6,4]=>0000000=>1111111=>1
[6,8,5,3,7,4,2,1]=>0000000=>1111111=>1
[7,2,8,1,5,6,4,3]=>0000000=>1111111=>1
[8,3,6,4,1,5,7,2]=>0000000=>1111111=>1
[7,5,6,1,4,8,2,3]=>0000000=>1111111=>1
[5,7,2,6,3,8,4,1]=>0000000=>1111111=>1
[8,4,1,2,3,6,7,5]=>0000000=>1111111=>1
[5,6,4,2,1,8,3,7]=>0000000=>1111111=>1
[6,8,1,3,2,7,5,4]=>0000000=>1111111=>1
[5,7,3,6,4,1,2,8]=>0000001=>1111110=>1
[7,2,4,3,8,1,5,6]=>0000000=>1111111=>1
[2,5,4,6,1,3,8,7]=>0000010=>1111101=>2
[2,4,3,5,8,1,6,7]=>0000000=>1111111=>1
[6,1,2,4,3,5,7,8]=>0000011=>1111100=>1
[1,7,6,8,4,3,2,5]=>1000000=>0111111=>1
[1,7,6,5,3,8,2,4]=>1000000=>0111111=>1
[6,1,2,4,3,5,8,7]=>0000010=>1111101=>2
[8,4,1,5,2,6,7,3]=>0000000=>1111111=>1
[6,4,5,3,1,8,7,2]=>0000000=>1111111=>1
[2,8,6,1,5,4,7,3]=>0000000=>1111111=>1
[3,8,6,4,7,1,2,5]=>0000000=>1111111=>1
[1,8,7,5,4,3,2,6]=>1000000=>0111111=>1
[8,6,4,7,1,3,2,5]=>0000000=>1111111=>1
[6,1,5,8,2,7,4,3]=>0000000=>1111111=>1
[7,1,2,3,6,4,5,8]=>0000001=>1111110=>1
[7,4,1,3,6,5,2,8]=>0000001=>1111110=>1
[5,7,2,8,1,3,6,4]=>0000000=>1111111=>1
[5,4,1,2,6,3,8,7]=>0000010=>1111101=>2
[2,7,8,4,1,3,6,5]=>0000000=>1111111=>1
[2,4,6,5,7,8,1,3]=>0000000=>1111111=>1
[2,4,6,7,5,8,1,3]=>0000000=>1111111=>1
[2,4,6,3,7,8,1,5]=>0000000=>1111111=>1
[2,4,5,6,8,7,1,3]=>0000000=>1111111=>1
[2,4,5,6,8,3,7,1]=>0000000=>1111111=>1
[2,4,5,6,3,8,1,7]=>0000000=>1111111=>1
[2,3,4,6,8,5,1,7]=>0000000=>1111111=>1
[3,6,4,1,2,7,8,5]=>0000000=>1111111=>1
[4,1,7,3,8,6,2,5]=>0000000=>1111111=>1
[8,4,1,2,5,3,7,6]=>0000000=>1111111=>1
[1,5,2,7,6,8,4,3]=>1000000=>0111111=>1
[4,7,6,8,3,1,2,5]=>0000000=>1111111=>1
[4,8,2,7,6,5,1,3]=>0000000=>1111111=>1
[7,4,2,8,6,5,1,3]=>0000000=>1111111=>1
[8,6,5,2,7,1,4,3]=>0000000=>1111111=>1
[6,5,8,2,7,1,4,3]=>0000000=>1111111=>1
[7,5,8,2,1,6,4,3]=>0000000=>1111111=>1
[3,2,1,6,5,8,4,7]=>0010000=>1101111=>2
[2,6,4,8,5,7,3,1]=>0000000=>1111111=>1
[6,3,1,4,5,8,2,7]=>0000000=>1111111=>1
[3,4,8,5,2,1,7,6]=>0000000=>1111111=>1
[4,8,7,1,3,2,6,5]=>0000000=>1111111=>1
[5,8,7,4,6,1,3,2]=>0000000=>1111111=>1
[3,4,1,8,7,6,2,5]=>0000000=>1111111=>1
[1,3,5,6,8,7,2,4]=>1000000=>0111111=>1
[2,8,7,5,4,1,6,3]=>0000000=>1111111=>1
[8,1,5,7,4,2,6,3]=>0000000=>1111111=>1
[5,8,7,3,4,1,6,2]=>0000000=>1111111=>1
[3,1,2,8,7,6,4,5]=>0010000=>1101111=>2
[3,4,5,7,8,1,6,2]=>0000000=>1111111=>1
[1,8,7,4,3,5,2,6]=>1000000=>0111111=>1
[2,4,5,8,1,3,7,6]=>0000000=>1111111=>1
[2,7,8,6,5,3,1,4]=>0000000=>1111111=>1
[2,8,3,5,6,1,4,7]=>0000000=>1111111=>1
[1,3,6,4,2,7,5,8]=>1000001=>0111110=>1
[2,3,7,5,8,1,4,6]=>0000000=>1111111=>1
[3,2,8,5,6,1,4,7]=>0000000=>1111111=>1
[7,2,5,8,1,4,6,3]=>0000000=>1111111=>1
[4,7,5,8,1,2,6,3]=>0000000=>1111111=>1
[4,7,5,8,1,2,3,6]=>0000000=>1111111=>1
[3,4,7,5,2,8,1,6]=>0000000=>1111111=>1
[4,3,2,5,7,8,1,6]=>0000000=>1111111=>1
[2,4,7,5,8,3,1,6]=>0000000=>1111111=>1
[2,5,4,7,3,8,1,6]=>0000000=>1111111=>1
[3,7,8,4,2,1,6,5]=>0000000=>1111111=>1
[1,5,4,8,7,6,2,3]=>1000000=>0111111=>1
[1,3,6,8,2,4,7,5]=>1000000=>0111111=>1
[1,6,7,4,3,8,2,5]=>1000000=>0111111=>1
[7,3,1,6,5,2,8,4]=>0000000=>1111111=>1
[4,7,2,8,5,1,6,3]=>0000000=>1111111=>1
[2,1,3,8,7,5,6,4]=>0110000=>1001111=>2
[1,6,4,7,3,8,5,2]=>1000000=>0111111=>1
[1,2,3,4,5,6,8,10,7,9]=>111111000=>000000111=>1
[4,5,6,7,8,1,2,3,9]=>00000001=>11111110=>1
[8,5,4,1,6,3,7,2]=>0000000=>1111111=>1
[1,7,6,2,4,8,5,3]=>1000000=>0111111=>1
[2,6,8,5,4,3,1,7]=>0000000=>1111111=>1
[8,3,6,1,2,7,4,5]=>0000000=>1111111=>1
[7,6,2,4,8,5,1,3]=>0000000=>1111111=>1
[4,7,5,2,6,3,8,1]=>0000000=>1111111=>1
[3,5,6,2,8,1,4,7]=>0000000=>1111111=>1
[8,9,10,4,5,6,2,3,1,7]=>000000000=>111111111=>1
[8,9,4,5,6,10,2,3,1,7]=>000000000=>111111111=>1
[8,9,10,4,5,2,3,6,1,7]=>000000000=>111111111=>1
[8,9,4,5,10,2,3,6,1,7]=>000000000=>111111111=>1
[8,9,4,5,2,3,6,10,1,7]=>000000000=>111111111=>1
[8,4,5,9,10,2,3,6,1,7]=>000000000=>111111111=>1
[8,4,5,9,2,3,6,10,1,7]=>000000000=>111111111=>1
[8,9,10,4,5,6,2,1,3,7]=>000000000=>111111111=>1
[8,9,4,5,6,10,2,1,3,7]=>000000000=>111111111=>1
[8,9,10,4,5,2,6,1,3,7]=>000000000=>111111111=>1
[8,9,4,5,10,2,6,1,3,7]=>000000000=>111111111=>1
[8,9,4,5,2,6,10,1,3,7]=>000000000=>111111111=>1
[8,4,5,9,10,2,6,1,3,7]=>000000000=>111111111=>1
[8,4,5,9,2,6,10,1,3,7]=>000000000=>111111111=>1
[8,9,10,4,5,2,1,3,6,7]=>000000000=>111111111=>1
[8,9,4,5,10,2,1,3,6,7]=>000000000=>111111111=>1
[8,9,4,5,2,10,1,3,6,7]=>000000000=>111111111=>1
[8,9,4,5,2,1,3,6,10,7]=>000000000=>111111111=>1
[8,4,5,9,10,2,1,3,6,7]=>000000000=>111111111=>1
[8,4,5,9,2,10,1,3,6,7]=>000000000=>111111111=>1
[8,4,5,9,2,1,3,6,10,7]=>000000000=>111111111=>1
[8,9,10,4,2,5,6,1,3,7]=>000000000=>111111111=>1
[8,9,4,10,2,5,6,1,3,7]=>000000000=>111111111=>1
[8,9,4,2,5,6,10,1,3,7]=>000000000=>111111111=>1
[8,4,9,10,2,5,6,1,3,7]=>000000000=>111111111=>1
[8,4,9,2,5,6,10,1,3,7]=>000000000=>111111111=>1
[8,9,10,4,2,5,1,3,6,7]=>000000000=>111111111=>1
[8,9,4,10,2,5,1,3,6,7]=>000000000=>111111111=>1
[8,9,4,2,5,10,1,3,6,7]=>000000000=>111111111=>1
[8,9,4,2,5,1,3,6,10,7]=>000000000=>111111111=>1
[8,4,9,10,2,5,1,3,6,7]=>000000000=>111111111=>1
[8,4,9,2,5,1,3,6,10,7]=>000000000=>111111111=>1
[8,4,2,5,9,10,1,3,6,7]=>000000000=>111111111=>1
[8,4,2,5,9,1,3,6,10,7]=>000000000=>111111111=>1
[4,8,9,10,2,5,6,1,3,7]=>000000000=>111111111=>1
[4,8,9,2,5,6,10,1,3,7]=>000000000=>111111111=>1
[4,8,9,10,2,5,1,3,6,7]=>000000000=>111111111=>1
[4,8,9,2,5,10,1,3,6,7]=>000000000=>111111111=>1
[4,8,9,2,5,1,3,6,10,7]=>000000000=>111111111=>1
[4,8,2,5,9,10,1,3,6,7]=>000000000=>111111111=>1
[4,8,2,5,9,1,3,6,10,7]=>000000000=>111111111=>1
[1,6,8,2,5,3,4,7]=>1000000=>0111111=>1
[8,6,3,5,2,1,4,7]=>0000000=>1111111=>1
[4,1,3,8,5,6,2,7]=>0000000=>1111111=>1
[5,2,8,3,1,6,7,4]=>0000000=>1111111=>1
[1,7,8,6,3,2,5,4]=>1000000=>0111111=>1
[3,2,8,1,5,7,4,6]=>0000000=>1111111=>1
[3,4,6,7,2,1,5,8]=>0000001=>1111110=>1
[2,6,7,1,4,3,8,5]=>0000000=>1111111=>1
[4,2,5,3,8,6,7,1]=>0000000=>1111111=>1
[3,2,7,4,8,5,6,1]=>0000000=>1111111=>1
[7,2,5,1,6,3,8,4]=>0000000=>1111111=>1
[4,5,2,8,3,7,1,6]=>0000000=>1111111=>1
[7,8,5,1,6,4,3,2]=>0000000=>1111111=>1
[8,7,5,1,6,4,3,2]=>0000000=>1111111=>1
[4,5,8,3,1,2,7,6]=>0000000=>1111111=>1
[1,4,6,3,7,5,2,8]=>1000001=>0111110=>1
[1,7,6,3,8,5,2,4]=>1000000=>0111111=>1
[6,2,4,3,7,5,8,1]=>0000000=>1111111=>1
[3,8,2,1,5,7,6,4]=>0000000=>1111111=>1
[1,3,2,8,7,4,6,5]=>1010000=>0101111=>2
[7,5,2,8,3,1,6,4]=>0000000=>1111111=>1
[4,6,3,7,8,1,2,5]=>0000000=>1111111=>1
[6,2,5,4,1,7,8,3]=>0000000=>1111111=>1
[4,1,5,6,3,8,7,2]=>0000000=>1111111=>1
[8,5,1,6,3,2,4,7]=>0000000=>1111111=>1
[8,1,5,4,6,7,3,2]=>0000000=>1111111=>1
[2,4,5,8,3,7,6,1]=>0000000=>1111111=>1
[6,4,5,1,3,8,7,2]=>0000000=>1111111=>1
[6,1,3,5,4,8,2,7]=>0000000=>1111111=>1
[1,3,8,7,2,5,6,4]=>1000000=>0111111=>1
[2,5,4,1,8,3,7,6]=>0000000=>1111111=>1
[5,1,4,8,3,7,6,2]=>0000000=>1111111=>1
[8,4,1,2,7,6,5,3]=>0000000=>1111111=>1
[4,8,3,2,7,6,5,1]=>0000000=>1111111=>1
[1,8,7,3,4,6,5,2]=>1000000=>0111111=>1
[5,3,1,2,4,6,8,7]=>0000110=>1111001=>2
[1,4,3,8,5,7,2,6]=>1000000=>0111111=>1
[4,8,1,3,6,2,7,5]=>0000000=>1111111=>1
[1,8,2,4,7,3,6,5]=>1000000=>0111111=>1
[2,7,1,6,5,8,3,4]=>0000000=>1111111=>1
[6,2,3,8,1,5,7,4]=>0000000=>1111111=>1
[2,5,7,4,8,3,6,1]=>0000000=>1111111=>1
[4,3,7,1,2,8,5,6]=>0000000=>1111111=>1
[3,8,6,2,7,5,4,1]=>0000000=>1111111=>1
[1,8,4,2,5,7,3,6]=>1000000=>0111111=>1
[5,8,3,1,2,4,6,7]=>0000000=>1111111=>1
[1,4,8,5,2,3,6,7]=>1000000=>0111111=>1
[7,1,4,2,6,8,3,5]=>0000000=>1111111=>1
[1,5,8,7,2,4,3,6]=>1000000=>0111111=>1
[1,5,4,2,8,3,7,6]=>1000000=>0111111=>1
[8,7,1,3,2,5,4,6]=>0000000=>1111111=>1
[6,7,4,2,8,1,3,5]=>0000000=>1111111=>1
[4,1,6,8,7,2,3,5]=>0000000=>1111111=>1
[2,1,4,3,6,5,9,7,10,8]=>010101000=>101010111=>4
[2,1,4,3,7,5,8,6,10,9]=>010100010=>101011101=>4
[2,1,4,3,7,5,9,6,10,8]=>010100000=>101011111=>3
[2,1,4,3,8,5,9,6,10,7]=>010100000=>101011111=>3
[2,1,5,3,6,4,8,7,10,9]=>010001010=>101110101=>4
[2,1,5,3,6,4,9,7,10,8]=>010001000=>101110111=>3
[2,1,5,3,7,4,8,6,10,9]=>010000010=>101111101=>3
[2,1,5,3,7,4,9,6,10,8]=>010000000=>101111111=>2
[2,1,5,3,8,4,9,6,10,7]=>010000000=>101111111=>2
[2,1,6,3,7,4,8,5,10,9]=>010000010=>101111101=>3
[2,1,6,3,7,4,9,5,10,8]=>010000000=>101111111=>2
[2,1,6,3,8,4,9,5,10,7]=>010000000=>101111111=>2
[2,1,7,3,8,4,9,5,10,6]=>010000000=>101111111=>2
[3,1,4,2,6,5,9,7,10,8]=>000101000=>111010111=>3
[3,1,4,2,7,5,8,6,10,9]=>000100010=>111011101=>3
[3,1,4,2,7,5,9,6,10,8]=>000100000=>111011111=>2
[3,1,4,2,8,5,9,6,10,7]=>000100000=>111011111=>2
[3,1,5,2,6,4,9,7,10,8]=>000001000=>111110111=>2
[3,1,5,2,8,4,9,6,10,7]=>000000000=>111111111=>1
[3,1,6,2,7,4,8,5,10,9]=>000000010=>111111101=>2
[3,1,6,2,7,4,9,5,10,8]=>000000000=>111111111=>1
[3,1,6,2,8,4,9,5,10,7]=>000000000=>111111111=>1
[3,1,7,2,8,4,9,5,10,6]=>000000000=>111111111=>1
[4,1,5,2,6,3,9,7,10,8]=>000001000=>111110111=>2
[4,1,5,2,7,3,8,6,10,9]=>000000010=>111111101=>2
[4,1,5,2,7,3,9,6,10,8]=>000000000=>111111111=>1
[4,1,5,2,8,3,9,6,10,7]=>000000000=>111111111=>1
[4,1,6,2,7,3,8,5,10,9]=>000000010=>111111101=>2
[4,1,6,2,7,3,9,5,10,8]=>000000000=>111111111=>1
[4,1,6,2,8,3,9,5,10,7]=>000000000=>111111111=>1
[4,1,7,2,8,3,9,5,10,6]=>000000000=>111111111=>1
[5,1,6,2,7,3,9,4,10,8]=>000000000=>111111111=>1
[5,1,6,2,8,3,9,4,10,7]=>000000000=>111111111=>1
[5,1,7,2,8,3,9,4,10,6]=>000000000=>111111111=>1
[3,1,5,2,7,4,9,6,10,8,12,11]=>00000000010=>11111111101=>2
[3,1,5,2,8,4,9,6,10,7,12,11]=>00000000010=>11111111101=>2
[3,1,6,2,7,4,9,5,10,8,12,11]=>00000000010=>11111111101=>2
[3,1,6,2,8,4,9,5,10,7,12,11]=>00000000010=>11111111101=>2
[3,1,7,2,8,4,9,5,10,6,12,11]=>00000000010=>11111111101=>2
[4,1,5,2,7,3,9,6,10,8,12,11]=>00000000010=>11111111101=>2
[4,1,5,2,8,3,9,6,10,7,12,11]=>00000000010=>11111111101=>2
[4,1,6,2,7,3,9,5,10,8,12,11]=>00000000010=>11111111101=>2
[4,1,6,2,8,3,9,5,10,7,12,11]=>00000000010=>11111111101=>2
[4,1,7,2,8,3,9,5,10,6,12,11]=>00000000010=>11111111101=>2
[5,1,6,2,7,3,9,4,10,8,12,11]=>00000000010=>11111111101=>2
[5,1,6,2,8,3,9,4,10,7,12,11]=>00000000010=>11111111101=>2
[5,1,7,2,8,3,9,4,10,6,12,11]=>00000000010=>11111111101=>2
[6,1,7,2,8,3,9,4,10,5,12,11]=>00000000010=>11111111101=>2
[6,1,7,3,5,8,2,4]=>0000000=>1111111=>1
[1,3,7,6,4,8,2,5]=>1000000=>0111111=>1
[2,1,8,7,3,5,4,6]=>0100000=>1011111=>2
[6,1,8,5,7,4,3,2]=>0000000=>1111111=>1
[8,5,1,4,7,6,3,2]=>0000000=>1111111=>1
[8,1,3,7,2,4,6,5]=>0000000=>1111111=>1
[5,3,1,6,4,8,2,7]=>0000000=>1111111=>1
[2,5,6,7,1,4,8,3]=>0000000=>1111111=>1
[4,7,5,3,2,8,1,6]=>0000000=>1111111=>1
[3,8,6,7,2,5,4,1]=>0000000=>1111111=>1
[5,8,1,2,7,4,3,6]=>0000000=>1111111=>1
[6,3,1,8,2,4,5,7]=>0000000=>1111111=>1
[4,6,3,7,8,1,5,2]=>0000000=>1111111=>1
[7,6,2,4,8,3,1,5]=>0000000=>1111111=>1
[8,1,4,2,7,5,6,3]=>0000000=>1111111=>1
[1,7,2,8,3,9,4,10,5,6]=>100000000=>011111111=>1
[1,7,2,8,3,9,10,4,5,6]=>100000000=>011111111=>1
[1,7,2,8,9,3,4,10,5,6]=>100000000=>011111111=>1
[1,7,2,8,9,3,10,4,5,6]=>100000000=>011111111=>1
[1,7,2,8,9,10,3,4,5,6]=>100000000=>011111111=>1
[1,7,8,2,3,9,4,10,5,6]=>100000000=>011111111=>1
[1,7,8,2,3,9,10,4,5,6]=>100000000=>011111111=>1
[1,7,8,2,9,3,4,10,5,6]=>100000000=>011111111=>1
[1,7,8,2,9,3,10,4,5,6]=>100000000=>011111111=>1
[1,7,8,2,9,10,3,4,5,6]=>100000000=>011111111=>1
[1,7,8,9,2,3,4,10,5,6]=>100000000=>011111111=>1
[1,7,8,9,2,3,10,4,5,6]=>100000000=>011111111=>1
[1,7,8,9,2,10,3,4,5,6]=>100000000=>011111111=>1
[7,1,2,8,3,9,4,10,5,6]=>000000000=>111111111=>1
[7,1,2,8,3,9,10,4,5,6]=>000000000=>111111111=>1
[7,1,2,8,9,3,4,10,5,6]=>000000000=>111111111=>1
[7,1,2,8,9,3,10,4,5,6]=>000000000=>111111111=>1
[7,1,2,8,9,10,3,4,5,6]=>000000000=>111111111=>1
[7,1,8,2,3,9,4,10,5,6]=>000000000=>111111111=>1
[7,1,8,2,3,9,10,4,5,6]=>000000000=>111111111=>1
[7,1,8,2,9,3,4,10,5,6]=>000000000=>111111111=>1
[7,1,8,2,9,10,3,4,5,6]=>000000000=>111111111=>1
[7,1,8,9,2,3,4,10,5,6]=>000000000=>111111111=>1
[7,1,8,9,2,3,10,4,5,6]=>000000000=>111111111=>1
[7,1,8,9,2,10,3,4,5,6]=>000000000=>111111111=>1
[7,1,8,9,10,2,3,4,5,6]=>000000000=>111111111=>1
[7,8,1,2,3,9,4,10,5,6]=>000000000=>111111111=>1
[7,8,1,2,3,9,10,4,5,6]=>000000000=>111111111=>1
[7,8,1,2,9,3,4,10,5,6]=>000000000=>111111111=>1
[7,8,1,2,9,3,10,4,5,6]=>000000000=>111111111=>1
[7,8,1,2,9,10,3,4,5,6]=>000000000=>111111111=>1
[7,8,1,9,2,3,4,10,5,6]=>000000000=>111111111=>1
[7,8,1,9,2,3,10,4,5,6]=>000000000=>111111111=>1
[7,8,1,9,2,10,3,4,5,6]=>000000000=>111111111=>1
[7,8,1,9,10,2,3,4,5,6]=>000000000=>111111111=>1
[7,8,9,1,2,3,4,10,5,6]=>000000000=>111111111=>1
[7,8,9,1,2,3,10,4,5,6]=>000000000=>111111111=>1
[7,8,9,1,2,10,3,4,5,6]=>000000000=>111111111=>1
[7,8,9,1,10,2,3,4,5,6]=>000000000=>111111111=>1
[1,8,2,9,3,10,4,11,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,3,10,4,11,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,3,10,11,4,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,3,10,11,4,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,3,10,11,12,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,10,3,4,11,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,10,3,4,11,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,10,3,11,4,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,10,3,11,4,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,10,3,11,12,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,10,11,3,4,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,10,11,3,4,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,10,11,3,12,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,2,9,10,11,12,3,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,3,10,4,11,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,3,10,4,11,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,3,10,11,4,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,3,10,11,4,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,3,10,11,12,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,10,3,4,11,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,10,3,4,11,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,10,3,11,4,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,10,3,11,4,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,10,3,11,12,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,10,11,3,4,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,10,11,3,4,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,10,11,3,12,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,2,10,11,12,3,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,2,3,4,11,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,2,3,4,11,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,2,3,11,4,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,2,3,11,4,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,2,3,11,12,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,2,11,3,4,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,2,11,3,4,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,2,11,3,12,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,2,11,12,3,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,11,2,3,4,5,12,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,11,2,3,4,12,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,11,2,3,12,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,11,2,12,3,4,5,6,7]=>10000000000=>01111111111=>1
