Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>=> [1,0,1,0]=>[1,2]=>0=>1 [1,1,0,0]=>[2,1]=>1=>0 [1,0,1,0,1,0]=>[1,2,3]=>00=>11 [1,0,1,1,0,0]=>[1,3,2]=>01=>10 [1,1,0,0,1,0]=>[2,1,3]=>10=>01 [1,1,0,1,0,0]=>[2,3,1]=>10=>01 [1,1,1,0,0,0]=>[3,2,1]=>11=>00 [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>000=>111 [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>001=>110 [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>010=>101 [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>010=>101 [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>011=>100 [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>100=>011 [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>101=>010 [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>100=>011 [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>100=>011 [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>101=>010 [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>110=>001 [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>110=>001 [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>110=>001 [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>111=>000 [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>0000=>1111 [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>0001=>1110 [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>0010=>1101 [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>0010=>1101 [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>0011=>1100 [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>0100=>1011 [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>0101=>1010 [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>0100=>1011 [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>0100=>1011 [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>0101=>1010 [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>0110=>1001 [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>0110=>1001 [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>0110=>1001 [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>0111=>1000 [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>1000=>0111 [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>1001=>0110 [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>1010=>0101 [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>1010=>0101 [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>1011=>0100 [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>1000=>0111 [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>1001=>0110 [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>1000=>0111 [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>1000=>0111 [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>1001=>0110 [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>1010=>0101 [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>1010=>0101 [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>1010=>0101 [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>1011=>0100 [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>1100=>0011 [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>1101=>0010 [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>1100=>0011 [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>1100=>0011 [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>1101=>0010 [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>1100=>0011 [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>1100=>0011 [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>1100=>0011 [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>1101=>0010 [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>1110=>0001 [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>1110=>0001 [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>1110=>0001 [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>1110=>0001 [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>1111=>0000 [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>00000=>11111 [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>00001=>11110 [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>00010=>11101 [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>00010=>11101 [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>00011=>11100 [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>00100=>11011 [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>00101=>11010 [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>00100=>11011 [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>00100=>11011 [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>00101=>11010 [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>00110=>11001 [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>00110=>11001 [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>00110=>11001 [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>00111=>11000 [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>01000=>10111 [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>01001=>10110 [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>01010=>10101 [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>01010=>10101 [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>01011=>10100 [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>01000=>10111 [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>01001=>10110 [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>01000=>10111 [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>01000=>10111 [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>01001=>10110 [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>01010=>10101 [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>01010=>10101 [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>01010=>10101 [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>01011=>10100 [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>01100=>10011 [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>01101=>10010 [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>01100=>10011 [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>01100=>10011 [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>01101=>10010 [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>01100=>10011 [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>01100=>10011 [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>01100=>10011 [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>01101=>10010 [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>01110=>10001 [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>01110=>10001 [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>01110=>10001 [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>01110=>10001 [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>01111=>10000 [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>10000=>01111 [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>10001=>01110 [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>10010=>01101 [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>10010=>01101 [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>10011=>01100 [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>10100=>01011 [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>10101=>01010 [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>10100=>01011 [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>10100=>01011 [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>10101=>01010 [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>10110=>01001 [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>10110=>01001 [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>10110=>01001 [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>10111=>01000 [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>10000=>01111 [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>10001=>01110 [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>10010=>01101 [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>10010=>01101 [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>10011=>01100 [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>10000=>01111 [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>10001=>01110 [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>10000=>01111 [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>10000=>01111 [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>10001=>01110 [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>10010=>01101 [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>10010=>01101 [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>10010=>01101 [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>10011=>01100 [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>10100=>01011 [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>10101=>01010 [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>10100=>01011 [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>10100=>01011 [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>10101=>01010 [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>10100=>01011 [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>10100=>01011 [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>10100=>01011 [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>10101=>01010 [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>10110=>01001 [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>10110=>01001 [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>10110=>01001 [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>10110=>01001 [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>10111=>01000 [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>11000=>00111 [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>11001=>00110 [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>11010=>00101 [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>11010=>00101 [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>11011=>00100 [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>11000=>00111 [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>11001=>00110 [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>11000=>00111 [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>11000=>00111 [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>11001=>00110 [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>11010=>00101 [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>11010=>00101 [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>11010=>00101 [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>11011=>00100 [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>11000=>00111 [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>11001=>00110 [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>11000=>00111 [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>11000=>00111 [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>11001=>00110 [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>11000=>00111 [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>11000=>00111 [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>11000=>00111 [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>11001=>00110 [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>11010=>00101 [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>11010=>00101 [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>11010=>00101 [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>11010=>00101 [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>11011=>00100 [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>11100=>00011 [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>11101=>00010 [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>11100=>00011 [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>11100=>00011 [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>11101=>00010 [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>11100=>00011 [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>11100=>00011 [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>11100=>00011 [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>11101=>00010 [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>11100=>00011 [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>11100=>00011 [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>11100=>00011 [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>11100=>00011 [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>11101=>00010 [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>11110=>00001 [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>11110=>00001 [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>11110=>00001 [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>11110=>00001 [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>11110=>00001 [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>11111=>00000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>000000=>111111 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>000001=>111110 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>000010=>111101 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>000010=>111101 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>000011=>111100 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>000100=>111011 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>000101=>111010 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>000100=>111011 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>000100=>111011 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>000101=>111010 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>000110=>111001 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>000110=>111001 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>000110=>111001 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>000111=>111000 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>001000=>110111 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>001001=>110110 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>001010=>110101 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>001010=>110101 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>001011=>110100 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>001000=>110111 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>001001=>110110 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>001000=>110111 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>001000=>110111 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>001001=>110110 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>001010=>110101 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>001010=>110101 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>001010=>110101 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>001011=>110100 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>001100=>110011 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>001101=>110010 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>001100=>110011 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>001100=>110011 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>001101=>110010 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>001100=>110011 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>001100=>110011 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>001100=>110011 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>001101=>110010 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>001110=>110001 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>001110=>110001 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>001110=>110001 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>001110=>110001 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>001111=>110000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>010000=>101111 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>010001=>101110 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>010010=>101101 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>010010=>101101 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>010011=>101100 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>010100=>101011 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>010101=>101010 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>010100=>101011 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>010100=>101011 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>010101=>101010 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>010110=>101001 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>010110=>101001 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>010110=>101001 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>010111=>101000 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>010000=>101111 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>010001=>101110 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>010010=>101101 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>010010=>101101 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>010011=>101100 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>010000=>101111 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>010001=>101110 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>010000=>101111 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>010000=>101111 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>010001=>101110 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>010010=>101101 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>010010=>101101 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>010010=>101101 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>010011=>101100 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>010100=>101011 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>010101=>101010 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>010100=>101011 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>010100=>101011 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>010101=>101010 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>010100=>101011 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>010100=>101011 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>010100=>101011 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>010101=>101010 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>010110=>101001 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>010110=>101001 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>010110=>101001 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>010110=>101001 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>010111=>101000 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>011000=>100111 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>011001=>100110 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>011010=>100101 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>011010=>100101 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>011011=>100100 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>011000=>100111 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>011001=>100110 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>011000=>100111 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>011000=>100111 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>011001=>100110 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>011010=>100101 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>011010=>100101 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>011010=>100101 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>011011=>100100 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>011000=>100111 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>011001=>100110 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>011000=>100111 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>011000=>100111 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>011001=>100110 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>011000=>100111 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>011000=>100111 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>011000=>100111 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>011001=>100110 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>011010=>100101 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>011010=>100101 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>011010=>100101 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>011010=>100101 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>011011=>100100 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>011100=>100011 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>011101=>100010 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>011100=>100011 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>011100=>100011 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>011101=>100010 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>011100=>100011 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>011100=>100011 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>011100=>100011 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>011101=>100010 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>011100=>100011 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>011100=>100011 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>011100=>100011 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>011100=>100011 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>011101=>100010 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>011110=>100001 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>011110=>100001 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>011110=>100001 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>011110=>100001 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>011110=>100001 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>011111=>100000 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>100000=>011111 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>100001=>011110 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>100010=>011101 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>100010=>011101 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>100011=>011100 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>100100=>011011 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>100101=>011010 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>100100=>011011 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>100100=>011011 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>100101=>011010 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>100110=>011001 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>100110=>011001 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>100110=>011001 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>100111=>011000 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>101000=>010111 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>101001=>010110 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>101010=>010101 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>101010=>010101 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>101011=>010100 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>101000=>010111 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>101001=>010110 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>101000=>010111 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>101000=>010111 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>101001=>010110 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>101010=>010101 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>101010=>010101 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>101010=>010101 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>101011=>010100 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>101100=>010011 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>101101=>010010 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>101100=>010011 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>101100=>010011 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>101101=>010010 