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Identifier
Values
=>
Cc0005;cc-rep
[1,0]=>0 [1,0,1,0]=>0 [1,1,0,0]=>0 [1,0,1,0,1,0]=>0 [1,0,1,1,0,0]=>0 [1,1,0,0,1,0]=>0 [1,1,0,1,0,0]=>0 [1,1,1,0,0,0]=>0 [1,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,1,0,0]=>0 [1,0,1,1,0,0,1,0]=>1 [1,0,1,1,0,1,0,0]=>0 [1,0,1,1,1,0,0,0]=>0 [1,1,0,0,1,0,1,0]=>0 [1,1,0,0,1,1,0,0]=>0 [1,1,0,1,0,0,1,0]=>0 [1,1,0,1,0,1,0,0]=>0 [1,1,0,1,1,0,0,0]=>0 [1,1,1,0,0,0,1,0]=>0 [1,1,1,0,0,1,0,0]=>0 [1,1,1,0,1,0,0,0]=>0 [1,1,1,1,0,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,0]=>1 [1,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,1,0,1,0,0]=>1 [1,0,1,0,1,1,1,0,0,0]=>0 [1,0,1,1,0,0,1,0,1,0]=>1 [1,0,1,1,0,0,1,1,0,0]=>1 [1,0,1,1,0,1,0,0,1,0]=>1 [1,0,1,1,0,1,0,1,0,0]=>2 [1,0,1,1,0,1,1,0,0,0]=>0 [1,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,0,0]=>2 [1,0,1,1,1,0,1,0,0,0]=>0 [1,0,1,1,1,1,0,0,0,0]=>0 [1,1,0,0,1,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,1,0,0]=>0 [1,1,0,0,1,1,0,0,1,0]=>1 [1,1,0,0,1,1,0,1,0,0]=>0 [1,1,0,0,1,1,1,0,0,0]=>0 [1,1,0,1,0,0,1,0,1,0]=>1 [1,1,0,1,0,0,1,1,0,0]=>0 [1,1,0,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,1,0,0]=>1 [1,1,0,1,0,1,1,0,0,0]=>0 [1,1,0,1,1,0,0,0,1,0]=>2 [1,1,0,1,1,0,0,1,0,0]=>1 [1,1,0,1,1,0,1,0,0,0]=>0 [1,1,0,1,1,1,0,0,0,0]=>0 [1,1,1,0,0,0,1,0,1,0]=>0 [1,1,1,0,0,0,1,1,0,0]=>0 [1,1,1,0,0,1,0,0,1,0]=>0 [1,1,1,0,0,1,0,1,0,0]=>0 [1,1,1,0,0,1,1,0,0,0]=>0 [1,1,1,0,1,0,0,0,1,0]=>0 [1,1,1,0,1,0,0,1,0,0]=>0 [1,1,1,0,1,0,1,0,0,0]=>0 [1,1,1,0,1,1,0,0,0,0]=>0 [1,1,1,1,0,0,0,0,1,0]=>0 [1,1,1,1,0,0,0,1,0,0]=>0 [1,1,1,1,0,0,1,0,0,0]=>0 [1,1,1,1,0,1,0,0,0,0]=>0 [1,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,0]=>3 [1,0,1,0,1,0,1,0,1,1,0,0]=>2 [1,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,0,1,0,1,1,1,0,0,0]=>1 [1,0,1,0,1,1,0,0,1,0,1,0]=>1 [1,0,1,0,1,1,0,0,1,1,0,0]=>1 [1,0,1,0,1,1,0,1,0,0,1,0]=>2 [1,0,1,0,1,1,0,1,0,1,0,0]=>3 [1,0,1,0,1,1,0,1,1,0,0,0]=>1 [1,0,1,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,0]=>2 [1,0,1,0,1,1,1,0,1,0,0,0]=>1 [1,0,1,0,1,1,1,1,0,0,0,0]=>0 [1,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,0]=>1 [1,0,1,1,0,0,1,1,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,0,1,0,0]=>1 [1,0,1,1,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,0,1,1,0,1,0,0,1,1,0,0]=>1 [1,0,1,1,0,1,0,1,0,0,1,0]=>4 [1,0,1,1,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,0]=>2 [1,0,1,1,0,1,1,0,0,1,0,0]=>2 [1,0,1,1,0,1,1,0,1,0,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,0]=>0 [1,0,1,1,1,0,0,0,1,0,1,0]=>1 [1,0,1,1,1,0,0,0,1,1,0,0]=>1 [1,0,1,1,1,0,0,1,0,0,1,0]=>2 [1,0,1,1,1,0,0,1,0,1,0,0]=>2 [1,0,1,1,1,0,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,1,0,0,1,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,1,0,0,0,0]=>0 [1,0,1,1,1,1,0,0,0,0,1,0]=>1 [1,0,1,1,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,1,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,1,0,0,0,0]=>0 [1,0,1,1,1,1,1,0,0,0,0,0]=>0 [1,1,0,0,1,0,1,0,1,0,1,0]=>2 [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]=>1 [1,1,0,0,1,0,1,1,0,1,0,0]=>1 [1,1,0,0,1,0,1,1,1,0,0,0]=>0 [1,1,0,0,1,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,1,0,0,1,1,0,0]=>1 [1,1,0,0,1,1,0,1,0,0,1,0]=>1 [1,1,0,0,1,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,1,0,0,0]=>0 [1,1,0,0,1,1,1,0,0,0,1,0]=>1 [1,1,0,0,1,1,1,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,0,0]=>0 [1,1,0,0,1,1,1,1,0,0,0,0]=>0 [1,1,0,1,0,0,1,0,1,0,1,0]=>2 [1,1,0,1,0,0,1,0,1,1,0,0]=>1 [1,1,0,1,0,0,1,1,0,0,1,0]=>1 [1,1,0,1,0,0,1,1,0,1,0,0]=>1 [1,1,0,1,0,0,1,1,1,0,0,0]=>0 [1,1,0,1,0,1,0,0,1,0,1,0]=>3 [1,1,0,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,0,1,0,1,0,1,1,0,0,0]=>1 [1,1,0,1,0,1,1,0,0,0,1,0]=>2 [1,1,0,1,0,1,1,0,0,1,0,0]=>3 [1,1,0,1,0,1,1,0,1,0,0,0]=>1 [1,1,0,1,0,1,1,1,0,0,0,0]=>0 [1,1,0,1,1,0,0,0,1,0,1,0]=>2 [1,1,0,1,1,0,0,0,1,1,0,0]=>2 [1,1,0,1,1,0,0,1,0,0,1,0]=>2 [1,1,0,1,1,0,0,1,0,1,0,0]=>3 [1,1,0,1,1,0,0,1,1,0,0,0]=>1 [1,1,0,1,1,0,1,0,0,0,1,0]=>2 [1,1,0,1,1,0,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,0,1,0,0,0]=>2 [1,1,0,1,1,0,1,1,0,0,0,0]=>0 [1,1,0,1,1,1,0,0,0,0,1,0]=>2 [1,1,0,1,1,1,0,0,0,1,0,0]=>4 [1,1,0,1,1,1,0,0,1,0,0,0]=>2 [1,1,0,1,1,1,0,1,0,0,0,0]=>0 [1,1,0,1,1,1,1,0,0,0,0,0]=>0 [1,1,1,0,0,0,1,0,1,0,1,0]=>1 [1,1,1,0,0,0,1,0,1,1,0,0]=>0 [1,1,1,0,0,0,1,1,0,0,1,0]=>1 [1,1,1,0,0,0,1,1,0,1,0,0]=>0 [1,1,1,0,0,0,1,1,1,0,0,0]=>0 [1,1,1,0,0,1,0,0,1,0,1,0]=>1 [1,1,1,0,0,1,0,0,1,1,0,0]=>0 [1,1,1,0,0,1,0,1,0,0,1,0]=>2 [1,1,1,0,0,1,0,1,0,1,0,0]=>1 [1,1,1,0,0,1,0,1,1,0,0,0]=>0 [1,1,1,0,0,1,1,0,0,0,1,0]=>2 [1,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,1,1,0,0,1,1,0,1,0,0,0]=>0 [1,1,1,0,0,1,1,1,0,0,0,0]=>0 [1,1,1,0,1,0,0,0,1,0,1,0]=>1 [1,1,1,0,1,0,0,0,1,1,0,0]=>0 [1,1,1,0,1,0,0,1,0,0,1,0]=>2 [1,1,1,0,1,0,0,1,0,1,0,0]=>1 [1,1,1,0,1,0,0,1,1,0,0,0]=>0 [1,1,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,0,1,0,0,1,0,0]=>2 [1,1,1,0,1,0,1,0,1,0,0,0]=>1 [1,1,1,0,1,0,1,1,0,0,0,0]=>0 [1,1,1,0,1,1,0,0,0,0,1,0]=>3 [1,1,1,0,1,1,0,0,0,1,0,0]=>2 [1,1,1,0,1,1,0,0,1,0,0,0]=>1 [1,1,1,0,1,1,0,1,0,0,0,0]=>0 [1,1,1,0,1,1,1,0,0,0,0,0]=>0 [1,1,1,1,0,0,0,0,1,0,1,0]=>0 [1,1,1,1,0,0,0,0,1,1,0,0]=>0 [1,1,1,1,0,0,0,1,0,0,1,0]=>0 [1,1,1,1,0,0,0,1,0,1,0,0]=>0 [1,1,1,1,0,0,0,1,1,0,0,0]=>0 [1,1,1,1,0,0,1,0,0,0,1,0]=>0 [1,1,1,1,0,0,1,0,0,1,0,0]=>0 [1,1,1,1,0,0,1,0,1,0,0,0]=>0 [1,1,1,1,0,0,1,1,0,0,0,0]=>0 [1,1,1,1,0,1,0,0,0,0,1,0]=>0 [1,1,1,1,0,1,0,0,0,1,0,0]=>0 [1,1,1,1,0,1,0,0,1,0,0,0]=>0 [1,1,1,1,0,1,0,1,0,0,0,0]=>0 [1,1,1,1,0,1,1,0,0,0,0,0]=>0 [1,1,1,1,1,0,0,0,0,0,1,0]=>0 [1,1,1,1,1,0,0,0,0,1,0,0]=>0 [1,1,1,1,1,0,0,0,1,0,0,0]=>0 [1,1,1,1,1,0,0,1,0,0,0,0]=>0 [1,1,1,1,1,0,1,0,0,0,0,0]=>0 [1,1,1,1,1,1,0,0,0,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>4 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>3 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>3 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>3 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>1 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>5 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>4 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>4 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>4 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>4 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>2 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>1 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>4 