[1,8,9,10,11,12,2,3,4,5,6,7]=>10000000000=>01111111111=>1
[1,7,6,5,4,3,2,9,8]=>10000010=>01111101=>2
[3,7,1,4,6,8,2,5]=>0000000=>1111111=>1
[2,4,7,3,6,8,1,5]=>0000000=>1111111=>1
[6,5,2,8,7,1,4,3]=>0000000=>1111111=>1
[2,6,1,3,8,5,4,7]=>0000000=>1111111=>1
[6,4,1,8,3,2,5,7]=>0000000=>1111111=>1
[5,8,1,4,2,7,3,6]=>0000000=>1111111=>1
[2,3,1,6,8,7,4,5]=>0010000=>1101111=>2
[6,4,8,2,1,7,3,5]=>0000000=>1111111=>1
[1,6,5,3,8,2,4,7]=>1000000=>0111111=>1
[5,6,1,2,4,8,3,7]=>0000000=>1111111=>1
[8,5,1,2,7,4,3,6]=>0000000=>1111111=>1
[1,4,7,5,8,2,3,6]=>1000000=>0111111=>1
[1,6,8,4,7,3,2,5]=>1000000=>0111111=>1
[2,1,5,7,4,6,8,3]=>0100000=>1011111=>2
[2,3,5,7,8,1,6,4]=>0000000=>1111111=>1
[1,5,7,4,2,3,6,8]=>1000001=>0111110=>1
[2,4,7,5,3,6,8,1]=>0000000=>1111111=>1
[8,1,7,2,4,6,3,5]=>0000000=>1111111=>1
[1,2,4,7,8,6,3,5]=>1100000=>0011111=>1
[2,4,7,8,3,5,1,6]=>0000000=>1111111=>1
[1,3,6,2,5,8,4,7]=>1000000=>0111111=>1
[1,5,3,6,8,2,4,7]=>1000000=>0111111=>1
[4,8,1,2,6,3,7,5]=>0000000=>1111111=>1
[5,8,1,2,6,3,7,4]=>0000000=>1111111=>1
[1,6,2,3,7,5,8,4]=>1000000=>0111111=>1
[4,1,2,6,5,7,8,3]=>0000000=>1111111=>1
[1,8,4,2,7,3,6,5]=>1000000=>0111111=>1
[1,7,5,2,3,8,6,4]=>1000000=>0111111=>1
[8,1,4,7,3,5,2,6]=>0000000=>1111111=>1
[8,4,3,6,1,7,2,5]=>0000000=>1111111=>1
[2,6,1,8,3,7,4,5]=>0000000=>1111111=>1
[8,4,2,1,3,7,5,6]=>0000000=>1111111=>1
[2,5,1,7,6,8,3,4]=>0000000=>1111111=>1
[5,3,1,8,2,4,7,6]=>0000000=>1111111=>1
[1,2,6,3,7,5,8,4]=>1100000=>0011111=>1
[5,1,8,3,2,4,7,6]=>0000000=>1111111=>1
[3,1,5,4,6,7,8,2]=>0000000=>1111111=>1
[2,8,5,7,3,1,4,6]=>0000000=>1111111=>1
[2,6,8,7,3,1,4,5]=>0000000=>1111111=>1
[7,4,2,1,3,8,5,6]=>0000000=>1111111=>1
[7,2,1,3,8,5,4,6]=>0000000=>1111111=>1
[2,1,7,3,8,6,4,5]=>0100000=>1011111=>2
[1,7,5,3,2,4,8,6]=>1000000=>0111111=>1
[1,4,2,7,6,5,8,3]=>1000000=>0111111=>1
[3,4,1,6,5,7,8,2]=>0000000=>1111111=>1
[2,8,7,3,4,1,5,6]=>0000000=>1111111=>1
[5,7,6,2,3,8,1,4]=>0000000=>1111111=>1
[4,5,7,6,2,8,1,3]=>0000000=>1111111=>1
[3,1,8,7,5,2,6,4]=>0000000=>1111111=>1
[4,5,6,8,7,2,1,3]=>0000000=>1111111=>1
[3,8,4,1,5,2,7,6]=>0000000=>1111111=>1
[1,8,6,2,4,3,7,5]=>1000000=>0111111=>1
[6,2,7,1,5,8,4,3]=>0000000=>1111111=>1
[1,4,5,6,7,8,9,3,2]=>10000000=>01111111=>1
[4,1,6,5,2,3,7,8]=>0000011=>1111100=>1
[4,1,3,6,7,2,5,8]=>0000001=>1111110=>1
[2,7,5,8,1,3,6,4]=>0000000=>1111111=>1
[5,1,6,7,3,2,4,8]=>0000001=>1111110=>1
[1,2,5,7,8,6,3,4]=>1100000=>0011111=>1
[1,2,6,7,4,5,3,8]=>1100001=>0011110=>1
[1,2,7,8,4,6,3,5]=>1100000=>0011111=>1
[8,6,5,2,1,7,4,3]=>0000000=>1111111=>1
[4,3,8,6,7,1,5,2]=>0000000=>1111111=>1
[8,3,2,4,7,1,6,5]=>0000000=>1111111=>1
[7,3,2,8,6,1,5,4]=>0000000=>1111111=>1
[7,5,8,2,6,1,4,3]=>0000000=>1111111=>1
[5,6,8,2,7,4,1,3]=>0000000=>1111111=>1
[7,4,1,2,6,5,8,3]=>0000000=>1111111=>1
[5,2,7,4,6,1,8,3]=>0000000=>1111111=>1
[7,4,1,2,3,6,8,5]=>0000000=>1111111=>1
[5,4,8,6,3,2,1,7]=>0000000=>1111111=>1
[8,4,6,7,3,1,5,2]=>0000000=>1111111=>1
[4,1,3,6,8,5,2,7]=>0000000=>1111111=>1
[6,3,5,7,1,2,8,4]=>0000000=>1111111=>1
[1,8,5,3,2,4,6,7]=>1000000=>0111111=>1
[1,6,8,3,4,2,5,7]=>1000000=>0111111=>1
[1,7,6,8,4,2,3,5]=>1000000=>0111111=>1
[9,8,7,6,5,2,1,3,4]=>00000000=>11111111=>1
[7,2,8,9,10,1,3,4,5,6]=>000000000=>111111111=>1
[5,1,7,8,4,2,3,6]=>0000000=>1111111=>1
[3,8,2,1,6,7,5,4]=>0000000=>1111111=>1
[2,8,3,1,7,5,6,4]=>0000000=>1111111=>1
[9,10,6,4,2,1,3,5,8,7]=>000000000=>111111111=>1
[10,7,8,4,2,1,3,6,5,9]=>000000000=>111111111=>1
[9,7,10,4,2,1,3,6,8,5]=>000000000=>111111111=>1
[8,9,10,4,2,1,3,7,6,5]=>000000000=>111111111=>1
[10,8,5,6,2,1,4,3,7,9]=>000000000=>111111111=>1
[9,10,5,6,2,1,4,3,8,7]=>000000000=>111111111=>1
[10,7,5,8,2,1,4,6,3,9]=>000000000=>111111111=>1
[9,7,5,10,2,1,4,6,8,3]=>000000000=>111111111=>1
[8,9,5,10,2,1,4,7,6,3]=>000000000=>111111111=>1
[10,6,7,8,2,1,5,4,3,9]=>000000000=>111111111=>1
[9,6,7,10,2,1,5,4,8,3]=>000000000=>111111111=>1
[8,6,9,10,2,1,5,7,4,3]=>000000000=>111111111=>1
[7,8,9,10,2,1,6,5,4,3]=>000000000=>111111111=>1
[10,8,6,3,4,2,1,5,7,9]=>000000000=>111111111=>1
[9,10,6,3,4,2,1,5,8,7]=>000000000=>111111111=>1
[10,7,8,3,4,2,1,6,5,9]=>000000000=>111111111=>1
[9,7,10,3,4,2,1,6,8,5]=>000000000=>111111111=>1
[8,9,10,3,4,2,1,7,6,5]=>000000000=>111111111=>1
[10,8,5,3,6,2,4,1,7,9]=>000000000=>111111111=>1
[9,10,5,3,6,2,4,1,8,7]=>000000000=>111111111=>1
[10,7,5,3,8,2,4,6,1,9]=>000000000=>111111111=>1
[9,7,5,3,10,2,4,6,8,1]=>000000000=>111111111=>1
[8,9,5,3,10,2,4,7,6,1]=>000000000=>111111111=>1
[10,6,7,3,8,2,5,4,1,9]=>000000000=>111111111=>1
[9,6,7,3,10,2,5,4,8,1]=>000000000=>111111111=>1
[8,6,9,3,10,2,5,7,4,1]=>000000000=>111111111=>1
[7,8,9,3,10,2,6,5,4,1]=>000000000=>111111111=>1
[10,8,4,5,6,3,2,1,7,9]=>000000000=>111111111=>1
[9,10,4,5,6,3,2,1,8,7]=>000000000=>111111111=>1
[10,7,4,5,8,3,2,6,1,9]=>000000000=>111111111=>1
[9,7,4,5,10,3,2,6,8,1]=>000000000=>111111111=>1
[8,9,4,5,10,3,2,7,6,1]=>000000000=>111111111=>1
[10,6,4,7,8,3,5,2,1,9]=>000000000=>111111111=>1
[9,6,4,7,10,3,5,2,8,1]=>000000000=>111111111=>1
[8,6,4,9,10,3,5,7,2,1]=>000000000=>111111111=>1
[7,8,4,9,10,3,6,5,2,1]=>000000000=>111111111=>1
[10,5,6,7,8,4,3,2,1,9]=>000000000=>111111111=>1
[9,5,6,7,10,4,3,2,8,1]=>000000000=>111111111=>1
[8,5,6,9,10,4,3,7,2,1]=>000000000=>111111111=>1
[7,5,8,9,10,4,6,3,2,1]=>000000000=>111111111=>1
[2,7,4,1,5,8,3,6]=>0000000=>1111111=>1
[4,7,5,3,8,2,6,1]=>0000000=>1111111=>1
[2,6,4,7,8,5,3,1]=>0000000=>1111111=>1
[2,5,1,8,4,6,7,3]=>0000000=>1111111=>1
[2,1,7,6,3,4,5,8]=>0100001=>1011110=>2
[6,1,5,3,8,2,4,7]=>0000000=>1111111=>1
[2,3,6,8,5,1,7,4]=>0000000=>1111111=>1
[3,2,4,8,6,1,7,5]=>0000000=>1111111=>1
[2,1,3,8,4,5,7,6]=>0110000=>1001111=>2
[3,1,2,8,5,4,7,6]=>0010000=>1101111=>2
[2,1,3,7,8,4,6,5]=>0110000=>1001111=>2
[2,1,3,8,4,7,6,5]=>0110000=>1001111=>2
[3,1,2,8,4,5,7,6]=>0010000=>1101111=>2
[1,2,8,7,5,4,6,3]=>1100000=>0011111=>1
[2,1,8,7,4,6,5,3]=>0100000=>1011111=>2
[1,4,6,8,5,7,2,3]=>1000000=>0111111=>1
[2,8,5,1,6,4,3,7]=>0000000=>1111111=>1
[5,8,4,3,6,7,2,1]=>0000000=>1111111=>1
[3,2,6,5,1,8,4,7]=>0000000=>1111111=>1
[6,5,3,8,1,7,2,4]=>0000000=>1111111=>1
[8,3,7,1,6,2,4,5]=>0000000=>1111111=>1
[8,1,4,6,5,7,2,3]=>0000000=>1111111=>1
[8,1,7,5,6,4,2,3]=>0000000=>1111111=>1
[8,6,1,5,3,7,2,4]=>0000000=>1111111=>1
[2,6,3,7,8,1,4,5]=>0000000=>1111111=>1
[7,2,3,6,8,5,4,1]=>0000000=>1111111=>1
[5,1,3,2,4,6,8,7]=>0000110=>1111001=>2
[6,5,3,4,1,8,2,7]=>0000000=>1111111=>1
[2,8,3,7,6,1,5,4]=>0000000=>1111111=>1
[5,4,2,6,8,7,3,1]=>0000000=>1111111=>1
[3,7,2,5,8,6,4,1]=>0000000=>1111111=>1
[4,6,5,3,8,1,7,2]=>0000000=>1111111=>1
[2,4,8,7,6,1,5,3]=>0000000=>1111111=>1
[8,2,6,5,1,4,3,7]=>0000000=>1111111=>1
[4,8,5,2,7,6,3,1]=>0000000=>1111111=>1
[2,8,6,5,7,1,3,4]=>0000000=>1111111=>1
[4,8,5,1,7,6,3,2]=>0000000=>1111111=>1
[5,8,1,7,6,2,3,4]=>0000000=>1111111=>1
[1,5,8,2,6,4,3,7]=>1000000=>0111111=>1
[10,9,8,6,4,2,1,3,5,7]=>000000000=>111111111=>1
[10,8,7,6,4,2,1,3,5,9]=>000000000=>111111111=>1
[10,7,9,6,4,2,1,3,8,5]=>000000000=>111111111=>1
[10,9,8,7,6,4,2,1,3,5]=>000000000=>111111111=>1
[10,8,6,5,4,2,1,3,7,9]=>000000000=>111111111=>1
[10,9,8,6,5,4,2,1,3,7]=>000000000=>111111111=>1
[10,8,5,7,4,2,1,6,3,9]=>000000000=>111111111=>1
[10,5,9,7,4,2,1,6,8,3]=>000000000=>111111111=>1
[10,9,8,5,7,4,2,1,6,3]=>000000000=>111111111=>1
[10,8,7,6,5,4,2,1,3,9]=>000000000=>111111111=>1
[10,7,9,6,5,4,2,1,8,3]=>000000000=>111111111=>1
[10,6,9,8,5,7,2,1,4,3]=>000000000=>111111111=>1
[10,8,6,4,3,2,1,5,7,9]=>000000000=>111111111=>1
[10,9,8,6,4,3,2,1,5,7]=>000000000=>111111111=>1
[10,8,7,6,4,3,2,1,5,9]=>000000000=>111111111=>1
[10,7,9,6,4,3,2,1,8,5]=>000000000=>111111111=>1
[10,8,6,3,5,2,4,1,7,9]=>000000000=>111111111=>1
[10,9,8,6,3,5,2,4,1,7]=>000000000=>111111111=>1
[10,8,3,7,5,2,4,6,1,9]=>000000000=>111111111=>1
[10,3,9,7,5,2,4,6,8,1]=>000000000=>111111111=>1
[10,9,8,3,7,5,2,4,6,1]=>000000000=>111111111=>1
[10,8,7,6,3,5,2,4,1,9]=>000000000=>111111111=>1
[10,7,9,6,3,5,2,4,8,1]=>000000000=>111111111=>1
[10,9,3,8,6,5,2,7,4,1]=>000000000=>111111111=>1
[10,9,8,7,6,3,5,2,4,1]=>000000000=>111111111=>1
[10,8,6,5,4,3,2,1,7,9]=>000000000=>111111111=>1
[10,8,5,7,4,3,2,6,1,9]=>000000000=>111111111=>1
[10,5,9,7,4,3,2,6,8,1]=>000000000=>111111111=>1
[10,9,8,5,7,4,3,2,6,1]=>000000000=>111111111=>1
[10,8,4,7,6,3,5,2,1,9]=>000000000=>111111111=>1
[10,4,9,7,6,3,5,2,8,1]=>000000000=>111111111=>1
[10,4,9,6,8,3,5,7,2,1]=>000000000=>111111111=>1
[10,9,8,4,7,6,3,5,2,1]=>000000000=>111111111=>1
[10,7,9,6,5,4,3,2,8,1]=>000000000=>111111111=>1
[10,6,9,8,5,4,3,7,2,1]=>000000000=>111111111=>1
[10,5,9,8,7,4,6,3,2,1]=>000000000=>111111111=>1
[3,1,8,2,5,4,6,7]=>0000000=>1111111=>1
[4,2,5,1,8,7,6,3]=>0000000=>1111111=>1
[5,2,4,8,1,7,6,3]=>0000000=>1111111=>1
[7,3,2,4,6,8,1,5]=>0000000=>1111111=>1
[1,4,8,6,7,2,5,3]=>1000000=>0111111=>1
[1,4,5,7,3,8,2,6]=>1000000=>0111111=>1
[8,2,5,4,1,3,7,6]=>0000000=>1111111=>1
[2,4,5,8,6,3,1,7]=>0000000=>1111111=>1
[2,5,7,8,6,1,4,3]=>0000000=>1111111=>1
[5,1,7,6,8,2,3,4]=>0000000=>1111111=>1
[1,7,6,2,4,3,8,5]=>1000000=>0111111=>1
[5,7,1,6,2,3,4,8]=>0000001=>1111110=>1
[5,6,8,7,1,3,2,4]=>0000000=>1111111=>1
[1,5,3,4,8,2,6,7]=>1000000=>0111111=>1
[2,1,3,6,5,8,4,7]=>0110000=>1001111=>2
[4,6,1,5,7,2,8,3]=>0000000=>1111111=>1
[2,5,8,4,6,3,7,1]=>0000000=>1111111=>1
[8,1,6,5,2,7,4,3]=>0000000=>1111111=>1
[6,8,1,5,2,7,4,3]=>0000000=>1111111=>1
[1,7,3,2,4,8,6,5]=>1000000=>0111111=>1
[4,3,1,8,2,6,7,5]=>0000000=>1111111=>1
[4,8,1,3,2,5,7,6]=>0000000=>1111111=>1
[1,7,5,3,8,6,2,4]=>1000000=>0111111=>1
[2,5,3,8,1,4,7,6]=>0000000=>1111111=>1
[4,2,5,8,1,3,7,6]=>0000000=>1111111=>1
[8,1,2,4,3,5,7,6]=>0000000=>1111111=>1
[2,4,3,8,1,5,7,6]=>0000000=>1111111=>1
[3,1,7,4,8,6,5,2]=>0000000=>1111111=>1
[6,4,5,3,2,8,7,1]=>0000000=>1111111=>1
[2,7,3,8,5,1,6,4]=>0000000=>1111111=>1
[8,7,3,2,5,6,4,1]=>0000000=>1111111=>1
[3,1,8,2,6,5,4,7]=>0000000=>1111111=>1
[7,6,2,8,1,4,5,3]=>0000000=>1111111=>1
[2,3,8,4,1,5,7,6]=>0000000=>1111111=>1
[8,4,2,3,1,5,7,6]=>0000000=>1111111=>1
[8,2,3,4,1,5,7,6]=>0000000=>1111111=>1
[5,7,2,8,4,1,6,3]=>0000000=>1111111=>1
[2,5,6,3,8,1,4,7]=>0000000=>1111111=>1
[1,3,4,5,6,7,2,8,9]=>10000011=>01111100=>1
[7,4,5,6,8,1,3,2]=>0000000=>1111111=>1
[7,5,1,8,4,6,3,2]=>0000000=>1111111=>1
[1,7,8,5,6,4,3,2]=>1000000=>0111111=>1
[2,8,1,7,4,5,3,6]=>0000000=>1111111=>1
[7,3,6,2,5,4,8,1]=>0000000=>1111111=>1
[1,6,2,3,5,8,4,7]=>1000000=>0111111=>1
[1,8,5,6,4,3,7,2]=>1000000=>0111111=>1
[2,6,8,4,5,1,7,3]=>0000000=>1111111=>1
[5,3,2,1,7,8,4,6]=>0000000=>1111111=>1
[8,4,1,3,6,7,2,5]=>0000000=>1111111=>1
[1,6,5,3,8,4,7,2]=>1000000=>0111111=>1
[7,6,2,3,5,1,4,8]=>0000001=>1111110=>1
[6,2,5,3,4,8,1,7]=>0000000=>1111111=>1
[6,2,5,3,4,8,7,1]=>0000000=>1111111=>1
[2,6,5,3,4,8,1,7]=>0000000=>1111111=>1
[5,3,4,8,1,7,2,6]=>0000000=>1111111=>1
[5,1,3,4,8,7,2,6]=>0000000=>1111111=>1
[1,5,3,4,8,7,2,6]=>1000000=>0111111=>1
[5,1,3,8,4,7,6,2]=>0000000=>1111111=>1
[5,3,8,1,4,7,6,2]=>0000000=>1111111=>1
[4,3,5,8,1,7,6,2]=>0000000=>1111111=>1
[3,6,5,4,8,1,2,7]=>0000000=>1111111=>1
[3,6,5,4,8,2,7,1]=>0000000=>1111111=>1
[3,5,2,4,8,7,6,1]=>0000000=>1111111=>1
[2,3,6,5,8,4,1,7]=>0000000=>1111111=>1
[2,3,1,7,4,8,6,5]=>0010000=>1101111=>2
[1,8,3,6,4,2,7,5]=>1000000=>0111111=>1
[2,1,7,4,8,5,3,6]=>0100000=>1011111=>2
[6,8,7,4,1,5,2,3]=>0000000=>1111111=>1
[8,6,4,7,5,1,3,2]=>0000000=>1111111=>1
[2,4,6,5,7,1,8,3]=>0000000=>1111111=>1
[3,2,8,9,10,1,4,5,6,7]=>000000000=>111111111=>1
[3,5,2,1,7,8,6,4]=>0000000=>1111111=>1
[4,2,7,8,6,5,1,3]=>0000000=>1111111=>1
[1,2,7,8,6,4,5,3]=>1100000=>0011111=>1
[4,8,1,2,6,5,3,7]=>0000000=>1111111=>1
[7,1,6,3,2,4,8,5]=>0000000=>1111111=>1
[6,4,8,1,2,3,7,5]=>0000000=>1111111=>1
[7,4,1,3,6,8,5,2]=>0000000=>1111111=>1
[7,1,8,3,2,6,5,4]=>0000000=>1111111=>1
[7,2,5,1,6,4,3,8]=>0000001=>1111110=>1
[5,2,7,1,4,6,3,8]=>0000001=>1111110=>1
[2,4,3,8,5,7,1,6]=>0000000=>1111111=>1
[3,7,1,6,5,8,2,4]=>0000000=>1111111=>1
[7,4,3,6,8,2,1,5]=>0000000=>1111111=>1
[3,8,5,4,7,6,1,2]=>0000000=>1111111=>1
[1,4,6,8,7,3,5,2]=>1000000=>0111111=>1
[4,6,5,1,3,8,7,2]=>0000000=>1111111=>1
[5,4,6,2,1,8,7,3]=>0000000=>1111111=>1
[5,3,8,1,4,2,6,7]=>0000000=>1111111=>1
[5,3,8,1,4,2,7,6]=>0000000=>1111111=>1
[7,3,5,6,4,1,8,2]=>0000000=>1111111=>1
[2,5,6,7,8,9,1,3,4]=>00000000=>11111111=>1
[2,1,6,7,8,9,3,4,5]=>01000000=>10111111=>2
[2,5,6,7,8,9,10,1,3,4]=>000000000=>111111111=>1
[4,6,7,2,3,8,5,1]=>0000000=>1111111=>1
[2,3,5,8,7,4,1,6]=>0000000=>1111111=>1
[2,3,5,8,7,4,6,1]=>0000000=>1111111=>1
[2,3,5,8,1,6,4,7]=>0000000=>1111111=>1
[1,7,4,5,8,3,6,2]=>1000000=>0111111=>1
[8,6,1,5,4,2,7,3]=>0000000=>1111111=>1
[2,8,5,6,3,1,4,7]=>0000000=>1111111=>1
[2,3,7,8,1,5,4,6]=>0000000=>1111111=>1
[5,2,6,7,8,3,1,4]=>0000000=>1111111=>1
[5,6,2,7,8,3,1,4]=>0000000=>1111111=>1
[2,3,7,5,8,4,6,1]=>0000000=>1111111=>1
[3,7,8,5,1,4,6,2]=>0000000=>1111111=>1
[2,3,7,8,5,4,6,1]=>0000000=>1111111=>1
[6,4,7,8,1,2,5,3]=>0000000=>1111111=>1
[7,5,8,1,2,3,6,4]=>0000000=>1111111=>1
[1,2,8,7,4,6,5,3]=>1100000=>0011111=>1
[5,1,4,8,7,3,6,2]=>0000000=>1111111=>1
[4,3,1,8,7,5,6,2]=>0000000=>1111111=>1
[4,3,2,7,6,1,5,8]=>0000001=>1111110=>1
[7,2,6,5,3,1,4,8]=>0000001=>1111110=>1
[1,3,7,6,2,4,8,5]=>1000000=>0111111=>1
[1,3,8,2,7,4,6,5]=>1000000=>0111111=>1
[8,2,7,1,6,4,3,5]=>0000000=>1111111=>1
[4,3,2,8,1,7,5,6]=>0000000=>1111111=>1
[7,5,4,1,6,3,8,2]=>0000000=>1111111=>1
[1,6,5,3,2,4,8,7]=>1000010=>0111101=>2
[1,7,3,5,2,4,8,6]=>1000000=>0111111=>1
[4,3,7,2,5,1,6,8]=>0000001=>1111110=>1
[5,1,4,3,2,6,8,7]=>0000110=>1111001=>2
[7,2,1,3,5,4,6,8]=>0000001=>1111110=>1
[8,3,7,5,4,2,6,1]=>0000000=>1111111=>1
[1,6,8,7,5,2,3,4]=>1000000=>0111111=>1
[1,3,6,2,5,4,8,7]=>1000010=>0111101=>2
[1,2,7,3,8,4,9,5,10,6]=>110000000=>001111111=>1
[5,4,1,8,7,3,6,2]=>0000000=>1111111=>1
[6,2,4,7,5,3,1,8]=>0000001=>1111110=>1
[3,2,6,1,5,8,7,4]=>0000000=>1111111=>1
[1,6,3,8,4,7,2,5]=>1000000=>0111111=>1
[8,1,5,2,4,7,3,6]=>0000000=>1111111=>1
[7,5,8,1,4,2,3,6]=>0000000=>1111111=>1
[4,1,2,3,6,5,8,7,9]=>00010101=>11101010=>3
[4,1,6,2,3,5,8,7,9]=>00000101=>11111010=>2
[1,3,4,8,5,6,2,7]=>1000000=>0111111=>1
