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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]=>0 [1,0,1,0,1,1,0,0]=>0 [1,0,1,1,0,0,1,0]=>0 [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]=>1 [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]=>0 [1,0,1,0,1,0,1,1,0,0]=>0 [1,0,1,0,1,1,0,0,1,0]=>0 [1,0,1,0,1,1,0,1,0,0]=>0 [1,0,1,0,1,1,1,0,0,0]=>0 [1,0,1,1,0,0,1,0,1,0]=>0 [1,0,1,1,0,0,1,1,0,0]=>1 [1,0,1,1,0,1,0,0,1,0]=>0 [1,0,1,1,0,1,0,1,0,0]=>0 [1,0,1,1,0,1,1,0,0,0]=>0 [1,0,1,1,1,0,0,0,1,0]=>0 [1,0,1,1,1,0,0,1,0,0]=>0 [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]=>0 [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]=>1 [1,1,0,0,1,1,1,0,0,0]=>2 [1,1,0,1,0,0,1,0,1,0]=>0 [1,1,0,1,0,0,1,1,0,0]=>1 [1,1,0,1,0,1,0,0,1,0]=>0 [1,1,0,1,0,1,0,1,0,0]=>0 [1,1,0,1,0,1,1,0,0,0]=>0 [1,1,0,1,1,0,0,0,1,0]=>0 [1,1,0,1,1,0,0,1,0,0]=>0 [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]=>2 [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]=>1 [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]=>0 [1,0,1,0,1,0,1,0,1,1,0,0]=>0 [1,0,1,0,1,0,1,1,0,0,1,0]=>0 [1,0,1,0,1,0,1,1,0,1,0,0]=>0 [1,0,1,0,1,0,1,1,1,0,0,0]=>0 [1,0,1,0,1,1,0,0,1,0,1,0]=>0 [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]=>0 [1,0,1,0,1,1,0,1,0,1,0,0]=>0 [1,0,1,0,1,1,0,1,1,0,0,0]=>0 [1,0,1,0,1,1,1,0,0,0,1,0]=>0 [1,0,1,0,1,1,1,0,0,1,0,0]=>0 [1,0,1,0,1,1,1,0,1,0,0,0]=>0 [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]=>0 [1,0,1,1,0,0,1,0,1,1,0,0]=>0 [1,0,1,1,0,0,1,1,0,0,1,0]=>1 [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]=>2 [1,0,1,1,0,1,0,0,1,0,1,0]=>0 [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]=>0 [1,0,1,1,0,1,0,1,0,1,0,0]=>0 [1,0,1,1,0,1,0,1,1,0,0,0]=>0 [1,0,1,1,0,1,1,0,0,0,1,0]=>0 [1,0,1,1,0,1,1,0,0,1,0,0]=>0 [1,0,1,1,0,1,1,0,1,0,0,0]=>0 [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]=>0 [1,0,1,1,1,0,0,0,1,1,0,0]=>2 [1,0,1,1,1,0,0,1,0,0,1,0]=>0 [1,0,1,1,1,0,0,1,0,1,0,0]=>0 [1,0,1,1,1,0,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,1,0,0,0,1,0]=>0 [1,0,1,1,1,0,1,0,0,1,0,0]=>0 [1,0,1,1,1,0,1,0,1,0,0,0]=>0 [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]=>0 [1,0,1,1,1,1,0,0,0,1,0,0]=>0 [1,0,1,1,1,1,0,0,1,0,0,0]=>0 [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]=>0 [1,1,0,0,1,0,1,0,1,1,0,0]=>0 [1,1,0,0,1,0,1,1,0,0,1,0]=>0 [1,1,0,0,1,0,1,1,0,1,0,0]=>0 [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]=>2 [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]=>1 [1,1,0,0,1,1,0,1,1,0,0,0]=>1 [1,1,0,0,1,1,1,0,0,0,1,0]=>2 [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]=>2 [1,1,0,0,1,1,1,1,0,0,0,0]=>3 [1,1,0,1,0,0,1,0,1,0,1,0]=>0 [1,1,0,1,0,0,1,0,1,1,0,0]=>0 [1,1,0,1,0,0,1,1,0,0,1,0]=>1 [1,1,0,1,0,0,1,1,0,1,0,0]=>1 [1,1,0,1,0,0,1,1,1,0,0,0]=>2 [1,1,0,1,0,1,0,0,1,0,1,0]=>0 [1,1,0,1,0,1,0,0,1,1,0,0]=>1 [1,1,0,1,0,1,0,1,0,0,1,0]=>0 [1,1,0,1,0,1,0,1,0,1,0,0]=>0 [1,1,0,1,0,1,0,1,1,0,0,0]=>0 [1,1,0,1,0,1,1,0,0,0,1,0]=>0 [1,1,0,1,0,1,1,0,0,1,0,0]=>0 [1,1,0,1,0,1,1,0,1,0,0,0]=>0 [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]=>0 [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]=>0 [1,1,0,1,1,0,0,1,0,1,0,0]=>0 [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]=>0 [1,1,0,1,1,0,1,0,0,1,0,0]=>0 [1,1,0,1,1,0,1,0,1,0,0,0]=>0 [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]=>0 [1,1,0,1,1,1,0,0,0,1,0,0]=>0 [1,1,0,1,1,1,0,0,1,0,0,0]=>0 [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]=>0 [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]=>2 [1,1,1,0,0,0,1,1,0,1,0,0]=>2 [1,1,1,0,0,0,1,1,1,0,0,0]=>4 [1,1,1,0,0,1,0,0,1,0,1,0]=>0 [1,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,1,1,0,0,1,0,1,0,0,1,0]=>0 [1,1,1,0,0,1,0,1,0,1,0,0]=>0 [1,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,1,1,0,0,1,1,0,0,0,1,0]=>1 [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]=>1 [1,1,1,0,0,1,1,1,0,0,0,0]=>2 [1,1,1,0,1,0,0,0,1,0,1,0]=>0 [1,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,1,0,0,1,0,0,1,0]=>0 [1,1,1,0,1,0,0,1,0,1,0,0]=>0 [1,1,1,0,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,1,0,0,0,1,0]=>0 [1,1,1,0,1,0,1,0,0,1,0,0]=>0 [1,1,1,0,1,0,1,0,1,0,0,0]=>0 [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]=>0 [1,1,1,0,1,1,0,0,0,1,0,0]=>0 [1,1,1,0,1,1,0,0,1,0,0,0]=>0 [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]=>3 [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]=>2 [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]=>1 [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]=>0 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>0 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>0 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>0 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>0 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>0 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>0 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>0 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>0 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>0 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>0 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>0 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>0 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>0 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1 [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]=>2 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>0 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>0 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>0 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>0 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>0 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>0 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>0 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>0 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>0 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>0 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>0 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>0 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>0 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>0 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>0 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>0 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>0 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>0 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>0 [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]=>0 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>0 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>0 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>0 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>0 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1 [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]=>1 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>1 [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]=>2 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>0 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>0 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>0 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>0 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>0 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>0 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>0 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>0 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>0 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>0 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>0 [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]=>0 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>0 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>1 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>0 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>0 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>0 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>0 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>0 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>0 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>0 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>0 [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]=>0 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>0 [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]=>2 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>4 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>0 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>0 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>0 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1 [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]=>0 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>0 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>0 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>0 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>0 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>0 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>0 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>0 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>0 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>0 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>0 [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]=>0 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>0 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>0 [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]=>0 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>0 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>0 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>0 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>0 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>0 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>0 [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]=>0 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>0 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>0 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>0 [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]=>0 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>0 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>0 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>0 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>0 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>0 [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]=>0 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>0 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>0 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>0 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>0 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>0 [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]=>1 [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]=>2 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>3 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>1 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>1 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>1 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>1 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>2 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>4 [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]=>3 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2 [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]=>2 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>3 [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]=>3 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>4 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>0 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>0 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>0 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>0 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>0 [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]=>2 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1 [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]=>2 [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]=>2 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>3 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>0 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>0 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1 [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]=>0 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>0 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>0 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>0 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>0 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>0 