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>3 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>0 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>0 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>3 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>4 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>0 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>0 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>3 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>0 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>1 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>1 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>3 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>2 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>0 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>1 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>1 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>0 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>3 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>0 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>0 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>3 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>1 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>2 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>1 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>0 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>4 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>4 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>5 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>5 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>4 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>0 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>3 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>2 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>2 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>2 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>5 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>4 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>3 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>6 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>5 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>4 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>5 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>5 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>5 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>2 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>3 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>5 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>0 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>2 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>4 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>4 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>4 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>3 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>4 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>5 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>2 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>4 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>6 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>0 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>2 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>4 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>6 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>3 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>0 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>0 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>1 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>1 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>0 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>1 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>1 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>0 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>1 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>2 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>0 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>0 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>1 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>1 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>0 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>1 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>2 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>1 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>0 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>2 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>4 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>0 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>2 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>4 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>0 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>0 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>1 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>0 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>3 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>2 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>3 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>2 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>0 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>4 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>4 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>4 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>4 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>5 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>1 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>3 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>5 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>1 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>0 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>3 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>3 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>4 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>2 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>5 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>3 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>6 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>4 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>2 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>0 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>3 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>6 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>4 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>0 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>0 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>0 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>1 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>0 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>0 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>0 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>0 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>2 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>1 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>0 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>0 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>0 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>2 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>0 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>2 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>0 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>3 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>2 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>1 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>0 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>0 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>0 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>2 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>1 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>0 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>2 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>0 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>4 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>3 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>2 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>0 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>4 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>3 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>2 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>0 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>0 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>0 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>0 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>0 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>0 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>0 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>0 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>0 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>0 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>0 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>0 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>0 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>0 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>0 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>0 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>0 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>0 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>0 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>0 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>0 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>0 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>0 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>0 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>0 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>0 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>0 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>0 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>5 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>4 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>4 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>5 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>3 [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2 [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>3 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>4 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>6 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>4 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>4 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>3 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>3 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>3 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>1 [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>4 [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>6 [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>6 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3 [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>4 [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>3 [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>7 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3 [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>3 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>5 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1 [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2 [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3 [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>5 [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>6 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>4 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2 [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2 [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3 [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>3 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>3 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>3 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2 [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3 [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>5 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1 [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2 [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>3 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>0 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>4 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3 [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>5 [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>3 