Identifier
Mp00267:
Signed permutations
—signs⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
=>
[1]=>0=>0
[-1]=>1=>1
[1,2]=>00=>00
[1,-2]=>01=>10
[-1,2]=>10=>01
[-1,-2]=>11=>11
[2,1]=>00=>00
[2,-1]=>01=>10
[-2,1]=>10=>01
[-2,-1]=>11=>11
[1,2,3]=>000=>000
[1,2,-3]=>001=>100
[1,-2,3]=>010=>010
[1,-2,-3]=>011=>110
[-1,2,3]=>100=>001
[-1,2,-3]=>101=>101
[-1,-2,3]=>110=>011
[-1,-2,-3]=>111=>111
[1,3,2]=>000=>000
[1,3,-2]=>001=>100
[1,-3,2]=>010=>010
[1,-3,-2]=>011=>110
[-1,3,2]=>100=>001
[-1,3,-2]=>101=>101
[-1,-3,2]=>110=>011
[-1,-3,-2]=>111=>111
[2,1,3]=>000=>000
[2,1,-3]=>001=>100
[2,-1,3]=>010=>010
[2,-1,-3]=>011=>110
[-2,1,3]=>100=>001
[-2,1,-3]=>101=>101
[-2,-1,3]=>110=>011
[-2,-1,-3]=>111=>111
[2,3,1]=>000=>000
[2,3,-1]=>001=>100
[2,-3,1]=>010=>010
[2,-3,-1]=>011=>110
[-2,3,1]=>100=>001
[-2,3,-1]=>101=>101
[-2,-3,1]=>110=>011
[-2,-3,-1]=>111=>111
[3,1,2]=>000=>000
[3,1,-2]=>001=>100
[3,-1,2]=>010=>010
[3,-1,-2]=>011=>110
[-3,1,2]=>100=>001
[-3,1,-2]=>101=>101
[-3,-1,2]=>110=>011
[-3,-1,-2]=>111=>111
[3,2,1]=>000=>000
[3,2,-1]=>001=>100
[3,-2,1]=>010=>010
[3,-2,-1]=>011=>110
[-3,2,1]=>100=>001
[-3,2,-1]=>101=>101
[-3,-2,1]=>110=>011
[-3,-2,-1]=>111=>111
[1,2,3,4]=>0000=>0000
[1,2,3,-4]=>0001=>1000
[1,2,-3,4]=>0010=>0100
[1,2,-3,-4]=>0011=>1100
[1,-2,3,4]=>0100=>0010
[1,-2,3,-4]=>0101=>1010
[1,-2,-3,4]=>0110=>0110
[1,-2,-3,-4]=>0111=>1110
[-1,2,3,4]=>1000=>0001
[-1,2,3,-4]=>1001=>1001
[-1,2,-3,4]=>1010=>0101
[-1,2,-3,-4]=>1011=>1101
[-1,-2,3,4]=>1100=>0011
[-1,-2,3,-4]=>1101=>1011
[-1,-2,-3,4]=>1110=>0111
[-1,-2,-3,-4]=>1111=>1111
[1,2,4,3]=>0000=>0000
[1,2,4,-3]=>0001=>1000
[1,2,-4,3]=>0010=>0100
[1,2,-4,-3]=>0011=>1100
[1,-2,4,3]=>0100=>0010
[1,-2,4,-3]=>0101=>1010
[1,-2,-4,3]=>0110=>0110
[1,-2,-4,-3]=>0111=>1110
[-1,2,4,3]=>1000=>0001
[-1,2,4,-3]=>1001=>1001
[-1,2,-4,3]=>1010=>0101
[-1,2,-4,-3]=>1011=>1101
[-1,-2,4,3]=>1100=>0011
[-1,-2,4,-3]=>1101=>1011
[-1,-2,-4,3]=>1110=>0111
[-1,-2,-4,-3]=>1111=>1111
[1,3,2,4]=>0000=>0000
[1,3,2,-4]=>0001=>1000
[1,3,-2,4]=>0010=>0100
[1,3,-2,-4]=>0011=>1100
[1,-3,2,4]=>0100=>0010
[1,-3,2,-4]=>0101=>1010
[1,-3,-2,4]=>0110=>0110
[1,-3,-2,-4]=>0111=>1110
[-1,3,2,4]=>1000=>0001
[-1,3,2,-4]=>1001=>1001
[-1,3,-2,4]=>1010=>0101
[-1,3,-2,-4]=>1011=>1101
[-1,-3,2,4]=>1100=>0011
[-1,-3,2,-4]=>1101=>1011
[-1,-3,-2,4]=>1110=>0111
[-1,-3,-2,-4]=>1111=>1111
[1,3,4,2]=>0000=>0000
[1,3,4,-2]=>0001=>1000
[1,3,-4,2]=>0010=>0100
[1,3,-4,-2]=>0011=>1100
[1,-3,4,2]=>0100=>0010
[1,-3,4,-2]=>0101=>1010
[1,-3,-4,2]=>0110=>0110
[1,-3,-4,-2]=>0111=>1110
[-1,3,4,2]=>1000=>0001
[-1,3,4,-2]=>1001=>1001
[-1,3,-4,2]=>1010=>0101
[-1,3,-4,-2]=>1011=>1101
[-1,-3,4,2]=>1100=>0011
[-1,-3,4,-2]=>1101=>1011
[-1,-3,-4,2]=>1110=>0111
[-1,-3,-4,-2]=>1111=>1111
[1,4,2,3]=>0000=>0000
[1,4,2,-3]=>0001=>1000
[1,4,-2,3]=>0010=>0100
[1,4,-2,-3]=>0011=>1100
[1,-4,2,3]=>0100=>0010
[1,-4,2,-3]=>0101=>1010
[1,-4,-2,3]=>0110=>0110
[1,-4,-2,-3]=>0111=>1110
[-1,4,2,3]=>1000=>0001
[-1,4,2,-3]=>1001=>1001
[-1,4,-2,3]=>1010=>0101
[-1,4,-2,-3]=>1011=>1101
[-1,-4,2,3]=>1100=>0011
[-1,-4,2,-3]=>1101=>1011
[-1,-4,-2,3]=>1110=>0111
[-1,-4,-2,-3]=>1111=>1111
[1,4,3,2]=>0000=>0000
[1,4,3,-2]=>0001=>1000
[1,4,-3,2]=>0010=>0100
[1,4,-3,-2]=>0011=>1100
[1,-4,3,2]=>0100=>0010
[1,-4,3,-2]=>0101=>1010
[1,-4,-3,2]=>0110=>0110
[1,-4,-3,-2]=>0111=>1110
[-1,4,3,2]=>1000=>0001
[-1,4,3,-2]=>1001=>1001
[-1,4,-3,2]=>1010=>0101
[-1,4,-3,-2]=>1011=>1101
[-1,-4,3,2]=>1100=>0011
[-1,-4,3,-2]=>1101=>1011
[-1,-4,-3,2]=>1110=>0111
[-1,-4,-3,-2]=>1111=>1111
[2,1,3,4]=>0000=>0000
[2,1,3,-4]=>0001=>1000
[2,1,-3,4]=>0010=>0100
[2,1,-3,-4]=>0011=>1100
[2,-1,3,4]=>0100=>0010
[2,-1,3,-4]=>0101=>1010
[2,-1,-3,4]=>0110=>0110
[2,-1,-3,-4]=>0111=>1110
[-2,1,3,4]=>1000=>0001
[-2,1,3,-4]=>1001=>1001
[-2,1,-3,4]=>1010=>0101
[-2,1,-3,-4]=>1011=>1101
[-2,-1,3,4]=>1100=>0011
[-2,-1,3,-4]=>1101=>1011
[-2,-1,-3,4]=>1110=>0111
[-2,-1,-3,-4]=>1111=>1111
[2,1,4,3]=>0000=>0000
[2,1,4,-3]=>0001=>1000
[2,1,-4,3]=>0010=>0100
[2,1,-4,-3]=>0011=>1100
[2,-1,4,3]=>0100=>0010
[2,-1,4,-3]=>0101=>1010
[2,-1,-4,3]=>0110=>0110
[2,-1,-4,-3]=>0111=>1110
[-2,1,4,3]=>1000=>0001
[-2,1,4,-3]=>1001=>1001
[-2,1,-4,3]=>1010=>0101
[-2,1,-4,-3]=>1011=>1101
[-2,-1,4,3]=>1100=>0011
[-2,-1,4,-3]=>1101=>1011
[-2,-1,-4,3]=>1110=>0111
[-2,-1,-4,-3]=>1111=>1111
[2,3,1,4]=>0000=>0000
[2,3,1,-4]=>0001=>1000
[2,3,-1,4]=>0010=>0100
[2,3,-1,-4]=>0011=>1100
[2,-3,1,4]=>0100=>0010
[2,-3,1,-4]=>0101=>1010
[2,-3,-1,4]=>0110=>0110
[2,-3,-1,-4]=>0111=>1110
[-2,3,1,4]=>1000=>0001
[-2,3,1,-4]=>1001=>1001
[-2,3,-1,4]=>1010=>0101
[-2,3,-1,-4]=>1011=>1101
[-2,-3,1,4]=>1100=>0011
[-2,-3,1,-4]=>1101=>1011
[-2,-3,-1,4]=>1110=>0111
[-2,-3,-1,-4]=>1111=>1111
[2,3,4,1]=>0000=>0000
[2,3,4,-1]=>0001=>1000
[2,3,-4,1]=>0010=>0100
[2,3,-4,-1]=>0011=>1100
[2,-3,4,1]=>0100=>0010
[2,-3,4,-1]=>0101=>1010
[2,-3,-4,1]=>0110=>0110
[2,-3,-4,-1]=>0111=>1110
[-2,3,4,1]=>1000=>0001
[-2,3,4,-1]=>1001=>1001
[-2,3,-4,1]=>1010=>0101
[-2,3,-4,-1]=>1011=>1101
[-2,-3,4,1]=>1100=>0011
[-2,-3,4,-1]=>1101=>1011
[-2,-3,-4,1]=>1110=>0111
[-2,-3,-4,-1]=>1111=>1111
[2,4,1,3]=>0000=>0000
[2,4,1,-3]=>0001=>1000
[2,4,-1,3]=>0010=>0100
[2,4,-1,-3]=>0011=>1100
[2,-4,1,3]=>0100=>0010
[2,-4,1,-3]=>0101=>1010
[2,-4,-1,3]=>0110=>0110
[2,-4,-1,-3]=>0111=>1110
[-2,4,1,3]=>1000=>0001
[-2,4,1,-3]=>1001=>1001
[-2,4,-1,3]=>1010=>0101
[-2,4,-1,-3]=>1011=>1101
[-2,-4,1,3]=>1100=>0011
[-2,-4,1,-3]=>1101=>1011
[-2,-4,-1,3]=>1110=>0111
[-2,-4,-1,-3]=>1111=>1111
[2,4,3,1]=>0000=>0000
[2,4,3,-1]=>0001=>1000
[2,4,-3,1]=>0010=>0100
[2,4,-3,-1]=>0011=>1100
[2,-4,3,1]=>0100=>0010
[2,-4,3,-1]=>0101=>1010
[2,-4,-3,1]=>0110=>0110
[2,-4,-3,-1]=>0111=>1110
[-2,4,3,1]=>1000=>0001
[-2,4,3,-1]=>1001=>1001
[-2,4,-3,1]=>1010=>0101
[-2,4,-3,-1]=>1011=>1101
[-2,-4,3,1]=>1100=>0011
[-2,-4,3,-1]=>1101=>1011
[-2,-4,-3,1]=>1110=>0111
[-2,-4,-3,-1]=>1111=>1111
[3,1,2,4]=>0000=>0000
[3,1,2,-4]=>0001=>1000
[3,1,-2,4]=>0010=>0100
[3,1,-2,-4]=>0011=>1100
[3,-1,2,4]=>0100=>0010
[3,-1,2,-4]=>0101=>1010
[3,-1,-2,4]=>0110=>0110
[3,-1,-2,-4]=>0111=>1110
[-3,1,2,4]=>1000=>0001
[-3,1,2,-4]=>1001=>1001
[-3,1,-2,4]=>1010=>0101
[-3,1,-2,-4]=>1011=>1101
[-3,-1,2,4]=>1100=>0011
[-3,-1,2,-4]=>1101=>1011
[-3,-1,-2,4]=>1110=>0111
[-3,-1,-2,-4]=>1111=>1111
[3,1,4,2]=>0000=>0000
[3,1,4,-2]=>0001=>1000
[3,1,-4,2]=>0010=>0100
[3,1,-4,-2]=>0011=>1100
[3,-1,4,2]=>0100=>0010
[3,-1,4,-2]=>0101=>1010
[3,-1,-4,2]=>0110=>0110
[3,-1,-4,-2]=>0111=>1110
[-3,1,4,2]=>1000=>0001
[-3,1,4,-2]=>1001=>1001
[-3,1,-4,2]=>1010=>0101
[-3,1,-4,-2]=>1011=>1101
[-3,-1,4,2]=>1100=>0011
[-3,-1,4,-2]=>1101=>1011
[-3,-1,-4,2]=>1110=>0111
[-3,-1,-4,-2]=>1111=>1111
[3,2,1,4]=>0000=>0000
[3,2,1,-4]=>0001=>1000
[3,2,-1,4]=>0010=>0100
[3,2,-1,-4]=>0011=>1100
[3,-2,1,4]=>0100=>0010
[3,-2,1,-4]=>0101=>1010
[3,-2,-1,4]=>0110=>0110
[3,-2,-1,-4]=>0111=>1110
[-3,2,1,4]=>1000=>0001
[-3,2,1,-4]=>1001=>1001
[-3,2,-1,4]=>1010=>0101
[-3,2,-1,-4]=>1011=>1101
[-3,-2,1,4]=>1100=>0011
[-3,-2,1,-4]=>1101=>1011
[-3,-2,-1,4]=>1110=>0111
[-3,-2,-1,-4]=>1111=>1111
[3,2,4,1]=>0000=>0000
[3,2,4,-1]=>0001=>1000
[3,2,-4,1]=>0010=>0100
[3,2,-4,-1]=>0011=>1100
[3,-2,4,1]=>0100=>0010
[3,-2,4,-1]=>0101=>1010
[3,-2,-4,1]=>0110=>0110
[3,-2,-4,-1]=>0111=>1110
[-3,2,4,1]=>1000=>0001
[-3,2,4,-1]=>1001=>1001
[-3,2,-4,1]=>1010=>0101
[-3,2,-4,-1]=>1011=>1101
[-3,-2,4,1]=>1100=>0011
[-3,-2,4,-1]=>1101=>1011
[-3,-2,-4,1]=>1110=>0111
[-3,-2,-4,-1]=>1111=>1111
[3,4,1,2]=>0000=>0000
[3,4,1,-2]=>0001=>1000
[3,4,-1,2]=>0010=>0100
[3,4,-1,-2]=>0011=>1100
[3,-4,1,2]=>0100=>0010
[3,-4,1,-2]=>0101=>1010
[3,-4,-1,2]=>0110=>0110
[3,-4,-1,-2]=>0111=>1110
[-3,4,1,2]=>1000=>0001
[-3,4,1,-2]=>1001=>1001
[-3,4,-1,2]=>1010=>0101
[-3,4,-1,-2]=>1011=>1101
[-3,-4,1,2]=>1100=>0011
[-3,-4,1,-2]=>1101=>1011
[-3,-4,-1,2]=>1110=>0111
[-3,-4,-1,-2]=>1111=>1111
[3,4,2,1]=>0000=>0000
[3,4,2,-1]=>0001=>1000
[3,4,-2,1]=>0010=>0100
[3,4,-2,-1]=>0011=>1100
[3,-4,2,1]=>0100=>0010
[3,-4,2,-1]=>0101=>1010
[3,-4,-2,1]=>0110=>0110
[3,-4,-2,-1]=>0111=>1110
[-3,4,2,1]=>1000=>0001
[-3,4,2,-1]=>1001=>1001
[-3,4,-2,1]=>1010=>0101
[-3,4,-2,-1]=>1011=>1101
[-3,-4,2,1]=>1100=>0011
[-3,-4,2,-1]=>1101=>1011
[-3,-4,-2,1]=>1110=>0111
[-3,-4,-2,-1]=>1111=>1111
[4,1,2,3]=>0000=>0000
[4,1,2,-3]=>0001=>1000
[4,1,-2,3]=>0010=>0100
[4,1,-2,-3]=>0011=>1100
[4,-1,2,3]=>0100=>0010
[4,-1,2,-3]=>0101=>1010
[4,-1,-2,3]=>0110=>0110
[4,-1,-2,-3]=>0111=>1110
[-4,1,2,3]=>1000=>0001
[-4,1,2,-3]=>1001=>1001
[-4,1,-2,3]=>1010=>0101
[-4,1,-2,-3]=>1011=>1101
[-4,-1,2,3]=>1100=>0011
[-4,-1,2,-3]=>1101=>1011
[-4,-1,-2,3]=>1110=>0111
[-4,-1,-2,-3]=>1111=>1111
[4,1,3,2]=>0000=>0000
[4,1,3,-2]=>0001=>1000
[4,1,-3,2]=>0010=>0100
[4,1,-3,-2]=>0011=>1100
[4,-1,3,2]=>0100=>0010
[4,-1,3,-2]=>0101=>1010
[4,-1,-3,2]=>0110=>0110
[4,-1,-3,-2]=>0111=>1110
[-4,1,3,2]=>1000=>0001
[-4,1,3,-2]=>1001=>1001
[-4,1,-3,2]=>1010=>0101
[-4,1,-3,-2]=>1011=>1101
[-4,-1,3,2]=>1100=>0011
[-4,-1,3,-2]=>1101=>1011
[-4,-1,-3,2]=>1110=>0111
[-4,-1,-3,-2]=>1111=>1111
[4,2,1,3]=>0000=>0000
[4,2,1,-3]=>0001=>1000
[4,2,-1,3]=>0010=>0100
[4,2,-1,-3]=>0011=>1100
[4,-2,1,3]=>0100=>0010
[4,-2,1,-3]=>0101=>1010
[4,-2,-1,3]=>0110=>0110
[4,-2,-1,-3]=>0111=>1110
[-4,2,1,3]=>1000=>0001
[-4,2,1,-3]=>1001=>1001
[-4,2,-1,3]=>1010=>0101
[-4,2,-1,-3]=>1011=>1101
[-4,-2,1,3]=>1100=>0011
[-4,-2,1,-3]=>1101=>1011
[-4,-2,-1,3]=>1110=>0111
[-4,-2,-1,-3]=>1111=>1111
[4,2,3,1]=>0000=>0000
[4,2,3,-1]=>0001=>1000
[4,2,-3,1]=>0010=>0100
[4,2,-3,-1]=>0011=>1100
[4,-2,3,1]=>0100=>0010
[4,-2,3,-1]=>0101=>1010
[4,-2,-3,1]=>0110=>0110
[4,-2,-3,-1]=>0111=>1110
[-4,2,3,1]=>1000=>0001
[-4,2,3,-1]=>1001=>1001
[-4,2,-3,1]=>1010=>0101
[-4,2,-3,-1]=>1011=>1101
[-4,-2,3,1]=>1100=>0011
[-4,-2,3,-1]=>1101=>1011
[-4,-2,-3,1]=>1110=>0111
[-4,-2,-3,-1]=>1111=>1111
[4,3,1,2]=>0000=>0000
[4,3,1,-2]=>0001=>1000
[4,3,-1,2]=>0010=>0100
[4,3,-1,-2]=>0011=>1100
[4,-3,1,2]=>0100=>0010
[4,-3,1,-2]=>0101=>1010
[4,-3,-1,2]=>0110=>0110
[4,-3,-1,-2]=>0111=>1110
[-4,3,1,2]=>1000=>0001
[-4,3,1,-2]=>1001=>1001
[-4,3,-1,2]=>1010=>0101
[-4,3,-1,-2]=>1011=>1101
[-4,-3,1,2]=>1100=>0011
[-4,-3,1,-2]=>1101=>1011
[-4,-3,-1,2]=>1110=>0111
[-4,-3,-1,-2]=>1111=>1111
[4,3,2,1]=>0000=>0000
[4,3,2,-1]=>0001=>1000
[4,3,-2,1]=>0010=>0100
[4,3,-2,-1]=>0011=>1100
[4,-3,2,1]=>0100=>0010
[4,-3,2,-1]=>0101=>1010
[4,-3,-2,1]=>0110=>0110
[4,-3,-2,-1]=>0111=>1110
[-4,3,2,1]=>1000=>0001
[-4,3,2,-1]=>1001=>1001
[-4,3,-2,1]=>1010=>0101
[-4,3,-2,-1]=>1011=>1101
[-4,-3,2,1]=>1100=>0011
[-4,-3,2,-1]=>1101=>1011
[-4,-3,-2,1]=>1110=>0111
[-4,-3,-2,-1]=>1111=>1111
[1,2,3,4,5]=>00000=>00000
[1,2,3,4,-5]=>00001=>10000
[1,2,3,-4,5]=>00010=>01000
[1,2,3,-4,-5]=>00011=>11000
[1,2,-3,4,5]=>00100=>00100
[1,2,-3,4,-5]=>00101=>10100
[1,2,-3,-4,5]=>00110=>01100
[1,2,-3,-4,-5]=>00111=>11100
[1,-2,3,4,5]=>01000=>00010
[1,-2,3,4,-5]=>01001=>10010
[1,-2,3,-4,5]=>01010=>01010
[1,-2,3,-4,-5]=>01011=>11010
[1,-2,-3,4,5]=>01100=>00110
[1,-2,-3,4,-5]=>01101=>10110
[1,-2,-3,-4,5]=>01110=>01110
[1,-2,-3,-4,-5]=>01111=>11110
[-1,2,3,4,5]=>10000=>00001
[-1,2,3,4,-5]=>10001=>10001
[-1,2,3,-4,5]=>10010=>01001
[-1,2,3,-4,-5]=>10011=>11001
[-1,2,-3,4,5]=>10100=>00101
[-1,2,-3,4,-5]=>10101=>10101
[-1,2,-3,-4,5]=>10110=>01101
[-1,2,-3,-4,-5]=>10111=>11101
[-1,-2,3,4,5]=>11000=>00011
[-1,-2,3,4,-5]=>11001=>10011
[-1,-2,3,-4,5]=>11010=>01011
[-1,-2,3,-4,-5]=>11011=>11011
[-1,-2,-3,4,5]=>11100=>00111
[-1,-2,-3,4,-5]=>11101=>10111
[-1,-2,-3,-4,5]=>11110=>01111
[-1,-2,-3,-4,-5]=>11111=>11111
[1,2,3,5,4]=>00000=>00000
[1,2,3,5,-4]=>00001=>10000
[1,2,3,-5,4]=>00010=>01000
[1,2,3,-5,-4]=>00011=>11000
[1,2,-3,5,4]=>00100=>00100
[1,2,-3,5,-4]=>00101=>10100
[1,2,-3,-5,4]=>00110=>01100
[1,2,-3,-5,-4]=>00111=>11100
[1,-2,3,5,4]=>01000=>00010
[1,-2,3,5,-4]=>01001=>10010
[1,-2,3,-5,4]=>01010=>01010
[1,-2,3,-5,-4]=>01011=>11010
[1,-2,-3,5,4]=>01100=>00110
[1,-2,-3,5,-4]=>01101=>10110
[1,-2,-3,-5,4]=>01110=>01110
[1,-2,-3,-5,-4]=>01111=>11110
[-1,2,3,5,4]=>10000=>00001
[-1,2,3,5,-4]=>10001=>10001
[-1,2,3,-5,4]=>10010=>01001
[-1,2,3,-5,-4]=>10011=>11001
[-1,2,-3,5,4]=>10100=>00101
[-1,2,-3,5,-4]=>10101=>10101
[-1,2,-3,-5,4]=>10110=>01101
[-1,2,-3,-5,-4]=>10111=>11101
[-1,-2,3,5,4]=>11000=>00011
[-1,-2,3,5,-4]=>11001=>10011
[-1,-2,3,-5,4]=>11010=>01011
[-1,-2,3,-5,-4]=>11011=>11011
[-1,-2,-3,5,4]=>11100=>00111
[-1,-2,-3,5,-4]=>11101=>10111
[-1,-2,-3,-5,4]=>11110=>01111
[-1,-2,-3,-5,-4]=>11111=>11111
[1,2,4,3,5]=>00000=>00000
[1,2,4,3,-5]=>00001=>10000
[1,2,4,-3,5]=>00010=>01000
[1,2,4,-3,-5]=>00011=>11000
[1,2,-4,3,5]=>00100=>00100
[1,2,-4,3,-5]=>00101=>10100
[1,2,-4,-3,5]=>00110=>01100
[1,2,-4,-3,-5]=>00111=>11100
[1,-2,4,3,5]=>01000=>00010
[1,-2,4,3,-5]=>01001=>10010
[1,-2,4,-3,5]=>01010=>01010
[1,-2,4,-3,-5]=>01011=>11010
[1,-2,-4,3,5]=>01100=>00110
[1,-2,-4,3,-5]=>01101=>10110
[1,-2,-4,-3,5]=>01110=>01110
[1,-2,-4,-3,-5]=>01111=>11110
[-1,2,4,3,5]=>10000=>00001
[-1,2,4,3,-5]=>10001=>10001
[-1,2,4,-3,5]=>10010=>01001
[-1,2,4,-3,-5]=>10011=>11001
[-1,2,-4,3,5]=>10100=>00101
[-1,2,-4,3,-5]=>10101=>10101
[-1,2,-4,-3,5]=>10110=>01101
[-1,2,-4,-3,-5]=>10111=>11101
[-1,-2,4,3,5]=>11000=>00011
[-1,-2,4,3,-5]=>11001=>10011
[-1,-2,4,-3,5]=>11010=>01011
[-1,-2,4,-3,-5]=>11011=>11011
[-1,-2,-4,3,5]=>11100=>00111
[-1,-2,-4,3,-5]=>11101=>10111
[-1,-2,-4,-3,5]=>11110=>01111
[-1,-2,-4,-3,-5]=>11111=>11111
[1,2,4,5,3]=>00000=>00000
[1,2,4,5,-3]=>00001=>10000
[1,2,4,-5,3]=>00010=>01000
[1,2,4,-5,-3]=>00011=>11000
[1,2,-4,5,3]=>00100=>00100
[1,2,-4,5,-3]=>00101=>10100
[1,2,-4,-5,3]=>00110=>01100
[1,2,-4,-5,-3]=>00111=>11100
[1,-2,4,5,3]=>01000=>00010
[1,-2,4,5,-3]=>01001=>10010
[1,-2,4,-5,3]=>01010=>01010
[1,-2,4,-5,-3]=>01011=>11010
[1,-2,-4,5,3]=>01100=>00110
[1,-2,-4,5,-3]=>01101=>10110
[1,-2,-4,-5,3]=>01110=>01110
[1,-2,-4,-5,-3]=>01111=>11110
[-1,2,4,5,3]=>10000=>00001
[-1,2,4,5,-3]=>10001=>10001
[-1,2,4,-5,3]=>10010=>01001
[-1,2,4,-5,-3]=>10011=>11001
[-1,2,-4,5,3]=>10100=>00101
[-1,2,-4,5,-3]=>10101=>10101
[-1,2,-4,-5,3]=>10110=>01101
[-1,2,-4,-5,-3]=>10111=>11101
[-1,-2,4,5,3]=>11000=>00011
[-1,-2,4,5,-3]=>11001=>10011
[-1,-2,4,-5,3]=>11010=>01011
[-1,-2,4,-5,-3]=>11011=>11011
[-1,-2,-4,5,3]=>11100=>00111
[-1,-2,-4,5,-3]=>11101=>10111
[-1,-2,-4,-5,3]=>11110=>01111
[-1,-2,-4,-5,-3]=>11111=>11111
[1,2,5,3,4]=>00000=>00000
[1,2,5,3,-4]=>00001=>10000
[1,2,5,-3,4]=>00010=>01000
[1,2,5,-3,-4]=>00011=>11000
[1,2,-5,3,4]=>00100=>00100
[1,2,-5,3,-4]=>00101=>10100
[1,2,-5,-3,4]=>00110=>01100
[1,2,-5,-3,-4]=>00111=>11100
[1,-2,5,3,4]=>01000=>00010
[1,-2,5,3,-4]=>01001=>10010
[1,-2,5,-3,4]=>01010=>01010
[1,-2,5,-3,-4]=>01011=>11010
[1,-2,-5,3,4]=>01100=>00110
[1,-2,-5,3,-4]=>01101=>10110
[1,-2,-5,-3,4]=>01110=>01110
[1,-2,-5,-3,-4]=>01111=>11110
[-1,2,5,3,4]=>10000=>00001
[-1,2,5,3,-4]=>10001=>10001
[-1,2,5,-3,4]=>10010=>01001
[-1,2,5,-3,-4]=>10011=>11001
[-1,2,-5,3,4]=>10100=>00101
[-1,2,-5,3,-4]=>10101=>10101
[-1,2,-5,-3,4]=>10110=>01101
[-1,2,-5,-3,-4]=>10111=>11101
[-1,-2,5,3,4]=>11000=>00011
[-1,-2,5,3,-4]=>11001=>10011
[-1,-2,5,-3,4]=>11010=>01011
[-1,-2,5,-3,-4]=>11011=>11011
[-1,-2,-5,3,4]=>11100=>00111
[-1,-2,-5,3,-4]=>11101=>10111
[-1,-2,-5,-3,4]=>11110=>01111
[-1,-2,-5,-3,-4]=>11111=>11111
[1,2,5,4,3]=>00000=>00000
[1,2,5,4,-3]=>00001=>10000
[1,2,5,-4,3]=>00010=>01000
[1,2,5,-4,-3]=>00011=>11000
[1,2,-5,4,3]=>00100=>00100
[1,2,-5,4,-3]=>00101=>10100
[1,2,-5,-4,3]=>00110=>01100
[1,2,-5,-4,-3]=>00111=>11100
[1,-2,5,4,3]=>01000=>00010
[1,-2,5,4,-3]=>01001=>10010
[1,-2,5,-4,3]=>01010=>01010
[1,-2,5,-4,-3]=>01011=>11010
[1,-2,-5,4,3]=>01100=>00110
[1,-2,-5,4,-3]=>01101=>10110
[1,-2,-5,-4,3]=>01110=>01110
[1,-2,-5,-4,-3]=>01111=>11110
[-1,2,5,4,3]=>10000=>00001
[-1,2,5,4,-3]=>10001=>10001
[-1,2,5,-4,3]=>10010=>01001
[-1,2,5,-4,-3]=>10011=>11001
[-1,2,-5,4,3]=>10100=>00101
[-1,2,-5,4,-3]=>10101=>10101
[-1,2,-5,-4,3]=>10110=>01101
[-1,2,-5,-4,-3]=>10111=>11101
[-1,-2,5,4,3]=>11000=>00011
[-1,-2,5,4,-3]=>11001=>10011
[-1,-2,5,-4,3]=>11010=>01011
[-1,-2,5,-4,-3]=>11011=>11011
[-1,-2,-5,4,3]=>11100=>00111
[-1,-2,-5,4,-3]=>11101=>10111
[-1,-2,-5,-4,3]=>11110=>01111
[-1,-2,-5,-4,-3]=>11111=>11111
[1,3,2,4,5]=>00000=>00000
[1,3,2,4,-5]=>00001=>10000
[1,3,2,-4,5]=>00010=>01000
[1,3,2,-4,-5]=>00011=>11000
[1,3,-2,4,5]=>00100=>00100
[1,3,-2,4,-5]=>00101=>10100
[1,3,-2,-4,5]=>00110=>01100
[1,3,-2,-4,-5]=>00111=>11100
[1,-3,2,4,5]=>01000=>00010
[1,-3,2,4,-5]=>01001=>10010
[1,-3,2,-4,5]=>01010=>01010
[1,-3,2,-4,-5]=>01011=>11010
[1,-3,-2,4,5]=>01100=>00110
[1,-3,-2,4,-5]=>01101=>10110
[1,-3,-2,-4,5]=>01110=>01110
[1,-3,-2,-4,-5]=>01111=>11110
[-1,3,2,4,5]=>10000=>00001
[-1,3,2,4,-5]=>10001=>10001
[-1,3,2,-4,5]=>10010=>01001
[-1,3,2,-4,-5]=>10011=>11001
[-1,3,-2,4,5]=>10100=>00101
[-1,3,-2,4,-5]=>10101=>10101
[-1,3,-2,-4,5]=>10110=>01101
[-1,3,-2,-4,-5]=>10111=>11101
[-1,-3,2,4,5]=>11000=>00011
[-1,-3,2,4,-5]=>11001=>10011
[-1,-3,2,-4,5]=>11010=>01011
[-1,-3,2,-4,-5]=>11011=>11011
[-1,-3,-2,4,5]=>11100=>00111
[-1,-3,-2,4,-5]=>11101=>10111
[-1,-3,-2,-4,5]=>11110=>01111
[-1,-3,-2,-4,-5]=>11111=>11111
[1,3,2,5,4]=>00000=>00000
[1,3,2,5,-4]=>00001=>10000
[1,3,2,-5,4]=>00010=>01000
[1,3,2,-5,-4]=>00011=>11000
[1,3,-2,5,4]=>00100=>00100
[1,3,-2,5,-4]=>00101=>10100
[1,3,-2,-5,4]=>00110=>01100
[1,3,-2,-5,-4]=>00111=>11100
[1,-3,2,5,4]=>01000=>00010
[1,-3,2,5,-4]=>01001=>10010
[1,-3,2,-5,4]=>01010=>01010
[1,-3,2,-5,-4]=>01011=>11010
[1,-3,-2,5,4]=>01100=>00110
[1,-3,-2,5,-4]=>01101=>10110
[1,-3,-2,-5,4]=>01110=>01110
[1,-3,-2,-5,-4]=>01111=>11110
[-1,3,2,5,4]=>10000=>00001
[-1,3,2,5,-4]=>10001=>10001
[-1,3,2,-5,4]=>10010=>01001
[-1,3,2,-5,-4]=>10011=>11001
[-1,3,-2,5,4]=>10100=>00101
[-1,3,-2,5,-4]=>10101=>10101
[-1,3,-2,-5,4]=>10110=>01101
[-1,3,-2,-5,-4]=>10111=>11101
[-1,-3,2,5,4]=>11000=>00011
[-1,-3,2,5,-4]=>11001=>10011
[-1,-3,2,-5,4]=>11010=>01011
[-1,-3,2,-5,-4]=>11011=>11011
[-1,-3,-2,5,4]=>11100=>00111
[-1,-3,-2,5,-4]=>11101=>10111
[-1,-3,-2,-5,4]=>11110=>01111
[-1,-3,-2,-5,-4]=>11111=>11111
[1,3,4,2,5]=>00000=>00000
[1,3,4,2,-5]=>00001=>10000
[1,3,4,-2,5]=>00010=>01000
[1,3,4,-2,-5]=>00011=>11000
[1,3,-4,2,5]=>00100=>00100
[1,3,-4,2,-5]=>00101=>10100
[1,3,-4,-2,5]=>00110=>01100
[1,3,-4,-2,-5]=>00111=>11100
[1,-3,4,2,5]=>01000=>00010
[1,-3,4,2,-5]=>01001=>10010
[1,-3,4,-2,5]=>01010=>01010
[1,-3,4,-2,-5]=>01011=>11010
[1,-3,-4,2,5]=>01100=>00110
[1,-3,-4,2,-5]=>01101=>10110
[1,-3,-4,-2,5]=>01110=>01110
[1,-3,-4,-2,-5]=>01111=>11110
[-1,3,4,2,5]=>10000=>00001
[-1,3,4,2,-5]=>10001=>10001
[-1,3,4,-2,5]=>10010=>01001
[-1,3,4,-2,-5]=>10011=>11001
[-1,3,-4,2,5]=>10100=>00101
[-1,3,-4,2,-5]=>10101=>10101
[-1,3,-4,-2,5]=>10110=>01101
[-1,3,-4,-2,-5]=>10111=>11101
[-1,-3,4,2,5]=>11000=>00011
[-1,-3,4,2,-5]=>11001=>10011
[-1,-3,4,-2,5]=>11010=>01011
[-1,-3,4,-2,-5]=>11011=>11011
[-1,-3,-4,2,5]=>11100=>00111
[-1,-3,-4,2,-5]=>11101=>10111
[-1,-3,-4,-2,5]=>11110=>01111
[-1,-3,-4,-2,-5]=>11111=>11111
[1,3,4,5,2]=>00000=>00000
[1,3,4,5,-2]=>00001=>10000
[1,3,4,-5,2]=>00010=>01000
[1,3,4,-5,-2]=>00011=>11000
[1,3,-4,5,2]=>00100=>00100
[1,3,-4,5,-2]=>00101=>10100
[1,3,-4,-5,2]=>00110=>01100
[1,3,-4,-5,-2]=>00111=>11100
[1,-3,4,5,2]=>01000=>00010
[1,-3,4,5,-2]=>01001=>10010
[1,-3,4,-5,2]=>01010=>01010
[1,-3,4,-5,-2]=>01011=>11010
[1,-3,-4,5,2]=>01100=>00110
[1,-3,-4,5,-2]=>01101=>10110
[1,-3,-4,-5,2]=>01110=>01110
[1,-3,-4,-5,-2]=>01111=>11110
[-1,3,4,5,2]=>10000=>00001
[-1,3,4,5,-2]=>10001=>10001
[-1,3,4,-5,2]=>10010=>01001
[-1,3,4,-5,-2]=>10011=>11001
[-1,3,-4,5,2]=>10100=>00101
[-1,3,-4,5,-2]=>10101=>10101
[-1,3,-4,-5,2]=>10110=>01101
[-1,3,-4,-5,-2]=>10111=>11101
[-1,-3,4,5,2]=>11000=>00011
[-1,-3,4,5,-2]=>11001=>10011
[-1,-3,4,-5,2]=>11010=>01011
[-1,-3,4,-5,-2]=>11011=>11011
[-1,-3,-4,5,2]=>11100=>00111
[-1,-3,-4,5,-2]=>11101=>10111
[-1,-3,-4,-5,2]=>11110=>01111
[-1,-3,-4,-5,-2]=>11111=>11111
[1,3,5,2,4]=>00000=>00000
[1,3,5,2,-4]=>00001=>10000
[1,3,5,-2,4]=>00010=>01000
[1,3,5,-2,-4]=>00011=>11000
[1,3,-5,2,4]=>00100=>00100
[1,3,-5,2,-4]=>00101=>10100
[1,3,-5,-2,4]=>00110=>01100
[1,3,-5,-2,-4]=>00111=>11100
[1,-3,5,2,4]=>01000=>00010
[1,-3,5,2,-4]=>01001=>10010
[1,-3,5,-2,4]=>01010=>01010
[1,-3,5,-2,-4]=>01011=>11010
[1,-3,-5,2,4]=>01100=>00110
[1,-3,-5,2,-4]=>01101=>10110
[1,-3,-5,-2,4]=>01110=>01110
[1,-3,-5,-2,-4]=>01111=>11110
[-1,3,5,2,4]=>10000=>00001
[-1,3,5,2,-4]=>10001=>10001
[-1,3,5,-2,4]=>10010=>01001
[-1,3,5,-2,-4]=>10011=>11001
[-1,3,-5,2,4]=>10100=>00101
[-1,3,-5,2,-4]=>10101=>10101
[-1,3,-5,-2,4]=>10110=>01101
[-1,3,-5,-2,-4]=>10111=>11101
[-1,-3,5,2,4]=>11000=>00011
[-1,-3,5,2,-4]=>11001=>10011
[-1,-3,5,-2,4]=>11010=>01011
[-1,-3,5,-2,-4]=>11011=>11011
[-1,-3,-5,2,4]=>11100=>00111
[-1,-3,-5,2,-4]=>11101=>10111
[-1,-3,-5,-2,4]=>11110=>01111
[-1,-3,-5,-2,-4]=>11111=>11111
[1,3,5,4,2]=>00000=>00000
[1,3,5,4,-2]=>00001=>10000
[1,3,5,-4,2]=>00010=>01000
[1,3,5,-4,-2]=>00011=>11000
[1,3,-5,4,2]=>00100=>00100
[1,3,-5,4,-2]=>00101=>10100
[1,3,-5,-4,2]=>00110=>01100
[1,3,-5,-4,-2]=>00111=>11100
[1,-3,5,4,2]=>01000=>00010
[1,-3,5,4,-2]=>01001=>10010
[1,-3,5,-4,2]=>01010=>01010
[1,-3,5,-4,-2]=>01011=>11010
[1,-3,-5,4,2]=>01100=>00110
[1,-3,-5,4,-2]=>01101=>10110
[1,-3,-5,-4,2]=>01110=>01110
[1,-3,-5,-4,-2]=>01111=>11110
[-1,3,5,4,2]=>10000=>00001
[-1,3,5,4,-2]=>10001=>10001
[-1,3,5,-4,2]=>10010=>01001
[-1,3,5,-4,-2]=>10011=>11001
[-1,3,-5,4,2]=>10100=>00101
[-1,3,-5,4,-2]=>10101=>10101
[-1,3,-5,-4,2]=>10110=>01101
[-1,3,-5,-4,-2]=>10111=>11101
[-1,-3,5,4,2]=>11000=>00011
[-1,-3,5,4,-2]=>11001=>10011
[-1,-3,5,-4,2]=>11010=>01011
[-1,-3,5,-4,-2]=>11011=>11011
[-1,-3,-5,4,2]=>11100=>00111
[-1,-3,-5,4,-2]=>11101=>10111
[-1,-3,-5,-4,2]=>11110=>01111
[-1,-3,-5,-4,-2]=>11111=>11111
[1,4,2,3,5]=>00000=>00000
[1,4,2,3,-5]=>00001=>10000
[1,4,2,-3,5]=>00010=>01000
[1,4,2,-3,-5]=>00011=>11000
[1,4,-2,3,5]=>00100=>00100
[1,4,-2,3,-5]=>00101=>10100
[1,4,-2,-3,5]=>00110=>01100
[1,4,-2,-3,-5]=>00111=>11100
[1,-4,2,3,5]=>01000=>00010
[1,-4,2,3,-5]=>01001=>10010
[1,-4,2,-3,5]=>01010=>01010
[1,-4,2,-3,-5]=>01011=>11010
[1,-4,-2,3,5]=>01100=>00110
[1,-4,-2,3,-5]=>01101=>10110
[1,-4,-2,-3,5]=>01110=>01110
[1,-4,-2,-3,-5]=>01111=>11110
[-1,4,2,3,5]=>10000=>00001
[-1,4,2,3,-5]=>10001=>10001
[-1,4,2,-3,5]=>10010=>01001
[-1,4,2,-3,-5]=>10011=>11001
[-1,4,-2,3,5]=>10100=>00101
[-1,4,-2,3,-5]=>10101=>10101
[-1,4,-2,-3,5]=>10110=>01101
[-1,4,-2,-3,-5]=>10111=>11101
[-1,-4,2,3,5]=>11000=>00011
[-1,-4,2,3,-5]=>11001=>10011
[-1,-4,2,-3,5]=>11010=>01011
[-1,-4,2,-3,-5]=>11011=>11011
[-1,-4,-2,3,5]=>11100=>00111
[-1,-4,-2,3,-5]=>11101=>10111
[-1,-4,-2,-3,5]=>11110=>01111
[-1,-4,-2,-3,-5]=>11111=>11111
[1,4,2,5,3]=>00000=>00000
[1,4,2,5,-3]=>00001=>10000
[1,4,2,-5,3]=>00010=>01000
[1,4,2,-5,-3]=>00011=>11000
[1,4,-2,5,3]=>00100=>00100
[1,4,-2,5,-3]=>00101=>10100
[1,4,-2,-5,3]=>00110=>01100
[1,4,-2,-5,-3]=>00111=>11100
[1,-4,2,5,3]=>01000=>00010
[1,-4,2,5,-3]=>01001=>10010
[1,-4,2,-5,3]=>01010=>01010
[1,-4,2,-5,-3]=>01011=>11010
[1,-4,-2,5,3]=>01100=>00110
[1,-4,-2,5,-3]=>01101=>10110
[1,-4,-2,-5,3]=>01110=>01110
[1,-4,-2,-5,-3]=>01111=>11110
[-1,4,2,5,3]=>10000=>00001
[-1,4,2,5,-3]=>10001=>10001
[-1,4,2,-5,3]=>10010=>01001
[-1,4,2,-5,-3]=>10011=>11001
[-1,4,-2,5,3]=>10100=>00101
[-1,4,-2,5,-3]=>10101=>10101
[-1,4,-2,-5,3]=>10110=>01101
[-1,4,-2,-5,-3]=>10111=>11101
[-1,-4,2,5,3]=>11000=>00011
[-1,-4,2,5,-3]=>11001=>10011
[-1,-4,2,-5,3]=>11010=>01011
[-1,-4,2,-5,-3]=>11011=>11011
[-1,-4,-2,5,3]=>11100=>00111
[-1,-4,-2,5,-3]=>11101=>10111
[-1,-4,-2,-5,3]=>11110=>01111
[-1,-4,-2,-5,-3]=>11111=>11111
[1,4,3,2,5]=>00000=>00000
[1,4,3,2,-5]=>00001=>10000
[1,4,3,-2,5]=>00010=>01000
[1,4,3,-2,-5]=>00011=>11000
[1,4,-3,2,5]=>00100=>00100
[1,4,-3,2,-5]=>00101=>10100
[1,4,-3,-2,5]=>00110=>01100
[1,4,-3,-2,-5]=>00111=>11100
[1,-4,3,2,5]=>01000=>00010
[1,-4,3,2,-5]=>01001=>10010
[1,-4,3,-2,5]=>01010=>01010
[1,-4,3,-2,-5]=>01011=>11010
[1,-4,-3,2,5]=>01100=>00110
[1,-4,-3,2,-5]=>01101=>10110
[1,-4,-3,-2,5]=>01110=>01110
[1,-4,-3,-2,-5]=>01111=>11110
[-1,4,3,2,5]=>10000=>00001
[-1,4,3,2,-5]=>10001=>10001
[-1,4,3,-2,5]=>10010=>01001
[-1,4,3,-2,-5]=>10011=>11001
[-1,4,-3,2,5]=>10100=>00101
[-1,4,-3,2,-5]=>10101=>10101
[-1,4,-3,-2,5]=>10110=>01101
[-1,4,-3,-2,-5]=>10111=>11101
[-1,-4,3,2,5]=>11000=>00011
[-1,-4,3,2,-5]=>11001=>10011
[-1,-4,3,-2,5]=>11010=>01011
[-1,-4,3,-2,-5]=>11011=>11011
[-1,-4,-3,2,5]=>11100=>00111
[-1,-4,-3,2,-5]=>11101=>10111
[-1,-4,-3,-2,5]=>11110=>01111
[-1,-4,-3,-2,-5]=>11111=>11111
[1,4,3,5,2]=>00000=>00000
[1,4,3,5,-2]=>00001=>10000
[1,4,3,-5,2]=>00010=>01000
[1,4,3,-5,-2]=>00011=>11000
[1,4,-3,5,2]=>00100=>00100
