Identifier
Mp00123: Dyck paths Barnabei-Castronuovo involutionDyck paths
Mp00024: Dyck paths to 321-avoiding permutationPermutations
Mp00131: Permutations descent bottomsBinary words
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,0]=>[1]=> [1,0,1,0]=>[1,0,1,0]=>[2,1]=>1 [1,1,0,0]=>[1,1,0,0]=>[1,2]=>0 [1,0,1,0,1,0]=>[1,1,0,1,0,0]=>[1,3,2]=>01 [1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[3,1,2]=>10 [1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[2,3,1]=>10 [1,1,0,1,0,0]=>[1,0,1,0,1,0]=>[2,1,3]=>10 [1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[1,2,3]=>00 [1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[2,1,4,3]=>101 [1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0]=>[2,4,1,3]=>100 [1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,0]=>[1,2,4,3]=>001 [1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>010 [1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>100 [1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]=>[3,1,4,2]=>110 [1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>100 [1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[1,3,4,2]=>010 [1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[1,3,2,4]=>010 [1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0]=>[3,1,2,4]=>100 [1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>100 [1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>[2,3,1,4]=>100 [1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>[2,1,3,4]=>100 [1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>000 [1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>0101 [1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>0100 [1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>1001 [1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>1100 [1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>1000 [1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>1001 [1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>1000 [1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>1001 [1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>1010 [1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>1000 [1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>0001 [1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>0010 [1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]=>0100 [1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>1000 [1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>0110 [1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>0100 [1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>1010 [1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>1100 [1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>1000 [1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>1010 [1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>1000 [1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>1010 [1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]=>1010 [1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>1000 [1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>0010 [1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>0010 [1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>0100 [1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>1000 [1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>1100 [1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>1000 [1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>1100 [1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>1100 [1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>1000 [1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>0100 [1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>0100 [1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>0100 [1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>1000 [1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>1000 [1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>1000 [1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>1000 [1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>1000 [1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>0000 [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]=>10101 [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>10100 [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>10001 [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>10100 [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>10000 [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>00101 [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>00100 [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>01001 [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>01100 [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>01000 [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>10001 [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>10100 [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>11000 [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>10000 [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>11001 [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>11000 [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>10001 [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>11000 [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>10000 [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>01001 [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>01000 [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>01001 [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>01010 [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>01000 [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>10001 [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>10010 [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>11000 [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>10000 [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>10001 [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>10000 [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>10001 [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>10010 [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>10000 [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>10001 [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>10010 [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>10100 [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>10000 [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>00001 [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>00010 [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>00100 [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>01000 [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>10000 [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>10110 [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>10100 [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>10010 [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>10100 [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>10000 [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>00110 [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>00100 [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>01010 [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>01100 [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>01000 [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>10010 [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>10100 [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>11000 [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>10000 [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>11010 [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>11000 [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>10010 [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>11000 [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>10000 [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>01010 [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>01000 [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>01010 [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>01010 [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>01000 [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>10010 [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>10010 [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>11000 [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>10000 [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>10010 [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>10000 [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>10010 [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>10010 [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>10000 [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>10010 [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>10010 [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>10100 [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>10000 [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>00010 [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>00010 [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>00100 [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>01000 [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>10000 [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>11100 [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>11000 [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>10100 [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>11000 [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>10000 [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>01100 [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>01000 [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>01100 [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>01100 [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>01000 [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>10100 [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>10100 [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>11000 [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>10000 [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>10100 [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>10000 [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>10100 [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>10100 [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>10000 [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>10100 [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>10100 [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>10100 [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>10000 [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>00100 [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>00100 [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>00100 [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>01000 [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>10000 [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>11000 [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>10000 [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>11000 [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>11000 [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>10000 [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>11000 [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>11000 [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>11000 [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>10000 [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>01000 [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>01000 [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>01000 [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>01000 [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>10000 [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>10000 [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>10000 [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>10000 [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>10000 [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>10000 [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>00000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>010101 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>010100 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>010001 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>010100 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>010000 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>100101 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>100100 