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>101100=>010011 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>101100=>010011 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>101100=>010011 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>101101=>010010 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>101110=>010001 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>101110=>010001 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>101110=>010001 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>101110=>010001 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>101111=>010000 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>100000=>011111 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>100001=>011110 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>100010=>011101 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>100010=>011101 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>100011=>011100 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>100100=>011011 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>100101=>011010 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>100100=>011011 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>100100=>011011 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>100101=>011010 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>100110=>011001 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>100110=>011001 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>100110=>011001 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>100111=>011000 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>100000=>011111 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>100001=>011110 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>100010=>011101 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>100010=>011101 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>100011=>011100 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>100000=>011111 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>100001=>011110 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>100000=>011111 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>100000=>011111 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>100001=>011110 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>100010=>011101 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>100010=>011101 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>100010=>011101 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>100011=>011100 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>100100=>011011 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>100101=>011010 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>100100=>011011 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>100100=>011011 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>100101=>011010 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>100100=>011011 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>100100=>011011 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>100100=>011011 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>100101=>011010 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>100110=>011001 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>100110=>011001 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>100110=>011001 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>100110=>011001 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>100111=>011000 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>101000=>010111 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>101001=>010110 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>101010=>010101 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>101010=>010101 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>101011=>010100 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>101000=>010111 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>101001=>010110 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>101000=>010111 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>101000=>010111 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>101001=>010110 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>101010=>010101 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>101010=>010101 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>101010=>010101 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>101011=>010100 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>101000=>010111 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>101001=>010110 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>101000=>010111 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>101000=>010111 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>101001=>010110 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>101000=>010111 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>101000=>010111 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>101000=>010111 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>101001=>010110 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>101010=>010101 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>101010=>010101 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>101010=>010101 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>101010=>010101 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>101011=>010100 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>101100=>010011 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>101101=>010010 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>101100=>010011 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>101100=>010011 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>101101=>010010 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>101100=>010011 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>101100=>010011 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>101100=>010011 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>101101=>010010 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>101100=>010011 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>101100=>010011 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>101100=>010011 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>101100=>010011 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>101101=>010010 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>101110=>010001 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>101110=>010001 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>101110=>010001 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>101110=>010001 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>101110=>010001 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>101111=>010000 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>110000=>001111 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>110001=>001110 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>110010=>001101 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>110010=>001101 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>110011=>001100 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>110100=>001011 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>110101=>001010 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>110100=>001011 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>110100=>001011 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>110101=>001010 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>110110=>001001 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>110110=>001001 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>110110=>001001 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>110111=>001000 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>110000=>001111 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>110001=>001110 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>110010=>001101 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>110010=>001101 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>110011=>001100 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>110000=>001111 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>110001=>001110 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>110000=>001111 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>110000=>001111 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>110001=>001110 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>110010=>001101 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>110010=>001101 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>110010=>001101 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>110011=>001100 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>110100=>001011 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>110101=>001010 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>110100=>001011 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>110100=>001011 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>110101=>001010 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>110100=>001011 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>110100=>001011 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>110100=>001011 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>110101=>001010 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>110110=>001001 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>110110=>001001 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>110110=>001001 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>110110=>001001 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>110111=>001000 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>110000=>001111 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>110001=>001110 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>110010=>001101 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>110010=>001101 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>110011=>001100 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>110000=>001111 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>110001=>001110 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>110000=>001111 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>110000=>001111 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>110001=>001110 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>110010=>001101 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>110010=>001101 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>110010=>001101 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>110011=>001100 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>110000=>001111 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>110001=>001110 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>110000=>001111 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>110000=>001111 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>110001=>001110 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>110000=>001111 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>110000=>001111 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>110000=>001111 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>110001=>001110 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>110010=>001101 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>110010=>001101 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>110010=>001101 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>110010=>001101 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>110011=>001100 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>110100=>001011 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>110101=>001010 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>110100=>001011 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>110100=>001011 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>110101=>001010 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>110100=>001011 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>110100=>001011 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>110100=>001011 