[1,4,-3,5,-2]=>00101=>10100
[1,4,-3,-5,2]=>00110=>01100
[1,4,-3,-5,-2]=>00111=>11100
[1,-4,3,5,2]=>01000=>00010
[1,-4,3,5,-2]=>01001=>10010
[1,-4,3,-5,2]=>01010=>01010
[1,-4,3,-5,-2]=>01011=>11010
[1,-4,-3,5,2]=>01100=>00110
[1,-4,-3,5,-2]=>01101=>10110
[1,-4,-3,-5,2]=>01110=>01110
[1,-4,-3,-5,-2]=>01111=>11110
[-1,4,3,5,2]=>10000=>00001
[-1,4,3,5,-2]=>10001=>10001
[-1,4,3,-5,2]=>10010=>01001
[-1,4,3,-5,-2]=>10011=>11001
[-1,4,-3,5,2]=>10100=>00101
[-1,4,-3,5,-2]=>10101=>10101
[-1,4,-3,-5,2]=>10110=>01101
[-1,4,-3,-5,-2]=>10111=>11101
[-1,-4,3,5,2]=>11000=>00011
[-1,-4,3,5,-2]=>11001=>10011
[-1,-4,3,-5,2]=>11010=>01011
[-1,-4,3,-5,-2]=>11011=>11011
[-1,-4,-3,5,2]=>11100=>00111
[-1,-4,-3,5,-2]=>11101=>10111
[-1,-4,-3,-5,2]=>11110=>01111
[-1,-4,-3,-5,-2]=>11111=>11111
[1,4,5,2,3]=>00000=>00000
[1,4,5,2,-3]=>00001=>10000
[1,4,5,-2,3]=>00010=>01000
[1,4,5,-2,-3]=>00011=>11000
[1,4,-5,2,3]=>00100=>00100
[1,4,-5,2,-3]=>00101=>10100
[1,4,-5,-2,3]=>00110=>01100
[1,4,-5,-2,-3]=>00111=>11100
[1,-4,5,2,3]=>01000=>00010
[1,-4,5,2,-3]=>01001=>10010
[1,-4,5,-2,3]=>01010=>01010
[1,-4,5,-2,-3]=>01011=>11010
[1,-4,-5,2,3]=>01100=>00110
[1,-4,-5,2,-3]=>01101=>10110
[1,-4,-5,-2,3]=>01110=>01110
[1,-4,-5,-2,-3]=>01111=>11110
[-1,4,5,2,3]=>10000=>00001
[-1,4,5,2,-3]=>10001=>10001
[-1,4,5,-2,3]=>10010=>01001
[-1,4,5,-2,-3]=>10011=>11001
[-1,4,-5,2,3]=>10100=>00101
[-1,4,-5,2,-3]=>10101=>10101
[-1,4,-5,-2,3]=>10110=>01101
[-1,4,-5,-2,-3]=>10111=>11101
[-1,-4,5,2,3]=>11000=>00011
[-1,-4,5,2,-3]=>11001=>10011
[-1,-4,5,-2,3]=>11010=>01011
[-1,-4,5,-2,-3]=>11011=>11011
[-1,-4,-5,2,3]=>11100=>00111
[-1,-4,-5,2,-3]=>11101=>10111
[-1,-4,-5,-2,3]=>11110=>01111
[-1,-4,-5,-2,-3]=>11111=>11111
[1,4,5,3,2]=>00000=>00000
[1,4,5,3,-2]=>00001=>10000
[1,4,5,-3,2]=>00010=>01000
[1,4,5,-3,-2]=>00011=>11000
[1,4,-5,3,2]=>00100=>00100
[1,4,-5,3,-2]=>00101=>10100
[1,4,-5,-3,2]=>00110=>01100
[1,4,-5,-3,-2]=>00111=>11100
[1,-4,5,3,2]=>01000=>00010
[1,-4,5,3,-2]=>01001=>10010
[1,-4,5,-3,2]=>01010=>01010
[1,-4,5,-3,-2]=>01011=>11010
[1,-4,-5,3,2]=>01100=>00110
[1,-4,-5,3,-2]=>01101=>10110
[1,-4,-5,-3,2]=>01110=>01110
[1,-4,-5,-3,-2]=>01111=>11110
[-1,4,5,3,2]=>10000=>00001
[-1,4,5,3,-2]=>10001=>10001
[-1,4,5,-3,2]=>10010=>01001
[-1,4,5,-3,-2]=>10011=>11001
[-1,4,-5,3,2]=>10100=>00101
[-1,4,-5,3,-2]=>10101=>10101
[-1,4,-5,-3,2]=>10110=>01101
[-1,4,-5,-3,-2]=>10111=>11101
[-1,-4,5,3,2]=>11000=>00011
[-1,-4,5,3,-2]=>11001=>10011
[-1,-4,5,-3,2]=>11010=>01011
[-1,-4,5,-3,-2]=>11011=>11011
[-1,-4,-5,3,2]=>11100=>00111
[-1,-4,-5,3,-2]=>11101=>10111
[-1,-4,-5,-3,2]=>11110=>01111
[-1,-4,-5,-3,-2]=>11111=>11111
[1,5,2,3,4]=>00000=>00000
[1,5,2,3,-4]=>00001=>10000
[1,5,2,-3,4]=>00010=>01000
[1,5,2,-3,-4]=>00011=>11000
[1,5,-2,3,4]=>00100=>00100
[1,5,-2,3,-4]=>00101=>10100
[1,5,-2,-3,4]=>00110=>01100
[1,5,-2,-3,-4]=>00111=>11100
[1,-5,2,3,4]=>01000=>00010
[1,-5,2,3,-4]=>01001=>10010
[1,-5,2,-3,4]=>01010=>01010
[1,-5,2,-3,-4]=>01011=>11010
[1,-5,-2,3,4]=>01100=>00110
[1,-5,-2,3,-4]=>01101=>10110
[1,-5,-2,-3,4]=>01110=>01110
[1,-5,-2,-3,-4]=>01111=>11110
[-1,5,2,3,4]=>10000=>00001
[-1,5,2,3,-4]=>10001=>10001
[-1,5,2,-3,4]=>10010=>01001
[-1,5,2,-3,-4]=>10011=>11001
[-1,5,-2,3,4]=>10100=>00101
[-1,5,-2,3,-4]=>10101=>10101
[-1,5,-2,-3,4]=>10110=>01101
[-1,5,-2,-3,-4]=>10111=>11101
[-1,-5,2,3,4]=>11000=>00011
[-1,-5,2,3,-4]=>11001=>10011
[-1,-5,2,-3,4]=>11010=>01011
[-1,-5,2,-3,-4]=>11011=>11011
[-1,-5,-2,3,4]=>11100=>00111
[-1,-5,-2,3,-4]=>11101=>10111
[-1,-5,-2,-3,4]=>11110=>01111
[-1,-5,-2,-3,-4]=>11111=>11111
[1,5,2,4,3]=>00000=>00000
[1,5,2,4,-3]=>00001=>10000
[1,5,2,-4,3]=>00010=>01000
[1,5,2,-4,-3]=>00011=>11000
[1,5,-2,4,3]=>00100=>00100
[1,5,-2,4,-3]=>00101=>10100
[1,5,-2,-4,3]=>00110=>01100
[1,5,-2,-4,-3]=>00111=>11100
[1,-5,2,4,3]=>01000=>00010
[1,-5,2,4,-3]=>01001=>10010
[1,-5,2,-4,3]=>01010=>01010
[1,-5,2,-4,-3]=>01011=>11010
[1,-5,-2,4,3]=>01100=>00110
[1,-5,-2,4,-3]=>01101=>10110
[1,-5,-2,-4,3]=>01110=>01110
[1,-5,-2,-4,-3]=>01111=>11110
[-1,5,2,4,3]=>10000=>00001
[-1,5,2,4,-3]=>10001=>10001
[-1,5,2,-4,3]=>10010=>01001
[-1,5,2,-4,-3]=>10011=>11001
[-1,5,-2,4,3]=>10100=>00101
[-1,5,-2,4,-3]=>10101=>10101
[-1,5,-2,-4,3]=>10110=>01101
[-1,5,-2,-4,-3]=>10111=>11101
[-1,-5,2,4,3]=>11000=>00011
[-1,-5,2,4,-3]=>11001=>10011
[-1,-5,2,-4,3]=>11010=>01011
[-1,-5,2,-4,-3]=>11011=>11011
[-1,-5,-2,4,3]=>11100=>00111
[-1,-5,-2,4,-3]=>11101=>10111
[-1,-5,-2,-4,3]=>11110=>01111
[-1,-5,-2,-4,-3]=>11111=>11111
[1,5,3,2,4]=>00000=>00000
[1,5,3,2,-4]=>00001=>10000
[1,5,3,-2,4]=>00010=>01000
[1,5,3,-2,-4]=>00011=>11000
[1,5,-3,2,4]=>00100=>00100
[1,5,-3,2,-4]=>00101=>10100
[1,5,-3,-2,4]=>00110=>01100
[1,5,-3,-2,-4]=>00111=>11100
[1,-5,3,2,4]=>01000=>00010
[1,-5,3,2,-4]=>01001=>10010
[1,-5,3,-2,4]=>01010=>01010
[1,-5,3,-2,-4]=>01011=>11010
[1,-5,-3,2,4]=>01100=>00110
[1,-5,-3,2,-4]=>01101=>10110
[1,-5,-3,-2,4]=>01110=>01110
[1,-5,-3,-2,-4]=>01111=>11110
[-1,5,3,2,4]=>10000=>00001
[-1,5,3,2,-4]=>10001=>10001
[-1,5,3,-2,4]=>10010=>01001
[-1,5,3,-2,-4]=>10011=>11001
[-1,5,-3,2,4]=>10100=>00101
[-1,5,-3,2,-4]=>10101=>10101
[-1,5,-3,-2,4]=>10110=>01101
[-1,5,-3,-2,-4]=>10111=>11101
[-1,-5,3,2,4]=>11000=>00011
[-1,-5,3,2,-4]=>11001=>10011
[-1,-5,3,-2,4]=>11010=>01011
[-1,-5,3,-2,-4]=>11011=>11011
[-1,-5,-3,2,4]=>11100=>00111
[-1,-5,-3,2,-4]=>11101=>10111
[-1,-5,-3,-2,4]=>11110=>01111
[-1,-5,-3,-2,-4]=>11111=>11111
[1,5,3,4,2]=>00000=>00000
[1,5,3,4,-2]=>00001=>10000
[1,5,3,-4,2]=>00010=>01000
[1,5,3,-4,-2]=>00011=>11000
[1,5,-3,4,2]=>00100=>00100
[1,5,-3,4,-2]=>00101=>10100
[1,5,-3,-4,2]=>00110=>01100
[1,5,-3,-4,-2]=>00111=>11100
[1,-5,3,4,2]=>01000=>00010
[1,-5,3,4,-2]=>01001=>10010
[1,-5,3,-4,2]=>01010=>01010
[1,-5,3,-4,-2]=>01011=>11010
[1,-5,-3,4,2]=>01100=>00110
[1,-5,-3,4,-2]=>01101=>10110
[1,-5,-3,-4,2]=>01110=>01110
[1,-5,-3,-4,-2]=>01111=>11110
[-1,5,3,4,2]=>10000=>00001
[-1,5,3,4,-2]=>10001=>10001
[-1,5,3,-4,2]=>10010=>01001
[-1,5,3,-4,-2]=>10011=>11001
[-1,5,-3,4,2]=>10100=>00101
[-1,5,-3,4,-2]=>10101=>10101
[-1,5,-3,-4,2]=>10110=>01101
[-1,5,-3,-4,-2]=>10111=>11101
[-1,-5,3,4,2]=>11000=>00011
[-1,-5,3,4,-2]=>11001=>10011
[-1,-5,3,-4,2]=>11010=>01011
[-1,-5,3,-4,-2]=>11011=>11011
[-1,-5,-3,4,2]=>11100=>00111
[-1,-5,-3,4,-2]=>11101=>10111
[-1,-5,-3,-4,2]=>11110=>01111
[-1,-5,-3,-4,-2]=>11111=>11111
[1,5,4,2,3]=>00000=>00000
[1,5,4,2,-3]=>00001=>10000
[1,5,4,-2,3]=>00010=>01000
[1,5,4,-2,-3]=>00011=>11000
[1,5,-4,2,3]=>00100=>00100
[1,5,-4,2,-3]=>00101=>10100
[1,5,-4,-2,3]=>00110=>01100
[1,5,-4,-2,-3]=>00111=>11100
[1,-5,4,2,3]=>01000=>00010
[1,-5,4,2,-3]=>01001=>10010
[1,-5,4,-2,3]=>01010=>01010
[1,-5,4,-2,-3]=>01011=>11010
[1,-5,-4,2,3]=>01100=>00110
[1,-5,-4,2,-3]=>01101=>10110
[1,-5,-4,-2,3]=>01110=>01110
[1,-5,-4,-2,-3]=>01111=>11110
[-1,5,4,2,3]=>10000=>00001
[-1,5,4,2,-3]=>10001=>10001
[-1,5,4,-2,3]=>10010=>01001
[-1,5,4,-2,-3]=>10011=>11001
[-1,5,-4,2,3]=>10100=>00101
[-1,5,-4,2,-3]=>10101=>10101
[-1,5,-4,-2,3]=>10110=>01101
[-1,5,-4,-2,-3]=>10111=>11101
[-1,-5,4,2,3]=>11000=>00011
[-1,-5,4,2,-3]=>11001=>10011
[-1,-5,4,-2,3]=>11010=>01011
[-1,-5,4,-2,-3]=>11011=>11011
[-1,-5,-4,2,3]=>11100=>00111
[-1,-5,-4,2,-3]=>11101=>10111
[-1,-5,-4,-2,3]=>11110=>01111
[-1,-5,-4,-2,-3]=>11111=>11111
[1,5,4,3,2]=>00000=>00000
[1,5,4,3,-2]=>00001=>10000
[1,5,4,-3,2]=>00010=>01000
[1,5,4,-3,-2]=>00011=>11000
[1,5,-4,3,2]=>00100=>00100
[1,5,-4,3,-2]=>00101=>10100
[1,5,-4,-3,2]=>00110=>01100
[1,5,-4,-3,-2]=>00111=>11100
[1,-5,4,3,2]=>01000=>00010
[1,-5,4,3,-2]=>01001=>10010
[1,-5,4,-3,2]=>01010=>01010
[1,-5,4,-3,-2]=>01011=>11010
[1,-5,-4,3,2]=>01100=>00110
[1,-5,-4,3,-2]=>01101=>10110
[1,-5,-4,-3,2]=>01110=>01110
[1,-5,-4,-3,-2]=>01111=>11110
[-1,5,4,3,2]=>10000=>00001
[-1,5,4,3,-2]=>10001=>10001
[-1,5,4,-3,2]=>10010=>01001
[-1,5,4,-3,-2]=>10011=>11001
[-1,5,-4,3,2]=>10100=>00101
[-1,5,-4,3,-2]=>10101=>10101
[-1,5,-4,-3,2]=>10110=>01101
[-1,5,-4,-3,-2]=>10111=>11101
[-1,-5,4,3,2]=>11000=>00011
[-1,-5,4,3,-2]=>11001=>10011
[-1,-5,4,-3,2]=>11010=>01011
[-1,-5,4,-3,-2]=>11011=>11011
[-1,-5,-4,3,2]=>11100=>00111
[-1,-5,-4,3,-2]=>11101=>10111
[-1,-5,-4,-3,2]=>11110=>01111
[-1,-5,-4,-3,-2]=>11111=>11111
[2,1,3,4,5]=>00000=>00000
[2,1,3,4,-5]=>00001=>10000
[2,1,3,-4,5]=>00010=>01000
[2,1,3,-4,-5]=>00011=>11000
[2,1,-3,4,5]=>00100=>00100
[2,1,-3,4,-5]=>00101=>10100
[2,1,-3,-4,5]=>00110=>01100
[2,1,-3,-4,-5]=>00111=>11100
[2,-1,3,4,5]=>01000=>00010
[2,-1,3,4,-5]=>01001=>10010
[2,-1,3,-4,5]=>01010=>01010
[2,-1,3,-4,-5]=>01011=>11010
[2,-1,-3,4,5]=>01100=>00110
[2,-1,-3,4,-5]=>01101=>10110
[2,-1,-3,-4,5]=>01110=>01110
[2,-1,-3,-4,-5]=>01111=>11110
[-2,1,3,4,5]=>10000=>00001
[-2,1,3,4,-5]=>10001=>10001
[-2,1,3,-4,5]=>10010=>01001
[-2,1,3,-4,-5]=>10011=>11001
[-2,1,-3,4,5]=>10100=>00101
[-2,1,-3,4,-5]=>10101=>10101
[-2,1,-3,-4,5]=>10110=>01101
[-2,1,-3,-4,-5]=>10111=>11101
[-2,-1,3,4,5]=>11000=>00011
[-2,-1,3,4,-5]=>11001=>10011
[-2,-1,3,-4,5]=>11010=>01011
[-2,-1,3,-4,-5]=>11011=>11011
[-2,-1,-3,4,5]=>11100=>00111
[-2,-1,-3,4,-5]=>11101=>10111
[-2,-1,-3,-4,5]=>11110=>01111
[-2,-1,-3,-4,-5]=>11111=>11111
[2,1,3,5,4]=>00000=>00000
[2,1,3,5,-4]=>00001=>10000
[2,1,3,-5,4]=>00010=>01000
[2,1,3,-5,-4]=>00011=>11000
[2,1,-3,5,4]=>00100=>00100
[2,1,-3,5,-4]=>00101=>10100
[2,1,-3,-5,4]=>00110=>01100
[2,1,-3,-5,-4]=>00111=>11100
[2,-1,3,5,4]=>01000=>00010
[2,-1,3,5,-4]=>01001=>10010
[2,-1,3,-5,4]=>01010=>01010
[2,-1,3,-5,-4]=>01011=>11010
[2,-1,-3,5,4]=>01100=>00110
[2,-1,-3,5,-4]=>01101=>10110
[2,-1,-3,-5,4]=>01110=>01110
[2,-1,-3,-5,-4]=>01111=>11110
[-2,1,3,5,4]=>10000=>00001
[-2,1,3,5,-4]=>10001=>10001
[-2,1,3,-5,4]=>10010=>01001
[-2,1,3,-5,-4]=>10011=>11001
[-2,1,-3,5,4]=>10100=>00101
[-2,1,-3,5,-4]=>10101=>10101
[-2,1,-3,-5,4]=>10110=>01101
[-2,1,-3,-5,-4]=>10111=>11101
[-2,-1,3,5,4]=>11000=>00011
[-2,-1,3,5,-4]=>11001=>10011
[-2,-1,3,-5,4]=>11010=>01011
[-2,-1,3,-5,-4]=>11011=>11011
[-2,-1,-3,5,4]=>11100=>00111
[-2,-1,-3,5,-4]=>11101=>10111
[-2,-1,-3,-5,4]=>11110=>01111
[-2,-1,-3,-5,-4]=>11111=>11111
[2,1,4,3,5]=>00000=>00000
[2,1,4,3,-5]=>00001=>10000
[2,1,4,-3,5]=>00010=>01000
[2,1,4,-3,-5]=>00011=>11000
[2,1,-4,3,5]=>00100=>00100
[2,1,-4,3,-5]=>00101=>10100
[2,1,-4,-3,5]=>00110=>01100
[2,1,-4,-3,-5]=>00111=>11100
[2,-1,4,3,5]=>01000=>00010
[2,-1,4,3,-5]=>01001=>10010
[2,-1,4,-3,5]=>01010=>01010
[2,-1,4,-3,-5]=>01011=>11010
[2,-1,-4,3,5]=>01100=>00110
[2,-1,-4,3,-5]=>01101=>10110
[2,-1,-4,-3,5]=>01110=>01110
[2,-1,-4,-3,-5]=>01111=>11110
[-2,1,4,3,5]=>10000=>00001
[-2,1,4,3,-5]=>10001=>10001
[-2,1,4,-3,5]=>10010=>01001
[-2,1,4,-3,-5]=>10011=>11001
[-2,1,-4,3,5]=>10100=>00101
[-2,1,-4,3,-5]=>10101=>10101
[-2,1,-4,-3,5]=>10110=>01101
[-2,1,-4,-3,-5]=>10111=>11101
[-2,-1,4,3,5]=>11000=>00011
[-2,-1,4,3,-5]=>11001=>10011
[-2,-1,4,-3,5]=>11010=>01011
[-2,-1,4,-3,-5]=>11011=>11011
[-2,-1,-4,3,5]=>11100=>00111
[-2,-1,-4,3,-5]=>11101=>10111
[-2,-1,-4,-3,5]=>11110=>01111
[-2,-1,-4,-3,-5]=>11111=>11111
[2,1,4,5,3]=>00000=>00000
[2,1,4,5,-3]=>00001=>10000
[2,1,4,-5,3]=>00010=>01000
[2,1,4,-5,-3]=>00011=>11000
[2,1,-4,5,3]=>00100=>00100
[2,1,-4,5,-3]=>00101=>10100
[2,1,-4,-5,3]=>00110=>01100
[2,1,-4,-5,-3]=>00111=>11100
[2,-1,4,5,3]=>01000=>00010
[2,-1,4,5,-3]=>01001=>10010
[2,-1,4,-5,3]=>01010=>01010
[2,-1,4,-5,-3]=>01011=>11010
[2,-1,-4,5,3]=>01100=>00110
[2,-1,-4,5,-3]=>01101=>10110
[2,-1,-4,-5,3]=>01110=>01110
[2,-1,-4,-5,-3]=>01111=>11110
[-2,1,4,5,3]=>10000=>00001
[-2,1,4,5,-3]=>10001=>10001
[-2,1,4,-5,3]=>10010=>01001
[-2,1,4,-5,-3]=>10011=>11001
[-2,1,-4,5,3]=>10100=>00101
[-2,1,-4,5,-3]=>10101=>10101
[-2,1,-4,-5,3]=>10110=>01101
[-2,1,-4,-5,-3]=>10111=>11101
[-2,-1,4,5,3]=>11000=>00011
[-2,-1,4,5,-3]=>11001=>10011
[-2,-1,4,-5,3]=>11010=>01011
[-2,-1,4,-5,-3]=>11011=>11011
[-2,-1,-4,5,3]=>11100=>00111
[-2,-1,-4,5,-3]=>11101=>10111
[-2,-1,-4,-5,3]=>11110=>01111
[-2,-1,-4,-5,-3]=>11111=>11111
[2,1,5,3,4]=>00000=>00000
[2,1,5,3,-4]=>00001=>10000
[2,1,5,-3,4]=>00010=>01000
[2,1,5,-3,-4]=>00011=>11000
[2,1,-5,3,4]=>00100=>00100
[2,1,-5,3,-4]=>00101=>10100
[2,1,-5,-3,4]=>00110=>01100
[2,1,-5,-3,-4]=>00111=>11100
[2,-1,5,3,4]=>01000=>00010
[2,-1,5,3,-4]=>01001=>10010
[2,-1,5,-3,4]=>01010=>01010
[2,-1,5,-3,-4]=>01011=>11010
[2,-1,-5,3,4]=>01100=>00110
[2,-1,-5,3,-4]=>01101=>10110
[2,-1,-5,-3,4]=>01110=>01110
[2,-1,-5,-3,-4]=>01111=>11110
[-2,1,5,3,4]=>10000=>00001
[-2,1,5,3,-4]=>10001=>10001
[-2,1,5,-3,4]=>10010=>01001
[-2,1,5,-3,-4]=>10011=>11001
[-2,1,-5,3,4]=>10100=>00101
[-2,1,-5,3,-4]=>10101=>10101
[-2,1,-5,-3,4]=>10110=>01101
[-2,1,-5,-3,-4]=>10111=>11101
[-2,-1,5,3,4]=>11000=>00011
[-2,-1,5,3,-4]=>11001=>10011
[-2,-1,5,-3,4]=>11010=>01011
[-2,-1,5,-3,-4]=>11011=>11011
[-2,-1,-5,3,4]=>11100=>00111
[-2,-1,-5,3,-4]=>11101=>10111
[-2,-1,-5,-3,4]=>11110=>01111
[-2,-1,-5,-3,-4]=>11111=>11111
[2,1,5,4,3]=>00000=>00000
[2,1,5,4,-3]=>00001=>10000
[2,1,5,-4,3]=>00010=>01000
[2,1,5,-4,-3]=>00011=>11000
[2,1,-5,4,3]=>00100=>00100
[2,1,-5,4,-3]=>00101=>10100
[2,1,-5,-4,3]=>00110=>01100
[2,1,-5,-4,-3]=>00111=>11100
[2,-1,5,4,3]=>01000=>00010
[2,-1,5,4,-3]=>01001=>10010
[2,-1,5,-4,3]=>01010=>01010
[2,-1,5,-4,-3]=>01011=>11010
[2,-1,-5,4,3]=>01100=>00110
[2,-1,-5,4,-3]=>01101=>10110
[2,-1,-5,-4,3]=>01110=>01110
[2,-1,-5,-4,-3]=>01111=>11110
[-2,1,5,4,3]=>10000=>00001
[-2,1,5,4,-3]=>10001=>10001
[-2,1,5,-4,3]=>10010=>01001
[-2,1,5,-4,-3]=>10011=>11001
[-2,1,-5,4,3]=>10100=>00101
[-2,1,-5,4,-3]=>10101=>10101
[-2,1,-5,-4,3]=>10110=>01101
[-2,1,-5,-4,-3]=>10111=>11101
[-2,-1,5,4,3]=>11000=>00011
[-2,-1,5,4,-3]=>11001=>10011
[-2,-1,5,-4,3]=>11010=>01011
[-2,-1,5,-4,-3]=>11011=>11011
[-2,-1,-5,4,3]=>11100=>00111
[-2,-1,-5,4,-3]=>11101=>10111
[-2,-1,-5,-4,3]=>11110=>01111
[-2,-1,-5,-4,-3]=>11111=>11111
[2,3,1,4,5]=>00000=>00000
[2,3,1,4,-5]=>00001=>10000
[2,3,1,-4,5]=>00010=>01000
[2,3,1,-4,-5]=>00011=>11000
[2,3,-1,4,5]=>00100=>00100
[2,3,-1,4,-5]=>00101=>10100
[2,3,-1,-4,5]=>00110=>01100
[2,3,-1,-4,-5]=>00111=>11100
[2,-3,1,4,5]=>01000=>00010
[2,-3,1,4,-5]=>01001=>10010
[2,-3,1,-4,5]=>01010=>01010
[2,-3,1,-4,-5]=>01011=>11010
[2,-3,-1,4,5]=>01100=>00110
[2,-3,-1,4,-5]=>01101=>10110
[2,-3,-1,-4,5]=>01110=>01110
[2,-3,-1,-4,-5]=>01111=>11110
[-2,3,1,4,5]=>10000=>00001
[-2,3,1,4,-5]=>10001=>10001
[-2,3,1,-4,5]=>10010=>01001
[-2,3,1,-4,-5]=>10011=>11001
[-2,3,-1,4,5]=>10100=>00101
[-2,3,-1,4,-5]=>10101=>10101
[-2,3,-1,-4,5]=>10110=>01101
[-2,3,-1,-4,-5]=>10111=>11101
[-2,-3,1,4,5]=>11000=>00011
[-2,-3,1,4,-5]=>11001=>10011
[-2,-3,1,-4,5]=>11010=>01011
[-2,-3,1,-4,-5]=>11011=>11011
[-2,-3,-1,4,5]=>11100=>00111
[-2,-3,-1,4,-5]=>11101=>10111
[-2,-3,-1,-4,5]=>11110=>01111
[-2,-3,-1,-4,-5]=>11111=>11111
[2,3,1,5,4]=>00000=>00000
[2,3,1,5,-4]=>00001=>10000
[2,3,1,-5,4]=>00010=>01000
[2,3,1,-5,-4]=>00011=>11000
[2,3,-1,5,4]=>00100=>00100
[2,3,-1,5,-4]=>00101=>10100
[2,3,-1,-5,4]=>00110=>01100
[2,3,-1,-5,-4]=>00111=>11100
[2,-3,1,5,4]=>01000=>00010
[2,-3,1,5,-4]=>01001=>10010
[2,-3,1,-5,4]=>01010=>01010
[2,-3,1,-5,-4]=>01011=>11010
[2,-3,-1,5,4]=>01100=>00110
[2,-3,-1,5,-4]=>01101=>10110
[2,-3,-1,-5,4]=>01110=>01110
[2,-3,-1,-5,-4]=>01111=>11110
[-2,3,1,5,4]=>10000=>00001
[-2,3,1,5,-4]=>10001=>10001
[-2,3,1,-5,4]=>10010=>01001
[-2,3,1,-5,-4]=>10011=>11001
[-2,3,-1,5,4]=>10100=>00101
[-2,3,-1,5,-4]=>10101=>10101
[-2,3,-1,-5,4]=>10110=>01101
[-2,3,-1,-5,-4]=>10111=>11101
[-2,-3,1,5,4]=>11000=>00011
[-2,-3,1,5,-4]=>11001=>10011
[-2,-3,1,-5,4]=>11010=>01011
[-2,-3,1,-5,-4]=>11011=>11011
[-2,-3,-1,5,4]=>11100=>00111
[-2,-3,-1,5,-4]=>11101=>10111
[-2,-3,-1,-5,4]=>11110=>01111
[-2,-3,-1,-5,-4]=>11111=>11111
[2,3,4,1,5]=>00000=>00000
[2,3,4,1,-5]=>00001=>10000
[2,3,4,-1,5]=>00010=>01000
[2,3,4,-1,-5]=>00011=>11000
[2,3,-4,1,5]=>00100=>00100
[2,3,-4,1,-5]=>00101=>10100
[2,3,-4,-1,5]=>00110=>01100
[2,3,-4,-1,-5]=>00111=>11100
[2,-3,4,1,5]=>01000=>00010
[2,-3,4,1,-5]=>01001=>10010
[2,-3,4,-1,5]=>01010=>01010
[2,-3,4,-1,-5]=>01011=>11010
[2,-3,-4,1,5]=>01100=>00110
[2,-3,-4,1,-5]=>01101=>10110
[2,-3,-4,-1,5]=>01110=>01110
[2,-3,-4,-1,-5]=>01111=>11110
[-2,3,4,1,5]=>10000=>00001
[-2,3,4,1,-5]=>10001=>10001
[-2,3,4,-1,5]=>10010=>01001
[-2,3,4,-1,-5]=>10011=>11001
[-2,3,-4,1,5]=>10100=>00101
[-2,3,-4,1,-5]=>10101=>10101
[-2,3,-4,-1,5]=>10110=>01101
[-2,3,-4,-1,-5]=>10111=>11101
[-2,-3,4,1,5]=>11000=>00011
[-2,-3,4,1,-5]=>11001=>10011
[-2,-3,4,-1,5]=>11010=>01011
[-2,-3,4,-1,-5]=>11011=>11011
[-2,-3,-4,1,5]=>11100=>00111
[-2,-3,-4,1,-5]=>11101=>10111
[-2,-3,-4,-1,5]=>11110=>01111
[-2,-3,-4,-1,-5]=>11111=>11111
[2,3,4,5,1]=>00000=>00000
[2,3,4,5,-1]=>00001=>10000
[2,3,4,-5,1]=>00010=>01000
[2,3,4,-5,-1]=>00011=>11000
[2,3,-4,5,1]=>00100=>00100
[2,3,-4,5,-1]=>00101=>10100
[2,3,-4,-5,1]=>00110=>01100
[2,3,-4,-5,-1]=>00111=>11100
[2,-3,4,5,1]=>01000=>00010
[2,-3,4,5,-1]=>01001=>10010
[2,-3,4,-5,1]=>01010=>01010
[2,-3,4,-5,-1]=>01011=>11010
[2,-3,-4,5,1]=>01100=>00110
[2,-3,-4,5,-1]=>01101=>10110
[2,-3,-4,-5,1]=>01110=>01110
[2,-3,-4,-5,-1]=>01111=>11110
[-2,3,4,5,1]=>10000=>00001
[-2,3,4,5,-1]=>10001=>10001
[-2,3,4,-5,1]=>10010=>01001
[-2,3,4,-5,-1]=>10011=>11001
[-2,3,-4,5,1]=>10100=>00101
[-2,3,-4,5,-1]=>10101=>10101
[-2,3,-4,-5,1]=>10110=>01101
[-2,3,-4,-5,-1]=>10111=>11101
[-2,-3,4,5,1]=>11000=>00011
[-2,-3,4,5,-1]=>11001=>10011
[-2,-3,4,-5,1]=>11010=>01011
[-2,-3,4,-5,-1]=>11011=>11011
[-2,-3,-4,5,1]=>11100=>00111
[-2,-3,-4,5,-1]=>11101=>10111
[-2,-3,-4,-5,1]=>11110=>01111
[-2,-3,-4,-5,-1]=>11111=>11111
[2,3,5,1,4]=>00000=>00000
[2,3,5,1,-4]=>00001=>10000
[2,3,5,-1,4]=>00010=>01000
[2,3,5,-1,-4]=>00011=>11000
[2,3,-5,1,4]=>00100=>00100
[2,3,-5,1,-4]=>00101=>10100
[2,3,-5,-1,4]=>00110=>01100
[2,3,-5,-1,-4]=>00111=>11100
[2,-3,5,1,4]=>01000=>00010
[2,-3,5,1,-4]=>01001=>10010
[2,-3,5,-1,4]=>01010=>01010
[2,-3,5,-1,-4]=>01011=>11010
[2,-3,-5,1,4]=>01100=>00110
[2,-3,-5,1,-4]=>01101=>10110
[2,-3,-5,-1,4]=>01110=>01110
[2,-3,-5,-1,-4]=>01111=>11110
[-2,3,5,1,4]=>10000=>00001
[-2,3,5,1,-4]=>10001=>10001
[-2,3,5,-1,4]=>10010=>01001
[-2,3,5,-1,-4]=>10011=>11001
[-2,3,-5,1,4]=>10100=>00101
[-2,3,-5,1,-4]=>10101=>10101
[-2,3,-5,-1,4]=>10110=>01101
[-2,3,-5,-1,-4]=>10111=>11101
[-2,-3,5,1,4]=>11000=>00011
[-2,-3,5,1,-4]=>11001=>10011
[-2,-3,5,-1,4]=>11010=>01011
[-2,-3,5,-1,-4]=>11011=>11011
[-2,-3,-5,1,4]=>11100=>00111
[-2,-3,-5,1,-4]=>11101=>10111
[-2,-3,-5,-1,4]=>11110=>01111
[-2,-3,-5,-1,-4]=>11111=>11111
[2,3,5,4,1]=>00000=>00000
[2,3,5,4,-1]=>00001=>10000
[2,3,5,-4,1]=>00010=>01000
[2,3,5,-4,-1]=>00011=>11000
[2,3,-5,4,1]=>00100=>00100
[2,3,-5,4,-1]=>00101=>10100
[2,3,-5,-4,1]=>00110=>01100
[2,3,-5,-4,-1]=>00111=>11100
[2,-3,5,4,1]=>01000=>00010
[2,-3,5,4,-1]=>01001=>10010
[2,-3,5,-4,1]=>01010=>01010
[2,-3,5,-4,-1]=>01011=>11010
[2,-3,-5,4,1]=>01100=>00110
[2,-3,-5,4,-1]=>01101=>10110
[2,-3,-5,-4,1]=>01110=>01110
[2,-3,-5,-4,-1]=>01111=>11110
[-2,3,5,4,1]=>10000=>00001
[-2,3,5,4,-1]=>10001=>10001
[-2,3,5,-4,1]=>10010=>01001
[-2,3,5,-4,-1]=>10011=>11001
[-2,3,-5,4,1]=>10100=>00101
[-2,3,-5,4,-1]=>10101=>10101
[-2,3,-5,-4,1]=>10110=>01101
[-2,3,-5,-4,-1]=>10111=>11101
[-2,-3,5,4,1]=>11000=>00011
[-2,-3,5,4,-1]=>11001=>10011
[-2,-3,5,-4,1]=>11010=>01011
[-2,-3,5,-4,-1]=>11011=>11011
[-2,-3,-5,4,1]=>11100=>00111
[-2,-3,-5,4,-1]=>11101=>10111
[-2,-3,-5,-4,1]=>11110=>01111
[-2,-3,-5,-4,-1]=>11111=>11111
[2,4,1,3,5]=>00000=>00000
[2,4,1,3,-5]=>00001=>10000
[2,4,1,-3,5]=>00010=>01000
[2,4,1,-3,-5]=>00011=>11000
[2,4,-1,3,5]=>00100=>00100
[2,4,-1,3,-5]=>00101=>10100
[2,4,-1,-3,5]=>00110=>01100
[2,4,-1,-3,-5]=>00111=>11100
[2,-4,1,3,5]=>01000=>00010
[2,-4,1,3,-5]=>01001=>10010
[2,-4,1,-3,5]=>01010=>01010
[2,-4,1,-3,-5]=>01011=>11010
[2,-4,-1,3,5]=>01100=>00110
[2,-4,-1,3,-5]=>01101=>10110
[2,-4,-1,-3,5]=>01110=>01110
[2,-4,-1,-3,-5]=>01111=>11110
[-2,4,1,3,5]=>10000=>00001
[-2,4,1,3,-5]=>10001=>10001
[-2,4,1,-3,5]=>10010=>01001
[-2,4,1,-3,-5]=>10011=>11001
[-2,4,-1,3,5]=>10100=>00101
[-2,4,-1,3,-5]=>10101=>10101
[-2,4,-1,-3,5]=>10110=>01101
[-2,4,-1,-3,-5]=>10111=>11101
[-2,-4,1,3,5]=>11000=>00011
[-2,-4,1,3,-5]=>11001=>10011
[-2,-4,1,-3,5]=>11010=>01011
[-2,-4,1,-3,-5]=>11011=>11011
[-2,-4,-1,3,5]=>11100=>00111
[-2,-4,-1,3,-5]=>11101=>10111
[-2,-4,-1,-3,5]=>11110=>01111
[-2,-4,-1,-3,-5]=>11111=>11111
[2,4,1,5,3]=>00000=>00000
[2,4,1,5,-3]=>00001=>10000
[2,4,1,-5,3]=>00010=>01000
[2,4,1,-5,-3]=>00011=>11000
[2,4,-1,5,3]=>00100=>00100
[2,4,-1,5,-3]=>00101=>10100
[2,4,-1,-5,3]=>00110=>01100
[2,4,-1,-5,-3]=>00111=>11100
[2,-4,1,5,3]=>01000=>00010
[2,-4,1,5,-3]=>01001=>10010
[2,-4,1,-5,3]=>01010=>01010
[2,-4,1,-5,-3]=>01011=>11010
[2,-4,-1,5,3]=>01100=>00110
[2,-4,-1,5,-3]=>01101=>10110
[2,-4,-1,-5,3]=>01110=>01110
[2,-4,-1,-5,-3]=>01111=>11110
[-2,4,1,5,3]=>10000=>00001
[-2,4,1,5,-3]=>10001=>10001
[-2,4,1,-5,3]=>10010=>01001
[-2,4,1,-5,-3]=>10011=>11001
[-2,4,-1,5,3]=>10100=>00101
[-2,4,-1,5,-3]=>10101=>10101
[-2,4,-1,-5,3]=>10110=>01101
[-2,4,-1,-5,-3]=>10111=>11101
[-2,-4,1,5,3]=>11000=>00011
[-2,-4,1,5,-3]=>11001=>10011
[-2,-4,1,-5,3]=>11010=>01011
[-2,-4,1,-5,-3]=>11011=>11011
[-2,-4,-1,5,3]=>11100=>00111
[-2,-4,-1,5,-3]=>11101=>10111
[-2,-4,-1,-5,3]=>11110=>01111
[-2,-4,-1,-5,-3]=>11111=>11111
[2,4,3,1,5]=>00000=>00000
[2,4,3,1,-5]=>00001=>10000
[2,4,3,-1,5]=>00010=>01000
[2,4,3,-1,-5]=>00011=>11000
[2,4,-3,1,5]=>00100=>00100
[2,4,-3,1,-5]=>00101=>10100
[2,4,-3,-1,5]=>00110=>01100
[2,4,-3,-1,-5]=>00111=>11100
[2,-4,3,1,5]=>01000=>00010
[2,-4,3,1,-5]=>01001=>10010
[2,-4,3,-1,5]=>01010=>01010
[2,-4,3,-1,-5]=>01011=>11010
[2,-4,-3,1,5]=>01100=>00110
[2,-4,-3,1,-5]=>01101=>10110
[2,-4,-3,-1,5]=>01110=>01110
[2,-4,-3,-1,-5]=>01111=>11110
[-2,4,3,1,5]=>10000=>00001
[-2,4,3,1,-5]=>10001=>10001
[-2,4,3,-1,5]=>10010=>01001
[-2,4,3,-1,-5]=>10011=>11001
[-2,4,-3,1,5]=>10100=>00101
[-2,4,-3,1,-5]=>10101=>10101
[-2,4,-3,-1,5]=>10110=>01101
[-2,4,-3,-1,-5]=>10111=>11101
[-2,-4,3,1,5]=>11000=>00011
[-2,-4,3,1,-5]=>11001=>10011
[-2,-4,3,-1,5]=>11010=>01011
[-2,-4,3,-1,-5]=>11011=>11011
[-2,-4,-3,1,5]=>11100=>00111
[-2,-4,-3,1,-5]=>11101=>10111
[-2,-4,-3,-1,5]=>11110=>01111
[-2,-4,-3,-1,-5]=>11111=>11111
[2,4,3,5,1]=>00000=>00000
[2,4,3,5,-1]=>00001=>10000
[2,4,3,-5,1]=>00010=>01000
[2,4,3,-5,-1]=>00011=>11000
[2,4,-3,5,1]=>00100=>00100
[2,4,-3,5,-1]=>00101=>10100
[2,4,-3,-5,1]=>00110=>01100
[2,4,-3,-5,-1]=>00111=>11100
[2,-4,3,5,1]=>01000=>00010
[2,-4,3,5,-1]=>01001=>10010
[2,-4,3,-5,1]=>01010=>01010
[2,-4,3,-5,-1]=>01011=>11010
[2,-4,-3,5,1]=>01100=>00110
[2,-4,-3,5,-1]=>01101=>10110
[2,-4,-3,-5,1]=>01110=>01110
[2,-4,-3,-5,-1]=>01111=>11110
[-2,4,3,5,1]=>10000=>00001
[-2,4,3,5,-1]=>10001=>10001
[-2,4,3,-5,1]=>10010=>01001
[-2,4,3,-5,-1]=>10011=>11001
[-2,4,-3,5,1]=>10100=>00101
[-2,4,-3,5,-1]=>10101=>10101
[-2,4,-3,-5,1]=>10110=>01101
[-2,4,-3,-5,-1]=>10111=>11101
[-2,-4,3,5,1]=>11000=>00011
[-2,-4,3,5,-1]=>11001=>10011
[-2,-4,3,-5,1]=>11010=>01011
[-2,-4,3,-5,-1]=>11011=>11011
[-2,-4,-3,5,1]=>11100=>00111
[-2,-4,-3,5,-1]=>11101=>10111
[-2,-4,-3,-5,1]=>11110=>01111
[-2,-4,-3,-5,-1]=>11111=>11111
[2,4,5,1,3]=>00000=>00000
[2,4,5,1,-3]=>00001=>10000
[2,4,5,-1,3]=>00010=>01000
[2,4,5,-1,-3]=>00011=>11000
[2,4,-5,1,3]=>00100=>00100
[2,4,-5,1,-3]=>00101=>10100
[2,4,-5,-1,3]=>00110=>01100
[2,4,-5,-1,-3]=>00111=>11100
[2,-4,5,1,3]=>01000=>00010
[2,-4,5,1,-3]=>01001=>10010
[2,-4,5,-1,3]=>01010=>01010
[2,-4,5,-1,-3]=>01011=>11010
[2,-4,-5,1,3]=>01100=>00110
[2,-4,-5,1,-3]=>01101=>10110
[2,-4,-5,-1,3]=>01110=>01110
[2,-4,-5,-1,-3]=>01111=>11110
[-2,4,5,1,3]=>10000=>00001
[-2,4,5,1,-3]=>10001=>10001
[-2,4,5,-1,3]=>10010=>01001
[-2,4,5,-1,-3]=>10011=>11001
[-2,4,-5,1,3]=>10100=>00101
[-2,4,-5,1,-3]=>10101=>10101
[-2,4,-5,-1,3]=>10110=>01101
[-2,4,-5,-1,-3]=>10111=>11101
[-2,-4,5,1,3]=>11000=>00011
[-2,-4,5,1,-3]=>11001=>10011
[-2,-4,5,-1,3]=>11010=>01011
[-2,-4,5,-1,-3]=>11011=>11011
[-2,-4,-5,1,3]=>11100=>00111
[-2,-4,-5,1,-3]=>11101=>10111
[-2,-4,-5,-1,3]=>11110=>01111
[-2,-4,-5,-1,-3]=>11111=>11111
[2,4,5,3,1]=>00000=>00000
[2,4,5,3,-1]=>00001=>10000
[2,4,5,-3,1]=>00010=>01000
[2,4,5,-3,-1]=>00011=>11000
[2,4,-5,3,1]=>00100=>00100
[2,4,-5,3,-1]=>00101=>10100
[2,4,-5,-3,1]=>00110=>01100
[2,4,-5,-3,-1]=>00111=>11100
[2,-4,5,3,1]=>01000=>00010
[2,-4,5,3,-1]=>01001=>10010
[2,-4,5,-3,1]=>01010=>01010
[2,-4,5,-3,-1]=>01011=>11010
[2,-4,-5,3,1]=>01100=>00110
[2,-4,-5,3,-1]=>01101=>10110
[2,-4,-5,-3,1]=>01110=>01110
[2,-4,-5,-3,-1]=>01111=>11110
[-2,4,5,3,1]=>10000=>00001
[-2,4,5,3,-1]=>10001=>10001
[-2,4,5,-3,1]=>10010=>01001
[-2,4,5,-3,-1]=>10011=>11001
[-2,4,-5,3,1]=>10100=>00101
[-2,4,-5,3,-1]=>10101=>10101
[-2,4,-5,-3,1]=>10110=>01101
