Identifier
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=> [1,0,1,0]=>[1,2]=>1 [1,1,0,0]=>[2,1]=>0 [1,0,1,0,1,0]=>[1,2,3]=>11 [1,0,1,1,0,0]=>[1,3,2]=>10 [1,1,0,0,1,0]=>[2,1,3]=>01 [1,1,0,1,0,0]=>[2,3,1]=>00 [1,1,1,0,0,0]=>[3,2,1]=>00 [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>111 [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>110 [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>101 [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>100 [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>100 [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>011 [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>010 [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>001 [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>000 [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>000 [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>001 [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>000 [1,1,1,0,1,0,0,0]=>[4,2,3,1]=>000 [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>000 [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>1111 [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>1110 [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>1101 [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>1100 [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>1100 [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>1011 [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>1010 [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>1001 [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>1000 [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>1000 [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>1001 [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>1000 [1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>1000 [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>1000 [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>0111 [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>0110 [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>0101 [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>0100 [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>0100 [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>0011 [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>0010 [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>0001 [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>0000 [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>0000 [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>0001 [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>0000 [1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>0000 [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>0000 [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>0011 [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>0010 [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>0001 [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>0000 [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>0000 [1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>0001 [1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>0000 [1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>0000 [1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>0000 [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>0001 [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>0000 [1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>0000 [1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>0000 [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>0000 [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>11111 [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>11110 [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>11101 [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>11100 [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>11100 [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>11011 [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>11010 [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>11001 [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>11000 [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>11000 [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>11001 [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>11000 [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>11000 [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>11000 [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>10111 [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>10110 [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>10101 [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>10100 [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>10100 [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>10011 [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>10010 [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>10001 [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>10000 [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>10000 [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>10001 [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>10000 [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>10000 [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>10000 [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>10011 [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>10010 [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>10001 [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>10000 [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>10000 [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>10001 [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>10000 [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>10000 [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>10000 [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>10001 [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>10000 [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>10000 [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>10000 [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>10000 [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>01111 [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>01110 [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>01101 [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>01100 [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>01100 [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>01011 [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>01010 [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>01001 [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>01000 [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>01000 [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>01001 [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>01000 [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>01000 [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>01000 [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>00111 [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>00110 [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>00101 [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>00100 [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>00100 [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>00011 [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>00010 [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>00001 [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>00000 [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>00000 [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>00001 [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>00000 [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>00000 [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>00000 [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>00011 [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>00010 [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>00001 [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>00000 [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>00000 [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>00001 [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>00000 [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>00000 [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>00000 [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>00001 [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>00000 [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>00000 [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>00000 [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>00000 [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>00111 [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>00110 [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>00101 [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>00100 [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>00100 [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>00011 [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>00010 [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>00001 [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>00000 [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>00000 [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>00001 [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>00000 [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>00000 [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>00000 [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>00011 [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>00010 [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>00001 [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>00000 [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>00000 [1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>00001 [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>00000 [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>00000 [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>00000 [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>00001 [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>00000 [1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>00000 [1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>00000 [1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>00000 [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>00011 [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>00010 [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>00001 [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>00000 [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>00000 [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>00001 [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>00000 [1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>00000 [1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>00000 [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>00001 [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>00000 [1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>00000 [1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>00000 [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>00000 [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>00001 [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>00000 [1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>00000 [1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>00000 [1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>00000 [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>00000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>111111 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>111110 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>111101 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>111100 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>111100 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>111011 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>111010 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>111001 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>111000 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>111000 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>111001 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>111000 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>111000 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>111000 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>110111 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>110110 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>110101 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>110100 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>110100 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>110011 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>110010 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>110001 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>110000 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>110000 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>110001 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>110000 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>110000 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>110000 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>110011 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>110010 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>110001 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>110000 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>110000 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>110001 