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>110101=>001010 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>110100=>001011 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>110100=>001011 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>110100=>001011 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>110100=>001011 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>110101=>001010 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>110110=>001001 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>110110=>001001 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>110110=>001001 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>110110=>001001 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>110110=>001001 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>110111=>001000 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>111000=>000111 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>111001=>000110 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>111010=>000101 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>111010=>000101 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>111011=>000100 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>111000=>000111 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>111001=>000110 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>111000=>000111 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>111000=>000111 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>111001=>000110 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>111010=>000101 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>111010=>000101 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>111010=>000101 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>111011=>000100 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>111000=>000111 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>111001=>000110 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>111000=>000111 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>111000=>000111 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>111001=>000110 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>111000=>000111 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>111000=>000111 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>111000=>000111 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>111001=>000110 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>111010=>000101 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>111010=>000101 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>111010=>000101 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>111010=>000101 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>111011=>000100 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>111000=>000111 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>111001=>000110 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>111000=>000111 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>111000=>000111 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>111001=>000110 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>111000=>000111 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>111000=>000111 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>111000=>000111 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>111001=>000110 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>111000=>000111 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>111000=>000111 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>111000=>000111 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>111000=>000111 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>111001=>000110 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>111010=>000101 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>111010=>000101 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>111010=>000101 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>111010=>000101 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>111010=>000101 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>111011=>000100 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>111100=>000011 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>111101=>000010 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>111100=>000011 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>111100=>000011 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>111101=>000010 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>111100=>000011 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>111100=>000011 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>111100=>000011 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>111101=>000010 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>111100=>000011 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>111100=>000011 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>111100=>000011 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>111100=>000011 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>111101=>000010 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>111100=>000011 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>111100=>000011 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>111100=>000011 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>111100=>000011 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>111100=>000011 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>111101=>000010 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>111110=>000001 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>111110=>000001 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>111110=>000001 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>111110=>000001 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>111110=>000001 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>111110=>000001 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>111111=>000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>0000000=>1111111 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>0000001=>1111110 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>0000010=>1111101 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>0000010=>1111101 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>0000011=>1111100 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>0000100=>1111011 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>0000101=>1111010 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>0000100=>1111011 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>0000100=>1111011 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>0000101=>1111010 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>0000110=>1111001 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>0000110=>1111001 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>0000110=>1111001 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>0000111=>1111000 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>0001000=>1110111 [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>0001010=>1110101 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>0001010=>1110101 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>0001011=>1110100 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>0001000=>1110111 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>0001001=>1110110 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>0001000=>1110111 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>0001000=>1110111 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>0001001=>1110110 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>0001010=>1110101 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>0001010=>1110101 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>0001010=>1110101 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>0001011=>1110100 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>0001101=>1110010 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>0001100=>1110011 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>0001100=>1110011 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>0001101=>1110010 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,5,4,8]=>0001100=>1110011 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>0001100=>1110011 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>0001100=>1110011 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>0001101=>1110010 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>0001110=>1110001 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>0001110=>1110001 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>0001110=>1110001 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>0001110=>1110001 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>0001111=>1110000 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>0010000=>1101111 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>0010001=>1101110 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>0010010=>1101101 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>0010100=>1101011 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>0010101=>1101010 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>0010100=>1101011 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>0010100=>1101011 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>0010101=>1101010 [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>0010110=>1101001 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,6,5]=>0010110=>1101001 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>0010111=>1101000 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,4,5,3,7,8,6]=>0010010=>1101101 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>0010011=>1101100 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>0010000=>1101111 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,7,8,6,3]=>0010010=>1101101 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,5,8,7,3]=>0010101=>1101010 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,5,3]=>0010100=>1101011 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,7,5,3]=>0010101=>1101010 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,6,5,8,3]=>0010110=>1101001 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>0010110=>1101001 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>0010111=>1101000 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>0011001=>1100110 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>0011010=>1100101 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>0011000=>1100111 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>0011001=>1100110 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,4,7,8,6,3]=>0011010=>1100101 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>0011011=>1100100 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,4,3,7,8]=>0011000=>1100111 [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,4,7,3,8]=>0011000=>1100111 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,5,6,7,4,3,8]=>0011000=>1100111 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,4,8,3]=>0011000=>1100111 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>0011000=>1100111 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,5,7,6,4,3,8]=>0011010=>1100101 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,6,4,8,3]=>0011010=>1100101 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,6,8,4,3]=>0011010=>1100101 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>0011100=>1100011 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>0011100=>1100011 [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>0011101=>1100010 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,5,7,8,4,3]=>0011100=>1100011 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,5,8,7,4,3]=>0011101=>1100010 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>0011100=>1100011 [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,6,5,8,4,3]=>0011110=>1100001 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>0011111=>1100000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>0100000=>1011111 