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>110001 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>110100 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>110000 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>100001 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>100100 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>110000 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>100000 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>100101 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>100100 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>100001 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>100100 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>100000 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>100101 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>100100 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>101001 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>101100 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>101000 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>100001 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>100100 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>101000 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>100000 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>000101 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>000100 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>001001 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>001100 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>001000 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>010001 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>010100 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>011000 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>010000 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>100001 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>100100 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>101000 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>110000 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>100000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>011001 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>011000 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>010001 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>011000 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>010000 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>101001 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>101000 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>110001 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]=>111000 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>110000 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>100001 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>101000 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>110000 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>100000 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>101001 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>101000 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>100001 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>101000 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>100000 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>101001 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>101000 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>101001 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>101010 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>101000 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>100001 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>100010 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>101000 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>100000 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>001001 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>001000 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>001001 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>001010 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>001000 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>010001 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>010010 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>011000 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>010000 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>100001 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>100010 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>101000 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>110000 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>100000 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>110001 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>110000 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>100001 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>110000 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>100000 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>110001 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>110000 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>110001 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>110010 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>110000 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>100001 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>100010 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>110000 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>100000 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>010001 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>010000 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>010001 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>010010 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>010000 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>010001 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>010010 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>010100 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>010000 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>100001 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>100010 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>100100 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>110000 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>100000 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>100001 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>100000 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>100001 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>100010 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>100000 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>100001 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>100010 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>100100 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>100000 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>100001 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>100010 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]=>100100 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>101000 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>100000 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>000001 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>000010 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>000100 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>001000 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6]=>010000 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>100000 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>010110 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>010100 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>010010 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>010100 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>010000 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>100110 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>100100 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>110010 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>110100 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>110000 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>100010 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>100100 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>110000 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>100000 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>100110 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>100100 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>100010 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>100100 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>100000 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>100110 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>100100 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>101010 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>101100 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>101000 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>100010 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>100100 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>101000 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>100000 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>000110 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>000100 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>001010 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>001100 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>001000 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>010010 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>010100 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>011000 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>010000 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>100010 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>100100 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]=>101000 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>110000 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>100000 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>011010 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>011000 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>010010 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>011000 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>010000 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>101010 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>101000 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>110010 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>111000 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>110000 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>100010 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>101000 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>110000 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>100000 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>101010 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>101000 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>100010 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>101000 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>100000 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>101010 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>101000 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>101010 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7]=>101010 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>101000 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>100010 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>100010 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>101000 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>100000 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>001010 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>001000 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>001010 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>001010 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>001000 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>010010 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>010010 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>011000 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>010000 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>100010 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>100010 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>101000 