[3,2,7,1,8,6,5,4]=>0000000=>1111111=>1
[6,7,2,3,8,1,4,5]=>0000000=>1111111=>1
[5,2,8,1,7,4,6,3]=>0000000=>1111111=>1
[2,5,4,7,3,1,8,6]=>0000000=>1111111=>1
[4,6,3,1,2,5,7,8]=>0000011=>1111100=>1
[7,4,6,8,3,1,2,5]=>0000000=>1111111=>1
[8,5,4,7,3,1,2,6]=>0000000=>1111111=>1
[7,3,2,1,5,4,8,6]=>0000000=>1111111=>1
[2,5,6,4,8,1,3,7]=>0000000=>1111111=>1
[5,4,1,6,2,3,7,8]=>0000011=>1111100=>1
[5,4,1,2,7,6,3,8]=>0000001=>1111110=>1
[8,4,3,7,2,5,6,1]=>0000000=>1111111=>1
[6,8,2,4,5,1,7,3]=>0000000=>1111111=>1
[8,3,7,6,2,4,5,1]=>0000000=>1111111=>1
[8,1,2,7,6,4,5,3]=>0000000=>1111111=>1
[2,3,1,9,8,7,6,5,4]=>00100000=>11011111=>2
[2,8,1,5,3,7,6,4]=>0000000=>1111111=>1
[2,3,8,4,7,1,6,5]=>0000000=>1111111=>1
[1,8,2,3,5,6,4,7]=>1000000=>0111111=>1
[1,4,7,6,2,3,5,8]=>1000001=>0111110=>1
[1,7,6,2,3,8,4,5]=>1000000=>0111111=>1
[1,8,2,3,7,6,4,5]=>1000000=>0111111=>1
[1,7,3,8,6,2,5,4]=>1000000=>0111111=>1
[1,3,5,6,4,8,2,7]=>1000000=>0111111=>1
[4,6,1,8,2,7,5,3]=>0000000=>1111111=>1
[3,4,8,5,6,1,2,7]=>0000000=>1111111=>1
[1,7,6,2,5,4,8,3]=>1000000=>0111111=>1
[3,7,2,1,5,6,8,4]=>0000000=>1111111=>1
[3,1,5,6,4,2,7,8]=>0000011=>1111100=>1
[8,1,6,4,3,5,2,7]=>0000000=>1111111=>1
[2,1,6,5,3,8,7,4]=>0100000=>1011111=>2
[3,7,5,6,4,2,1,8]=>0000001=>1111110=>1
[4,6,8,5,3,7,2,1]=>0000000=>1111111=>1
[4,6,8,5,1,3,7,2]=>0000000=>1111111=>1
[8,3,5,4,6,1,2,7]=>0000000=>1111111=>1
[3,4,5,6,1,7,2,9,8]=>00000010=>11111101=>2
[1,7,4,5,2,6,8,3]=>1000000=>0111111=>1
[1,4,5,9,6,7,2,8,3]=>10000000=>01111111=>1
[3,4,5,6,7,1,8,2,10,9]=>000000010=>111111101=>2
[2,4,5,9,6,1,7,3,8]=>00000000=>11111111=>1
[3,4,5,7,6,1,9,2,8]=>00000000=>11111111=>1
[1,4,2,6,5,3,8,7]=>1000010=>0111101=>2
[3,1,5,8,4,6,2,7]=>0000000=>1111111=>1
[3,5,6,9,7,1,8,2,4]=>00000000=>11111111=>1
[1,4,8,5,6,2,7,9,3]=>10000000=>01111111=>1
[1,4,5,6,10,7,8,2,9,3]=>100000000=>011111111=>1
[3,4,5,6,7,8,1,9,2,11,10]=>0000000010=>1111111101=>2
[2,4,5,6,10,7,1,8,3,9]=>000000000=>111111111=>1
[3,4,5,6,8,7,1,10,2,9]=>000000000=>111111111=>1
[2,5,9,6,7,3,1,4,8]=>00000000=>11111111=>1
[4,1,5,2,7,6,3,9,8]=>00000010=>11111101=>2
[3,4,1,6,9,5,7,2,8]=>00000000=>11111111=>1
[8,2,6,3,4,1,5,7]=>0000000=>1111111=>1
[4,6,5,8,2,1,3,7]=>0000000=>1111111=>1
[1,4,8,3,5,6,2,7]=>1000000=>0111111=>1
[1,8,7,4,2,3,6,5]=>1000000=>0111111=>1
[6,7,9,8,1,3,4,2,5]=>00000000=>11111111=>1
[9,1,5,2,8,6,3,7,4]=>00000000=>11111111=>1
[3,5,6,7,10,8,1,9,2,4]=>000000000=>111111111=>1
[1,7,4,5,2,6,8,9,3]=>10000000=>01111111=>1
[1,4,5,9,6,7,2,8,10,3]=>100000000=>011111111=>1
[1,4,5,6,7,11,8,9,2,10,3]=>1000000000=>0111111111=>1
[4,3,1,8,5,7,2,6]=>0000000=>1111111=>1
[7,3,2,4,8,1,6,5]=>0000000=>1111111=>1
[3,7,2,4,5,8,1,6]=>0000000=>1111111=>1
[3,2,7,4,6,1,8,5]=>0000000=>1111111=>1
[8,3,2,4,6,1,7,5]=>0000000=>1111111=>1
[8,3,2,4,5,7,1,6]=>0000000=>1111111=>1
[7,4,6,2,1,3,8,5]=>0000000=>1111111=>1
[3,6,7,2,4,1,8,5]=>0000000=>1111111=>1
[8,4,7,2,3,5,6,1]=>0000000=>1111111=>1
[3,8,6,7,1,5,4,2]=>0000000=>1111111=>1
[4,3,2,8,6,1,5,7]=>0000000=>1111111=>1
[4,1,6,3,2,5,7,8]=>0000011=>1111100=>1
[5,7,1,8,4,3,6,2]=>0000000=>1111111=>1
[5,4,8,7,6,2,3,1]=>0000000=>1111111=>1
[8,4,6,3,1,5,2,7]=>0000000=>1111111=>1
[3,6,1,5,2,4,7,8]=>0000011=>1111100=>1
[3,7,6,2,5,4,1,8]=>0000001=>1111110=>1
[2,7,1,5,3,4,6,8]=>0000001=>1111110=>1
[8,4,5,1,2,7,6,3]=>0000000=>1111111=>1
[5,2,3,8,7,1,6,4]=>0000000=>1111111=>1
[7,5,2,4,1,3,8,6]=>0000000=>1111111=>1
[7,2,6,8,5,1,3,4]=>0000000=>1111111=>1
[8,6,5,4,1,3,7,2]=>0000000=>1111111=>1
[8,2,3,4,1,6,7,5]=>0000000=>1111111=>1
[7,4,3,8,1,6,5,2]=>0000000=>1111111=>1
[6,5,1,4,3,8,7,2]=>0000000=>1111111=>1
[4,7,6,2,5,8,1,3]=>0000000=>1111111=>1
[6,3,2,4,5,8,1,7]=>0000000=>1111111=>1
[7,3,5,2,8,1,4,6]=>0000000=>1111111=>1
[1,5,8,7,4,2,3,6]=>1000000=>0111111=>1
[1,7,2,4,5,8,6,3]=>1000000=>0111111=>1
[1,4,6,8,7,2,5,3]=>1000000=>0111111=>1
[1,6,2,7,5,3,4,8]=>1000001=>0111110=>1
[1,3,7,2,6,4,5,8]=>1000001=>0111110=>1
[1,7,3,2,8,5,6,4]=>1000000=>0111111=>1
[1,6,5,2,4,8,3,7]=>1000000=>0111111=>1
[1,7,3,8,4,2,5,6]=>1000000=>0111111=>1
[1,6,2,4,7,5,8,3]=>1000000=>0111111=>1
[1,6,2,7,4,3,8,5]=>1000000=>0111111=>1
[1,5,8,2,3,6,4,7]=>1000000=>0111111=>1
[6,8,9,1,2,3,4,5,7]=>00000000=>11111111=>1
[5,8,9,1,2,3,4,6,7]=>00000000=>11111111=>1
[1,2,7,3,8,5,6,4]=>1100000=>0011111=>1
[1,5,7,4,3,8,6,2]=>1000000=>0111111=>1
[2,7,3,1,4,5,8,6]=>0000000=>1111111=>1
[2,3,4,5,1,7,6,9,8]=>00001010=>11110101=>3
[2,3,4,1,6,5,8,7,9]=>00010101=>11101010=>3
[2,3,4,5,6,7,1,9,8,10]=>000000101=>111111010=>2
[2,3,4,5,1,8,6,9,7]=>00001000=>11110111=>2
[2,3,4,1,7,5,8,6,9]=>00010001=>11101110=>2
[2,3,4,5,1,7,6,9,8,10]=>000010101=>111101010=>3
[6,5,8,3,2,7,1,4]=>0000000=>1111111=>1
[8,4,3,1,7,6,5,2]=>0000000=>1111111=>1
[1,2,6,7,5,3,4,8]=>1100001=>0011110=>1
[3,4,5,6,7,9,1,8,2]=>00000000=>11111111=>1
[3,4,5,6,8,2,7,1]=>0000000=>1111111=>1
[3,4,5,6,7,8,10,1,9,2]=>000000000=>111111111=>1
[3,4,5,6,7,9,2,8,1]=>00000000=>11111111=>1
[3,4,5,6,7,1,9,8,2]=>00000000=>11111111=>1
[7,2,1,4,5,6,3,8]=>0000001=>1111110=>1
[1,6,7,8,2,4,5,3]=>1000000=>0111111=>1
[5,3,4,2,1,9,8,7,6]=>00001000=>11110111=>2
[6,5,3,4,2,1,9,8,7]=>00000100=>11111011=>2
[7,6,4,5,3,2,1,9,8]=>00000010=>11111101=>2
[1,3,5,8,7,2,6,4]=>1000000=>0111111=>1
[6,4,1,8,5,7,3,2]=>0000000=>1111111=>1
[7,2,5,6,1,3,8,4]=>0000000=>1111111=>1
[6,4,1,2,5,8,3,7]=>0000000=>1111111=>1
[2,3,5,4,7,1,8,6]=>0000000=>1111111=>1
[6,8,4,1,5,7,3,2]=>0000000=>1111111=>1
[8,1,6,2,3,7,5,4]=>0000000=>1111111=>1
[2,8,3,6,4,1,7,5]=>0000000=>1111111=>1
[4,2,3,5,6,7,8,9,10,1]=>000000000=>111111111=>1
[1,7,8,4,3,6,5,2]=>1000000=>0111111=>1
[1,7,8,3,6,5,4,2]=>1000000=>0111111=>1
[1,6,5,7,3,8,2,4]=>1000000=>0111111=>1
[1,8,5,3,7,6,2,4]=>1000000=>0111111=>1
[6,5,1,3,8,4,2,7]=>0000000=>1111111=>1
[6,1,4,2,7,8,3,5]=>0000000=>1111111=>1
[6,5,1,3,7,8,4,2]=>0000000=>1111111=>1
[5,6,8,2,4,7,1,3]=>0000000=>1111111=>1
[5,1,3,2,6,8,4,7]=>0000000=>1111111=>1
[1,4,3,7,6,2,8,5]=>1000000=>0111111=>1
[1,6,2,5,7,3,8,4]=>1000000=>0111111=>1
[1,4,3,8,2,5,7,6]=>1000000=>0111111=>1
[1,5,7,3,6,4,2,8]=>1000001=>0111110=>1
[1,6,7,2,4,8,3,5]=>1000000=>0111111=>1
[3,7,2,8,4,1,5,6]=>0000000=>1111111=>1
[2,4,1,5,3,6,8,7,9]=>00001101=>11110010=>2
[2,4,1,7,3,8,5,6,9]=>00000001=>11111110=>1
[5,3,4,1,7,8,6,2]=>0000000=>1111111=>1
[7,2,6,3,1,8,4,5]=>0000000=>1111111=>1
[5,8,4,1,3,7,2,6]=>0000000=>1111111=>1
[8,1,3,5,6,4,7,2]=>0000000=>1111111=>1
[3,4,7,1,5,6,2,8]=>0000001=>1111110=>1
[8,1,7,4,2,5,3,6]=>0000000=>1111111=>1
[5,2,6,4,1,3,8,7]=>0000010=>1111101=>2
[8,6,4,7,1,3,5,2]=>0000000=>1111111=>1
[2,1,8,5,4,3,7,6]=>0100000=>1011111=>2
[9,10,6,7,4,5,2,3,1,8]=>000000000=>111111111=>1
[8,5,4,6,2,7,1,3]=>0000000=>1111111=>1
[6,8,5,4,7,2,3,1]=>0000000=>1111111=>1
[2,5,7,3,4,8,1,6]=>0000000=>1111111=>1
[5,2,4,7,8,1,3,6]=>0000000=>1111111=>1
[8,5,9,3,6,1,2,4,7]=>00000000=>11111111=>1
[9,7,1,5,8,3,6,2,4]=>00000000=>11111111=>1
[9,7,5,4,1,3,8,2,6]=>00000000=>11111111=>1
[8,9,4,5,10,1,2,3,6,7]=>000000000=>111111111=>1
[8,4,3,9,10,1,2,5,6,7]=>000000000=>111111111=>1
[9,6,10,1,3,7,8,2,4,5]=>000000000=>111111111=>1
[9,10,6,7,4,5,1,2,3,8]=>000000000=>111111111=>1
[9,6,4,10,3,7,1,2,5,8]=>000000000=>111111111=>1
[10,1,8,9,6,7,4,5,2,3]=>000000000=>111111111=>1
[10,8,6,1,4,9,3,7,2,5]=>000000000=>111111111=>1
[10,8,6,5,4,1,3,9,2,7]=>000000000=>111111111=>1
[10,8,7,6,5,4,3,1,2,9]=>000000000=>111111111=>1
[4,6,8,1,5,2,7,3]=>0000000=>1111111=>1
[8,2,3,6,4,1,7,5]=>0000000=>1111111=>1
[2,3,7,5,8,6,1,4]=>0000000=>1111111=>1
[3,8,5,1,2,4,7,6]=>0000000=>1111111=>1
[1,3,6,4,8,2,7,5]=>1000000=>0111111=>1
[1,2,3,4,6,5,7,8,9,10]=>111101111=>000010000=>1
[1,2,3,4,5,6,8,7,9,10]=>111111011=>000000100=>1
[1,7,6,2,8,5,3,4]=>1000000=>0111111=>1
[1,5,8,6,4,7,2,3]=>1000000=>0111111=>1
[5,6,2,8,1,7,3,4]=>0000000=>1111111=>1
[1,6,8,3,2,4,5,7]=>1000000=>0111111=>1
[9,6,5,4,3,2,1,7,8]=>00000000=>11111111=>1
[9,8,5,4,3,2,1,6,7]=>00000000=>11111111=>1
[1,6,5,7,4,2,8,3]=>1000000=>0111111=>1
[1,2,7,4,8,5,6,3]=>1100000=>0011111=>1
[5,6,3,4,2,8,7,1]=>0000000=>1111111=>1
[2,5,7,4,6,8,1,3]=>0000000=>1111111=>1
[2,5,6,4,1,3,8,7]=>0000010=>1111101=>2
[4,6,1,3,5,7,2,8]=>0000001=>1111110=>1
[3,2,7,5,8,1,6,4]=>0000000=>1111111=>1
[4,3,6,8,5,2,1,7]=>0000000=>1111111=>1
[4,5,3,2,1,8,6,7]=>0000100=>1111011=>2
[3,6,5,8,1,7,4,2]=>0000000=>1111111=>1
[4,1,6,8,5,2,3,7]=>0000000=>1111111=>1
[4,5,2,8,6,7,1,3]=>0000000=>1111111=>1
[4,5,2,8,6,7,3,1]=>0000000=>1111111=>1
[3,5,8,6,2,4,7,1]=>0000000=>1111111=>1
[2,5,1,6,4,8,3,7]=>0000000=>1111111=>1
[3,2,4,5,8,6,1,7]=>0000000=>1111111=>1
[4,5,2,1,3,8,6,7]=>0000100=>1111011=>2
[4,2,3,6,8,5,1,7]=>0000000=>1111111=>1
[4,5,1,3,2,8,6,7]=>0000100=>1111011=>2
[3,4,5,8,6,1,7,2]=>0000000=>1111111=>1
[3,4,5,8,6,1,2,7]=>0000000=>1111111=>1
[6,4,1,3,7,8,2,5]=>0000000=>1111111=>1
[8,2,6,4,1,3,7,5]=>0000000=>1111111=>1
[1,5,8,2,4,3,7,6]=>1000000=>0111111=>1
[1,4,8,5,7,2,3,6]=>1000000=>0111111=>1
[1,8,7,3,2,4,5,6]=>1000000=>0111111=>1
[8,6,2,7,3,4,1,5]=>0000000=>1111111=>1
[8,6,2,7,3,4,5,1]=>0000000=>1111111=>1
[5,6,3,2,8,7,1,4]=>0000000=>1111111=>1
[5,1,6,7,8,3,2,4]=>0000000=>1111111=>1
[1,5,6,3,7,2,4,8]=>1000001=>0111110=>1
[1,5,6,7,4,2,3,8]=>1000001=>0111110=>1
[5,1,6,7,3,4,2,8]=>0000001=>1111110=>1
[8,6,1,7,3,4,5,2]=>0000000=>1111111=>1
[6,8,5,1,7,4,2,3]=>0000000=>1111111=>1
[8,4,2,3,5,7,6,1]=>0000000=>1111111=>1
[4,8,5,2,3,1,6,7]=>0000000=>1111111=>1
[5,4,8,3,1,2,6,7]=>0000000=>1111111=>1
[8,4,7,3,2,5,6,1]=>0000000=>1111111=>1
[6,8,5,1,7,3,4,2]=>0000000=>1111111=>1
[6,2,7,3,8,1,4,5]=>0000000=>1111111=>1
[8,4,2,6,7,1,5,3]=>0000000=>1111111=>1
[1,7,8,3,6,5,2,4]=>1000000=>0111111=>1
[4,6,7,5,1,8,2,3]=>0000000=>1111111=>1
[3,5,2,6,8,7,4,1]=>0000000=>1111111=>1
[7,3,6,8,4,1,2,5]=>0000000=>1111111=>1
[6,4,2,3,7,5,8,1]=>0000000=>1111111=>1
[6,3,7,5,1,2,8,4]=>0000000=>1111111=>1
[7,2,5,4,8,6,3,1]=>0000000=>1111111=>1
[6,2,3,8,7,4,5,1]=>0000000=>1111111=>1
[7,1,2,8,4,6,5,3]=>0000000=>1111111=>1
[3,5,8,1,2,7,6,4]=>0000000=>1111111=>1
[1,4,3,6,8,5,2,7]=>1000000=>0111111=>1
[7,6,2,8,5,3,4,1]=>0000000=>1111111=>1
[6,8,3,5,4,7,2,1]=>0000000=>1111111=>1
[8,2,7,6,4,1,3,5]=>0000000=>1111111=>1
[8,3,7,5,1,6,2,4]=>0000000=>1111111=>1
[8,5,7,1,4,2,6,3]=>0000000=>1111111=>1
[4,7,1,5,6,3,2,8]=>0000001=>1111110=>1
[4,5,7,1,6,3,8,2]=>0000000=>1111111=>1
[4,6,5,7,2,3,8,1]=>0000000=>1111111=>1
[3,6,7,2,5,8,4,1]=>0000000=>1111111=>1
[5,3,6,7,4,8,1,2]=>0000000=>1111111=>1
[4,2,7,8,3,6,5,1]=>0000000=>1111111=>1
[4,2,7,8,5,6,1,3]=>0000000=>1111111=>1
[5,4,3,7,8,1,6,2]=>0000000=>1111111=>1
[3,5,7,8,4,2,1,6]=>0000000=>1111111=>1
[4,6,7,3,2,8,1,5]=>0000000=>1111111=>1
[4,6,5,3,7,8,1,2]=>0000000=>1111111=>1
[5,6,2,4,7,8,3,1]=>0000000=>1111111=>1
[5,6,3,2,8,4,7,1]=>0000000=>1111111=>1
[5,6,2,8,3,4,7,1]=>0000000=>1111111=>1
[3,7,4,8,1,6,5,2]=>0000000=>1111111=>1
[5,2,4,8,6,7,3,1]=>0000000=>1111111=>1
[5,2,6,4,8,7,3,1]=>0000000=>1111111=>1
[2,4,7,8,6,5,1,3]=>0000000=>1111111=>1
[3,4,5,6,8,9,1,7,2]=>00000000=>11111111=>1
[3,4,6,7,8,9,1,5,2]=>00000000=>11111111=>1
[3,5,6,7,8,9,1,4,2]=>00000000=>11111111=>1
[4,5,6,7,8,9,1,3,2]=>00000000=>11111111=>1
[3,4,5,6,7,9,10,1,8,2]=>000000000=>111111111=>1
[3,4,5,7,8,9,10,1,6,2]=>000000000=>111111111=>1
[5,2,6,7,8,1,4,3]=>0000000=>1111111=>1
[3,4,6,7,8,9,10,1,5,2]=>000000000=>111111111=>1
[4,5,6,7,8,9,10,1,3,2]=>000000000=>111111111=>1
[4,8,2,7,5,3,1,6]=>0000000=>1111111=>1
[3,5,8,1,7,4,2,6]=>0000000=>1111111=>1
[5,8,6,1,7,2,3,4]=>0000000=>1111111=>1
[5,1,4,3,8,2,6,7]=>0000000=>1111111=>1
[8,4,7,5,6,2,1,3]=>0000000=>1111111=>1
[3,8,6,7,5,2,4,1]=>0000000=>1111111=>1
[8,2,5,4,7,3,6,1]=>0000000=>1111111=>1
[4,2,8,7,3,6,5,1]=>0000000=>1111111=>1
[3,7,8,6,1,4,5,2]=>0000000=>1111111=>1
[4,6,7,8,2,1,5,3]=>0000000=>1111111=>1
[4,7,6,3,8,1,5,2]=>0000000=>1111111=>1
[3,8,1,4,6,2,5,7]=>0000000=>1111111=>1
[2,4,5,3,8,7,1,6]=>0000000=>1111111=>1
[6,8,4,7,3,5,2,1]=>0000000=>1111111=>1
[3,6,4,2,8,1,7,5]=>0000000=>1111111=>1
[3,4,8,6,2,1,7,5]=>0000000=>1111111=>1
[3,1,8,2,4,6,5,7]=>0000000=>1111111=>1
[8,1,7,6,2,5,4,3]=>0000000=>1111111=>1
[8,5,4,3,7,6,1,2]=>0000000=>1111111=>1
[4,8,1,3,6,7,5,2]=>0000000=>1111111=>1
[3,5,8,6,1,7,4,2]=>0000000=>1111111=>1
[8,1,4,7,5,2,6,3]=>0000000=>1111111=>1
[1,4,8,6,7,3,5,2]=>1000000=>0111111=>1
[4,1,6,7,8,5,3,2]=>0000000=>1111111=>1
[3,7,8,6,4,1,5,2]=>0000000=>1111111=>1
[5,4,2,3,6,7,8,9,1]=>00000000=>11111111=>1
[6,5,4,2,3,7,8,9,1]=>00000000=>11111111=>1
[7,6,5,4,2,3,8,9,1]=>00000000=>11111111=>1
[4,6,1,5,7,2,3,8]=>0000001=>1111110=>1
[3,4,7,8,6,1,2,5]=>0000000=>1111111=>1
[1,8,5,6,4,2,3,7]=>1000000=>0111111=>1
[1,8,7,6,2,4,5,3]=>1000000=>0111111=>1
[1,6,4,7,2,5,8,3]=>1000000=>0111111=>1
[8,3,1,4,6,2,7,5]=>0000000=>1111111=>1
[7,2,6,4,5,8,1,3]=>0000000=>1111111=>1
[4,6,7,8,9,1,2,3,5]=>00000000=>11111111=>1
[5,7,8,9,1,2,3,4,6]=>00000000=>11111111=>1
[2,7,1,5,3,8,6,4]=>0000000=>1111111=>1
[3,5,7,2,8,4,1,6]=>0000000=>1111111=>1
[7,3,2,1,4,8,6,5]=>0000000=>1111111=>1
[8,7,2,6,1,5,3,4]=>0000000=>1111111=>1
[7,1,3,8,2,6,4,5]=>0000000=>1111111=>1
[2,7,3,4,1,5,8,6]=>0000000=>1111111=>1
[2,5,8,1,6,7,3,4]=>0000000=>1111111=>1
[8,3,6,2,7,5,4,1]=>0000000=>1111111=>1
[8,4,2,6,5,3,7,1]=>0000000=>1111111=>1
[5,4,2,7,1,8,6,3]=>0000000=>1111111=>1
[4,1,7,6,5,3,2,8]=>0000001=>1111110=>1
[2,3,6,7,1,8,5,4]=>0000000=>1111111=>1
[3,6,1,2,7,8,5,4]=>0000000=>1111111=>1
[4,5,1,8,7,6,3,2]=>0000000=>1111111=>1
[8,4,5,2,7,6,3,1]=>0000000=>1111111=>1
[4,1,3,6,7,5,2,8]=>0000001=>1111110=>1
[3,1,4,5,7,6,2,8]=>0000001=>1111110=>1
[4,5,1,3,6,8,7,2]=>0000000=>1111111=>1
[3,8,5,1,2,4,6,7]=>0000000=>1111111=>1
[8,5,1,2,4,3,6,7]=>0000000=>1111111=>1
[5,8,4,1,2,3,6,7]=>0000000=>1111111=>1
[3,5,8,1,4,2,7,6]=>0000000=>1111111=>1
[2,8,5,7,1,4,3,6]=>0000000=>1111111=>1
[4,8,7,5,1,2,3,6]=>0000000=>1111111=>1
[8,1,2,4,6,3,7,5]=>0000000=>1111111=>1
[7,6,1,4,2,3,8,5]=>0000000=>1111111=>1
[6,1,2,7,8,4,3,5]=>0000000=>1111111=>1
[7,8,1,2,5,3,4,6]=>0000000=>1111111=>1
[1,8,4,7,5,2,3,6]=>1000000=>0111111=>1
[8,4,7,2,1,6,3,5]=>0000000=>1111111=>1
[4,5,8,2,1,6,7,3]=>0000000=>1111111=>1
[7,4,2,5,3,6,1,8]=>0000001=>1111110=>1
[3,1,6,7,5,2,4,8]=>0000001=>1111110=>1
[8,4,2,5,3,6,7,1]=>0000000=>1111111=>1
[4,8,1,5,3,6,7,2]=>0000000=>1111111=>1
[4,1,7,5,2,6,3,8]=>0000001=>1111110=>1
[5,1,8,6,7,3,4,2]=>0000000=>1111111=>1
[6,5,2,4,1,7,8,3]=>0000000=>1111111=>1
[5,4,8,2,1,3,6,7]=>0000000=>1111111=>1
[1,4,8,3,2,6,5,7]=>1000000=>0111111=>1
[1,3,8,4,2,7,5,6]=>1000000=>0111111=>1
[7,2,8,3,1,4,5,6]=>0000000=>1111111=>1
[9,8,7,5,6,4,3,2,10,1]=>000000000=>111111111=>1
[8,7,5,4,6,3,2,9,1]=>00000000=>11111111=>1
[8,7,4,6,5,3,2,9,1]=>00000000=>11111111=>1
[7,6,1,8,2,5,4,3]=>0000000=>1111111=>1