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>0100010=>1011101 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>0100010=>1011101 [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>0100100=>1011011 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>0100101=>1011010 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>0100100=>1011011 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>0100101=>1011010 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>0100110=>1011001 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>0100110=>1011001 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>0100111=>1011000 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>0101000=>1010111 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>0101010=>1010101 [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>0101010=>1010101 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>0101011=>1010100 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>0101000=>1010111 [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,5,6,7,4,8]=>0101000=>1010111 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,6,4,8]=>0101010=>1010101 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,6,8,4]=>0101010=>1010101 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,6,4]=>0101010=>1010101 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>0101100=>1010011 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>0101100=>1010011 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>0101101=>1010010 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,6,8,7,5,4]=>0101101=>1010010 [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,6,5,8,4]=>0101110=>1010001 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>0101111=>1010000 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>0100000=>1011111 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>0100001=>1011110 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>0100010=>1011101 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>0100010=>1011101 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,7,6]=>0100011=>1011100 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>0100100=>1011011 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>0100100=>1011011 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>0100101=>1011010 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>0100110=>1011001 [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,6,5]=>0100110=>1011001 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>0100111=>1011000 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>0100000=>1011111 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,5,2,6,8,7]=>0100001=>1011110 [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,8]=>0100010=>1011101 [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>0100010=>1011101 [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,5,2,8,7,6]=>0100011=>1011100 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>0100000=>1011111 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,7,6,2]=>0100011=>1011100 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,5,2]=>0100100=>1011011 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>0100110=>1011001 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,7,6,8,5,2]=>0100110=>1011001 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>0100111=>1011000 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,4,2,6,7,8]=>0101000=>1010111 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,4,2,6,8,7]=>0101001=>1010110 [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,4,2,7,6,8]=>0101010=>1010101 [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,4,2,7,8,6]=>0101010=>1010101 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>0101010=>1010101 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,4,7,6,8,2]=>0101010=>1010101 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,4,7,8,6,2]=>0101010=>1010101 [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,4,2,7,8]=>0101000=>1010111 [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,5,6,7,4,2,8]=>0101000=>1010111 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>0101000=>1010111 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,6,4,2,8]=>0101010=>1010101 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,6,4,8,2]=>0101010=>1010101 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,7,6,8,4,2]=>0101010=>1010101 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>0101010=>1010101 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,7,6,4,2]=>0101011=>1010100 [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,6,5,4,2,8,7]=>0101101=>1010010 [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,5,4,7,2,8]=>0101100=>1010011 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>0101101=>1010010 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,5,7,8,4,2]=>0101100=>1010011 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,6,7,8,5,4,2]=>0101100=>1010011 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,6,8,7,5,4,2]=>0101101=>1010010 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>0101111=>1010000 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>0110000=>1001111 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>0110001=>1001110 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>0110010=>1001101 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,3,2,5,7,8,6]=>0110010=>1001101 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>0110011=>1001100 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,3,2,6,7,5,8]=>0110100=>1001011 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>0110100=>1001011 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>0110110=>1001001 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>0110110=>1001001 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>0110111=>1001000 [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,3,5,2,7,6,8]=>0110010=>1001101 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3,5,2,7,8,6]=>0110010=>1001101 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,3,5,7,6,2,8]=>0110010=>1001101 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,3,5,7,8,6,2]=>0110010=>1001101 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>0110011=>1001100 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>0110100=>1001011 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>0110100=>1001011 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,3,6,5,7,8,2]=>0110100=>1001011 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>0110101=>1001010 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,6,8,7,5,2]=>0110101=>1001010 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,3,7,6,8,5,2]=>0110110=>1001001 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,7,8,6,5,2]=>0110110=>1001001 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>0110111=>1001000 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,6,3,2,7,8]=>0110000=>1001111 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,7,8,6,3,2]=>0110010=>1001101 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,4,6,5,3,2,7,8]=>0110100=>1001011 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,5,3,8,7,2]=>0110101=>1001010 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,5,7,3,2,8]=>0110100=>1001011 [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,5,8,7,3,2]=>0110101=>1001010 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,4,6,7,8,5,3,2]=>0110100=>1001011 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,7,5,3,2]=>0110101=>1001010 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,4,7,6,5,8,3,2]=>0110110=>1001001 [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,4,7,8,6,5,3,2]=>0110110=>1001001 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>0110111=>1001000 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>0111000=>1000111 [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,5,4,3,6,7,2,8]=>0111000=>1000111 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>0111000=>1000111 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>0111001=>1000110 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,4,3,8,7,6,2]=>0111011=>1000100 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,4,6,3,2,7,8]=>0111000=>1000111 [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,4,6,3,2,8,7]=>0111001=>1000110 [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,4,6,3,7,2,8]=>0111000=>1000111 [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,3,2]=>0111000=>1000111 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,4,6,8,7,3,2]=>0111001=>1000110 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,4,7,8,6,3,2]=>0111010=>1000101 [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,6,4,3,2,7,8]=>0111000=>1000111 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,4,3,8,7,2]=>0111001=>1000110 [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,5,6,7,4,3,2,8]=>0111000=>1000111 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>0111000=>1000111 [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,6,8,4,3,2]=>0111010=>1000101 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>0111101=>1000010 [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,6,5,4,7,8,3,2]=>0111100=>1000011 [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,4,3,2]=>0111100=>1000011 [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,5,4,3,8,2]=>0111100=>1000011 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,5,8,4,3,2]=>0111100=>1000011 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>0111100=>1000011 [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>0111101=>1000010 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>0111110=>1000001 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>0111110=>1000001 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>0111110=>1000001 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>0111111=>1000000 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>1000000=>0111111 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>1000001=>0111110 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>1000100=>0111011 [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>1000101=>0111010 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>1000100=>0111011 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>1000110=>0111001 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>1000111=>0111000 [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>1001001=>0110110 [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>1001011=>0110100 [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>1001101=>0110010 [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,5,4,8]=>1001100=>0110011 [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,6,8,7,5,4]=>1001101=>0110010 [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,3,7,8,6,5,4]=>1001110=>0110001 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>1001111=>0110000 [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>1010000=>0101111 [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>1010001=>0101110 [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>1010100=>0101011 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>1010101=>0101010 [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,3,6,7,5,8]=>1010100=>0101011 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>1010100=>0101011 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>1010101=>0101010 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>1010110=>0101001 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>1010110=>0101001 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>1010111=>0101000 [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>1010001=>0101110 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>1010001=>0101110 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>1010000=>0101111 [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>1010001=>0101110 [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,6,3]=>1010010=>0101101 