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>110000 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>100000 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>110010 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>110000 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>100010 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>110000 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>100000 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>110010 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>110000 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>110010 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]=>110010 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>110000 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>100010 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>100010 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>110000 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>100000 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>010010 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>010000 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>010010 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>010010 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>010000 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>010010 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>010010 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>010100 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>010000 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>100010 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>100010 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>100100 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>110000 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>100000 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>100010 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>100000 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>100010 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>100010 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>100000 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>100010 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>100010 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>100100 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>100000 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>100010 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>100010 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>100100 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>101000 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>100000 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>000010 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>000010 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>000100 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>001000 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>010000 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>100000 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>011100 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>011000 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>010100 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>011000 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>010000 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>101100 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>101000 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]=>110100 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>111000 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>110000 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>100100 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>101000 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>110000 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>100000 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>101100 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>101000 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>100100 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>101000 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>100000 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>101100 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>101000 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>101100 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>101100 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>101000 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>100100 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>100100 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>101000 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>100000 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>001100 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>001000 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>001100 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>001100 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>001000 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>010100 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>010100 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>011000 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>010000 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>100100 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>100100 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>101000 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>110000 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>100000 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>110100 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>110000 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>100100 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>110000 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>100000 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>110100 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>110000 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>110100 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]=>110100 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>110000 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>100100 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>100100 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>110000 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>100000 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>010100 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>010000 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>010100 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>010100 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>010000 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>010100 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>010100 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>010100 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>010000 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>100100 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>100100 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>100100 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>110000 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>100000 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>100100 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>100000 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>100100 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>100100 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>100000 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>100100 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>100100 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>100100 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>100000 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>100100 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>100100 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>100100 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>101000 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>100000 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>000100 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>000100 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>000100 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>001000 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>010000 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>100000 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>111000 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>110000 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>101000 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>110000 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>100000 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>111000 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>110000 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>111000 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>111000 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>110000 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>101000 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>101000 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>110000 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>100000 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>011000 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>010000 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>011000 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>011000 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>010000 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>011000 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>011000 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>011000 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>010000 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>101000 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>101000 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>101000 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>110000 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>100000 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>101000 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>100000 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>101000 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>101000 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>100000 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>101000 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>101000 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>101000 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>100000 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>101000 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>101000 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>101000 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>101000 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>100000 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>001000 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>001000 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>001000 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>001000 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>010000 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>100000 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>110000 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>100000 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>110000 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>110000 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>100000 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>110000 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>110000 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>110000 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>100000 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>110000 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>110000 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>110000 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>110000 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>100000 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>010000 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>010000 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>010000 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>010000 