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>110000 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>110000 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>110000 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>110001 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>110000 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>110000 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>110000 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>110000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>101111 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>101110 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>101101 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>101100 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>101100 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>101011 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>101010 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>101001 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>101000 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>101000 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>101001 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>101000 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>101000 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>101000 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>100111 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>100110 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>100101 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>100100 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>100100 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>100011 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>100010 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>100001 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>100000 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>100000 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>100001 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>100000 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>100000 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>100000 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>100011 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>100010 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>100001 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>100000 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>100000 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>100001 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>100000 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>100000 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>100000 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>100001 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>100000 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>100000 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>100000 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>100000 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>100111 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>100110 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>100101 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>100100 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>100100 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>100011 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>100010 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>100001 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>100000 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>100000 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>100001 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>100000 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>100000 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>100000 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>100011 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>100010 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>100001 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>100000 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>100000 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>100001 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>100000 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>100000 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>100000 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>100001 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>100000 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>100000 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>100000 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>100000 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>100011 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>100010 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>100001 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>100000 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>100000 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>100001 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>100000 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>100000 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>100000 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>100001 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>100000 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>100000 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>100000 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>100000 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>100001 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>100000 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>100000 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>100000 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>100000 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>100000 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>011111 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>011110 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>011101 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>011100 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>011100 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>011011 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>011010 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>011001 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>011000 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>011000 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>011001 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>011000 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>011000 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>011000 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>010111 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>010110 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>010101 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>010100 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>010100 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>010011 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>010010 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>010001 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>010000 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>010000 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>010001 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>010000 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>010000 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>010000 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>010011 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>010010 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>010001 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>010000 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>010000 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>010001 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>010000 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>010000 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>010000 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>010001 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>010000 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>010000 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>010000 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>010000 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>001111 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>001110 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>001101 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>001100 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>001100 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>001011 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>001010 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>001001 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>001000 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>001000 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>001001 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>001000 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>001000 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>001000 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>000111 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>000110 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>000101 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>000100 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>000100 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>000011 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>000010 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>000001 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>000000 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>000000 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>000001 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>000000 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>000000 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>000000 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>000011 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>000010 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>000001 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>000000 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>000000 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>000001 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>000000 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>000000 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>000000 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>000001 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>000000 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>000000 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>000000 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>000000 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>000111 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>000110 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>000101 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>000100 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>000100 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>000011 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>000010 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>000001 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>000000 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>000000 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>000001 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>000000 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>000000 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>000000 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>000011 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>000010 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>000001 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>000000 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>000000 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>000001 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>000000 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>000000 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>000000 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>000001 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>000000 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>000000 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>000000 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>000000 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>000011 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>000010 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>000001 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>000000 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>000000 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>000001 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>000000 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>000000 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>000000 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>000001 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>000000 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>000000 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>000000 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>000000 