[-2,4,-5,-3,-1]=>10111=>11101
[-2,-4,5,3,1]=>11000=>00011
[-2,-4,5,3,-1]=>11001=>10011
[-2,-4,5,-3,1]=>11010=>01011
[-2,-4,5,-3,-1]=>11011=>11011
[-2,-4,-5,3,1]=>11100=>00111
[-2,-4,-5,3,-1]=>11101=>10111
[-2,-4,-5,-3,1]=>11110=>01111
[-2,-4,-5,-3,-1]=>11111=>11111
[2,5,1,3,4]=>00000=>00000
[2,5,1,3,-4]=>00001=>10000
[2,5,1,-3,4]=>00010=>01000
[2,5,1,-3,-4]=>00011=>11000
[2,5,-1,3,4]=>00100=>00100
[2,5,-1,3,-4]=>00101=>10100
[2,5,-1,-3,4]=>00110=>01100
[2,5,-1,-3,-4]=>00111=>11100
[2,-5,1,3,4]=>01000=>00010
[2,-5,1,3,-4]=>01001=>10010
[2,-5,1,-3,4]=>01010=>01010
[2,-5,1,-3,-4]=>01011=>11010
[2,-5,-1,3,4]=>01100=>00110
[2,-5,-1,3,-4]=>01101=>10110
[2,-5,-1,-3,4]=>01110=>01110
[2,-5,-1,-3,-4]=>01111=>11110
[-2,5,1,3,4]=>10000=>00001
[-2,5,1,3,-4]=>10001=>10001
[-2,5,1,-3,4]=>10010=>01001
[-2,5,1,-3,-4]=>10011=>11001
[-2,5,-1,3,4]=>10100=>00101
[-2,5,-1,3,-4]=>10101=>10101
[-2,5,-1,-3,4]=>10110=>01101
[-2,5,-1,-3,-4]=>10111=>11101
[-2,-5,1,3,4]=>11000=>00011
[-2,-5,1,3,-4]=>11001=>10011
[-2,-5,1,-3,4]=>11010=>01011
[-2,-5,1,-3,-4]=>11011=>11011
[-2,-5,-1,3,4]=>11100=>00111
[-2,-5,-1,3,-4]=>11101=>10111
[-2,-5,-1,-3,4]=>11110=>01111
[-2,-5,-1,-3,-4]=>11111=>11111
[2,5,1,4,3]=>00000=>00000
[2,5,1,4,-3]=>00001=>10000
[2,5,1,-4,3]=>00010=>01000
[2,5,1,-4,-3]=>00011=>11000
[2,5,-1,4,3]=>00100=>00100
[2,5,-1,4,-3]=>00101=>10100
[2,5,-1,-4,3]=>00110=>01100
[2,5,-1,-4,-3]=>00111=>11100
[2,-5,1,4,3]=>01000=>00010
[2,-5,1,4,-3]=>01001=>10010
[2,-5,1,-4,3]=>01010=>01010
[2,-5,1,-4,-3]=>01011=>11010
[2,-5,-1,4,3]=>01100=>00110
[2,-5,-1,4,-3]=>01101=>10110
[2,-5,-1,-4,3]=>01110=>01110
[2,-5,-1,-4,-3]=>01111=>11110
[-2,5,1,4,3]=>10000=>00001
[-2,5,1,4,-3]=>10001=>10001
[-2,5,1,-4,3]=>10010=>01001
[-2,5,1,-4,-3]=>10011=>11001
[-2,5,-1,4,3]=>10100=>00101
[-2,5,-1,4,-3]=>10101=>10101
[-2,5,-1,-4,3]=>10110=>01101
[-2,5,-1,-4,-3]=>10111=>11101
[-2,-5,1,4,3]=>11000=>00011
[-2,-5,1,4,-3]=>11001=>10011
[-2,-5,1,-4,3]=>11010=>01011
[-2,-5,1,-4,-3]=>11011=>11011
[-2,-5,-1,4,3]=>11100=>00111
[-2,-5,-1,4,-3]=>11101=>10111
[-2,-5,-1,-4,3]=>11110=>01111
[-2,-5,-1,-4,-3]=>11111=>11111
[2,5,3,1,4]=>00000=>00000
[2,5,3,1,-4]=>00001=>10000
[2,5,3,-1,4]=>00010=>01000
[2,5,3,-1,-4]=>00011=>11000
[2,5,-3,1,4]=>00100=>00100
[2,5,-3,1,-4]=>00101=>10100
[2,5,-3,-1,4]=>00110=>01100
[2,5,-3,-1,-4]=>00111=>11100
[2,-5,3,1,4]=>01000=>00010
[2,-5,3,1,-4]=>01001=>10010
[2,-5,3,-1,4]=>01010=>01010
[2,-5,3,-1,-4]=>01011=>11010
[2,-5,-3,1,4]=>01100=>00110
[2,-5,-3,1,-4]=>01101=>10110
[2,-5,-3,-1,4]=>01110=>01110
[2,-5,-3,-1,-4]=>01111=>11110
[-2,5,3,1,4]=>10000=>00001
[-2,5,3,1,-4]=>10001=>10001
[-2,5,3,-1,4]=>10010=>01001
[-2,5,3,-1,-4]=>10011=>11001
[-2,5,-3,1,4]=>10100=>00101
[-2,5,-3,1,-4]=>10101=>10101
[-2,5,-3,-1,4]=>10110=>01101
[-2,5,-3,-1,-4]=>10111=>11101
[-2,-5,3,1,4]=>11000=>00011
[-2,-5,3,1,-4]=>11001=>10011
[-2,-5,3,-1,4]=>11010=>01011
[-2,-5,3,-1,-4]=>11011=>11011
[-2,-5,-3,1,4]=>11100=>00111
[-2,-5,-3,1,-4]=>11101=>10111
[-2,-5,-3,-1,4]=>11110=>01111
[-2,-5,-3,-1,-4]=>11111=>11111
[2,5,3,4,1]=>00000=>00000
[2,5,3,4,-1]=>00001=>10000
[2,5,3,-4,1]=>00010=>01000
[2,5,3,-4,-1]=>00011=>11000
[2,5,-3,4,1]=>00100=>00100
[2,5,-3,4,-1]=>00101=>10100
[2,5,-3,-4,1]=>00110=>01100
[2,5,-3,-4,-1]=>00111=>11100
[2,-5,3,4,1]=>01000=>00010
[2,-5,3,4,-1]=>01001=>10010
[2,-5,3,-4,1]=>01010=>01010
[2,-5,3,-4,-1]=>01011=>11010
[2,-5,-3,4,1]=>01100=>00110
[2,-5,-3,4,-1]=>01101=>10110
[2,-5,-3,-4,1]=>01110=>01110
[2,-5,-3,-4,-1]=>01111=>11110
[-2,5,3,4,1]=>10000=>00001
[-2,5,3,4,-1]=>10001=>10001
[-2,5,3,-4,1]=>10010=>01001
[-2,5,3,-4,-1]=>10011=>11001
[-2,5,-3,4,1]=>10100=>00101
[-2,5,-3,4,-1]=>10101=>10101
[-2,5,-3,-4,1]=>10110=>01101
[-2,5,-3,-4,-1]=>10111=>11101
[-2,-5,3,4,1]=>11000=>00011
[-2,-5,3,4,-1]=>11001=>10011
[-2,-5,3,-4,1]=>11010=>01011
[-2,-5,3,-4,-1]=>11011=>11011
[-2,-5,-3,4,1]=>11100=>00111
[-2,-5,-3,4,-1]=>11101=>10111
[-2,-5,-3,-4,1]=>11110=>01111
[-2,-5,-3,-4,-1]=>11111=>11111
[2,5,4,1,3]=>00000=>00000
[2,5,4,1,-3]=>00001=>10000
[2,5,4,-1,3]=>00010=>01000
[2,5,4,-1,-3]=>00011=>11000
[2,5,-4,1,3]=>00100=>00100
[2,5,-4,1,-3]=>00101=>10100
[2,5,-4,-1,3]=>00110=>01100
[2,5,-4,-1,-3]=>00111=>11100
[2,-5,4,1,3]=>01000=>00010
[2,-5,4,1,-3]=>01001=>10010
[2,-5,4,-1,3]=>01010=>01010
[2,-5,4,-1,-3]=>01011=>11010
[2,-5,-4,1,3]=>01100=>00110
[2,-5,-4,1,-3]=>01101=>10110
[2,-5,-4,-1,3]=>01110=>01110
[2,-5,-4,-1,-3]=>01111=>11110
[-2,5,4,1,3]=>10000=>00001
[-2,5,4,1,-3]=>10001=>10001
[-2,5,4,-1,3]=>10010=>01001
[-2,5,4,-1,-3]=>10011=>11001
[-2,5,-4,1,3]=>10100=>00101
[-2,5,-4,1,-3]=>10101=>10101
[-2,5,-4,-1,3]=>10110=>01101
[-2,5,-4,-1,-3]=>10111=>11101
[-2,-5,4,1,3]=>11000=>00011
[-2,-5,4,1,-3]=>11001=>10011
[-2,-5,4,-1,3]=>11010=>01011
[-2,-5,4,-1,-3]=>11011=>11011
[-2,-5,-4,1,3]=>11100=>00111
[-2,-5,-4,1,-3]=>11101=>10111
[-2,-5,-4,-1,3]=>11110=>01111
[-2,-5,-4,-1,-3]=>11111=>11111
[2,5,4,3,1]=>00000=>00000
[2,5,4,3,-1]=>00001=>10000
[2,5,4,-3,1]=>00010=>01000
[2,5,4,-3,-1]=>00011=>11000
[2,5,-4,3,1]=>00100=>00100
[2,5,-4,3,-1]=>00101=>10100
[2,5,-4,-3,1]=>00110=>01100
[2,5,-4,-3,-1]=>00111=>11100
[2,-5,4,3,1]=>01000=>00010
[2,-5,4,3,-1]=>01001=>10010
[2,-5,4,-3,1]=>01010=>01010
[2,-5,4,-3,-1]=>01011=>11010
[2,-5,-4,3,1]=>01100=>00110
[2,-5,-4,3,-1]=>01101=>10110
[2,-5,-4,-3,1]=>01110=>01110
[2,-5,-4,-3,-1]=>01111=>11110
[-2,5,4,3,1]=>10000=>00001
[-2,5,4,3,-1]=>10001=>10001
[-2,5,4,-3,1]=>10010=>01001
[-2,5,4,-3,-1]=>10011=>11001
[-2,5,-4,3,1]=>10100=>00101
[-2,5,-4,3,-1]=>10101=>10101
[-2,5,-4,-3,1]=>10110=>01101
[-2,5,-4,-3,-1]=>10111=>11101
[-2,-5,4,3,1]=>11000=>00011
[-2,-5,4,3,-1]=>11001=>10011
[-2,-5,4,-3,1]=>11010=>01011
[-2,-5,4,-3,-1]=>11011=>11011
[-2,-5,-4,3,1]=>11100=>00111
[-2,-5,-4,3,-1]=>11101=>10111
[-2,-5,-4,-3,1]=>11110=>01111
[-2,-5,-4,-3,-1]=>11111=>11111
[3,1,2,4,5]=>00000=>00000
[3,1,2,4,-5]=>00001=>10000
[3,1,2,-4,5]=>00010=>01000
[3,1,2,-4,-5]=>00011=>11000
[3,1,-2,4,5]=>00100=>00100
[3,1,-2,4,-5]=>00101=>10100
[3,1,-2,-4,5]=>00110=>01100
[3,1,-2,-4,-5]=>00111=>11100
[3,-1,2,4,5]=>01000=>00010
[3,-1,2,4,-5]=>01001=>10010
[3,-1,2,-4,5]=>01010=>01010
[3,-1,2,-4,-5]=>01011=>11010
[3,-1,-2,4,5]=>01100=>00110
[3,-1,-2,4,-5]=>01101=>10110
[3,-1,-2,-4,5]=>01110=>01110
[3,-1,-2,-4,-5]=>01111=>11110
[-3,1,2,4,5]=>10000=>00001
[-3,1,2,4,-5]=>10001=>10001
[-3,1,2,-4,5]=>10010=>01001
[-3,1,2,-4,-5]=>10011=>11001
[-3,1,-2,4,5]=>10100=>00101
[-3,1,-2,4,-5]=>10101=>10101
[-3,1,-2,-4,5]=>10110=>01101
[-3,1,-2,-4,-5]=>10111=>11101
[-3,-1,2,4,5]=>11000=>00011
[-3,-1,2,4,-5]=>11001=>10011
[-3,-1,2,-4,5]=>11010=>01011
[-3,-1,2,-4,-5]=>11011=>11011
[-3,-1,-2,4,5]=>11100=>00111
[-3,-1,-2,4,-5]=>11101=>10111
[-3,-1,-2,-4,5]=>11110=>01111
[-3,-1,-2,-4,-5]=>11111=>11111
[3,1,2,5,4]=>00000=>00000
[3,1,2,5,-4]=>00001=>10000
[3,1,2,-5,4]=>00010=>01000
[3,1,2,-5,-4]=>00011=>11000
[3,1,-2,5,4]=>00100=>00100
[3,1,-2,5,-4]=>00101=>10100
[3,1,-2,-5,4]=>00110=>01100
[3,1,-2,-5,-4]=>00111=>11100
[3,-1,2,5,4]=>01000=>00010
[3,-1,2,5,-4]=>01001=>10010
[3,-1,2,-5,4]=>01010=>01010
[3,-1,2,-5,-4]=>01011=>11010
[3,-1,-2,5,4]=>01100=>00110
[3,-1,-2,5,-4]=>01101=>10110
[3,-1,-2,-5,4]=>01110=>01110
[3,-1,-2,-5,-4]=>01111=>11110
[-3,1,2,5,4]=>10000=>00001
[-3,1,2,5,-4]=>10001=>10001
[-3,1,2,-5,4]=>10010=>01001
[-3,1,2,-5,-4]=>10011=>11001
[-3,1,-2,5,4]=>10100=>00101
[-3,1,-2,5,-4]=>10101=>10101
[-3,1,-2,-5,4]=>10110=>01101
[-3,1,-2,-5,-4]=>10111=>11101
[-3,-1,2,5,4]=>11000=>00011
[-3,-1,2,5,-4]=>11001=>10011
[-3,-1,2,-5,4]=>11010=>01011
[-3,-1,2,-5,-4]=>11011=>11011
[-3,-1,-2,5,4]=>11100=>00111
[-3,-1,-2,5,-4]=>11101=>10111
[-3,-1,-2,-5,4]=>11110=>01111
[-3,-1,-2,-5,-4]=>11111=>11111
[3,1,4,2,5]=>00000=>00000
[3,1,4,2,-5]=>00001=>10000
[3,1,4,-2,5]=>00010=>01000
[3,1,4,-2,-5]=>00011=>11000
[3,1,-4,2,5]=>00100=>00100
[3,1,-4,2,-5]=>00101=>10100
[3,1,-4,-2,5]=>00110=>01100
[3,1,-4,-2,-5]=>00111=>11100
[3,-1,4,2,5]=>01000=>00010
[3,-1,4,2,-5]=>01001=>10010
[3,-1,4,-2,5]=>01010=>01010
[3,-1,4,-2,-5]=>01011=>11010
[3,-1,-4,2,5]=>01100=>00110
[3,-1,-4,2,-5]=>01101=>10110
[3,-1,-4,-2,5]=>01110=>01110
[3,-1,-4,-2,-5]=>01111=>11110
[-3,1,4,2,5]=>10000=>00001
[-3,1,4,2,-5]=>10001=>10001
[-3,1,4,-2,5]=>10010=>01001
[-3,1,4,-2,-5]=>10011=>11001
[-3,1,-4,2,5]=>10100=>00101
[-3,1,-4,2,-5]=>10101=>10101
[-3,1,-4,-2,5]=>10110=>01101
[-3,1,-4,-2,-5]=>10111=>11101
[-3,-1,4,2,5]=>11000=>00011
[-3,-1,4,2,-5]=>11001=>10011
[-3,-1,4,-2,5]=>11010=>01011
[-3,-1,4,-2,-5]=>11011=>11011
[-3,-1,-4,2,5]=>11100=>00111
[-3,-1,-4,2,-5]=>11101=>10111
[-3,-1,-4,-2,5]=>11110=>01111
[-3,-1,-4,-2,-5]=>11111=>11111
[3,1,4,5,2]=>00000=>00000
[3,1,4,5,-2]=>00001=>10000
[3,1,4,-5,2]=>00010=>01000
[3,1,4,-5,-2]=>00011=>11000
[3,1,-4,5,2]=>00100=>00100
[3,1,-4,5,-2]=>00101=>10100
[3,1,-4,-5,2]=>00110=>01100
[3,1,-4,-5,-2]=>00111=>11100
[3,-1,4,5,2]=>01000=>00010
[3,-1,4,5,-2]=>01001=>10010
[3,-1,4,-5,2]=>01010=>01010
[3,-1,4,-5,-2]=>01011=>11010
[3,-1,-4,5,2]=>01100=>00110
[3,-1,-4,5,-2]=>01101=>10110
[3,-1,-4,-5,2]=>01110=>01110
[3,-1,-4,-5,-2]=>01111=>11110
[-3,1,4,5,2]=>10000=>00001
[-3,1,4,5,-2]=>10001=>10001
[-3,1,4,-5,2]=>10010=>01001
[-3,1,4,-5,-2]=>10011=>11001
[-3,1,-4,5,2]=>10100=>00101
[-3,1,-4,5,-2]=>10101=>10101
[-3,1,-4,-5,2]=>10110=>01101
[-3,1,-4,-5,-2]=>10111=>11101
[-3,-1,4,5,2]=>11000=>00011
[-3,-1,4,5,-2]=>11001=>10011
[-3,-1,4,-5,2]=>11010=>01011
[-3,-1,4,-5,-2]=>11011=>11011
[-3,-1,-4,5,2]=>11100=>00111
[-3,-1,-4,5,-2]=>11101=>10111
[-3,-1,-4,-5,2]=>11110=>01111
[-3,-1,-4,-5,-2]=>11111=>11111
[3,1,5,2,4]=>00000=>00000
[3,1,5,2,-4]=>00001=>10000
[3,1,5,-2,4]=>00010=>01000
[3,1,5,-2,-4]=>00011=>11000
[3,1,-5,2,4]=>00100=>00100
[3,1,-5,2,-4]=>00101=>10100
[3,1,-5,-2,4]=>00110=>01100
[3,1,-5,-2,-4]=>00111=>11100
[3,-1,5,2,4]=>01000=>00010
[3,-1,5,2,-4]=>01001=>10010
[3,-1,5,-2,4]=>01010=>01010
[3,-1,5,-2,-4]=>01011=>11010
[3,-1,-5,2,4]=>01100=>00110
[3,-1,-5,2,-4]=>01101=>10110
[3,-1,-5,-2,4]=>01110=>01110
[3,-1,-5,-2,-4]=>01111=>11110
[-3,1,5,2,4]=>10000=>00001
[-3,1,5,2,-4]=>10001=>10001
[-3,1,5,-2,4]=>10010=>01001
[-3,1,5,-2,-4]=>10011=>11001
[-3,1,-5,2,4]=>10100=>00101
[-3,1,-5,2,-4]=>10101=>10101
[-3,1,-5,-2,4]=>10110=>01101
[-3,1,-5,-2,-4]=>10111=>11101
[-3,-1,5,2,4]=>11000=>00011
[-3,-1,5,2,-4]=>11001=>10011
[-3,-1,5,-2,4]=>11010=>01011
[-3,-1,5,-2,-4]=>11011=>11011
[-3,-1,-5,2,4]=>11100=>00111
[-3,-1,-5,2,-4]=>11101=>10111
[-3,-1,-5,-2,4]=>11110=>01111
[-3,-1,-5,-2,-4]=>11111=>11111
[3,1,5,4,2]=>00000=>00000
[3,1,5,4,-2]=>00001=>10000
[3,1,5,-4,2]=>00010=>01000
[3,1,5,-4,-2]=>00011=>11000
[3,1,-5,4,2]=>00100=>00100
[3,1,-5,4,-2]=>00101=>10100
[3,1,-5,-4,2]=>00110=>01100
[3,1,-5,-4,-2]=>00111=>11100
[3,-1,5,4,2]=>01000=>00010
[3,-1,5,4,-2]=>01001=>10010
[3,-1,5,-4,2]=>01010=>01010
[3,-1,5,-4,-2]=>01011=>11010
[3,-1,-5,4,2]=>01100=>00110
[3,-1,-5,4,-2]=>01101=>10110
[3,-1,-5,-4,2]=>01110=>01110
[3,-1,-5,-4,-2]=>01111=>11110
[-3,1,5,4,2]=>10000=>00001
[-3,1,5,4,-2]=>10001=>10001
[-3,1,5,-4,2]=>10010=>01001
[-3,1,5,-4,-2]=>10011=>11001
[-3,1,-5,4,2]=>10100=>00101
[-3,1,-5,4,-2]=>10101=>10101
[-3,1,-5,-4,2]=>10110=>01101
[-3,1,-5,-4,-2]=>10111=>11101
[-3,-1,5,4,2]=>11000=>00011
[-3,-1,5,4,-2]=>11001=>10011
[-3,-1,5,-4,2]=>11010=>01011
[-3,-1,5,-4,-2]=>11011=>11011
[-3,-1,-5,4,2]=>11100=>00111
[-3,-1,-5,4,-2]=>11101=>10111
[-3,-1,-5,-4,2]=>11110=>01111
[-3,-1,-5,-4,-2]=>11111=>11111
[3,2,1,4,5]=>00000=>00000
[3,2,1,4,-5]=>00001=>10000
[3,2,1,-4,5]=>00010=>01000
[3,2,1,-4,-5]=>00011=>11000
[3,2,-1,4,5]=>00100=>00100
[3,2,-1,4,-5]=>00101=>10100
[3,2,-1,-4,5]=>00110=>01100
[3,2,-1,-4,-5]=>00111=>11100
[3,-2,1,4,5]=>01000=>00010
[3,-2,1,4,-5]=>01001=>10010
[3,-2,1,-4,5]=>01010=>01010
[3,-2,1,-4,-5]=>01011=>11010
[3,-2,-1,4,5]=>01100=>00110
[3,-2,-1,4,-5]=>01101=>10110
[3,-2,-1,-4,5]=>01110=>01110
[3,-2,-1,-4,-5]=>01111=>11110
[-3,2,1,4,5]=>10000=>00001
[-3,2,1,4,-5]=>10001=>10001
[-3,2,1,-4,5]=>10010=>01001
[-3,2,1,-4,-5]=>10011=>11001
[-3,2,-1,4,5]=>10100=>00101
[-3,2,-1,4,-5]=>10101=>10101
[-3,2,-1,-4,5]=>10110=>01101
[-3,2,-1,-4,-5]=>10111=>11101
[-3,-2,1,4,5]=>11000=>00011
[-3,-2,1,4,-5]=>11001=>10011
[-3,-2,1,-4,5]=>11010=>01011
[-3,-2,1,-4,-5]=>11011=>11011
[-3,-2,-1,4,5]=>11100=>00111
[-3,-2,-1,4,-5]=>11101=>10111
[-3,-2,-1,-4,5]=>11110=>01111
[-3,-2,-1,-4,-5]=>11111=>11111
[3,2,1,5,4]=>00000=>00000
[3,2,1,5,-4]=>00001=>10000
[3,2,1,-5,4]=>00010=>01000
[3,2,1,-5,-4]=>00011=>11000
[3,2,-1,5,4]=>00100=>00100
[3,2,-1,5,-4]=>00101=>10100
[3,2,-1,-5,4]=>00110=>01100
[3,2,-1,-5,-4]=>00111=>11100
[3,-2,1,5,4]=>01000=>00010
[3,-2,1,5,-4]=>01001=>10010
[3,-2,1,-5,4]=>01010=>01010
[3,-2,1,-5,-4]=>01011=>11010
[3,-2,-1,5,4]=>01100=>00110
[3,-2,-1,5,-4]=>01101=>10110
[3,-2,-1,-5,4]=>01110=>01110
[3,-2,-1,-5,-4]=>01111=>11110
[-3,2,1,5,4]=>10000=>00001
[-3,2,1,5,-4]=>10001=>10001
[-3,2,1,-5,4]=>10010=>01001
[-3,2,1,-5,-4]=>10011=>11001
[-3,2,-1,5,4]=>10100=>00101
[-3,2,-1,5,-4]=>10101=>10101
[-3,2,-1,-5,4]=>10110=>01101
[-3,2,-1,-5,-4]=>10111=>11101
[-3,-2,1,5,4]=>11000=>00011
[-3,-2,1,5,-4]=>11001=>10011
[-3,-2,1,-5,4]=>11010=>01011
[-3,-2,1,-5,-4]=>11011=>11011
[-3,-2,-1,5,4]=>11100=>00111
[-3,-2,-1,5,-4]=>11101=>10111
[-3,-2,-1,-5,4]=>11110=>01111
[-3,-2,-1,-5,-4]=>11111=>11111
[3,2,4,1,5]=>00000=>00000
[3,2,4,1,-5]=>00001=>10000
[3,2,4,-1,5]=>00010=>01000
[3,2,4,-1,-5]=>00011=>11000
[3,2,-4,1,5]=>00100=>00100
[3,2,-4,1,-5]=>00101=>10100
[3,2,-4,-1,5]=>00110=>01100
[3,2,-4,-1,-5]=>00111=>11100
[3,-2,4,1,5]=>01000=>00010
[3,-2,4,1,-5]=>01001=>10010
[3,-2,4,-1,5]=>01010=>01010
[3,-2,4,-1,-5]=>01011=>11010
[3,-2,-4,1,5]=>01100=>00110
[3,-2,-4,1,-5]=>01101=>10110
[3,-2,-4,-1,5]=>01110=>01110
[3,-2,-4,-1,-5]=>01111=>11110
[-3,2,4,1,5]=>10000=>00001
[-3,2,4,1,-5]=>10001=>10001
[-3,2,4,-1,5]=>10010=>01001
[-3,2,4,-1,-5]=>10011=>11001
[-3,2,-4,1,5]=>10100=>00101
[-3,2,-4,1,-5]=>10101=>10101
[-3,2,-4,-1,5]=>10110=>01101
[-3,2,-4,-1,-5]=>10111=>11101
[-3,-2,4,1,5]=>11000=>00011
[-3,-2,4,1,-5]=>11001=>10011
[-3,-2,4,-1,5]=>11010=>01011
[-3,-2,4,-1,-5]=>11011=>11011
[-3,-2,-4,1,5]=>11100=>00111
[-3,-2,-4,1,-5]=>11101=>10111
[-3,-2,-4,-1,5]=>11110=>01111
[-3,-2,-4,-1,-5]=>11111=>11111
[3,2,4,5,1]=>00000=>00000
[3,2,4,5,-1]=>00001=>10000
[3,2,4,-5,1]=>00010=>01000
[3,2,4,-5,-1]=>00011=>11000
[3,2,-4,5,1]=>00100=>00100
[3,2,-4,5,-1]=>00101=>10100
[3,2,-4,-5,1]=>00110=>01100
[3,2,-4,-5,-1]=>00111=>11100
[3,-2,4,5,1]=>01000=>00010
[3,-2,4,5,-1]=>01001=>10010
[3,-2,4,-5,1]=>01010=>01010
[3,-2,4,-5,-1]=>01011=>11010
[3,-2,-4,5,1]=>01100=>00110
[3,-2,-4,5,-1]=>01101=>10110
[3,-2,-4,-5,1]=>01110=>01110
[3,-2,-4,-5,-1]=>01111=>11110
[-3,2,4,5,1]=>10000=>00001
[-3,2,4,5,-1]=>10001=>10001
[-3,2,4,-5,1]=>10010=>01001
[-3,2,4,-5,-1]=>10011=>11001
[-3,2,-4,5,1]=>10100=>00101
[-3,2,-4,5,-1]=>10101=>10101
[-3,2,-4,-5,1]=>10110=>01101
[-3,2,-4,-5,-1]=>10111=>11101
[-3,-2,4,5,1]=>11000=>00011
[-3,-2,4,5,-1]=>11001=>10011
[-3,-2,4,-5,1]=>11010=>01011
[-3,-2,4,-5,-1]=>11011=>11011
[-3,-2,-4,5,1]=>11100=>00111
[-3,-2,-4,5,-1]=>11101=>10111
[-3,-2,-4,-5,1]=>11110=>01111
[-3,-2,-4,-5,-1]=>11111=>11111
[3,2,5,1,4]=>00000=>00000
[3,2,5,1,-4]=>00001=>10000
[3,2,5,-1,4]=>00010=>01000
[3,2,5,-1,-4]=>00011=>11000
[3,2,-5,1,4]=>00100=>00100
[3,2,-5,1,-4]=>00101=>10100
[3,2,-5,-1,4]=>00110=>01100
[3,2,-5,-1,-4]=>00111=>11100
[3,-2,5,1,4]=>01000=>00010
[3,-2,5,1,-4]=>01001=>10010
[3,-2,5,-1,4]=>01010=>01010
[3,-2,5,-1,-4]=>01011=>11010
[3,-2,-5,1,4]=>01100=>00110
[3,-2,-5,1,-4]=>01101=>10110
[3,-2,-5,-1,4]=>01110=>01110
[3,-2,-5,-1,-4]=>01111=>11110
[-3,2,5,1,4]=>10000=>00001
[-3,2,5,1,-4]=>10001=>10001
[-3,2,5,-1,4]=>10010=>01001
[-3,2,5,-1,-4]=>10011=>11001
[-3,2,-5,1,4]=>10100=>00101
[-3,2,-5,1,-4]=>10101=>10101
[-3,2,-5,-1,4]=>10110=>01101
[-3,2,-5,-1,-4]=>10111=>11101
[-3,-2,5,1,4]=>11000=>00011
[-3,-2,5,1,-4]=>11001=>10011
[-3,-2,5,-1,4]=>11010=>01011
[-3,-2,5,-1,-4]=>11011=>11011
[-3,-2,-5,1,4]=>11100=>00111
[-3,-2,-5,1,-4]=>11101=>10111
[-3,-2,-5,-1,4]=>11110=>01111
[-3,-2,-5,-1,-4]=>11111=>11111
[3,2,5,4,1]=>00000=>00000
[3,2,5,4,-1]=>00001=>10000
[3,2,5,-4,1]=>00010=>01000
[3,2,5,-4,-1]=>00011=>11000
[3,2,-5,4,1]=>00100=>00100
[3,2,-5,4,-1]=>00101=>10100
[3,2,-5,-4,1]=>00110=>01100
[3,2,-5,-4,-1]=>00111=>11100
[3,-2,5,4,1]=>01000=>00010
[3,-2,5,4,-1]=>01001=>10010
[3,-2,5,-4,1]=>01010=>01010
[3,-2,5,-4,-1]=>01011=>11010
[3,-2,-5,4,1]=>01100=>00110
[3,-2,-5,4,-1]=>01101=>10110
[3,-2,-5,-4,1]=>01110=>01110
[3,-2,-5,-4,-1]=>01111=>11110
[-3,2,5,4,1]=>10000=>00001
[-3,2,5,4,-1]=>10001=>10001
[-3,2,5,-4,1]=>10010=>01001
[-3,2,5,-4,-1]=>10011=>11001
[-3,2,-5,4,1]=>10100=>00101
[-3,2,-5,4,-1]=>10101=>10101
[-3,2,-5,-4,1]=>10110=>01101
[-3,2,-5,-4,-1]=>10111=>11101
[-3,-2,5,4,1]=>11000=>00011
[-3,-2,5,4,-1]=>11001=>10011
[-3,-2,5,-4,1]=>11010=>01011
[-3,-2,5,-4,-1]=>11011=>11011
[-3,-2,-5,4,1]=>11100=>00111
[-3,-2,-5,4,-1]=>11101=>10111
[-3,-2,-5,-4,1]=>11110=>01111
[-3,-2,-5,-4,-1]=>11111=>11111
[3,4,1,2,5]=>00000=>00000
[3,4,1,2,-5]=>00001=>10000
[3,4,1,-2,5]=>00010=>01000
[3,4,1,-2,-5]=>00011=>11000
[3,4,-1,2,5]=>00100=>00100
[3,4,-1,2,-5]=>00101=>10100
[3,4,-1,-2,5]=>00110=>01100
[3,4,-1,-2,-5]=>00111=>11100
[3,-4,1,2,5]=>01000=>00010
[3,-4,1,2,-5]=>01001=>10010
[3,-4,1,-2,5]=>01010=>01010
[3,-4,1,-2,-5]=>01011=>11010
[3,-4,-1,2,5]=>01100=>00110
[3,-4,-1,2,-5]=>01101=>10110
[3,-4,-1,-2,5]=>01110=>01110
[3,-4,-1,-2,-5]=>01111=>11110
[-3,4,1,2,5]=>10000=>00001
[-3,4,1,2,-5]=>10001=>10001
[-3,4,1,-2,5]=>10010=>01001
[-3,4,1,-2,-5]=>10011=>11001
[-3,4,-1,2,5]=>10100=>00101
[-3,4,-1,2,-5]=>10101=>10101
[-3,4,-1,-2,5]=>10110=>01101
[-3,4,-1,-2,-5]=>10111=>11101
[-3,-4,1,2,5]=>11000=>00011
[-3,-4,1,2,-5]=>11001=>10011
[-3,-4,1,-2,5]=>11010=>01011
[-3,-4,1,-2,-5]=>11011=>11011
[-3,-4,-1,2,5]=>11100=>00111
[-3,-4,-1,2,-5]=>11101=>10111
[-3,-4,-1,-2,5]=>11110=>01111
[-3,-4,-1,-2,-5]=>11111=>11111
[3,4,1,5,2]=>00000=>00000
[3,4,1,5,-2]=>00001=>10000
[3,4,1,-5,2]=>00010=>01000
[3,4,1,-5,-2]=>00011=>11000
[3,4,-1,5,2]=>00100=>00100
[3,4,-1,5,-2]=>00101=>10100
[3,4,-1,-5,2]=>00110=>01100
[3,4,-1,-5,-2]=>00111=>11100
[3,-4,1,5,2]=>01000=>00010
[3,-4,1,5,-2]=>01001=>10010
[3,-4,1,-5,2]=>01010=>01010
[3,-4,1,-5,-2]=>01011=>11010
[3,-4,-1,5,2]=>01100=>00110
[3,-4,-1,5,-2]=>01101=>10110
[3,-4,-1,-5,2]=>01110=>01110
[3,-4,-1,-5,-2]=>01111=>11110
[-3,4,1,5,2]=>10000=>00001
[-3,4,1,5,-2]=>10001=>10001
[-3,4,1,-5,2]=>10010=>01001
[-3,4,1,-5,-2]=>10011=>11001
[-3,4,-1,5,2]=>10100=>00101
[-3,4,-1,5,-2]=>10101=>10101
[-3,4,-1,-5,2]=>10110=>01101
[-3,4,-1,-5,-2]=>10111=>11101
[-3,-4,1,5,2]=>11000=>00011
[-3,-4,1,5,-2]=>11001=>10011
[-3,-4,1,-5,2]=>11010=>01011
[-3,-4,1,-5,-2]=>11011=>11011
[-3,-4,-1,5,2]=>11100=>00111
[-3,-4,-1,5,-2]=>11101=>10111
[-3,-4,-1,-5,2]=>11110=>01111
[-3,-4,-1,-5,-2]=>11111=>11111
[3,4,2,1,5]=>00000=>00000
[3,4,2,1,-5]=>00001=>10000
[3,4,2,-1,5]=>00010=>01000
[3,4,2,-1,-5]=>00011=>11000
[3,4,-2,1,5]=>00100=>00100
[3,4,-2,1,-5]=>00101=>10100
[3,4,-2,-1,5]=>00110=>01100
[3,4,-2,-1,-5]=>00111=>11100
[3,-4,2,1,5]=>01000=>00010
[3,-4,2,1,-5]=>01001=>10010
[3,-4,2,-1,5]=>01010=>01010
[3,-4,2,-1,-5]=>01011=>11010
[3,-4,-2,1,5]=>01100=>00110
[3,-4,-2,1,-5]=>01101=>10110
[3,-4,-2,-1,5]=>01110=>01110
[3,-4,-2,-1,-5]=>01111=>11110
[-3,4,2,1,5]=>10000=>00001
[-3,4,2,1,-5]=>10001=>10001
[-3,4,2,-1,5]=>10010=>01001
[-3,4,2,-1,-5]=>10011=>11001
[-3,4,-2,1,5]=>10100=>00101
[-3,4,-2,1,-5]=>10101=>10101
[-3,4,-2,-1,5]=>10110=>01101
[-3,4,-2,-1,-5]=>10111=>11101
[-3,-4,2,1,5]=>11000=>00011
[-3,-4,2,1,-5]=>11001=>10011
[-3,-4,2,-1,5]=>11010=>01011
[-3,-4,2,-1,-5]=>11011=>11011
[-3,-4,-2,1,5]=>11100=>00111
[-3,-4,-2,1,-5]=>11101=>10111
[-3,-4,-2,-1,5]=>11110=>01111
[-3,-4,-2,-1,-5]=>11111=>11111
[3,4,2,5,1]=>00000=>00000
[3,4,2,5,-1]=>00001=>10000
[3,4,2,-5,1]=>00010=>01000
[3,4,2,-5,-1]=>00011=>11000
[3,4,-2,5,1]=>00100=>00100
[3,4,-2,5,-1]=>00101=>10100
[3,4,-2,-5,1]=>00110=>01100
[3,4,-2,-5,-1]=>00111=>11100
[3,-4,2,5,1]=>01000=>00010
[3,-4,2,5,-1]=>01001=>10010
[3,-4,2,-5,1]=>01010=>01010
[3,-4,2,-5,-1]=>01011=>11010
[3,-4,-2,5,1]=>01100=>00110
[3,-4,-2,5,-1]=>01101=>10110
[3,-4,-2,-5,1]=>01110=>01110
[3,-4,-2,-5,-1]=>01111=>11110
[-3,4,2,5,1]=>10000=>00001
[-3,4,2,5,-1]=>10001=>10001
[-3,4,2,-5,1]=>10010=>01001
[-3,4,2,-5,-1]=>10011=>11001
[-3,4,-2,5,1]=>10100=>00101
[-3,4,-2,5,-1]=>10101=>10101
[-3,4,-2,-5,1]=>10110=>01101
[-3,4,-2,-5,-1]=>10111=>11101
[-3,-4,2,5,1]=>11000=>00011
[-3,-4,2,5,-1]=>11001=>10011
[-3,-4,2,-5,1]=>11010=>01011
[-3,-4,2,-5,-1]=>11011=>11011
[-3,-4,-2,5,1]=>11100=>00111
[-3,-4,-2,5,-1]=>11101=>10111
[-3,-4,-2,-5,1]=>11110=>01111
[-3,-4,-2,-5,-1]=>11111=>11111
[3,4,5,1,2]=>00000=>00000
[3,4,5,1,-2]=>00001=>10000
[3,4,5,-1,2]=>00010=>01000
[3,4,5,-1,-2]=>00011=>11000
[3,4,-5,1,2]=>00100=>00100
[3,4,-5,1,-2]=>00101=>10100
[3,4,-5,-1,2]=>00110=>01100
[3,4,-5,-1,-2]=>00111=>11100
[3,-4,5,1,2]=>01000=>00010
[3,-4,5,1,-2]=>01001=>10010
[3,-4,5,-1,2]=>01010=>01010
[3,-4,5,-1,-2]=>01011=>11010
[3,-4,-5,1,2]=>01100=>00110
[3,-4,-5,1,-2]=>01101=>10110
[3,-4,-5,-1,2]=>01110=>01110
[3,-4,-5,-1,-2]=>01111=>11110
[-3,4,5,1,2]=>10000=>00001
[-3,4,5,1,-2]=>10001=>10001
[-3,4,5,-1,2]=>10010=>01001
[-3,4,5,-1,-2]=>10011=>11001
[-3,4,-5,1,2]=>10100=>00101
[-3,4,-5,1,-2]=>10101=>10101
[-3,4,-5,-1,2]=>10110=>01101
[-3,4,-5,-1,-2]=>10111=>11101
[-3,-4,5,1,2]=>11000=>00011
[-3,-4,5,1,-2]=>11001=>10011
[-3,-4,5,-1,2]=>11010=>01011
[-3,-4,5,-1,-2]=>11011=>11011
[-3,-4,-5,1,2]=>11100=>00111
[-3,-4,-5,1,-2]=>11101=>10111
[-3,-4,-5,-1,2]=>11110=>01111
[-3,-4,-5,-1,-2]=>11111=>11111
[3,4,5,2,1]=>00000=>00000
[3,4,5,2,-1]=>00001=>10000
[3,4,5,-2,1]=>00010=>01000
[3,4,5,-2,-1]=>00011=>11000
[3,4,-5,2,1]=>00100=>00100
[3,4,-5,2,-1]=>00101=>10100
[3,4,-5,-2,1]=>00110=>01100
[3,4,-5,-2,-1]=>00111=>11100
[3,-4,5,2,1]=>01000=>00010
[3,-4,5,2,-1]=>01001=>10010
[3,-4,5,-2,1]=>01010=>01010
[3,-4,5,-2,-1]=>01011=>11010
[3,-4,-5,2,1]=>01100=>00110
[3,-4,-5,2,-1]=>01101=>10110
[3,-4,-5,-2,1]=>01110=>01110
[3,-4,-5,-2,-1]=>01111=>11110
[-3,4,5,2,1]=>10000=>00001
[-3,4,5,2,-1]=>10001=>10001
[-3,4,5,-2,1]=>10010=>01001
[-3,4,5,-2,-1]=>10011=>11001
[-3,4,-5,2,1]=>10100=>00101
[-3,4,-5,2,-1]=>10101=>10101
[-3,4,-5,-2,1]=>10110=>01101
[-3,4,-5,-2,-1]=>10111=>11101
[-3,-4,5,2,1]=>11000=>00011
[-3,-4,5,2,-1]=>11001=>10011
[-3,-4,5,-2,1]=>11010=>01011
[-3,-4,5,-2,-1]=>11011=>11011
[-3,-4,-5,2,1]=>11100=>00111
[-3,-4,-5,2,-1]=>11101=>10111
[-3,-4,-5,-2,1]=>11110=>01111
[-3,-4,-5,-2,-1]=>11111=>11111
[3,5,1,2,4]=>00000=>00000
[3,5,1,2,-4]=>00001=>10000
[3,5,1,-2,4]=>00010=>01000
[3,5,1,-2,-4]=>00011=>11000
[3,5,-1,2,4]=>00100=>00100
[3,5,-1,2,-4]=>00101=>10100
[3,5,-1,-2,4]=>00110=>01100
[3,5,-1,-2,-4]=>00111=>11100
[3,-5,1,2,4]=>01000=>00010
[3,-5,1,2,-4]=>01001=>10010
[3,-5,1,-2,4]=>01010=>01010
[3,-5,1,-2,-4]=>01011=>11010
[3,-5,-1,2,4]=>01100=>00110
[3,-5,-1,2,-4]=>01101=>10110
[3,-5,-1,-2,4]=>01110=>01110
[3,-5,-1,-2,-4]=>01111=>11110
[-3,5,1,2,4]=>10000=>00001
[-3,5,1,2,-4]=>10001=>10001
[-3,5,1,-2,4]=>10010=>01001
[-3,5,1,-2,-4]=>10011=>11001
[-3,5,-1,2,4]=>10100=>00101
[-3,5,-1,2,-4]=>10101=>10101
[-3,5,-1,-2,4]=>10110=>01101
[-3,5,-1,-2,-4]=>10111=>11101
[-3,-5,1,2,4]=>11000=>00011
[-3,-5,1,2,-4]=>11001=>10011
[-3,-5,1,-2,4]=>11010=>01011
[-3,-5,1,-2,-4]=>11011=>11011
[-3,-5,-1,2,4]=>11100=>00111
[-3,-5,-1,2,-4]=>11101=>10111
[-3,-5,-1,-2,4]=>11110=>01111
[-3,-5,-1,-2,-4]=>11111=>11111
[3,5,1,4,2]=>00000=>00000
[3,5,1,4,-2]=>00001=>10000
[3,5,1,-4,2]=>00010=>01000
[3,5,1,-4,-2]=>00011=>11000
[3,5,-1,4,2]=>00100=>00100
[3,5,-1,4,-2]=>00101=>10100
[3,5,-1,-4,2]=>00110=>01100
[3,5,-1,-4,-2]=>00111=>11100
[3,-5,1,4,2]=>01000=>00010
[3,-5,1,4,-2]=>01001=>10010
[3,-5,1,-4,2]=>01010=>01010
[3,-5,1,-4,-2]=>01011=>11010
[3,-5,-1,4,2]=>01100=>00110
[3,-5,-1,4,-2]=>01101=>10110
[3,-5,-1,-4,2]=>01110=>01110
[3,-5,-1,-4,-2]=>01111=>11110
[-3,5,1,4,2]=>10000=>00001
[-3,5,1,4,-2]=>10001=>10001
[-3,5,1,-4,2]=>10010=>01001
[-3,5,1,-4,-2]=>10011=>11001
[-3,5,-1,4,2]=>10100=>00101
[-3,5,-1,4,-2]=>10101=>10101
[-3,5,-1,-4,2]=>10110=>01101
[-3,5,-1,-4,-2]=>10111=>11101
[-3,-5,1,4,2]=>11000=>00011
[-3,-5,1,4,-2]=>11001=>10011
[-3,-5,1,-4,2]=>11010=>01011
[-3,-5,1,-4,-2]=>11011=>11011
[-3,-5,-1,4,2]=>11100=>00111
[-3,-5,-1,4,-2]=>11101=>10111
[-3,-5,-1,-4,2]=>11110=>01111
[-3,-5,-1,-4,-2]=>11111=>11111
[3,5,2,1,4]=>00000=>00000
[3,5,2,1,-4]=>00001=>10000
[3,5,2,-1,4]=>00010=>01000
[3,5,2,-1,-4]=>00011=>11000
[3,5,-2,1,4]=>00100=>00100
[3,5,-2,1,-4]=>00101=>10100
[3,5,-2,-1,4]=>00110=>01100
[3,5,-2,-1,-4]=>00111=>11100
[3,-5,2,1,4]=>01000=>00010