[5,8,4,2,1,6,3,7]=>0000000=>1111111=>1
[7,6,4,1,2,5,3,8]=>0000001=>1111110=>1
[7,2,8,4,3,6,1,5]=>0000000=>1111111=>1
[1,7,5,4,8,6,2,3]=>1000000=>0111111=>1
[4,8,6,3,5,2,1,7]=>0000000=>1111111=>1
[5,8,6,3,2,7,1,4]=>0000000=>1111111=>1
[5,7,6,3,2,4,8,1]=>0000000=>1111111=>1
[1,2,4,5,6,8,10,9,3,7]=>110000000=>001111111=>1
[1,2,3,5,7,8,10,6,9,4]=>111000000=>000111111=>1
[1,2,4,5,7,8,10,3,9,6]=>110000000=>001111111=>1
[1,2,4,6,7,5,10,8,3,9]=>110000000=>001111111=>1
[1,3,4,2,7,8,10,5,9,6]=>100100000=>011011111=>2
[1,3,4,6,7,2,10,8,5,9]=>100000000=>011111111=>1
[1,2,3,5,6,9,8,10,7,4]=>111000000=>000111111=>1
[1,2,4,5,6,9,8,10,3,7]=>110000000=>001111111=>1
[1,2,3,5,7,9,6,10,8,4]=>111000000=>000111111=>1
[1,2,4,5,7,9,3,10,8,6]=>110000000=>001111111=>1
[1,2,4,6,5,9,7,10,3,8]=>110000000=>001111111=>1
[1,3,4,2,7,9,5,10,8,6]=>100100000=>011011111=>2
[1,3,4,6,2,9,7,10,5,8]=>100000000=>011111111=>1
[1,2,3,5,8,7,9,6,10,4]=>111000000=>000111111=>1
[1,2,4,5,8,7,9,3,10,6]=>110000000=>001111111=>1
[1,2,4,6,8,5,9,3,10,7]=>110000000=>001111111=>1
[1,2,4,7,6,8,5,9,3,10]=>110000001=>001111110=>1
[1,3,4,2,8,7,9,5,10,6]=>100100000=>011011111=>2
[1,3,4,6,8,2,9,5,10,7]=>100000000=>011111111=>1
[1,3,4,7,6,8,2,9,5,10]=>100000001=>011111110=>1
[1,2,3,6,5,9,7,10,8,4]=>111000000=>000111111=>1
[1,2,4,6,3,9,7,10,8,5]=>110000000=>001111111=>1
[1,2,5,4,6,9,7,10,3,8]=>110000000=>001111111=>1
[1,3,2,6,4,9,7,10,8,5]=>101000000=>010111111=>2
[1,3,5,2,6,9,7,10,4,8]=>100000000=>011111111=>1
[1,2,3,6,8,5,9,7,10,4]=>111000000=>000111111=>1
[1,2,4,6,8,3,9,7,10,5]=>110000000=>001111111=>1
[1,2,5,4,8,6,9,3,10,7]=>110000000=>001111111=>1
[1,2,5,7,4,8,6,9,3,10]=>110000001=>001111110=>1
[1,3,2,6,8,4,9,7,10,5]=>101000000=>010111111=>2
[1,3,5,2,8,6,9,4,10,7]=>100000000=>011111111=>1
[1,3,5,7,2,8,6,9,4,10]=>100000001=>011111110=>1
[1,4,3,5,8,2,9,6,10,7]=>100000000=>011111111=>1
[1,4,3,7,5,8,2,9,6,10]=>100000001=>011111110=>1
[2,1,3,6,4,9,7,10,8,5]=>011000000=>100111111=>2
[2,1,5,3,6,9,7,10,4,8]=>010000000=>101111111=>2
[2,1,3,6,8,4,9,7,10,5]=>011000000=>100111111=>2
[2,1,5,3,8,6,9,4,10,7]=>010000000=>101111111=>2
[2,1,5,7,3,8,6,9,4,10]=>010000001=>101111110=>2
[2,4,1,5,8,3,9,6,10,7]=>000000000=>111111111=>1
[2,4,1,7,5,8,3,9,6,10]=>000000001=>111111110=>1
[1,6,3,7,2,4,8,5]=>1000000=>0111111=>1
[8,9,7,6,5,4,3,1,2]=>00000000=>11111111=>1
[8,6,7,5,4,3,2,1,9]=>00000001=>11111110=>1
[8,7,9,6,5,4,3,1,2]=>00000000=>11111111=>1
[9,7,8,6,5,4,3,1,2]=>00000000=>11111111=>1
[4,3,1,6,7,2,5,8]=>0000001=>1111110=>1
[6,3,1,5,7,2,4,8]=>0000001=>1111110=>1
[8,7,5,4,3,6,9,2,1]=>00000000=>11111111=>1
[8,7,6,9,5,3,4,2,1]=>00000000=>11111111=>1
[8,7,9,6,5,4,2,3,1]=>00000000=>11111111=>1
[5,2,1,4,8,6,7,3]=>0000000=>1111111=>1
[4,5,2,1,3,7,6,8]=>0000101=>1111010=>2
[7,1,6,5,4,2,8,3]=>0000000=>1111111=>1
[2,7,6,4,5,1,8,3]=>0000000=>1111111=>1
[2,8,3,1,6,7,4,5]=>0000000=>1111111=>1
[4,5,6,8,2,1,7,3]=>0000000=>1111111=>1
[4,5,6,8,1,3,7,2]=>0000000=>1111111=>1
[4,5,8,3,2,1,7,6]=>0000000=>1111111=>1
[4,5,1,3,2,6,7,8]=>0000111=>1111000=>1
[4,7,3,2,1,6,5,8]=>0000001=>1111110=>1
[4,7,8,3,5,1,6,2]=>0000000=>1111111=>1
[4,7,1,3,5,6,2,8]=>0000001=>1111110=>1
[4,8,3,2,1,6,7,5]=>0000000=>1111111=>1
[5,2,8,1,4,6,7,3]=>0000000=>1111111=>1
[5,6,3,7,8,1,4,2]=>0000000=>1111111=>1
[5,7,1,4,3,6,2,8]=>0000001=>1111110=>1
[6,2,3,7,1,5,4,8]=>0000001=>1111110=>1
[6,2,8,1,5,4,7,3]=>0000000=>1111111=>1
[6,1,3,4,5,2,7,8]=>0000011=>1111100=>1
[7,1,3,4,5,6,2,8]=>0000001=>1111110=>1
[7,2,5,1,3,6,4,8]=>0000001=>1111110=>1
[7,5,3,6,4,2,1,8]=>0000001=>1111110=>1
[2,3,6,5,8,4,7,1]=>0000000=>1111111=>1
[3,2,1,5,6,7,8,9,4]=>00100000=>11011111=>2
[3,2,6,1,4,7,8,9,5]=>00000000=>11111111=>1
[4,3,2,1,6,7,8,9,5]=>00010000=>11101111=>2
[3,2,7,8,1,4,5,9,6]=>00000000=>11111111=>1
[4,7,2,5,1,3,8,9,6]=>00000000=>11111111=>1
[4,3,2,7,1,5,8,9,6]=>00000000=>11111111=>1
[5,4,3,2,1,7,8,9,6]=>00001000=>11110111=>2
[4,3,2,8,9,1,5,6,7]=>00000000=>11111111=>1
[8,5,6,3,4,1,2,9,7]=>00000000=>11111111=>1
[5,3,8,2,6,1,4,9,7]=>00000000=>11111111=>1
[5,4,3,2,8,1,6,9,7]=>00000000=>11111111=>1
[6,5,4,3,2,1,8,9,7]=>00000100=>11111011=>2
[6,9,4,7,2,5,1,3,8]=>00000000=>11111111=>1
[6,4,3,9,2,7,1,5,8]=>00000000=>11111111=>1
[6,5,4,3,2,9,1,7,8]=>00000000=>11111111=>1
[5,6,1,2,3,7,8,9,10,4]=>000000000=>111111111=>1
[2,5,1,3,6,7,8,9,10,4]=>000000000=>111111111=>1
[3,2,1,5,6,7,8,9,10,4]=>001000000=>110111111=>2
[6,7,8,1,2,3,4,9,10,5]=>000000000=>111111111=>1
[2,6,7,1,3,4,8,9,10,5]=>000000000=>111111111=>1
[6,3,4,1,2,7,8,9,10,5]=>000000000=>111111111=>1
[3,2,6,1,4,7,8,9,10,5]=>000000000=>111111111=>1
[4,3,2,1,6,7,8,9,10,5]=>000100000=>111011111=>2
[2,7,8,9,1,3,4,5,10,6]=>000000000=>111111111=>1
[7,3,4,8,1,2,5,9,10,6]=>000000000=>111111111=>1
[3,2,7,8,1,4,5,9,10,6]=>000000000=>111111111=>1
[4,7,2,5,1,3,8,9,10,6]=>000000000=>111111111=>1
[4,3,2,7,1,5,8,9,10,6]=>000000000=>111111111=>1
[5,4,3,2,1,7,8,9,10,6]=>000010000=>111101111=>2
[8,3,4,9,10,1,2,5,6,7]=>000000000=>111111111=>1
[8,9,4,5,6,1,2,3,10,7]=>000000000=>111111111=>1
[4,3,2,8,9,1,5,6,10,7]=>000000000=>111111111=>1
[8,5,6,3,4,1,2,9,10,7]=>000000000=>111111111=>1
[5,3,8,2,6,1,4,9,10,7]=>000000000=>111111111=>1
[5,4,3,2,8,1,6,9,10,7]=>000000000=>111111111=>1
[6,5,4,3,2,1,8,9,10,7]=>000001000=>111110111=>2
[5,9,10,2,6,7,1,3,4,8]=>000000000=>111111111=>1
[9,5,6,3,4,10,1,2,7,8]=>000000000=>111111111=>1
[5,3,9,2,6,10,1,4,7,8]=>000000000=>111111111=>1
[5,4,3,2,9,10,1,6,7,8]=>000000000=>111111111=>1
[6,9,4,7,2,5,1,3,10,8]=>000000000=>111111111=>1
[6,4,3,9,2,7,1,5,10,8]=>000000000=>111111111=>1
[6,5,4,3,2,9,1,7,10,8]=>000000000=>111111111=>1
[7,6,5,4,3,2,1,9,10,8]=>000000100=>111111011=>2
[10,7,8,5,6,3,4,1,2,9]=>000000000=>111111111=>1
[7,5,10,3,8,2,6,1,4,9]=>000000000=>111111111=>1
[7,5,4,3,10,2,8,1,6,9]=>000000000=>111111111=>1
[7,6,5,4,3,2,10,1,8,9]=>000000000=>111111111=>1
[5,3,4,7,2,1,6,8]=>0000001=>1111110=>1
[4,8,5,7,1,2,3,6]=>0000000=>1111111=>1
[4,2,6,3,1,5,7,8]=>0000011=>1111100=>1
[5,8,4,3,2,6,1,7]=>0000000=>1111111=>1
[1,5,7,4,8,6,2,3]=>1000000=>0111111=>1
[6,1,5,7,3,8,2,4]=>0000000=>1111111=>1
[1,2,7,8,6,4,3,5]=>1100000=>0011111=>1
[3,5,1,7,8,6,2,4]=>0000000=>1111111=>1
[5,2,4,1,7,6,8,3]=>0000000=>1111111=>1
[2,1,4,3,6,5,7,9,10,8]=>010101100=>101010011=>4
[2,1,4,3,5,7,8,6,10,9]=>010110010=>101001101=>4
[2,1,4,3,5,7,6,9,10,8]=>010110100=>101001011=>4
[2,1,4,3,5,6,8,9,10,7]=>010111000=>101000111=>3
[2,1,3,5,6,4,8,7,10,9]=>011001010=>100110101=>4
[2,1,3,5,6,4,7,9,10,8]=>011001100=>100110011=>3
[2,1,3,5,4,7,8,6,10,9]=>011010010=>100101101=>4
[2,1,3,5,4,7,6,9,10,8]=>011010100=>100101011=>4
[2,1,3,5,4,6,8,9,10,7]=>011011000=>100100111=>3
[2,1,3,4,6,7,8,5,10,9]=>011100010=>100011101=>3
[2,1,3,4,6,7,5,9,10,8]=>011100100=>100011011=>3
[2,1,3,4,6,5,8,9,10,7]=>011101000=>100010111=>3
[2,1,3,4,5,7,8,9,10,6]=>011110000=>100001111=>2
[1,3,4,2,6,5,7,9,10,8]=>100101100=>011010011=>3
[1,3,4,2,5,7,8,6,10,9]=>100110010=>011001101=>3
[1,3,4,2,5,7,6,9,10,8]=>100110100=>011001011=>3
[1,3,4,2,5,6,8,9,10,7]=>100111000=>011000111=>2
[1,3,2,5,6,4,8,7,10,9]=>101001010=>010110101=>4
[1,3,2,5,6,4,7,9,10,8]=>101001100=>010110011=>3
[1,3,2,5,4,7,8,6,10,9]=>101010010=>010101101=>4
[1,3,2,5,4,7,6,9,10,8]=>101010100=>010101011=>4
[1,3,2,5,4,6,8,9,10,7]=>101011000=>010100111=>3
[1,3,2,4,6,7,8,5,10,9]=>101100010=>010011101=>3
[1,3,2,4,6,7,5,9,10,8]=>101100100=>010011011=>3
[1,3,2,4,6,5,8,9,10,7]=>101101000=>010010111=>3
[1,3,2,4,5,7,8,9,10,6]=>101110000=>010001111=>2
[1,2,4,5,6,3,8,7,10,9]=>110001010=>001110101=>3
[1,2,4,5,6,3,7,9,10,8]=>110001100=>001110011=>2
[1,2,4,5,3,7,8,6,10,9]=>110010010=>001101101=>3
[1,2,4,5,3,7,6,9,10,8]=>110010100=>001101011=>3
[1,2,4,5,3,6,8,9,10,7]=>110011000=>001100111=>2
[1,2,4,3,6,7,8,5,10,9]=>110100010=>001011101=>3
[1,2,4,3,6,7,5,9,10,8]=>110100100=>001011011=>3
[1,2,4,3,6,5,8,9,10,7]=>110101000=>001010111=>3
[1,2,4,3,5,7,8,9,10,6]=>110110000=>001001111=>2
[1,2,3,5,6,7,8,4,10,9]=>111000010=>000111101=>2
[1,2,3,5,6,7,4,9,10,8]=>111000100=>000111011=>2
[1,2,3,5,6,4,8,9,10,7]=>111001000=>000110111=>2
[1,2,3,5,4,7,8,9,10,6]=>111010000=>000101111=>2
[1,3,2,4,5,6,8,9,10,11,12,7]=>10111100000=>01000011111=>2
[1,9,4,5,6,7,8,3,2]=>10000000=>01111111=>1
[5,4,3,8,1,7,2,6]=>0000000=>1111111=>1
[7,2,3,1,6,8,4,5]=>0000000=>1111111=>1
[5,7,8,1,6,2,3,4]=>0000000=>1111111=>1
[1,4,2,5,8,6,3,7]=>1000000=>0111111=>1
[4,8,2,1,5,7,3,6]=>0000000=>1111111=>1
[5,2,7,1,6,3,4,8]=>0000001=>1111110=>1
[4,8,2,5,1,6,3,7]=>0000000=>1111111=>1
[5,8,1,2,4,6,3,7]=>0000000=>1111111=>1
[5,1,7,3,6,4,2,8]=>0000001=>1111110=>1
[3,2,7,5,6,1,4,8]=>0000001=>1111110=>1
[3,2,7,1,6,4,5,8]=>0000001=>1111110=>1
[6,3,1,7,5,4,2,8]=>0000001=>1111110=>1
[5,6,2,8,3,1,7,4]=>0000000=>1111111=>1
[1,4,7,5,6,2,8,3]=>1000000=>0111111=>1
[1,7,4,8,3,5,6,2]=>1000000=>0111111=>1
[7,4,5,1,8,6,2,3]=>0000000=>1111111=>1
[8,1,5,7,6,3,2,4]=>0000000=>1111111=>1
[7,4,8,3,1,6,5,2]=>0000000=>1111111=>1
[8,1,5,3,7,6,2,4]=>0000000=>1111111=>1
[6,4,8,7,3,5,1,2]=>0000000=>1111111=>1
[6,1,4,2,3,5,7,8]=>0000011=>1111100=>1
[6,5,1,8,3,7,4,2]=>0000000=>1111111=>1
[7,1,4,3,8,6,5,2]=>0000000=>1111111=>1
[8,5,4,1,7,3,2,6]=>0000000=>1111111=>1
[4,5,3,8,1,7,6,2]=>0000000=>1111111=>1
[4,7,6,3,2,8,5,1]=>0000000=>1111111=>1
[5,7,6,3,8,2,4,1]=>0000000=>1111111=>1
[6,8,4,7,1,2,5,3]=>0000000=>1111111=>1
[1,3,7,6,8,4,5,2]=>1000000=>0111111=>1
[6,1,5,7,2,8,3,4]=>0000000=>1111111=>1
[1,8,7,2,5,6,3,4]=>1000000=>0111111=>1
[1,8,2,6,7,4,3,5]=>1000000=>0111111=>1
[2,5,4,8,7,6,1,3]=>0000000=>1111111=>1
[1,8,7,6,3,5,4,2]=>1000000=>0111111=>1
[1,8,5,7,6,4,3,2]=>1000000=>0111111=>1
[1,6,2,7,3,8,4,9,5]=>10000000=>01111111=>1
[1,8,5,2,9,6,3,10,7,4]=>100000000=>011111111=>1
[7,2,4,1,8,5,3,6]=>0000000=>1111111=>1
[7,3,2,1,4,6,8,5]=>0000000=>1111111=>1
[7,5,3,2,1,6,8,4]=>0000000=>1111111=>1
[1,4,7,2,5,3,6,8]=>1000001=>0111110=>1
[4,5,3,1,2,6,8,7]=>0000110=>1111001=>2
[4,5,1,3,8,2,6,7]=>0000000=>1111111=>1
[4,1,5,3,2,7,6,8]=>0000101=>1111010=>2
[7,3,5,1,4,2,6,8]=>0000001=>1111110=>1
[6,2,1,7,4,3,8,5]=>0000000=>1111111=>1
[2,4,3,6,7,1,5,8]=>0000001=>1111110=>1
[7,3,5,2,1,6,4,8]=>0000001=>1111110=>1
[4,6,5,2,1,3,7,8]=>0000011=>1111100=>1
[2,5,6,1,4,3,7,8]=>0000011=>1111100=>1
[6,1,5,3,7,2,4,8]=>0000001=>1111110=>1
[3,6,5,4,1,7,2,8]=>0000001=>1111110=>1
[10,9,3,8,7,6,5,4,2,1]=>000000000=>111111111=>1
[8,7,6,4,5,3,2,1,10,9]=>000000010=>111111101=>2
[6,8,7,5,4,2,1,3]=>0000000=>1111111=>1
[1,6,8,7,3,2,4,5]=>1000000=>0111111=>1
[8,7,5,4,6,1,3,2]=>0000000=>1111111=>1
[1,7,8,2,4,6,3,5]=>1000000=>0111111=>1
[7,5,4,8,1,3,6,2]=>0000000=>1111111=>1
[1,8,2,6,7,5,4,3]=>1000000=>0111111=>1
[8,5,4,2,7,3,6,1]=>0000000=>1111111=>1
[3,8,6,1,2,4,5,7]=>0000000=>1111111=>1
[1,8,5,3,2,7,4,6]=>1000000=>0111111=>1
[1,8,4,7,2,3,5,6]=>1000000=>0111111=>1
[3,2,8,1,7,5,4,6]=>0000000=>1111111=>1
[7,1,5,6,2,3,4,8]=>0000001=>1111110=>1
[6,5,1,7,2,3,4,8]=>0000001=>1111110=>1
[1,6,8,2,7,3,4,5]=>1000000=>0111111=>1
[4,1,3,6,7,8,5,2]=>0000000=>1111111=>1
[4,1,2,6,7,8,5,3]=>0000000=>1111111=>1
[3,4,5,8,9,1,2,6,7]=>00000000=>11111111=>1
[3,4,7,8,9,1,2,5,6]=>00000000=>11111111=>1
[3,6,7,8,9,1,2,4,5]=>00000000=>11111111=>1
[3,4,5,6,1,7,2,8,9]=>00000011=>11111100=>1
[3,4,5,1,6,2,7,8,9]=>00000111=>11111000=>1
[3,4,5,6,7,10,1,2,8,9]=>000000000=>111111111=>1
[3,4,1,5,9,2,6,7,8]=>00000000=>11111111=>1
[3,4,5,6,9,10,1,2,7,8]=>000000000=>111111111=>1
[3,4,5,8,9,10,1,2,6,7]=>000000000=>111111111=>1
[1,3,7,8,9,2,4,5,6]=>10000000=>01111111=>1
[3,4,7,8,9,10,1,2,5,6]=>000000000=>111111111=>1
[2,6,7,8,9,1,3,4,5]=>00000000=>11111111=>1
[3,6,7,8,9,10,1,2,4,5]=>000000000=>111111111=>1
[3,7,8,2,1,4,5,6]=>0000000=>1111111=>1
[5,1,4,7,8,3,6,2]=>0000000=>1111111=>1
[4,8,1,5,6,2,3,7]=>0000000=>1111111=>1
[5,6,4,1,7,3,8,2]=>0000000=>1111111=>1
[4,6,1,7,3,2,8,5]=>0000000=>1111111=>1
[1,7,3,6,4,2,8,5]=>1000000=>0111111=>1
[4,7,3,5,1,2,8,6]=>0000000=>1111111=>1
[1,6,4,2,3,5,8,7]=>1000010=>0111101=>2
[4,8,3,5,2,1,6,7]=>0000000=>1111111=>1
[1,6,8,4,7,5,3,2]=>1000000=>0111111=>1
[5,2,3,8,7,1,4,6]=>0000000=>1111111=>1
[8,7,1,3,2,6,4,5]=>0000000=>1111111=>1
[7,5,1,2,3,8,4,6]=>0000000=>1111111=>1
[4,2,3,6,8,5,7,1]=>0000000=>1111111=>1
[4,7,3,2,6,5,1,8]=>0000001=>1111110=>1
[4,3,7,8,2,1,6,5]=>0000000=>1111111=>1
[4,8,7,2,1,5,6,3]=>0000000=>1111111=>1
[7,3,8,2,5,1,6,4]=>0000000=>1111111=>1
[4,5,3,8,6,1,2,7]=>0000000=>1111111=>1
[6,3,5,8,4,1,2,7]=>0000000=>1111111=>1
[7,3,8,4,5,1,2,6]=>0000000=>1111111=>1
[4,8,7,5,1,2,6,3]=>0000000=>1111111=>1
[7,8,4,6,1,3,5,2]=>0000000=>1111111=>1
[4,8,7,5,1,3,6,2]=>0000000=>1111111=>1
[4,5,3,6,8,1,2,7]=>0000000=>1111111=>1
[7,8,6,2,1,4,3,5]=>0000000=>1111111=>1
[7,8,6,3,1,2,5,4]=>0000000=>1111111=>1
[5,2,8,4,7,1,3,6]=>0000000=>1111111=>1
[7,3,1,2,8,6,5,4]=>0000000=>1111111=>1
[8,7,1,3,2,4,5,6]=>0000000=>1111111=>1
[4,3,1,2,6,5,7,8]=>0001011=>1110100=>2
[6,1,5,2,8,7,4,3]=>0000000=>1111111=>1
[4,6,3,5,7,1,2,8]=>0000001=>1111110=>1
[1,4,7,2,6,5,8,3]=>1000000=>0111111=>1
[1,5,7,2,6,4,8,3]=>1000000=>0111111=>1
[1,2,7,8,3,5,4,6]=>1100000=>0011111=>1
[1,7,6,2,8,5,4,3]=>1000000=>0111111=>1
[1,2,7,8,3,4,6,5]=>1100000=>0011111=>1
[3,4,1,7,8,6,5,2]=>0000000=>1111111=>1
[2,4,8,6,5,7,1,3]=>0000000=>1111111=>1
[5,1,3,4,8,2,7,6]=>0000000=>1111111=>1
[8,7,3,6,1,4,2,5]=>0000000=>1111111=>1
[6,5,1,8,3,4,7,2]=>0000000=>1111111=>1
[8,2,1,5,6,4,7,3]=>0000000=>1111111=>1
[7,5,6,1,3,4,8,2]=>0000000=>1111111=>1
[5,7,2,4,6,1,8,3]=>0000000=>1111111=>1
[2,1,5,6,3,8,7,4]=>0100000=>1011111=>2
[3,2,7,5,8,6,4,1]=>0000000=>1111111=>1
[2,4,5,3,8,1,7,6]=>0000000=>1111111=>1
[7,2,5,4,3,8,6,1]=>0000000=>1111111=>1
[8,5,3,1,2,6,7,4]=>0000000=>1111111=>1
[7,2,5,1,3,6,8,4]=>0000000=>1111111=>1
[1,8,7,3,5,2,6,4]=>1000000=>0111111=>1
[4,6,7,8,5,2,1,3]=>0000000=>1111111=>1
[4,7,2,1,8,6,5,3]=>0000000=>1111111=>1
[5,6,2,8,4,1,7,3]=>0000000=>1111111=>1
[5,7,2,4,8,6,1,3]=>0000000=>1111111=>1
[6,7,2,4,8,5,1,3]=>0000000=>1111111=>1
[6,7,3,2,8,5,1,4]=>0000000=>1111111=>1
[7,2,3,1,8,6,5,4]=>0000000=>1111111=>1
[7,2,8,3,5,6,1,4]=>0000000=>1111111=>1
[7,2,3,8,4,6,1,5]=>0000000=>1111111=>1
[1,7,3,4,8,5,2,6]=>1000000=>0111111=>1
[1,7,3,8,5,4,2,6]=>1000000=>0111111=>1
[7,2,8,4,5,3,1,6]=>0000000=>1111111=>1
[2,8,6,4,3,1,7,5]=>0000000=>1111111=>1
[1,7,3,4,8,2,5,6]=>1000000=>0111111=>1
[1,5,8,3,4,6,2,7]=>1000000=>0111111=>1
[1,3,8,4,2,5,7,6]=>1000000=>0111111=>1
[1,4,7,6,2,3,8,5]=>1000000=>0111111=>1
[1,8,4,6,7,2,3,5]=>1000000=>0111111=>1
[1,4,2,3,7,8,6,5]=>1001000=>0110111=>2
[5,7,1,6,4,8,3,2]=>0000000=>1111111=>1
[1,2,9,7,5,3,10,8,6,4]=>110000000=>001111111=>1
[7,4,5,8,1,3,6,2]=>0000000=>1111111=>1
[1,4,3,6,2,5,8,7]=>1000010=>0111101=>2
[1,3,6,5,8,2,4,7]=>1000000=>0111111=>1
[1,4,6,3,2,8,5,7]=>1000000=>0111111=>1