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>000001 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>000000 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>000000 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>000000 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>000000 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>000000 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>001111 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>001110 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>001101 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>001100 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>001100 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>001011 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>001010 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>001001 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>001000 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>001000 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>001001 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>001000 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>001000 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>001000 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>000111 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>000110 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>000101 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>000100 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>000100 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>000011 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>000010 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>000001 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>000000 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>000000 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>000001 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>000000 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>000000 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>000000 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>000011 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>000010 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>000001 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>000000 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>000000 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>000001 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>000000 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>000000 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>000000 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>000001 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>000000 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>000000 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>000000 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>000000 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>000111 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>000110 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>000101 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>000100 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>000100 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>000011 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>000010 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>000001 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>000000 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>000000 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>000001 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>000000 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>000000 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>000000 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>000011 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>000010 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>000001 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>000000 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>000000 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>000001 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>000000 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>000000 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>000000 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>000001 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>000000 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>000000 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>000000 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>000000 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>000011 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>000010 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>000001 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>000000 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>000000 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>000001 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>000000 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>000000 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>000000 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>000001 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>000000 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>000000 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>000000 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>000000 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>000001 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>000000 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>000000 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>000000 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>000000 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>000000 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>000111 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>000110 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>000101 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>000100 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>000100 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>000011 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>000010 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>000001 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>000000 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>000000 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>000001 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>000000 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>000000 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>000000 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>000011 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>000010 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>000001 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>000000 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>000000 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>000001 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>000000 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>000000 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>000000 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>000001 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>000000 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>000000 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>000000 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>000000 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>000011 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>000010 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>000001 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>000000 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>000000 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>000001 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>000000 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>000000 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>000000 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>000001 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>000000 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>000000 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>000000 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>000000 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>000001 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>000000 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>000000 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>000000 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>000000 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>000000 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>000011 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>000010 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>000001 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>000000 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>000000 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>000001 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>000000 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>000000 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>000000 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>000001 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>000000 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>000000 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>000000 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>000000 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>000001 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>000000 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>000000 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>000000 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>000000 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>000000 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>000001 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>000000 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>000000 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>000000 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>000000 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>000000 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>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]=>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]=>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]=>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]=>1111100 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>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]=>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]=>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]=>1111001 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>1111000 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>1111000 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>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]=>1111000 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,8,6,7,5]=>1111000 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>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]=>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]=>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]=>1110100 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>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]=>1110011 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>1110010 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>1110001 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>1110000 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>1110000 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>1110001 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>1110000 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,8,6,7,4]=>1110000 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>1110000 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>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]=>1110001 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>1110000 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>1110000 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,7,5,6,4,8]=>1110001 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,7,5,6,8,4]=>1110000 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,8,5,6,7,4]=>1110000 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,8,5,7,6,4]=>1110000 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>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]=>1110000 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,8,6,5,7,4]=>1110000 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,8,6,7,5,4]=>1110000 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>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]=>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]=>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]=>1101100 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>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]=>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]=>1101001 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>1101000 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>1101000 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>1101000 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>1100100 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>1100011 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,8,6,7,3]=>1100000 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,5,8,7,3]=>1100000 