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>3 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>3 [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1 [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>3 [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>1 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>4 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>6 [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>7 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>4 [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>4 [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>7 [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>7 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>6 [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>4 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>6 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>6 [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>4 [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>4 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>4 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>2 [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>5 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>4 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>8 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>7 [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>6 [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>7 [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>7 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>7 [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>5 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>6 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>7 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>4 [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>4 [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>5 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>6 [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>4 [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>6 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>8 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>5 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2 [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>2 [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>4 [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>6 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>0 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1 [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>3 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>4 [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3 [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>6 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>2 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3 [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2 [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>2 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>5 [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>4 [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>5 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>4 [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>7 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>6 [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>7 [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>7 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>7 [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>8 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>6 [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>8 [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>6 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>3 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>3 [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>3 [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>5 [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>7 [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>5 [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>6 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>9 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>7 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>5 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>3 [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>3 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>6 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>5 [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>3 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>0 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2 [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>2 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>2 [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>4 [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>3 [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>5 [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>6 [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>5
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Description
The number of indecomposable modules of the linear Nakayama algebra corresponding to a Dyck path whose projective dimension and injective dimension are at least two.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
References
[1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. zbMATH:06820683
Code
gap('LoadPackage("QPA");')

def NthRadical(M, n):
    if n == 0:
        f = gap.IdentityMapping(M)
    else:
        f = gap.RadicalOfModuleInclusion(M)
        N = gap.Source(f)
        for i in range(n-1):
            h = gap.RadicalOfModuleInclusion(N)
            N = gap.Source(h)
            f = h * f
    return f

def ARQuiverNak(A):
    injA = gap.IndecInjectiveModules(A)
    L = [gap.Source(NthRadical(inj, j))
         for inj in injA
         for j in range(gap.Dimension(inj).sage())]
    return L

def kupisch(D):
    DR = D.reverse()
    H = DR.heights()
    return [1 + H[i] for i, s in enumerate(DR) if s == 0] + [1]

def statistic(D):
    K = kupisch(D)
    A = gap.NakayamaAlgebra(K, gap.GF(3))
    L = ARQuiverNak(A)
    return sum(1 for x in L
               if gap.ProjDimensionOfModule(x, 30) >= 2 and gap.InjDimensionOfModule(x, 30) >= 2)
Created
Apr 09, 2018 at 14:30 by Rene Marczinzik
Updated
Mar 13, 2026 at 16:39 by Nupur Jain