[3,-5,2,1,-4]=>01001=>10010
[3,-5,2,-1,4]=>01010=>01010
[3,-5,2,-1,-4]=>01011=>11010
[3,-5,-2,1,4]=>01100=>00110
[3,-5,-2,1,-4]=>01101=>10110
[3,-5,-2,-1,4]=>01110=>01110
[3,-5,-2,-1,-4]=>01111=>11110
[-3,5,2,1,4]=>10000=>00001
[-3,5,2,1,-4]=>10001=>10001
[-3,5,2,-1,4]=>10010=>01001
[-3,5,2,-1,-4]=>10011=>11001
[-3,5,-2,1,4]=>10100=>00101
[-3,5,-2,1,-4]=>10101=>10101
[-3,5,-2,-1,4]=>10110=>01101
[-3,5,-2,-1,-4]=>10111=>11101
[-3,-5,2,1,4]=>11000=>00011
[-3,-5,2,1,-4]=>11001=>10011
[-3,-5,2,-1,4]=>11010=>01011
[-3,-5,2,-1,-4]=>11011=>11011
[-3,-5,-2,1,4]=>11100=>00111
[-3,-5,-2,1,-4]=>11101=>10111
[-3,-5,-2,-1,4]=>11110=>01111
[-3,-5,-2,-1,-4]=>11111=>11111
[3,5,2,4,1]=>00000=>00000
[3,5,2,4,-1]=>00001=>10000
[3,5,2,-4,1]=>00010=>01000
[3,5,2,-4,-1]=>00011=>11000
[3,5,-2,4,1]=>00100=>00100
[3,5,-2,4,-1]=>00101=>10100
[3,5,-2,-4,1]=>00110=>01100
[3,5,-2,-4,-1]=>00111=>11100
[3,-5,2,4,1]=>01000=>00010
[3,-5,2,4,-1]=>01001=>10010
[3,-5,2,-4,1]=>01010=>01010
[3,-5,2,-4,-1]=>01011=>11010
[3,-5,-2,4,1]=>01100=>00110
[3,-5,-2,4,-1]=>01101=>10110
[3,-5,-2,-4,1]=>01110=>01110
[3,-5,-2,-4,-1]=>01111=>11110
[-3,5,2,4,1]=>10000=>00001
[-3,5,2,4,-1]=>10001=>10001
[-3,5,2,-4,1]=>10010=>01001
[-3,5,2,-4,-1]=>10011=>11001
[-3,5,-2,4,1]=>10100=>00101
[-3,5,-2,4,-1]=>10101=>10101
[-3,5,-2,-4,1]=>10110=>01101
[-3,5,-2,-4,-1]=>10111=>11101
[-3,-5,2,4,1]=>11000=>00011
[-3,-5,2,4,-1]=>11001=>10011
[-3,-5,2,-4,1]=>11010=>01011
[-3,-5,2,-4,-1]=>11011=>11011
[-3,-5,-2,4,1]=>11100=>00111
[-3,-5,-2,4,-1]=>11101=>10111
[-3,-5,-2,-4,1]=>11110=>01111
[-3,-5,-2,-4,-1]=>11111=>11111
[3,5,4,1,2]=>00000=>00000
[3,5,4,1,-2]=>00001=>10000
[3,5,4,-1,2]=>00010=>01000
[3,5,4,-1,-2]=>00011=>11000
[3,5,-4,1,2]=>00100=>00100
[3,5,-4,1,-2]=>00101=>10100
[3,5,-4,-1,2]=>00110=>01100
[3,5,-4,-1,-2]=>00111=>11100
[3,-5,4,1,2]=>01000=>00010
[3,-5,4,1,-2]=>01001=>10010
[3,-5,4,-1,2]=>01010=>01010
[3,-5,4,-1,-2]=>01011=>11010
[3,-5,-4,1,2]=>01100=>00110
[3,-5,-4,1,-2]=>01101=>10110
[3,-5,-4,-1,2]=>01110=>01110
[3,-5,-4,-1,-2]=>01111=>11110
[-3,5,4,1,2]=>10000=>00001
[-3,5,4,1,-2]=>10001=>10001
[-3,5,4,-1,2]=>10010=>01001
[-3,5,4,-1,-2]=>10011=>11001
[-3,5,-4,1,2]=>10100=>00101
[-3,5,-4,1,-2]=>10101=>10101
[-3,5,-4,-1,2]=>10110=>01101
[-3,5,-4,-1,-2]=>10111=>11101
[-3,-5,4,1,2]=>11000=>00011
[-3,-5,4,1,-2]=>11001=>10011
[-3,-5,4,-1,2]=>11010=>01011
[-3,-5,4,-1,-2]=>11011=>11011
[-3,-5,-4,1,2]=>11100=>00111
[-3,-5,-4,1,-2]=>11101=>10111
[-3,-5,-4,-1,2]=>11110=>01111
[-3,-5,-4,-1,-2]=>11111=>11111
[3,5,4,2,1]=>00000=>00000
[3,5,4,2,-1]=>00001=>10000
[3,5,4,-2,1]=>00010=>01000
[3,5,4,-2,-1]=>00011=>11000
[3,5,-4,2,1]=>00100=>00100
[3,5,-4,2,-1]=>00101=>10100
[3,5,-4,-2,1]=>00110=>01100
[3,5,-4,-2,-1]=>00111=>11100
[3,-5,4,2,1]=>01000=>00010
[3,-5,4,2,-1]=>01001=>10010
[3,-5,4,-2,1]=>01010=>01010
[3,-5,4,-2,-1]=>01011=>11010
[3,-5,-4,2,1]=>01100=>00110
[3,-5,-4,2,-1]=>01101=>10110
[3,-5,-4,-2,1]=>01110=>01110
[3,-5,-4,-2,-1]=>01111=>11110
[-3,5,4,2,1]=>10000=>00001
[-3,5,4,2,-1]=>10001=>10001
[-3,5,4,-2,1]=>10010=>01001
[-3,5,4,-2,-1]=>10011=>11001
[-3,5,-4,2,1]=>10100=>00101
[-3,5,-4,2,-1]=>10101=>10101
[-3,5,-4,-2,1]=>10110=>01101
[-3,5,-4,-2,-1]=>10111=>11101
[-3,-5,4,2,1]=>11000=>00011
[-3,-5,4,2,-1]=>11001=>10011
[-3,-5,4,-2,1]=>11010=>01011
[-3,-5,4,-2,-1]=>11011=>11011
[-3,-5,-4,2,1]=>11100=>00111
[-3,-5,-4,2,-1]=>11101=>10111
[-3,-5,-4,-2,1]=>11110=>01111
[-3,-5,-4,-2,-1]=>11111=>11111
[4,1,2,3,5]=>00000=>00000
[4,1,2,3,-5]=>00001=>10000
[4,1,2,-3,5]=>00010=>01000
[4,1,2,-3,-5]=>00011=>11000
[4,1,-2,3,5]=>00100=>00100
[4,1,-2,3,-5]=>00101=>10100
[4,1,-2,-3,5]=>00110=>01100
[4,1,-2,-3,-5]=>00111=>11100
[4,-1,2,3,5]=>01000=>00010
[4,-1,2,3,-5]=>01001=>10010
[4,-1,2,-3,5]=>01010=>01010
[4,-1,2,-3,-5]=>01011=>11010
[4,-1,-2,3,5]=>01100=>00110
[4,-1,-2,3,-5]=>01101=>10110
[4,-1,-2,-3,5]=>01110=>01110
[4,-1,-2,-3,-5]=>01111=>11110
[-4,1,2,3,5]=>10000=>00001
[-4,1,2,3,-5]=>10001=>10001
[-4,1,2,-3,5]=>10010=>01001
[-4,1,2,-3,-5]=>10011=>11001
[-4,1,-2,3,5]=>10100=>00101
[-4,1,-2,3,-5]=>10101=>10101
[-4,1,-2,-3,5]=>10110=>01101
[-4,1,-2,-3,-5]=>10111=>11101
[-4,-1,2,3,5]=>11000=>00011
[-4,-1,2,3,-5]=>11001=>10011
[-4,-1,2,-3,5]=>11010=>01011
[-4,-1,2,-3,-5]=>11011=>11011
[-4,-1,-2,3,5]=>11100=>00111
[-4,-1,-2,3,-5]=>11101=>10111
[-4,-1,-2,-3,5]=>11110=>01111
[-4,-1,-2,-3,-5]=>11111=>11111
[4,1,2,5,3]=>00000=>00000
[4,1,2,5,-3]=>00001=>10000
[4,1,2,-5,3]=>00010=>01000
[4,1,2,-5,-3]=>00011=>11000
[4,1,-2,5,3]=>00100=>00100
[4,1,-2,5,-3]=>00101=>10100
[4,1,-2,-5,3]=>00110=>01100
[4,1,-2,-5,-3]=>00111=>11100
[4,-1,2,5,3]=>01000=>00010
[4,-1,2,5,-3]=>01001=>10010
[4,-1,2,-5,3]=>01010=>01010
[4,-1,2,-5,-3]=>01011=>11010
[4,-1,-2,5,3]=>01100=>00110
[4,-1,-2,5,-3]=>01101=>10110
[4,-1,-2,-5,3]=>01110=>01110
[4,-1,-2,-5,-3]=>01111=>11110
[-4,1,2,5,3]=>10000=>00001
[-4,1,2,5,-3]=>10001=>10001
[-4,1,2,-5,3]=>10010=>01001
[-4,1,2,-5,-3]=>10011=>11001
[-4,1,-2,5,3]=>10100=>00101
[-4,1,-2,5,-3]=>10101=>10101
[-4,1,-2,-5,3]=>10110=>01101
[-4,1,-2,-5,-3]=>10111=>11101
[-4,-1,2,5,3]=>11000=>00011
[-4,-1,2,5,-3]=>11001=>10011
[-4,-1,2,-5,3]=>11010=>01011
[-4,-1,2,-5,-3]=>11011=>11011
[-4,-1,-2,5,3]=>11100=>00111
[-4,-1,-2,5,-3]=>11101=>10111
[-4,-1,-2,-5,3]=>11110=>01111
[-4,-1,-2,-5,-3]=>11111=>11111
[4,1,3,2,5]=>00000=>00000
[4,1,3,2,-5]=>00001=>10000
[4,1,3,-2,5]=>00010=>01000
[4,1,3,-2,-5]=>00011=>11000
[4,1,-3,2,5]=>00100=>00100
[4,1,-3,2,-5]=>00101=>10100
[4,1,-3,-2,5]=>00110=>01100
[4,1,-3,-2,-5]=>00111=>11100
[4,-1,3,2,5]=>01000=>00010
[4,-1,3,2,-5]=>01001=>10010
[4,-1,3,-2,5]=>01010=>01010
[4,-1,3,-2,-5]=>01011=>11010
[4,-1,-3,2,5]=>01100=>00110
[4,-1,-3,2,-5]=>01101=>10110
[4,-1,-3,-2,5]=>01110=>01110
[4,-1,-3,-2,-5]=>01111=>11110
[-4,1,3,2,5]=>10000=>00001
[-4,1,3,2,-5]=>10001=>10001
[-4,1,3,-2,5]=>10010=>01001
[-4,1,3,-2,-5]=>10011=>11001
[-4,1,-3,2,5]=>10100=>00101
[-4,1,-3,2,-5]=>10101=>10101
[-4,1,-3,-2,5]=>10110=>01101
[-4,1,-3,-2,-5]=>10111=>11101
[-4,-1,3,2,5]=>11000=>00011
[-4,-1,3,2,-5]=>11001=>10011
[-4,-1,3,-2,5]=>11010=>01011
[-4,-1,3,-2,-5]=>11011=>11011
[-4,-1,-3,2,5]=>11100=>00111
[-4,-1,-3,2,-5]=>11101=>10111
[-4,-1,-3,-2,5]=>11110=>01111
[-4,-1,-3,-2,-5]=>11111=>11111
[4,1,3,5,2]=>00000=>00000
[4,1,3,5,-2]=>00001=>10000
[4,1,3,-5,2]=>00010=>01000
[4,1,3,-5,-2]=>00011=>11000
[4,1,-3,5,2]=>00100=>00100
[4,1,-3,5,-2]=>00101=>10100
[4,1,-3,-5,2]=>00110=>01100
[4,1,-3,-5,-2]=>00111=>11100
[4,-1,3,5,2]=>01000=>00010
[4,-1,3,5,-2]=>01001=>10010
[4,-1,3,-5,2]=>01010=>01010
[4,-1,3,-5,-2]=>01011=>11010
[4,-1,-3,5,2]=>01100=>00110
[4,-1,-3,5,-2]=>01101=>10110
[4,-1,-3,-5,2]=>01110=>01110
[4,-1,-3,-5,-2]=>01111=>11110
[-4,1,3,5,2]=>10000=>00001
[-4,1,3,5,-2]=>10001=>10001
[-4,1,3,-5,2]=>10010=>01001
[-4,1,3,-5,-2]=>10011=>11001
[-4,1,-3,5,2]=>10100=>00101
[-4,1,-3,5,-2]=>10101=>10101
[-4,1,-3,-5,2]=>10110=>01101
[-4,1,-3,-5,-2]=>10111=>11101
[-4,-1,3,5,2]=>11000=>00011
[-4,-1,3,5,-2]=>11001=>10011
[-4,-1,3,-5,2]=>11010=>01011
[-4,-1,3,-5,-2]=>11011=>11011
[-4,-1,-3,5,2]=>11100=>00111
[-4,-1,-3,5,-2]=>11101=>10111
[-4,-1,-3,-5,2]=>11110=>01111
[-4,-1,-3,-5,-2]=>11111=>11111
[4,1,5,2,3]=>00000=>00000
[4,1,5,2,-3]=>00001=>10000
[4,1,5,-2,3]=>00010=>01000
[4,1,5,-2,-3]=>00011=>11000
[4,1,-5,2,3]=>00100=>00100
[4,1,-5,2,-3]=>00101=>10100
[4,1,-5,-2,3]=>00110=>01100
[4,1,-5,-2,-3]=>00111=>11100
[4,-1,5,2,3]=>01000=>00010
[4,-1,5,2,-3]=>01001=>10010
[4,-1,5,-2,3]=>01010=>01010
[4,-1,5,-2,-3]=>01011=>11010
[4,-1,-5,2,3]=>01100=>00110
[4,-1,-5,2,-3]=>01101=>10110
[4,-1,-5,-2,3]=>01110=>01110
[4,-1,-5,-2,-3]=>01111=>11110
[-4,1,5,2,3]=>10000=>00001
[-4,1,5,2,-3]=>10001=>10001
[-4,1,5,-2,3]=>10010=>01001
[-4,1,5,-2,-3]=>10011=>11001
[-4,1,-5,2,3]=>10100=>00101
[-4,1,-5,2,-3]=>10101=>10101
[-4,1,-5,-2,3]=>10110=>01101
[-4,1,-5,-2,-3]=>10111=>11101
[-4,-1,5,2,3]=>11000=>00011
[-4,-1,5,2,-3]=>11001=>10011
[-4,-1,5,-2,3]=>11010=>01011
[-4,-1,5,-2,-3]=>11011=>11011
[-4,-1,-5,2,3]=>11100=>00111
[-4,-1,-5,2,-3]=>11101=>10111
[-4,-1,-5,-2,3]=>11110=>01111
[-4,-1,-5,-2,-3]=>11111=>11111
[4,1,5,3,2]=>00000=>00000
[4,1,5,3,-2]=>00001=>10000
[4,1,5,-3,2]=>00010=>01000
[4,1,5,-3,-2]=>00011=>11000
[4,1,-5,3,2]=>00100=>00100
[4,1,-5,3,-2]=>00101=>10100
[4,1,-5,-3,2]=>00110=>01100
[4,1,-5,-3,-2]=>00111=>11100
[4,-1,5,3,2]=>01000=>00010
[4,-1,5,3,-2]=>01001=>10010
[4,-1,5,-3,2]=>01010=>01010
[4,-1,5,-3,-2]=>01011=>11010
[4,-1,-5,3,2]=>01100=>00110
[4,-1,-5,3,-2]=>01101=>10110
[4,-1,-5,-3,2]=>01110=>01110
[4,-1,-5,-3,-2]=>01111=>11110
[-4,1,5,3,2]=>10000=>00001
[-4,1,5,3,-2]=>10001=>10001
[-4,1,5,-3,2]=>10010=>01001
[-4,1,5,-3,-2]=>10011=>11001
[-4,1,-5,3,2]=>10100=>00101
[-4,1,-5,3,-2]=>10101=>10101
[-4,1,-5,-3,2]=>10110=>01101
[-4,1,-5,-3,-2]=>10111=>11101
[-4,-1,5,3,2]=>11000=>00011
[-4,-1,5,3,-2]=>11001=>10011
[-4,-1,5,-3,2]=>11010=>01011
[-4,-1,5,-3,-2]=>11011=>11011
[-4,-1,-5,3,2]=>11100=>00111
[-4,-1,-5,3,-2]=>11101=>10111
[-4,-1,-5,-3,2]=>11110=>01111
[-4,-1,-5,-3,-2]=>11111=>11111
[4,2,1,3,5]=>00000=>00000
[4,2,1,3,-5]=>00001=>10000
[4,2,1,-3,5]=>00010=>01000
[4,2,1,-3,-5]=>00011=>11000
[4,2,-1,3,5]=>00100=>00100
[4,2,-1,3,-5]=>00101=>10100
[4,2,-1,-3,5]=>00110=>01100
[4,2,-1,-3,-5]=>00111=>11100
[4,-2,1,3,5]=>01000=>00010
[4,-2,1,3,-5]=>01001=>10010
[4,-2,1,-3,5]=>01010=>01010
[4,-2,1,-3,-5]=>01011=>11010
[4,-2,-1,3,5]=>01100=>00110
[4,-2,-1,3,-5]=>01101=>10110
[4,-2,-1,-3,5]=>01110=>01110
[4,-2,-1,-3,-5]=>01111=>11110
[-4,2,1,3,5]=>10000=>00001
[-4,2,1,3,-5]=>10001=>10001
[-4,2,1,-3,5]=>10010=>01001
[-4,2,1,-3,-5]=>10011=>11001
[-4,2,-1,3,5]=>10100=>00101
[-4,2,-1,3,-5]=>10101=>10101
[-4,2,-1,-3,5]=>10110=>01101
[-4,2,-1,-3,-5]=>10111=>11101
[-4,-2,1,3,5]=>11000=>00011
[-4,-2,1,3,-5]=>11001=>10011
[-4,-2,1,-3,5]=>11010=>01011
[-4,-2,1,-3,-5]=>11011=>11011
[-4,-2,-1,3,5]=>11100=>00111
[-4,-2,-1,3,-5]=>11101=>10111
[-4,-2,-1,-3,5]=>11110=>01111
[-4,-2,-1,-3,-5]=>11111=>11111
[4,2,1,5,3]=>00000=>00000
[4,2,1,5,-3]=>00001=>10000
[4,2,1,-5,3]=>00010=>01000
[4,2,1,-5,-3]=>00011=>11000
[4,2,-1,5,3]=>00100=>00100
[4,2,-1,5,-3]=>00101=>10100
[4,2,-1,-5,3]=>00110=>01100
[4,2,-1,-5,-3]=>00111=>11100
[4,-2,1,5,3]=>01000=>00010
[4,-2,1,5,-3]=>01001=>10010
[4,-2,1,-5,3]=>01010=>01010
[4,-2,1,-5,-3]=>01011=>11010
[4,-2,-1,5,3]=>01100=>00110
[4,-2,-1,5,-3]=>01101=>10110
[4,-2,-1,-5,3]=>01110=>01110
[4,-2,-1,-5,-3]=>01111=>11110
[-4,2,1,5,3]=>10000=>00001
[-4,2,1,5,-3]=>10001=>10001
[-4,2,1,-5,3]=>10010=>01001
[-4,2,1,-5,-3]=>10011=>11001
[-4,2,-1,5,3]=>10100=>00101
[-4,2,-1,5,-3]=>10101=>10101
[-4,2,-1,-5,3]=>10110=>01101
[-4,2,-1,-5,-3]=>10111=>11101
[-4,-2,1,5,3]=>11000=>00011
[-4,-2,1,5,-3]=>11001=>10011
[-4,-2,1,-5,3]=>11010=>01011
[-4,-2,1,-5,-3]=>11011=>11011
[-4,-2,-1,5,3]=>11100=>00111
[-4,-2,-1,5,-3]=>11101=>10111
[-4,-2,-1,-5,3]=>11110=>01111
[-4,-2,-1,-5,-3]=>11111=>11111
[4,2,3,1,5]=>00000=>00000
[4,2,3,1,-5]=>00001=>10000
[4,2,3,-1,5]=>00010=>01000
[4,2,3,-1,-5]=>00011=>11000
[4,2,-3,1,5]=>00100=>00100
[4,2,-3,1,-5]=>00101=>10100
[4,2,-3,-1,5]=>00110=>01100
[4,2,-3,-1,-5]=>00111=>11100
[4,-2,3,1,5]=>01000=>00010
[4,-2,3,1,-5]=>01001=>10010
[4,-2,3,-1,5]=>01010=>01010
[4,-2,3,-1,-5]=>01011=>11010
[4,-2,-3,1,5]=>01100=>00110
[4,-2,-3,1,-5]=>01101=>10110
[4,-2,-3,-1,5]=>01110=>01110
[4,-2,-3,-1,-5]=>01111=>11110
[-4,2,3,1,5]=>10000=>00001
[-4,2,3,1,-5]=>10001=>10001
[-4,2,3,-1,5]=>10010=>01001
[-4,2,3,-1,-5]=>10011=>11001
[-4,2,-3,1,5]=>10100=>00101
[-4,2,-3,1,-5]=>10101=>10101
[-4,2,-3,-1,5]=>10110=>01101
[-4,2,-3,-1,-5]=>10111=>11101
[-4,-2,3,1,5]=>11000=>00011
[-4,-2,3,1,-5]=>11001=>10011
[-4,-2,3,-1,5]=>11010=>01011
[-4,-2,3,-1,-5]=>11011=>11011
[-4,-2,-3,1,5]=>11100=>00111
[-4,-2,-3,1,-5]=>11101=>10111
[-4,-2,-3,-1,5]=>11110=>01111
[-4,-2,-3,-1,-5]=>11111=>11111
[4,2,3,5,1]=>00000=>00000
[4,2,3,5,-1]=>00001=>10000
[4,2,3,-5,1]=>00010=>01000
[4,2,3,-5,-1]=>00011=>11000
[4,2,-3,5,1]=>00100=>00100
[4,2,-3,5,-1]=>00101=>10100
[4,2,-3,-5,1]=>00110=>01100
[4,2,-3,-5,-1]=>00111=>11100
[4,-2,3,5,1]=>01000=>00010
[4,-2,3,5,-1]=>01001=>10010
[4,-2,3,-5,1]=>01010=>01010
[4,-2,3,-5,-1]=>01011=>11010
[4,-2,-3,5,1]=>01100=>00110
[4,-2,-3,5,-1]=>01101=>10110
[4,-2,-3,-5,1]=>01110=>01110
[4,-2,-3,-5,-1]=>01111=>11110
[-4,2,3,5,1]=>10000=>00001
[-4,2,3,5,-1]=>10001=>10001
[-4,2,3,-5,1]=>10010=>01001
[-4,2,3,-5,-1]=>10011=>11001
[-4,2,-3,5,1]=>10100=>00101
[-4,2,-3,5,-1]=>10101=>10101
[-4,2,-3,-5,1]=>10110=>01101
[-4,2,-3,-5,-1]=>10111=>11101
[-4,-2,3,5,1]=>11000=>00011
[-4,-2,3,5,-1]=>11001=>10011
[-4,-2,3,-5,1]=>11010=>01011
[-4,-2,3,-5,-1]=>11011=>11011
[-4,-2,-3,5,1]=>11100=>00111
[-4,-2,-3,5,-1]=>11101=>10111
[-4,-2,-3,-5,1]=>11110=>01111
[-4,-2,-3,-5,-1]=>11111=>11111
[4,2,5,1,3]=>00000=>00000
[4,2,5,1,-3]=>00001=>10000
[4,2,5,-1,3]=>00010=>01000
[4,2,5,-1,-3]=>00011=>11000
[4,2,-5,1,3]=>00100=>00100
[4,2,-5,1,-3]=>00101=>10100
[4,2,-5,-1,3]=>00110=>01100
[4,2,-5,-1,-3]=>00111=>11100
[4,-2,5,1,3]=>01000=>00010
[4,-2,5,1,-3]=>01001=>10010
[4,-2,5,-1,3]=>01010=>01010
[4,-2,5,-1,-3]=>01011=>11010
[4,-2,-5,1,3]=>01100=>00110
[4,-2,-5,1,-3]=>01101=>10110
[4,-2,-5,-1,3]=>01110=>01110
[4,-2,-5,-1,-3]=>01111=>11110
[-4,2,5,1,3]=>10000=>00001
[-4,2,5,1,-3]=>10001=>10001
[-4,2,5,-1,3]=>10010=>01001
[-4,2,5,-1,-3]=>10011=>11001
[-4,2,-5,1,3]=>10100=>00101
[-4,2,-5,1,-3]=>10101=>10101
[-4,2,-5,-1,3]=>10110=>01101
[-4,2,-5,-1,-3]=>10111=>11101
[-4,-2,5,1,3]=>11000=>00011
[-4,-2,5,1,-3]=>11001=>10011
[-4,-2,5,-1,3]=>11010=>01011
[-4,-2,5,-1,-3]=>11011=>11011
[-4,-2,-5,1,3]=>11100=>00111
[-4,-2,-5,1,-3]=>11101=>10111
[-4,-2,-5,-1,3]=>11110=>01111
[-4,-2,-5,-1,-3]=>11111=>11111
[4,2,5,3,1]=>00000=>00000
[4,2,5,3,-1]=>00001=>10000
[4,2,5,-3,1]=>00010=>01000
[4,2,5,-3,-1]=>00011=>11000
[4,2,-5,3,1]=>00100=>00100
[4,2,-5,3,-1]=>00101=>10100
[4,2,-5,-3,1]=>00110=>01100
[4,2,-5,-3,-1]=>00111=>11100
[4,-2,5,3,1]=>01000=>00010
[4,-2,5,3,-1]=>01001=>10010
[4,-2,5,-3,1]=>01010=>01010
[4,-2,5,-3,-1]=>01011=>11010
[4,-2,-5,3,1]=>01100=>00110
[4,-2,-5,3,-1]=>01101=>10110
[4,-2,-5,-3,1]=>01110=>01110
[4,-2,-5,-3,-1]=>01111=>11110
[-4,2,5,3,1]=>10000=>00001
[-4,2,5,3,-1]=>10001=>10001
[-4,2,5,-3,1]=>10010=>01001
[-4,2,5,-3,-1]=>10011=>11001
[-4,2,-5,3,1]=>10100=>00101
[-4,2,-5,3,-1]=>10101=>10101
[-4,2,-5,-3,1]=>10110=>01101
[-4,2,-5,-3,-1]=>10111=>11101
[-4,-2,5,3,1]=>11000=>00011
[-4,-2,5,3,-1]=>11001=>10011
[-4,-2,5,-3,1]=>11010=>01011
[-4,-2,5,-3,-1]=>11011=>11011
[-4,-2,-5,3,1]=>11100=>00111
[-4,-2,-5,3,-1]=>11101=>10111
[-4,-2,-5,-3,1]=>11110=>01111
[-4,-2,-5,-3,-1]=>11111=>11111
[4,3,1,2,5]=>00000=>00000
[4,3,1,2,-5]=>00001=>10000
[4,3,1,-2,5]=>00010=>01000
[4,3,1,-2,-5]=>00011=>11000
[4,3,-1,2,5]=>00100=>00100
[4,3,-1,2,-5]=>00101=>10100
[4,3,-1,-2,5]=>00110=>01100
[4,3,-1,-2,-5]=>00111=>11100
[4,-3,1,2,5]=>01000=>00010
[4,-3,1,2,-5]=>01001=>10010
[4,-3,1,-2,5]=>01010=>01010
[4,-3,1,-2,-5]=>01011=>11010
[4,-3,-1,2,5]=>01100=>00110
[4,-3,-1,2,-5]=>01101=>10110
[4,-3,-1,-2,5]=>01110=>01110
[4,-3,-1,-2,-5]=>01111=>11110
[-4,3,1,2,5]=>10000=>00001
[-4,3,1,2,-5]=>10001=>10001
[-4,3,1,-2,5]=>10010=>01001
[-4,3,1,-2,-5]=>10011=>11001
[-4,3,-1,2,5]=>10100=>00101
[-4,3,-1,2,-5]=>10101=>10101
[-4,3,-1,-2,5]=>10110=>01101
[-4,3,-1,-2,-5]=>10111=>11101
[-4,-3,1,2,5]=>11000=>00011
[-4,-3,1,2,-5]=>11001=>10011
[-4,-3,1,-2,5]=>11010=>01011
[-4,-3,1,-2,-5]=>11011=>11011
[-4,-3,-1,2,5]=>11100=>00111
[-4,-3,-1,2,-5]=>11101=>10111
[-4,-3,-1,-2,5]=>11110=>01111
[-4,-3,-1,-2,-5]=>11111=>11111
[4,3,1,5,2]=>00000=>00000
[4,3,1,5,-2]=>00001=>10000
[4,3,1,-5,2]=>00010=>01000
[4,3,1,-5,-2]=>00011=>11000
[4,3,-1,5,2]=>00100=>00100
[4,3,-1,5,-2]=>00101=>10100
[4,3,-1,-5,2]=>00110=>01100
[4,3,-1,-5,-2]=>00111=>11100
[4,-3,1,5,2]=>01000=>00010
[4,-3,1,5,-2]=>01001=>10010
[4,-3,1,-5,2]=>01010=>01010
[4,-3,1,-5,-2]=>01011=>11010
[4,-3,-1,5,2]=>01100=>00110
[4,-3,-1,5,-2]=>01101=>10110
[4,-3,-1,-5,2]=>01110=>01110
[4,-3,-1,-5,-2]=>01111=>11110
[-4,3,1,5,2]=>10000=>00001
[-4,3,1,5,-2]=>10001=>10001
[-4,3,1,-5,2]=>10010=>01001
[-4,3,1,-5,-2]=>10011=>11001
[-4,3,-1,5,2]=>10100=>00101
[-4,3,-1,5,-2]=>10101=>10101
[-4,3,-1,-5,2]=>10110=>01101
[-4,3,-1,-5,-2]=>10111=>11101
[-4,-3,1,5,2]=>11000=>00011
[-4,-3,1,5,-2]=>11001=>10011
[-4,-3,1,-5,2]=>11010=>01011
[-4,-3,1,-5,-2]=>11011=>11011
[-4,-3,-1,5,2]=>11100=>00111
[-4,-3,-1,5,-2]=>11101=>10111
[-4,-3,-1,-5,2]=>11110=>01111
[-4,-3,-1,-5,-2]=>11111=>11111
[4,3,2,1,5]=>00000=>00000
[4,3,2,1,-5]=>00001=>10000
[4,3,2,-1,5]=>00010=>01000
[4,3,2,-1,-5]=>00011=>11000
[4,3,-2,1,5]=>00100=>00100
[4,3,-2,1,-5]=>00101=>10100
[4,3,-2,-1,5]=>00110=>01100
[4,3,-2,-1,-5]=>00111=>11100
[4,-3,2,1,5]=>01000=>00010
[4,-3,2,1,-5]=>01001=>10010
[4,-3,2,-1,5]=>01010=>01010
[4,-3,2,-1,-5]=>01011=>11010
[4,-3,-2,1,5]=>01100=>00110
[4,-3,-2,1,-5]=>01101=>10110
[4,-3,-2,-1,5]=>01110=>01110
[4,-3,-2,-1,-5]=>01111=>11110
[-4,3,2,1,5]=>10000=>00001
[-4,3,2,1,-5]=>10001=>10001
[-4,3,2,-1,5]=>10010=>01001
[-4,3,2,-1,-5]=>10011=>11001
[-4,3,-2,1,5]=>10100=>00101
[-4,3,-2,1,-5]=>10101=>10101
[-4,3,-2,-1,5]=>10110=>01101
[-4,3,-2,-1,-5]=>10111=>11101
[-4,-3,2,1,5]=>11000=>00011
[-4,-3,2,1,-5]=>11001=>10011
[-4,-3,2,-1,5]=>11010=>01011
[-4,-3,2,-1,-5]=>11011=>11011
[-4,-3,-2,1,5]=>11100=>00111
[-4,-3,-2,1,-5]=>11101=>10111
[-4,-3,-2,-1,5]=>11110=>01111
[-4,-3,-2,-1,-5]=>11111=>11111
[4,3,2,5,1]=>00000=>00000
[4,3,2,5,-1]=>00001=>10000
[4,3,2,-5,1]=>00010=>01000
[4,3,2,-5,-1]=>00011=>11000
[4,3,-2,5,1]=>00100=>00100
[4,3,-2,5,-1]=>00101=>10100
[4,3,-2,-5,1]=>00110=>01100
[4,3,-2,-5,-1]=>00111=>11100
[4,-3,2,5,1]=>01000=>00010
[4,-3,2,5,-1]=>01001=>10010
[4,-3,2,-5,1]=>01010=>01010
[4,-3,2,-5,-1]=>01011=>11010
[4,-3,-2,5,1]=>01100=>00110
[4,-3,-2,5,-1]=>01101=>10110
[4,-3,-2,-5,1]=>01110=>01110
[4,-3,-2,-5,-1]=>01111=>11110
[-4,3,2,5,1]=>10000=>00001
[-4,3,2,5,-1]=>10001=>10001
[-4,3,2,-5,1]=>10010=>01001
[-4,3,2,-5,-1]=>10011=>11001
[-4,3,-2,5,1]=>10100=>00101
[-4,3,-2,5,-1]=>10101=>10101
[-4,3,-2,-5,1]=>10110=>01101
[-4,3,-2,-5,-1]=>10111=>11101
[-4,-3,2,5,1]=>11000=>00011
[-4,-3,2,5,-1]=>11001=>10011
[-4,-3,2,-5,1]=>11010=>01011
[-4,-3,2,-5,-1]=>11011=>11011
[-4,-3,-2,5,1]=>11100=>00111
[-4,-3,-2,5,-1]=>11101=>10111
[-4,-3,-2,-5,1]=>11110=>01111
[-4,-3,-2,-5,-1]=>11111=>11111
[4,3,5,1,2]=>00000=>00000
[4,3,5,1,-2]=>00001=>10000
[4,3,5,-1,2]=>00010=>01000
[4,3,5,-1,-2]=>00011=>11000
[4,3,-5,1,2]=>00100=>00100
[4,3,-5,1,-2]=>00101=>10100
[4,3,-5,-1,2]=>00110=>01100
[4,3,-5,-1,-2]=>00111=>11100
[4,-3,5,1,2]=>01000=>00010
[4,-3,5,1,-2]=>01001=>10010
[4,-3,5,-1,2]=>01010=>01010
[4,-3,5,-1,-2]=>01011=>11010
[4,-3,-5,1,2]=>01100=>00110
[4,-3,-5,1,-2]=>01101=>10110
[4,-3,-5,-1,2]=>01110=>01110
[4,-3,-5,-1,-2]=>01111=>11110
[-4,3,5,1,2]=>10000=>00001
[-4,3,5,1,-2]=>10001=>10001
[-4,3,5,-1,2]=>10010=>01001
[-4,3,5,-1,-2]=>10011=>11001
[-4,3,-5,1,2]=>10100=>00101
[-4,3,-5,1,-2]=>10101=>10101
[-4,3,-5,-1,2]=>10110=>01101
[-4,3,-5,-1,-2]=>10111=>11101
[-4,-3,5,1,2]=>11000=>00011
[-4,-3,5,1,-2]=>11001=>10011
[-4,-3,5,-1,2]=>11010=>01011
[-4,-3,5,-1,-2]=>11011=>11011
[-4,-3,-5,1,2]=>11100=>00111
[-4,-3,-5,1,-2]=>11101=>10111
[-4,-3,-5,-1,2]=>11110=>01111
[-4,-3,-5,-1,-2]=>11111=>11111
[4,3,5,2,1]=>00000=>00000
[4,3,5,2,-1]=>00001=>10000
[4,3,5,-2,1]=>00010=>01000
[4,3,5,-2,-1]=>00011=>11000
[4,3,-5,2,1]=>00100=>00100
[4,3,-5,2,-1]=>00101=>10100
[4,3,-5,-2,1]=>00110=>01100
[4,3,-5,-2,-1]=>00111=>11100
[4,-3,5,2,1]=>01000=>00010
[4,-3,5,2,-1]=>01001=>10010
[4,-3,5,-2,1]=>01010=>01010
[4,-3,5,-2,-1]=>01011=>11010
[4,-3,-5,2,1]=>01100=>00110
[4,-3,-5,2,-1]=>01101=>10110
[4,-3,-5,-2,1]=>01110=>01110
[4,-3,-5,-2,-1]=>01111=>11110
[-4,3,5,2,1]=>10000=>00001
[-4,3,5,2,-1]=>10001=>10001
[-4,3,5,-2,1]=>10010=>01001
[-4,3,5,-2,-1]=>10011=>11001
[-4,3,-5,2,1]=>10100=>00101
[-4,3,-5,2,-1]=>10101=>10101
[-4,3,-5,-2,1]=>10110=>01101
[-4,3,-5,-2,-1]=>10111=>11101
[-4,-3,5,2,1]=>11000=>00011
[-4,-3,5,2,-1]=>11001=>10011
[-4,-3,5,-2,1]=>11010=>01011
[-4,-3,5,-2,-1]=>11011=>11011
[-4,-3,-5,2,1]=>11100=>00111
[-4,-3,-5,2,-1]=>11101=>10111
[-4,-3,-5,-2,1]=>11110=>01111
[-4,-3,-5,-2,-1]=>11111=>11111
[4,5,1,2,3]=>00000=>00000
[4,5,1,2,-3]=>00001=>10000
[4,5,1,-2,3]=>00010=>01000
[4,5,1,-2,-3]=>00011=>11000
[4,5,-1,2,3]=>00100=>00100
[4,5,-1,2,-3]=>00101=>10100
[4,5,-1,-2,3]=>00110=>01100
[4,5,-1,-2,-3]=>00111=>11100
[4,-5,1,2,3]=>01000=>00010
[4,-5,1,2,-3]=>01001=>10010
[4,-5,1,-2,3]=>01010=>01010
[4,-5,1,-2,-3]=>01011=>11010
[4,-5,-1,2,3]=>01100=>00110
[4,-5,-1,2,-3]=>01101=>10110
[4,-5,-1,-2,3]=>01110=>01110
[4,-5,-1,-2,-3]=>01111=>11110
[-4,5,1,2,3]=>10000=>00001
[-4,5,1,2,-3]=>10001=>10001
[-4,5,1,-2,3]=>10010=>01001
[-4,5,1,-2,-3]=>10011=>11001
[-4,5,-1,2,3]=>10100=>00101
[-4,5,-1,2,-3]=>10101=>10101
[-4,5,-1,-2,3]=>10110=>01101
[-4,5,-1,-2,-3]=>10111=>11101
[-4,-5,1,2,3]=>11000=>00011
[-4,-5,1,2,-3]=>11001=>10011
[-4,-5,1,-2,3]=>11010=>01011
[-4,-5,1,-2,-3]=>11011=>11011
[-4,-5,-1,2,3]=>11100=>00111
[-4,-5,-1,2,-3]=>11101=>10111
[-4,-5,-1,-2,3]=>11110=>01111
[-4,-5,-1,-2,-3]=>11111=>11111
[4,5,1,3,2]=>00000=>00000
[4,5,1,3,-2]=>00001=>10000
[4,5,1,-3,2]=>00010=>01000
[4,5,1,-3,-2]=>00011=>11000
[4,5,-1,3,2]=>00100=>00100
[4,5,-1,3,-2]=>00101=>10100
[4,5,-1,-3,2]=>00110=>01100
[4,5,-1,-3,-2]=>00111=>11100
[4,-5,1,3,2]=>01000=>00010
[4,-5,1,3,-2]=>01001=>10010
[4,-5,1,-3,2]=>01010=>01010
[4,-5,1,-3,-2]=>01011=>11010
[4,-5,-1,3,2]=>01100=>00110
[4,-5,-1,3,-2]=>01101=>10110
[4,-5,-1,-3,2]=>01110=>01110
[4,-5,-1,-3,-2]=>01111=>11110
[-4,5,1,3,2]=>10000=>00001
[-4,5,1,3,-2]=>10001=>10001
[-4,5,1,-3,2]=>10010=>01001
[-4,5,1,-3,-2]=>10011=>11001
[-4,5,-1,3,2]=>10100=>00101
[-4,5,-1,3,-2]=>10101=>10101
[-4,5,-1,-3,2]=>10110=>01101
[-4,5,-1,-3,-2]=>10111=>11101
[-4,-5,1,3,2]=>11000=>00011
[-4,-5,1,3,-2]=>11001=>10011
[-4,-5,1,-3,2]=>11010=>01011
[-4,-5,1,-3,-2]=>11011=>11011
[-4,-5,-1,3,2]=>11100=>00111
[-4,-5,-1,3,-2]=>11101=>10111
[-4,-5,-1,-3,2]=>11110=>01111
[-4,-5,-1,-3,-2]=>11111=>11111
[4,5,2,1,3]=>00000=>00000
[4,5,2,1,-3]=>00001=>10000
[4,5,2,-1,3]=>00010=>01000
[4,5,2,-1,-3]=>00011=>11000
[4,5,-2,1,3]=>00100=>00100
[4,5,-2,1,-3]=>00101=>10100
[4,5,-2,-1,3]=>00110=>01100
[4,5,-2,-1,-3]=>00111=>11100
[4,-5,2,1,3]=>01000=>00010
[4,-5,2,1,-3]=>01001=>10010
[4,-5,2,-1,3]=>01010=>01010
[4,-5,2,-1,-3]=>01011=>11010
[4,-5,-2,1,3]=>01100=>00110
[4,-5,-2,1,-3]=>01101=>10110
[4,-5,-2,-1,3]=>01110=>01110
[4,-5,-2,-1,-3]=>01111=>11110
[-4,5,2,1,3]=>10000=>00001
[-4,5,2,1,-3]=>10001=>10001
[-4,5,2,-1,3]=>10010=>01001
[-4,5,2,-1,-3]=>10011=>11001
[-4,5,-2,1,3]=>10100=>00101
[-4,5,-2,1,-3]=>10101=>10101
[-4,5,-2,-1,3]=>10110=>01101
[-4,5,-2,-1,-3]=>10111=>11101
[-4,-5,2,1,3]=>11000=>00011
[-4,-5,2,1,-3]=>11001=>10011
[-4,-5,2,-1,3]=>11010=>01011
[-4,-5,2,-1,-3]=>11011=>11011
[-4,-5,-2,1,3]=>11100=>00111
[-4,-5,-2,1,-3]=>11101=>10111
[-4,-5,-2,-1,3]=>11110=>01111
[-4,-5,-2,-1,-3]=>11111=>11111
[4,5,2,3,1]=>00000=>00000
[4,5,2,3,-1]=>00001=>10000
[4,5,2,-3,1]=>00010=>01000
[4,5,2,-3,-1]=>00011=>11000
[4,5,-2,3,1]=>00100=>00100
[4,5,-2,3,-1]=>00101=>10100
[4,5,-2,-3,1]=>00110=>01100
[4,5,-2,-3,-1]=>00111=>11100
[4,-5,2,3,1]=>01000=>00010
[4,-5,2,3,-1]=>01001=>10010
[4,-5,2,-3,1]=>01010=>01010
[4,-5,2,-3,-1]=>01011=>11010
[4,-5,-2,3,1]=>01100=>00110
[4,-5,-2,3,-1]=>01101=>10110
[4,-5,-2,-3,1]=>01110=>01110
[4,-5,-2,-3,-1]=>01111=>11110
[-4,5,2,3,1]=>10000=>00001
[-4,5,2,3,-1]=>10001=>10001
[-4,5,2,-3,1]=>10010=>01001
[-4,5,2,-3,-1]=>10011=>11001
[-4,5,-2,3,1]=>10100=>00101
[-4,5,-2,3,-1]=>10101=>10101
[-4,5,-2,-3,1]=>10110=>01101
[-4,5,-2,-3,-1]=>10111=>11101
[-4,-5,2,3,1]=>11000=>00011
[-4,-5,2,3,-1]=>11001=>10011
[-4,-5,2,-3,1]=>11010=>01011
[-4,-5,2,-3,-1]=>11011=>11011
[-4,-5,-2,3,1]=>11100=>00111
[-4,-5,-2,3,-1]=>11101=>10111
[-4,-5,-2,-3,1]=>11110=>01111
[-4,-5,-2,-3,-1]=>11111=>11111
[4,5,3,1,2]=>00000=>00000
[4,5,3,1,-2]=>00001=>10000
[4,5,3,-1,2]=>00010=>01000
[4,5,3,-1,-2]=>00011=>11000
[4,5,-3,1,2]=>00100=>00100
[4,5,-3,1,-2]=>00101=>10100
[4,5,-3,-1,2]=>00110=>01100
[4,5,-3,-1,-2]=>00111=>11100
[4,-5,3,1,2]=>01000=>00010
[4,-5,3,1,-2]=>01001=>10010
[4,-5,3,-1,2]=>01010=>01010
[4,-5,3,-1,-2]=>01011=>11010
[4,-5,-3,1,2]=>01100=>00110
[4,-5,-3,1,-2]=>01101=>10110
[4,-5,-3,-1,2]=>01110=>01110
[4,-5,-3,-1,-2]=>01111=>11110
[-4,5,3,1,2]=>10000=>00001
[-4,5,3,1,-2]=>10001=>10001
[-4,5,3,-1,2]=>10010=>01001
[-4,5,3,-1,-2]=>10011=>11001
[-4,5,-3,1,2]=>10100=>00101
[-4,5,-3,1,-2]=>10101=>10101
[-4,5,-3,-1,2]=>10110=>01101
[-4,5,-3,-1,-2]=>10111=>11101
[-4,-5,3,1,2]=>11000=>00011
[-4,-5,3,1,-2]=>11001=>10011
[-4,-5,3,-1,2]=>11010=>01011