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,6,5,8,3]=>1100000 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,8,6,5,7,3]=>1100000 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>1100000 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>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]=>1100100 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>1100001 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>1100000 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,4,8,6,7,3]=>1100000 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>1100000 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,6,4,5,3,7,8]=>1100011 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,8,4,5,6,7,3]=>1100000 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>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]=>1100000 [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,7,5,4,6,8,3]=>1100000 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,8,5,4,6,7,3]=>1100000 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,8,5,4,7,6,3]=>1100000 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>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]=>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]=>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]=>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]=>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]=>1011000 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>1011000 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>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]=>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]=>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]=>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]=>1010100 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>1010100 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>1010001 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>1010000 [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,7,5,6,8,4]=>1010000 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,8,5,7,6,4]=>1010000 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>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]=>1001111 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>1001100 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>1001001 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>1001000 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>1001000 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>1000001 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>1000000 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>1000000 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,4,2,6,8,7]=>1000110 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>1000001 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,6,4,5,2,8,7]=>1000010 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,4,5,7,2,8]=>1000001 [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,4,5,8,7,2]=>1000000 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,8,4,5,6,7,2]=>1000000 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,8,4,6,7,5,2]=>1000000 [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,6,5,4,2,8,7]=>1000010 [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,5,4,7,2,8]=>1000001 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>1000000 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,8,5,4,6,7,2]=>1000000 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,8,5,6,7,4,2]=>1000000 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,8,5,7,6,4,2]=>1000000 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,8,6,5,7,4,2]=>1000000 [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,7,5,6,4,2]=>1000000 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>1000000 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>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]=>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]=>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]=>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]=>1001001 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>1001000 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>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]=>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]=>1000101 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,3,5,7,6,2,8]=>1000001 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>1000000 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>1000011 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>1000001 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>1000000 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,8,5,6,7,2]=>1000000 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,8,5,7,6,2]=>1000000 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,8,6,7,5,2]=>1000000 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>1000000 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,5,3,4,2,7,8,6]=>1000100 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,3,4,2,8,7,6]=>1000100 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,3,4,8,6,7,2]=>1000000 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,8,3,4,6,7,5,2]=>1000000 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,6,3,5,4,2,7,8]=>1000011 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,6,3,5,4,8,7,2]=>1000000 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,8,3,5,6,4,7,2]=>1000000 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,8,3,5,7,6,4,2]=>1000000 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,8,3,6,5,4,7,2]=>1000000 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,8,3,7,6,5,4,2]=>1000000 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>1000011 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>1000000 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>1000000 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,6,4,3,5,2,7,8]=>1000011 [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,8,4,3,5,6,7,2]=>1000000 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,8,4,3,5,7,6,2]=>1000000 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,6,4,5,3,8,7,2]=>1000000 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,8,4,5,6,7,3,2]=>1000000 [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,8,4,6,5,7,3,2]=>1000000 [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,8,4,7,6,5,3,2]=>1000000 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>1000000 [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,7,5,4,3,6,8,2]=>1000000 [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,8,5,4,3,6,7,2]=>1000000 [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,8,5,4,6,3,7,2]=>1000000 [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,8,5,4,6,7,3,2]=>1000000 [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,8,5,4,7,6,3,2]=>1000000 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,8,6,4,5,7,3,2]=>1000000 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,8,6,5,4,7,3,2]=>1000000 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,8,7,5,6,4,3,2]=>1000000 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>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]=>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]=>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]=>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]=>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]=>0111000 [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,8,6,7,5]=>0111000 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>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]=>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]=>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]=>0110010 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>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]=>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]=>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]=>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]=>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]=>0101001 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>0101000 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>0101000 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>0100010 [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>0100000 [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>0100011 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>0100000 [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>0100000 [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,8,6,5,7,3]=>0100000 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>0100000 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>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]=>0100000 [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,6,4,5,8,7,3]=>0100000 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>0100010 [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,8,5,4,6,7,3]=>0100000 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,8,5,4,7,6,3]=>0100000 [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,7,5,6,4,8,3]=>0100000 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,8,7,5,6,4,3]=>0100000 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>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]=>0011111 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>0011100 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>0011000 [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>0010101 [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>0010000 [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>0010010 [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>0010001 [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>0010000 [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,8,6,7,5,4]=>0010000 [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>0010000 [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>0001111 [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>0001000 [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>0001000 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>0000111 [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>0000100 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>0000000 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>0000000 [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>0000000 [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>0000000 [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>0000001 [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>0000000 [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>0000000 [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>0000111 [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>0000100 [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>0000000 [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,6,4,5,7,8,1]=>0000000 [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,7,4,5,6,8,1]=>0000000 [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,8,4,5,6,7,1]=>0000000 [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,7,4,6,5,8,1]=>0000000 [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]=>0000000 [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,7,5,4,6,8,1]=>0000000 [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,7,5,6,4,1,8]=>0000001 [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,7,5,6,4,8,1]=>0000000 [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>0000001 [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>0000000 [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>0000000 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>0001111 [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>0001000 [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>0001000 [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>0000111 [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>0000101 [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>0000100 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>0000000 [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>0000000 [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>0000000 [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,4,3,5,8,6,7,1]=>0000000 [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>0000001 [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>0000000 [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>0000000 [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>0000000 [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>0000000 [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,3,4,1,6,7,8]=>0000111 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,5,3,4,1,8,7,6]=>0000100 [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,3,4,6,7,1,8]=>0000001 [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,5,3,4,8,7,6,1]=>0000000 [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,6,3,4,5,7,8,1]=>0000000 [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,6,3,5,4,1,8,7]=>0000010 [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,6,3,5,4,7,8,1]=>0000000 [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,7,3,5,4,6,8,1]=>0000000 [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,7,3,5,6,4,8,1]=>0000000 [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,8,3,5,7,6,4,1]=>0000000 [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,7,3,6,5,4,1,8]=>0000001 [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>0000111 [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,5,4,3,1,6,8,7]=>0000110 [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>0000100 [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>0000001 [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>0000000 [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>0000000 [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>0000000 [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,8,6,7,1]=>0000000 [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>0000000 [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,6,4,3,5,7,8,1]=>0000000 [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,8,4,3,5,6,7,1]=>0000000 [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,8,4,3,7,6,5,1]=>0000000 [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,6,4,5,3,1,7,8]=>0000011 [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,6,4,5,3,7,8,1]=>0000000 [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>0000000 [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,7,5,4,3,6,8,1]=>0000000 [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,7,5,4,6,3,8,1]=>0000000 [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,8,5,4,7,6,3,1]=>0000000 [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,7,5,4,6,3,1]=>0000000 [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,7,5,6,4,3,1]=>0000000 [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>0000000 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>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]=>0011100 [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>0011100 [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>0011000 [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>0011001 [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,8,6,7,5]=>0011000 [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>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]=>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]=>0010011 [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>0010000 [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>0010000 [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>0010001 [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>0010000 [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,8,6,7,4]=>0010000 [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>0010000 [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,2,1,6,5,7,4,8]=>0010001 [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>0010000 [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>0010000 [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,2,1,7,5,6,4,8]=>0010001 [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,7,5,6,8,4]=>0010000 [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,8,5,6,7,4]=>0010000 [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,8,5,7,6,4]=>0010000 [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>0010000 [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,8,6,5,7,4]=>0010000 [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,8,6,7,5,4]=>0010000 [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>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]=>0001111 [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>0001100 [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>0001011 [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>0001010 [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>0001000 [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,8,6,7,5]=>0001000 [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>0001000 [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>0000111 [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>0000100 [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>0000000 [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>0000000 [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>0000111 [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,5,4,1,6,8,7]=>0000110 [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>0000101 [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>0000100 [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>0000100 [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>0000001 [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,7,4,6,5,1,8]=>0000001 [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,7,4,6,5,8,1]=>0000000 [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,2,6,5,4,7,1,8]=>0000001 [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,2,8,5,4,6,7,1]=>0000000 [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,7,5,6,4,1,8]=>0000001 [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,8,5,7,6,4,1]=>0000000 [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>0000001 [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>0000000 [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7,8]=>0001111 [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,2,3,1,8,6,7,5]=>0001000 [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,2,3,1,8,7,6,5]=>0001000 [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,2,3,5,1,6,7,8]=>0000111 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,2,3,5,1,7,8,6]=>0000100 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,2,3,5,1,8,7,6]=>0000100 [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,2,3,5,6,8,7,1]=>0000000 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,3,7,5,6,1,8]=>0000001 [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,3,8,5,6,7,1]=>0000000 [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[4,2,3,7,6,5,8,1]=>0000000 [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,2,3,8,7,6,5,1]=>0000000 [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,2,3,4,1,6,7,8]=>0000111 [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,2,3,4,1,8,7,6]=>0000100 [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,2,3,4,8,7,6,1]=>0000000 [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,2,3,4,5,7,1,8]=>0000001 [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,2,3,5,4,1,7,8]=>0000011 [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,2,3,5,4,1,8,7]=>0000010 [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,2,3,5,4,7,1,8]=>0000001 [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,2,3,5,6,4,1,8]=>0000001 [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,6,5,4,1,8]=>0000001 [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,2,4,3,1,6,7,8]=>0000111 [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,2,4,3,1,6,8,7]=>0000110 [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,4,3,1,7,6,8]=>0000101 [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,2,4,3,1,8,7,6]=>0000100 [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,2,4,3,6,1,7,8]=>0000011 [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,2,4,3,6,1,8,7]=>0000010 [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,2,4,3,7,6,1,8]=>0000001 [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,2,4,3,7,6,8,1]=>0000000 [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,2,4,3,6,5,1,8]=>0000001 [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,2,4,3,6,5,8,1]=>0000000 [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,2,4,5,3,1,7,8]=>0000011 [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,2,4,5,3,6,1,8]=>0000001 [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,2,4,5,3,6,8,1]=>0000000 [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[8,2,4,7,6,5,3,1]=>0000000 [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,2,5,4,3,1,8,7]=>0000010 [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,2,5,4,3,6,1,8]=>0000001 [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,2,6,4,5,7,3,1]=>0000000 [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[8,2,7,5,6,4,3,1]=>0000000 [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[8,2,7,6,5,4,3,1]=>0000000 [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>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]=>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]=>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]=>0001100 [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>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]=>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]=>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]=>0001001 [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>0001000 [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>0001000 [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>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]=>0001000 [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,8,6,7,5]=>0001000 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>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]=>0000111 [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>0000100 [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]=>0000000 [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>0000000 [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,3,2,6,5,1,7,8]=>0000011 [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>0000000 [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]=>0000000 [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,7,5,6,8,1]=>0000000 [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,8,5,6,7,1]=>0000000 [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>0000000 [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,8,6,7,5,1]=>0000000 [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>0000000 [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,3,2,4,1,6,7,8]=>0000111 [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,3,2,4,1,6,8,7]=>0000110 [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,3,2,4,1,8,7,6]=>0000100 [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,3,2,4,6,1,7,8]=>0000011 [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,3,2,4,6,1,8,7]=>0000010 [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[6,3,2,4,5,7,1,8]=>0000001 [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[6,3,2,5,4,1,7,8]=>0000011 [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,3,2,5,4,1,8,7]=>0000010 [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[6,3,2,5,4,7,1,8]=>0000001 [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8,3,2,5,4,7,6,1]=>0000000 [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[8,3,2,5,6,4,7,1]=>0000000 [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>0000000 [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,3,4,2,1,6,7,8]=>0000111 [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,3,4,2,1,7,8,6]=>0000100 [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,3,4,2,1,8,7,6]=>0000100 [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,3,4,2,7,6,1,8]=>0000001 [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,6,5,1,8]=>0000001 [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,3,4,2,6,5,8,1]=>0000000 [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[6,3,4,5,2,7,1,8]=>0000001 [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1,8]=>0000001 [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,3,4,6,5,2,1,8]=>0000001 [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[6,3,5,4,2,7,1,8]=>0000001 [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,5,4,6,2,1,8]=>0000001 [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,3,6,4,5,2,1,8]=>0000001 [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,3,6,5,4,2,1,8]=>0000001 [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>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]=>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]=>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]=>0000100 [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>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]=>0000011 [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>0000010 [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>0000001 [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>0000000 [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>0000000 [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>0000001 [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>0000000 [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,8,6,7,1]=>0000000 [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>0000000 [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,4,3,2,5,1,7,8]=>0000011 [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,4,3,5,2,1,8,7]=>0000010 [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1,8]=>0000001 [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,4,3,6,5,2,1,8]=>0000001 [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,4,3,6,5,2,8,1]=>0000000 [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,5,3,4,2,1,8,7]=>0000010 [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[8,5,3,4,7,6,2,1]=>0000000 [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,6,3,4,5,2,1,8]=>0000001 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[8,7,3,6,5,4,2,1]=>0000000 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>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]=>0000000 [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>0000000 [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>0000000 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8,7,4,3,6,5,2,1]=>0000000 [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,6,4,5,3,2,1,8]=>0000001 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>0000001 [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[8,7,5,4,3,6,2,1]=>0000000 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>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]=>111110000
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.