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Identifier
Values
=>
Cc0005;cc-rep
[1,0]=>1 [1,0,1,0]=>0 [1,1,0,0]=>2 [1,0,1,0,1,0]=>1 [1,0,1,1,0,0]=>0 [1,1,0,0,1,0]=>0 [1,1,0,1,0,0]=>1 [1,1,1,0,0,0]=>3 [1,0,1,0,1,0,1,0]=>0 [1,0,1,0,1,1,0,0]=>1 [1,0,1,1,0,0,1,0]=>2 [1,0,1,1,0,1,0,0]=>2 [1,0,1,1,1,0,0,0]=>0 [1,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,1,0,0]=>0 [1,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,0]=>2 [1,1,0,1,1,0,0,0]=>1 [1,1,1,0,0,0,1,0]=>0 [1,1,1,0,0,1,0,0]=>1 [1,1,1,0,1,0,0,0]=>2 [1,1,1,1,0,0,0,0]=>4 [1,0,1,0,1,0,1,0,1,0]=>1 [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]=>1 [1,0,1,1,0,0,1,0,1,0]=>0 [1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,0,0,1,0]=>1 [1,0,1,1,0,1,0,1,0,0]=>1 [1,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,0,1,0]=>3 [1,0,1,1,1,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,0,0,0]=>3 [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]=>1 [1,1,0,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,1,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,0,0]=>0 [1,1,0,1,0,0,1,0,1,0]=>0 [1,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,1,0,0,1,0]=>1 [1,1,0,1,0,1,0,1,0,0]=>1 [1,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,1,0,0,0,1,0]=>3 [1,1,0,1,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,1,1,0,0,0,0]=>1 [1,1,1,0,0,0,1,0,1,0]=>1 [1,1,1,0,0,0,1,1,0,0]=>0 [1,1,1,0,0,1,0,0,1,0]=>2 [1,1,1,0,0,1,0,1,0,0]=>2 [1,1,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,1,0,1,0,0,0]=>3 [1,1,1,0,1,1,0,0,0,0]=>2 [1,1,1,1,0,0,0,0,1,0]=>0 [1,1,1,1,0,0,0,1,0,0]=>1 [1,1,1,1,0,0,1,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,0]=>3 [1,1,1,1,1,0,0,0,0,0]=>5 [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]=>1 [1,0,1,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,0,1,1,0,1,0,0]=>1 [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]=>2 [1,0,1,0,1,1,0,0,1,1,0,0]=>0 [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]=>2 [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]=>1 [1,0,1,1,0,0,1,0,1,0,1,0]=>1 [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]=>0 [1,0,1,1,0,0,1,1,0,1,0,0]=>0 [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]=>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]=>2 [1,0,1,1,0,1,0,1,0,1,0,0]=>2 [1,0,1,1,0,1,0,1,1,0,0,0]=>1 [1,0,1,1,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,0,1,1,0,0,1,0,0]=>1 [1,0,1,1,0,1,1,0,1,0,0,0]=>1 [1,0,1,1,0,1,1,1,0,0,0,0]=>2 [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]=>3 [1,0,1,1,1,0,0,1,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,1,0,0,0,1,0]=>2 [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]=>2 [1,0,1,1,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,0]=>4 [1,0,1,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,0,0]=>4 [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]=>1 [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]=>1 [1,1,0,0,1,1,0,0,1,0,1,0]=>0 [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]=>2 [1,1,0,0,1,1,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,0,1,0,0]=>3 [1,1,0,0,1,1,1,0,1,0,0,0]=>3 [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]=>1 [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]=>0 [1,1,0,1,0,0,1,1,0,1,0,0]=>0 [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]=>2 [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]=>2 [1,1,0,1,0,1,0,1,0,1,0,0]=>2 [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]=>1 [1,1,0,1,0,1,1,0,0,1,0,0]=>1 [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]=>2 [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]=>3 [1,1,0,1,1,0,0,1,0,0,1,0]=>1 [1,1,0,1,1,0,0,1,0,1,0,0]=>1 [1,1,0,1,1,0,0,1,1,0,0,0]=>3 [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]=>2 [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]=>3 [1,1,0,1,1,1,0,0,0,0,1,0]=>4 [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]=>4 [1,1,0,1,1,1,0,1,0,0,0,0]=>4 [1,1,0,1,1,1,1,0,0,0,0,0]=>1 [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]=>1 [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]=>0 [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]=>2 [1,1,1,0,0,1,0,1,0,0,1,0]=>1 [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]=>2 [1,1,1,0,0,1,1,0,0,0,1,0]=>3 [1,1,1,0,0,1,1,0,0,1,0,0]=>3 [1,1,1,0,0,1,1,0,1,0,0,0]=>3 [1,1,1,0,0,1,1,1,0,0,0,0]=>1 [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]=>3 [1,1,1,0,1,0,0,1,0,0,1,0]=>1 [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]=>3 [1,1,1,0,1,0,1,0,0,0,1,0]=>2 [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]=>2 [1,1,1,0,1,0,1,1,0,0,0,0]=>3 [1,1,1,0,1,1,0,0,0,0,1,0]=>4 [1,1,1,0,1,1,0,0,0,1,0,0]=>4 [1,1,1,0,1,1,0,0,1,0,0,0]=>4 [1,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,1,1,0,1,1,1,0,0,0,0,0]=>2 [1,1,1,1,0,0,0,0,1,0,1,0]=>1 [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]=>2 [1,1,1,1,0,0,0,1,0,1,0,0]=>2 [1,1,1,1,0,0,0,1,1,0,0,0]=>1 [1,1,1,1,0,0,1,0,0,0,1,0]=>3 [1,1,1,1,0,0,1,0,0,1,0,0]=>3 [1,1,1,1,0,0,1,0,1,0,0,0]=>3 [1,1,1,1,0,0,1,1,0,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,0,1,0]=>4 [1,1,1,1,0,1,0,0,0,1,0,0]=>4 [1,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,1,1,1,0,1,0,1,0,0,0,0]=>4 [1,1,1,1,0,1,1,0,0,0,0,0]=>3 [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]=>1 [1,1,1,1,1,0,0,0,1,0,0,0]=>2 [1,1,1,1,1,0,0,1,0,0,0,0]=>3 [1,1,1,1,1,0,1,0,0,0,0,0]=>4 [1,1,1,1,1,1,0,0,0,0,0,0]=>6 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>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]=>1 [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]=>1 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1 [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]=>2 [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]=>2 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>0 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1 [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]=>1 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2 [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]=>3 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>0 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>0 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3 [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]=>3 [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]=>1 [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]=>1 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1 [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]=>2 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>0 [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]=>2 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>0 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>0 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>0 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>0 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2 [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]=>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]=>1 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>1 [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]=>3 [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]=>3 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>1 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1 [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]=>0 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>0 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2 [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]=>2 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2 [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]=>3 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3 [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]=>3 [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]=>3 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>3 [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]=>4 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>2 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3 [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]=>3 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>4 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>5 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>5 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5 [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]=>1 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1 [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]=>2 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>0 [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]=>2 [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]=>1 [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]=>0 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>0 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>0 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>2 [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]=>2 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2 [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]=>2 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>0 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>3 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>1 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>1 [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]=>3 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>4 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>4 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>4 [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]=>0 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>1 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>1 [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]=>2 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>0 [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]=>2 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>0 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>0 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>0 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>0 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2 [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]=>2 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>1 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2 [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]=>3 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3 [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]=>3 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3 [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]=>1 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1 [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]=>2 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1 [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]=>0 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>0 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>3 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2 [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]=>2 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2 [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]=>3 [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]=>3 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>3 [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]=>2 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>2 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2 [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]=>3 [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]=>4 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1 [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]=>2 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>2 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>4 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>3 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3 [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]=>4 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>5 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>5 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>5 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>5 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>5 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>1 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>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]=>1 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>0 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2 [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]=>1 [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]=>3 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>3 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>3 [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]=>1 [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]=>0 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>0 [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]=>2 [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]=>2 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2 [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]=>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]=>0 [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]=>3 [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]=>2 [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]=>3 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>4 [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]=>4 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>4 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>1 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1 [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]=>0 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>0 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>3 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2 [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]=>2 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2 [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]=>3 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3 [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]=>3 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3 [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]=>3 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3 [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]=>2 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>3 [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]=>4 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>1 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>4 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>2 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>4 [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]=>3 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>4 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>5 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>5 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>5 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>5 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>5 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2 [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]=>1 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>2 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2 [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]=>0 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>2 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>1 [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]=>2 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>3 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>3 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>3 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>1 [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]=>3 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>1 [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]=>3 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>2 [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]=>2 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>3 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>4 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>4 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>4 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>4 [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]=>4 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1 [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]=>4 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>2 [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]=>2 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>4 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>3 [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]=>3 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>4 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>5 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>5 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>5 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>5 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>5 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>3 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1 [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]=>2 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>2 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>1 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>3 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>3 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>3 [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]=>4 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>4 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>4 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>4 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>3 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>5 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>5 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>5 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>5 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>5 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>4 [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]=>1 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>2 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>3 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>4 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>5 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7 [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]=>1 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1 [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]=>1 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>0 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1 [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]=>1 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2 [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]=>0 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>0 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>0 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2 [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]=>1 [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]=>1 [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]=>1 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1 [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]=>1 [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]=>2 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>0 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>0 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>0 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2 [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]=>0 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2 [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1 [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]=>2 [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]=>2 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1 [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1 [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>1 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1 [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1 [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]=>1 [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>1 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2 [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1 [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>1 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2 [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]=>3 [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>3 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>0 [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>3 [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>3 [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]=>3 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>0 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2 [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2 [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2 [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]=>2 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2 [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3 [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3 [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]=>4 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>0 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>0 [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>0 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>4 [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]=>4 [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]=>1 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>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]=>1 [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]=>1 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1 [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1 [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]=>0 [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]=>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]=>0 [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]=>2 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>2 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2 [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>0 [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>3 [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>0 [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]=>0 [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>3 [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]=>3 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>0 [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>0 [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>0 [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>0 [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>0 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1 [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]=>2 [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>0 [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]=>0 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>0 [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]=>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]=>1 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1 [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]=>2 [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]=>2 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2 [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>1 [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]=>1 [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>1 [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>1 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>1 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1 [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2 [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1 [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]=>3 [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]=>3 [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>1 [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]=>1 [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1 [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>3 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2 [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2 [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2 [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>3 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>1 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>4 [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1 [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]=>1 [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]=>4 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>4 [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]=>4 [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>4 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>1 [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1 [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1 [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1 [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2 [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]=>1 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>1 [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]=>0 [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]=>0 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>0 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>0 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>0 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>3 [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]=>2 [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>2 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>2 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>2 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>2 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>3 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>3 [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>1 [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>1 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1 [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]=>3 [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>3 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1 [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3 [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>1 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1 [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]=>3 [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3 [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]=>2 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3 [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2 [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2 [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>3 [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>2 [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]=>4 [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]=>4 [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>2 [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2 [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2 [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2 [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1 [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]=>0 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>0 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>4 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>2 [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]=>2 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1 [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>1 [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1 [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]=>3 [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]=>3 [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3 [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]=>3 [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>2 [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>2 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>2 [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>3 [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>4 [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>3 [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>4 [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>3 [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>3 [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>3 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>3 [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>4 [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>0 [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5 [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1 [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>5 [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>2 [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>2 [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2 [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>5 [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>3 [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>3 [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>5 [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>4 [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>4 [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>4 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>4 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>4 [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>5 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6 [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>6 [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>6 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>6 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>0 [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>0 [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>0 [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>0 [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1 [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>0 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>0 [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1 [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>0 [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>0 [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2 [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2 [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>0 [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1 [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1 [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2 [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>0 [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3 [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>0 [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3 [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3 [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>0 [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3 [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>0 [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>0 [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>0 [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>0 [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>0 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1 [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>0 [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>1 [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1 [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1 [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>0 [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>0 [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>0 [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>0 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>0 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>0 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2 [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>0 [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2 [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>1 [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1 [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2 [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1 [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>1 [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>1 [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>1 [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1 [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1 [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1 [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>0 [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>0 [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>0 [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3 [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2 [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1 [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1 [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>3 [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>3 [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>3 [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2 [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>3 [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>0 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4 [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1 [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1 [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>4 [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>2 [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4 [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>3 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3 [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>4 [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5 [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>5 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>5 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>0 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>0 [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>0 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>0 [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>0 [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1 [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>0 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>0 [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1 [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>0
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Description
The height of the middle non-run of a Dyck path.
A non-run of a Dyck path is a pair of steps which are not both up or both down, that is, which either form a peak or a valley. The number of non-runs is odd. This statistic returns the height of the middle non-run.
Code
def statistic(D):
    H = D.heights()
    T := [H[i+1] for i in range(len(D)-1) if D[i] != D[i+1]]
    return T[(len(T)-1)/2]
Created
Aug 07, 2023 at 18:04 by Martin Rubey
Updated
Aug 07, 2023 at 18:04 by Martin Rubey