[-4,-5,3,-1,-2]=>11011=>11011
[-4,-5,-3,1,2]=>11100=>00111
[-4,-5,-3,1,-2]=>11101=>10111
[-4,-5,-3,-1,2]=>11110=>01111
[-4,-5,-3,-1,-2]=>11111=>11111
[4,5,3,2,1]=>00000=>00000
[4,5,3,2,-1]=>00001=>10000
[4,5,3,-2,1]=>00010=>01000
[4,5,3,-2,-1]=>00011=>11000
[4,5,-3,2,1]=>00100=>00100
[4,5,-3,2,-1]=>00101=>10100
[4,5,-3,-2,1]=>00110=>01100
[4,5,-3,-2,-1]=>00111=>11100
[4,-5,3,2,1]=>01000=>00010
[4,-5,3,2,-1]=>01001=>10010
[4,-5,3,-2,1]=>01010=>01010
[4,-5,3,-2,-1]=>01011=>11010
[4,-5,-3,2,1]=>01100=>00110
[4,-5,-3,2,-1]=>01101=>10110
[4,-5,-3,-2,1]=>01110=>01110
[4,-5,-3,-2,-1]=>01111=>11110
[-4,5,3,2,1]=>10000=>00001
[-4,5,3,2,-1]=>10001=>10001
[-4,5,3,-2,1]=>10010=>01001
[-4,5,3,-2,-1]=>10011=>11001
[-4,5,-3,2,1]=>10100=>00101
[-4,5,-3,2,-1]=>10101=>10101
[-4,5,-3,-2,1]=>10110=>01101
[-4,5,-3,-2,-1]=>10111=>11101
[-4,-5,3,2,1]=>11000=>00011
[-4,-5,3,2,-1]=>11001=>10011
[-4,-5,3,-2,1]=>11010=>01011
[-4,-5,3,-2,-1]=>11011=>11011
[-4,-5,-3,2,1]=>11100=>00111
[-4,-5,-3,2,-1]=>11101=>10111
[-4,-5,-3,-2,1]=>11110=>01111
[-4,-5,-3,-2,-1]=>11111=>11111
[5,1,2,3,4]=>00000=>00000
[5,1,2,3,-4]=>00001=>10000
[5,1,2,-3,4]=>00010=>01000
[5,1,2,-3,-4]=>00011=>11000
[5,1,-2,3,4]=>00100=>00100
[5,1,-2,3,-4]=>00101=>10100
[5,1,-2,-3,4]=>00110=>01100
[5,1,-2,-3,-4]=>00111=>11100
[5,-1,2,3,4]=>01000=>00010
[5,-1,2,3,-4]=>01001=>10010
[5,-1,2,-3,4]=>01010=>01010
[5,-1,2,-3,-4]=>01011=>11010
[5,-1,-2,3,4]=>01100=>00110
[5,-1,-2,3,-4]=>01101=>10110
[5,-1,-2,-3,4]=>01110=>01110
[5,-1,-2,-3,-4]=>01111=>11110
[-5,1,2,3,4]=>10000=>00001
[-5,1,2,3,-4]=>10001=>10001
[-5,1,2,-3,4]=>10010=>01001
[-5,1,2,-3,-4]=>10011=>11001
[-5,1,-2,3,4]=>10100=>00101
[-5,1,-2,3,-4]=>10101=>10101
[-5,1,-2,-3,4]=>10110=>01101
[-5,1,-2,-3,-4]=>10111=>11101
[-5,-1,2,3,4]=>11000=>00011
[-5,-1,2,3,-4]=>11001=>10011
[-5,-1,2,-3,4]=>11010=>01011
[-5,-1,2,-3,-4]=>11011=>11011
[-5,-1,-2,3,4]=>11100=>00111
[-5,-1,-2,3,-4]=>11101=>10111
[-5,-1,-2,-3,4]=>11110=>01111
[-5,-1,-2,-3,-4]=>11111=>11111
[5,1,2,4,3]=>00000=>00000
[5,1,2,4,-3]=>00001=>10000
[5,1,2,-4,3]=>00010=>01000
[5,1,2,-4,-3]=>00011=>11000
[5,1,-2,4,3]=>00100=>00100
[5,1,-2,4,-3]=>00101=>10100
[5,1,-2,-4,3]=>00110=>01100
[5,1,-2,-4,-3]=>00111=>11100
[5,-1,2,4,3]=>01000=>00010
[5,-1,2,4,-3]=>01001=>10010
[5,-1,2,-4,3]=>01010=>01010
[5,-1,2,-4,-3]=>01011=>11010
[5,-1,-2,4,3]=>01100=>00110
[5,-1,-2,4,-3]=>01101=>10110
[5,-1,-2,-4,3]=>01110=>01110
[5,-1,-2,-4,-3]=>01111=>11110
[-5,1,2,4,3]=>10000=>00001
[-5,1,2,4,-3]=>10001=>10001
[-5,1,2,-4,3]=>10010=>01001
[-5,1,2,-4,-3]=>10011=>11001
[-5,1,-2,4,3]=>10100=>00101
[-5,1,-2,4,-3]=>10101=>10101
[-5,1,-2,-4,3]=>10110=>01101
[-5,1,-2,-4,-3]=>10111=>11101
[-5,-1,2,4,3]=>11000=>00011
[-5,-1,2,4,-3]=>11001=>10011
[-5,-1,2,-4,3]=>11010=>01011
[-5,-1,2,-4,-3]=>11011=>11011
[-5,-1,-2,4,3]=>11100=>00111
[-5,-1,-2,4,-3]=>11101=>10111
[-5,-1,-2,-4,3]=>11110=>01111
[-5,-1,-2,-4,-3]=>11111=>11111
[5,1,3,2,4]=>00000=>00000
[5,1,3,2,-4]=>00001=>10000
[5,1,3,-2,4]=>00010=>01000
[5,1,3,-2,-4]=>00011=>11000
[5,1,-3,2,4]=>00100=>00100
[5,1,-3,2,-4]=>00101=>10100
[5,1,-3,-2,4]=>00110=>01100
[5,1,-3,-2,-4]=>00111=>11100
[5,-1,3,2,4]=>01000=>00010
[5,-1,3,2,-4]=>01001=>10010
[5,-1,3,-2,4]=>01010=>01010
[5,-1,3,-2,-4]=>01011=>11010
[5,-1,-3,2,4]=>01100=>00110
[5,-1,-3,2,-4]=>01101=>10110
[5,-1,-3,-2,4]=>01110=>01110
[5,-1,-3,-2,-4]=>01111=>11110
[-5,1,3,2,4]=>10000=>00001
[-5,1,3,2,-4]=>10001=>10001
[-5,1,3,-2,4]=>10010=>01001
[-5,1,3,-2,-4]=>10011=>11001
[-5,1,-3,2,4]=>10100=>00101
[-5,1,-3,2,-4]=>10101=>10101
[-5,1,-3,-2,4]=>10110=>01101
[-5,1,-3,-2,-4]=>10111=>11101
[-5,-1,3,2,4]=>11000=>00011
[-5,-1,3,2,-4]=>11001=>10011
[-5,-1,3,-2,4]=>11010=>01011
[-5,-1,3,-2,-4]=>11011=>11011
[-5,-1,-3,2,4]=>11100=>00111
[-5,-1,-3,2,-4]=>11101=>10111
[-5,-1,-3,-2,4]=>11110=>01111
[-5,-1,-3,-2,-4]=>11111=>11111
[5,1,3,4,2]=>00000=>00000
[5,1,3,4,-2]=>00001=>10000
[5,1,3,-4,2]=>00010=>01000
[5,1,3,-4,-2]=>00011=>11000
[5,1,-3,4,2]=>00100=>00100
[5,1,-3,4,-2]=>00101=>10100
[5,1,-3,-4,2]=>00110=>01100
[5,1,-3,-4,-2]=>00111=>11100
[5,-1,3,4,2]=>01000=>00010
[5,-1,3,4,-2]=>01001=>10010
[5,-1,3,-4,2]=>01010=>01010
[5,-1,3,-4,-2]=>01011=>11010
[5,-1,-3,4,2]=>01100=>00110
[5,-1,-3,4,-2]=>01101=>10110
[5,-1,-3,-4,2]=>01110=>01110
[5,-1,-3,-4,-2]=>01111=>11110
[-5,1,3,4,2]=>10000=>00001
[-5,1,3,4,-2]=>10001=>10001
[-5,1,3,-4,2]=>10010=>01001
[-5,1,3,-4,-2]=>10011=>11001
[-5,1,-3,4,2]=>10100=>00101
[-5,1,-3,4,-2]=>10101=>10101
[-5,1,-3,-4,2]=>10110=>01101
[-5,1,-3,-4,-2]=>10111=>11101
[-5,-1,3,4,2]=>11000=>00011
[-5,-1,3,4,-2]=>11001=>10011
[-5,-1,3,-4,2]=>11010=>01011
[-5,-1,3,-4,-2]=>11011=>11011
[-5,-1,-3,4,2]=>11100=>00111
[-5,-1,-3,4,-2]=>11101=>10111
[-5,-1,-3,-4,2]=>11110=>01111
[-5,-1,-3,-4,-2]=>11111=>11111
[5,1,4,2,3]=>00000=>00000
[5,1,4,2,-3]=>00001=>10000
[5,1,4,-2,3]=>00010=>01000
[5,1,4,-2,-3]=>00011=>11000
[5,1,-4,2,3]=>00100=>00100
[5,1,-4,2,-3]=>00101=>10100
[5,1,-4,-2,3]=>00110=>01100
[5,1,-4,-2,-3]=>00111=>11100
[5,-1,4,2,3]=>01000=>00010
[5,-1,4,2,-3]=>01001=>10010
[5,-1,4,-2,3]=>01010=>01010
[5,-1,4,-2,-3]=>01011=>11010
[5,-1,-4,2,3]=>01100=>00110
[5,-1,-4,2,-3]=>01101=>10110
[5,-1,-4,-2,3]=>01110=>01110
[5,-1,-4,-2,-3]=>01111=>11110
[-5,1,4,2,3]=>10000=>00001
[-5,1,4,2,-3]=>10001=>10001
[-5,1,4,-2,3]=>10010=>01001
[-5,1,4,-2,-3]=>10011=>11001
[-5,1,-4,2,3]=>10100=>00101
[-5,1,-4,2,-3]=>10101=>10101
[-5,1,-4,-2,3]=>10110=>01101
[-5,1,-4,-2,-3]=>10111=>11101
[-5,-1,4,2,3]=>11000=>00011
[-5,-1,4,2,-3]=>11001=>10011
[-5,-1,4,-2,3]=>11010=>01011
[-5,-1,4,-2,-3]=>11011=>11011
[-5,-1,-4,2,3]=>11100=>00111
[-5,-1,-4,2,-3]=>11101=>10111
[-5,-1,-4,-2,3]=>11110=>01111
[-5,-1,-4,-2,-3]=>11111=>11111
[5,1,4,3,2]=>00000=>00000
[5,1,4,3,-2]=>00001=>10000
[5,1,4,-3,2]=>00010=>01000
[5,1,4,-3,-2]=>00011=>11000
[5,1,-4,3,2]=>00100=>00100
[5,1,-4,3,-2]=>00101=>10100
[5,1,-4,-3,2]=>00110=>01100
[5,1,-4,-3,-2]=>00111=>11100
[5,-1,4,3,2]=>01000=>00010
[5,-1,4,3,-2]=>01001=>10010
[5,-1,4,-3,2]=>01010=>01010
[5,-1,4,-3,-2]=>01011=>11010
[5,-1,-4,3,2]=>01100=>00110
[5,-1,-4,3,-2]=>01101=>10110
[5,-1,-4,-3,2]=>01110=>01110
[5,-1,-4,-3,-2]=>01111=>11110
[-5,1,4,3,2]=>10000=>00001
[-5,1,4,3,-2]=>10001=>10001
[-5,1,4,-3,2]=>10010=>01001
[-5,1,4,-3,-2]=>10011=>11001
[-5,1,-4,3,2]=>10100=>00101
[-5,1,-4,3,-2]=>10101=>10101
[-5,1,-4,-3,2]=>10110=>01101
[-5,1,-4,-3,-2]=>10111=>11101
[-5,-1,4,3,2]=>11000=>00011
[-5,-1,4,3,-2]=>11001=>10011
[-5,-1,4,-3,2]=>11010=>01011
[-5,-1,4,-3,-2]=>11011=>11011
[-5,-1,-4,3,2]=>11100=>00111
[-5,-1,-4,3,-2]=>11101=>10111
[-5,-1,-4,-3,2]=>11110=>01111
[-5,-1,-4,-3,-2]=>11111=>11111
[5,2,1,3,4]=>00000=>00000
[5,2,1,3,-4]=>00001=>10000
[5,2,1,-3,4]=>00010=>01000
[5,2,1,-3,-4]=>00011=>11000
[5,2,-1,3,4]=>00100=>00100
[5,2,-1,3,-4]=>00101=>10100
[5,2,-1,-3,4]=>00110=>01100
[5,2,-1,-3,-4]=>00111=>11100
[5,-2,1,3,4]=>01000=>00010
[5,-2,1,3,-4]=>01001=>10010
[5,-2,1,-3,4]=>01010=>01010
[5,-2,1,-3,-4]=>01011=>11010
[5,-2,-1,3,4]=>01100=>00110
[5,-2,-1,3,-4]=>01101=>10110
[5,-2,-1,-3,4]=>01110=>01110
[5,-2,-1,-3,-4]=>01111=>11110
[-5,2,1,3,4]=>10000=>00001
[-5,2,1,3,-4]=>10001=>10001
[-5,2,1,-3,4]=>10010=>01001
[-5,2,1,-3,-4]=>10011=>11001
[-5,2,-1,3,4]=>10100=>00101
[-5,2,-1,3,-4]=>10101=>10101
[-5,2,-1,-3,4]=>10110=>01101
[-5,2,-1,-3,-4]=>10111=>11101
[-5,-2,1,3,4]=>11000=>00011
[-5,-2,1,3,-4]=>11001=>10011
[-5,-2,1,-3,4]=>11010=>01011
[-5,-2,1,-3,-4]=>11011=>11011
[-5,-2,-1,3,4]=>11100=>00111
[-5,-2,-1,3,-4]=>11101=>10111
[-5,-2,-1,-3,4]=>11110=>01111
[-5,-2,-1,-3,-4]=>11111=>11111
[5,2,1,4,3]=>00000=>00000
[5,2,1,4,-3]=>00001=>10000
[5,2,1,-4,3]=>00010=>01000
[5,2,1,-4,-3]=>00011=>11000
[5,2,-1,4,3]=>00100=>00100
[5,2,-1,4,-3]=>00101=>10100
[5,2,-1,-4,3]=>00110=>01100
[5,2,-1,-4,-3]=>00111=>11100
[5,-2,1,4,3]=>01000=>00010
[5,-2,1,4,-3]=>01001=>10010
[5,-2,1,-4,3]=>01010=>01010
[5,-2,1,-4,-3]=>01011=>11010
[5,-2,-1,4,3]=>01100=>00110
[5,-2,-1,4,-3]=>01101=>10110
[5,-2,-1,-4,3]=>01110=>01110
[5,-2,-1,-4,-3]=>01111=>11110
[-5,2,1,4,3]=>10000=>00001
[-5,2,1,4,-3]=>10001=>10001
[-5,2,1,-4,3]=>10010=>01001
[-5,2,1,-4,-3]=>10011=>11001
[-5,2,-1,4,3]=>10100=>00101
[-5,2,-1,4,-3]=>10101=>10101
[-5,2,-1,-4,3]=>10110=>01101
[-5,2,-1,-4,-3]=>10111=>11101
[-5,-2,1,4,3]=>11000=>00011
[-5,-2,1,4,-3]=>11001=>10011
[-5,-2,1,-4,3]=>11010=>01011
[-5,-2,1,-4,-3]=>11011=>11011
[-5,-2,-1,4,3]=>11100=>00111
[-5,-2,-1,4,-3]=>11101=>10111
[-5,-2,-1,-4,3]=>11110=>01111
[-5,-2,-1,-4,-3]=>11111=>11111
[5,2,3,1,4]=>00000=>00000
[5,2,3,1,-4]=>00001=>10000
[5,2,3,-1,4]=>00010=>01000
[5,2,3,-1,-4]=>00011=>11000
[5,2,-3,1,4]=>00100=>00100
[5,2,-3,1,-4]=>00101=>10100
[5,2,-3,-1,4]=>00110=>01100
[5,2,-3,-1,-4]=>00111=>11100
[5,-2,3,1,4]=>01000=>00010
[5,-2,3,1,-4]=>01001=>10010
[5,-2,3,-1,4]=>01010=>01010
[5,-2,3,-1,-4]=>01011=>11010
[5,-2,-3,1,4]=>01100=>00110
[5,-2,-3,1,-4]=>01101=>10110
[5,-2,-3,-1,4]=>01110=>01110
[5,-2,-3,-1,-4]=>01111=>11110
[-5,2,3,1,4]=>10000=>00001
[-5,2,3,1,-4]=>10001=>10001
[-5,2,3,-1,4]=>10010=>01001
[-5,2,3,-1,-4]=>10011=>11001
[-5,2,-3,1,4]=>10100=>00101
[-5,2,-3,1,-4]=>10101=>10101
[-5,2,-3,-1,4]=>10110=>01101
[-5,2,-3,-1,-4]=>10111=>11101
[-5,-2,3,1,4]=>11000=>00011
[-5,-2,3,1,-4]=>11001=>10011
[-5,-2,3,-1,4]=>11010=>01011
[-5,-2,3,-1,-4]=>11011=>11011
[-5,-2,-3,1,4]=>11100=>00111
[-5,-2,-3,1,-4]=>11101=>10111
[-5,-2,-3,-1,4]=>11110=>01111
[-5,-2,-3,-1,-4]=>11111=>11111
[5,2,3,4,1]=>00000=>00000
[5,2,3,4,-1]=>00001=>10000
[5,2,3,-4,1]=>00010=>01000
[5,2,3,-4,-1]=>00011=>11000
[5,2,-3,4,1]=>00100=>00100
[5,2,-3,4,-1]=>00101=>10100
[5,2,-3,-4,1]=>00110=>01100
[5,2,-3,-4,-1]=>00111=>11100
[5,-2,3,4,1]=>01000=>00010
[5,-2,3,4,-1]=>01001=>10010
[5,-2,3,-4,1]=>01010=>01010
[5,-2,3,-4,-1]=>01011=>11010
[5,-2,-3,4,1]=>01100=>00110
[5,-2,-3,4,-1]=>01101=>10110
[5,-2,-3,-4,1]=>01110=>01110
[5,-2,-3,-4,-1]=>01111=>11110
[-5,2,3,4,1]=>10000=>00001
[-5,2,3,4,-1]=>10001=>10001
[-5,2,3,-4,1]=>10010=>01001
[-5,2,3,-4,-1]=>10011=>11001
[-5,2,-3,4,1]=>10100=>00101
[-5,2,-3,4,-1]=>10101=>10101
[-5,2,-3,-4,1]=>10110=>01101
[-5,2,-3,-4,-1]=>10111=>11101
[-5,-2,3,4,1]=>11000=>00011
[-5,-2,3,4,-1]=>11001=>10011
[-5,-2,3,-4,1]=>11010=>01011
[-5,-2,3,-4,-1]=>11011=>11011
[-5,-2,-3,4,1]=>11100=>00111
[-5,-2,-3,4,-1]=>11101=>10111
[-5,-2,-3,-4,1]=>11110=>01111
[-5,-2,-3,-4,-1]=>11111=>11111
[5,2,4,1,3]=>00000=>00000
[5,2,4,1,-3]=>00001=>10000
[5,2,4,-1,3]=>00010=>01000
[5,2,4,-1,-3]=>00011=>11000
[5,2,-4,1,3]=>00100=>00100
[5,2,-4,1,-3]=>00101=>10100
[5,2,-4,-1,3]=>00110=>01100
[5,2,-4,-1,-3]=>00111=>11100
[5,-2,4,1,3]=>01000=>00010
[5,-2,4,1,-3]=>01001=>10010
[5,-2,4,-1,3]=>01010=>01010
[5,-2,4,-1,-3]=>01011=>11010
[5,-2,-4,1,3]=>01100=>00110
[5,-2,-4,1,-3]=>01101=>10110
[5,-2,-4,-1,3]=>01110=>01110
[5,-2,-4,-1,-3]=>01111=>11110
[-5,2,4,1,3]=>10000=>00001
[-5,2,4,1,-3]=>10001=>10001
[-5,2,4,-1,3]=>10010=>01001
[-5,2,4,-1,-3]=>10011=>11001
[-5,2,-4,1,3]=>10100=>00101
[-5,2,-4,1,-3]=>10101=>10101
[-5,2,-4,-1,3]=>10110=>01101
[-5,2,-4,-1,-3]=>10111=>11101
[-5,-2,4,1,3]=>11000=>00011
[-5,-2,4,1,-3]=>11001=>10011
[-5,-2,4,-1,3]=>11010=>01011
[-5,-2,4,-1,-3]=>11011=>11011
[-5,-2,-4,1,3]=>11100=>00111
[-5,-2,-4,1,-3]=>11101=>10111
[-5,-2,-4,-1,3]=>11110=>01111
[-5,-2,-4,-1,-3]=>11111=>11111
[5,2,4,3,1]=>00000=>00000
[5,2,4,3,-1]=>00001=>10000
[5,2,4,-3,1]=>00010=>01000
[5,2,4,-3,-1]=>00011=>11000
[5,2,-4,3,1]=>00100=>00100
[5,2,-4,3,-1]=>00101=>10100
[5,2,-4,-3,1]=>00110=>01100
[5,2,-4,-3,-1]=>00111=>11100
[5,-2,4,3,1]=>01000=>00010
[5,-2,4,3,-1]=>01001=>10010
[5,-2,4,-3,1]=>01010=>01010
[5,-2,4,-3,-1]=>01011=>11010
[5,-2,-4,3,1]=>01100=>00110
[5,-2,-4,3,-1]=>01101=>10110
[5,-2,-4,-3,1]=>01110=>01110
[5,-2,-4,-3,-1]=>01111=>11110
[-5,2,4,3,1]=>10000=>00001
[-5,2,4,3,-1]=>10001=>10001
[-5,2,4,-3,1]=>10010=>01001
[-5,2,4,-3,-1]=>10011=>11001
[-5,2,-4,3,1]=>10100=>00101
[-5,2,-4,3,-1]=>10101=>10101
[-5,2,-4,-3,1]=>10110=>01101
[-5,2,-4,-3,-1]=>10111=>11101
[-5,-2,4,3,1]=>11000=>00011
[-5,-2,4,3,-1]=>11001=>10011
[-5,-2,4,-3,1]=>11010=>01011
[-5,-2,4,-3,-1]=>11011=>11011
[-5,-2,-4,3,1]=>11100=>00111
[-5,-2,-4,3,-1]=>11101=>10111
[-5,-2,-4,-3,1]=>11110=>01111
[-5,-2,-4,-3,-1]=>11111=>11111
[5,3,1,2,4]=>00000=>00000
[5,3,1,2,-4]=>00001=>10000
[5,3,1,-2,4]=>00010=>01000
[5,3,1,-2,-4]=>00011=>11000
[5,3,-1,2,4]=>00100=>00100
[5,3,-1,2,-4]=>00101=>10100
[5,3,-1,-2,4]=>00110=>01100
[5,3,-1,-2,-4]=>00111=>11100
[5,-3,1,2,4]=>01000=>00010
[5,-3,1,2,-4]=>01001=>10010
[5,-3,1,-2,4]=>01010=>01010
[5,-3,1,-2,-4]=>01011=>11010
[5,-3,-1,2,4]=>01100=>00110
[5,-3,-1,2,-4]=>01101=>10110
[5,-3,-1,-2,4]=>01110=>01110
[5,-3,-1,-2,-4]=>01111=>11110
[-5,3,1,2,4]=>10000=>00001
[-5,3,1,2,-4]=>10001=>10001
[-5,3,1,-2,4]=>10010=>01001
[-5,3,1,-2,-4]=>10011=>11001
[-5,3,-1,2,4]=>10100=>00101
[-5,3,-1,2,-4]=>10101=>10101
[-5,3,-1,-2,4]=>10110=>01101
[-5,3,-1,-2,-4]=>10111=>11101
[-5,-3,1,2,4]=>11000=>00011
[-5,-3,1,2,-4]=>11001=>10011
[-5,-3,1,-2,4]=>11010=>01011
[-5,-3,1,-2,-4]=>11011=>11011
[-5,-3,-1,2,4]=>11100=>00111
[-5,-3,-1,2,-4]=>11101=>10111
[-5,-3,-1,-2,4]=>11110=>01111
[-5,-3,-1,-2,-4]=>11111=>11111
[5,3,1,4,2]=>00000=>00000
[5,3,1,4,-2]=>00001=>10000
[5,3,1,-4,2]=>00010=>01000
[5,3,1,-4,-2]=>00011=>11000
[5,3,-1,4,2]=>00100=>00100
[5,3,-1,4,-2]=>00101=>10100
[5,3,-1,-4,2]=>00110=>01100
[5,3,-1,-4,-2]=>00111=>11100
[5,-3,1,4,2]=>01000=>00010
[5,-3,1,4,-2]=>01001=>10010
[5,-3,1,-4,2]=>01010=>01010
[5,-3,1,-4,-2]=>01011=>11010
[5,-3,-1,4,2]=>01100=>00110
[5,-3,-1,4,-2]=>01101=>10110
[5,-3,-1,-4,2]=>01110=>01110
[5,-3,-1,-4,-2]=>01111=>11110
[-5,3,1,4,2]=>10000=>00001
[-5,3,1,4,-2]=>10001=>10001
[-5,3,1,-4,2]=>10010=>01001
[-5,3,1,-4,-2]=>10011=>11001
[-5,3,-1,4,2]=>10100=>00101
[-5,3,-1,4,-2]=>10101=>10101
[-5,3,-1,-4,2]=>10110=>01101
[-5,3,-1,-4,-2]=>10111=>11101
[-5,-3,1,4,2]=>11000=>00011
[-5,-3,1,4,-2]=>11001=>10011
[-5,-3,1,-4,2]=>11010=>01011
[-5,-3,1,-4,-2]=>11011=>11011
[-5,-3,-1,4,2]=>11100=>00111
[-5,-3,-1,4,-2]=>11101=>10111
[-5,-3,-1,-4,2]=>11110=>01111
[-5,-3,-1,-4,-2]=>11111=>11111
[5,3,2,1,4]=>00000=>00000
[5,3,2,1,-4]=>00001=>10000
[5,3,2,-1,4]=>00010=>01000
[5,3,2,-1,-4]=>00011=>11000
[5,3,-2,1,4]=>00100=>00100
[5,3,-2,1,-4]=>00101=>10100
[5,3,-2,-1,4]=>00110=>01100
[5,3,-2,-1,-4]=>00111=>11100
[5,-3,2,1,4]=>01000=>00010
[5,-3,2,1,-4]=>01001=>10010
[5,-3,2,-1,4]=>01010=>01010
[5,-3,2,-1,-4]=>01011=>11010
[5,-3,-2,1,4]=>01100=>00110
[5,-3,-2,1,-4]=>01101=>10110
[5,-3,-2,-1,4]=>01110=>01110
[5,-3,-2,-1,-4]=>01111=>11110
[-5,3,2,1,4]=>10000=>00001
[-5,3,2,1,-4]=>10001=>10001
[-5,3,2,-1,4]=>10010=>01001
[-5,3,2,-1,-4]=>10011=>11001
[-5,3,-2,1,4]=>10100=>00101
[-5,3,-2,1,-4]=>10101=>10101
[-5,3,-2,-1,4]=>10110=>01101
[-5,3,-2,-1,-4]=>10111=>11101
[-5,-3,2,1,4]=>11000=>00011
[-5,-3,2,1,-4]=>11001=>10011
[-5,-3,2,-1,4]=>11010=>01011
[-5,-3,2,-1,-4]=>11011=>11011
[-5,-3,-2,1,4]=>11100=>00111
[-5,-3,-2,1,-4]=>11101=>10111
[-5,-3,-2,-1,4]=>11110=>01111
[-5,-3,-2,-1,-4]=>11111=>11111
[5,3,2,4,1]=>00000=>00000
[5,3,2,4,-1]=>00001=>10000
[5,3,2,-4,1]=>00010=>01000
[5,3,2,-4,-1]=>00011=>11000
[5,3,-2,4,1]=>00100=>00100
[5,3,-2,4,-1]=>00101=>10100
[5,3,-2,-4,1]=>00110=>01100
[5,3,-2,-4,-1]=>00111=>11100
[5,-3,2,4,1]=>01000=>00010
[5,-3,2,4,-1]=>01001=>10010
[5,-3,2,-4,1]=>01010=>01010
[5,-3,2,-4,-1]=>01011=>11010
[5,-3,-2,4,1]=>01100=>00110
[5,-3,-2,4,-1]=>01101=>10110
[5,-3,-2,-4,1]=>01110=>01110
[5,-3,-2,-4,-1]=>01111=>11110
[-5,3,2,4,1]=>10000=>00001
[-5,3,2,4,-1]=>10001=>10001
[-5,3,2,-4,1]=>10010=>01001
[-5,3,2,-4,-1]=>10011=>11001
[-5,3,-2,4,1]=>10100=>00101
[-5,3,-2,4,-1]=>10101=>10101
[-5,3,-2,-4,1]=>10110=>01101
[-5,3,-2,-4,-1]=>10111=>11101
[-5,-3,2,4,1]=>11000=>00011
[-5,-3,2,4,-1]=>11001=>10011
[-5,-3,2,-4,1]=>11010=>01011
[-5,-3,2,-4,-1]=>11011=>11011
[-5,-3,-2,4,1]=>11100=>00111
[-5,-3,-2,4,-1]=>11101=>10111
[-5,-3,-2,-4,1]=>11110=>01111
[-5,-3,-2,-4,-1]=>11111=>11111
[5,3,4,1,2]=>00000=>00000
[5,3,4,1,-2]=>00001=>10000
[5,3,4,-1,2]=>00010=>01000
[5,3,4,-1,-2]=>00011=>11000
[5,3,-4,1,2]=>00100=>00100
[5,3,-4,1,-2]=>00101=>10100
[5,3,-4,-1,2]=>00110=>01100
[5,3,-4,-1,-2]=>00111=>11100
[5,-3,4,1,2]=>01000=>00010
[5,-3,4,1,-2]=>01001=>10010
[5,-3,4,-1,2]=>01010=>01010
[5,-3,4,-1,-2]=>01011=>11010
[5,-3,-4,1,2]=>01100=>00110
[5,-3,-4,1,-2]=>01101=>10110
[5,-3,-4,-1,2]=>01110=>01110
[5,-3,-4,-1,-2]=>01111=>11110
[-5,3,4,1,2]=>10000=>00001
[-5,3,4,1,-2]=>10001=>10001
[-5,3,4,-1,2]=>10010=>01001
[-5,3,4,-1,-2]=>10011=>11001
[-5,3,-4,1,2]=>10100=>00101
[-5,3,-4,1,-2]=>10101=>10101
[-5,3,-4,-1,2]=>10110=>01101
[-5,3,-4,-1,-2]=>10111=>11101
[-5,-3,4,1,2]=>11000=>00011
[-5,-3,4,1,-2]=>11001=>10011
[-5,-3,4,-1,2]=>11010=>01011
[-5,-3,4,-1,-2]=>11011=>11011
[-5,-3,-4,1,2]=>11100=>00111
[-5,-3,-4,1,-2]=>11101=>10111
[-5,-3,-4,-1,2]=>11110=>01111
[-5,-3,-4,-1,-2]=>11111=>11111
[5,3,4,2,1]=>00000=>00000
[5,3,4,2,-1]=>00001=>10000
[5,3,4,-2,1]=>00010=>01000
[5,3,4,-2,-1]=>00011=>11000
[5,3,-4,2,1]=>00100=>00100
[5,3,-4,2,-1]=>00101=>10100
[5,3,-4,-2,1]=>00110=>01100
[5,3,-4,-2,-1]=>00111=>11100
[5,-3,4,2,1]=>01000=>00010
[5,-3,4,2,-1]=>01001=>10010
[5,-3,4,-2,1]=>01010=>01010
[5,-3,4,-2,-1]=>01011=>11010
[5,-3,-4,2,1]=>01100=>00110
[5,-3,-4,2,-1]=>01101=>10110
[5,-3,-4,-2,1]=>01110=>01110
[5,-3,-4,-2,-1]=>01111=>11110
[-5,3,4,2,1]=>10000=>00001
[-5,3,4,2,-1]=>10001=>10001
[-5,3,4,-2,1]=>10010=>01001
[-5,3,4,-2,-1]=>10011=>11001
[-5,3,-4,2,1]=>10100=>00101
[-5,3,-4,2,-1]=>10101=>10101
[-5,3,-4,-2,1]=>10110=>01101
[-5,3,-4,-2,-1]=>10111=>11101
[-5,-3,4,2,1]=>11000=>00011
[-5,-3,4,2,-1]=>11001=>10011
[-5,-3,4,-2,1]=>11010=>01011
[-5,-3,4,-2,-1]=>11011=>11011
[-5,-3,-4,2,1]=>11100=>00111
[-5,-3,-4,2,-1]=>11101=>10111
[-5,-3,-4,-2,1]=>11110=>01111
[-5,-3,-4,-2,-1]=>11111=>11111
[5,4,1,2,3]=>00000=>00000
[5,4,1,2,-3]=>00001=>10000
[5,4,1,-2,3]=>00010=>01000
[5,4,1,-2,-3]=>00011=>11000
[5,4,-1,2,3]=>00100=>00100
[5,4,-1,2,-3]=>00101=>10100
[5,4,-1,-2,3]=>00110=>01100
[5,4,-1,-2,-3]=>00111=>11100
[5,-4,1,2,3]=>01000=>00010
[5,-4,1,2,-3]=>01001=>10010
[5,-4,1,-2,3]=>01010=>01010
[5,-4,1,-2,-3]=>01011=>11010
[5,-4,-1,2,3]=>01100=>00110
[5,-4,-1,2,-3]=>01101=>10110
[5,-4,-1,-2,3]=>01110=>01110
[5,-4,-1,-2,-3]=>01111=>11110
[-5,4,1,2,3]=>10000=>00001
[-5,4,1,2,-3]=>10001=>10001
[-5,4,1,-2,3]=>10010=>01001
[-5,4,1,-2,-3]=>10011=>11001
[-5,4,-1,2,3]=>10100=>00101
[-5,4,-1,2,-3]=>10101=>10101
[-5,4,-1,-2,3]=>10110=>01101
[-5,4,-1,-2,-3]=>10111=>11101
[-5,-4,1,2,3]=>11000=>00011
[-5,-4,1,2,-3]=>11001=>10011
[-5,-4,1,-2,3]=>11010=>01011
[-5,-4,1,-2,-3]=>11011=>11011
[-5,-4,-1,2,3]=>11100=>00111
[-5,-4,-1,2,-3]=>11101=>10111
[-5,-4,-1,-2,3]=>11110=>01111
[-5,-4,-1,-2,-3]=>11111=>11111
[5,4,1,3,2]=>00000=>00000
[5,4,1,3,-2]=>00001=>10000
[5,4,1,-3,2]=>00010=>01000
[5,4,1,-3,-2]=>00011=>11000
[5,4,-1,3,2]=>00100=>00100
[5,4,-1,3,-2]=>00101=>10100
[5,4,-1,-3,2]=>00110=>01100
[5,4,-1,-3,-2]=>00111=>11100
[5,-4,1,3,2]=>01000=>00010
[5,-4,1,3,-2]=>01001=>10010
[5,-4,1,-3,2]=>01010=>01010
[5,-4,1,-3,-2]=>01011=>11010
[5,-4,-1,3,2]=>01100=>00110
[5,-4,-1,3,-2]=>01101=>10110
[5,-4,-1,-3,2]=>01110=>01110
[5,-4,-1,-3,-2]=>01111=>11110
[-5,4,1,3,2]=>10000=>00001
[-5,4,1,3,-2]=>10001=>10001
[-5,4,1,-3,2]=>10010=>01001
[-5,4,1,-3,-2]=>10011=>11001
[-5,4,-1,3,2]=>10100=>00101
[-5,4,-1,3,-2]=>10101=>10101
[-5,4,-1,-3,2]=>10110=>01101
[-5,4,-1,-3,-2]=>10111=>11101
[-5,-4,1,3,2]=>11000=>00011
[-5,-4,1,3,-2]=>11001=>10011
[-5,-4,1,-3,2]=>11010=>01011
[-5,-4,1,-3,-2]=>11011=>11011
[-5,-4,-1,3,2]=>11100=>00111
[-5,-4,-1,3,-2]=>11101=>10111
[-5,-4,-1,-3,2]=>11110=>01111
[-5,-4,-1,-3,-2]=>11111=>11111
[5,4,2,1,3]=>00000=>00000
[5,4,2,1,-3]=>00001=>10000
[5,4,2,-1,3]=>00010=>01000
[5,4,2,-1,-3]=>00011=>11000
[5,4,-2,1,3]=>00100=>00100
[5,4,-2,1,-3]=>00101=>10100
[5,4,-2,-1,3]=>00110=>01100
[5,4,-2,-1,-3]=>00111=>11100
[5,-4,2,1,3]=>01000=>00010
[5,-4,2,1,-3]=>01001=>10010
[5,-4,2,-1,3]=>01010=>01010
[5,-4,2,-1,-3]=>01011=>11010
[5,-4,-2,1,3]=>01100=>00110
[5,-4,-2,1,-3]=>01101=>10110
[5,-4,-2,-1,3]=>01110=>01110
[5,-4,-2,-1,-3]=>01111=>11110
[-5,4,2,1,3]=>10000=>00001
[-5,4,2,1,-3]=>10001=>10001
[-5,4,2,-1,3]=>10010=>01001
[-5,4,2,-1,-3]=>10011=>11001
[-5,4,-2,1,3]=>10100=>00101
[-5,4,-2,1,-3]=>10101=>10101
[-5,4,-2,-1,3]=>10110=>01101
[-5,4,-2,-1,-3]=>10111=>11101
[-5,-4,2,1,3]=>11000=>00011
[-5,-4,2,1,-3]=>11001=>10011
[-5,-4,2,-1,3]=>11010=>01011
[-5,-4,2,-1,-3]=>11011=>11011
[-5,-4,-2,1,3]=>11100=>00111
[-5,-4,-2,1,-3]=>11101=>10111
[-5,-4,-2,-1,3]=>11110=>01111
[-5,-4,-2,-1,-3]=>11111=>11111
[5,4,2,3,1]=>00000=>00000
[5,4,2,3,-1]=>00001=>10000
[5,4,2,-3,1]=>00010=>01000
[5,4,2,-3,-1]=>00011=>11000
[5,4,-2,3,1]=>00100=>00100
[5,4,-2,3,-1]=>00101=>10100
[5,4,-2,-3,1]=>00110=>01100
[5,4,-2,-3,-1]=>00111=>11100
[5,-4,2,3,1]=>01000=>00010
[5,-4,2,3,-1]=>01001=>10010
[5,-4,2,-3,1]=>01010=>01010
[5,-4,2,-3,-1]=>01011=>11010
[5,-4,-2,3,1]=>01100=>00110
[5,-4,-2,3,-1]=>01101=>10110
[5,-4,-2,-3,1]=>01110=>01110
[5,-4,-2,-3,-1]=>01111=>11110
[-5,4,2,3,1]=>10000=>00001
[-5,4,2,3,-1]=>10001=>10001
[-5,4,2,-3,1]=>10010=>01001
[-5,4,2,-3,-1]=>10011=>11001
[-5,4,-2,3,1]=>10100=>00101
[-5,4,-2,3,-1]=>10101=>10101
[-5,4,-2,-3,1]=>10110=>01101
[-5,4,-2,-3,-1]=>10111=>11101
[-5,-4,2,3,1]=>11000=>00011
[-5,-4,2,3,-1]=>11001=>10011
[-5,-4,2,-3,1]=>11010=>01011
[-5,-4,2,-3,-1]=>11011=>11011
[-5,-4,-2,3,1]=>11100=>00111
[-5,-4,-2,3,-1]=>11101=>10111
[-5,-4,-2,-3,1]=>11110=>01111
[-5,-4,-2,-3,-1]=>11111=>11111
[5,4,3,1,2]=>00000=>00000
[5,4,3,1,-2]=>00001=>10000
[5,4,3,-1,2]=>00010=>01000
[5,4,3,-1,-2]=>00011=>11000
[5,4,-3,1,2]=>00100=>00100
[5,4,-3,1,-2]=>00101=>10100
[5,4,-3,-1,2]=>00110=>01100
[5,4,-3,-1,-2]=>00111=>11100
[5,-4,3,1,2]=>01000=>00010
[5,-4,3,1,-2]=>01001=>10010
[5,-4,3,-1,2]=>01010=>01010
[5,-4,3,-1,-2]=>01011=>11010
[5,-4,-3,1,2]=>01100=>00110
[5,-4,-3,1,-2]=>01101=>10110
[5,-4,-3,-1,2]=>01110=>01110
[5,-4,-3,-1,-2]=>01111=>11110
[-5,4,3,1,2]=>10000=>00001
[-5,4,3,1,-2]=>10001=>10001
[-5,4,3,-1,2]=>10010=>01001
[-5,4,3,-1,-2]=>10011=>11001
[-5,4,-3,1,2]=>10100=>00101
[-5,4,-3,1,-2]=>10101=>10101
[-5,4,-3,-1,2]=>10110=>01101
[-5,4,-3,-1,-2]=>10111=>11101
[-5,-4,3,1,2]=>11000=>00011
[-5,-4,3,1,-2]=>11001=>10011
[-5,-4,3,-1,2]=>11010=>01011
[-5,-4,3,-1,-2]=>11011=>11011
[-5,-4,-3,1,2]=>11100=>00111
[-5,-4,-3,1,-2]=>11101=>10111
[-5,-4,-3,-1,2]=>11110=>01111
[-5,-4,-3,-1,-2]=>11111=>11111
[5,4,3,2,1]=>00000=>00000
[5,4,3,2,-1]=>00001=>10000
[5,4,3,-2,1]=>00010=>01000
[5,4,3,-2,-1]=>00011=>11000
[5,4,-3,2,1]=>00100=>00100
[5,4,-3,2,-1]=>00101=>10100
[5,4,-3,-2,1]=>00110=>01100
[5,4,-3,-2,-1]=>00111=>11100
[5,-4,3,2,1]=>01000=>00010
[5,-4,3,2,-1]=>01001=>10010
[5,-4,3,-2,1]=>01010=>01010
[5,-4,3,-2,-1]=>01011=>11010
[5,-4,-3,2,1]=>01100=>00110
[5,-4,-3,2,-1]=>01101=>10110
[5,-4,-3,-2,1]=>01110=>01110
[5,-4,-3,-2,-1]=>01111=>11110
[-5,4,3,2,1]=>10000=>00001
[-5,4,3,2,-1]=>10001=>10001
[-5,4,3,-2,1]=>10010=>01001
[-5,4,3,-2,-1]=>10011=>11001
[-5,4,-3,2,1]=>10100=>00101
[-5,4,-3,2,-1]=>10101=>10101
[-5,4,-3,-2,1]=>10110=>01101
[-5,4,-3,-2,-1]=>10111=>11101
[-5,-4,3,2,1]=>11000=>00011
[-5,-4,3,2,-1]=>11001=>10011
[-5,-4,3,-2,1]=>11010=>01011
[-5,-4,3,-2,-1]=>11011=>11011
[-5,-4,-3,2,1]=>11100=>00111
[-5,-4,-3,2,-1]=>11101=>10111
[-5,-4,-3,-2,1]=>11110=>01111
[-5,-4,-3,-2,-1]=>11111=>11111
[1,2,3,4,5,6]=>000000=>000000
[1,2,3,6,4,5]=>000000=>000000
[1,2,5,3,4,6]=>000000=>000000
[1,2,5,6,3,4]=>000000=>000000
[1,4,2,3,5,6]=>000000=>000000
[1,4,2,6,3,5]=>000000=>000000
[1,4,5,2,3,6]=>000000=>000000
[1,4,5,6,2,3]=>000000=>000000
[1,5,2,3,4,6]=>000000=>000000
[1,5,6,2,3,4]=>000000=>000000
[1,6,2,3,4,5]=>000000=>000000
[1,6,2,5,3,4]=>000000=>000000
[1,6,4,2,3,5]=>000000=>000000
[1,6,4,5,2,3]=>000000=>000000
[3,1,2,4,5,6]=>000000=>000000
[3,1,2,6,4,5]=>000000=>000000
[3,1,5,2,4,6]=>000000=>000000
[3,1,5,6,2,4]=>000000=>000000
[3,4,1,2,5,6]=>000000=>000000
[3,4,1,6,2,5]=>000000=>000000
[3,4,5,1,2,6]=>000000=>000000
[3,4,5,6,1,2]=>000000=>000000
[3,4,6,1,2,5]=>000000=>000000
[3,5,1,2,4,6]=>000000=>000000
[3,5,6,1,2,4]=>000000=>000000
[3,6,1,2,4,5]=>000000=>000000
[3,6,1,5,2,4]=>000000=>000000
[3,6,4,1,2,5]=>000000=>000000
[3,6,4,5,1,2]=>000000=>000000
[4,1,2,3,5,6]=>000000=>000000
[4,5,1,2,3,6]=>000000=>000000
[4,5,6,1,2,3]=>000000=>000000
[4,6,1,2,3,5]=>000000=>000000
[4,6,5,1,2,3]=>000000=>000000
[5,1,2,3,4,6]=>000000=>000000
[5,1,2,6,3,4]=>000000=>000000
[5,1,4,2,3,6]=>000000=>000000
[5,1,4,6,2,3]=>000000=>000000
[5,1,6,2,3,4]=>000000=>000000
[5,3,1,2,4,6]=>000000=>000000
[5,3,1,6,2,4]=>000000=>000000
[5,3,4,1,2,6]=>000000=>000000
[5,3,4,6,1,2]=>000000=>000000