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>010000 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>100000 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>100000 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>100000 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>100000 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>100000 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>100000 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>100000 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7]=>1010101 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,8,5,7]=>1010100 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>1010001 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,8,5,7]=>1010100 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,8,3,5,7]=>1010000 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>1000101 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7]=>1000100 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7]=>1010001 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>1010100 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,8,3,5,7]=>1010000 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,8,7]=>1000001 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,8,5,7]=>1000100 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>1010000 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>1000000 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7]=>0010101 [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,8,5,7]=>0010100 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,8,5,7]=>0010100 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,8,3,5,7]=>0010000 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7]=>0100101 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,8,7]=>0110001 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>0110100 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,8,3,5,7]=>0110000 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]=>0100100 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,8,3,5,7]=>0110000 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>0100000 [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>1000101 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,8,5,7]=>1000100 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>1010001 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>1010100 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,5,7]=>1110000 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,8,2,3,5,7]=>1100000 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,8,5,7]=>1000100 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,8,3,5,7]=>1010000 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,8,2,3,5,7]=>1100000 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,8,1,2,3,5,7]=>1000000 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7]=>1100101 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,8,5,7]=>1100100 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>1100100 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,8,2,5,7]=>1100000 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>1000101 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,8,5,7]=>1000100 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,8,2,5,7]=>1100000 [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,8,7]=>1000001 [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,8,7]=>0100001 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,8,2,5,7]=>0100000 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,8,7]=>0100101 [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>0100100 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>0101100 [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>0100100 [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,8,5,7]=>1000100 [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,8,7]=>1001001 [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,8,7]=>1100001 [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,8,5,7]=>1100100 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,8,4,5,7]=>1101000 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,8,2,4,5,7]=>1100000 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,8,5,7]=>1000100 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,8,2,4,5,7]=>1100000 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,6,8,1,2,4,5,7]=>1000000 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7]=>1000101 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,8,5,7]=>1000100 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,8,5,7]=>1000100 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>1001100 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,8,4,5,7]=>1001000 [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,8,7]=>1000001 [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,8,5,7]=>1000100 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,8,4,5,7]=>1001000 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,8,1,4,5,7]=>1000000 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>1000101 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,8,7]=>1010001 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,8,5,7]=>1010100 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,8,7]=>1000001 [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,8,3,4,5,7]=>1010000 [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,6,8,1,3,4,5,7]=>1000000 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7]=>0000101 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7]=>0000100 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,8,7]=>0001001 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,8,5,7]=>0001100 [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,8,7]=>0010001 [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,8,5,7]=>0010100 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>0011000 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>0010000 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,8,7]=>0100001 [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>0100100 [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,8,4,5,7]=>0101000 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,8,3,4,5,7]=>0110000 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,6,8,2,3,4,5,7]=>0100000 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>1000001 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,5,7]=>1010000 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,8,2,3,4,5,7]=>1100000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7]=>1011001 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,8,4,7]=>1011000 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>1010001 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,8,4,7]=>1001000 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,8,4,7]=>1011000 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,8,3,4,7]=>1010000 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,8,7]=>0011001 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,8,7]=>0010001 [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,8,4,7]=>0011000 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,8,3,4,7]=>0010000 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,8,7]=>0101001 [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,8,4,7]=>0101000 [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,8,7]=>0110001 [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>0111000 [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,8,3,4,7]=>0110000 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,8,7]=>0100001 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]=>0101000 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]=>0110000 [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>0100000 [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>1001000 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,8,7]=>1010001 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,8,4,7]=>1011000 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,8,3,4,7]=>1010000 [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,8,4,7]=>1101000 [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,8,3,4,7]=>1110000 [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,8,4,7]=>1001000 [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,8,3,4,7]=>1010000 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,8,1,2,3,4,7]=>1000000 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7]=>1101001 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,8,7]=>1100001 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,8,4,7]=>1101000 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,8,2,4,7]=>1100000 [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,8,4,7]=>1001000 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,8,7]=>1100001 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,8,2,4,7]=>1100000 [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,8,7]=>1000001 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,8,4,7]=>1001000 [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>1100000 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,8,7]=>0101001 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,8,4,7]=>0101000 [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,8,7]=>0100001 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>0101010 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,5,8,4,6,7]=>0101000 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,8,7]=>0100001 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,8,6,7]=>0100010 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>0101000 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>0100000 [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,8,4,7]=>1001000 [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,8,7]=>1001001 [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,5,8,4,6,7]=>1001000 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,8,6,7]=>1100010 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>1101000 [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,8,2,4,6,7]=>1100000 [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]=>1000001 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,8,6,7]=>1000010 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,8,4,6,7]=>1001000 [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,8,2,4,6,7]=>1100000 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,8,7]=>1001001 [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,8,7]=>1000001 [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,8,4,7]=>1001000 [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,6,8,1,4,7]=>1000000 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,8,6,7]=>1000010 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,8,1,4,6,7]=>1000000 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>1001001 [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,8,7]=>1010001 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,3,8,4,6,7]=>1011000 [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,8,3,4,6,7]=>1010000 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,8,3,4,6,7]=>1010000 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,8,7]=>0001001 [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,8,4,7]=>0001000 [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,8,6,7]=>0001010 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>0001000 [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>0010010 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>0011000 [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>0010000 [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,8,7]=>0100001 [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>0100010 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,2,3,8,4,6,7]=>0101000 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,2,8,3,4,6,7]=>0110000 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,6,7]=>1010000 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7]=>1110001 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,8,3,7]=>1110000 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>1100001 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,8,3,7]=>1110000 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,8,2,3,7]=>1100000 [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,8,7]=>1010001 [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,8,3,7]=>1010000 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,8,7]=>1100001 