[6,8,4,1,5,7,2,3]=>0000000=>1111111=>1
[5,2,6,7,4,1,8,3]=>0000000=>1111111=>1
[8,5,6,4,1,7,3,2]=>0000000=>1111111=>1
[7,8,3,1,6,4,5,2]=>0000000=>1111111=>1
[5,8,2,6,3,1,7,4]=>0000000=>1111111=>1
[4,5,8,1,6,3,7,2]=>0000000=>1111111=>1
[8,1,4,6,2,5,7,3]=>0000000=>1111111=>1
[4,5,8,1,6,2,7,3]=>0000000=>1111111=>1
[5,2,6,8,1,4,3,7]=>0000000=>1111111=>1
[6,7,3,8,2,1,4,5]=>0000000=>1111111=>1
[2,7,3,5,4,1,8,6]=>0000000=>1111111=>1
[2,6,3,7,4,1,8,5]=>0000000=>1111111=>1
[4,8,7,2,5,3,1,6]=>0000000=>1111111=>1
[1,6,3,2,8,7,4,5]=>1000000=>0111111=>1
[8,7,3,1,2,5,6,4]=>0000000=>1111111=>1
[7,4,5,1,2,6,8,3]=>0000000=>1111111=>1
[1,3,5,7,2,8,4,9,6]=>10000000=>01111111=>1
[1,3,5,6,2,7,4,9,8]=>10000010=>01111101=>2
[1,3,4,5,2,7,6,9,8]=>10001010=>01110101=>3
[3,5,7,1,2,4,6,9,8]=>00000010=>11111101=>2
[1,3,5,7,2,9,4,6,8,10]=>100000001=>011111110=>1
[3,5,7,8,1,9,2,4,6]=>00000000=>11111111=>1
[1,3,5,7,2,9,4,10,6,8]=>100000000=>011111111=>1
[3,5,6,7,1,8,2,9,4]=>00000000=>11111111=>1
[1,3,5,7,2,8,4,9,6,10]=>100000001=>011111110=>1
[1,3,5,6,2,7,4,9,8,10]=>100000101=>011111010=>2
[1,3,4,5,2,7,6,9,8,10]=>100010101=>011101010=>3
[5,4,3,6,1,7,8,2]=>0000000=>1111111=>1
[3,2,7,8,5,6,1,4]=>0000000=>1111111=>1
[4,8,3,2,1,7,5,6]=>0000000=>1111111=>1
[1,9,8,7,6,4,3,2,5]=>10000000=>01111111=>1
[1,9,8,7,5,4,3,2,6]=>10000000=>01111111=>1
[1,9,8,6,5,4,3,2,7]=>10000000=>01111111=>1
[1,9,7,6,5,4,3,2,8]=>10000000=>01111111=>1
[1,9,8,7,6,5,2,3,4]=>10000000=>01111111=>1
[1,10,9,8,7,6,5,3,2,4]=>100000000=>011111111=>1
[1,9,8,7,6,3,4,2,5]=>10000000=>01111111=>1
[1,10,9,8,7,6,4,3,2,5]=>100000000=>011111111=>1
[1,9,8,7,4,5,3,2,6]=>10000000=>01111111=>1
[1,10,9,8,7,5,4,3,2,6]=>100000000=>011111111=>1
[1,9,8,5,6,4,3,2,7]=>10000000=>01111111=>1
[1,10,9,8,6,5,4,3,2,7]=>100000000=>011111111=>1
[1,8,4,5,6,3,2,7]=>1000000=>0111111=>1
[1,9,6,7,5,4,3,2,8]=>10000000=>01111111=>1
[1,10,9,7,6,5,4,3,2,8]=>100000000=>011111111=>1
[1,7,8,6,5,4,3,2,9]=>10000001=>01111110=>1
[1,10,8,7,6,5,4,3,2,9]=>100000000=>011111111=>1
[8,5,1,7,4,6,3,2]=>0000000=>1111111=>1
[1,3,7,8,4,6,2,5]=>1000000=>0111111=>1
[5,8,4,3,7,1,2,6]=>0000000=>1111111=>1
[5,6,4,8,7,2,1,3]=>0000000=>1111111=>1
[2,8,4,7,1,3,6,5]=>0000000=>1111111=>1
[8,9,2,3,4,5,6,1,7]=>00000000=>11111111=>1
[7,8,9,2,3,4,5,1,6]=>00000000=>11111111=>1
[6,7,8,9,2,3,4,1,5]=>00000000=>11111111=>1
[5,6,7,8,9,2,3,1,4]=>00000000=>11111111=>1
[9,10,2,3,4,5,6,7,1,8]=>000000000=>111111111=>1
[8,9,10,2,3,4,5,6,1,7]=>000000000=>111111111=>1
[7,8,9,2,3,4,1,5,6]=>00000000=>11111111=>1
[7,8,9,10,2,3,4,5,1,6]=>000000000=>111111111=>1
[6,7,8,9,2,3,1,4,5]=>00000000=>11111111=>1
[5,6,7,8,9,10,2,3,1,4]=>000000000=>111111111=>1
[4,5,6,7,8,1,9,2,3]=>00000000=>11111111=>1
[4,5,6,7,8,9,10,2,1,3]=>000000000=>111111111=>1
[6,8,3,4,5,2,1,7]=>0000000=>1111111=>1
[3,7,1,4,5,6,2,8]=>0000001=>1111110=>1
[7,9,3,4,5,6,2,1,8]=>00000000=>11111111=>1
[3,9,2,1,5,6,7,8,4]=>00000000=>11111111=>1
[3,6,1,4,5,2,7,8]=>0000011=>1111100=>1
[3,8,1,4,5,6,7,2,9]=>00000001=>11111110=>1
[8,10,3,4,5,6,7,2,1,9]=>000000000=>111111111=>1
[6,9,3,4,5,2,7,1,8]=>00000000=>11111111=>1
[3,8,2,4,5,1,7,6]=>0000000=>1111111=>1
[3,9,2,4,1,6,7,8,5]=>00000000=>11111111=>1
[3,7,2,1,5,6,4,8]=>0000001=>1111110=>1
[3,6,8,1,5,4,7,2]=>0000000=>1111111=>1
[3,8,9,1,5,6,7,4,2]=>00000000=>11111111=>1
[3,10,2,1,5,6,7,8,9,4]=>000000000=>111111111=>1
[3,7,1,4,5,6,2,8,9]=>00000011=>11111100=>1
[3,9,1,4,5,6,7,8,2,10]=>000000001=>111111110=>1
[1,7,4,6,3,5,2,8]=>1000001=>0111110=>1
[1,3,6,5,7,2,4,8]=>1000001=>0111110=>1
[1,7,2,5,6,4,3,8]=>1000001=>0111110=>1
[1,6,8,5,4,3,7,2]=>1000000=>0111111=>1
[2,5,7,8,4,3,1,6]=>0000000=>1111111=>1
[6,8,5,3,2,4,1,7]=>0000000=>1111111=>1
[1,6,8,5,3,2,7,4]=>1000000=>0111111=>1
[4,6,1,8,7,5,3,2]=>0000000=>1111111=>1
[1,3,7,6,8,5,2,4]=>1000000=>0111111=>1
[4,1,7,8,6,5,2,3]=>0000000=>1111111=>1
[5,4,3,7,6,1,2,8]=>0000001=>1111110=>1
[4,7,6,1,2,3,8,5]=>0000000=>1111111=>1
[4,5,2,6,7,8,1,3]=>0000000=>1111111=>1
[2,8,7,6,5,4,3,1,9]=>00000001=>11111110=>1
[2,1,4,9,8,7,6,5,3]=>01000000=>10111111=>2
[1,7,6,2,3,8,5,4]=>1000000=>0111111=>1
[4,5,1,3,7,6,2,8]=>0000001=>1111110=>1
[7,2,3,8,6,4,5,1]=>0000000=>1111111=>1
[1,5,4,3,8,6,2,7]=>1000000=>0111111=>1
[1,3,7,5,8,4,6,2]=>1000000=>0111111=>1
[5,8,1,2,7,6,4,3]=>0000000=>1111111=>1
[1,4,2,6,7,5,3,8]=>1000001=>0111110=>1
[1,8,2,4,6,5,3,7]=>1000000=>0111111=>1
[7,2,1,6,4,3,8,5]=>0000000=>1111111=>1
[1,4,8,7,2,3,6,5]=>1000000=>0111111=>1
[4,1,3,6,5,8,2,7]=>0000000=>1111111=>1
[4,3,7,1,5,8,2,6]=>0000000=>1111111=>1
[1,8,6,5,2,7,4,3]=>1000000=>0111111=>1
[1,8,6,2,7,4,3,5]=>1000000=>0111111=>1
[3,5,4,1,7,8,6,2]=>0000000=>1111111=>1
[6,8,7,2,1,5,4,3]=>0000000=>1111111=>1
[8,1,6,3,7,5,4,2]=>0000000=>1111111=>1
[8,5,1,3,7,6,4,2]=>0000000=>1111111=>1
[8,3,6,5,4,2,1,7]=>0000000=>1111111=>1
[6,1,3,5,7,2,8,4]=>0000000=>1111111=>1
[2,8,1,5,6,4,3,7]=>0000000=>1111111=>1
[1,6,7,5,8,4,2,3]=>1000000=>0111111=>1
[7,4,2,8,6,5,3,1]=>0000000=>1111111=>1
[6,8,4,7,3,2,5,1]=>0000000=>1111111=>1
[5,8,7,3,2,1,6,4]=>0000000=>1111111=>1
[5,8,7,2,6,4,3,1]=>0000000=>1111111=>1
[6,8,7,3,5,1,4,2]=>0000000=>1111111=>1
[4,8,5,2,6,7,3,1]=>0000000=>1111111=>1
[7,8,1,9,2,3,4,5,6]=>00000000=>11111111=>1
[6,7,8,1,9,2,3,4,5]=>00000000=>11111111=>1
[5,6,7,8,1,9,2,3,4]=>00000000=>11111111=>1
[9,1,2,3,4,5,7,6,8]=>00000000=>11111111=>1
[2,1,3,4,5,9,6,7,8]=>01111000=>10000111=>2
[1,5,7,2,4,3,8,6]=>1000000=>0111111=>1
[1,2,7,5,8,4,3,6]=>1100000=>0011111=>1
[5,1,3,8,2,7,4,6]=>0000000=>1111111=>1
[5,7,1,3,2,8,4,6]=>0000000=>1111111=>1
[7,1,6,3,2,8,4,5]=>0000000=>1111111=>1
[8,1,7,2,3,6,5,4]=>0000000=>1111111=>1
[7,1,2,6,4,3,8,5]=>0000000=>1111111=>1
[1,4,7,8,3,2,5,6]=>1000000=>0111111=>1
[8,7,1,3,2,4,6,5]=>0000000=>1111111=>1
[8,1,6,3,2,4,7,5]=>0000000=>1111111=>1
[1,8,2,7,6,3,5,4]=>1000000=>0111111=>1
[8,1,6,3,2,7,4,5]=>0000000=>1111111=>1
[8,2,1,7,6,3,4,5]=>0000000=>1111111=>1
[8,7,2,4,3,1,5,6]=>0000000=>1111111=>1
[4,7,6,1,3,2,8,5]=>0000000=>1111111=>1
[7,2,6,5,4,3,1,9,8]=>00000010=>11111101=>2
[3,2,1,9,5,8,7,6,4]=>00100000=>11011111=>2
[6,3,5,4,2,1,9,8,7]=>00000100=>11111011=>2
[4,3,2,1,9,7,8,6,5]=>00010000=>11101111=>2
[2,8,1,3,5,6,4,7]=>0000000=>1111111=>1
[2,6,3,4,7,8,5,1]=>0000000=>1111111=>1
[7,6,3,1,8,5,2,4]=>0000000=>1111111=>1
[7,2,1,3,6,8,5,4]=>0000000=>1111111=>1
[7,6,3,8,1,5,2,4]=>0000000=>1111111=>1
[1,6,4,7,8,5,3,2]=>1000000=>0111111=>1
[7,2,5,8,6,1,3,4]=>0000000=>1111111=>1
[4,1,3,6,2,5,8,7]=>0000010=>1111101=>2
[7,1,4,6,3,2,5,8]=>0000001=>1111110=>1
[6,7,2,3,8,4,1,5]=>0000000=>1111111=>1
[2,7,8,1,5,4,3,6]=>0000000=>1111111=>1
[1,5,2,6,8,7,4,3]=>1000000=>0111111=>1
[1,2,3,4,5,6,8,9,7,10]=>111111001=>000000110=>1
[1,8,3,7,5,2,6,4]=>1000000=>0111111=>1
[8,1,3,6,5,2,7,4]=>0000000=>1111111=>1
[7,1,3,8,5,2,6,4]=>0000000=>1111111=>1
[4,7,1,5,2,6,8,3]=>0000000=>1111111=>1
[7,4,1,5,2,6,8,3]=>0000000=>1111111=>1
[3,1,6,7,5,2,8,4]=>0000000=>1111111=>1
[8,6,2,4,5,1,7,3]=>0000000=>1111111=>1
[8,6,7,5,2,1,4,3]=>0000000=>1111111=>1
[7,1,4,5,2,6,8,3]=>0000000=>1111111=>1
[4,1,7,6,5,2,8,3]=>0000000=>1111111=>1
[8,4,1,5,6,2,7,3]=>0000000=>1111111=>1
[2,8,4,7,3,5,6,1]=>0000000=>1111111=>1
[1,5,4,8,3,2,6,7]=>1000000=>0111111=>1
[1,5,7,6,3,8,2,4]=>1000000=>0111111=>1
[2,6,3,1,7,8,4,5]=>0000000=>1111111=>1
[2,1,7,8,3,5,4,6]=>0100000=>1011111=>2
[1,5,8,6,7,4,2,3]=>1000000=>0111111=>1
[5,3,7,4,6,1,8,2]=>0000000=>1111111=>1
[3,6,7,1,5,4,8,2]=>0000000=>1111111=>1
[6,4,7,1,5,2,8,3]=>0000000=>1111111=>1
[1,6,5,2,8,7,4,3]=>1000000=>0111111=>1
[1,3,4,5,2,6,7,8,9]=>10001111=>01110000=>1
[1,2,3,4,5,7,8,6,9,10]=>111110011=>000001100=>1
[1,2,3,4,5,7,8,9,6,10]=>111110001=>000001110=>1
[2,3,4,5,1,6,7,9,8]=>00001110=>11110001=>2
[2,1,4,5,3,6,7,8,9]=>01001111=>10110000=>2
[1,3,2,5,4,6,7,8,9]=>10101111=>01010000=>2
[4,1,7,2,5,8,3,6]=>0000000=>1111111=>1
[3,2,5,8,6,1,7,4]=>0000000=>1111111=>1
[4,7,1,8,5,3,6,2]=>0000000=>1111111=>1
[6,4,7,2,5,3,1,8]=>0000001=>1111110=>1
[4,1,6,2,8,3,5,7,9]=>00000001=>11111110=>1
[4,1,6,2,8,3,9,5,7]=>00000000=>11111111=>1
[4,1,6,2,7,3,8,5,9]=>00000001=>11111110=>1
[4,8,7,3,5,1,6,2]=>0000000=>1111111=>1
[5,3,8,7,1,6,2,4]=>0000000=>1111111=>1
[5,2,6,7,4,3,1,8]=>0000001=>1111110=>1
[8,5,1,6,4,3,2,7]=>0000000=>1111111=>1
[8,6,3,5,2,7,1,4]=>0000000=>1111111=>1
[8,4,6,2,1,5,7,3]=>0000000=>1111111=>1
[8,5,2,1,6,4,7,3]=>0000000=>1111111=>1
[1,7,2,8,5,4,6,3]=>1000000=>0111111=>1
[6,7,1,4,8,5,3,2]=>0000000=>1111111=>1
[7,3,2,8,5,1,4,6]=>0000000=>1111111=>1
[4,1,7,3,2,8,5,6]=>0000000=>1111111=>1
[8,3,5,2,4,7,1,6]=>0000000=>1111111=>1
[4,3,7,8,6,1,5,2]=>0000000=>1111111=>1
[1,2,6,3,7,8,5,4]=>1100000=>0011111=>1
[6,1,3,7,8,5,4,2]=>0000000=>1111111=>1
[2,6,4,7,5,3,1,8]=>0000001=>1111110=>1
[5,6,1,8,7,2,3,4]=>0000000=>1111111=>1
[3,9,2,4,5,6,7,8,1]=>00000000=>11111111=>1
[3,8,6,1,5,2,4,7]=>0000000=>1111111=>1
[3,2,8,1,5,6,4,7]=>0000000=>1111111=>1
[5,8,7,3,2,1,4,6]=>0000000=>1111111=>1
[3,4,7,6,8,2,1,5]=>0000000=>1111111=>1
[2,8,1,3,7,5,6,4]=>0000000=>1111111=>1
[1,8,7,2,5,6,4,3]=>1000000=>0111111=>1
[3,4,7,1,5,8,2,6]=>0000000=>1111111=>1
[1,3,5,2,4,6,7,8,9]=>10001111=>01110000=>1
[4,1,2,3,5,6,8,7,9]=>00011101=>11100010=>2
[1,2,4,7,3,5,6,8,9]=>11000011=>00111100=>1
[5,1,2,3,4,7,6,8,9]=>00001011=>11110100=>2
[1,4,7,5,2,3,6,8]=>1000001=>0111110=>1
[1,5,3,6,8,4,7,2]=>1000000=>0111111=>1
[8,5,1,4,6,7,3,2]=>0000000=>1111111=>1
[3,4,7,5,6,8,2,1]=>0000000=>1111111=>1
[3,4,7,8,5,2,6,1]=>0000000=>1111111=>1
[4,8,1,7,5,6,3,2]=>0000000=>1111111=>1
[1,8,7,5,2,6,3,4]=>1000000=>0111111=>1
[1,7,6,3,4,5,8,2]=>1000000=>0111111=>1
[1,8,7,4,5,6,2,3]=>1000000=>0111111=>1
[1,8,7,3,6,4,2,5]=>1000000=>0111111=>1
[1,4,7,5,8,2,6,3]=>1000000=>0111111=>1
[1,4,7,2,3,6,5,8]=>1000001=>0111110=>1
[1,7,2,5,6,3,4,8]=>1000001=>0111110=>1
[1,2,6,5,8,3,4,7]=>1100000=>0011111=>1
[1,5,8,2,6,3,4,7]=>1000000=>0111111=>1
[6,8,3,2,7,5,1,4]=>0000000=>1111111=>1
[7,3,6,8,1,2,5,4]=>0000000=>1111111=>1
[4,1,5,7,2,6,3,8]=>0000001=>1111110=>1
[5,7,2,1,3,6,4,8]=>0000001=>1111110=>1
[3,5,6,7,2,4,1,8]=>0000001=>1111110=>1
[6,4,7,5,2,3,1,8]=>0000001=>1111110=>1
[1,5,6,4,8,3,2,7]=>1000000=>0111111=>1
[2,1,5,6,4,8,3,7]=>0100000=>1011111=>2
[5,1,4,7,8,6,2,3]=>0000000=>1111111=>1
[1,6,7,2,8,5,4,3]=>1000000=>0111111=>1
[5,3,2,1,7,8,6,4]=>0000000=>1111111=>1
[7,4,3,8,6,1,5,2]=>0000000=>1111111=>1
[4,3,7,1,5,8,6,2]=>0000000=>1111111=>1
[8,2,4,5,3,1,7,6]=>0000000=>1111111=>1
[1,4,3,2,7,5,8,6]=>1001000=>0110111=>2
[1,5,2,8,6,3,10,9,7,4]=>100000000=>011111111=>1
[4,1,5,2,8,6,3,10,9,7]=>000000000=>111111111=>1
[1,7,5,2,8,6,3,10,9,4]=>100000000=>011111111=>1
[4,1,7,5,2,8,3,10,9,6]=>000000000=>111111111=>1
[6,4,1,7,5,2,8,3,10,9]=>000000010=>111111101=>2
[3,4,1,7,2,8,5,10,9,6]=>000000000=>111111111=>1
[3,6,4,1,7,2,8,5,10,9]=>000000010=>111111101=>2
[1,5,2,9,8,6,3,10,7,4]=>100000000=>011111111=>1
[4,1,5,2,9,8,6,3,10,7]=>000000000=>111111111=>1
[1,7,5,2,9,6,3,10,8,4]=>100000000=>011111111=>1
[4,1,7,5,2,9,3,10,8,6]=>000000000=>111111111=>1
[4,1,9,6,5,2,7,3,10,8]=>000000000=>111111111=>1
[3,4,1,7,2,9,5,10,8,6]=>000000000=>111111111=>1
[3,6,1,9,4,2,7,5,10,8]=>000000000=>111111111=>1
[1,8,7,5,2,9,6,3,10,4]=>100000000=>011111111=>1
[4,1,8,7,5,2,9,3,10,6]=>000000000=>111111111=>1
[6,4,1,8,5,2,9,3,10,7]=>000000000=>111111111=>1
[7,6,4,1,8,5,2,9,3,10]=>000000001=>111111110=>1
[3,4,1,8,7,2,9,5,10,6]=>000000000=>111111111=>1
[3,6,4,1,8,2,9,5,10,7]=>000000000=>111111111=>1
[3,7,6,4,1,8,2,9,5,10]=>000000001=>111111110=>1
[1,9,6,5,2,7,3,10,8,4]=>100000000=>011111111=>1
[6,1,9,4,2,7,3,10,8,5]=>000000000=>111111111=>1
[5,4,1,9,6,2,7,3,10,8]=>000000000=>111111111=>1
[9,3,1,6,2,7,4,10,8,5]=>000000000=>111111111=>1
[9,5,3,1,6,2,7,4,10,8]=>000000000=>111111111=>1
[6,1,8,5,2,9,7,3,10,4]=>000000000=>111111111=>1
[6,4,1,8,2,9,7,3,10,5]=>000000000=>111111111=>1
[8,5,4,1,6,2,9,3,10,7]=>000000000=>111111111=>1
[5,7,4,1,8,6,2,9,3,10]=>000000001=>111111110=>1
[3,6,1,8,2,9,7,4,10,5]=>000000000=>111111111=>1
[5,8,3,1,6,2,9,4,10,7]=>000000000=>111111111=>1
[5,3,7,1,8,6,2,9,4,10]=>000000001=>111111110=>1
[4,3,8,1,9,5,2,6,10,7]=>000000000=>111111111=>1
[7,4,3,5,1,8,2,9,6,10]=>000000001=>111111110=>1
[9,6,2,1,3,7,4,10,8,5]=>000000000=>111111111=>1
[5,9,2,1,6,3,7,4,10,8]=>000000000=>111111111=>1
[6,8,2,1,3,9,7,4,10,5]=>000000000=>111111111=>1
[8,2,5,1,6,3,9,4,10,7]=>000000000=>111111111=>1
[2,5,7,1,8,6,3,9,4,10]=>000000001=>111111110=>1
[2,4,8,1,9,5,3,6,10,7]=>000000000=>111111111=>1
[5,6,4,3,2,1,7,8,9]=>00000111=>11111000=>1
[5,6,4,3,2,1,7,8,9,10]=>000001111=>111110000=>1
[4,5,3,2,1,6,7,8,9]=>00001111=>11110000=>1
[6,7,5,4,3,2,1,8,9,10]=>000000111=>111111000=>1
[6,7,4,3,2,1,5,8,9]=>00000011=>11111100=>1
[5,6,4,3,2,7,1,8,9]=>00000011=>11111100=>1
[7,5,4,3,1,2,6,8,9]=>00000011=>11111100=>1
[6,5,4,3,7,1,2,8,9]=>00000011=>11111100=>1
[6,3,1,8,2,7,5,4]=>0000000=>1111111=>1
[4,1,7,8,3,2,5,6]=>0000000=>1111111=>1
[5,8,2,1,3,6,4,7]=>0000000=>1111111=>1
[7,6,4,3,5,2,1,9,8]=>00000010=>11111101=>2
[7,6,3,5,4,2,1,9,8]=>00000010=>11111101=>2
[5,7,6,3,4,1,8,2]=>0000000=>1111111=>1
[7,8,9,10,1,5,6,3,4,2]=>000000000=>111111111=>1
[9,8,6,1,2,3,4,5,7]=>00000000=>11111111=>1
[9,8,7,5,1,2,3,4,6]=>00000000=>11111111=>1
[9,8,7,6,4,1,2,3,5]=>00000000=>11111111=>1
[9,8,7,6,5,3,1,2,4]=>00000000=>11111111=>1
[7,1,2,6,4,3,5,8]=>0000001=>1111110=>1
[7,1,2,6,5,3,4,8]=>0000001=>1111110=>1
[4,7,8,6,2,3,5,1]=>0000000=>1111111=>1
[7,1,2,4,8,6,5,3]=>0000000=>1111111=>1
[9,8,4,7,6,5,3,2,1]=>00000000=>11111111=>1
[9,8,3,7,6,5,4,2,1]=>00000000=>11111111=>1
[9,3,8,7,6,5,4,2,1]=>00000000=>11111111=>1
[9,2,8,7,6,5,4,3,1]=>00000000=>11111111=>1
[10,9,8,5,7,6,4,3,2,1]=>000000000=>111111111=>1
[9,8,4,6,5,7,3,2,1]=>00000000=>11111111=>1
[10,9,8,4,7,6,5,3,2,1]=>000000000=>111111111=>1
[9,8,3,6,5,4,7,2,1]=>00000000=>11111111=>1
[10,9,4,8,7,6,5,3,2,1]=>000000000=>111111111=>1
[9,3,7,6,5,4,8,2,1]=>00000000=>11111111=>1
[9,2,7,6,5,4,3,8,1]=>00000000=>11111111=>1
[10,3,9,8,7,6,5,4,2,1]=>000000000=>111111111=>1
[10,2,9,8,7,6,5,4,3,1]=>000000000=>111111111=>1
[7,4,3,1,6,5,2,8]=>0000001=>1111110=>1
[3,5,1,2,6,8,7,4]=>0000000=>1111111=>1
[3,1,2,4,8,7,5,6]=>0011000=>1100111=>2
[2,7,4,6,3,8,1,5]=>0000000=>1111111=>1
[8,2,4,1,3,7,5,6]=>0000000=>1111111=>1
[4,2,6,7,5,1,8,3]=>0000000=>1111111=>1
[4,7,2,5,3,8,1,6]=>0000000=>1111111=>1
[3,5,7,4,2,8,1,6]=>0000000=>1111111=>1
[2,4,7,6,3,8,1,5]=>0000000=>1111111=>1
[4,6,8,5,1,2,3,7]=>0000000=>1111111=>1
[4,6,5,7,1,2,3,8]=>0000001=>1111110=>1
[4,6,5,7,1,3,8,2]=>0000000=>1111111=>1
[3,4,7,6,1,8,2,5]=>0000000=>1111111=>1
[8,5,2,1,6,3,4,7]=>0000000=>1111111=>1
[7,1,8,5,3,2,4,6]=>0000000=>1111111=>1
[9,10,2,1,6,4,3,5,7,8]=>000000000=>111111111=>1