[5,6,1,2,3,4]=>000000=>000000
[5,6,1,4,2,3]=>000000=>000000
[5,6,3,1,2,4]=>000000=>000000
[5,6,3,4,1,2]=>000000=>000000
[6,1,2,3,4,5]=>000000=>000000
[6,2,1,5,3,4]=>000000=>000000
[6,2,4,1,3,5]=>000000=>000000
[6,3,1,2,4,5]=>000000=>000000
[1,2,3,4,7,5,6]=>0000000=>0000000
[1,2,5,3,7,4,6]=>0000000=>0000000
[1,2,7,3,4,5,6]=>0000000=>0000000
[1,2,7,3,6,4,5]=>0000000=>0000000
[1,4,7,2,3,5,6]=>0000000=>0000000
[1,5,7,2,3,4,6]=>0000000=>0000000
[1,6,7,2,3,4,5]=>0000000=>0000000
[1,6,7,2,5,3,4]=>0000000=>0000000
[1,6,7,4,2,3,5]=>0000000=>0000000
[3,1,7,2,4,5,6]=>0000000=>0000000
[3,1,7,5,2,4,6]=>0000000=>0000000
[3,4,7,1,2,5,6]=>0000000=>0000000
[3,4,7,1,6,2,5]=>0000000=>0000000
[3,4,7,5,1,2,6]=>0000000=>0000000
[3,4,7,5,6,1,2]=>0000000=>0000000
[3,5,7,1,2,4,6]=>0000000=>0000000
[3,6,1,2,7,4,5]=>0000000=>0000000
[3,7,4,1,2,5,6]=>0000000=>0000000
[3,7,4,5,1,2,6]=>0000000=>0000000
[3,7,4,5,6,1,2]=>0000000=>0000000
[3,7,4,6,1,2,5]=>0000000=>0000000
[3,7,5,1,2,4,6]=>0000000=>0000000
[3,7,5,6,1,2,4]=>0000000=>0000000
[3,7,6,1,2,4,5]=>0000000=>0000000
[4,7,5,6,1,2,3]=>0000000=>0000000
[5,3,4,7,1,2,6]=>0000000=>0000000
[5,3,7,1,2,4,6]=>0000000=>0000000
[5,4,7,1,2,3,6]=>0000000=>0000000
[7,1,2,5,3,4,6]=>0000000=>0000000
[7,1,3,2,4,5,6]=>0000000=>0000000
[7,1,4,2,3,5,6]=>0000000=>0000000
[7,1,4,2,6,3,5]=>0000000=>0000000
[7,1,4,5,2,3,6]=>0000000=>0000000
[7,1,4,6,2,3,5]=>0000000=>0000000
[7,1,5,2,3,4,6]=>0000000=>0000000
[7,1,5,6,2,3,4]=>0000000=>0000000
[7,1,6,2,3,4,5]=>0000000=>0000000
[7,1,6,4,5,2,3]=>0000000=>0000000
[7,2,4,1,3,5,6]=>0000000=>0000000
[7,2,5,1,3,4,6]=>0000000=>0000000
[7,2,6,1,3,4,5]=>0000000=>0000000
[7,3,1,2,4,5,6]=>0000000=>0000000
[7,3,5,1,2,4,6]=>0000000=>0000000
[7,3,5,6,1,2,4]=>0000000=>0000000
[7,3,6,1,2,4,5]=>0000000=>0000000
[7,5,1,4,2,3,6]=>0000000=>0000000
[7,8,5,6,3,4,1,2]=>00000000=>00000000
[5,6,7,8,3,4,1,2]=>00000000=>00000000
[-1,2,3,4,5,6]=>100000=>000001
[6,2,3,4,5,-1]=>000001=>100000
[-1,2,3,4,6,5]=>100000=>000001
[5,2,3,4,6,-1]=>000001=>100000
[5,2,3,4,-1,6]=>000010=>010000
[-1,2,3,5,4,6]=>100000=>000001
[6,2,3,5,4,-1]=>000001=>100000
[-1,2,3,6,4,5]=>100000=>000001
[4,2,3,5,6,-1]=>000001=>100000
[4,2,3,5,-1,6]=>000010=>010000
[-1,2,3,6,5,4]=>100000=>000001
[4,2,3,6,5,-1]=>000001=>100000
[4,2,3,-1,5,6]=>000100=>001000
[4,2,3,-1,6,5]=>000100=>001000
[-1,2,4,3,5,6]=>100000=>000001
[6,2,4,3,5,-1]=>000001=>100000
[-1,2,4,3,6,5]=>100000=>000001
[5,2,4,3,6,-1]=>000001=>100000
[5,2,4,3,-1,6]=>000010=>010000
[-1,2,5,3,4,6]=>100000=>000001
[6,2,5,3,4,-1]=>000001=>100000
[-1,2,6,3,4,5]=>100000=>000001
[3,2,4,5,6,-1]=>000001=>100000
[3,2,4,5,-1,6]=>000010=>010000
[-1,2,6,3,5,4]=>100000=>000001
[3,2,4,6,5,-1]=>000001=>100000
[3,2,4,-1,5,6]=>000100=>001000
[3,2,4,-1,6,5]=>000100=>001000
[-1,2,5,4,3,6]=>100000=>000001
[6,2,5,4,3,-1]=>000001=>100000
[-1,2,6,4,3,5]=>100000=>000001
[3,2,5,4,6,-1]=>000001=>100000
[3,2,5,4,-1,6]=>000010=>010000
[-1,2,6,5,3,4]=>100000=>000001
[3,2,6,4,5,-1]=>000001=>100000
[3,2,-1,4,5,6]=>001000=>000100
[3,2,-1,4,6,5]=>001000=>000100
[-1,2,6,5,4,3]=>100000=>000001
[3,2,6,5,4,-1]=>000001=>100000
[3,2,-1,5,4,6]=>001000=>000100
[3,2,-1,6,4,5]=>001000=>000100
[3,2,-1,6,5,4]=>001000=>000100
[-1,3,2,4,5,6]=>100000=>000001
[6,3,2,4,5,-1]=>000001=>100000
[-1,3,2,4,6,5]=>100000=>000001
[5,3,2,4,6,-1]=>000001=>100000
[5,3,2,4,-1,6]=>000010=>010000
[-1,3,2,5,4,6]=>100000=>000001
[6,3,2,5,4,-1]=>000001=>100000
[-1,3,2,6,4,5]=>100000=>000001
[4,3,2,5,6,-1]=>000001=>100000
[4,3,2,5,-1,6]=>000010=>010000
[-1,3,2,6,5,4]=>100000=>000001
[4,3,2,6,5,-1]=>000001=>100000
[4,3,2,-1,5,6]=>000100=>001000
[4,3,2,-1,6,5]=>000100=>001000
[-1,4,2,3,5,6]=>100000=>000001
[6,4,2,3,5,-1]=>000001=>100000
[-1,4,2,3,6,5]=>100000=>000001
[5,4,2,3,6,-1]=>000001=>100000
[5,4,2,3,-1,6]=>000010=>010000
[-1,5,2,3,4,6]=>100000=>000001
[6,5,2,3,4,-1]=>000001=>100000
[-1,6,2,3,4,5]=>100000=>000001
[2,3,4,5,6,-1]=>000001=>100000
[2,3,4,5,-1,6]=>000010=>010000
[-1,6,2,3,5,4]=>100000=>000001
[2,3,4,6,5,-1]=>000001=>100000
[2,3,4,-1,5,6]=>000100=>001000
[2,3,4,-1,6,5]=>000100=>001000
[-1,5,2,4,3,6]=>100000=>000001
[6,5,2,4,3,-1]=>000001=>100000
[-1,6,2,4,3,5]=>100000=>000001
[2,3,5,4,6,-1]=>000001=>100000
[2,3,5,4,-1,6]=>000010=>010000
[-1,6,2,5,3,4]=>100000=>000001
[2,3,6,4,5,-1]=>000001=>100000
[2,3,-1,4,5,6]=>001000=>000100
[2,3,-1,4,6,5]=>001000=>000100
[-1,6,2,5,4,3]=>100000=>000001
[2,3,6,5,4,-1]=>000001=>100000
[2,3,-1,5,4,6]=>001000=>000100
[2,3,-1,6,4,5]=>001000=>000100
[2,3,-1,6,5,4]=>001000=>000100
[-1,4,3,2,5,6]=>100000=>000001
[6,4,3,2,5,-1]=>000001=>100000
[-1,4,3,2,6,5]=>100000=>000001
[5,4,3,2,6,-1]=>000001=>100000
[5,4,3,2,-1,6]=>000010=>010000
[-1,5,3,2,4,6]=>100000=>000001
[6,5,3,2,4,-1]=>000001=>100000
[-1,6,3,2,4,5]=>100000=>000001
[2,4,3,5,6,-1]=>000001=>100000
[2,4,3,5,-1,6]=>000010=>010000
[-1,6,3,2,5,4]=>100000=>000001
[2,4,3,6,5,-1]=>000001=>100000
[2,4,3,-1,5,6]=>000100=>001000
[2,4,3,-1,6,5]=>000100=>001000
[-1,5,4,2,3,6]=>100000=>000001
[6,5,4,2,3,-1]=>000001=>100000
[-1,6,4,2,3,5]=>100000=>000001
[2,5,3,4,6,-1]=>000001=>100000
[2,5,3,4,-1,6]=>000010=>010000
[-1,6,5,2,3,4]=>100000=>000001
[2,6,3,4,5,-1]=>000001=>100000
[2,-1,3,4,5,6]=>010000=>000010
[2,-1,3,4,6,5]=>010000=>000010
[-1,6,5,2,4,3]=>100000=>000001
[2,6,3,5,4,-1]=>000001=>100000
[2,-1,3,5,4,6]=>010000=>000010
[2,-1,3,6,4,5]=>010000=>000010
[2,-1,3,6,5,4]=>010000=>000010
[-1,5,4,3,2,6]=>100000=>000001
[6,5,4,3,2,-1]=>000001=>100000
[-1,6,4,3,2,5]=>100000=>000001
[2,5,4,3,6,-1]=>000001=>100000
[2,5,4,3,-1,6]=>000010=>010000
[-1,6,5,3,2,4]=>100000=>000001
[2,6,4,3,5,-1]=>000001=>100000
[2,-1,4,3,5,6]=>010000=>000010
[2,-1,4,3,6,5]=>010000=>000010
[-1,6,5,4,2,3]=>100000=>000001
[2,6,5,3,4,-1]=>000001=>100000
[2,-1,5,3,4,6]=>010000=>000010
[2,-1,6,3,4,5]=>010000=>000010
[2,-1,6,3,5,4]=>010000=>000010
[-1,6,5,4,3,2]=>100000=>000001
[2,6,5,4,3,-1]=>000001=>100000
[2,-1,5,4,3,6]=>010000=>000010
[2,-1,6,4,3,5]=>010000=>000010
[2,-1,6,5,3,4]=>010000=>000010
[2,-1,6,5,4,3]=>010000=>000010
[4,5,6,-1,2,3]=>000100=>001000
[4,5,6,3,-1,2]=>000010=>010000
[4,5,-1,3,2,6]=>001000=>000100
[4,5,3,6,-1,2]=>000010=>010000
[4,5,3,-1,2,6]=>000100=>001000
[4,6,3,-1,5,2]=>000100=>001000
[4,6,3,2,-1,5]=>000010=>010000
[4,6,-1,3,5,2]=>001000=>000100
[4,2,5,6,-1,3]=>000010=>010000
[4,2,5,-1,3,6]=>000100=>001000
[4,-1,3,2,5,6]=>010000=>000010
[4,2,6,3,-1,5]=>000010=>010000
[4,2,6,-1,5,3]=>000100=>001000
[4,2,-1,3,5,6]=>001000=>000100
[5,2,6,-1,4,3]=>000100=>001000
[5,2,6,4,-1,3]=>000010=>010000
[5,2,-1,4,3,6]=>001000=>000100
[5,2,3,6,-1,4]=>000010=>010000
[5,2,3,-1,4,6]=>000100=>001000
[5,6,3,-1,4,2]=>000100=>001000
[5,6,3,4,-1,2]=>000010=>010000
[5,6,-1,4,3,2]=>001000=>000100
[3,4,5,6,-1,2]=>000010=>010000
[3,4,5,-1,2,6]=>000100=>001000
[5,-1,3,4,2,6]=>010000=>000010
[3,4,6,2,-1,5]=>000010=>010000
[3,4,6,-1,5,2]=>000100=>001000
[3,4,-1,2,5,6]=>001000=>000100
[6,2,3,-1,5,4]=>000100=>001000
[6,2,3,4,-1,5]=>000010=>010000
[6,2,-1,4,5,3]=>001000=>000100
[3,5,2,6,-1,4]=>000010=>010000
[3,5,2,-1,4,6]=>000100=>001000
[6,-1,3,4,5,2]=>010000=>000010
[3,5,6,4,-1,2]=>000010=>010000
[3,5,6,-1,4,2]=>000100=>001000
[3,5,-1,4,2,6]=>001000=>000100
[3,6,2,4,-1,5]=>000010=>010000
[3,6,2,-1,5,4]=>000100=>001000
[3,6,-1,4,5,2]=>001000=>000100
[3,-1,2,4,5,6]=>010000=>000010
[4,5,6,7,-1,3,2]=>0000100=>0010000
[4,5,6,7,2,-1,3]=>0000010=>0100000
[4,5,6,-1,2,3,7]=>0001000=>0001000
[4,5,6,3,7,-1,2]=>0000010=>0100000
[4,5,6,3,-1,2,7]=>0000100=>0010000
[4,5,7,3,-1,6,2]=>0000100=>0010000
[4,5,7,3,2,-1,6]=>0000010=>0100000
[4,5,7,-1,2,6,3]=>0001000=>0001000
[4,5,3,6,7,-1,2]=>0000010=>0100000
[4,5,3,6,-1,2,7]=>0000100=>0010000
[4,5,-1,3,2,6,7]=>0010000=>0000100
[4,5,3,7,2,-1,6]=>0000010=>0100000
[4,5,3,7,-1,6,2]=>0000100=>0010000
[4,5,3,-1,2,6,7]=>0001000=>0001000
[4,6,3,7,-1,5,2]=>0000100=>0010000
[4,6,3,7,5,-1,2]=>0000010=>0100000
[4,6,3,-1,5,2,7]=>0001000=>0001000
[4,6,3,2,7,-1,5]=>0000010=>0100000
[4,6,3,2,-1,5,7]=>0000100=>0010000
[4,6,7,3,-1,5,2]=>0000100=>0010000
[4,6,7,3,5,-1,2]=>0000010=>0100000
[4,6,7,-1,5,2,3]=>0001000=>0001000
[4,2,5,6,7,-1,3]=>0000010=>0100000
[4,2,5,6,-1,3,7]=>0000100=>0010000
[4,6,-1,3,5,2,7]=>0010000=>0000100
[4,2,5,7,3,-1,6]=>0000010=>0100000
[4,2,5,7,-1,6,3]=>0000100=>0010000
[4,2,5,-1,3,6,7]=>0001000=>0001000
[4,7,3,2,-1,6,5]=>0000100=>0010000
[4,7,3,2,5,-1,6]=>0000010=>0100000
[4,7,3,-1,5,6,2]=>0001000=>0001000
[4,2,6,3,7,-1,5]=>0000010=>0100000
[4,2,6,3,-1,5,7]=>0000100=>0010000
[4,7,-1,3,5,6,2]=>0010000=>0000100
[4,2,6,7,5,-1,3]=>0000010=>0100000
[4,2,6,7,-1,5,3]=>0000100=>0010000
[4,2,6,-1,5,3,7]=>0001000=>0001000
[4,-1,3,2,5,6,7]=>0100000=>0000010
[4,2,7,3,5,-1,6]=>0000010=>0100000
[4,2,7,3,-1,6,5]=>0000100=>0010000
[4,2,7,-1,5,6,3]=>0001000=>0001000
[4,2,-1,3,5,6,7]=>0010000=>0000100
[5,2,6,7,-1,3,4]=>0000100=>0010000
[5,2,6,7,4,-1,3]=>0000010=>0100000
[5,2,6,-1,4,3,7]=>0001000=>0001000
[5,2,6,4,7,-1,3]=>0000010=>0100000
[5,2,6,4,-1,3,7]=>0000100=>0010000
[5,2,7,4,-1,6,3]=>0000100=>0010000
[5,2,7,4,3,-1,6]=>0000010=>0100000
[5,2,7,-1,4,6,3]=>0001000=>0001000
[5,2,3,6,7,-1,4]=>0000010=>0100000
[5,2,3,6,-1,4,7]=>0000100=>0010000
[5,2,-1,4,3,6,7]=>0010000=>0000100
[5,2,3,7,4,-1,6]=>0000010=>0100000
[5,2,3,7,-1,6,4]=>0000100=>0010000
[5,2,3,-1,4,6,7]=>0001000=>0001000
[5,6,3,7,-1,2,4]=>0000100=>0010000
[5,6,3,7,4,-1,2]=>0000010=>0100000
[5,6,3,-1,4,2,7]=>0001000=>0001000
[5,6,3,4,7,-1,2]=>0000010=>0100000
[5,6,3,4,-1,2,7]=>0000100=>0010000
[5,6,7,4,-1,2,3]=>0000100=>0010000
[5,6,7,4,3,-1,2]=>0000010=>0100000
[5,6,7,-1,4,2,3]=>0001000=>0001000
[3,4,5,6,7,-1,2]=>0000010=>0100000
[3,4,5,6,-1,2,7]=>0000100=>0010000
[5,6,-1,4,3,2,7]=>0010000=>0000100
[3,4,5,7,2,-1,6]=>0000010=>0100000
[3,4,5,7,-1,6,2]=>0000100=>0010000
[3,4,5,-1,2,6,7]=>0001000=>0001000
[5,7,3,4,-1,6,2]=>0000100=>0010000
[5,7,3,4,2,-1,6]=>0000010=>0100000
[5,7,3,-1,4,6,2]=>0001000=>0001000
[3,4,6,2,7,-1,5]=>0000010=>0100000
[3,4,6,2,-1,5,7]=>0000100=>0010000
[5,7,-1,4,3,6,2]=>0010000=>0000100
[3,4,6,7,5,-1,2]=>0000010=>0100000
[3,4,6,7,-1,5,2]=>0000100=>0010000
[3,4,6,-1,5,2,7]=>0001000=>0001000
[5,-1,3,4,2,6,7]=>0100000=>0000010
[3,4,7,2,5,-1,6]=>0000010=>0100000
[3,4,7,2,-1,6,5]=>0000100=>0010000
[3,4,7,-1,5,6,2]=>0001000=>0001000
[3,4,-1,2,5,6,7]=>0010000=>0000100
[6,2,3,7,-1,5,4]=>0000100=>0010000
[6,2,3,7,5,-1,4]=>0000010=>0100000
[6,2,3,-1,5,4,7]=>0001000=>0001000
[6,2,3,4,7,-1,5]=>0000010=>0100000
[6,2,3,4,-1,5,7]=>0000100=>0010000
[6,2,7,4,-1,5,3]=>0000100=>0010000
[6,2,7,4,5,-1,3]=>0000010=>0100000
[6,2,7,-1,5,4,3]=>0001000=>0001000
[3,5,2,6,7,-1,4]=>0000010=>0100000
[3,5,2,6,-1,4,7]=>0000100=>0010000
[6,2,-1,4,5,3,7]=>0010000=>0000100
[3,5,2,7,4,-1,6]=>0000010=>0100000
[3,5,2,7,-1,6,4]=>0000100=>0010000
[3,5,2,-1,4,6,7]=>0001000=>0001000
[6,7,3,4,-1,5,2]=>0000100=>0010000
[6,7,3,4,5,-1,2]=>0000010=>0100000
[6,7,3,-1,5,4,2]=>0001000=>0001000
[3,5,6,4,7,-1,2]=>0000010=>0100000
[3,5,6,4,-1,2,7]=>0000100=>0010000
[6,7,-1,4,5,3,2]=>0010000=>0000100
[3,5,6,7,4,-1,2]=>0000010=>0100000
[3,5,6,7,-1,2,4]=>0000100=>0010000
[3,5,6,-1,4,2,7]=>0001000=>0001000
[6,-1,3,4,5,2,7]=>0100000=>0000010
[3,5,7,4,2,-1,6]=>0000010=>0100000
[3,5,7,4,-1,6,2]=>0000100=>0010000
[3,5,7,-1,4,6,2]=>0001000=>0001000
[3,5,-1,4,2,6,7]=>0010000=>0000100
[7,2,3,4,-1,6,5]=>0000100=>0010000
[7,2,3,4,5,-1,6]=>0000010=>0100000
[7,2,3,-1,5,6,4]=>0001000=>0001000
[3,6,2,4,7,-1,5]=>0000010=>0100000
[3,6,2,4,-1,5,7]=>0000100=>0010000
[7,2,-1,4,5,6,3]=>0010000=>0000100
[3,6,2,7,5,-1,4]=>0000010=>0100000
[3,6,2,7,-1,5,4]=>0000100=>0010000
[3,6,2,-1,5,4,7]=>0001000=>0001000
[7,-1,3,4,5,6,2]=>0100000=>0000010
[3,6,7,4,5,-1,2]=>0000010=>0100000
[3,6,7,4,-1,5,2]=>0000100=>0010000
[3,6,7,-1,5,4,2]=>0001000=>0001000
[3,6,-1,4,5,2,7]=>0010000=>0000100
[-1,2,3,4,5,6,7]=>1000000=>0000001
[3,7,2,4,5,-1,6]=>0000010=>0100000
[3,7,2,4,-1,6,5]=>0000100=>0010000
[3,7,2,-1,5,6,4]=>0001000=>0001000
[3,7,-1,4,5,6,2]=>0010000=>0000100
[3,-1,2,4,5,6,7]=>0100000=>0000010
[-6,-5,-4,-3,-2,1]=>111110=>011111
[-5,-4,-3,-2,1,6]=>111100=>001111
[5,-6,-4,-3,-2,1]=>011110=>011110
[-4,-3,-2,1,5,6]=>111000=>000111
[-6,-4,-3,-2,1,5]=>111100=>001111
[4,-6,-5,-3,-2,1]=>011110=>011110
[4,-5,-3,-2,1,6]=>011100=>001110
[4,6,-5,-3,-2,1]=>001110=>011100
[-3,-2,1,4,5,6]=>110000=>000011
[-6,-3,-2,1,4,5]=>111000=>000111
[-5,4,-6,-3,-2,1]=>101110=>011101
[-5,-3,-2,1,4,6]=>111000=>000111
[-6,-5,-3,-2,1,4]=>111100=>001111
[5,-6,-3,-2,1,4]=>011100=>001110
[3,-6,-5,-4,-2,1]=>011110=>011110
[3,-5,-4,-2,1,6]=>011100=>001110
[3,5,-6,-4,-2,1]=>001110=>011100
[3,-4,-2,1,5,6]=>011000=>000110
[3,-6,-4,-2,1,5]=>011100=>001110
[3,6,-5,-4,-2,1]=>001110=>011100
[3,5,-4,-2,1,6]=>001100=>001100
[3,5,6,-4,-2,1]=>000110=>011000
[-2,1,3,4,5,6]=>100000=>000001
[-6,-2,1,3,4,5]=>110000=>000011
[-6,3,5,-4,-2,1]=>100110=>011001
[-5,-2,1,3,4,6]=>110000=>000011
[-6,-5,-2,1,3,4]=>111000=>000111
[5,-6,-2,1,3,4]=>011000=>000110
[-4,3,-6,-5,-2,1]=>101110=>011101
[-4,3,-5,-2,1,6]=>101100=>001101
[-4,3,6,-5,-2,1]=>100110=>011001
[-4,-2,1,3,5,6]=>110000=>000011
[-6,-4,-2,1,3,5]=>111000=>000111
[-6,-4,3,-5,-2,1]=>110110=>011011
[-5,-4,-2,1,3,6]=>111000=>000111
[-6,-5,-4,-2,1,3]=>111100=>001111
[5,-6,-4,-2,1,3]=>011100=>001110
[4,-5,3,-6,-2,1]=>010110=>011010
[4,-5,-2,1,3,6]=>011000=>000110
[4,-6,-5,-2,1,3]=>011100=>001110
[4,6,-5,-2,1,3]=>001100=>001100
[-5,4,-6,-2,1,3]=>101100=>001101
[2,-6,-5,-4,-3,1]=>011110=>011110
[2,-5,-4,-3,1,6]=>011100=>001110
[2,5,-6,-4,-3,1]=>001110=>011100
[2,-4,-3,1,5,6]=>011000=>000110
[2,-6,-4,-3,1,5]=>011100=>001110
[2,4,-6,-5,-3,1]=>001110=>011100
[2,4,-5,-3,1,6]=>001100=>001100
[2,4,6,-5,-3,1]=>000110=>011000
[2,-3,1,4,5,6]=>010000=>000010
[2,-6,-3,1,4,5]=>011000=>000110
[-5,2,4,-6,-3,1]=>100110=>011001
[2,-5,-3,1,4,6]=>011000=>000110
[2,-6,-5,-3,1,4]=>011100=>001110
[2,5,-6,-3,1,4]=>001100=>001100
[2,6,-5,-4,-3,1]=>001110=>011100
[2,5,-4,-3,1,6]=>001100=>001100
[-5,2,-6,-4,-3,1]=>101110=>011101
[2,4,-3,1,5,6]=>001000=>000100
[2,6,-4,-3,1,5]=>001100=>001100
[2,5,6,-4,-3,1]=>000110=>011000
[2,4,5,-3,1,6]=>000100=>001000
[2,4,5,6,-3,1]=>000010=>010000
[-6,1,2,3,4,5]=>100000=>000001
[-6,2,4,5,-3,1]=>100010=>010001
[-5,1,2,3,4,6]=>100000=>000001
[-6,-5,1,2,3,4]=>110000=>000011
[5,-6,1,2,3,4]=>010000=>000010
[-4,2,6,-5,-3,1]=>100110=>011001
[-5,2,4,-3,1,6]=>100100=>001001
[-5,2,4,6,-3,1]=>100010=>010001
[-4,1,2,3,5,6]=>100000=>000001
[-6,-4,1,2,3,5]=>110000=>000011
[-6,-5,2,4,-3,1]=>110010=>010011
[-5,-4,1,2,3,6]=>110000=>000011
[-6,-5,-4,1,2,3]=>111000=>000111
[5,-6,-4,1,2,3]=>011000=>000110
[5,-6,2,4,-3,1]=>010010=>010010
[4,-5,1,2,3,6]=>010000=>000010
[4,-6,-5,1,2,3]=>011000=>000110
[4,6,-5,1,2,3]=>001000=>000100
[-5,4,-6,1,2,3]=>101000=>000101
[-3,2,-6,-5,-4,1]=>101110=>011101
[-3,2,-5,-4,1,6]=>101100=>001101
[-3,2,5,-6,-4,1]=>100110=>011001
[-3,2,-4,1,5,6]=>101000=>000101
[-3,2,-6,-4,1,5]=>101100=>001101
[-3,2,6,-5,-4,1]=>100110=>011001
[-3,2,5,-4,1,6]=>100100=>001001
[-3,2,5,6,-4,1]=>100010=>010001
[-3,1,2,4,5,6]=>100000=>000001
[-6,-3,1,2,4,5]=>110000=>000011
[-6,-3,2,5,-4,1]=>110010=>010011
[-5,-3,1,2,4,6]=>110000=>000011
[-6,-5,-3,1,2,4]=>111000=>000111
[5,-6,-3,1,2,4]=>011000=>000110
[-6,-3,2,-5,-4,1]=>110110=>011011
[-5,-3,2,-4,1,6]=>110100=>001011
[-5,-3,2,6,-4,1]=>110010=>010011
[-4,-3,1,2,5,6]=>110000=>000011
[-6,-4,-3,1,2,5]=>111000=>000111
[-6,-5,-3,2,-4,1]=>111010=>010111
[-5,-4,-3,1,2,6]=>111000=>000111
[-6,-5,-4,-3,1,2]=>111100=>001111
[5,-6,-4,-3,1,2]=>011100=>001110
[5,-6,-3,2,-4,1]=>011010=>010110
[4,-5,-3,1,2,6]=>011000=>000110
[4,-6,-5,-3,1,2]=>011100=>001110
[4,6,-5,-3,1,2]=>001100=>001100
[-5,4,-6,-3,1,2]=>101100=>001101
[3,-4,2,-6,-5,1]=>010110=>011010
[3,-4,2,-5,1,6]=>010100=>001010
[3,-4,2,6,-5,1]=>010010=>010010
[3,-4,1,2,5,6]=>010000=>000010
[3,-6,-4,1,2,5]=>011000=>000110
[3,-6,-4,2,-5,1]=>011010=>010110
[3,-5,-4,1,2,6]=>011000=>000110
[3,-6,-5,-4,1,2]=>011100=>001110
[3,5,-6,-4,1,2]=>001100=>001100
[3,6,-4,2,-5,1]=>001010=>010100
[3,5,-4,1,2,6]=>001000=>000100
[3,6,-5,-4,1,2]=>001100=>001100
[3,5,6,-4,1,2]=>000100=>001000
[-6,3,5,-4,1,2]=>100100=>001001
[-4,3,-5,2,-6,1]=>101010=>010101
[-4,3,-5,1,2,6]=>101000=>000101
[-4,3,-6,-5,1,2]=>101100=>001101
[-4,3,6,-5,1,2]=>100100=>001001
[-6,-4,3,-5,1,2]=>110100=>001011
[4,-5,3,-6,1,2]=>010100=>001010
[6,5,4,3,-1,2]=>000010=>010000
[6,5,4,-1,3,2]=>000100=>001000
[6,5,4,-1,2,3]=>000100=>001000
[6,5,3,4,2,-1]=>000001=>100000
[6,5,3,4,-1,2]=>000010=>010000
[6,5,-1,4,3,2]=>001000=>000100
[6,5,-1,4,2,3]=>001000=>000100
[6,5,-1,3,4,2]=>001000=>000100
[6,5,-1,3,2,4]=>001000=>000100
[6,5,-1,2,3,4]=>001000=>000100
[6,4,5,3,2,-1]=>000001=>100000
[6,4,5,3,-1,2]=>000010=>010000
[6,4,5,2,3,-1]=>000001=>100000
[6,4,5,-1,3,2]=>000100=>001000
[6,4,5,-1,2,3]=>000100=>001000
[6,4,3,5,2,-1]=>000001=>100000
[6,4,3,5,-1,2]=>000010=>010000
[6,-1,5,4,3,2]=>010000=>000010
[6,-1,5,4,2,3]=>010000=>000010
[6,-1,5,3,4,2]=>010000=>000010
[6,-1,5,3,2,4]=>010000=>000010
[6,-1,5,2,3,4]=>010000=>000010
[6,3,4,5,2,-1]=>000001=>100000
[6,3,4,5,-1,2]=>000010=>010000
[6,3,4,2,5,-1]=>000001=>100000
[6,-1,4,5,3,2]=>010000=>000010
[6,-1,4,5,2,3]=>010000=>000010
[6,-1,4,3,5,2]=>010000=>000010
[6,-1,4,3,2,5]=>010000=>000010
[6,-1,4,2,3,5]=>010000=>000010
[6,-1,3,4,2,5]=>010000=>000010
[6,-1,3,2,4,5]=>010000=>000010
[6,-1,2,3,4,5]=>010000=>000010
[5,6,4,3,2,-1]=>000001=>100000
[5,6,4,3,-1,2]=>000010=>010000
[5,6,4,2,3,-1]=>000001=>100000
[5,6,4,-1,3,2]=>000100=>001000
[5,6,4,-1,2,3]=>000100=>001000
[5,6,3,4,2,-1]=>000001=>100000
[5,6,3,2,4,-1]=>000001=>100000
[5,6,-1,4,2,3]=>001000=>000100
[5,6,2,3,4,-1]=>000001=>100000
[5,6,-1,3,4,2]=>001000=>000100
[5,6,-1,3,2,4]=>001000=>000100
[5,6,-1,2,3,4]=>001000=>000100
[5,4,6,3,2,-1]=>000001=>100000
[5,4,6,3,-1,2]=>000010=>010000
[5,4,6,2,3,-1]=>000001=>100000
[5,4,6,-1,3,2]=>000100=>001000
[5,4,6,-1,2,3]=>000100=>001000
[5,4,3,6,2,-1]=>000001=>100000
[5,4,3,6,-1,2]=>000010=>010000
[-1,6,5,3,4,2]=>100000=>000001
[5,3,4,6,2,-1]=>000001=>100000
[5,3,4,6,-1,2]=>000010=>010000
[5,3,4,2,6,-1]=>000001=>100000
[-1,6,4,5,3,2]=>100000=>000001
[-1,6,4,5,2,3]=>100000=>000001
[-1,6,4,3,5,2]=>100000=>000001
[-1,6,3,4,5,2]=>100000=>000001
[-1,6,3,4,2,5]=>100000=>000001
[4,5,6,3,2,-1]=>000001=>100000
[4,5,6,2,3,-1]=>000001=>100000
[4,5,6,-1,3,2]=>000100=>001000
[4,5,3,6,2,-1]=>000001=>100000
[4,5,3,2,6,-1]=>000001=>100000
[-1,5,6,4,3,2]=>100000=>000001
[-1,5,6,4,2,3]=>100000=>000001
[4,5,2,3,6,-1]=>000001=>100000
[-1,5,6,3,4,2]=>100000=>000001
[-1,5,6,3,2,4]=>100000=>000001
[-1,5,6,2,3,4]=>100000=>000001
[4,3,5,6,2,-1]=>000001=>100000
[4,3,5,6,-1,2]=>000010=>010000
[4,3,5,2,6,-1]=>000001=>100000
[-1,5,4,6,3,2]=>100000=>000001
[-1,5,4,6,2,3]=>100000=>000001
[-1,5,4,3,6,2]=>100000=>000001
[-1,5,3,4,6,2]=>100000=>000001
[-1,5,3,4,2,6]=>100000=>000001
[3,4,5,6,2,-1]=>000001=>100000
[3,4,5,2,6,-1]=>000001=>100000
[-1,4,5,6,3,2]=>100000=>000001
[-1,4,5,6,2,3]=>100000=>000001
[3,4,2,5,6,-1]=>000001=>100000
[-1,4,5,3,6,2]=>100000=>000001
[-1,4,5,3,2,6]=>100000=>000001
[-1,4,5,2,3,6]=>100000=>000001
[-1,4,3,5,6,2]=>100000=>000001
[-1,4,3,5,2,6]=>100000=>000001
[-1,3,4,5,6,2]=>100000=>000001
[-1,3,4,5,2,6]=>100000=>000001
[-1,3,4,2,5,6]=>100000=>000001
[1,-4,-6,2,3,5]=>011000=>000110
[4,1,-6,-5,2,3]=>001100=>001100
[3,1,-6,2,4,5]=>001000=>000100
[-6,-3,-5,1,2,4]=>111000=>000111
[3,-6,5,1,2,4]=>010000=>000010
[-4,3,6,1,2,5]=>100000=>000001
[-6,2,1,3,4,5]=>100000=>000001
[-2,-6,-5,1,3,4]=>111000=>000111
[-3,6,-5,-4,1,2]=>101100=>001101
[2,6,-4,1,3,5]=>001000=>000100
[5,2,-6,1,3,4]=>001000=>000100
[2,-6,-5,-4,1,3]=>011100=>001110
[2,-5,-6,1,3,4]=>011000=>000110
[4,2,-6,1,3,5]=>001000=>000100
[-4,2,-6,-5,1,3]=>101100=>001101
[2,3,-6,1,4,5]=>001000=>000100
[3,-6,-5,-2,1,4]=>011100=>001110
[-5,-6,3,1,2,4]=>110000=>000011
[3,-6,4,1,2,5]=>010000=>000010
[-5,4,1,-6,2,3]=>100100=>001001
[1,2,-6,3,4,5]=>001000=>000100
[1,6,-5,2,3,4]=>001000=>000100
[-4,-3,6,-5,1,2]=>110100=>001011
[-4,6,1,2,3,5]=>100000=>000001
[-6,1,5,2,3,4]=>100000=>000001
[1,-6,-5,-4,2,3]=>011100=>001110
[-5,3,-6,-2,1,4]=>101100=>001101
[4,-6,-3,-2,1,5]=>011100=>001110
[-5,-4,2,-6,1,3]=>110100=>001011
[-6,3,1,2,4,5]=>100000=>000001
[5,6,-3,1,2,4]=>001000=>000100
[3,-6,4,5,1,2]=>010000=>000010
[-6,1,4,2,3,5]=>100000=>000001
[1,-5,-6,2,3,4]=>011000=>000110
[-6,-4,-5,1,2,3]=>111000=>000111
[-4,-6,-3,1,2,5]=>111000=>000111
[-6,3,5,1,2,4]=>100000=>000001
[4,-6,5,1,2,3]=>010000=>000010
[6,-5,-4,-3,1,2]=>011100=>001110
[1,6,2,-7,3,4,5]=>0001000=>0001000
[1,-7,5,2,3,4,6]=>0100000=>0000010
[6,1,7,-5,2,3,4]=>0001000=>0001000
[1,-7,4,2,3,5,6]=>0100000=>0000010
[1,-4,-7,-6,2,3,5]=>0111000=>0001110
[-4,7,6,1,2,3,5]=>1000000=>0000001
[4,-5,7,1,2,3,6]=>0100000=>0000010
[7,-5,1,6,2,3,4]=>0100000=>0000010
[3,1,-7,-6,2,4,5]=>0011000=>0001100
[4,1,-7,-6,-5,2,3]=>0011100=>0011100
[-7,-3,-6,-5,1,2,4]=>1111000=>0001111
[3,6,1,-7,2,4,5]=>0001000=>0001000
[5,-3,7,-6,1,2,4]=>0101000=>0001010
[-7,-4,3,1,2,5,6]=>1100000=>0000011
[-3,6,7,-4,1,2,5]=>1001000=>0001001
[-4,6,1,-7,2,3,5]=>1001000=>0001001
[-4,7,5,1,2,3,6]=>1000000=>0000001
[7,5,1,-6,2,3,4]=>0001000=>0001000
[-2,1,-7,3,4,5,6]=>1010000=>0000101
[-2,7,-6,1,3,4,5]=>1010000=>0000101
[7,-5,-4,-6,1,2,3]=>0111000=>0001110
[-7,2,-5,1,3,4,6]=>1010000=>0000101
[-2,-7,-6,-5,1,3,4]=>1111000=>0001111
[-7,-4,3,6,1,2,5]=>1100000=>0000011
[-5,-3,-7,-4,1,2,6]=>1111000=>0001111
[-4,2,-7,1,3,5,6]=>1010000=>0000101
[2,7,-6,-4,1,3,5]=>0011000=>0001100
[4,5,-7,6,1,2,3]=>0010000=>0000100
[-2,-6,-7,1,3,4,5]=>1110000=>0000111
[5,2,-7,-6,1,3,4]=>0011000=>0001100
[-3,7,-6,-5,-4,1,2]=>1011100=>0011101
[2,5,-7,-4,1,3,6]=>0011000=>0001100
[-7,2,6,-4,1,3,5]=>1001000=>0001001
[6,-5,2,-7,1,3,4]=>0101000=>0001010
[2,-7,-6,-5,-4,1,3]=>0111100=>0011110
[7,-6,2,1,3,4,5]=>0100000=>0000010
[-2,-5,-7,1,3,4,6]=>1110000=>0000111
[2,-5,-7,-6,1,3,4]=>0111000=>0001110
[4,2,-7,-6,1,3,5]=>0011000=>0001100
[6,-4,2,-7,1,3,5]=>0101000=>0001010
[-4,2,7,-5,1,3,6]=>1001000=>0001001
[5,6,2,-7,1,3,4]=>0001000=>0001000
[-2,3,-7,1,4,5,6]=>1010000=>0000101
[2,3,-7,-6,1,4,5]=>0011000=>0001100
[-4,2,-7,-6,-5,1,3]=>1011100=>0011101
[3,7,-5,-2,1,4,6]=>0011000=>0001100
[-6,2,3,-7,1,4,5]=>1001000=>0001001
[3,-7,-6,-5,-2,1,4]=>0111100=>0011110
[-6,7,3,1,2,4,5]=>1000000=>0000001
[3,5,1,-7,2,4,6]=>0001000=>0001000
[-3,-5,7,-6,1,2,4]=>1101000=>0001011
[4,-3,7,-6,1,2,5]=>0101000=>0001010
[7,4,1,-6,2,3,5]=>0001000=>0001000
[5,4,1,-7,2,3,6]=>0001000=>0001000
[-7,1,-6,5,2,3,4]=>1010000=>0000101
[1,2,-7,-6,3,4,5]=>0011000=>0001100
[-5,4,1,-7,-6,2,3]=>1001100=>0011001
[1,7,-6,-5,2,3,4]=>0011000=>0001100
[-7,5,3,6,1,2,4]=>1000000=>0000001
[-7,1,-4,2,3,5,6]=>1010000=>0000101
[-6,7,-4,1,2,3,5]=>1010000=>0000101
[-5,4,7,6,1,2,3]=>1000000=>0000001
[6,1,2,-7,3,4,5]=>0001000=>0001000
[-5,1,7,-6,2,3,4]=>1001000=>0001001
[-4,-3,7,-6,-5,1,2]=>1101100=>0011011
[1,5,-7,-4,2,3,6]=>0011000=>0001100
[-7,-4,6,1,2,3,5]=>1100000=>0000011
[1,-7,-6,-5,-4,2,3]=>0111100=>0011110
[6,2,3,-7,1,4,5]=>0001000=>0001000
[-5,2,3,-7,1,4,6]=>1001000=>0001001
[-5,3,-7,-6,-2,1,4]=>1011100=>0011101
[3,4,-7,-2,1,5,6]=>0011000=>0001100
[4,-7,-6,-3,-2,1,5]=>0111100=>0011110
[-4,-6,2,-7,1,3,5]=>1101000=>0001011
[5,-4,2,-7,1,3,6]=>0101000=>0001010
[-5,2,-6,-7,1,3,4]=>1011000=>0001101
[-3,7,-6,1,2,4,5]=>1010000=>0000101
[-5,-4,2,-7,-6,1,3]=>1101100=>0011011
[6,7,-5,-3,1,2,4]=>0011000=>0001100
[3,6,-7,4,1,2,5]=>0010000=>0000100
[6,5,-7,3,1,2,4]=>0010000=>0000100
[-4,1,7,-6,2,3,5]=>1001000=>0001001
[6,4,5,1,-7,2,3]=>0000100=>0010000
[5,1,2,-7,3,4,6]=>0001000=>0001000
[1,-6,7,2,3,4,5]=>0100000=>0000010
[1,-5,-7,-6,2,3,4]=>0111000=>0001110
[-5,-4,-3,7,-6,1,2]=>1110100=>0010111
[-5,7,6,1,2,3,4]=>1000000=>0000001
[-7,-4,-6,-5,1,2,3]=>1111000=>0001111
[-6,4,-7,-3,-2,1,5]=>1011100=>0011101
[5,-7,-4,-3,-2,1,6]=>0111100=>0011110
[-6,-5,3,-7,-2,1,4]=>1101100=>0011011
[-7,4,-3,1,2,5,6]=>1010000=>0000101
[-4,-7,-6,-3,1,2,5]=>1111000=>0001111
[-6,-5,-4,2,-7,1,3]=>1110100=>0010111
[6,-7,3,1,2,4,5]=>0100000=>0000010
[-6,5,7,-3,1,2,4]=>1001000=>0001001
[6,-7,1,4,2,3,5]=>0100000=>0000010
[6,5,1,-7,2,3,4]=>0001000=>0001000
[5,-4,7,-6,1,2,3]=>0101000=>0001010
[-7,-6,-5,-4,-3,-2,1]=>1111110=>0111111
[-5,-7,-4,-3,1,2,6]=>1111000=>0001111
[6,4,-7,-3,1,2,5]=>0011000=>0001100
[7,-6,-5,-4,-3,1,2]=>0111100=>0011110
[-3,-4,2,-6,1,5]=>110100=>001011
[-5,3,2,-6,1,4]=>100100=>001001
[-3,-6,2,-5,1,4]=>110100=>001011
[-4,-3,2,-5,1,6]=>110100=>001011
[4,-3,2,-6,1,5]=>010100=>001010
[-4,2,-5,-6,1,3]=>101100=>001101