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,8,3,7]=>1110000 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,8,7]=>1000001 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>1000000 [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,8,7]=>0110001 [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,8,3,7]=>0110000 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,8,3,7]=>0110000 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,6,8,2,3,7]=>0100000 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,8,7]=>0110001 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>0110010 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,8,3,6,7]=>0110000 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]=>0100010 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,8,3,6,7]=>0110000 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,8,2,3,6,7]=>0100000 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>1010001 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>1010000 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,8,6,7]=>1010010 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,8,3,6,7]=>1010000 [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,8,6,7]=>1100010 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,8,3,6,7]=>1110000 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,8,2,3,6,7]=>1100000 [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,8,6,7]=>1000010 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,8,3,6,7]=>1010000 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,8,2,3,6,7]=>1100000 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,8,1,2,3,6,7]=>1000000 [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>1010000 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,8,3,7]=>1010000 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,5,6,8,1,3,7]=>1000000 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,8,7]=>1010001 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>1010010 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,5,8,3,6,7]=>1010000 [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,8,1,3,6,7]=>1000000 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>1010001 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,8,3,7]=>1010000 [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>1010001 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,4,5,8,3,6,7]=>1010000 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,8,7]=>1010001 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,8,5,6,7]=>1010100 [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,4,8,3,5,6,7]=>1010000 [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,8,5,6,7]=>1000100 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,5,6,7]=>1010000 [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,8,3,7]=>0010000 [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,8,6,7]=>0010010 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,4,5,8,3,6,7]=>0010000 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,8,7]=>0010001 [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>0010010 [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>0010100 [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>0010000 [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,8,7]=>0100001 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>0100010 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,4,2,3,8,5,6,7]=>0100100 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,4,2,8,3,5,6,7]=>0110000 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,4,8,2,3,5,6,7]=>0100000 [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>1000001 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,8,6,7]=>1000010 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,8,5,6,7]=>1000100 [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,7]=>1010000 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,8,1,2,3,5,6,7]=>1000000 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,8,7]=>1100001 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,8,7]=>1000001 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,8,2,7]=>1100000 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,6,8,1,2,7]=>1000000 [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,8,2,7]=>1100000 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,8,6,7]=>1100010 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,5,8,2,6,7]=>1100000 [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]=>1000010 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>1000000 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>1100001 [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,8,6,7]=>1100010 [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,2,8,5,6,7]=>1100100 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,8,2,5,6,7]=>1100000 [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,8,7]=>1000001 [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,8,6,7]=>1000010 [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,8,5,6,7]=>1000100 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,8,2,5,6,7]=>1100000 [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,8,1,2,5,6,7]=>1000000 [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,8,7]=>0100001 [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,8,6,7]=>0100010 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,3,4,5,8,2,6,7]=>0100000 [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,8,7]=>0100001 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>0100010 [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>0100100 [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>0100000 [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>0100010 [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,3,2,4,8,5,6,7]=>0100100 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,3,2,8,4,5,6,7]=>0101000 [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,3,8,2,4,5,6,7]=>0100000 [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,8,6,7]=>1000010 [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,7]=>1000100 [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,8,4,5,6,7]=>1001000 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>1100000 [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7]=>1000001 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,8,1,6,7]=>1000000 [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,8,7]=>1000001 [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,8,6,7]=>1000010 [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>1000100 [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>1000000 [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,7]=>1000100 [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,1,8,4,5,6,7]=>1001000 [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,8,1,4,5,6,7]=>1000000 [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>1000001 [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,3,4,8,5,6,7]=>1000100 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,8,4,5,6,7]=>1001000 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7]=>1010000 [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7]=>1000000 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7]=>0000001 [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,7]=>0000010 [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>0000100 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>0001000 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,8,3,4,5,6,7]=>0010000 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7]=>0100000 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>1000000 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6]=>1010110 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,7,8,5,6]=>1010100 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,8,6]=>1000110 [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,7,8,5,6]=>1000100 [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>1010010 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>1010100 [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,8,3,5,6]=>1010000 [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,8,6]=>1000010 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,4,7,1,3,8,5,6]=>1000100 [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,7,1,8,3,5,6]=>1010000 [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,8,6]=>0010110 [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,7,8,5,6]=>0010100 [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,4,7,3,8,5,6]=>0010100 [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,4,7,8,3,5,6]=>0010000 [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>0100100 [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,8,6]=>0110010 [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>0110100 [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,7,8,3,5,6]=>0110000 [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,8,6]=>0100010 [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,7,2,3,8,5,6]=>0100100 [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,7,2,8,3,5,6]=>0110000 [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>1000110 [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,7,8,5,6]=>1000100 [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>1010010 [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,7,8,3,5,6]=>1010000 [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,8,6]=>1100010 [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,7,2,3,8,5,6]=>1100100 [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,7,2,8,3,5,6]=>1110000 [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,7,1,2,8,3,5,6]=>1010000 [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,7,1,8,2,3,5,6]=>1100000 [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6]=>1100110 [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,7,8,5,6]=>1100100 [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,8,6]=>1000110 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6]=>1000100 [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,8,6]=>1000010 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>1100000 [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,7,8,5,6]=>0100100 [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,8,6]=>0100010 [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]=>0100110 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>0100100 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>0101100 [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,8,6]=>0100010 [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,3,7,2,4,8,5,6]=>0100100 [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>0101000 [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>1000110 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,7,8,5,6]=>1000100 [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,7,4,8,5,6]=>1001100 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,7,8,4,5,6]=>1001000 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,7,8,2,4,5,6]=>1100000 [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,8,6]=>1000010 [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,7,1,2,4,8,5,6]=>1000100 [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,7,1,2,8,4,5,6]=>1001000 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,8,6]=>1000110 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>1000100 [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,8,6]=>1000010 [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,4,7,8,1,5,6]=>1000000 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>1000100 [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>1001010 [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,1,7,8,4,5,6]=>1001000 [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,8,6]=>1000010 [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>1000000 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,7,8,5,6]=>1000100 [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,7,4,8,5,6]=>1001100 [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,8,6]=>1010010 [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,1,7,3,4,8,5,6]=>1010100 [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,7,8,3,4,5,6]=>1010000 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,7,1,3,8,4,5,6]=>1001000 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>1010000 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,7,8,1,3,4,5,6]=>1000000 [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6]=>0000110 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,6]=>0000100 [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,8,6]=>0001010 [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,6]=>0001100 [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>0001000 [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,8,6]=>0010010 [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>0010100 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>0010000 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,7,2,8,3,4,5,6]=>0110000 [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,8,2,3,4,5,6]=>0100000 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1,2,3,8,4,5,6]=>1001000 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,1,2,8,3,4,5,6]=>1010000 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>1000000 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6]=>1011010 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,7,8,4,6]=>1011000 [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,8,6]=>1010010 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,7,3,8,4,6]=>1011000 [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,7,8,3,4,6]=>1010000 [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>1001010 [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,8,4,6]=>1001000 [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>1010010 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,7,3,8,4,6]=>1011000 [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,7,8,3,4,6]=>1010000 [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,8,6]=>1000010 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,7,1,3,8,4,6]=>1001000 [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,8,6]=>0011010 [1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,7,8,4,6]=>0011000 [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,8,6]=>0010010 [1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,3,8,4,6]=>0011000 [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,7,8,3,4,6]=>0010000 [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,8,6]=>0101010 [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,8,4,6]=>0101000 [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>0110010 [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>0111000 [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,7,8,3,4,6]=>0110000 [1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,8,6]=>0100010 [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,7,2,3,8,4,6]=>0101000 [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>0110000 [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,7,8,2,3,4,6]=>0100000 [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>1001010 [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,7,8,4,6]=>1001000 [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>1010010 [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,7,3,8,4,6]=>1011000 [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,7,8,3,4,6]=>1010000 [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,8,6]=>1100010 [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,7,2,8,3,4,6]=>1110000 [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,7,1,2,8,3,4,6]=>1010000 [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,7,8,1,2,3,4,6]=>1000000 [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6]=>1101010 [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,7,8,4,6]=>1101000 [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>1100010 [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,7,2,8,4,6]=>1101000 [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,7,8,2,4,6]=>1100000 [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,8,6]=>1001010 [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,7,8,4,6]=>1001000 [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,8,6]=>1100010 [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>1101000 [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,7,8,2,4,6]=>1100000 [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,8,6]=>1000010 [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>1000000 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,6]=>0101010 [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,7,8,4,6]=>0101000 [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,8,6]=>0100010 [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,6]=>0101000 [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>0100000 [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,7,4,8,6]=>0101010 [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>0101000 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>0101010 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,8]=>0101010 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6,8]=>0101000 [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,7,8,6]=>0100010 [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6,8]=>0100010 [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>0101000 [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>0100000 [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>1001010 [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>1001010 [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]=>1001000 [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,8]=>1100010 [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6,8]=>1101000 [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6,8]=>1100000 [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,8,6]=>1000010 [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>1000010 [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6,8]=>1001000 [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6,8]=>1100000 [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6,8]=>1000000 [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,7,4,8,6]=>1001010 [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,8,6]=>1000010 [1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,7,1,8,4,6]=>1001000 [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,8]=>1001010 [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6,8]=>1000000 [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6,8]=>1010000 [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6,8]=>1001000 [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,7,4,8,6]=>0001010 [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,7,8,4,6]=>0001000 [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,7,8,6]=>0001010 [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,8]=>0001010 [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6,8]=>0001000 [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,7,8,6]=>0010010 [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>0010000 [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,7,8,6]=>0100010 [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6,8]=>0100010 [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6,8]=>0110000 [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6,8]=>1010000 [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6,8]=>1000000 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6]=>1110010 [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,7,8,3,6]=>1110000 [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,7,2,8,3,6]=>1110000 [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,8,6]=>1010010 [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,7,8,3,6]=>1010000 [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,8,6]=>1100010 [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>1110000 [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,7,8,2,3,6]=>1100000 [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>1010000 [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,7,3,8,6]=>0110010 [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,7,8,3,6]=>0110000 [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,8,6]=>0100010 [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,7,8,2,3,6]=>0100000 [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]=>0110010 [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,7,8,3,6]=>0110000 [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,7,8,6]=>0110010 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,8]=>0110010 [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6,8]=>0110000 [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,7,8,6]=>0100010 [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6,8]=>0100010 [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6,8]=>0110000 [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>0100000 [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,7,3,8,6]=>1010010 [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,7,8,3,6]=>1010000 [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,7,8,6]=>1010010 [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6,8]=>1010000 [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>1100010 [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6,8]=>1110000 [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6,8]=>1100000 [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]=>1000010 [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6,8]=>1010000 [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6,8]=>1100000 [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,7,3,8,6]=>1010010 [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,8,6]=>1000010 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,7,8,1,3,6]=>1000000 [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]=>1010010 [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,7,8,6]=>1010010 [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,8]=>1010010 [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,7,8,6]=>1000010 [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>1010000 [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>1010010 [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,8,6]=>1000010 [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,7,3,8,6]=>0010010 [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,7,8,6]=>0010010 [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,7,8,6]=>0010010 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,7,8,6]=>0100010 [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6,8]=>0100010 [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6,8]=>0100100 [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6,8]=>0110000 [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,8,6]=>1000010 [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>1000010 [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>1000100 [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,7,8,2,6]=>1100000 [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,8,6]=>1000010 [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,7,2,8,6]=>1100010 [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>1100000 [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6,8]=>1100010 [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6,8]=>1100000 [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,8,2,6]=>1100000 [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,7,8,6]=>1100010 [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>1100010 [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>1100010 [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6,8]=>1100100 [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,7,8,6]=>1000010 [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6,8]=>1000010 [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6,8]=>1000100 [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,7,2,8,6]=>0100010 [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,7,8,2,6]=>0100000 [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,7,8,6]=>0100010 [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6,8]=>0100010 [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6,8]=>0100000 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,7,8,6]=>0100010 [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6,8]=>0100010 [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>0100010 [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6,8]=>0100010 [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6,8]=>0101000 [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>1000100 [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6,8]=>1000000 [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,7,8,6]=>1000010 [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6,8]=>1000010 [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6,8]=>1000100 [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>1000000 [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>1000010 [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,6]=>0000010 [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8]=>0000010 [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,8]=>0000100 [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>0001000 [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6,8]=>0010000 [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8]=>0100000 [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>1000000 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5]=>1011100 [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,6,3,7,8,4,5]=>1011000 [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,1,6,7,3,8,4,5]=>1011000 [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,6,7,8,3,4,5]=>1010000 [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,8,5]=>1001100 [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,6,1,7,3,8,4,5]=>1011000 [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,6,1,7,8,3,4,5]=>1010000 [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>1000100 [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>1000000 [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,8,5]=>0011100 [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>0011000 [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,8,5]=>0010100 [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,8,4,5]=>0011000 [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,7,8,3,4,5]=>0010000 [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>0101100 [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,8,5]=>0110100 [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>0111000 [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,8,5]=>0100100 [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,6,7,2,3,8,4,5]=>0101000 [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,6,7,2,8,3,4,5]=>0110000 [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>0100000 [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[6,1,2,3,7,8,4,5]=>1001000 [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,8,5]=>1010100 [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,8,5]=>1100100 [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,7,2,3,8,4,5]=>1101000 [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,4,5]=>1110000 [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,1,7,8,2,3,4,5]=>1100000 [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,8,5]=>1000100 [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,7,1,2,3,8,4,5]=>1001000 [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,7,1,8,2,3,4,5]=>1100000 [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>1000000 [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5]=>1101100 [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,6,7,2,8,4,5]=>1101000 [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,8,5]=>1001100 [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,8,5]=>1100100 [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>1101000 [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,6,1,7,8,2,4,5]=>1100000 [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,8,5]=>1000100 [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>1001000 [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>1000000 [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,6,2,7,4,8,5]=>0101100 [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,8,4,5]=>0101000 [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,6,7,2,4,8,5]=>0100100 [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,7,8,5]=>0101100 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5,8]=>0101100 [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5,8]=>0101000 [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,7,8,5]=>0100100 [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5,8]=>0100100 [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>1001100 [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,8,5]=>1001100 [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5,8]=>1001100 [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,7,8,5]=>1100100 [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5,8]=>1100100 [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5,8]=>1100000 [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,8,5]=>1000100 [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]=>1000100 [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5,8]=>1000000 [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>1001000 [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,3,6,7,1,4,8,5]=>1000100 [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,8,4,5]=>1001000 [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,6,7,8,1,4,5]=>1000000 [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>1001000 [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,8]=>1001100 [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>1000100 [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5,8]=>1000100 [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5,8]=>1000000 [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>1001100 [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>1010100 [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5,8]=>1010000 [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5,8]=>1000000 [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,6,7,4,8,5]=>0001100 [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,6,7,8,4,5]=>0001000 [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,7,8,5]=>0001100 [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,8]=>0001100 [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5,8]=>0001000 [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,7,8,5]=>0010100 [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5,8]=>0010100 [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,8,5]=>0100100 [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5,8]=>0100100 [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5,8]=>0110000 [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5,8]=>0100000 [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,8,5]=>1000100 [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5,8]=>1100000 [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5,8]=>1000000 [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5]=>1110100 [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,8,5]=>1100100 [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,6,1,2,7,8,3,5]=>1010000 [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,8,5]=>1000100 [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>1100000 [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>1000000 [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,2,7,3,8,5]=>0110100 [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>0110000 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,8,3,5]=>0110000 [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>0110000 [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5,8]=>0110100 [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5,8]=>0110000 [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,7,8,5]=>0100100 [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>0110000 [1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,5]=>1010100 [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,8,5]=>1010100 [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5,8]=>1010100 [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5,8]=>1010000 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>1100100 [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5,8]=>1100100 [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5,8]=>1110000 [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5,8]=>1100000 [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>1000100 [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5,8]=>1010000 [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8]=>1100000 [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,6,1,7,3,8,5]=>1010100 [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,8,3,5]=>1010000 [1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,8,5]=>1000100 [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,8,3,5]=>1010000 [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,7,8,1,3,5]=>1000000 [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]=>1010100 [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>1010000 [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>1010100 [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8]=>1010100 [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,6,1,3,7,8,5]=>1000100 [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5,8]=>1000100 [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>1000000 [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,6,3,7,8,5]=>1010100 [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>1010100 [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5,8]=>1010100 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>1010100 [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,7,8,5]=>1000100 [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7,8]=>1000100 [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,6,7,3,8,5]=>0010100 [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,6,7,8,5]=>0010100 [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5,8]=>0010100 [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>0010100 [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]=>0010000 [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,6,7,8,5]=>0100100 [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7,8]=>0100100 [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7,8]=>0110000 [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,6,7,8,5]=>1000100 [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>1000100 [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7,8]=>1000100 [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,6,1,7,2,8,5]=>1100100 [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]=>1100000 [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,8,2,5]=>1100000 [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,6,7,8,1,2,5]=>1000000 [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5,8]=>1100100 [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,6,1,2,7,8,5]=>1000100 [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5,8]=>1000100 [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,6,7,8,2,5]=>1100000 [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>1100100 [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5,8]=>1100100 [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>1100100 [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,7,8,5]=>1000100 [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5,8]=>1000100 [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7,8]=>1000100 [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,6,7,2,8,5]=>0100100 [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,6,7,8,5]=>0100100 [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5,8]=>0100100 [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>0100100 [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7,8]=>0100100 [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7,8]=>0101000 [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7,8]=>0100000 [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,8,5]=>1000100 [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8]=>1000100 [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]=>1100000 [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,7,8,1,5]=>1000000 [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,5]=>1000100 [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5,8]=>1000100 [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>1000100 [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>1000100 [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8]=>1000100 [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7,8]=>1000000 [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,6,7,8,5]=>1000100 [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7,8]=>1000100 [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,5]=>0000100 [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5,8]=>0000100 [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8]=>0000100 [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>0001000 [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8]=>0010000 [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7,8]=>0100000 [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4]=>1111000 [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>1101000 [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[5,1,6,7,2,8,3,4]=>1110000 [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,1,6,7,8,2,3,4]=>1100000 [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,8,4]=>1011000 [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,8,4]=>1101000 [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,6,1,7,8,2,3,4]=>1100000 [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,8,4]=>1001000 [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>1010000 [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>1100000 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>1000000 [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,8,4]=>0101000 [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,5,6,7,8,2,3,4]=>0100000 [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]=>0111000 [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4,8]=>0111000 [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4,8]=>0110000 [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,7,8,4]=>0101000 [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4,8]=>0100000 [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,6,7,3,8,4]=>1011000 [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[5,1,2,6,7,8,3,4]=>1010000 [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,8,4]=>1011000 [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4,8]=>1011000 [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4,8]=>1010000 [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>1101000 [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4,8]=>1101000 [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4,8]=>1110000 [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,7,8,4]=>1001000 [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4,8]=>1000000 [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,5,6,1,7,8,3,4]=>1010000 [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>1000000 [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>1011000 [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>1010000 [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]=>1011000 [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4,8]=>1011000 [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4,8]=>1010000 [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5,6,1,3,7,8,4]=>1001000 [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4,8]=>1001000 [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,3,8,4]=>1011000 [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,5,6,7,8,3,4]=>1010000 [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,6,3,7,8,4]=>1011000 [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4,8]=>1011000 [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4,8]=>1010000 [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]=>1011000 [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4,8]=>1011000 [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7,8]=>1010000 [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,7,8,4]=>1001000 [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7,8]=>1010000 [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,5,6,7,8,3,4]=>0010000 [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,5,6,3,7,8,4]=>0011000 [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4,8]=>0011000 [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,6,7,8,4]=>0011000 [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>0010000 [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,6,7,8,4]=>0101000 [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7,8]=>0110000 [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,6,7,8,4]=>1001000 [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4,8]=>1001000 [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7,8]=>1010000 [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7,8]=>1100000 [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,7,2,8,4]=>1101000 [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>1100000 [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5,6,7,8,1,2,4]=>1000000 [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]=>1101000 [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>1100000 [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>1101000 [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4,8]=>1101000 [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5,6,1,2,7,8,4]=>1001000 [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4,8]=>1001000 [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8]=>1100000 [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>1101000 [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,5,6,7,8,2,4]=>1100000 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,5,6,2,7,8,4]=>1101000 [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,6,7,8,4]=>1101000 [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7,8]=>1100000 [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,7,8,4]=>1001000 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7,8]=>1100000 [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7,8]=>1000000 [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,6,7,8,2,4]=>0100000 [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,5,6,2,7,8,4]=>0101000 [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,8]=>0101000 [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4,8]=>0100000 [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4,8]=>0101000 [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7,8]=>0101000 [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>0100000 [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4,8]=>0101000 [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7,8]=>0101000 [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7,8]=>0101000 [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7,8]=>0100000 [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,5,6,7,8,4]=>1001000 [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4,8]=>1001000 [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7,8]=>1000000 [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,7,1,8,4]=>1001000 [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,6,7,8,1,4]=>1000000 [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,7,8,4]=>1001000 [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4,8]=>1001000 [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,8,4]=>1001000 [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]=>1000000 [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>1001000 [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4,8]=>1001000 [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7,8]=>1000000 [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4]=>0001000 [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4,8]=>0001000 [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7,8]=>0001000 [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>0001000 [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7,8]=>0100000 [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8]=>1000000 [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5,6,1,7,2,8,3]=>1110000 [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,6,7,1,2,8,3]=>1010000 [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,3]=>1100000 [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>1000000 [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>1110000 [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>1100000 [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[4,5,1,6,2,7,8,3]=>1110000 [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3,8]=>1110000 [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3,8]=>1100000 [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>1000000 [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>1110000 [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3,8]=>1100000 [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>1110000 [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7,8]=>1100000 [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,7,8,3]=>1010000 [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7,8]=>1100000 [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,5,6,7,2,8,3]=>0110000 [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3,8]=>0100000 [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,5,2,6,7,8,3]=>0110000 [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>0110000 [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3,8]=>0110000 [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7,8]=>0110000 [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7,8]=>0100000 [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,8,3]=>1010000 [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3,8]=>1010000 [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7,8]=>1010000 [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7,8]=>1000000 [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,5,6,7,1,8,3]=>1010000 [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3,8]=>1000000 [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>1010000 [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>1000000 [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,5,6,7,8,3]=>1010000 [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7,8]=>1010000 [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,3]=>1010000 [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>1010000 [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8]=>1000000 [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7,8]=>0010000 [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8]=>0010000 [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8]=>0100000 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8]=>1000000 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>1000000 [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,5,6,1,7,8,2]=>1100000 [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2,8]=>1100000 [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>1000000 [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,5,1,6,7,8,2]=>1100000 [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>1100000 [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2,8]=>1100000 [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7,8]=>1100000 [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2]=>1100000 [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>1100000 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8]=>1000000 [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2,8]=>0100000 [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>0100000 [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7,8]=>0100000 [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8]=>0100000 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8]=>1000000 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>1000000 [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>1000000 [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8]=>1000000 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8]=>1000000 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8]=>1000000 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>0000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>101010101 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,10,7,9]=>011010100 [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>100000000 [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,9,6,8,10]=>110101000
Map
Barnabei-Castronuovo involution
Description
The Barnabei-Castronuovo Sch├╝tzenberger involution on Dyck paths.
The image of a Dyck path is obtained by reversing the canonical decompositions of the two halves of the Dyck path. More precisely, let $D_1, 1, D_2, 1, \dots$ be the canonical decomposition of the first half, then the canonical decomposition of the first half of the image is $\dots, 1, D_2, 1, D_1$.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.