[7,10,2,1,8,4,3,5,6,9]=>000000000=>111111111=>1
[2,9,1,10,7,4,3,5,6,8]=>000000000=>111111111=>1
[2,8,1,9,4,3,10,5,6,7]=>000000000=>111111111=>1
[10,8,5,2,1,6,3,4,7,9]=>000000000=>111111111=>1
[9,5,2,1,10,6,3,4,7,8]=>000000000=>111111111=>1
[10,7,2,1,8,5,3,4,6,9]=>000000000=>111111111=>1
[9,2,1,10,7,5,3,4,6,8]=>000000000=>111111111=>1
[2,8,1,9,3,10,5,4,6,7]=>000000000=>111111111=>1
[10,6,2,1,7,3,8,4,5,9]=>000000000=>111111111=>1
[9,2,1,10,6,3,7,4,5,8]=>000000000=>111111111=>1
[8,2,1,9,3,10,6,4,5,7]=>000000000=>111111111=>1
[7,2,1,8,3,9,4,10,5,6]=>000000000=>111111111=>1
[10,8,6,3,1,4,2,5,7,9]=>000000000=>111111111=>1
[3,9,1,10,6,4,2,5,7,8]=>000000000=>111111111=>1
[10,7,3,1,8,4,2,5,6,9]=>000000000=>111111111=>1
[9,3,1,10,7,4,2,5,6,8]=>000000000=>111111111=>1
[8,3,1,9,4,2,10,5,6,7]=>000000000=>111111111=>1
[10,8,5,1,6,3,2,4,7,9]=>000000000=>111111111=>1
[9,5,1,10,6,3,2,4,7,8]=>000000000=>111111111=>1
[10,7,1,8,5,3,2,4,6,9]=>000000000=>111111111=>1
[9,1,10,7,5,3,2,4,6,8]=>000000000=>111111111=>1
[8,3,1,9,2,10,5,4,6,7]=>000000000=>111111111=>1
[10,6,1,7,3,2,8,4,5,9]=>000000000=>111111111=>1
[9,1,10,6,3,2,7,4,5,8]=>000000000=>111111111=>1
[8,1,9,3,2,10,6,4,5,7]=>000000000=>111111111=>1
[7,1,8,3,2,9,4,10,5,6]=>000000000=>111111111=>1
[10,8,4,1,5,2,6,3,7,9]=>000000000=>111111111=>1
[9,4,1,10,5,2,6,3,7,8]=>000000000=>111111111=>1
[10,7,1,8,4,2,5,3,6,9]=>000000000=>111111111=>1
[9,1,10,7,4,2,5,3,6,8]=>000000000=>111111111=>1
[8,1,9,4,2,10,5,3,6,7]=>000000000=>111111111=>1
[10,6,1,7,2,8,4,3,5,9]=>000000000=>111111111=>1
[9,1,10,6,2,7,4,3,5,8]=>000000000=>111111111=>1
[8,1,9,2,10,6,4,3,5,7]=>000000000=>111111111=>1
[7,1,8,2,9,4,3,10,5,6]=>000000000=>111111111=>1
[10,5,1,6,2,7,3,8,4,9]=>000000000=>111111111=>1
[9,1,10,5,2,6,3,7,4,8]=>000000000=>111111111=>1
[8,1,9,2,10,5,3,6,4,7]=>000000000=>111111111=>1
[7,1,8,2,9,3,10,5,4,6]=>000000000=>111111111=>1
[4,2,8,5,7,1,6,3]=>0000000=>1111111=>1
[6,8,7,4,5,3,2,1]=>0000000=>1111111=>1
[6,4,8,1,5,2,3,7]=>0000000=>1111111=>1
[7,2,4,1,6,3,5,8]=>0000001=>1111110=>1
[2,8,7,3,1,4,5,6]=>0000000=>1111111=>1
[9,8,4,5,7,6,3,2,1]=>00000000=>11111111=>1
[9,8,5,4,6,7,3,2,1]=>00000000=>11111111=>1
[10,9,8,6,5,7,4,3,2,1]=>000000000=>111111111=>1
[10,9,8,4,5,7,6,3,2,1]=>000000000=>111111111=>1
[9,8,4,5,3,7,6,2,1]=>00000000=>11111111=>1
[9,8,3,5,7,6,4,2,1]=>00000000=>11111111=>1
[9,8,5,4,6,3,7,2,1]=>00000000=>11111111=>1
[9,8,4,3,6,7,5,2,1]=>00000000=>11111111=>1
[10,9,8,5,4,6,7,3,2,1]=>000000000=>111111111=>1
[8,4,7,6,3,1,2,5]=>0000000=>1111111=>1
[6,4,7,5,3,2,8,1]=>0000000=>1111111=>1
[6,7,3,4,2,1,8,5]=>0000000=>1111111=>1
[6,4,8,3,1,5,7,2]=>0000000=>1111111=>1
[7,4,2,3,5,1,8,6]=>0000000=>1111111=>1
[3,1,6,5,2,4,8,7]=>0000010=>1111101=>2
[5,8,4,1,3,2,7,6]=>0000000=>1111111=>1
[5,3,4,7,6,1,8,2]=>0000000=>1111111=>1
[4,5,2,1,6,3,8,7]=>0000010=>1111101=>2
[4,5,2,1,6,7,3,8]=>0000001=>1111110=>1
[5,3,8,6,2,4,7,1]=>0000000=>1111111=>1
[2,5,1,6,4,3,8,7]=>0000010=>1111101=>2
[3,6,2,8,5,7,1,4]=>0000000=>1111111=>1
[4,6,8,1,5,7,2,3]=>0000000=>1111111=>1
[4,1,2,5,7,6,3,8]=>0000001=>1111110=>1
[4,6,5,8,1,7,3,2]=>0000000=>1111111=>1
[2,1,3,6,4,8,7,5]=>0110000=>1001111=>2
[4,8,1,2,7,5,6,3]=>0000000=>1111111=>1
[1,6,4,3,8,7,5,2]=>1000000=>0111111=>1
[4,5,1,6,8,7,2,3]=>0000000=>1111111=>1
[3,4,7,2,5,8,6,1]=>0000000=>1111111=>1
[2,5,1,8,6,4,7,3]=>0000000=>1111111=>1
[2,5,8,7,3,1,4,6]=>0000000=>1111111=>1
[9,8,7,4,3,2,1,5,6]=>00000000=>11111111=>1
[9,8,7,6,3,2,1,4,5]=>00000000=>11111111=>1
[3,8,7,2,6,1,4,5]=>0000000=>1111111=>1
[8,4,5,1,6,7,2,3]=>0000000=>1111111=>1
[2,5,1,8,3,6,4,7]=>0000000=>1111111=>1
[5,8,4,7,3,2,1,6]=>0000000=>1111111=>1
[5,8,1,3,4,7,2,6]=>0000000=>1111111=>1
[7,2,4,5,3,1,6,8]=>0000001=>1111110=>1
[3,7,4,6,2,1,8,5]=>0000000=>1111111=>1
[4,3,7,6,5,1,8,2]=>0000000=>1111111=>1
[5,1,4,8,2,3,7,6]=>0000000=>1111111=>1
[3,2,8,5,4,1,6,7]=>0000000=>1111111=>1
[7,8,9,1,3,4,5,6,2]=>00000000=>11111111=>1
[6,1,2,9,3,4,5,7,8]=>00000000=>11111111=>1
[4,1,2,3,5,9,6,7,8]=>00011000=>11100111=>2
[3,1,2,4,5,6,9,7,8]=>00111100=>11000011=>2
[1,2,8,3,4,6,5,7]=>1100000=>0011111=>1
[8,1,2,7,3,5,4,6]=>0000000=>1111111=>1
[5,7,1,2,6,3,4,8]=>0000001=>1111110=>1
[1,2,7,5,6,3,4,8]=>1100001=>0011110=>1
[5,1,4,7,2,3,6,8]=>0000001=>1111110=>1
[4,8,1,2,3,6,5,7]=>0000000=>1111111=>1
[1,3,4,2,5,6,7,8,9]=>10011111=>01100000=>1
[1,2,4,5,6,3,7,8,9]=>11000111=>00111000=>1
[1,2,3,5,6,7,8,4,9]=>11100001=>00011110=>1
[2,1,5,3,6,7,4,8,9]=>01000011=>10111100=>2
[1,3,5,6,4,2,7,8,9]=>10000111=>01111000=>1
[3,5,2,1,6,4,7,8,9]=>00000111=>11111000=>1
[2,1,3,6,4,7,8,9,5]=>01100000=>10011111=>2
[1,3,4,6,7,2,8,5,9]=>10000001=>01111110=>1
[3,2,6,1,4,7,8,5,9]=>00000001=>11111110=>1
[2,4,6,1,7,5,3,8,9]=>00000011=>11111100=>1
[4,6,3,2,1,7,5,8,9]=>00000011=>11111100=>1
[2,4,1,7,5,8,3,9,6]=>00000000=>11111111=>1
[4,3,7,2,1,5,8,9,6]=>00000000=>11111111=>1
[1,3,5,7,8,6,4,2,9]=>10000001=>01111110=>1
[3,5,7,2,1,8,6,4,9]=>00000001=>11111110=>1
[5,7,4,3,2,1,8,6,9]=>00000001=>11111110=>1
[2,4,6,8,1,9,7,5,3]=>00000000=>11111111=>1
[4,6,8,3,2,1,9,7,5]=>00000000=>11111111=>1
[6,8,5,4,3,2,1,9,7]=>00000000=>11111111=>1
[1,3,4,2,5,6,7,8,9,10]=>100111111=>011000000=>1
[1,2,4,5,6,3,7,8,9,10]=>110001111=>001110000=>1
[1,2,3,5,6,7,8,4,9,10]=>111000011=>000111100=>1
[2,1,5,3,6,7,4,8,9,10]=>010000111=>101111000=>2
[1,3,5,6,4,2,7,8,9,10]=>100001111=>011110000=>1
[3,5,2,1,6,4,7,8,9,10]=>000001111=>111110000=>1
[2,1,3,6,4,7,8,9,5,10]=>011000001=>100111110=>2
[1,3,4,6,7,2,8,5,9,10]=>100000011=>011111100=>1
[3,2,6,1,4,7,8,5,9,10]=>000000011=>111111100=>1
[2,4,6,1,7,5,3,8,9,10]=>000000111=>111111000=>1
[4,6,3,2,1,7,5,8,9,10]=>000000111=>111111000=>1
[1,3,4,2,7,8,5,9,10,6]=>100100000=>011011111=>2
[3,2,1,7,4,5,8,9,10,6]=>001000000=>110111111=>2
[1,2,4,5,7,8,9,6,3,10]=>110000001=>001111110=>1
[4,3,7,2,1,5,8,9,6,10]=>000000001=>111111110=>1
[1,3,5,7,8,6,4,2,9,10]=>100000011=>011111100=>1
[3,5,7,2,1,8,6,4,9,10]=>000000011=>111111100=>1
[5,7,4,3,2,1,8,6,9,10]=>000000011=>111111100=>1
[2,1,5,3,8,6,9,10,7,4]=>010000000=>101111111=>2
[1,3,5,6,8,9,4,2,10,7]=>100000000=>011111111=>1
[3,5,2,8,1,6,9,4,10,7]=>000000000=>111111111=>1
[5,4,8,3,2,1,6,9,10,7]=>000000000=>111111111=>1
[2,4,6,8,1,9,7,5,3,10]=>000000001=>111111110=>1
[4,6,8,3,2,1,9,7,5,10]=>000000001=>111111110=>1
[6,8,5,4,3,2,1,9,7,10]=>000000001=>111111110=>1
[3,5,7,9,2,1,10,8,6,4]=>000000000=>111111111=>1
[5,7,9,4,3,2,1,10,8,6]=>000000000=>111111111=>1
[7,9,6,5,4,3,2,1,10,8]=>000000000=>111111111=>1
[6,2,3,8,7,1,4,5]=>0000000=>1111111=>1
[8,2,3,6,4,7,5,1]=>0000000=>1111111=>1
[7,2,3,6,4,8,1,5]=>0000000=>1111111=>1
[4,5,1,3,2,6,8,7]=>0000110=>1111001=>2
[6,4,7,5,1,3,2,8]=>0000001=>1111110=>1
[5,3,1,6,2,7,8,4]=>0000000=>1111111=>1
[6,7,2,4,1,8,3,5]=>0000000=>1111111=>1
[5,1,6,3,2,7,8,4]=>0000000=>1111111=>1
[5,2,1,6,4,7,3,8]=>0000001=>1111110=>1
[5,4,1,6,2,7,8,3]=>0000000=>1111111=>1
[6,7,2,5,4,1,3,8]=>0000001=>1111110=>1
[7,1,3,5,4,2,8,6]=>0000000=>1111111=>1
[6,3,2,4,8,7,1,5]=>0000000=>1111111=>1
[2,7,1,5,8,6,4,3]=>0000000=>1111111=>1
[7,1,4,3,6,5,8,2]=>0000000=>1111111=>1
[7,1,5,6,3,4,8,2]=>0000000=>1111111=>1
[6,1,8,5,4,7,3,2]=>0000000=>1111111=>1
[7,6,1,5,4,2,8,3]=>0000000=>1111111=>1
[5,1,6,8,7,2,4,3]=>0000000=>1111111=>1
[4,6,7,5,3,1,8,2]=>0000000=>1111111=>1
[5,3,2,6,8,7,4,1]=>0000000=>1111111=>1
[5,4,6,2,8,7,3,1]=>0000000=>1111111=>1
[4,5,8,6,7,2,3,1]=>0000000=>1111111=>1
[4,5,7,6,1,2,8,3]=>0000000=>1111111=>1
[4,6,5,7,2,1,8,3]=>0000000=>1111111=>1
[7,4,8,6,3,5,1,2]=>0000000=>1111111=>1
[4,6,3,5,1,8,2,7]=>0000000=>1111111=>1
[8,5,7,6,2,3,4,1]=>0000000=>1111111=>1
[3,5,6,7,8,9,2,4,1]=>00000000=>11111111=>1
[3,4,6,7,8,2,5,1]=>0000000=>1111111=>1
[2,4,6,7,8,9,1,3,5]=>00000000=>11111111=>1
[2,5,6,7,3,8,1,4]=>0000000=>1111111=>1
[2,5,6,7,8,9,3,1,4]=>00000000=>11111111=>1
[2,4,7,5,8,6,3,1]=>0000000=>1111111=>1
[1,6,8,3,4,2,7,5]=>1000000=>0111111=>1
[2,6,5,3,7,4,8,1]=>0000000=>1111111=>1
[1,4,6,5,3,8,2,7]=>1000000=>0111111=>1
[2,4,5,8,7,1,3,6]=>0000000=>1111111=>1
[3,1,6,8,7,5,4,2]=>0000000=>1111111=>1
[3,1,8,7,5,6,4,2]=>0000000=>1111111=>1
[5,1,8,7,6,3,4,2]=>0000000=>1111111=>1
[8,2,7,5,3,6,4,1]=>0000000=>1111111=>1
[8,7,2,3,1,5,6,4]=>0000000=>1111111=>1
[2,8,5,7,6,1,3,4]=>0000000=>1111111=>1
[1,8,7,2,6,4,5,3]=>1000000=>0111111=>1
[8,7,2,1,6,4,5,3]=>0000000=>1111111=>1
[1,8,4,7,6,2,5,3]=>1000000=>0111111=>1
[8,7,1,6,4,3,5,2]=>0000000=>1111111=>1
[8,4,1,7,3,6,5,2]=>0000000=>1111111=>1
[4,5,6,7,8,9,1,10,2,3]=>000000000=>111111111=>1
[2,5,6,7,8,1,9,3,4]=>00000000=>11111111=>1
[4,5,6,7,1,2,8,3,9]=>00000001=>11111110=>1
[1,3,6,7,8,9,2,4,5]=>10000000=>01111111=>1
[3,5,6,7,8,1,2,9,4]=>00000000=>11111111=>1
[4,5,1,8,7,3,6,2]=>0000000=>1111111=>1
[4,3,8,5,2,6,1,7]=>0000000=>1111111=>1
[5,7,4,1,2,6,8,3]=>0000000=>1111111=>1
[2,8,6,7,5,3,1,4]=>0000000=>1111111=>1
[8,4,7,3,1,2,5,6]=>0000000=>1111111=>1
[4,8,3,2,6,1,7,5]=>0000000=>1111111=>1
[4,3,7,6,1,5,2,8]=>0000001=>1111110=>1
[7,5,4,3,6,1,8,2]=>0000000=>1111111=>1
[4,6,8,5,3,1,2,7]=>0000000=>1111111=>1
[5,6,8,4,3,7,2,1]=>0000000=>1111111=>1
[7,5,8,4,2,1,6,3]=>0000000=>1111111=>1
[8,4,2,6,5,7,3,1]=>0000000=>1111111=>1
[1,7,4,2,8,5,6,3]=>1000000=>0111111=>1
[3,2,1,7,4,6,8,5]=>0010000=>1101111=>2
[6,2,5,7,1,4,3,8]=>0000001=>1111110=>1
[4,8,5,3,1,2,6,7]=>0000000=>1111111=>1
[8,5,2,4,6,1,3,7]=>0000000=>1111111=>1
[1,5,3,4,7,2,6,8]=>1000001=>0111110=>1
[8,4,6,1,5,7,3,2]=>0000000=>1111111=>1
[6,4,7,2,1,3,8,5]=>0000000=>1111111=>1
[6,7,3,1,2,4,8,5]=>0000000=>1111111=>1
[3,1,8,7,6,2,5,4]=>0000000=>1111111=>1
[1,3,8,6,7,2,5,4]=>1000000=>0111111=>1
[5,2,3,6,1,8,4,7]=>0000000=>1111111=>1
[3,2,6,4,7,1,5,8]=>0000001=>1111110=>1
[3,6,2,5,7,8,4,1]=>0000000=>1111111=>1
[2,7,4,6,8,3,5,1]=>0000000=>1111111=>1
[3,7,6,8,1,5,4,2]=>0000000=>1111111=>1
[1,5,7,6,8,4,2,3]=>1000000=>0111111=>1
[2,7,4,6,8,5,3,1]=>0000000=>1111111=>1
[3,7,6,8,5,1,4,2]=>0000000=>1111111=>1
[7,1,3,8,6,2,4,5]=>0000000=>1111111=>1
[2,7,1,8,6,5,3,4]=>0000000=>1111111=>1
[2,3,4,5,7,6,8,9,1]=>00000000=>11111111=>1
[2,3,4,5,8,7,6,9,1]=>00000000=>11111111=>1
[5,3,4,7,6,2,1,8]=>0000001=>1111110=>1
[7,4,5,3,8,1,6,2]=>0000000=>1111111=>1
[7,3,6,1,4,2,8,5]=>0000000=>1111111=>1
[1,2,3,4,7,9,5,6,8]=>11110000=>00001111=>1
[1,2,3,4,6,7,9,5,8]=>11110000=>00001111=>1
[1,2,3,4,8,5,6,9,7]=>11110000=>00001111=>1
[1,2,3,4,7,8,5,9,6]=>11110000=>00001111=>1
[1,2,4,8,5,7,3,6]=>1100000=>0011111=>1
[7,1,4,6,8,5,3,2]=>0000000=>1111111=>1
[7,2,5,1,6,4,8,3]=>0000000=>1111111=>1
[2,7,1,5,6,4,8,3]=>0000000=>1111111=>1
[1,5,7,8,4,6,3,2]=>1000000=>0111111=>1
[1,4,8,5,7,6,3,2]=>1000000=>0111111=>1
[2,8,1,5,6,4,7,3]=>0000000=>1111111=>1
[3,7,2,8,1,5,6,4]=>0000000=>1111111=>1
[7,3,2,5,1,6,8,4]=>0000000=>1111111=>1
[8,7,2,1,3,6,5,4]=>0000000=>1111111=>1
[7,3,2,8,1,4,6,5]=>0000000=>1111111=>1
[3,6,2,1,8,4,7,5]=>0000000=>1111111=>1
[4,6,5,3,1,8,7,2]=>0000000=>1111111=>1
[8,6,7,4,3,1,5,2]=>0000000=>1111111=>1
[8,6,7,1,4,3,5,2]=>0000000=>1111111=>1
[8,6,7,2,1,3,5,4]=>0000000=>1111111=>1
[8,5,6,1,7,4,2,3]=>0000000=>1111111=>1
[6,1,5,4,2,7,8,3]=>0000000=>1111111=>1
[3,8,6,1,5,7,4,2]=>0000000=>1111111=>1
[6,4,2,3,7,8,1,5]=>0000000=>1111111=>1
[4,3,6,2,5,8,1,7]=>0000000=>1111111=>1
[9,8,10,7,6,5,4,3,1,2]=>000000000=>111111111=>1
[8,7,9,6,5,4,2,1,3]=>00000000=>11111111=>1
[8,9,7,6,5,4,2,1,3]=>00000000=>11111111=>1
[8,9,7,6,5,4,2,3,1]=>00000000=>11111111=>1
[8,2,4,3,1,7,5,6]=>0000000=>1111111=>1
[8,2,1,4,3,7,5,6]=>0000000=>1111111=>1
[7,1,6,8,3,2,4,5]=>0000000=>1111111=>1
[5,7,2,6,4,1,8,3]=>0000000=>1111111=>1
[5,7,1,8,3,2,6,4]=>0000000=>1111111=>1
[2,6,1,8,4,7,5,3]=>0000000=>1111111=>1
[2,3,4,5,8,6,7,9,1]=>00000000=>11111111=>1
[2,3,4,5,9,6,8,7,1]=>00000000=>11111111=>1
[9,3,4,5,2,6,7,8,1]=>00000000=>11111111=>1
[6,2,3,4,5,7,8,9,10,1]=>000000000=>111111111=>1
[2,6,3,4,5,7,8,9,10,1]=>000000000=>111111111=>1
[2,3,6,4,5,7,8,9,10,1]=>000000000=>111111111=>1
[5,4,7,2,1,3,8,6]=>0000000=>1111111=>1
[5,1,4,6,2,7,8,3]=>0000000=>1111111=>1
[1,2,5,3,7,8,6,4]=>1100000=>0011111=>1
[4,8,3,5,1,2,7,6]=>0000000=>1111111=>1
[6,1,3,7,2,8,4,5]=>0000000=>1111111=>1
[3,8,5,4,1,7,2,6]=>0000000=>1111111=>1
[3,1,5,8,2,6,7,4]=>0000000=>1111111=>1
[2,8,5,3,1,7,4,6]=>0000000=>1111111=>1
[6,5,2,3,7,1,8,4]=>0000000=>1111111=>1
[7,2,1,6,4,8,3,5]=>0000000=>1111111=>1
[2,1,3,7,5,8,4,6]=>0110000=>1001111=>2
[6,2,4,5,7,1,8,3]=>0000000=>1111111=>1
[2,3,8,7,1,4,6,5]=>0000000=>1111111=>1
[4,2,7,5,6,8,1,3]=>0000000=>1111111=>1
[2,1,3,4,5,8,6,7,9]=>01111001=>10000110=>2
[6,8,2,5,4,7,3,1]=>0000000=>1111111=>1
[10,7,1,2,3,4,5,9,6,8]=>000000000=>111111111=>1
[5,3,2,7,6,1,8,4]=>0000000=>1111111=>1
[6,4,7,1,2,3,8,5]=>0000000=>1111111=>1
[6,1,7,3,8,4,5,2]=>0000000=>1111111=>1
[8,2,3,1,6,4,7,5]=>0000000=>1111111=>1
[1,8,7,2,3,4,6,5]=>1000000=>0111111=>1
[1,8,3,7,6,2,5,4]=>1000000=>0111111=>1
[1,3,8,2,5,6,4,7]=>1000000=>0111111=>1
[1,3,2,7,4,6,8,5]=>1010000=>0101111=>2
[1,3,8,4,6,2,7,5]=>1000000=>0111111=>1
[8,2,3,6,7,4,5,1]=>0000000=>1111111=>1
[5,6,4,2,1,7,3,8]=>0000001=>1111110=>1
[6,4,7,1,2,5,3,8]=>0000001=>1111110=>1
[4,5,6,7,8,9,1,2,10,3]=>000000000=>111111111=>1
[4,5,6,7,8,1,3,9,2]=>00000000=>11111111=>1
[1,2,7,5,8,6,3,4]=>1100000=>0011111=>1
[7,4,5,1,6,8,2,3]=>0000000=>1111111=>1
[1,7,8,4,2,6,3,5]=>1000000=>0111111=>1
[6,3,2,5,7,4,1,8]=>0000001=>1111110=>1
[6,2,1,5,3,7,8,4]=>0000000=>1111111=>1
[4,1,7,8,3,6,5,2]=>0000000=>1111111=>1
[6,4,2,1,7,3,5,8]=>0000001=>1111110=>1
[5,8,4,2,1,3,6,7]=>0000000=>1111111=>1
[4,5,3,6,7,8,9,1,2]=>00000000=>11111111=>1
[5,3,4,6,7,8,9,1,2]=>00000000=>11111111=>1
[1,7,5,8,4,3,6,2]=>1000000=>0111111=>1
[5,8,1,6,4,7,2,3]=>0000000=>1111111=>1
[2,4,7,5,1,8,6,3]=>0000000=>1111111=>1
[2,3,7,1,8,5,6,4]=>0000000=>1111111=>1
[6,5,1,2,7,4,8,3]=>0000000=>1111111=>1
[3,6,5,7,8,2,4,1]=>0000000=>1111111=>1
[3,6,5,1,8,7,4,2]=>0000000=>1111111=>1
[7,8,1,2,5,4,3,6]=>0000000=>1111111=>1
[5,2,4,7,6,8,1,3]=>0000000=>1111111=>1
[3,1,5,7,4,8,6,2]=>0000000=>1111111=>1
[4,1,7,6,8,2,5,3]=>0000000=>1111111=>1
[7,2,6,4,1,5,3,8]=>0000001=>1111110=>1
[1,2,6,5,8,3,7,4]=>1100000=>0011111=>1
[7,3,5,6,1,4,2,8]=>0000001=>1111110=>1
[5,8,3,1,6,7,4,2]=>0000000=>1111111=>1
[4,5,8,1,7,3,6,2]=>0000000=>1111111=>1
[4,7,1,6,8,5,2,3]=>0000000=>1111111=>1
[5,8,7,1,6,4,2,3]=>0000000=>1111111=>1
[1,7,3,8,2,5,4,6]=>1000000=>0111111=>1
[8,4,1,3,6,7,5,2]=>0000000=>1111111=>1
[6,2,7,1,4,3,5,8]=>0000001=>1111110=>1
[8,3,2,6,5,1,7,4]=>0000000=>1111111=>1
[1,6,4,8,2,3,5,7]=>1000000=>0111111=>1
[1,4,7,3,5,8,6,2]=>1000000=>0111111=>1
[3,7,8,2,5,1,6,4]=>0000000=>1111111=>1
[8,6,1,4,3,2,7,5]=>0000000=>1111111=>1
[7,3,8,2,4,1,5,6]=>0000000=>1111111=>1
[6,3,7,8,1,2,5,4]=>0000000=>1111111=>1
[7,6,1,5,2,3,8,4]=>0000000=>1111111=>1