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>0 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>0 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>0 [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]=>0 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>0 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>0 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>0 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>0 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>0 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>0 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>0 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>0 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>0 [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]=>0 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>0 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>2 [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]=>4 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>0 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>0 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>0 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>1 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>2 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>0 [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]=>0 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>0 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>1 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>0 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>0 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>0 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>0 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>0 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>0 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>0 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>0 [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]=>0 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>3 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>0 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>0 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>2 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>0 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>0 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>0 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>0 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>0 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>0 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>0 [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]=>0 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>0 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>0 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>0 [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]=>0 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>0 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>0 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>0 [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]=>2 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>3 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2 [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]=>2 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>4 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>4 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>4 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>6 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>0 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>0 [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]=>2 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>0 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>1 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>0 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>0 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>0 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1 [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]=>2 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>3 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>1 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>2 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>1 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>1 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>1 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>2 [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]=>2 [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]=>2 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>3 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>0 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>0 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>2 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>4 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>0 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>0 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>0 [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]=>1 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1 [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]=>2 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>0 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>0 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>0 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>0 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>0 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>0 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>0 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>0 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>0 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>0 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>0 [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]=>0 [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]=>0 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>0 [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]=>0 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>0 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>0 [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]=>0 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>0 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>0 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>0 [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]=>0 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>0 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>0 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>0 [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]=>0 [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]=>3 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>3 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>6 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>0 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>0 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>0 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2 [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]=>2 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>4 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>0 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>0 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>0 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>0 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>0 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>0 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>1 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>1 [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]=>1 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>0 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>3 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>0 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>0 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>2 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>0 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>0 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>0 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>0 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>0 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>0 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>0 [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]=>0 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>0 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>0 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>0 [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]=>4 [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]=>3 [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]=>2 [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]=>1 [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]=>0 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>0 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>0 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>0 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>0 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>0 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>0 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>0 [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1 [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]=>0 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>0 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>0 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>0 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>0 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>0 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>0 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>0 [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>0 [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]=>0 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>0 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>0 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>0 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>0 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>0 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>0 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>0 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>0 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>0 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>0 [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>0 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>0 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>0 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>1 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>1 [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]=>2 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>0 [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1 [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]=>0 [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1 [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>0 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>0 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>0 [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>0 [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>0 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>0 [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>0 [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>0 [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>0 [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>0 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>1 [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>0 [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>0 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>0 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>0 [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>0 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>0 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>0 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>0 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>0 [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]=>2 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>0 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>0 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>0 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1 [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1 [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]=>0 [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]=>0 [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>0 [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>1 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>0 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>0 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>0 [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>0 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>0 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>0 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>0 [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>0 [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>0 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>0 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>0 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>0 [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]=>0 [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>0 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>0 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>0 [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>0 [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>0 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>0 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>0 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>0 [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>0 [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>0 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>0 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>0 [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]=>0 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>0 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>0 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>0 [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>0 [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>0 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1 [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>0 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>0 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>0 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>0 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>0 [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>0 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>0 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1 [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2 [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]=>3 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1 [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]=>1 [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>1 [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>1 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>1 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1 [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]=>4 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>2 [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]=>2 [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>3 [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]=>3 [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>4 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>0 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>0 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>0 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>0 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>0 [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1 [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]=>1 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1 [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]=>2 [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]=>3 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>0 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>0 [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1 [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1 [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>0 [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>0 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>0 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>0 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>0 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>0 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>0 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>0 [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>0 [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>0 [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>0 [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1 [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>0 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>0 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>0 [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>0 [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>0 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>0 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>0 [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>0 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>0 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>0 [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>2 [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]=>4 [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>0 [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>0 [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>0 [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>1 [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]=>0 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>0 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>0 [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>1 [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>0 [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>0 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>0 [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>0 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>0 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>0 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>0 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>0 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>0 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>0 [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>3 [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>0 [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>0 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>0 [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>0 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>0 [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1 [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>0 [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>0 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>0 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>0 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>0 [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>0 [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>0 [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>0 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>0 [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>0 [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]=>0 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>0 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>0 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>0 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>0 [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]=>3 [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]=>2 [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>6 [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>0 [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>0 [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1 [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]=>0 [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>0 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>0 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>0 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>1 [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]=>1 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>3 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>1 [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]=>2 [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2 [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]=>3 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>0 [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>0 [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]=>4 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>0 [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1 [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>0 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>0 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1 [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]=>0 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>0 [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>0 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>0 [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>0 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>0 [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>0 [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>0 [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>0 [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>0 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>0 [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>0 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>0 [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]=>0 [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>0 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>0 [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>0 [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>0 [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1 [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>0 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>0 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>0 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>0 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>0 [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>0 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>0 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>0 [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>0 [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>0 [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]=>0 [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>0 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>6 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>0 [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1 [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>0 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>0 [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]=>2 [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>2 [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]=>4 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>0 [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2 [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>0 [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>0 [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2 [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>0 [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>0
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Description
The dimension of $\operatorname{Hom}(I,P)$ for the linear Nakayama algebra corresponding to a Dyck path.
Here $I$ is the direct sum of all indecomposable injective non-projective modules and $P$ is the direct sum of all indecomposable projective non-injective modules.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
This statistic was discussed in [Theorem 5.7, 1].
References
[1] https://pub.uni-bielefeld.de/download/1775756/2312013
Code
gap('LoadPackage("QPA");')

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(gap.GF(3), K)
    projA = gap.IndecProjectiveModules(A)
    injA = gap.IndecInjectiveModules(A)
    rprojA = gap.Filtered(projA, gap('x -> IsInjectiveModule(x) = false'))
    rinjA = gap.Filtered(injA, gap('x -> IsProjectiveModule(x) = false'))
    M = gap.DirectSumOfQPAModules(rinjA)
    N = gap.DirectSumOfQPAModules(rprojA)
    return ZZ(gap.Size(gap.HomOverAlgebra(M, N)))
Created
Jan 12, 2017 at 02:00 by Rene Marczinzik
Updated
Mar 12, 2026 at 18:07 by Nupur Jain