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>1010011=>0101100 [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>1010100=>0101011 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>1010101=>0101010 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>1010101=>0101010 [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,5,3,8]=>1010100=>0101011 [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,5,8,3]=>1010100=>0101011 [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,4,6,7,8,5,3]=>1010100=>0101011 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,7,5,3]=>1010101=>0101010 [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>1010110=>0101001 [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,6,5,3]=>1010110=>0101001 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>1010111=>0101000 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>1011001=>0100110 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>1011001=>0100110 [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>1011010=>0100101 [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,6,4,3,7,8]=>1011000=>0100111 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>1011001=>0100110 [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,4,7,8,3]=>1011000=>0100111 [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,4,3,8]=>1011000=>0100111 [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,4,8,3]=>1011000=>0100111 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>1011000=>0100111 [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,6,4,8,3]=>1011010=>0100101 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,6,4,3]=>1011010=>0100101 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>1011101=>0100010 [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>1011100=>0100011 [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>1011100=>0100011 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>1011101=>0100010 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>1011100=>0100011 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>1011100=>0100011 [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,6,8,7,5,4,3]=>1011101=>0100010 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>1011110=>0100001 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,6,8,5,4,3]=>1011110=>0100001 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,6,5,4,3]=>1011110=>0100001 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>1011111=>0100000 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>1000000=>0111111 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>1000010=>0111101 [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>1000100=>0111011 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>1000100=>0111011 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>1000110=>0111001 [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,6,5]=>1000110=>0111001 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>1000111=>0111000 [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>1001010=>0110101 [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>1001000=>0110111 [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>1001000=>0110111 [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>1001101=>0110010 [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>1001100=>0110011 [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>1001101=>0110010 [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,6,7,5,4,8]=>1001100=>0110011 [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,5,4]=>1001100=>0110011 [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,7,5,4]=>1001101=>0110010 [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,6,8,5,4]=>1001110=>0110001 [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>1001111=>0110000 [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>1000000=>0111111 [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>1000001=>0111110 [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>1000010=>0111101 [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>1000010=>0111101 [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>1000011=>0111100 [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>1000100=>0111011 [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>1000101=>0111010 [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>1000100=>0111011 [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>1000100=>0111011 [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>1000101=>0111010 [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>1000110=>0111001 [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>1000110=>0111001 [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>1000110=>0111001 [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>1000111=>0111000 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>1000000=>0111111 [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>1000011=>0111100 [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>1000001=>0111110 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>1000000=>0111111 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>1000001=>0111110 [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>1000010=>0111101 [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>1000011=>0111100 [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>1000100=>0111011 [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>1000101=>0111010 [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]=>1000100=>0111011 [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>1000110=>0111001 [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>1000110=>0111001 [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>1000111=>0111000 [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>1001000=>0110111 [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>1001011=>0110100 [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>1001000=>0110111 [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>1001010=>0110101 [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>1001011=>0110100 [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,4,1,8,7]=>1001001=>0110110 [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]=>1001000=>0110111 [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,5,6,7,4,1,8]=>1001000=>0110111 [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>1001000=>0110111 [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,5,7,6,4,1,8]=>1001010=>0110101 [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]=>1001010=>0110101 [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,8,7,6,4,1]=>1001011=>0110100 [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>1001101=>0110010 [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]=>1001100=>0110011 [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,6,5,7,4,1,8]=>1001100=>0110011 [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,6,7,5,4,1,8]=>1001100=>0110011 [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,5,4,1]=>1001100=>0110011 [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>1001110=>0110001 [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>1001110=>0110001 [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,6,5,8,4,1]=>1001110=>0110001 [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>1001111=>0110000 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>1010000=>0101111 [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>1010101=>0101010 [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>1010100=>0101011 [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>1010101=>0101010 [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>1010110=>0101001 [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>1010111=>0101000 [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>1010000=>0101111 [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>1010010=>0101101 [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,3,5,1,7,8,6]=>1010010=>0101101 [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>1010011=>0101100 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>1010000=>0101111 [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>1010001=>0101110 [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>1010010=>0101101 [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,4,3,5,8,7,6,1]=>1010011=>0101100 [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>1010101=>0101010 [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>1010100=>0101011 [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>1010100=>0101011 [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>1010101=>0101010 [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,3,6,8,7,5,1]=>1010101=>0101010 [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>1010110=>0101001 [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>1010111=>0101000 [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,4,5,3,1,6,7,8]=>1010000=>0101111 [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,4,5,3,1,6,8,7]=>1010001=>0101110 [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,4,5,3,1,7,6,8]=>1010010=>0101101 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>1010011=>0101100 [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,4,5,3,6,1,8,7]=>1010001=>0101110 [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]=>1010000=>0101111 [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,3,8,7,6,1]=>1010011=>0101100 [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,3,1,7,8]=>1010000=>0101111 [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,3,8,1]=>1010000=>0101111 [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,6,3,1]=>1010010=>0101101 [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,4,6,5,3,1,7,8]=>1010100=>0101011 [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,5,3,1,8,7]=>1010101=>0101010 [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,5,3,8,7,1]=>1010101=>0101010 [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]=>1010100=>0101011 [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,5,8,7,3,1]=>1010101=>0101010 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,5,3,1,8]=>1010100=>0101011 [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,5,3,1]=>1010100=>0101011 [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>1010101=>0101010 [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,6,5,8,3,1]=>1010110=>0101001 [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>1010111=>0101000 [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>1011000=>0100111 [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,5,4,3,1,6,8,7]=>1011001=>0100110 [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,5,4,3,1,7,6,8]=>1011010=>0100101 [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,4,3,1,7,8,6]=>1011010=>0100101 [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>1011011=>0100100 [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,4,3,6,1,8,7]=>1011001=>0100110 [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>1011000=>0100111 [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>1011000=>0100111 [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>1011001=>0100110 [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>1011010=>0100101 [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>1011010=>0100101 [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>1011011=>0100100 [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,4,6,3,7,1,8]=>1011000=>0100111 [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,4,6,3,7,8,1]=>1011000=>0100111 [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]=>1011010=>0100101 [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,4,8,7,6,3,1]=>1011011=>0100100 [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,5,6,4,3,1,8,7]=>1011001=>0100110 [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,4,8,7,3,1]=>1011001=>0100110 [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,5,6,7,4,3,1,8]=>1011000=>0100111 [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>1011000=>0100111 [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,6,5,4,3,1,8,7]=>1011101=>0100010 [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>1011100=>0100011 [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,6,5,4,3,8,7,1]=>1011101=>0100010 [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,3,1]=>1011100=>0100011 [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,6,7,5,4,8,3,1]=>1011100=>0100011 [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>1011110=>0100001 [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,6,8,5,4,3,1]=>1011110=>0100001 [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>1011111=>0100000 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>1100000=>0011111 [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>1100010=>0011101 [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>1100011=>0011100 [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>1100100=>0011011 [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>1100101=>0011010 [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>1100110=>0011001 [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>1100110=>0011001 [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,7,8,6,5]=>1100110=>0011001 [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>1100111=>0011000 [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>1101010=>0010101 [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>1101000=>0010111 [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,5,6,7,4,8]=>1101000=>0010111 [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>1101000=>0010111 [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>1101001=>0010110 [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>1101010=>0010101 [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>1101010=>0010101 [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>1101010=>0010101 [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>1101011=>0010100 [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,2,1,6,5,7,4,8]=>1101100=>0010011 [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>1101100=>0010011 [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>1101101=>0010010 [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>1101100=>0010011 [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,6,7,8,5,4]=>1101100=>0010011 [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>1101101=>0010010 [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>1101110=>0010001 [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>1101110=>0010001 [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>1101110=>0010001 [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>1101111=>0010000 [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>1100000=>0011111 [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>1100001=>0011110 [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>1100010=>0011101 [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>1100010=>0011101 [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>1100011=>0011100 [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>1100100=>0011011 [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>1100101=>0011010 [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>1100100=>0011011 [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>1100100=>0011011 [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>1100101=>0011010 [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>1100110=>0011001 [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>1100110=>0011001 [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>1100110=>0011001 [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>1100111=>0011000 [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>1100000=>0011111 [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>1100011=>0011100 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>1100000=>0011111 [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>1100010=>0011101 [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,2,4,6,7,5,1,8]=>1100100=>0011011 [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>1100110=>0011001 [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>1100111=>0011000 [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>1101000=>0010111 [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,5,4,1,6,8,7]=>1101001=>0010110 [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>1101010=>0010101 [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>1101010=>0010101 [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>1101011=>0010100 [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,5,4,6,7,8,1]=>1101000=>0010111 [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>1101010=>0010101 [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>1101010=>0010101 [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]=>1101000=>0010111 [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,5,7,6,4,1,8]=>1101010=>0010101 [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,5,7,6,8,4,1]=>1101010=>0010101 [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,2,6,5,4,7,1,8]=>1101100=>0010011 [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>1101100=>0010011 [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]=>1101100=>0010011 [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,6,8,7,5,4,1]=>1101101=>0010010 [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>1101110=>0010001 [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>1101111=>0010000 [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8]=>1100000=>0011111 [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,4,2,1,5,8,7,6]=>1100011=>0011100 [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>1100101=>0011010 [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>1100100=>0011011 [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>1100101=>0011010 [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>1100110=>0011001 [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>1100110=>0011001 [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>1100111=>0011000 [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8]=>1100000=>0011111 [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,2,5,1,7,6,8]=>1100010=>0011101 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,2,5,1,7,8,6]=>1100010=>0011101 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>1100011=>0011100 [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,4,2,5,6,1,8,7]=>1100001=>0011110 [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>1100000=>0011111 [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,8,7,1]=>1100001=>0011110 [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,2,6,5,7,1,8]=>1100100=>0011011 [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,2,6,5,7,8,1]=>1100100=>0011011 [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,8,7,1]=>1100101=>0011010 [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,2,7,6,5,8,1]=>1100110=>0011001 [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,4,2,7,8,6,5,1]=>1100110=>0011001 [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>1100111=>0011000 [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8]=>1100000=>0011111 [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,5,2,1,7,8,6]=>1100010=>0011101 [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>1100011=>0011100 [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,2,6,1,8,7]=>1100001=>0011110 [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,2,1,7,8]=>1100000=>0011111 [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,2,1,8,7]=>1100001=>0011110 [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,2,7,1,8]=>1100000=>0011111 [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]=>1100000=>0011111 [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]=>1100010=>0011101 [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,5,2,7,1,8]=>1100100=>0011011 [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,5,7,8,2,1]=>1100100=>0011011 [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,5,2,1]=>1100100=>0011011 [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,6,5,2,1,8]=>1100110=>0011001 [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,6,5,2,8,1]=>1100110=>0011001 [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,7,6,5,8,2,1]=>1100110=>0011001 [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>1100111=>0011000 [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,4,2,1,6,7,8]=>1101000=>0010111 [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,4,2,1,6,8,7]=>1101001=>0010110 [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,4,2,1,7,6,8]=>1101010=>0010101 [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,4,2,1,7,8,6]=>1101010=>0010101 [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>1101011=>0010100 [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,5,4,2,6,1,7,8]=>1101000=>0010111 [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,5,4,2,6,1,8,7]=>1101001=>0010110 [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>1101000=>0010111 [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,4,2,6,7,8,1]=>1101000=>0010111 [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,4,2,7,6,1,8]=>1101010=>0010101 [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,4,6,2,7,1,8]=>1101000=>0010111 [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,4,6,7,2,8,1]=>1101000=>0010111 [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,5,4,7,6,2,1,8]=>1101010=>0010101 [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,4,2,1,8,7]=>1101001=>0010110 [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,4,2,7,8,1]=>1101000=>0010111 [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,4,2,8,7,1]=>1101001=>0010110 [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]=>1101000=>0010111 [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,5,6,7,4,2,1,8]=>1101000=>0010111 [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>1101000=>0010111 [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>1101000=>0010111 [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,7,4,2,1]=>1101001=>0010110 [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,6,4,2,1,8]=>1101010=>0010101 [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,6,4,2,8,1]=>1101010=>0010101 [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]=>1101010=>0010101 [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>1101011=>0010100 [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,6,5,4,2,1,7,8]=>1101100=>0010011 [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>1101101=>0010010 [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,6,5,4,2,7,1,8]=>1101100=>0010011 [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,5,4,2,7,8,1]=>1101100=>0010011 [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,6,5,4,2,8,7,1]=>1101101=>0010010 [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]=>1101100=>0010011 [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,5,8,4,2,1]=>1101100=>0010011 [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,6,5,8,4,2,1]=>1101110=>0010001 [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]=>1101111=>0010000 [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>1110000=>0001111 [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>1110001=>0001110 [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>1110010=>0001101 [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>1110010=>0001101 [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>1110011=>0001100 [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>1110100=>0001011 [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>1110101=>0001010 [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>1110100=>0001011 [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>1110100=>0001011 [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>1110101=>0001010 [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>1110110=>0001001 [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>1110110=>0001001 [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>1110110=>0001001 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>1110111=>0001000 [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>1110000=>0001111 [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>1110011=>0001100 [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>1110000=>0001111 [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]=>1110001=>0001110 [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,3,2,5,7,6,1,8]=>1110010=>0001101 [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,3,2,5,7,6,8,1]=>1110010=>0001101 [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>1110011=>0001100 [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,3,2,6,5,1,7,8]=>1110100=>0001011 [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>1110100=>0001011 [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]=>1110101=>0001010 [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,6,7,5,8,1]=>1110100=>0001011 [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,3,2,6,8,7,5,1]=>1110101=>0001010 [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>1110110=>0001001 [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,7,8,6,5,1]=>1110110=>0001001 [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>1110111=>0001000 [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,3,5,2,1,6,7,8]=>1110000=>0001111 [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>1110011=>0001100 [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>1110001=>0001110 [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]=>1110000=>0001111 [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,3,5,2,8,7,6,1]=>1110011=>0001100 [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,8,7,2,1]=>1110001=>0001110 [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,3,5,7,6,2,1,8]=>1110010=>0001101 [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,3,5,7,6,8,2,1]=>1110010=>0001101 [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,7,8,6,2,1]=>1110010=>0001101 [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,3,6,5,2,1,7,8]=>1110100=>0001011 [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,3,6,5,2,1,8,7]=>1110101=>0001010 [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>1110101=>0001010 [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>1110101=>0001010 [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,6,7,5,2,8,1]=>1110100=>0001011 [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,5,2,1]=>1110100=>0001011 [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,7,6,5,2,8,1]=>1110110=>0001001 [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8]=>1110000=>0001111 [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,3,2,1,6,8,7]=>1110001=>0001110 [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,5,3,2,1,7,6,8]=>1110010=>0001101 [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>1110011=>0001100 [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,5,3,2,6,1,7,8]=>1110000=>0001111 [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,3,2,6,1,8,7]=>1110001=>0001110 [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,3,2,7,6,1,8]=>1110010=>0001101 [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,3,2,8,7,6,1]=>1110011=>0001100 [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>1110001=>0001110 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>1110000=>0001111 [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,6,8,7,2,1]=>1110001=>0001110 [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,3,7,6,2,1,8]=>1110010=>0001101 [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,3,7,6,8,2,1]=>1110010=>0001101 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,3,7,8,6,2,1]=>1110010=>0001101 [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,6,3,2,1,7,8]=>1110000=>0001111 [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>1110001=>0001110 [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,3,2,8,7,1]=>1110001=>0001110 [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>1110000=>0001111 [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,3,8,7,2,1]=>1110001=>0001110 [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>1110000=>0001111 [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>1110000=>0001111 [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>1110000=>0001111 [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>1110000=>0001111 [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,7,3,2,1]=>1110001=>0001110 [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,5,7,6,3,2,1,8]=>1110010=>0001101 [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,6,8,3,2,1]=>1110010=>0001101 [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,6,3,2,1]=>1110010=>0001101 [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]=>1110011=>0001100 [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,6,5,3,2,1,8,7]=>1110101=>0001010 [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,5,3,2,8,7,1]=>1110101=>0001010 [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,5,3,7,2,8,1]=>1110100=>0001011 [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,6,5,7,3,2,1,8]=>1110100=>0001011 [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,5,7,3,2,8,1]=>1110100=>0001011 [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,3,2,1]=>1110100=>0001011 [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]=>1110101=>0001010 [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,6,7,5,3,2,1,8]=>1110100=>0001011 [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,5,8,3,2,1]=>1110100=>0001011 [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,5,3,2,1]=>1110100=>0001011 [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>1110101=>0001010 [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>1110110=>0001001 [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,6,5,3,2,8,1]=>1110110=>0001001 [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,6,5,3,8,2,1]=>1110110=>0001001 [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>1110110=>0001001 [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,6,8,5,3,2,1]=>1110110=>0001001 [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,6,5,3,2,1]=>1110110=>0001001 [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>1110111=>0001000 [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>1111000=>0000111 [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>1111001=>0000110 [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>1111010=>0000101 [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>1111010=>0000101 [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>1111011=>0000100 [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>1111000=>0000111 [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>1111001=>0000110 [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>1111000=>0000111 [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>1111000=>0000111 [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>1111001=>0000110 [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>1111010=>0000101 [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>1111010=>0000101 [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>1111010=>0000101 [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>1111011=>0000100 [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,4,3,6,2,1,7,8]=>1111000=>0000111 [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,4,3,6,2,1,8,7]=>1111001=>0000110 [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,4,3,6,2,7,1,8]=>1111000=>0000111 [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,1]=>1111000=>0000111 [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,4,3,6,2,8,7,1]=>1111001=>0000110 [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,4,3,6,7,2,1,8]=>1111000=>0000111 [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,4,3,6,7,2,8,1]=>1111000=>0000111 [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,4,3,6,8,7,2,1]=>1111001=>0000110 [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,4,3,7,6,2,8,1]=>1111010=>0000101 [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,3,7,8,6,2,1]=>1111010=>0000101 [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,4,6,3,2,1,7,8]=>1111000=>0000111 [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,4,6,3,2,1,8,7]=>1111001=>0000110 [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,4,6,3,2,7,1,8]=>1111000=>0000111 [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,4,6,3,2,7,8,1]=>1111000=>0000111 [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,4,6,3,2,8,7,1]=>1111001=>0000110 [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,4,6,3,7,2,1,8]=>1111000=>0000111 [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>1111000=>0000111 [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>1111000=>0000111 [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>1111000=>0000111 [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,4,7,6,8,3,2,1]=>1111010=>0000101 [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,4,3,2,1,7,8]=>1111000=>0000111 [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,6,4,3,2,1,8,7]=>1111001=>0000110 [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,6,4,7,3,2,1,8]=>1111000=>0000111 [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>1111000=>0000111 [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>1111000=>0000111 [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>1111000=>0000111 [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>1111000=>0000111 [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]=>1111001=>0000110 [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>1111010=>0000101 [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]=>1111010=>0000101 [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,6,4,8,3,2,1]=>1111010=>0000101 [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>1111010=>0000101 [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]=>1111010=>0000101 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>1111011=>0000100 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>1111101=>0000010 [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>1111100=>0000011 [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>1111101=>0000010 [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,5,4,3,7,2,1,8]=>1111100=>0000011 [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>1111100=>0000011 [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>1111100=>0000011 [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>1111100=>0000011 [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]=>1111100=>0000011 [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>1111100=>0000011 [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>1111100=>0000011 [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>1111100=>0000011 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>1111101=>0000010 [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>1111100=>0000011 [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,5,4,8,3,2,1]=>1111100=>0000011 [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>1111100=>0000011 [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>1111100=>0000011 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>1111101=>0000010 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>1111110=>0000001 [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>1111110=>0000001 [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>1111110=>0000001 [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>1111110=>0000001 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>1111110=>0000001 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>1111110=>0000001 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>1111111=>0000000 [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5,10,9,8,7,6]=>000001111=>111110000 [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>111110000=>000001111 [1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,1,7,8,9,10,6,5,4,3]=>101111000=>010000111
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.