[5,1,8,6,7,2,3,4]=>0000000=>1111111=>1
[5,7,1,6,8,2,3,4]=>0000000=>1111111=>1
[6,8,4,2,1,7,3,5]=>0000000=>1111111=>1
[6,3,2,8,1,7,4,5]=>0000000=>1111111=>1
[6,4,1,3,7,8,5,2]=>0000000=>1111111=>1
[6,8,5,4,3,7,1,2]=>0000000=>1111111=>1
[6,1,2,4,8,3,7,5]=>0000000=>1111111=>1
[2,5,6,8,1,4,7,3]=>0000000=>1111111=>1
[7,4,1,6,5,2,3,8]=>0000001=>1111110=>1
[4,1,6,5,2,3,8,7]=>0000010=>1111101=>2
[4,5,1,7,8,6,2,3]=>0000000=>1111111=>1
[4,8,6,2,5,7,3,1]=>0000000=>1111111=>1
[1,6,8,7,4,5,3,2]=>1000000=>0111111=>1
[1,2,3,7,4,8,5,9,6]=>11100000=>00011111=>1
[1,2,3,4,7,5,9,8,6]=>11110000=>00001111=>1
[1,2,6,3,7,4,9,8,5]=>11000000=>00111111=>1
[1,2,3,8,6,4,9,7,5]=>11100000=>00011111=>1
[1,2,3,6,4,9,8,7,5]=>11100000=>00011111=>1
[5,1,6,2,7,3,9,8,4]=>00000000=>11111111=>1
[1,5,2,8,6,3,9,7,4]=>10000000=>01111111=>1
[1,5,2,6,3,9,8,7,4]=>10000000=>01111111=>1
[1,2,7,5,3,9,8,6,4]=>11000000=>00111111=>1
[1,2,5,3,9,8,7,6,4]=>11000000=>00111111=>1
[4,1,7,5,2,9,8,6,3]=>00000000=>11111111=>1
[4,1,5,2,9,8,7,6,3]=>00000000=>11111111=>1
[1,6,4,2,9,8,7,5,3]=>10000000=>01111111=>1
[1,4,2,9,8,7,6,5,3]=>10000000=>01111111=>1
[7,5,3,1,9,8,6,4,2]=>00000000=>11111111=>1
[5,3,1,9,8,7,6,4,2]=>00000000=>11111111=>1
[1,2,3,4,8,5,9,6,10,7]=>111100000=>000011111=>1
[1,2,3,4,5,8,6,10,9,7]=>111110000=>000001111=>1
[1,2,3,7,4,8,5,10,9,6]=>111000000=>000111111=>1
[1,2,3,4,9,7,5,10,8,6]=>111100000=>000011111=>1
[1,2,3,4,7,5,10,9,8,6]=>111100000=>000011111=>1
[1,6,2,7,3,8,4,10,9,5]=>100000000=>011111111=>1
[1,2,6,3,9,7,4,10,8,5]=>110000000=>001111111=>1
[1,2,6,3,7,4,10,9,8,5]=>110000000=>001111111=>1
[1,2,3,8,6,4,10,9,7,5]=>111000000=>000111111=>1
[1,2,3,6,4,10,9,8,7,5]=>111000000=>000111111=>1
[5,1,6,2,9,7,3,10,8,4]=>000000000=>111111111=>1
[5,1,6,2,7,3,10,9,8,4]=>000000000=>111111111=>1
[1,5,2,6,3,10,9,8,7,4]=>100000000=>011111111=>1
[1,2,7,5,3,10,9,8,6,4]=>110000000=>001111111=>1
[1,2,5,3,10,9,8,7,6,4]=>110000000=>001111111=>1
[7,4,1,8,5,2,10,9,6,3]=>000000000=>111111111=>1
[4,1,9,7,5,2,10,8,6,3]=>000000000=>111111111=>1
[4,1,7,5,2,10,9,8,6,3]=>000000000=>111111111=>1
[4,1,5,2,10,9,8,7,6,3]=>000000000=>111111111=>1
[1,8,6,4,2,10,9,7,5,3]=>100000000=>011111111=>1
[1,6,4,2,10,9,8,7,5,3]=>100000000=>011111111=>1
[1,4,2,10,9,8,7,6,5,3]=>100000000=>011111111=>1
[7,5,3,1,10,9,8,6,4,2]=>000000000=>111111111=>1
[5,3,1,10,9,8,7,6,4,2]=>000000000=>111111111=>1
[4,3,1,6,2,5,8,7]=>0000010=>1111101=>2
[5,3,1,4,7,8,2,6]=>0000000=>1111111=>1
[5,2,4,1,6,8,3,7]=>0000000=>1111111=>1
[2,5,3,4,6,8,1,7]=>0000000=>1111111=>1
[4,7,1,2,5,6,3,8]=>0000001=>1111110=>1
[6,7,3,1,8,2,4,5]=>0000000=>1111111=>1
[7,3,1,4,6,2,8,5]=>0000000=>1111111=>1
[7,4,1,2,5,6,3,8]=>0000001=>1111110=>1
[5,4,1,3,6,8,7,2]=>0000000=>1111111=>1
[5,7,4,8,1,6,3,2]=>0000000=>1111111=>1
[4,3,1,2,5,7,6,8]=>0001101=>1110010=>2
[1,2,3,4,5,8,9,7,6]=>11111000=>00000111=>1
[1,2,3,4,8,9,6,7,5]=>11110000=>00001111=>1
[1,2,3,8,9,5,6,7,4]=>11100000=>00011111=>1
[1,2,4,7,8,5,6,3]=>1100000=>0011111=>1
[1,2,8,9,4,5,6,7,3]=>11000000=>00111111=>1
[2,1,6,5,8,7,3,4]=>0100000=>1011111=>2
[3,1,8,4,2,7,6,5]=>0000000=>1111111=>1
[2,8,7,4,1,3,6,5]=>0000000=>1111111=>1
[8,2,3,1,7,6,4,5]=>0000000=>1111111=>1
[8,7,2,3,1,6,4,5]=>0000000=>1111111=>1
[7,2,5,8,3,1,4,6]=>0000000=>1111111=>1
[6,8,2,3,1,7,4,5]=>0000000=>1111111=>1
[8,2,5,7,3,1,4,6]=>0000000=>1111111=>1
[8,2,7,3,1,4,5,6]=>0000000=>1111111=>1
[5,3,2,8,7,1,6,4]=>0000000=>1111111=>1
[4,8,3,2,6,5,7,1]=>0000000=>1111111=>1
[1,4,2,5,6,7,9,8,3]=>10000000=>01111111=>1
[2,3,4,5,6,7,8,9,1,11,10]=>0000000010=>1111111101=>2
[2,1,4,5,6,9,7,3,8]=>01000000=>10111111=>2
[3,5,4,6,1,2,8,7]=>0000010=>1111101=>2
[3,1,5,2,9,6,7,8,4]=>00000000=>11111111=>1
[4,5,1,6,8,7,9,2,3]=>00000000=>11111111=>1
[1,4,2,5,6,7,8,10,9,3]=>100000000=>011111111=>1
[1,3,4,5,6,7,8,9,11,2,10]=>1000000000=>0111111111=>1
[2,1,4,5,6,7,10,8,3,9]=>010000000=>101111111=>2
[2,3,1,5,9,6,7,4,8]=>00100000=>11011111=>2
[1,2,4,5,7,9,6,3,8]=>11000000=>00111111=>1
[3,4,6,5,7,1,2,9,8]=>00000010=>11111101=>2
[3,1,9,4,2,6,7,8,5]=>00000000=>11111111=>1
[7,3,5,6,1,8,2,4]=>0000000=>1111111=>1
[1,2,5,3,9,6,8,7,4]=>11000000=>00111111=>1
[3,1,5,2,6,10,7,8,9,4]=>000000000=>111111111=>1
[4,5,1,7,6,8,2,9,3]=>00000000=>11111111=>1
[4,5,1,6,7,9,8,10,2,3]=>000000000=>111111111=>1
[1,4,2,5,6,7,8,9,11,10,3]=>1000000000=>0111111111=>1
[5,7,6,3,4,2,8,1]=>0000000=>1111111=>1
[4,6,7,2,3,5,8,1]=>0000000=>1111111=>1
[6,5,4,8,7,2,3,1]=>0000000=>1111111=>1
[7,2,8,3,9,4,10,5,1,6]=>000000000=>111111111=>1
[7,2,8,3,9,4,10,1,5,6]=>000000000=>111111111=>1
[7,2,8,3,9,10,4,5,1,6]=>000000000=>111111111=>1
[7,2,8,3,9,10,4,1,5,6]=>000000000=>111111111=>1
[7,2,8,3,9,10,1,4,5,6]=>000000000=>111111111=>1
[7,2,8,9,3,4,10,5,1,6]=>000000000=>111111111=>1
[7,2,8,9,3,4,10,1,5,6]=>000000000=>111111111=>1
[7,2,8,9,3,10,4,5,1,6]=>000000000=>111111111=>1
[7,2,8,9,3,10,4,1,5,6]=>000000000=>111111111=>1
[7,2,8,9,3,10,1,4,5,6]=>000000000=>111111111=>1
[7,2,8,9,10,3,4,5,1,6]=>000000000=>111111111=>1
[7,2,8,9,10,3,4,1,5,6]=>000000000=>111111111=>1
[7,2,8,9,10,3,1,4,5,6]=>000000000=>111111111=>1
[7,8,2,3,9,4,10,5,1,6]=>000000000=>111111111=>1
[7,8,2,3,9,4,10,1,5,6]=>000000000=>111111111=>1
[7,8,2,3,9,10,4,5,1,6]=>000000000=>111111111=>1
[7,8,2,3,9,10,4,1,5,6]=>000000000=>111111111=>1
[7,8,2,3,9,10,1,4,5,6]=>000000000=>111111111=>1
[7,8,2,9,3,4,10,5,1,6]=>000000000=>111111111=>1
[7,8,2,9,3,4,10,1,5,6]=>000000000=>111111111=>1
[7,8,2,9,3,10,4,5,1,6]=>000000000=>111111111=>1
[7,8,2,9,3,10,4,1,5,6]=>000000000=>111111111=>1
[7,8,2,9,3,10,1,4,5,6]=>000000000=>111111111=>1
[7,8,2,9,10,3,4,5,1,6]=>000000000=>111111111=>1
[7,8,2,9,10,3,4,1,5,6]=>000000000=>111111111=>1
[7,8,2,9,10,3,1,4,5,6]=>000000000=>111111111=>1
[7,8,2,9,10,1,3,4,5,6]=>000000000=>111111111=>1
[7,8,9,2,3,4,10,5,1,6]=>000000000=>111111111=>1
[7,8,9,2,3,4,10,1,5,6]=>000000000=>111111111=>1
[7,8,9,2,3,10,4,5,1,6]=>000000000=>111111111=>1
[7,8,9,2,3,10,4,1,5,6]=>000000000=>111111111=>1
[7,8,9,2,3,10,1,4,5,6]=>000000000=>111111111=>1
[7,8,9,2,10,3,4,5,1,6]=>000000000=>111111111=>1
[7,8,9,2,10,3,4,1,5,6]=>000000000=>111111111=>1
[7,8,9,2,10,3,1,4,5,6]=>000000000=>111111111=>1
[7,8,9,2,10,1,3,4,5,6]=>000000000=>111111111=>1
[7,8,9,10,2,3,4,1,5,6]=>000000000=>111111111=>1
[7,8,9,10,2,3,1,4,5,6]=>000000000=>111111111=>1
[7,8,9,10,2,1,3,4,5,6]=>000000000=>111111111=>1
[4,8,7,6,5,3,2,1,9]=>00000001=>11111110=>1
[5,9,8,7,6,4,3,2,1,10]=>000000001=>111111110=>1
[5,8,7,4,6,3,2,1,9]=>00000001=>11111110=>1
[8,4,7,6,5,3,2,1,9]=>00000001=>11111110=>1
[5,7,4,3,6,2,1,8]=>0000001=>1111110=>1
[6,9,8,5,7,4,1,3,2]=>00000000=>11111111=>1
[9,8,7,5,1,6,4,3,2]=>00000000=>11111111=>1
[10,9,8,6,1,7,5,4,3,2]=>000000000=>111111111=>1
[1,2,8,3,4,5,6,9,7]=>11000000=>00111111=>1
[1,9,5,2,3,8,4,6,7]=>10000000=>01111111=>1
[1,2,9,3,4,5,6,7,10,8]=>110000000=>001111111=>1
[1,8,2,9,4,3,5,6,7]=>10000000=>01111111=>1
[1,3,2,4,9,8,5,6,7]=>10110000=>01001111=>2
[2,1,3,4,5,9,8,6,7]=>01111000=>10000111=>2
[1,2,3,4,5,9,6,7,10,8]=>111110000=>000001111=>1
[9,1,7,2,3,4,5,8,6]=>00000000=>11111111=>1
[1,10,6,2,3,4,9,5,7,8]=>100000000=>011111111=>1
[1,8,5,2,3,4,6,9,7]=>10000000=>01111111=>1
[9,8,1,2,3,5,6,4,7]=>00000000=>11111111=>1
[1,5,2,9,3,10,4,6,7,8]=>100000000=>011111111=>1
[1,4,2,3,9,5,6,8,7]=>10010000=>01101111=>2
[1,8,5,6,2,3,7,4]=>1000000=>0111111=>1
[4,9,8,1,2,5,3,6,7]=>00000000=>11111111=>1
[1,2,4,3,10,9,5,6,7,8]=>110100000=>001011111=>2
[1,3,2,4,5,9,6,8,7]=>10111000=>01000111=>2
[1,8,3,9,4,2,5,6,7]=>10000000=>01111111=>1
[1,3,2,4,5,10,9,6,7,8]=>101110000=>010001111=>2
[1,2,3,4,5,10,6,7,8,11,9]=>1111100000=>0000011111=>1
[2,3,1,4,9,8,5,6,7]=>00110000=>11001111=>2
[2,1,3,4,5,9,6,10,7,8]=>011110000=>100001111=>2
[8,5,6,1,3,2,7,4]=>0000000=>1111111=>1
[4,5,8,3,6,1,7,2]=>0000000=>1111111=>1
[4,5,8,7,2,3,1,6]=>0000000=>1111111=>1
[8,2,6,4,3,7,5,1]=>0000000=>1111111=>1
[6,3,1,8,7,4,5,2]=>0000000=>1111111=>1
[8,6,3,2,7,4,5,1]=>0000000=>1111111=>1
[1,3,6,8,7,4,5,2]=>1000000=>0111111=>1
[5,7,1,3,6,2,4,8]=>0000001=>1111110=>1
[4,7,1,3,2,5,8,6]=>0000000=>1111111=>1
[6,3,1,5,4,8,2,7]=>0000000=>1111111=>1
[4,7,6,3,5,2,8,1]=>0000000=>1111111=>1
[1,7,5,3,4,8,6,2]=>1000000=>0111111=>1
[5,8,2,3,4,7,6,1]=>0000000=>1111111=>1
[8,7,3,2,6,4,5,1]=>0000000=>1111111=>1
[8,3,1,4,7,5,2,6]=>0000000=>1111111=>1
[5,3,1,6,4,8,7,2]=>0000000=>1111111=>1
[3,4,8,5,7,2,6,1]=>0000000=>1111111=>1
[8,5,1,2,7,6,4,3]=>0000000=>1111111=>1
[3,7,8,5,6,2,4,1]=>0000000=>1111111=>1
[7,4,3,6,2,5,8,1]=>0000000=>1111111=>1
[4,3,8,7,1,6,2,5]=>0000000=>1111111=>1
[1,5,3,8,4,7,2,6]=>1000000=>0111111=>1
[8,2,3,1,6,5,7,4]=>0000000=>1111111=>1
[8,4,2,7,1,3,6,5]=>0000000=>1111111=>1
[8,4,2,3,1,6,7,5]=>0000000=>1111111=>1
[4,7,2,3,6,5,8,1]=>0000000=>1111111=>1
[3,8,2,6,4,7,1,5]=>0000000=>1111111=>1
[1,7,5,8,6,2,4,3]=>1000000=>0111111=>1
[6,5,1,7,4,8,3,2]=>0000000=>1111111=>1
[10,9,8,6,7,5,4,3,2,1]=>000000000=>111111111=>1
[7,6,3,5,1,4,8,2]=>0000000=>1111111=>1
[6,5,4,1,7,2,3,8]=>0000001=>1111110=>1
[8,3,6,1,7,4,5,2]=>0000000=>1111111=>1
[7,1,2,6,4,8,3,5]=>0000000=>1111111=>1
[3,5,1,8,6,2,4,7]=>0000000=>1111111=>1
[8,7,5,6,4,3,2,1,9]=>00000001=>11111110=>1
[8,6,5,7,4,3,2,1,9]=>00000001=>11111110=>1
[9,8,7,6,4,3,2,5,1]=>00000000=>11111111=>1
[9,8,7,6,4,3,5,2,1]=>00000000=>11111111=>1
[8,5,6,7,4,3,2,1,9]=>00000001=>11111110=>1
[10,9,7,6,8,5,4,3,2,1]=>000000000=>111111111=>1
[6,7,5,8,4,3,2,1,9]=>00000001=>11111110=>1
[10,8,7,6,9,5,4,3,2,1]=>000000000=>111111111=>1
[8,9,7,6,4,3,2,1,5]=>00000000=>11111111=>1
[7,6,5,3,2,1,4,8,9]=>00000011=>11111100=>1
[9,8,7,6,4,3,5,1,2]=>00000000=>11111111=>1
[9,8,7,6,4,3,2,5,1,10]=>000000001=>111111110=>1
[9,8,7,6,4,5,2,3,1]=>00000000=>11111111=>1
[9,8,7,6,4,3,5,2,1,10]=>000000001=>111111110=>1
[9,8,7,6,5,3,4,2,1]=>00000000=>11111111=>1
[1,8,7,5,4,6,2,3]=>1000000=>0111111=>1
[8,1,6,7,4,5,3,2]=>0000000=>1111111=>1
[8,1,6,4,7,5,3,2]=>0000000=>1111111=>1
[1,6,4,3,5,8,2,7]=>1000000=>0111111=>1
[5,1,4,3,7,8,6,2]=>0000000=>1111111=>1
[5,7,1,8,6,3,2,4]=>0000000=>1111111=>1
[5,7,6,3,4,2,1,8]=>0000001=>1111110=>1
[4,1,3,7,6,5,2,8]=>0000001=>1111110=>1
[4,3,6,1,2,7,8,5]=>0000000=>1111111=>1
[1,10,9,8,6,5,7,4,3,2]=>100000000=>011111111=>1
[2,9,8,6,5,7,4,3,1]=>00000000=>11111111=>1
[5,8,3,6,7,2,4,1]=>0000000=>1111111=>1
[8,1,6,2,5,7,4,3]=>0000000=>1111111=>1
[2,7,1,5,3,6,8,4]=>0000000=>1111111=>1
[6,8,7,3,4,2,5,1]=>0000000=>1111111=>1
[1,8,6,2,4,7,5,3]=>1000000=>0111111=>1
[5,7,3,6,4,2,1,8]=>0000001=>1111110=>1
[5,7,3,6,4,1,8,2]=>0000000=>1111111=>1
[3,7,5,6,4,1,8,2]=>0000000=>1111111=>1
[9,6,7,4,5,2,3,1,8]=>00000000=>11111111=>1
[2,8,5,7,3,4,6,1]=>0000000=>1111111=>1
[2,1,3,8,5,4,6,7]=>0110000=>1001111=>2
[5,3,6,8,2,4,1,7]=>0000000=>1111111=>1
[1,7,8,6,3,2,4,5]=>1000000=>0111111=>1
[7,1,2,5,3,8,4,6]=>0000000=>1111111=>1
[3,7,4,2,5,1,8,6]=>0000000=>1111111=>1
[1,8,3,4,5,7,2,6]=>1000000=>0111111=>1
[4,5,7,6,2,1,3,8]=>0000001=>1111110=>1
[7,8,2,6,5,4,3,1]=>0000000=>1111111=>1
[5,3,7,8,4,2,1,6]=>0000000=>1111111=>1
[7,3,6,8,1,5,4,2]=>0000000=>1111111=>1
[3,8,5,2,1,6,7,4]=>0000000=>1111111=>1
[4,8,7,1,2,5,3,6]=>0000000=>1111111=>1
[8,7,2,6,1,4,3,5]=>0000000=>1111111=>1
[6,1,7,3,8,2,4,5]=>0000000=>1111111=>1
[7,1,8,6,4,2,3,5]=>0000000=>1111111=>1
[4,1,3,5,8,2,6,7]=>0000000=>1111111=>1
[1,8,5,7,4,6,3,2]=>1000000=>0111111=>1
[1,4,7,6,8,3,5,2]=>1000000=>0111111=>1
[1,7,2,8,6,5,3,4]=>1000000=>0111111=>1
[5,7,1,6,4,2,3,8]=>0000001=>1111110=>1
[4,8,2,7,5,1,6,3]=>0000000=>1111111=>1
[2,8,4,6,7,1,5,3]=>0000000=>1111111=>1
[3,8,5,1,4,2,6,7]=>0000000=>1111111=>1
[1,7,6,2,5,3,8,4]=>1000000=>0111111=>1
[1,7,5,2,4,3,8,6]=>1000000=>0111111=>1
[2,8,5,1,4,3,6,7]=>0000000=>1111111=>1
[9,7,6,5,4,3,2,8,1]=>00000000=>11111111=>1
[3,1,4,6,2,5,8,7,9]=>00000101=>11111010=>2
[1,3,2,5,7,4,6,9,8]=>10100010=>01011101=>3
[1,9,8,5,6,7,4,3,2]=>10000000=>01111111=>1
[1,10,9,8,5,6,7,4,3,2]=>100000000=>011111111=>1
[1,9,8,5,4,6,7,3,2]=>10000000=>01111111=>1
[1,10,9,5,6,7,8,4,3,2]=>100000000=>011111111=>1
[1,9,5,4,6,7,8,3,2]=>10000000=>01111111=>1
[1,10,4,5,6,7,8,9,3,2]=>100000000=>011111111=>1
[5,1,7,3,2,6,8,4]=>0000000=>1111111=>1
[4,1,7,5,6,8,2,3]=>0000000=>1111111=>1
[3,7,6,2,1,4,5,8]=>0000001=>1111110=>1
[1,6,8,7,2,5,4,3]=>1000000=>0111111=>1
[1,4,8,7,6,3,5,2]=>1000000=>0111111=>1
[1,2,3,4,7,5,6,9,8]=>11110010=>00001101=>2
[9,8,7,6,5,3,1,4,2]=>00000000=>11111111=>1
[4,6,7,5,2,3,1,8]=>0000001=>1111110=>1
[6,2,5,3,1,8,7,4]=>0000000=>1111111=>1
[6,2,5,3,8,7,1,4]=>0000000=>1111111=>1
[6,4,5,3,8,7,1,2]=>0000000=>1111111=>1
[1,6,4,5,8,7,3,2]=>1000000=>0111111=>1
[8,4,7,5,2,3,1,6]=>0000000=>1111111=>1
[8,2,7,4,5,3,1,6]=>0000000=>1111111=>1
[8,2,4,7,5,3,1,6]=>0000000=>1111111=>1
[8,2,6,7,5,3,1,4]=>0000000=>1111111=>1
[8,4,6,7,5,3,1,2]=>0000000=>1111111=>1
[6,4,5,8,7,3,1,2]=>0000000=>1111111=>1
[6,2,8,7,5,3,1,4]=>0000000=>1111111=>1
[4,6,5,3,8,7,1,2]=>0000000=>1111111=>1
[6,7,2,4,5,3,1,8]=>0000001=>1111110=>1
[6,8,7,4,5,3,1,2]=>0000000=>1111111=>1
[2,8,4,7,5,3,1,6]=>0000000=>1111111=>1
[5,8,7,4,6,3,1,2]=>0000000=>1111111=>1
[6,5,8,4,7,2,1,3]=>0000000=>1111111=>1
[4,8,6,2,5,7,1,3]=>0000000=>1111111=>1
[8,1,6,2,5,7,3,4]=>0000000=>1111111=>1
[6,8,1,2,4,7,3,5]=>0000000=>1111111=>1
[8,1,5,3,2,7,4,6]=>0000000=>1111111=>1
[8,3,7,6,2,5,4,1]=>0000000=>1111111=>1
[1,2,7,4,5,6,8,9,3]=>11000000=>00111111=>1
[1,2,3,4,7,8,5,6,9]=>11110001=>00001110=>1
[1,2,3,4,6,5,8,7,9]=>11110101=>00001010=>2
[1,2,3,4,8,9,5,6,7]=>11110000=>00001111=>1
[2,1,7,8,9,3,4,5,6]=>01000000=>10111111=>2
[2,6,7,8,9,10,1,3,4,5]=>000000000=>111111111=>1
[1,6,2,3,8,5,7,4]=>1000000=>0111111=>1
[3,4,2,6,8,5,7,1]=>0000000=>1111111=>1
[7,4,1,3,6,8,2,5]=>0000000=>1111111=>1
[6,8,1,2,7,3,4,5]=>0000000=>1111111=>1
[1,6,2,8,7,3,4,5]=>1000000=>0111111=>1
[2,3,8,1,4,6,5,7]=>0000000=>1111111=>1
[3,6,2,4,7,5,8,1]=>0000000=>1111111=>1
[3,1,8,4,6,2,5,7]=>0000000=>1111111=>1
[4,2,7,3,5,8,1,6]=>0000000=>1111111=>1
[3,1,8,4,5,6,2,7]=>0000000=>1111111=>1
[4,2,7,8,6,3,1,5]=>0000000=>1111111=>1
[7,1,4,2,8,6,3,5]=>0000000=>1111111=>1
[2,3,7,4,8,1,6,5]=>0000000=>1111111=>1
[1,6,3,5,8,7,4,2]=>1000000=>0111111=>1
[8,4,6,3,5,1,7,2]=>0000000=>1111111=>1
[7,3,2,6,8,4,5,1]=>0000000=>1111111=>1
[2,4,5,7,1,6,8,3]=>0000000=>1111111=>1
[8,4,2,6,7,3,5,1]=>0000000=>1111111=>1
[2,3,1,5,6,8,9,4,7]=>00100000=>11011111=>2
[5,6,2,4,8,7,3,1]=>0000000=>1111111=>1
[8,5,6,2,3,7,4,1]=>0000000=>1111111=>1
[7,8,1,4,5,6,2,3]=>0000000=>1111111=>1
[5,6,7,8,9,1,3,4,2]=>00000000=>11111111=>1
[6,7,8,9,1,3,4,5,2]=>00000000=>11111111=>1
[6,7,8,9,1,4,5,2,3]=>00000000=>11111111=>1
[6,7,8,9,1,4,5,3,2]=>00000000=>11111111=>1
[6,7,8,9,1,5,4,3,2]=>00000000=>11111111=>1
[7,8,9,1,4,5,6,2,3]=>00000000=>11111111=>1
[7,8,9,1,4,5,6,3,2]=>00000000=>11111111=>1