[-6,4,2,-5,1,3]=>100100=>001001
[2,5,-4,-6,1,3]=>001100=>001100
[2,-6,-4,-5,1,3]=>011100=>001110
[2,-5,6,-4,1,3]=>010100=>001010
[4,2,3,-5,1,6]=>000100=>001000
[2,-4,3,-6,1,5]=>010100=>001010
[-5,2,3,-4,1,6]=>100100=>001001
[2,5,3,-6,1,4]=>000100=>001000
[2,-6,3,-5,1,4]=>010100=>001010
[-3,2,4,-5,1,6]=>100100=>001001
[3,2,4,-6,1,5]=>000100=>001000
[-5,4,-6,3,1,2]=>101000=>000101
[4,6,-5,3,1,2]=>001000=>000100
[4,5,-6,3,1,2]=>001000=>000100
[4,-6,-5,3,1,2]=>011000=>000110
[-6,-5,-4,3,1,2]=>111000=>000111
[2,3,4,-5,1,6]=>000100=>001000
[-2,3,4,-6,1,5]=>100100=>001001
[2,3,-5,-4,1,6]=>001100=>001100
[-6,5,3,4,1,2]=>100000=>000001
[-4,-6,3,5,1,2]=>110000=>000011
[4,-5,3,6,1,2]=>010000=>000010
[-5,-4,3,6,1,2]=>110000=>000011
[-4,3,5,6,1,2]=>100000=>000001
[4,-5,3,1,2,6]=>010000=>000010
[-4,-6,3,1,2,5]=>110000=>000011
[-5,-4,3,1,2,6]=>110000=>000011
[-6,5,3,1,2,4]=>100000=>000001
[-4,3,5,1,2,6]=>100000=>000001
[-4,-6,1,-5,2,3]=>110100=>001011
[4,5,1,-6,2,3]=>000100=>001000
[6,-4,1,-5,2,3]=>010100=>001010
[-6,-5,1,-4,2,3]=>110100=>001011
[2,-4,-5,1,3,6]=>011000=>000110
[-2,-4,-6,1,3,5]=>111000=>000111
[5,2,-4,1,3,6]=>001000=>000100
[-5,-6,2,1,3,4]=>110000=>000011
[6,-5,2,1,3,4]=>010000=>000010
[3,2,-5,1,4,6]=>001000=>000100
[2,-3,-6,1,4,5]=>011000=>000110
[3,5,-4,2,-6,1]=>001010=>010100
[-2,3,-5,1,4,6]=>101000=>000101
[-3,-2,-6,1,4,5]=>111000=>000111
[2,3,-4,1,5,6]=>001000=>000100
[3,4,-5,2,-6,1]=>001010=>010100
[4,-6,-3,2,-5,1]=>011010=>010110
[3,-5,-4,2,-6,1]=>011010=>010110
[-5,-4,-3,2,-6,1]=>111010=>010111
[-4,-3,2,6,-5,1]=>110010=>010011
[4,1,-5,2,3,6]=>001000=>000100
[-5,1,-4,2,3,6]=>101000=>000101
[1,-6,5,2,3,4]=>010000=>000010
[-4,3,1,2,5,6]=>100000=>000001
[-5,4,2,3,-6,1]=>100010=>010001
[4,6,2,3,-5,1]=>000010=>010000
[4,5,2,3,-6,1]=>000010=>010000
[6,-4,2,3,-5,1]=>010010=>010010
[-6,-5,2,3,-4,1]=>110010=>010011
[-5,2,1,3,4,6]=>100000=>000001
[-2,1,-6,3,4,5]=>101000=>000101
[-2,-4,1,3,5,6]=>110000=>000011
[-3,-5,2,4,-6,1]=>110010=>010011
[3,-6,2,4,-5,1]=>010010=>010010
[3,-4,2,5,-6,1]=>010010=>010010
[-4,-3,2,5,-6,1]=>110010=>010011
[-4,-3,2,-6,-5,1]=>110110=>011011
[1,-4,2,3,5,6]=>010000=>000010
[2,-5,3,4,-6,1]=>010010=>010010
[6,2,3,4,-5,1]=>000010=>010000
[4,2,3,5,-6,1]=>000010=>010000
[4,2,3,-6,-5,1]=>000110=>011000
[-6,2,3,-5,-4,1]=>100110=>011001
[-3,2,4,5,-6,1]=>100010=>010001
[-3,2,4,-6,-5,1]=>100110=>011001
[2,3,4,5,-6,1]=>000010=>010000
[2,3,4,-6,-5,1]=>000110=>011000
[2,3,-6,-5,-4,1]=>001110=>011100
[-4,6,1,2,-5,3]=>100010=>010001
[-6,3,1,2,-5,4]=>100010=>010001
[-6,5,1,-3,2,4]=>100100=>001001
[6,-3,1,-4,2,5]=>010100=>001010
[-6,5,-4,1,2,3]=>101000=>000101
[-2,1,3,6,4,5]=>100000=>000001
[-2,6,1,3,-5,4]=>100010=>010001
[-5,-3,1,6,-4,2]=>110010=>010011
[-2,6,1,-4,3,5]=>100100=>001001
[-2,1,-6,5,3,4]=>101000=>000101
[5,-2,1,6,-4,3]=>010010=>010010
[-6,-2,1,5,3,4]=>110000=>000011
[-6,-2,4,1,3,5]=>110000=>000011
[6,-2,-4,1,-5,3]=>011010=>010110
[3,-2,1,6,4,5]=>010000=>000010
[3,6,-2,1,-5,4]=>001010=>010100
[-6,5,1,4,2,3]=>100000=>000001
[1,6,2,3,-5,4]=>000010=>010000
[4,6,-3,1,-5,2]=>001010=>010100
[1,6,2,-4,3,5]=>000100=>001000
[1,2,-6,5,3,4]=>001000=>000100
[5,1,2,6,-4,3]=>000010=>010000
[3,-2,-6,5,1,4]=>011000=>000110
[3,4,-2,6,1,5]=>001000=>000100
[-6,-2,4,5,1,3]=>110000=>000011
[1,6,-3,2,4,5]=>001000=>000100
[-6,1,-3,2,-5,4]=>101010=>010101
[-6,1,2,5,3,4]=>100000=>000001
[6,1,-4,2,-5,3]=>001010=>010100
[3,4,5,6,-2,1]=>000010=>010000
[-4,1,-3,6,2,5]=>101000=>000101
[5,1,-6,-3,2,4]=>001100=>001100
[-6,1,4,5,2,3]=>100000=>000001
[-4,1,5,6,-3,2]=>100010=>010001
[1,6,7,2,3,-5,4]=>0000010=>0100000
[7,1,4,2,3,-6,5]=>0000010=>0100000
[4,1,6,-7,2,3,5]=>0001000=>0001000
[-4,1,7,2,-5,3,6]=>1000100=>0010001
[1,7,2,-5,6,3,4]=>0001000=>0001000
[7,3,1,2,4,-6,5]=>0000010=>0100000
[-4,6,1,2,7,-5,3]=>1000010=>0100001
[7,3,1,2,-5,4,6]=>0000100=>0010000
[-6,3,1,2,7,-5,4]=>1000010=>0100001
[7,1,6,-3,2,4,5]=>0001000=>0001000
[7,5,1,-3,2,4,6]=>0001000=>0001000
[-7,-5,1,-3,2,-6,4]=>1101010=>0101011
[-3,7,1,-4,2,5,6]=>1001000=>0001001
[-7,-3,1,-4,2,-6,5]=>1101010=>0101011
[7,-4,6,1,2,3,5]=>0100000=>0000010
[7,5,-4,1,2,3,6]=>0010000=>0000100
[-6,1,7,2,5,3,4]=>1000000=>0000001
[-2,1,3,4,7,5,6]=>1000000=>0000001
[-2,1,7,3,4,-6,5]=>1000010=>0100001
[-7,-5,1,-6,2,-4,3]=>1101010=>0101011
[-2,1,7,3,-5,4,6]=>1000100=>0010001
[-2,1,3,-7,6,4,5]=>1001000=>0001001
[-2,6,1,3,7,-5,4]=>1000010=>0100001
[6,-3,1,-7,-4,2,5]=>0101100=>0011010
[-5,-3,1,-4,7,2,6]=>1101000=>0001011
[7,5,1,-3,6,2,4]=>0001000=>0001000
[-2,1,7,-4,3,5,6]=>1001000=>0001001
[7,-2,1,-4,3,-6,5]=>0101010=>0101010
[7,5,-4,1,6,2,3]=>0010000=>0000100
[-2,-7,1,5,3,4,6]=>1100000=>0000011
[-2,-7,1,3,6,4,5]=>1100000=>0000011
[-2,7,1,-5,3,-6,4]=>1001010=>0101001
[-5,-3,1,6,7,-4,2]=>1100010=>0100011
[5,-2,1,-4,7,3,6]=>0101000=>0001010
[-2,6,1,-7,-4,3,5]=>1001100=>0011001
[-2,-7,1,5,6,3,4]=>1100000=>0000011
[5,-2,1,6,7,-4,3]=>0100010=>0100010
[-2,1,3,6,7,4,5]=>1000000=>0000001
[7,-2,1,5,3,4,6]=>0100000=>0000010
[-2,-5,7,1,3,-6,4]=>1100010=>0100011
[7,-2,4,1,3,5,6]=>0100000=>0000010
[-2,-7,4,1,3,-6,5]=>1100010=>0100011
[-4,6,-2,-7,1,3,5]=>1011000=>0001101
[-2,7,-4,1,-5,3,6]=>1010100=>0010101
[5,6,-2,-7,1,3,4]=>0011000=>0001100
[3,-2,1,4,7,5,6]=>0100000=>0000010
[3,-2,7,1,4,-6,5]=>0100010=>0100010
[6,-2,-4,1,7,-5,3]=>0110010=>0100110
[3,-2,7,1,-5,4,6]=>0100100=>0010010
[3,-2,1,-7,6,4,5]=>0101000=>0001010
[3,6,-2,1,7,-5,4]=>0010010=>0100100
[5,3,7,1,2,-6,4]=>0000010=>0100000
[7,3,4,1,2,-6,5]=>0000010=>0100000
[1,2,7,3,4,-6,5]=>0000010=>0100000
[-4,-5,7,1,2,-6,3]=>1100010=>0100011
[1,2,7,3,-5,4,6]=>0000100=>0010000
[1,2,3,-7,6,4,5]=>0001000=>0001000
[1,6,2,3,7,-5,4]=>0000010=>0100000
[4,-3,1,-7,6,2,5]=>0101000=>0001010
[4,-3,7,1,-5,2,6]=>0100100=>0010010
[-3,5,1,-7,6,2,4]=>1001000=>0001001
[1,2,7,-4,3,5,6]=>0001000=>0001000
[7,1,2,-4,3,-6,5]=>0001010=>0101000
[-4,-7,6,-5,1,2,3]=>1101000=>0001011
[1,-7,2,5,3,4,6]=>0100000=>0000010
[1,-7,2,3,6,4,5]=>0100000=>0000010
[1,7,2,-5,3,-6,4]=>0001010=>0101000
[4,6,-3,1,7,-5,2]=>0010010=>0100100
[5,1,2,-4,7,3,6]=>0001000=>0001000
[1,6,2,-7,-4,3,5]=>0001100=>0011000
[1,-7,2,5,6,3,4]=>0100000=>0000010
[5,1,2,6,7,-4,3]=>0000010=>0100000
[3,-7,-2,1,6,4,5]=>0110000=>0000110
[3,-7,-2,5,1,4,6]=>0110000=>0000110
[3,7,-2,-5,1,-6,4]=>0011010=>0101100
[3,4,-2,1,7,5,6]=>0010000=>0000100
[3,4,7,-2,1,-6,5]=>0001010=>0101000
[7,-2,4,1,6,3,5]=>0100000=>0000010
[7,-2,4,5,1,3,6]=>0100000=>0000010
[-6,-7,-2,1,5,3,4]=>1110000=>0000111
[1,-3,7,2,4,5,6]=>0100000=>0000010
[7,1,-3,2,4,-6,5]=>0010010=>0100100
[-2,5,7,-4,1,-6,3]=>1001010=>0101001
[7,1,-3,2,-5,4,6]=>0010100=>0010100
[1,6,-3,-7,2,4,5]=>0011000=>0001100
[-6,1,-3,2,7,-5,4]=>1010010=>0100101
[3,-7,6,1,5,2,4]=>0100000=>0000010
[1,-7,4,2,3,-6,5]=>0100010=>0100010
[1,-5,7,2,3,-6,4]=>0100010=>0100010
[4,5,7,-6,1,-3,2]=>0001010=>0101000
[1,7,-4,2,-5,3,6]=>0010100=>0010100
[5,6,1,-7,2,3,4]=>0001000=>0001000
[6,1,-4,2,7,-5,3]=>0010010=>0100100
[3,4,-2,-7,6,1,5]=>0011000=>0001100
[3,4,5,-2,7,1,6]=>0001000=>0001000
[3,-7,-2,5,6,1,4]=>0110000=>0000110
[-4,1,-3,2,7,5,6]=>1010000=>0000101
[-4,1,7,-3,2,-6,5]=>1001010=>0101001
[-7,2,4,5,6,1,3]=>1000000=>0000001
[5,-7,1,-3,2,4,6]=>0101000=>0001010
[1,-7,6,-3,2,4,5]=>0101000=>0001010
[-7,1,-3,-5,2,-6,4]=>1011010=>0101101
[-6,-7,1,2,5,3,4]=>1100000=>0000011
[1,5,7,-4,2,-6,3]=>0001010=>0101000
[3,4,5,6,7,-2,1]=>0000010=>0100000
[-4,1,5,-3,7,2,6]=>1001000=>0001001
[-4,1,-3,-7,6,2,5]=>1011000=>0001101
[5,-3,-7,1,6,2,4]=>0110000=>0000110
[-4,1,7,5,6,2,3]=>1000000=>0000001
[-4,1,5,6,7,-3,2]=>1000010=>0100001
[3,4,2,6,5,-1]=>000001=>100000
[2,5,3,6,4,-1]=>000001=>100000
[3,5,2,6,4,-1]=>000001=>100000
[4,5,2,6,3,-1]=>000001=>100000
[3,4,2,-1,5,6]=>000100=>001000
[2,5,3,-1,4,6]=>000100=>001000
[4,5,2,-1,3,6]=>000100=>001000
[2,6,3,-1,4,5]=>000100=>001000
[3,6,2,-1,4,5]=>000100=>001000
[4,6,2,-1,3,5]=>000100=>001000
[5,6,2,-1,3,4]=>000100=>001000
[2,4,3,6,-1,5]=>000010=>010000
[3,4,2,6,-1,5]=>000010=>010000
[2,5,3,6,-1,4]=>000010=>010000
[4,5,2,6,-1,3]=>000010=>010000
[3,4,2,5,-1,6]=>000010=>010000
[3,5,2,4,-1,6]=>000010=>010000
[4,5,2,3,-1,6]=>000010=>010000
[2,6,3,4,-1,5]=>000010=>010000
[4,6,2,3,-1,5]=>000010=>010000
[5,6,2,3,-1,4]=>000010=>010000
[3,5,2,4,6,-1]=>000001=>100000
[3,6,2,4,5,-1]=>000001=>100000
[4,6,2,3,5,-1]=>000001=>100000
[4,-1,2,3,5,6]=>010000=>000010
[5,-1,2,3,4,6]=>010000=>000010
[2,4,6,3,5,-1]=>000001=>100000
[3,4,6,2,5,-1]=>000001=>100000
[2,5,6,3,4,-1]=>000001=>100000
[3,5,6,2,4,-1]=>000001=>100000
[2,4,-1,3,5,6]=>001000=>000100
[2,5,-1,3,4,6]=>001000=>000100
[3,5,-1,2,4,6]=>001000=>000100
[4,5,-1,2,3,6]=>001000=>000100
[2,6,-1,3,4,5]=>001000=>000100
[3,6,-1,2,4,5]=>001000=>000100
[4,6,-1,2,3,5]=>001000=>000100
[2,4,6,3,-1,5]=>000010=>010000
[2,5,6,3,-1,4]=>000010=>010000
[3,5,6,2,-1,4]=>000010=>010000
[4,5,6,2,-1,3]=>000010=>010000
[2,4,5,3,-1,6]=>000010=>010000
[3,4,5,2,-1,6]=>000010=>010000
[4,2,5,3,-1,6]=>000010=>010000
[2,3,6,4,-1,5]=>000010=>010000
[3,2,6,4,-1,5]=>000010=>010000
[5,2,6,3,-1,4]=>000010=>010000
[2,4,5,3,6,-1]=>000001=>100000
[4,2,5,3,6,-1]=>000001=>100000
[4,2,6,3,5,-1]=>000001=>100000
[5,2,6,3,4,-1]=>000001=>100000
[5,2,-1,3,4,6]=>001000=>000100
[6,2,-1,3,4,5]=>001000=>000100
[2,4,6,-1,3,5]=>000100=>001000
[3,4,6,-1,2,5]=>000100=>001000
[2,5,6,-1,3,4]=>000100=>001000
[3,5,6,-1,2,4]=>000100=>001000
[2,4,5,-1,3,6]=>000100=>001000
[2,3,5,-1,4,6]=>000100=>001000
[3,2,5,-1,4,6]=>000100=>001000
[2,3,6,-1,4,5]=>000100=>001000
[3,2,6,-1,4,5]=>000100=>001000
[4,2,6,-1,3,5]=>000100=>001000
[5,2,6,-1,3,4]=>000100=>001000
[2,4,5,6,3,-1]=>000001=>100000
[2,3,5,6,4,-1]=>000001=>100000
[3,2,5,6,4,-1]=>000001=>100000
[4,2,5,6,3,-1]=>000001=>100000
[5,2,3,6,4,-1]=>000001=>100000
[6,2,3,-1,4,5]=>000100=>001000
[2,4,5,6,-1,3]=>000010=>010000
[2,3,5,6,-1,4]=>000010=>010000
[3,2,5,6,-1,4]=>000010=>010000
[2,3,4,6,-1,5]=>000010=>010000
[3,2,4,6,-1,5]=>000010=>010000
[4,2,3,6,-1,5]=>000010=>010000
[-2,-3,-4,-5,1,6]=>111100=>001111
[-2,-3,-6,-4,1,5]=>111100=>001111
[2,-3,-5,-4,1,6]=>011100=>001110
[-2,-5,-6,-3,1,4]=>111100=>001111
[4,2,-3,-5,1,6]=>001100=>001100
[4,2,-6,-3,1,5]=>001100=>001100
[-5,2,-3,-4,1,6]=>101100=>001101
[-4,-5,-6,-2,1,3]=>111100=>001111
[-4,-6,-5,2,1,3]=>111000=>000111
[5,2,-4,-3,1,6]=>001100=>001100
[2,-4,-6,5,1,3]=>011000=>000110
[6,-4,-5,2,1,3]=>011000=>000110
[2,-5,-4,6,1,3]=>011000=>000110
[-4,2,3,-5,1,6]=>100100=>001001
[-4,2,-6,3,1,5]=>101000=>000101
[5,2,3,-4,1,6]=>000100=>001000
[5,2,-6,3,1,4]=>001000=>000100
[2,6,-5,3,1,4]=>001000=>000100
[-2,-5,4,-3,1,6]=>110100=>001011
[-6,-2,4,-3,1,5]=>110100=>001011
[-2,-3,5,-4,1,6]=>110100=>001011
[-4,-5,-6,3,1,2]=>111000=>000111
[2,-4,5,-3,1,6]=>010100=>001010
[-4,6,-5,3,1,2]=>101000=>000101
[5,6,-4,3,1,2]=>001000=>000100
[5,3,4,-2,1,6]=>000100=>001000
[3,6,4,-2,1,5]=>000100=>001000
[2,3,5,-4,1,6]=>000100=>001000
[-2,4,5,-3,1,6]=>100100=>001001
[-6,-4,3,5,1,2]=>110000=>000011
[-4,-5,3,6,1,2]=>110000=>000011
[5,-4,3,6,1,2]=>010000=>000010
[3,4,5,-2,1,6]=>000100=>001000
[-4,-5,3,1,2,6]=>110000=>000011
[-6,-4,3,1,2,5]=>110000=>000011
[5,-4,3,1,2,6]=>010000=>000010
[-4,-5,-2,1,3,6]=>111000=>000111
[-5,-4,2,1,3,6]=>110000=>000011
[-6,5,-2,1,3,4]=>101000=>000101
[-5,6,2,1,3,4]=>100000=>000001
[-2,-5,-3,1,4,6]=>111000=>000111
[-6,-2,-3,1,4,5]=>111000=>000111
[-2,-3,-4,1,5,6]=>111000=>000111
[-2,-3,-4,-5,-6,1]=>111110=>011111
[2,-3,-4,-6,-5,1]=>011110=>011110
[3,2,-5,-4,-6,1]=>001110=>011100
[-3,2,-6,-4,-5,1]=>101110=>011101
[3,2,-6,-5,-4,1]=>001110=>011100
[2,-5,3,1,4,6]=>010000=>000010
[-6,2,3,1,4,5]=>100000=>000001
[-3,4,2,-5,-6,1]=>100110=>011001
[3,4,2,-6,-5,1]=>000110=>011000
[-2,4,-3,1,5,6]=>101000=>000101
[-5,-3,2,-6,-4,1]=>110110=>011011
[-6,-3,2,-4,-5,1]=>110110=>011011
[6,-3,2,-5,-4,1]=>010110=>011010
[3,4,-2,1,5,6]=>001000=>000100
[4,5,2,-6,-3,1]=>000110=>011000
[4,6,2,-3,-5,1]=>000110=>011000
[-5,6,2,-3,-4,1]=>100110=>011001
[5,6,2,-4,-3,1]=>000110=>011000
[-4,-5,2,3,-6,1]=>110010=>010011
[4,-6,2,3,-5,1]=>010010=>010010
[-4,6,2,3,-5,1]=>100010=>010001
[5,6,2,3,-4,1]=>000010=>010000
[5,-2,1,3,4,6]=>010000=>000010
[-2,6,1,3,4,5]=>100000=>000001
[-2,-5,-6,4,-3,1]=>111010=>010111
[-3,-6,2,4,-5,1]=>110010=>010011
[-2,-3,1,4,5,6]=>110000=>000011
[-2,-3,-6,5,-4,1]=>111010=>010111
[-2,-3,-4,6,-5,1]=>111010=>010111
[2,-3,-5,6,-4,1]=>011010=>010110
[3,-2,1,4,5,6]=>010000=>000010
[4,-3,2,5,-6,1]=>010010=>010010
[4,2,-3,6,-5,1]=>001010=>010100
[-5,2,-3,6,-4,1]=>101010=>010101
[5,2,-4,6,-3,1]=>001010=>010100
[2,5,3,4,-6,1]=>000010=>010000
[5,6,3,4,-2,1]=>000010=>010000
[-4,2,3,6,-5,1]=>100010=>010001
[5,2,3,6,-4,1]=>000010=>010000
[2,-6,4,5,-3,1]=>010010=>010010
[-2,-5,4,6,-3,1]=>110010=>010011
[-2,-3,5,6,-4,1]=>110010=>010011
[2,-4,5,6,-3,1]=>010010=>010010
[3,6,4,5,-2,1]=>000010=>010000
[5,3,4,6,-2,1]=>000010=>010000
[2,3,5,6,-4,1]=>000010=>010000
[-2,4,5,6,-3,1]=>100010=>010001
[3,4,5,-2,-6,1]=>000110=>011000
[3,4,-2,1,-6,5]=>001010=>010100
[3,4,-2,6,-5,1]=>001010=>010100
[3,4,-2,-5,1,6]=>001100=>001100
[3,6,4,-2,-5,1]=>000110=>011000
[3,-2,1,4,-6,5]=>010010=>010010
[3,4,-2,-5,-6,1]=>001110=>011100
[3,-2,1,-5,4,6]=>010100=>001010
[3,-2,1,6,-5,4]=>010010=>010010
[3,-2,1,-5,-6,4]=>010110=>011010
[3,-2,5,6,-4,1]=>010010=>010010
[3,-2,5,-4,1,6]=>010100=>001010
[3,-2,5,-4,-6,1]=>010110=>011010
[3,-2,-4,1,5,6]=>011000=>000110
[3,-2,-4,1,-6,5]=>011010=>010110
[5,3,-2,6,-4,1]=>001010=>010100
[5,3,-2,-4,1,6]=>001100=>001100
[5,6,3,-2,-4,1]=>000110=>011000
[-2,1,3,4,-6,5]=>100010=>010001
[5,3,-2,-4,-6,1]=>001110=>011100
[-2,1,3,-5,4,6]=>100100=>001001
[-2,1,3,6,-5,4]=>100010=>010001
[-2,1,3,-5,-6,4]=>100110=>011001
[3,-2,-4,6,-5,1]=>011010=>010110
[3,-2,-4,-5,1,6]=>011100=>001110
[6,-2,3,-4,-5,1]=>010110=>011010
[-2,1,-4,3,5,6]=>101000=>000101
[-2,1,-4,3,-6,5]=>101010=>010101
[4,3,-2,-6,-5,1]=>001110=>011100
[-2,1,5,-4,3,6]=>100100=>001001
[-2,1,5,6,-4,3]=>100010=>010001
[-2,1,5,-4,-6,3]=>100110=>011001
[3,-2,-4,-5,-6,1]=>011110=>011110
[-2,1,-4,-5,3,6]=>101100=>001101
[-2,1,-4,6,-5,3]=>101010=>010101
[-2,1,4,-6,-5,3]=>100110=>011001
[-2,1,-4,-5,-6,3]=>101110=>011101
[-2,4,5,-3,-6,1]=>100110=>011001
[-2,4,-3,1,-6,5]=>101010=>010101
[-2,4,-3,6,-5,1]=>101010=>010101
[-2,4,-3,-5,1,6]=>101100=>001101
[-2,6,4,-3,-5,1]=>100110=>011001
[-2,-3,1,4,-6,5]=>110010=>010011
[-2,4,-3,-5,-6,1]=>101110=>011101
[-2,-3,1,-5,4,6]=>110100=>001011
[-2,-3,1,6,-5,4]=>110010=>010011
[-2,-3,1,-5,-6,4]=>110110=>011011
[2,-4,5,-3,-6,1]=>010110=>011010
[2,-4,-3,1,-6,5]=>011010=>010110
[1,2,3,4,-6,5]=>000010=>010000
[5,2,-4,-3,-6,1]=>001110=>011100
[1,2,3,-5,4,6]=>000100=>001000
[1,2,3,6,-5,4]=>000010=>010000
[1,2,3,-5,-6,4]=>000110=>011000
[2,-4,-3,6,-5,1]=>011010=>010110
[2,-4,-3,-5,1,6]=>011100=>001110
[6,-4,2,-3,-5,1]=>010110=>011010
[1,2,-4,3,5,6]=>001000=>000100
[1,2,-4,3,-6,5]=>001010=>010100
[4,2,-6,-3,-5,1]=>001110=>011100
[1,2,5,-4,3,6]=>000100=>001000
[1,2,5,6,-4,3]=>000010=>010000
[1,2,5,-4,-6,3]=>000110=>011000
[2,-4,-3,-5,-6,1]=>011110=>011110
[1,2,-4,-5,3,6]=>001100=>001100
[1,2,-4,6,-5,3]=>001010=>010100
[1,2,4,-6,-5,3]=>000110=>011000
[1,2,-4,-5,-6,3]=>001110=>011100
[-2,-3,5,-4,-6,1]=>110110=>011011
[-2,-3,-4,1,-6,5]=>111010=>010111
[1,-3,2,4,5,6]=>010000=>000010
[1,-3,2,4,-6,5]=>010010=>010010
[-5,2,-3,-4,-6,1]=>101110=>011101
[1,-3,2,-5,4,6]=>010100=>001010
[1,-3,2,6,-5,4]=>010010=>010010
[1,-3,2,-5,-6,4]=>010110=>011010
[1,4,-3,2,5,6]=>001000=>000100
[1,4,-3,2,-6,5]=>001010=>010100
[1,4,5,-3,2,6]=>000100=>001000
[1,4,5,6,-3,2]=>000010=>010000
[1,4,5,-3,-6,2]=>000110=>011000
[2,-3,-5,-4,-6,1]=>011110=>011110
[1,4,-3,-5,2,6]=>001100=>001100
[1,4,-3,6,-5,2]=>001010=>010100
[1,6,4,-3,-5,2]=>000110=>011000
[1,4,-3,-5,-6,2]=>001110=>011100
[1,-3,-4,2,5,6]=>011000=>000110
[1,-3,-4,2,-6,5]=>011010=>010110
[1,-3,5,-4,2,6]=>010100=>001010
[1,-3,5,6,-4,2]=>010010=>010010
[1,-3,5,-4,-6,2]=>010110=>011010
[1,3,-5,-4,2,6]=>001100=>001100
[1,3,-5,6,-4,2]=>001010=>010100
[1,6,3,-5,-4,2]=>000110=>011000
[1,3,-5,-4,-6,2]=>001110=>011100
[1,-3,-4,-5,2,6]=>011100=>001110
[1,-3,-4,6,-5,2]=>011010=>010110
[1,-6,3,-4,-5,2]=>010110=>011010
[1,3,-4,-6,-5,2]=>001110=>011100
[1,-3,-4,-5,-6,2]=>011110=>011110
[5,-3,1,2,4,6]=>010000=>000010
[3,-5,1,2,4,6]=>010000=>000010
[-5,3,1,2,4,6]=>100000=>000001
[6,-5,-3,1,2,4]=>011000=>000110
[3,-6,-5,1,2,4]=>011000=>000110
[-3,6,-5,1,2,4]=>101000=>000101
[3,6,-5,1,2,4]=>001000=>000100
[-5,3,6,1,2,4]=>100000=>000001
[-6,-5,3,1,2,4]=>110000=>000011
[3,-6,1,2,4,5]=>010000=>000010
[-3,-6,1,2,4,5]=>110000=>000011
[6,-3,1,2,4,5]=>010000=>000010
[6,-4,-3,1,2,5]=>011000=>000110
[4,6,-3,1,2,5]=>001000=>000100
[4,-6,-3,1,2,5]=>011000=>000110
[-6,3,4,1,2,5]=>100000=>000001
[4,-3,1,2,5,6]=>010000=>000010
[5,-4,-3,1,2,6]=>011000=>000110
[4,5,-3,1,2,6]=>001000=>000100
[5,6,-4,-3,1,2]=>001100=>001100
[4,5,6,-3,1,2]=>000100=>001000
[5,-4,1,2,3,6]=>010000=>000010
[1,-5,-4,2,3,6]=>011000=>000110
[-4,5,1,2,3,6]=>100000=>000001
[6,-5,-4,1,2,3]=>011000=>000110
[5,6,-4,1,2,3]=>001000=>000100
[-5,6,-4,1,2,3]=>101000=>000101
[-6,1,-5,-4,2,3]=>101100=>001101
[-4,5,6,1,2,3]=>100000=>000001
[-5,-4,6,1,2,3]=>110000=>000011
[-6,4,1,2,3,5]=>100000=>000001
[-6,1,-4,2,3,5]=>101000=>000101
[4,1,-6,2,3,5]=>001000=>000100
[6,-4,1,2,3,5]=>010000=>000010
[1,-6,-4,2,3,5]=>011000=>000110
[2,-6,-4,1,3,5]=>011000=>000110
[4,-6,1,2,3,5]=>010000=>000010
[4,-6,-2,1,3,5]=>011000=>000110
[-4,2,-6,1,3,5]=>101000=>000101
[2,-4,1,3,5,6]=>010000=>000010
[2,-5,-4,1,3,6]=>011000=>000110
[2,5,-4,1,3,6]=>001000=>000100
[2,6,-5,-4,1,3]=>001100=>001100
[2,5,6,-4,1,3]=>000100=>001000
[-5,6,1,2,3,4]=>100000=>000001
[-6,1,-5,2,3,4]=>101000=>000101
[6,1,-5,2,3,4]=>001000=>000100
[1,-6,-5,2,3,4]=>011000=>000110
[6,-5,1,2,3,4]=>010000=>000010
[2,-6,-5,1,3,4]=>011000=>000110
[2,6,-5,1,3,4]=>001000=>000100
[-6,2,-5,1,3,4]=>101000=>000101
[6,2,-5,1,3,4]=>001000=>000100
[1,-5,2,3,4,6]=>010000=>000010
[2,-5,1,3,4,6]=>010000=>000010
[-2,-5,1,3,4,6]=>110000=>000011
[3,-5,-2,1,4,6]=>011000=>000110
[3,6,-5,-2,1,4]=>001100=>001100
[1,-6,2,3,4,5]=>010000=>000010
[-2,-6,1,3,4,5]=>110000=>000011
[2,-6,1,3,4,5]=>010000=>000010
[3,-6,-2,1,4,5]=>011000=>000110
[3,1,2,-5,4,6]=>000100=>001000
[1,-3,5,2,4,6]=>010000=>000010
[5,1,-3,2,4,6]=>001000=>000100
[3,1,2,6,-5,4]=>000010=>010000
[1,6,-3,2,-5,4]=>001010=>010100
[3,6,1,2,-5,4]=>000010=>010000
[1,-3,5,6,2,4]=>010000=>000010
[5,1,-3,6,2,4]=>001000=>000100
[5,6,1,-3,2,4]=>000100=>001000
[1,-3,-6,2,4,5]=>011000=>000110
[1,-3,2,6,4,5]=>010000=>000010
[3,1,2,4,-6,5]=>000010=>010000
[-4,1,-3,2,-6,5]=>101010=>010101
[3,4,1,2,-6,5]=>000010=>010000
[1,4,-3,6,2,5]=>001000=>000100
[-4,6,1,-3,2,5]=>100100=>001001
[-4,1,-3,2,5,6]=>101000=>000101
[-4,1,5,-3,2,6]=>100100=>001001
[5,-4,1,-3,2,6]=>010100=>001010
[5,-4,1,6,-3,2]=>010010=>010010
[5,6,-4,1,-3,2]=>001010=>010100
[1,-5,2,-4,3,6]=>010100=>001010
[5,1,2,-4,3,6]=>000100=>001000
[-4,1,5,2,3,6]=>100000=>000001
[1,-5,2,6,-4,3]=>010010=>010010
[1,6,-5,2,-4,3]=>001010=>010100
[-6,1,-5,2,-4,3]=>101010=>010101
[5,6,1,2,-4,3]=>000010=>010000
[-4,1,5,6,2,3]=>100000=>000001
[5,-4,1,6,2,3]=>010000=>000010
[-6,1,2,-4,3,5]=>100100=>001001
[-4,1,2,6,3,5]=>100000=>000001
[-4,1,2,3,-6,5]=>100010=>010001
[1,4,2,3,-6,5]=>000010=>010000
[-2,4,1,3,-6,5]=>100010=>010001
[1,2,-4,6,3,5]=>001000=>000100
[-2,1,-4,6,3,5]=>101000=>000101
[-2,4,1,6,3,5]=>100000=>000001
[-2,4,1,3,5,6]=>100000=>000001
[5,-2,1,-4,3,6]=>010100=>001010
[-2,4,5,1,3,6]=>100000=>000001
[5,6,-2,1,-4,3]=>001010=>010100
[-2,4,5,6,1,3]=>100000=>000001
[-6,1,2,3,-5,4]=>100010=>010001
[1,2,-6,3,-5,4]=>001010=>010100
[-2,1,-6,3,-5,4]=>101010=>010101
[1,-5,2,6,3,4]=>010000=>000010
[-2,-5,1,6,3,4]=>110000=>000011
[-2,6,-5,1,3,4]=>101000=>000101
[-2,1,5,6,3,4]=>100000=>000001
[-2,1,5,3,4,6]=>100000=>000001
[3,-2,5,1,4,6]=>010000=>000010
[3,-2,5,6,1,4]=>010000=>000010
[3,-2,-6,1,4,5]=>011000=>000110
[3,2,6,-5,1,4]=>000100=>001000
[-5,-3,2,4,-6,1]=>110010=>010011
[4,-5,-6,-3,1,2]=>011100=>001110
[3,6,5,-4,1,2]=>000100=>001000
[-8,-6,-4,-2,1,3,5,7]=>11110000=>00001111
[6,8,-4,-3,1,2,5,7]=>00110000=>00001100
[-3,2,-8,-6,-4,1,5,7]=>10111000=>00011101
[3,2,8,-6,-5,1,4,7]=>00011000=>00011000
[-5,-3,2,4,-8,-6,1,7]=>11001100=>00110011
[5,-3,2,4,8,-7,1,6]=>01000100=>00100010
[-7,-5,-3,2,4,6,-8,1]=>11100010=>01000111
[5,7,-4,2,3,6,-8,1]=>00100010=>01000100
[-4,5,2,3,8,-7,1,6]=>10000100=>00100001
[4,5,2,3,-8,-6,1,7]=>00001100=>00110000
[2,-8,-4,-6,-5,1,3,7]=>01111000=>00011110
[-8,-6,1,-5,-4,2,3,7]=>11011000=>00011011
[-3,6,8,-5,1,2,4,7]=>10010000=>00001001
[2,8,-6,-5,1,3,4,7]=>00110000=>00001100
[-5,4,-8,-6,-2,1,3,7]=>10111000=>00011101
[4,-5,-8,-6,-3,1,2,7]=>01111000=>00011110
[3,-8,-5,-6,-4,1,2,7]=>01111000=>00011110
[-6,4,3,8,-5,1,2,7]=>10001000=>00010001
[-4,3,-5,2,-8,-6,1,7]=>10101100=>00110101
[4,3,-5,2,8,-7,1,6]=>00100100=>00100100
[-4,3,-7,-5,2,6,-8,1]=>10110010=>01001101
[4,3,7,-6,2,5,-8,1]=>00010010=>01001000
[3,-4,-8,-6,2,-7,1,5]=>01110100=>00101110
[8,4,-7,-6,3,1,2,5]=>00110000=>00001100
[-5,4,-7,3,8,1,2,6]=>10100000=>00000101
[5,8,-4,3,-7,1,2,6]=>00101000=>00010100
[5,-3,4,8,-7,1,2,6]=>01001000=>00010010
[-5,2,4,8,-7,1,3,6]=>10001000=>00010001
[-7,-5,4,6,-8,-2,1,3]=>11001100=>00110011
[4,-7,-5,6,-8,-3,1,2]=>01101100=>00110110
[-7,3,-5,6,-8,-4,1,2]=>10101100=>00110101
[-4,3,6,-7,-8,-5,1,2]=>10011100=>00111001
[-4,3,5,8,7,-6,1,2]=>10000100=>00100001
[4,-8,6,-7,3,5,1,2]=>01010000=>00001010
[-6,-4,3,5,-7,2,-8,1]=>11001010=>01010011
[5,6,3,4,-7,2,-8,1]=>00001010=>01010000
[3,-8,5,7,4,-6,1,2]=>01000100=>00100010
[-7,-6,3,-8,4,-5,1,2]=>11010100=>00101011
[-7,-6,5,3,-8,-4,1,2]=>11001100=>00110011
[-7,4,-6,5,-8,-3,1,2]=>10101100=>00110101
[6,7,4,5,-8,-2,1,3]=>00001100=>00110000
[8,-6,2,4,-7,1,3,5]=>01001000=>00010010
[4,-8,-6,-3,-7,1,2,5]=>01111000=>00011110
[-4,3,-8,-6,-7,1,2,5]=>10111000=>00011101
[-7,6,8,1,3,-5,2,4]=>10000100=>00100001
[-7,-6,5,8,3,1,2,4]=>11000000=>00000011
[5,-6,3,8,2,-7,1,4]=>01000100=>00100010
[3,-7,-5,-6,2,4,-8,1]=>01110010=>01001110
[-7,-6,2,-5,3,4,-8,1]=>11010010=>01001011
[-5,2,6,8,3,-7,1,4]=>10000100=>00100001
[-5,7,8,-6,2,1,3,4]=>10010000=>00001001
[5,6,7,1,8,2,3,4]=>00000000=>00000000
[-4,-8,-7,1,-6,2,3,5]=>11101000=>00010111
[8,-7,-6,3,1,2,4,5]=>01100000=>00000110
[2,-7,8,-6,1,3,4,5]=>01010000=>00001010
[-5,2,8,-7,1,3,4,6]=>10010000=>00001001
[-7,-5,3,8,1,2,4,6]=>11000000=>00000011
[5,-7,-4,8,1,2,3,6]=>01100000=>00000110
[-4,-8,-7,2,-5,1,3,6]=>11101000=>00010111
[4,2,-7,8,-6,1,3,5]=>00101000=>00010100
[-8,-4,-6,2,3,-7,1,5]=>11100100=>00100111
[-6,4,7,2,3,5,-8,1]=>10000010=>01000001
[3,7,-6,2,4,5,-8,1]=>00100010=>01000100
[6,8,-3,2,4,-7,1,5]=>00100100=>00100100
[2,-8,-7,-3,-6,1,4,5]=>01111000=>00011110
[3,-7,2,8,-5,1,4,6]=>01001000=>00010010
[-3,2,7,8,-4,1,5,6]=>10001000=>00010001
[3,4,7,8,1,2,5,6]=>00000000=>00000000
[4,8,-7,-2,1,3,5,6]=>00110000=>00001100
[-7,6,-8,-4,-2,1,3,5]=>10111000=>00011101
[6,-7,-8,-4,-3,1,2,5]=>01111000=>00011110
[-7,-3,2,6,-8,-4,1,5]=>11001100=>00110011
[3,7,2,6,-8,-5,1,4]=>00001100=>00110000
[-7,-8,-3,2,5,-6,1,4]=>11100100=>00100111
[-8,5,-6,-3,2,-7,1,4]=>10110100=>00101101
[-6,5,-7,-3,2,4,-8,1]=>10110010=>01001101
[5,-6,-7,-4,2,3,-8,1]=>01110010=>01001110
[-8,-6,5,-4,2,-7,1,3]=>11010100=>00101011
[-8,4,7,2,5,-6,1,3]=>10000100=>00100001
[-7,2,-4,6,-8,-5,1,3]=>10101100=>00110101
[-7,6,1,-8,-5,-4,2,3]=>10011100=>00111001
[6,-7,-3,-8,-5,1,2,4]=>01111000=>00011110
[7,2,6,-8,-5,1,3,4]=>00011000=>00011000
[7,-8,2,5,-6,1,3,4]=>01001000=>00010010
[7,-8,-5,-3,-6,1,2,4]=>01111000=>00011110
[-8,6,7,5,-4,1,2,3]=>10001000=>00010001
[-8,6,7,1,4,-5,2,3]=>10000100=>00100001
[-8,2,5,7,4,-6,1,3]=>10000100=>00100001
[-8,-6,-5,4,2,-7,1,3]=>11100100=>00100111
[4,7,6,-5,2,3,-8,1]=>00010010=>01001000
[5,7,-6,4,2,3,-8,1]=>00100010=>01000100
[4,-8,-5,2,-6,-7,1,3]=>01101100=>00110110
[4,-8,-5,-7,1,-6,2,3]=>01110100=>00101110
[-8,-7,5,6,4,1,2,3]=>11000000=>00000011
[8,6,-7,-4,5,1,2,3]=>00110000=>00001100
[-8,6,-7,3,5,1,2,4]=>10100000=>00000101
[5,8,-6,2,-7,1,3,4]=>00101000=>00010100
[-6,5,-7,4,-8,-2,1,3]=>10101100=>00110101
[5,-6,-7,4,-8,-3,1,2]=>01101100=>00110110
[7,-8,6,3,5,-4,1,2]=>01000100=>00100010
[6,-7,-4,-8,3,-5,1,2]=>01110100=>00101110
[5,7,-8,4,3,-6,1,2]=>00100100=>00100100
[5,8,-6,4,-7,3,1,2]=>00101000=>00010100
[-5,4,-6,3,-7,2,-8,1]=>10101010=>01010101
[1,-4,2,5,-6,3]=>010010=>010010
[1,-3,4,5,-6,2]=>010010=>010010
[-3,1,4,-5,2,6]=>100100=>001001
[-3,1,4,6,-5,2]=>100010=>010001
[3,1,4,5,-6,2]=>000010=>010000
[-3,1,4,-5,-6,2]=>100110=>011001