[7,8,9,1,5,6,3,4,2]=>00000000=>11111111=>1
[7,8,9,1,5,6,4,3,2]=>00000000=>11111111=>1
[7,8,9,1,6,5,4,3,2]=>00000000=>11111111=>1
[8,9,1,5,6,7,3,4,2]=>00000000=>11111111=>1
[8,9,1,5,6,7,4,3,2]=>00000000=>11111111=>1
[8,9,1,6,7,4,5,2,3]=>00000000=>11111111=>1
[8,9,1,6,7,4,5,3,2]=>00000000=>11111111=>1
[8,9,1,6,7,5,4,3,2]=>00000000=>11111111=>1
[9,1,7,8,5,6,3,4,2]=>00000000=>11111111=>1
[9,1,7,8,5,6,4,3,2]=>00000000=>11111111=>1
[5,6,7,8,9,10,1,3,4,2]=>000000000=>111111111=>1
[5,6,7,8,9,10,1,4,3,2]=>000000000=>111111111=>1
[7,8,9,10,1,4,5,6,2,3]=>000000000=>111111111=>1
[7,8,9,10,1,4,5,6,3,2]=>000000000=>111111111=>1
[7,8,9,10,1,5,6,4,3,2]=>000000000=>111111111=>1
[7,8,9,10,1,6,5,4,3,2]=>000000000=>111111111=>1
[8,9,10,1,4,5,6,7,2,3]=>000000000=>111111111=>1
[8,9,10,1,4,5,6,7,3,2]=>000000000=>111111111=>1
[8,9,10,1,5,6,7,2,3,4]=>000000000=>111111111=>1
[8,9,10,1,5,6,7,4,3,2]=>000000000=>111111111=>1
[8,9,10,1,6,7,4,5,2,3]=>000000000=>111111111=>1
[8,9,10,1,6,7,4,5,3,2]=>000000000=>111111111=>1
[8,9,10,1,6,7,5,4,3,2]=>000000000=>111111111=>1
[8,9,10,1,7,6,5,4,3,2]=>000000000=>111111111=>1
[9,10,1,6,7,8,3,4,5,2]=>000000000=>111111111=>1
[9,10,1,6,7,8,4,5,2,3]=>000000000=>111111111=>1
[9,10,1,6,7,8,4,5,3,2]=>000000000=>111111111=>1
[9,10,1,6,7,8,5,4,3,2]=>000000000=>111111111=>1
[9,10,1,7,8,5,6,3,4,2]=>000000000=>111111111=>1
[9,10,1,7,8,5,6,4,3,2]=>000000000=>111111111=>1
[9,10,1,7,8,6,5,4,3,2]=>000000000=>111111111=>1
[10,1,8,9,6,7,4,5,3,2]=>000000000=>111111111=>1
[10,1,8,9,6,7,5,4,3,2]=>000000000=>111111111=>1
[10,1,8,9,7,6,5,4,3,2]=>000000000=>111111111=>1
[8,3,1,2,5,4,7,6]=>0000000=>1111111=>1
[8,1,5,3,7,4,2,6]=>0000000=>1111111=>1
[1,2,6,7,8,3,5,4]=>1100000=>0011111=>1
[1,2,4,8,6,7,3,5]=>1100000=>0011111=>1
[8,1,2,6,5,7,3,4]=>0000000=>1111111=>1
[7,1,2,6,5,8,3,4]=>0000000=>1111111=>1
[2,6,1,4,7,5,8,3]=>0000000=>1111111=>1
[3,1,5,7,2,6,8,4]=>0000000=>1111111=>1
[3,1,7,5,2,6,8,4]=>0000000=>1111111=>1
[3,2,7,5,1,6,8,4]=>0000000=>1111111=>1
[5,2,7,3,1,6,8,4]=>0000000=>1111111=>1
[6,7,2,1,3,4,8,5]=>0000000=>1111111=>1
[4,6,3,1,2,7,8,5]=>0000000=>1111111=>1
[2,3,4,5,7,9,6,8,1]=>00000000=>11111111=>1
[2,3,4,6,9,5,7,8,1]=>00000000=>11111111=>1
[2,3,5,6,8,4,7,1]=>0000000=>1111111=>1
[2,3,5,9,4,6,7,8,1]=>00000000=>11111111=>1
[2,4,5,8,3,6,7,1]=>0000000=>1111111=>1
[2,4,9,3,5,6,7,8,1]=>00000000=>11111111=>1
[8,1,4,3,6,2,5,7]=>0000000=>1111111=>1
[1,6,3,7,8,4,2,5]=>1000000=>0111111=>1
[5,2,1,3,8,4,6,7]=>0000000=>1111111=>1
[1,4,3,5,8,2,6,7]=>1000000=>0111111=>1
[2,1,3,8,6,4,5,7]=>0110000=>1001111=>2
[1,3,6,4,5,8,2,7]=>1000000=>0111111=>1
[6,1,4,3,5,8,2,7]=>0000000=>1111111=>1
[6,5,1,3,8,2,4,7]=>0000000=>1111111=>1
[1,4,3,8,6,2,5,7]=>1000000=>0111111=>1
[4,1,3,8,6,2,5,7]=>0000000=>1111111=>1
[6,4,7,8,3,5,1,2]=>0000000=>1111111=>1
[3,5,6,7,1,8,4,2]=>0000000=>1111111=>1
[3,5,2,4,8,6,7,1]=>0000000=>1111111=>1
[3,7,6,1,4,8,5,2]=>0000000=>1111111=>1
[8,4,7,1,5,6,2,3]=>0000000=>1111111=>1
[2,3,4,5,6,1,8,9,7]=>00000100=>11111011=>2
[2,3,4,5,1,7,8,9,6]=>00001000=>11110111=>2
[2,6,3,1,4,7,8,5]=>0000000=>1111111=>1
[2,9,3,4,5,6,1,7,8]=>00000000=>11111111=>1
[2,3,4,5,6,7,1,9,10,8]=>000000100=>111111011=>2
[2,7,3,4,1,8,5,6]=>0000000=>1111111=>1
[2,8,3,4,5,1,6,9,7]=>00000000=>11111111=>1
[2,7,3,4,1,5,8,9,6]=>00000000=>11111111=>1
[2,3,4,5,1,7,8,9,10,6]=>000010000=>111101111=>2
[2,6,3,1,4,7,8,9,5]=>00000000=>11111111=>1
[2,3,1,5,6,7,8,9,10,4]=>001000000=>110111111=>2
[8,6,4,5,1,3,7,2]=>0000000=>1111111=>1
[7,4,8,5,3,6,1,2]=>0000000=>1111111=>1
[8,4,6,5,1,3,7,2]=>0000000=>1111111=>1
[4,5,3,8,7,1,2,6]=>0000000=>1111111=>1
[8,5,4,7,6,1,2,3]=>0000000=>1111111=>1
[2,3,7,8,1,4,6,5]=>0000000=>1111111=>1
[8,2,3,5,4,1,7,6]=>0000000=>1111111=>1
[7,1,3,8,2,4,6,5]=>0000000=>1111111=>1
[7,2,3,6,4,1,8,5]=>0000000=>1111111=>1
[6,5,2,4,1,8,3,7]=>0000000=>1111111=>1
[5,7,2,4,1,3,8,6]=>0000000=>1111111=>1
[6,2,5,4,1,8,3,7]=>0000000=>1111111=>1
[4,2,5,3,7,6,9,8,1]=>00000000=>11111111=>1
[4,2,6,3,7,5,9,8,1]=>00000000=>11111111=>1
[4,2,6,3,8,5,9,7,1]=>00000000=>11111111=>1
[4,2,6,3,8,5,1,7,9]=>00000001=>11111110=>1
[4,2,6,3,5,8,1,7]=>0000000=>1111111=>1
[4,2,6,3,8,5,7,1,9]=>00000001=>11111110=>1
[4,2,6,3,5,8,7,1,9]=>00000001=>11111110=>1
[4,2,3,6,5,8,7,1,9]=>00000001=>11111110=>1
[4,2,5,3,7,6,9,8,1,10]=>000000001=>111111110=>1
[5,2,6,3,7,4,9,8,1]=>00000000=>11111111=>1
[4,2,6,3,7,5,9,8,1,10]=>000000001=>111111110=>1
[4,2,7,3,8,5,9,6,1]=>00000000=>11111111=>1
[4,2,6,3,8,5,9,7,1,10]=>000000001=>111111110=>1
[4,2,6,3,9,5,1,7,8]=>00000000=>11111111=>1
[4,2,6,3,8,5,10,7,1,9]=>000000000=>111111111=>1
[4,2,6,3,8,5,7,9,1]=>00000000=>11111111=>1
[4,2,6,3,8,5,10,7,9,1]=>000000000=>111111111=>1
[4,2,6,3,5,8,1,7,9]=>00000001=>11111110=>1
[4,2,6,3,8,5,7,10,9,1]=>000000000=>111111111=>1
[4,2,3,6,8,5,7,1,9]=>00000001=>11111110=>1
[4,2,6,3,5,8,7,10,9,1]=>000000000=>111111111=>1
[2,4,6,3,5,8,7,1,9]=>00000001=>11111110=>1
[4,2,3,6,5,8,7,10,9,1]=>000000000=>111111111=>1
[1,8,5,4,2,6,3,7]=>1000000=>0111111=>1
[3,4,5,6,9,2,1,8,7]=>00000000=>11111111=>1
[3,4,5,8,2,9,1,7,6]=>00000000=>11111111=>1
[3,4,7,2,8,9,1,5,6]=>00000000=>11111111=>1
[3,6,2,7,8,9,1,5,4]=>00000000=>11111111=>1
[5,2,6,7,8,9,1,4,3]=>00000000=>11111111=>1
[3,4,5,6,9,1,7,8,2]=>00000000=>11111111=>1
[3,4,5,6,7,10,2,1,9,8]=>000000000=>111111111=>1
[3,4,5,8,9,6,1,7,2]=>00000000=>11111111=>1
[3,4,5,6,9,2,10,1,8,7]=>000000000=>111111111=>1
[3,4,7,8,5,9,1,2,6]=>00000000=>11111111=>1
[3,4,5,9,2,6,1,8,7]=>00000000=>11111111=>1
[3,4,5,8,2,9,10,1,6,7]=>000000000=>111111111=>1
[3,6,7,4,8,9,1,5,2]=>00000000=>11111111=>1
[3,4,8,2,5,9,1,7,6]=>00000000=>11111111=>1
[3,4,7,2,8,9,10,1,6,5]=>000000000=>111111111=>1
[5,6,3,7,8,9,1,4,2]=>00000000=>11111111=>1
[3,7,2,4,8,9,1,5,6]=>00000000=>11111111=>1
[3,6,2,7,8,9,10,1,5,4]=>000000000=>111111111=>1
[6,2,3,7,8,9,1,5,4]=>00000000=>11111111=>1
[5,2,6,7,8,9,10,1,3,4]=>000000000=>111111111=>1
[1,3,2,4,5,6,9,7,8]=>10111100=>01000011=>2
[2,3,1,4,5,6,9,7,8]=>00111100=>11000011=>2
[6,2,5,7,4,1,8,3]=>0000000=>1111111=>1
[3,6,1,8,7,4,5,2]=>0000000=>1111111=>1
[5,3,2,7,6,4,1,8]=>0000001=>1111110=>1
[5,3,7,4,6,2,1,8]=>0000001=>1111110=>1
[5,7,3,2,1,8,6,4]=>0000000=>1111111=>1
[5,7,6,3,2,1,8,4]=>0000000=>1111111=>1
[3,2,7,5,4,1,8,6]=>0000000=>1111111=>1
[1,7,3,5,4,2,6,8]=>1000001=>0111110=>1
[5,3,7,4,1,8,6,2]=>0000000=>1111111=>1
[7,3,5,4,1,6,8,2]=>0000000=>1111111=>1
[7,5,1,6,8,3,2,4]=>0000000=>1111111=>1
[5,3,1,7,6,8,2,4]=>0000000=>1111111=>1
[7,1,5,3,2,4,8,6]=>0000000=>1111111=>1
[5,6,7,8,9,3,2,1,4]=>00000000=>11111111=>1
[6,7,8,9,3,4,1,2,5]=>00000000=>11111111=>1
[6,7,8,9,3,4,2,1,5]=>00000000=>11111111=>1
[7,8,9,3,4,5,1,2,6]=>00000000=>11111111=>1
[7,8,9,3,4,5,2,1,6]=>00000000=>11111111=>1
[7,8,9,4,5,2,3,1,6]=>00000000=>11111111=>1
[7,8,9,4,5,3,2,1,6]=>00000000=>11111111=>1
[8,9,4,5,6,2,3,1,7]=>00000000=>11111111=>1
[8,9,4,5,6,3,2,1,7]=>00000000=>11111111=>1
[8,9,5,6,3,4,1,2,7]=>00000000=>11111111=>1
[8,9,5,6,3,4,2,1,7]=>00000000=>11111111=>1
[8,9,5,6,4,3,2,1,7]=>00000000=>11111111=>1
[9,6,7,4,5,3,2,1,8]=>00000000=>11111111=>1
[5,6,7,8,9,10,3,2,1,4]=>000000000=>111111111=>1
[7,8,9,10,3,4,5,1,2,6]=>000000000=>111111111=>1
[7,8,9,10,3,4,5,2,1,6]=>000000000=>111111111=>1
[7,8,9,10,4,5,2,3,1,6]=>000000000=>111111111=>1
[7,8,9,10,4,5,3,2,1,6]=>000000000=>111111111=>1
[7,8,9,10,5,4,3,2,1,6]=>000000000=>111111111=>1
[8,9,10,3,4,5,6,1,2,7]=>000000000=>111111111=>1
[8,9,10,3,4,5,6,2,1,7]=>000000000=>111111111=>1
[8,9,10,4,5,6,1,2,3,7]=>000000000=>111111111=>1
[8,9,10,4,5,6,3,2,1,7]=>000000000=>111111111=>1
[8,9,10,5,6,3,4,1,2,7]=>000000000=>111111111=>1
[8,9,10,5,6,3,4,2,1,7]=>000000000=>111111111=>1
[8,9,10,5,6,4,3,2,1,7]=>000000000=>111111111=>1
[8,9,10,6,5,4,3,2,1,7]=>000000000=>111111111=>1
[9,10,5,6,7,2,3,4,1,8]=>000000000=>111111111=>1
[9,10,5,6,7,3,4,1,2,8]=>000000000=>111111111=>1
[9,10,5,6,7,3,4,2,1,8]=>000000000=>111111111=>1
[9,10,5,6,7,4,3,2,1,8]=>000000000=>111111111=>1
[9,10,6,7,4,5,3,2,1,8]=>000000000=>111111111=>1
[9,10,6,7,5,4,3,2,1,8]=>000000000=>111111111=>1
[9,10,7,6,5,4,3,2,1,8]=>000000000=>111111111=>1
[10,7,8,5,6,3,4,2,1,9]=>000000000=>111111111=>1
[10,7,8,5,6,4,3,2,1,9]=>000000000=>111111111=>1
[10,7,8,6,5,4,3,2,1,9]=>000000000=>111111111=>1
[1,8,3,6,2,4,7,5]=>1000000=>0111111=>1
[1,8,7,5,6,4,2,3]=>1000000=>0111111=>1
[6,8,2,1,5,4,3,7]=>0000000=>1111111=>1
[6,3,2,1,5,8,4,7]=>0000000=>1111111=>1
[4,3,5,6,2,8,1,7]=>0000000=>1111111=>1
[6,3,5,2,7,8,4,1]=>0000000=>1111111=>1
[4,5,3,1,6,8,2,7]=>0000000=>1111111=>1
[3,4,6,7,5,1,8,2]=>0000000=>1111111=>1
[7,4,1,2,5,6,8,3]=>0000000=>1111111=>1
[4,8,2,6,7,1,5,3]=>0000000=>1111111=>1
[9,7,1,8,2,3,4,5,6]=>00000000=>11111111=>1
[9,6,1,7,2,8,3,4,5]=>00000000=>11111111=>1
[8,6,1,9,7,2,3,4,5]=>00000000=>11111111=>1
[9,8,6,1,7,2,3,4,5]=>00000000=>11111111=>1
[8,5,1,9,6,2,7,3,4]=>00000000=>11111111=>1
[9,8,5,1,6,2,7,3,4]=>00000000=>11111111=>1
[9,7,5,1,8,6,2,3,4]=>00000000=>11111111=>1
[9,8,7,5,1,6,2,3,4]=>00000000=>11111111=>1
[9,7,4,1,8,5,2,6,3]=>00000000=>11111111=>1
[9,8,7,4,1,5,2,6,3]=>00000000=>11111111=>1
[8,6,4,1,9,7,5,2,3]=>00000000=>11111111=>1
[9,8,6,4,1,7,5,2,3]=>00000000=>11111111=>1
[9,8,7,6,4,1,5,2,3]=>00000000=>11111111=>1
[9,8,7,5,3,1,6,4,2]=>00000000=>11111111=>1
[10,7,1,8,2,9,3,4,5,6]=>000000000=>111111111=>1
[9,7,1,10,8,2,3,4,5,6]=>000000000=>111111111=>1
[10,9,7,1,8,2,3,4,5,6]=>000000000=>111111111=>1
[10,6,1,7,2,8,3,9,4,5]=>000000000=>111111111=>1
[9,6,1,10,7,2,8,3,4,5]=>000000000=>111111111=>1
[10,9,6,1,7,2,8,3,4,5]=>000000000=>111111111=>1
[10,8,6,1,9,7,2,3,4,5]=>000000000=>111111111=>1
[10,9,8,6,1,7,2,3,4,5]=>000000000=>111111111=>1
[9,5,1,10,6,2,7,3,8,4]=>000000000=>111111111=>1
[10,9,5,1,6,2,7,3,8,4]=>000000000=>111111111=>1
[8,5,1,9,6,2,10,7,3,4]=>000000000=>111111111=>1
[10,8,5,1,9,6,2,7,3,4]=>000000000=>111111111=>1
[10,9,8,5,1,6,2,7,3,4]=>000000000=>111111111=>1
[9,7,5,1,10,8,6,2,3,4]=>000000000=>111111111=>1
[10,9,7,5,1,8,6,2,3,4]=>000000000=>111111111=>1
[10,9,8,7,5,1,6,2,3,4]=>000000000=>111111111=>1
[9,7,4,1,10,8,5,2,6,3]=>000000000=>111111111=>1
[10,9,7,4,1,8,5,2,6,3]=>000000000=>111111111=>1
[10,9,8,7,4,1,5,2,6,3]=>000000000=>111111111=>1
[10,8,6,4,1,9,7,5,2,3]=>000000000=>111111111=>1
[10,9,8,6,4,1,7,5,2,3]=>000000000=>111111111=>1
[10,9,8,7,6,4,1,5,2,3]=>000000000=>111111111=>1
[10,9,7,5,3,1,8,6,4,2]=>000000000=>111111111=>1
[10,9,8,7,5,3,1,6,4,2]=>000000000=>111111111=>1
[10,9,8,7,6,5,3,1,4,2]=>000000000=>111111111=>1
[1,5,2,4,7,6,8,3]=>1000000=>0111111=>1
[1,4,3,6,5,8,7,9,2]=>10000000=>01111111=>1
[1,4,2,6,5,8,7,9,3]=>10000000=>01111111=>1
[1,5,2,6,4,8,7,9,3]=>10000000=>01111111=>1
[1,5,2,7,4,8,6,9,3]=>10000000=>01111111=>1
[1,5,2,7,4,9,6,8,3]=>10000000=>01111111=>1
[1,5,2,7,4,6,9,8,3]=>10000000=>01111111=>1
[1,5,2,4,7,6,9,8,3]=>10000000=>01111111=>1
[1,2,5,4,7,6,9,8,3]=>11000000=>00111111=>1
[1,4,2,6,5,8,7,10,9,3]=>100000000=>011111111=>1
[1,5,2,6,3,8,7,9,4]=>10000000=>01111111=>1
[1,5,2,6,4,8,7,10,9,3]=>100000000=>011111111=>1
[1,6,2,7,4,8,5,9,3]=>10000000=>01111111=>1
[1,5,2,7,4,8,6,10,9,3]=>100000000=>011111111=>1
[1,5,2,8,4,9,6,7,3]=>10000000=>01111111=>1
[1,5,2,7,4,9,6,10,8,3]=>100000000=>011111111=>1
[1,5,2,7,4,6,8,9,3]=>10000000=>01111111=>1
[1,5,2,7,4,9,6,8,10,3]=>100000000=>011111111=>1
[1,5,2,4,7,9,6,8,3]=>10000000=>01111111=>1
[1,5,2,7,4,6,9,8,10,3]=>100000000=>011111111=>1
[1,2,5,7,4,6,9,8,3]=>11000000=>00111111=>1
[1,5,2,4,7,6,9,8,10,3]=>100000000=>011111111=>1
[1,2,5,4,7,6,9,8,10,3]=>110000000=>001111111=>1
[3,4,5,6,8,9,7,1,2]=>00000000=>11111111=>1
[3,4,5,7,8,9,6,1,2]=>00000000=>11111111=>1
[3,5,6,7,8,9,4,1,2]=>00000000=>11111111=>1
[4,5,6,7,8,9,3,1,2]=>00000000=>11111111=>1
[3,4,5,6,7,9,10,8,1,2]=>000000000=>111111111=>1
[3,4,5,8,1,9,7,6,2]=>00000000=>11111111=>1
[3,4,5,6,8,9,10,7,1,2]=>000000000=>111111111=>1
[3,4,7,1,8,9,6,5,2]=>00000000=>11111111=>1
[3,6,1,7,8,9,4,5,2]=>00000000=>11111111=>1
[3,4,6,7,8,9,10,5,1,2]=>000000000=>111111111=>1
[5,1,6,7,8,9,4,3,2]=>00000000=>11111111=>1
[3,5,6,7,8,9,10,4,1,2]=>000000000=>111111111=>1
[1,5,6,7,8,9,3,2,4]=>10000000=>01111111=>1
[3,4,5,6,7,10,1,8,9,2]=>000000000=>111111111=>1
[3,4,5,8,9,6,7,1,2]=>00000000=>11111111=>1
[3,4,5,6,9,1,10,8,7,2]=>000000000=>111111111=>1
[3,4,7,8,5,9,6,1,2]=>00000000=>11111111=>1
[3,4,5,9,1,6,7,8,2]=>00000000=>11111111=>1
[3,4,5,8,1,9,10,7,6,2]=>000000000=>111111111=>1
[3,4,8,1,5,9,7,6,2]=>00000000=>11111111=>1
[3,4,7,1,8,9,10,5,6,2]=>000000000=>111111111=>1
[5,6,3,7,8,9,4,1,2]=>00000000=>11111111=>1
[3,7,8,4,5,6,1,2]=>0000000=>1111111=>1
[3,7,1,4,8,9,6,5,2]=>00000000=>11111111=>1
[3,6,1,7,8,9,10,5,4,2]=>000000000=>111111111=>1
[5,2,6,7,8,9,3,1,4]=>00000000=>11111111=>1
[6,1,3,7,8,9,4,5,2]=>00000000=>11111111=>1
[5,1,6,7,8,9,10,4,3,2]=>000000000=>111111111=>1
[1,2,6,7,8,9,4,3,5]=>11000000=>00111111=>1
[3,7,5,6,4,2,8,1]=>0000000=>1111111=>1
[5,2,3,8,6,1,4,7]=>0000000=>1111111=>1
[1,4,3,8,5,6,2,7]=>1000000=>0111111=>1
[7,8,2,6,4,3,5,1]=>0000000=>1111111=>1
[4,5,8,7,2,3,6,1]=>0000000=>1111111=>1
[7,8,6,1,4,2,5,3]=>0000000=>1111111=>1
[8,3,6,5,2,7,1,4]=>0000000=>1111111=>1
[5,1,3,6,4,2,7,8]=>0000011=>1111100=>1
[6,1,2,4,7,5,3,8]=>0000001=>1111110=>1
[6,4,5,1,8,7,3,2]=>0000000=>1111111=>1
[8,6,2,1,7,3,5,4]=>0000000=>1111111=>1
[7,8,6,1,4,3,5,2]=>0000000=>1111111=>1
[1,2,3,4,8,5,9,6,7]=>11110000=>00001111=>1
[1,2,3,4,5,8,6,9,7,10]=>111110001=>000001110=>1
[1,2,3,7,4,5,8,6,9]=>11100001=>00011110=>1
[1,2,3,4,8,6,5,7,9]=>11110001=>00001110=>1
[1,2,3,4,9,7,5,6,8]=>11110000=>00001111=>1
[1,2,3,4,5,9,6,10,7,8]=>111110000=>000001111=>1
[8,2,6,5,1,7,4,3]=>0000000=>1111111=>1
[7,6,4,1,2,5,8,3]=>0000000=>1111111=>1
[2,6,5,4,8,7,1,3]=>0000000=>1111111=>1
[5,6,7,1,3,2,4,8]=>0000001=>1111110=>1
[7,1,8,4,3,2,6,5]=>0000000=>1111111=>1
[1,8,5,2,7,6,4,3]=>1000000=>0111111=>1
[1,7,6,8,2,5,4,3]=>1000000=>0111111=>1
[1,7,8,6,2,5,4,3]=>1000000=>0111111=>1
[1,6,3,4,2,5,8,7]=>1000010=>0111101=>2
[1,5,7,6,2,3,8,4]=>1000000=>0111111=>1
[1,4,3,7,6,2,5,8]=>1000001=>0111110=>1
[1,3,7,4,6,8,5,2]=>1000000=>0111111=>1
[3,7,4,6,8,1,5,2]=>0000000=>1111111=>1
[5,6,1,4,3,8,7,2]=>0000000=>1111111=>1
[5,8,6,4,3,1,7,2]=>0000000=>1111111=>1
[4,1,3,7,8,6,5,2]=>0000000=>1111111=>1
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Description
The number of runs of ones in a binary word.
Map
connectivity set
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(π)={i∈[n−1]|∀1≤j≤i<k≤n:π(j)<π(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(π)={i∈[n−1]|∀1≤j≤i<k≤n:π(j)<π(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.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
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