[1,-3,-6,5,-4,2]=>011010=>010110
[-5,1,3,-4,-6,2]=>100110=>011001
[-2,-4,1,5,-6,3]=>110010=>010011
[3,-2,4,5,-6,1]=>010010=>010010
[-2,3,4,-5,1,6]=>100100=>001001
[-2,3,4,6,-5,1]=>100010=>010001
[-2,3,4,-5,-6,1]=>100110=>011001
[3,-2,-6,5,-4,1]=>011010=>010110
[-2,5,3,-4,-6,1]=>100110=>011001
[-2,-3,4,5,-6,1]=>110010=>010011
[2,3,-4,1,-6,5]=>001010=>010100
[2,3,5,-4,-6,1]=>000110=>011000
[5,3,4,-2,-6,1]=>000110=>011000
[2,3,-4,-5,1,6]=>001100=>001100
[2,3,-4,6,-5,1]=>001010=>010100
[2,-4,3,5,-6,1]=>010010=>010010
[4,5,3,-2,-6,1]=>000110=>011000
[2,3,-4,-5,-6,1]=>001110=>011100
[-2,-5,4,-3,-6,1]=>110110=>011011
[4,2,-3,-5,-6,1]=>001110=>011100
[-2,-3,5,1,4,6]=>110000=>000011
[-4,-2,5,1,3,6]=>110000=>000011
[-5,2,4,1,3,6]=>100000=>000001
[-2,-3,1,6,4,5]=>110000=>000011
[-4,-2,1,6,3,5]=>110000=>000011
[-4,3,1,6,2,5]=>100000=>000001
[5,-2,1,6,3,4]=>010000=>000010
[6,2,-3,5,1,4]=>001000=>000100
[6,-4,2,5,1,3]=>010000=>000010
[-4,6,3,5,1,2]=>100000=>000001
[2,-5,6,4,1,3]=>010000=>000010
[-2,-3,-4,6,1,5]=>111000=>000111
[-2,-5,-3,6,1,4]=>111000=>000111
[-4,-5,-2,6,1,3]=>111000=>000111
[-6,-2,-3,5,1,4]=>111000=>000111
[-6,-4,-2,5,1,3]=>111000=>000111
[5,-6,2,4,1,3]=>010000=>000010
[6,4,3,-1,2,5]=>000100=>001000
[-1,4,3,6,5,2]=>100000=>000001
[4,-1,2,6,5,3]=>010000=>000010
[5,-1,6,2,4,3]=>010000=>000010
[3,2,5,4,7,6,-1,8]=>00000010=>01000000
[4,5,2,3,7,6,-1,8]=>00000010=>01000000
[5,4,3,2,7,6,-1,8]=>00000010=>01000000
[6,4,3,7,2,5,-1,8]=>00000010=>01000000
[7,4,3,6,5,2,-1,8]=>00000010=>01000000
[8,4,3,6,5,-1,2,7]=>00000100=>00100000
[-1,4,3,6,5,8,7,2]=>10000000=>00000001
[-1,5,6,3,4,8,7,2]=>10000000=>00000001
[8,5,6,3,4,-1,2,7]=>00000100=>00100000
[7,5,6,3,4,2,-1,8]=>00000010=>01000000
[6,5,7,3,2,4,-1,8]=>00000010=>01000000
[5,6,7,2,3,4,-1,8]=>00000010=>01000000
[4,6,2,7,3,5,-1,8]=>00000010=>01000000
[3,2,6,7,4,5,-1,8]=>00000010=>01000000
[3,2,7,6,5,4,-1,8]=>00000010=>01000000
[4,7,2,6,5,3,-1,8]=>00000010=>01000000
[5,7,6,2,4,3,-1,8]=>00000010=>01000000
[6,7,5,4,2,3,-1,8]=>00000010=>01000000
[7,6,5,4,3,2,-1,8]=>00000010=>01000000
[8,6,5,4,3,-1,2,7]=>00000100=>00100000
[-1,6,5,4,3,8,7,2]=>10000000=>00000001
[-1,7,5,4,8,3,6,2]=>10000000=>00000001
[8,7,5,4,-1,3,2,6]=>00001000=>00010000
[7,8,5,4,-1,2,3,6]=>00001000=>00010000
[6,8,5,4,2,-1,3,7]=>00000100=>00100000
[5,8,6,2,4,-1,3,7]=>00000100=>00100000
[4,8,2,6,5,-1,3,7]=>00000100=>00100000
[3,2,8,6,5,-1,4,7]=>00000100=>00100000
[3,2,-1,6,5,8,7,4]=>00100000=>00000100
[4,-1,2,6,5,8,7,3]=>01000000=>00000010
[5,-1,6,2,4,8,7,3]=>01000000=>00000010
[6,-1,5,4,2,8,7,3]=>01000000=>00000010
[7,-1,5,4,8,2,6,3]=>01000000=>00000010
[8,-1,5,4,7,6,2,3]=>01000000=>00000010
[-1,8,5,4,7,6,3,2]=>10000000=>00000001
[-1,8,6,7,4,5,3,2]=>10000000=>00000001
[8,-1,6,7,4,5,2,3]=>01000000=>00000010
[7,-1,6,8,4,2,5,3]=>01000000=>00000010
[6,-1,7,8,2,4,5,3]=>01000000=>00000010
[5,-1,7,2,8,4,6,3]=>01000000=>00000010
[4,-1,2,7,8,5,6,3]=>01000000=>00000010
[3,2,-1,7,8,5,6,4]=>00100000=>00000100
[3,2,8,7,-1,5,4,6]=>00001000=>00010000
[4,8,2,7,-1,5,3,6]=>00001000=>00010000
[5,8,7,2,-1,4,3,6]=>00001000=>00010000
[6,8,7,-1,2,4,3,5]=>00010000=>00001000
[7,8,6,-1,4,2,3,5]=>00010000=>00001000
[8,7,6,-1,4,3,2,5]=>00010000=>00001000
[-1,7,6,8,4,3,5,2]=>10000000=>00000001
[-1,6,7,8,3,4,5,2]=>10000000=>00000001
[8,6,7,-1,3,4,2,5]=>00010000=>00001000
[7,6,8,-1,3,2,4,5]=>00010000=>00001000
[6,7,8,-1,2,3,4,5]=>00010000=>00001000
[5,7,8,2,-1,3,4,6]=>00001000=>00010000
[4,7,2,8,-1,3,5,6]=>00001000=>00010000
[3,2,7,8,-1,4,5,6]=>00001000=>00010000
[3,2,6,8,4,-1,5,7]=>00000100=>00100000
[4,6,2,8,3,-1,5,7]=>00000100=>00100000
[5,6,8,2,3,-1,4,7]=>00000100=>00100000
[6,5,8,3,2,-1,4,7]=>00000100=>00100000
[7,5,8,3,-1,2,4,6]=>00001000=>00010000
[8,5,7,3,-1,4,2,6]=>00001000=>00010000
[-1,5,7,3,8,4,6,2]=>10000000=>00000001
[-1,4,3,7,8,5,6,2]=>10000000=>00000001
[8,4,3,7,-1,5,2,6]=>00001000=>00010000
[7,4,3,8,-1,2,5,6]=>00001000=>00010000
[6,4,3,8,2,-1,5,7]=>00000100=>00100000
[5,4,3,2,8,-1,6,7]=>00000100=>00100000
[4,5,2,3,8,-1,6,7]=>00000100=>00100000
[3,2,5,4,8,-1,6,7]=>00000100=>00100000
[3,2,5,4,-1,8,7,6]=>00001000=>00010000
[4,5,2,3,-1,8,7,6]=>00001000=>00010000
[5,4,3,2,-1,8,7,6]=>00001000=>00010000
[6,4,3,-1,2,8,7,5]=>00010000=>00001000
[7,4,3,-1,8,2,6,5]=>00010000=>00001000
[8,4,3,-1,7,6,2,5]=>00010000=>00001000
[-1,4,3,8,7,6,5,2]=>10000000=>00000001
[-1,5,8,3,7,6,4,2]=>10000000=>00000001
[8,5,-1,3,7,6,2,4]=>00100000=>00000100
[7,5,-1,3,8,2,6,4]=>00100000=>00000100
[6,5,-1,3,2,8,7,4]=>00100000=>00000100
[5,6,-1,2,3,8,7,4]=>00100000=>00000100
[4,6,2,-1,3,8,7,5]=>00010000=>00001000
[3,2,6,-1,4,8,7,5]=>00010000=>00001000
[3,2,7,-1,8,4,6,5]=>00010000=>00001000
[4,7,2,-1,8,3,6,5]=>00010000=>00001000
[5,7,-1,2,8,3,6,4]=>00100000=>00000100
[6,7,-1,8,2,3,5,4]=>00100000=>00000100
[7,6,-1,8,3,2,5,4]=>00100000=>00000100
[8,6,-1,7,3,5,2,4]=>00100000=>00000100
[-1,6,8,7,3,5,4,2]=>10000000=>00000001
[-1,7,8,6,5,3,4,2]=>10000000=>00000001
[8,7,-1,6,5,3,2,4]=>00100000=>00000100
[7,8,-1,6,5,2,3,4]=>00100000=>00000100
[6,8,-1,7,2,5,3,4]=>00100000=>00000100
[5,8,-1,2,7,6,3,4]=>00100000=>00000100
[4,8,2,-1,7,6,3,5]=>00010000=>00001000
[3,2,8,-1,7,6,4,5]=>00010000=>00001000
[3,2,-1,8,7,6,5,4]=>00100000=>00000100
[4,-1,2,8,7,6,5,3]=>01000000=>00000010
[5,-1,8,2,7,6,4,3]=>01000000=>00000010
[6,-1,8,7,2,5,4,3]=>01000000=>00000010
[7,-1,8,6,5,2,4,3]=>01000000=>00000010
[8,-1,7,6,5,4,2,3]=>01000000=>00000010
[-1,8,7,6,5,4,3,2]=>10000000=>00000001
[4,5,-6,1,2,3]=>001000=>000100
[4,5,-6,-3,1,2]=>001100=>001100
[3,4,-5,1,2,6]=>001000=>000100
[3,4,-6,-5,1,2]=>001100=>001100
[3,4,5,-6,1,2]=>000100=>001000
[-5,3,4,-6,1,2]=>100100=>001001
[-4,3,5,-6,1,2]=>100100=>001001
[-5,-4,3,-6,1,2]=>110100=>001011
[4,5,-6,-2,1,3]=>001100=>001100
[4,5,-6,-3,-2,1]=>001110=>011100
[3,4,-5,-2,1,6]=>001100=>001100
[3,4,-6,-5,-2,1]=>001110=>011100
[3,4,5,-6,-2,1]=>000110=>011000
[-5,3,4,-6,-2,1]=>100110=>011001
[-4,3,5,-6,-2,1]=>100110=>011001
[-5,-4,3,-6,-2,1]=>110110=>011011
[2,4,5,-6,-3,1]=>000110=>011000
[2,3,-6,-4,1,5]=>001100=>001100
[2,3,5,-6,-4,1]=>000110=>011000
[-5,2,3,4,-6,1]=>100010=>010001
[-4,2,3,-6,-5,1]=>100110=>011001
[-4,2,3,5,-6,1]=>100010=>010001
[-5,-4,2,3,-6,1]=>110010=>010011
[4,-5,2,3,-6,1]=>010010=>010010
[4,-5,-3,2,-6,1]=>011010=>010110
[2,5,-3,1,4,6]=>001000=>000100
[-5,2,-4,1,3,6]=>101000=>000101
[4,2,-5,1,3,6]=>001000=>000100
[-3,2,-6,1,4,5]=>101000=>000101
[6,2,-4,1,3,5]=>001000=>000100
[6,-2,-5,1,3,4]=>011000=>000110
[6,-5,3,1,2,4]=>010000=>000010
[-2,-5,-6,1,3,4]=>111000=>000111
[-5,-3,2,-6,1,4]=>110100=>001011
[5,-6,2,-4,1,3]=>010100=>001010
[4,-6,3,5,1,2]=>010000=>000010
[-4,-6,2,-5,1,3]=>110100=>001011
[-3,2,6,-4,1,5]=>100100=>001001
[6,-4,2,-5,1,3]=>010100=>001010
[5,-3,2,-6,1,4]=>010100=>001010
[4,5,2,-6,1,3]=>000100=>001000
[-5,4,2,-6,1,3]=>100100=>001001
[2,3,-1,5,6,4]=>001000=>000100
[2,-1,3,5,6,4]=>010000=>000010
[2,6,4,5,3,-1]=>000001=>100000
[2,-1,4,5,3,6]=>010000=>000010
[2,-1,4,5,6,3]=>010000=>000010
[2,-1,4,6,5,3]=>010000=>000010
[2,-1,5,4,6,3]=>010000=>000010
[2,-1,6,4,5,3]=>010000=>000010
[3,2,-1,5,6,4]=>001000=>000100
[-1,2,3,5,6,4]=>100000=>000001
[6,2,4,5,3,-1]=>000001=>100000
[-1,2,4,5,3,6]=>100000=>000001
[-1,2,4,5,6,3]=>100000=>000001
[-1,2,4,6,5,3]=>100000=>000001
[-1,2,5,4,6,3]=>100000=>000001
[-1,2,6,4,5,3]=>100000=>000001
[-1,3,2,5,6,4]=>100000=>000001
[5,3,4,2,-1,6]=>000010=>010000
[-1,3,4,2,6,5]=>100000=>000001
[-1,3,4,6,5,2]=>100000=>000001
[6,3,5,4,2,-1]=>000001=>100000
[-1,3,5,4,2,6]=>100000=>000001
[-1,3,5,4,6,2]=>100000=>000001
[-1,3,6,4,5,2]=>100000=>000001
[-1,3,6,5,4,2]=>100000=>000001
[-1,6,3,5,4,2]=>100000=>000001
[5,3,2,6,4,-1]=>000001=>100000
[5,3,6,2,4,-1]=>000001=>100000
[5,3,6,4,2,-1]=>000001=>100000
[5,3,2,6,-1,4]=>000010=>010000
[5,3,6,2,-1,4]=>000010=>010000
[5,6,3,2,-1,4]=>000010=>010000
[5,3,6,-1,2,4]=>000100=>001000
[5,6,3,-1,2,4]=>000100=>001000
[5,3,6,4,-1,2]=>000010=>010000
[5,3,6,-1,4,2]=>000100=>001000
[6,4,2,-1,5,3]=>000100=>001000
[6,4,-1,2,5,3]=>001000=>000100
[6,-1,4,2,5,3]=>010000=>000010
[6,4,-1,5,2,3]=>001000=>000100
[6,4,3,2,-1,5]=>000010=>010000
[6,4,-1,3,2,5]=>001000=>000100
[6,4,3,-1,5,2]=>000100=>001000
[6,4,-1,3,5,2]=>001000=>000100
[6,4,-1,5,3,2]=>001000=>000100
[-5,4,1,-3,-6,2]=>100110=>011001
[5,-4,3,1,-6,2]=>010010=>010010
[-2,1,-4,3,-6,5,-8,7]=>10101010=>01010101
[3,4,1,2,-6,5,-8,7]=>00001010=>01010000
[-2,-3,-4,1,-6,5,-8,7]=>11101010=>01010111
[-2,-5,-3,6,1,4,-8,7]=>11100010=>01000111
[-2,-5,4,-3,-6,1,-8,7]=>11011010=>01011011
[-2,-5,4,-7,-3,8,1,6]=>11011000=>00011011
[-2,-5,-3,4,6,-7,-8,1]=>11100110=>01100111
[7,5,2,3,6,-4,-8,1]=>00000110=>01100000
[4,5,2,-7,3,8,1,6]=>00010000=>00001000
[4,5,2,3,-6,1,-8,7]=>00001010=>01010000
[6,-4,-5,2,1,3,-8,7]=>01100010=>01000110
[1,4,5,6,2,3,-8,7]=>00000010=>01000000
[5,6,1,-3,2,4,-8,7]=>00010010=>01001000
[-2,-5,1,6,3,4,-8,7]=>11000010=>01000011
[-2,1,-4,-5,-6,3,-8,7]=>10111010=>01011101
[-5,4,1,-3,-6,2,-8,7]=>10011010=>01011001
[5,-4,3,1,-6,2,-8,7]=>01001010=>01010010
[4,-6,-5,3,1,2,-8,7]=>01100010=>01000110
[-2,-3,-4,-5,-6,1,-8,7]=>11111010=>01011111
[-2,-3,-4,-7,-5,8,1,6]=>11111000=>00011111
[-2,-3,-4,-7,6,-5,-8,1]=>11110110=>01101111
[-7,-3,-8,-6,2,5,-4,1]=>11110010=>01001111
[8,-3,-4,-6,-7,2,1,5]=>01111000=>00011110
[-7,-6,4,3,1,8,2,5]=>11000000=>00000011
[-3,8,-7,-4,1,-5,2,6]=>10110100=>00101101
[5,-4,3,-7,1,8,2,6]=>01010000=>00001010
[-5,4,1,-7,-3,8,2,6]=>10011000=>00011001
[-2,1,-4,-7,-5,8,3,6]=>10111000=>00011101
[-2,1,-4,-7,6,-5,-8,3]=>10110110=>01101101
[-5,4,-3,1,6,-7,-8,2]=>10100110=>01100101
[-4,5,3,1,6,-7,-8,2]=>10000110=>01100001
[6,-3,-7,-4,1,-5,-8,2]=>01110110=>01101110
[-3,-4,-8,7,5,1,-6,2]=>11100010=>01000111
[-6,-8,4,3,-7,5,1,2]=>11001000=>00010011
[-5,-3,-6,2,-7,-4,-8,1]=>11101110=>01110111
[-5,6,3,4,2,-7,-8,1]=>10000110=>01100001
[3,7,-5,-8,4,1,-6,2]=>00110010=>01001100
[5,1,6,7,3,4,-8,2]=>00000010=>01000000
[7,-6,3,1,-8,5,-4,2]=>01001010=>01010010
[-6,-3,1,7,4,5,-8,2]=>11000010=>01000011
[-7,-2,-6,1,4,5,-8,3]=>11100010=>01000111
[-2,-8,1,-6,-7,4,3,5]=>11011000=>00011011
[6,1,8,4,-7,-3,2,5]=>00001100=>00110000
[-8,-6,3,1,-7,-4,2,5]=>11001100=>00110011
[5,6,3,8,-7,1,2,4]=>00001000=>00010000
[7,-6,5,8,3,1,2,4]=>01000000=>00000010
[-8,-3,-5,-6,-7,2,1,4]=>11111000=>00011111
[-7,3,-5,-8,2,4,-6,1]=>10110010=>01001101
[5,8,6,7,3,4,-2,1]=>00000010=>01000000
[2,5,6,8,-7,3,1,4]=>00001000=>00010000
[2,-5,-6,7,1,8,3,4]=>01100000=>00000110
[1,2,5,6,7,8,3,4]=>00000000=>00000000
[-4,6,7,8,1,2,3,5]=>10000000=>00000001
[1,6,7,-3,2,8,4,5]=>00010000=>00001000
[-6,-2,1,3,7,8,4,5]=>11000000=>00000011
[-2,-7,1,8,3,-5,4,6]=>11000100=>00100011
[7,8,1,-3,2,-5,4,6]=>00010100=>00101000
[5,1,7,8,2,-4,3,6]=>00000100=>00100000
[8,-7,2,-4,1,-5,3,6]=>01010100=>00101010
[-4,-6,7,2,1,8,3,5]=>11000000=>00000011
[2,-6,8,3,-7,-4,1,5]=>01001100=>00110010
[-6,2,7,-4,3,5,-8,1]=>10010010=>01001001
[-6,2,-3,7,4,5,-8,1]=>10100010=>01000101
[-6,-2,4,8,-7,-3,1,5]=>11001100=>00110011
[-6,-2,-3,1,7,8,4,5]=>11100000=>00000111
[-2,-7,-3,8,1,-5,4,6]=>11100100=>00100111
[-2,-3,-4,-7,1,8,5,6]=>11110000=>00001111
[3,4,1,-7,2,8,5,6]=>00010000=>00001000
[-2,1,-4,-7,3,8,5,6]=>10110000=>00001101
[-2,1,-4,3,-6,-7,-8,5]=>10101110=>01110101
[3,4,1,2,-6,-7,-8,5]=>00001110=>01110000
[-2,-3,-4,1,-6,-7,-8,5]=>11101110=>01110111
[-2,-3,-7,6,1,-5,-8,4]=>11100110=>01100111
[-2,-7,-3,-6,5,1,-8,4]=>11110010=>01001111
[-2,-6,-3,-8,-7,5,1,4]=>11111000=>00011111
[-2,-5,4,-3,-6,-7,-8,1]=>11011110=>01111011
[-6,5,2,3,-4,-7,-8,1]=>10001110=>01110001
[-8,6,-4,2,-7,5,1,3]=>10101000=>00010101
[7,-8,-4,2,5,1,-6,3]=>01100010=>01000110
[6,2,-7,-4,1,-5,-8,3]=>00110110=>01101100
[5,7,1,6,2,-4,-8,3]=>00000110=>01100000
[-7,6,1,-3,2,-5,-8,4]=>10010110=>01101001
[-2,1,-7,6,3,-5,-8,4]=>10100110=>01100101
[-2,-7,1,-6,5,3,-8,4]=>11010010=>01001011
[7,5,1,-6,-3,2,-8,4]=>00011010=>01011000
[8,7,1,5,-6,2,-4,3]=>00001010=>01010000
[5,6,7,1,4,2,-8,3]=>00000010=>01000000
[4,-7,-5,-6,2,1,-8,3]=>01110010=>01001110
[-8,5,6,-7,2,4,1,3]=>10010000=>00001001
[6,4,-5,2,3,-7,-8,1]=>00100110=>01100100
[5,4,-7,-6,2,3,-8,1]=>00110010=>01001100
[4,-5,-8,-6,-7,2,1,3]=>01111000=>00011110
[7,8,-6,5,1,4,2,3]=>00100000=>00000100
[5,8,6,1,-7,4,2,3]=>00001000=>00010000
[8,1,6,-4,-7,5,2,3]=>00011000=>00011000
[6,5,1,-8,-7,-3,2,4]=>00011100=>00111000
[-2,-6,1,-8,-7,5,3,4]=>11011000=>00011011
[-2,1,-4,-5,-6,-7,-8,3]=>10111110=>01111101
[-5,4,1,-3,-6,-7,-8,2]=>10011110=>01111001
[-5,-6,3,1,-4,-7,-8,2]=>11001110=>01110011
[4,-6,-5,3,1,-7,-8,2]=>01100110=>01100110
[4,-5,-7,-6,3,1,-8,2]=>01110010=>01001110
[4,-5,-6,-8,-7,3,1,2]=>01111000=>00011110
[-2,-3,-4,-5,-6,-7,-8,1]=>11111110=>01111111
[8,-1,6,7,2,3,4,5]=>01000000=>00000010
[6,7,-1,8,2,3,4,5]=>00100000=>00000100
[8,7,6,-1,2,3,4,5]=>00010000=>00001000
[5,7,-1,2,8,3,4,6]=>00100000=>00000100
[8,-1,5,2,7,3,4,6]=>01000000=>00000010
[5,6,7,8,3,1,2,4]=>00000000=>00000000
[5,6,7,8,4,1,2,3]=>00000000=>00000000
[5,6,7,8,1,4,2,3]=>00000000=>00000000
[6,4,2,-1,3,5]=>000100=>001000
[-1,4,2,6,3,5]=>100000=>000001
[4,-1,2,6,3,5]=>010000=>000010
[5,-1,6,2,3,4]=>010000=>000010
[5,4,2,3,7,6,-1,8]=>00000010=>01000000
[6,4,2,7,3,5,-1,8]=>00000010=>01000000
[7,4,2,6,3,5,-1,8]=>00000010=>01000000
[8,4,2,6,3,-1,5,7]=>00000100=>00100000
[-1,4,2,6,3,8,5,7]=>10000000=>00000001
[-1,5,6,2,3,8,4,7]=>10000000=>00000001
[8,5,6,2,3,-1,4,7]=>00000100=>00100000
[7,5,6,2,3,4,-1,8]=>00000010=>01000000
[6,5,7,2,3,4,-1,8]=>00000010=>01000000
[3,2,7,6,4,5,-1,8]=>00000010=>01000000
[4,7,2,6,3,5,-1,8]=>00000010=>01000000
[5,7,6,2,3,4,-1,8]=>00000010=>01000000
[6,7,5,2,3,4,-1,8]=>00000010=>01000000
[7,6,5,2,3,4,-1,8]=>00000010=>01000000
[8,6,5,2,3,-1,4,7]=>00000100=>00100000
[-1,6,5,2,3,8,4,7]=>10000000=>00000001
[-1,7,5,2,8,3,4,6]=>10000000=>00000001
[8,7,5,2,-1,3,4,6]=>00001000=>00010000
[7,8,5,2,-1,3,4,6]=>00001000=>00010000
[6,8,5,2,3,-1,4,7]=>00000100=>00100000
[5,8,6,2,3,-1,4,7]=>00000100=>00100000
[4,8,2,6,3,-1,5,7]=>00000100=>00100000
[3,2,8,6,4,-1,5,7]=>00000100=>00100000
[3,2,-1,6,4,8,5,7]=>00100000=>00000100
[4,-1,2,6,3,8,5,7]=>01000000=>00000010
[5,-1,6,2,3,8,4,7]=>01000000=>00000010
[6,-1,5,2,3,8,4,7]=>01000000=>00000010
[7,-1,5,2,8,3,4,6]=>01000000=>00000010
[-1,8,5,2,7,3,4,6]=>10000000=>00000001
[-1,8,6,7,2,3,4,5]=>10000000=>00000001
[7,-1,6,8,2,3,4,5]=>01000000=>00000010
[6,-1,7,8,2,3,4,5]=>01000000=>00000010
[5,-1,7,2,8,3,4,6]=>01000000=>00000010
[4,-1,2,7,8,3,5,6]=>01000000=>00000010
[3,2,-1,7,8,4,5,6]=>00100000=>00000100
[3,2,8,7,-1,4,5,6]=>00001000=>00010000
[4,8,2,7,-1,3,5,6]=>00001000=>00010000
[5,8,7,2,-1,3,4,6]=>00001000=>00010000
[6,8,7,-1,2,3,4,5]=>00010000=>00001000
[7,8,6,-1,2,3,4,5]=>00010000=>00001000
[-1,7,6,8,2,3,4,5]=>10000000=>00000001
[-1,6,7,8,2,3,4,5]=>10000000=>00000001
[8,6,7,-1,2,3,4,5]=>00010000=>00001000
[7,6,8,-1,2,3,4,5]=>00010000=>00001000
[6,5,8,2,3,-1,4,7]=>00000100=>00100000
[7,5,8,2,-1,3,4,6]=>00001000=>00010000
[8,5,7,2,-1,3,4,6]=>00001000=>00010000
[-1,5,7,2,8,3,4,6]=>10000000=>00000001
[-1,4,2,7,8,3,5,6]=>10000000=>00000001
[8,4,2,7,-1,3,5,6]=>00001000=>00010000
[7,4,2,8,-1,3,5,6]=>00001000=>00010000
[6,4,2,8,3,-1,5,7]=>00000100=>00100000
[5,4,2,3,8,-1,6,7]=>00000100=>00100000
[3,2,5,4,-1,8,6,7]=>00001000=>00010000
[4,5,2,3,-1,8,6,7]=>00001000=>00010000
[5,4,2,3,-1,8,6,7]=>00001000=>00010000
[6,4,2,-1,3,8,5,7]=>00010000=>00001000
[7,4,2,-1,8,3,5,6]=>00010000=>00001000
[8,4,2,-1,7,3,5,6]=>00010000=>00001000
[-1,4,2,8,7,3,5,6]=>10000000=>00000001
[-1,5,8,2,7,3,4,6]=>10000000=>00000001
[8,5,-1,2,7,3,4,6]=>00100000=>00000100
[7,5,-1,2,8,3,4,6]=>00100000=>00000100
[6,5,-1,2,3,8,4,7]=>00100000=>00000100
[5,6,-1,2,3,8,4,7]=>00100000=>00000100
[4,6,2,-1,3,8,5,7]=>00010000=>00001000
[3,2,6,-1,4,8,5,7]=>00010000=>00001000
[3,2,7,-1,8,4,5,6]=>00010000=>00001000
[4,7,2,-1,8,3,5,6]=>00010000=>00001000
[7,6,-1,8,2,3,4,5]=>00100000=>00000100
[8,6,-1,7,2,3,4,5]=>00100000=>00000100
[-1,6,8,7,2,3,4,5]=>10000000=>00000001
[-1,7,8,6,2,3,4,5]=>10000000=>00000001
[8,7,-1,6,2,3,4,5]=>00100000=>00000100
[7,8,-1,6,2,3,4,5]=>00100000=>00000100
[6,8,-1,7,2,3,4,5]=>00100000=>00000100
[5,8,-1,2,7,3,4,6]=>00100000=>00000100
[4,8,2,-1,7,3,5,6]=>00010000=>00001000
[3,2,8,-1,7,4,5,6]=>00010000=>00001000
[3,2,-1,8,7,4,5,6]=>00100000=>00000100
[4,-1,2,8,7,3,5,6]=>01000000=>00000010
[5,-1,8,2,7,3,4,6]=>01000000=>00000010
[6,-1,8,7,2,3,4,5]=>01000000=>00000010
[7,-1,8,6,2,3,4,5]=>01000000=>00000010
[8,-1,7,6,2,3,4,5]=>01000000=>00000010
[-1,8,7,6,2,3,4,5]=>10000000=>00000001
[-3,2,6,-5,1,4]=>100100=>001001
[-6,2,4,-5,-3,1]=>100110=>011001
[6,4,-5,-3,1,2]=>001100=>001100
[3,-5,6,-4,1,2]=>010100=>001010
[2,8,-6,-4,-3,1,5,7]=>00111000=>00011100
[-3,2,8,-6,-5,1,4,7]=>10011000=>00011001
[-8,2,4,-6,-5,-3,1,7]=>10011100=>00111001
[-8,-7,2,4,-5,-3,1,6]=>11001100=>00110011
[8,2,4,6,-7,-5,-3,1]=>00001110=>01110000
[6,8,2,3,-7,-5,-4,1]=>00001110=>01110000
[5,-7,2,3,8,-4,1,6]=>01000100=>00100010
[-8,-6,2,3,-5,-4,1,7]=>11001100=>00110011
[2,-6,8,-5,-4,1,3,7]=>01011000=>00011010
[4,8,-6,-5,-2,1,3,7]=>00111000=>00011100
[8,4,-6,-5,-3,1,2,7]=>00111000=>00011100
[3,-6,8,-5,-4,1,2,7]=>01011000=>00011010
[3,-5,6,8,-4,1,2,7]=>01001000=>00010010
[-8,-6,-3,2,-5,-4,1,7]=>11101100=>00110111
[5,-7,-3,2,8,-4,1,6]=>01100100=>00100110
[3,8,-6,2,-7,-5,-4,1]=>00101110=>01110100
[5,8,-7,-3,2,-6,-4,1]=>00110110=>01101100
[3,8,-7,-4,2,-6,1,5]=>00110100=>00101100
[4,8,-7,-6,3,1,2,5]=>00110000=>00001100
[5,-7,-4,3,8,1,2,6]=>01100000=>00000110
[5,-8,-7,3,-4,1,2,6]=>01101000=>00010110
[4,-7,8,-5,-3,1,2,6]=>01011000=>00011010
[-5,4,8,-7,-2,1,3,6]=>10011000=>00011001
[-8,4,6,-7,-5,-2,1,3]=>10011100=>00111001
[4,-8,6,-7,-5,-3,1,2]=>01011100=>00111010
[-8,6,3,-7,-5,-4,1,2]=>10011100=>00111001
[3,8,-7,6,-5,-4,1,2]=>00101100=>00110100
[3,8,-7,-6,5,-4,1,2]=>00110100=>00101100
[4,8,-7,-6,3,5,1,2]=>00110000=>00001100
[3,8,-7,-6,2,5,-4,1]=>00110010=>01001100
[4,7,8,-6,-3,2,-5,1]=>00011010=>01011000
[3,6,7,8,4,-5,1,2]=>00000100=>00100000
[3,7,8,-6,4,-5,1,2]=>00010100=>00101000
[-5,8,-7,3,-6,-4,1,2]=>10101100=>00110101
[7,8,4,5,-6,-3,1,2]=>00001100=>00110000
[-8,-7,4,5,-6,-2,1,3]=>11001100=>00110011
[-8,-7,2,4,-6,1,3,5]=>11001000=>00010011
[-8,-7,-4,-3,-6,1,2,5]=>11111000=>00011111
[-4,3,-7,8,-6,1,2,5]=>10101000=>00010101
[6,7,8,1,3,-5,2,4]=>00000100=>00100000
[-3,7,8,-6,2,-5,1,4]=>10010100=>00101001
[3,7,8,-6,2,4,-5,1]=>00010010=>01001000
[6,7,8,2,3,4,-5,1]=>00000010=>01000000
[2,7,8,-6,3,-5,1,4]=>00010100=>00101000
[6,7,8,-5,2,1,3,4]=>00010000=>00001000
[5,-8,-7,2,-4,1,3,6]=>01101000=>00010110
[-4,2,-7,8,-6,1,3,5]=>10101000=>00010101
[7,8,-4,2,3,-6,1,5]=>00100100=>00100100
[5,8,-7,2,3,-6,-4,1]=>00100110=>01100100
[8,-7,2,4,5,-6,-3,1]=>01000110=>01100010
[-8,-7,-3,2,4,-6,1,5]=>11100100=>00100111
[3,-8,-7,2,-6,1,4,5]=>01101000=>00010110
[-7,-3,2,8,-5,1,4,6]=>11001000=>00010011
[2,4,7,8,-3,1,5,6]=>00001000=>00010000
[6,8,-7,-4,-2,1,3,5]=>00111000=>00011100
[8,6,-7,-4,-3,1,2,5]=>00111000=>00011100
[-8,2,6,-7,-4,-3,1,5]=>10011100=>00111001
[-8,-3,2,6,-7,-5,1,4]=>11001100=>00110011
[-8,-7,-3,2,5,-6,1,4]=>11100100=>00100111
[-8,-7,-5,-3,2,-6,1,4]=>11110100=>00101111
[5,-8,-7,2,4,-6,-3,1]=>01100110=>01100110
[7,8,-6,2,3,5,-4,1]=>00100010=>01000100
[6,7,8,2,5,-4,1,3]=>00000100=>00100000
[-5,8,-7,2,-6,-4,1,3]=>10101100=>00110101
[-8,6,2,-7,-5,-4,1,3]=>10011100=>00111001
[-6,-8,1,-7,-5,-4,2,3]=>11011100=>00111011
[-8,-6,-3,-7,-5,1,2,4]=>11111000=>00011111
[-8,2,6,-7,-5,1,3,4]=>10011000=>00011001
[-8,-7,2,5,-6,1,3,4]=>11001000=>00010011
[-8,-7,-5,-3,-6,1,2,4]=>11111000=>00011111
[6,7,8,5,-4,1,2,3]=>00001000=>00010000
[6,7,8,1,4,-5,2,3]=>00000100=>00100000
[2,7,8,-6,4,-5,1,3]=>00010100=>00101000
[-4,7,8,-6,2,-5,1,3]=>10010100=>00101001
[4,7,8,-6,2,3,-5,1]=>00010010=>01001000
[4,6,7,8,2,3,-5,1]=>00000010=>01000000
[-6,4,7,8,2,-5,1,3]=>10000100=>00100001
[-4,7,8,-6,1,-5,2,3]=>10010100=>00101001
[7,8,-6,-4,5,1,2,3]=>00110000=>00001100
[8,-7,-6,3,5,1,2,4]=>01100000=>00000110
[-8,-7,-5,2,-6,1,3,4]=>11101000=>00010111
[-8,-7,-5,4,-6,-2,1,3]=>11101100=>00110111
[5,8,-7,4,-6,-3,1,2]=>00101100=>00110100
[6,7,8,3,5,-4,1,2]=>00000100=>00100000
[-4,7,8,-6,3,-5,1,2]=>10010100=>00101001
[-6,4,7,8,3,-5,1,2]=>10000100=>00100001
[4,6,7,8,-5,3,1,2]=>00001000=>00010000
[3,6,7,8,-4,2,-5,1]=>00001010=>01010000
[-5,2,-3,6,1,4]=>101000=>000101
[2,-6,4,-3,-5,1]=>010110=>011010
[4,-6,1,-3,-5,2]=>010110=>011010
[5,6,3,1,-4,2]=>000010=>010000
[2,-4,-3,1,-6,5,-8,7]=>01101010=>01010110
[-5,2,-3,6,1,4,-8,7]=>10100010=>01000101
[2,-6,4,-3,-5,1,-8,7]=>01011010=>01011010
[-7,2,4,-3,-5,8,1,6]=>10011000=>00011001
[2,-8,4,-3,6,-5,-7,1]=>01010110=>01101010
[5,8,2,3,6,-4,-7,1]=>00000110=>01100000
[5,2,7,3,-4,8,1,6]=>00001000=>00010000
[5,6,2,3,-4,1,-8,7]=>00001010=>01010000
[2,-5,-4,6,1,3,-8,7]=>01100010=>01000110
[-2,1,4,-6,-5,3,-8,7]=>10011010=>01011001
[4,-6,1,-3,-5,2,-8,7]=>01011010=>01011010
[5,6,3,1,-4,2,-8,7]=>00001010=>01010000
[5,6,-4,3,1,2,-8,7]=>00100010=>01000100
[3,2,-6,-5,-4,1,-8,7]=>00111010=>01011100
[3,-7,2,-5,-4,8,1,6]=>01011000=>00011010
[3,2,-8,-5,6,-4,-7,1]=>00110110=>01101100
[7,-3,8,-6,2,5,-4,1]=>01010010=>01001010
[-7,3,8,-6,2,-4,1,5]=>10010100=>00101001
[-4,6,7,3,1,8,2,5]=>10000000=>00000001
[-7,3,8,-5,1,-4,2,6]=>10010100=>00101001
[5,3,7,1,-4,8,2,6]=>00001000=>00010000
[-7,4,1,-3,-5,8,2,6]=>10011000=>00011001
[-2,1,-7,4,-5,8,3,6]=>10101000=>00010101
[-2,1,4,-8,6,-5,-7,3]=>10010110=>01101001
[4,-8,1,-3,6,-5,-7,2]=>01010110=>01101010
[5,8,3,1,6,-4,-7,2]=>00000110=>01100000
[3,6,-8,-5,1,-4,-7,2]=>00110110=>01101100
[7,-3,8,-6,5,1,-4,2]=>01010010=>01001010
[7,8,-4,3,-6,5,1,2]=>00101000=>00010100
[3,5,-8,2,-7,-4,-6,1]=>00101110=>01110100
[7,8,3,4,2,-6,-5,1]=>00000110=>01100000
[7,8,-3,-6,4,1,-5,2]=>00110010=>01001100
[1,6,7,8,3,4,-5,2]=>00000010=>01000000
[7,8,3,1,-6,5,-4,2]=>00001010=>01010000
[-7,8,-3,1,4,5,-6,2]=>10100010=>01000101
[-2,-7,1,8,4,5,-6,3]=>11000010=>01000011
[-2,1,4,-7,-6,8,3,5]=>10011000=>00011001
[7,8,1,4,-6,-3,2,5]=>00001100=>00110000
[3,-7,8,-6,1,-4,2,5]=>01010100=>00101010
[3,6,7,8,-5,1,2,4]=>00001000=>00010000
[3,8,-7,-6,-5,2,1,4]=>00111000=>00011100
[7,8,-3,-6,2,4,-5,1]=>00110010=>01001100
[5,6,7,8,3,4,-2,1]=>00000010=>01000000
[2,6,7,8,-5,3,1,4]=>00001000=>00010000
[-6,2,-5,7,1,8,3,4]=>10100000=>00000101
[2,-7,8,-5,1,-4,3,6]=>01010100=>00101010
[-6,2,-4,1,7,8,3,5]=>10100000=>00000101
[2,-7,8,-6,3,-4,1,5]=>01010100=>00101010
[7,8,2,3,-6,5,-4,1]=>00001010=>01010000
[-7,2,-3,8,4,5,-6,1]=>10100010=>01000101
[-7,2,4,8,-6,-3,1,5]=>10001100=>00110001
[6,2,-3,1,7,8,4,5]=>00100000=>00000100
[-7,2,-3,8,1,-5,4,6]=>10100100=>00100101
[2,-4,-3,-7,1,8,5,6]=>01110000=>00001110
[-2,1,-4,3,6,-8,-7,5]=>10100110=>01100101
[3,4,1,2,6,-8,-7,5]=>00000110=>01100000
[2,-4,-3,1,6,-8,-7,5]=>01100110=>01100110
[2,-8,6,-3,1,-5,-7,4]=>01010110=>01101010
[-7,2,-3,8,5,1,-6,4]=>10100010=>01000101
[-7,2,-3,8,-6,5,1,4]=>10101000=>00010101
[2,-8,5,4,-3,-7,-6,1]=>01001110=>01110010
[5,2,-8,3,-7,-4,-6,1]=>00101110=>01110100
[2,-7,-4,8,-6,5,1,3]=>01101000=>00010110
[2,-7,8,-6,5,1,-4,3]=>01010010=>01001010
[6,2,-8,-5,1,-4,-7,3]=>00110110=>01101100
[5,8,6,1,2,-4,-7,3]=>00000110=>01100000
[6,-8,1,-3,2,-5,-7,4]=>01010110=>01101010
[-2,1,6,-8,3,-5,-7,4]=>10010110=>01101001
[-2,-7,1,8,5,3,-6,4]=>11000010=>01000011
[7,8,1,-3,5,2,-6,4]=>00010010=>01001000
[7,8,5,1,-6,2,-4,3]=>00001010=>01010000
[1,6,7,8,4,2,-5,3]=>00000010=>01000000
[2,8,-7,-6,4,1,-5,3]=>00110010=>01001100
[2,6,7,-5,8,4,1,3]=>00010000=>00001000
[7,8,4,2,3,-6,-5,1]=>00000110=>01100000
[7,8,4,-6,2,3,-5,1]=>00010010=>01001000
[2,8,-7,-6,-5,4,1,3]=>00111000=>00011100
[1,6,7,8,-5,4,2,3]=>00001000=>00010000
[7,8,5,-4,-6,1,2,3]=>00011000=>00011000
[7,8,1,-3,-6,5,2,4]=>00011000=>00011000
[-2,-7,1,8,-6,5,3,4]=>11001000=>00010011
[-2,1,5,4,-8,-7,-6,3]=>10001110=>01110001
[5,-8,1,4,-3,-7,-6,2]=>01001110=>01110010
[5,3,-8,1,-7,-4,-6,2]=>00101110=>01110100
[7,8,4,3,1,-6,-5,2]=>00000110=>01100000
[7,8,4,-6,3,1,-5,2]=>00010010=>01001000
[7,8,4,-6,-5,3,1,2]=>00011000=>00011000
[4,3,2,-8,-7,-6,-5,1]=>00011110=>01111000
Map
signs
Description
The binary word recording the signs of a signed permutation.
This map sends a signed permutation $\pi\in\mathfrak H_n$ to the binary word $w$ of length $n$ such that $w_i = 0$ if $\pi(i) > 0$.
This map sends a signed permutation $\pi\in\mathfrak H_n$ to the binary word $w$ of length $n$ such that $w_i = 0$ if $\pi(i) > 0$.
Map
reverse
Description
Return the reversal of a binary word.
searching the database
Sorry, this map was not found in the database.