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Identifier
Values
=>
Cc0005;cc-rep
[1,0]=>0 [1,0,1,0]=>1 [1,1,0,0]=>1 [1,0,1,0,1,0]=>2 [1,0,1,1,0,0]=>1 [1,1,0,0,1,0]=>2 [1,1,0,1,0,0]=>2 [1,1,1,0,0,0]=>0 [1,0,1,0,1,0,1,0]=>3 [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]=>2 [1,1,0,0,1,0,1,0]=>3 [1,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,0,0,0]=>1 [1,1,1,0,0,0,1,0]=>1 [1,1,1,0,0,1,0,0]=>1 [1,1,1,0,1,0,0,0]=>1 [1,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,0]=>4 [1,0,1,0,1,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,1,0,1,0,0]=>2 [1,0,1,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,0,1,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,1,0,0]=>3 [1,0,1,1,0,1,1,0,0,0]=>3 [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]=>1 [1,1,0,0,1,0,1,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,0]=>2 [1,1,0,0,1,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,1,1,0,0,0]=>3 [1,1,0,1,0,0,1,0,1,0]=>4 [1,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,0]=>4 [1,1,0,1,0,1,0,1,0,0]=>4 [1,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,1,0,0,0,1,0]=>2 [1,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,1,1,1,0,0,0,0]=>2 [1,1,1,0,0,0,1,0,1,0]=>2 [1,1,1,0,0,0,1,1,0,0]=>1 [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]=>2 [1,1,1,0,1,0,0,0,1,0]=>2 [1,1,1,0,1,0,0,1,0,0]=>2 [1,1,1,0,1,0,1,0,0,0]=>2 [1,1,1,0,1,1,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,0]=>2 [1,1,1,1,0,0,0,1,0,0]=>2 [1,1,1,1,0,0,1,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,0]=>2 [1,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,0]=>5 [1,0,1,0,1,0,1,0,1,1,0,0]=>3 [1,0,1,0,1,0,1,1,0,0,1,0]=>3 [1,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,0,1,1,0,0,1,0,1,0]=>3 [1,0,1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,1,0,0,1,0]=>3 [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]=>3 [1,0,1,0,1,1,1,0,0,0,1,0]=>3 [1,0,1,0,1,1,1,0,0,1,0,0]=>3 [1,0,1,0,1,1,1,0,1,0,0,0]=>3 [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]=>4 [1,0,1,1,0,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,1,0,0]=>3 [1,0,1,1,0,0,1,1,1,0,0,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,0]=>4 [1,0,1,1,0,1,0,0,1,1,0,0]=>3 [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]=>4 [1,0,1,1,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,0,1,0]=>4 [1,0,1,1,0,1,1,0,0,1,0,0]=>4 [1,0,1,1,0,1,1,0,1,0,0,0]=>4 [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]=>4 [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]=>4 [1,0,1,1,1,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,1,0,0,0,1,0]=>4 [1,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,1,1,0,0,0,0,1,0]=>2 [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]=>2 [1,0,1,1,1,1,0,1,0,0,0,0]=>2 [1,0,1,1,1,1,1,0,0,0,0,0]=>2 [1,1,0,0,1,0,1,0,1,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,0,1,1,0,0,1,0]=>3 [1,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,0,1,1,1,0,0,0]=>3 [1,1,0,0,1,1,0,0,1,0,1,0]=>4 [1,1,0,0,1,1,0,0,1,1,0,0]=>3 [1,1,0,0,1,1,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,0,1,0,0]=>4 [1,1,0,0,1,1,0,1,1,0,0,0]=>4 [1,1,0,0,1,1,1,0,0,0,1,0]=>4 [1,1,0,0,1,1,1,0,0,1,0,0]=>4 [1,1,0,0,1,1,1,0,1,0,0,0]=>4 [1,1,0,0,1,1,1,1,0,0,0,0]=>2 [1,1,0,1,0,0,1,0,1,0,1,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,1,0,0,1,1,0,0,1,0]=>4 [1,1,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,0,0]=>4 [1,1,0,1,0,1,0,0,1,0,1,0]=>5 [1,1,0,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,1,0,1,0,1,1,0,0,0,1,0]=>3 [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]=>3 [1,1,0,1,0,1,1,1,0,0,0,0]=>3 [1,1,0,1,1,0,0,0,1,0,1,0]=>3 [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]=>3 [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]=>3 [1,1,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,1,0,0,0]=>3 [1,1,0,1,1,0,1,1,0,0,0,0]=>2 [1,1,0,1,1,1,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,0,0,0,1,0,0]=>3 [1,1,0,1,1,1,0,0,1,0,0,0]=>3 [1,1,0,1,1,1,0,1,0,0,0,0]=>3 [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]=>3 [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]=>2 [1,1,1,0,0,1,0,0,1,0,1,0]=>3 [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]=>3 [1,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,1,0,0,1,0,1,1,0,0,0]=>3 [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]=>3 [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]=>3 [1,1,1,0,1,0,0,1,0,1,0,0]=>3 [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]=>3 [1,1,1,0,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,1,0,1,0,1,0,0,0]=>3 [1,1,1,0,1,0,1,1,0,0,0,0]=>1 [1,1,1,0,1,1,0,0,0,0,1,0]=>2 [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]=>2 [1,1,1,0,1,1,0,1,0,0,0,0]=>2 [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]=>3 [1,1,1,1,0,0,0,0,1,1,0,0]=>2 [1,1,1,1,0,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,0,0,1,0,1,0,0]=>3 [1,1,1,1,0,0,0,1,1,0,0,0]=>3 [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]=>3 [1,1,1,1,0,1,0,0,0,1,0,0]=>3 [1,1,1,1,0,1,0,0,1,0,0,0]=>3 [1,1,1,1,0,1,0,1,0,0,0,0]=>3 [1,1,1,1,0,1,1,0,0,0,0,0]=>1 [1,1,1,1,1,0,0,0,0,0,1,0]=>1 [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]=>1 [1,1,1,1,1,0,0,1,0,0,0,0]=>1 [1,1,1,1,1,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>6 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>4 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>4 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>4 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4 [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]=>4 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>4 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>4 [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]=>3 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>4 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4 [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]=>4 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>4 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>4 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>4 [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]=>2 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2 [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]=>2 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>5 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>4 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>4 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>4 [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]=>5 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>4 [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]=>5 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>5 [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]=>5 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>5 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>5 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>5 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>5 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>3 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>3 [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]=>3 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>5 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>4 [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]=>5 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>5 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>5 [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]=>5 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>4 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>5 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>5 [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]=>5 [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]=>3 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>3 [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]=>2 [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]=>3 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>3 [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]=>3 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>3 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>6 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>4 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>4 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>4 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>4 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>4 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>4 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>5 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>5 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>5 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>5 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>5 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>5 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>3 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>5 [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]=>5 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>5 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>5 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>5 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>5 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>5 [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]=>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]=>3 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>6 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>4 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>4 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>5 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>5 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>5 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>5 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>5 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>5 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>5 [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]=>6 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>4 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>5 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>5 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>6 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>6 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>4 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>4 [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]=>4 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>4 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>4 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>3 [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]=>4 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>4 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>4 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>4 [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]=>3 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>4 [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]=>4 [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]=>4 [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]=>3 [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]=>4 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>4 [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]=>4 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>4 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>4 [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]=>4 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>4 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>4 [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]=>4 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>4 [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]=>3 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3 [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]=>4 [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]=>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]=>4 [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]=>4 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>3 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>4 [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]=>4 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2 [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]=>2 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>2 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>2 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>4 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>2 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>3 [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]=>3 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>3 [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]=>1 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>4 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>2 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>3 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>4 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>4 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>4 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>4 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>4 [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]=>4 [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]=>4 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>4 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>4 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>4 [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]=>4 [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]=>2 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>4 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>3 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3 [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]=>4 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>4 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>4 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>4 [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]=>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]=>4 [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]=>4 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>4 [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]=>2 [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]=>2 [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]=>3 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>3 [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]=>3 [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]=>2 [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]=>3 [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]=>3 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>3 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>3 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>3 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>4 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2 [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]=>3 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>3 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>4 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>4 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>4 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>4 [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]=>4 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>4 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>4 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>4 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>4 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>4 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2 [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]=>3 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>3 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>3 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>3 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>4 [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]=>4 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>4 [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]=>4 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>3 [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]=>4 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>4 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>2 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>2 [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]=>2 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>2 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>1 [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]=>2 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>2 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>2 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>1 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>2 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>2 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>2 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>2 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>2 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>2 [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]=>2 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2 [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]=>7 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>5 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>5 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>5 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>4 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>5 [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]=>5 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>5 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>5 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>5 [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>4 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>4 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>5 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>4 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>5 [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]=>5 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>5 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>5 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>5 [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]=>3 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3 [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]=>3 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>3 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>5 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>3 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>4 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>4 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4 [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>5 [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]=>4 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>4 [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>5 [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]=>5 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>5 [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]=>5 [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4 [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>5 [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]=>5 [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]=>5 [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]=>3 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3 [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]=>3 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>5 [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]=>4 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>4 [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]=>5 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>5 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>5 [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>3 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>5 [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>4 [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]=>5 [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>5 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>5 [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]=>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]=>3 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>3 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>3 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>3 [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>3 [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]=>2 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3 [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]=>3 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>3 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3 [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>3 [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]=>3 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>3 [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]=>6 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>4 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>4 [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>4 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4 [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]=>4 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>4 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>5 [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4 [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>5 [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4 [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]=>5 [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>5 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>5 [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>5 [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]=>5 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>5 [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>3 [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]=>3 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>6 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>4 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>4 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>5 [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>4 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>5 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>5 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>5 [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]=>6 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>4 [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]=>5 [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]=>6 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>6 [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]=>6 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>4 [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>6 [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>5 [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]=>6 [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>6 [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>6 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>6 [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]=>4 [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]=>4 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>4 [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>5 [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>5 [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>6 [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>5 [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]=>6 [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>6 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>6 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>6 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>6 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>5 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>6 [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]=>6 [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>6 [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]=>4 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>4 [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]=>4 [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]=>3 [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]=>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]=>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]=>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]=>4 [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>4 [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]=>4 [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]=>4 [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]=>6 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>4 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>5 [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>5 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>5 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>5 [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]=>6 [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>5 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>6 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>6 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>6 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>6 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>6 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>6 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>6 [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>6 [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]=>6 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>4 [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]=>4 [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]=>4 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>4 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>4 [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>5 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>6 [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>6 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>6 [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>6 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>6 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>6 [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]=>4 [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>4 [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]=>4 [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]=>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]=>4 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>4 [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]=>3 [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]=>4 [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>4 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>4 [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]=>4 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>4 [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2 [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]=>3 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4 [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>3 [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]=>4 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4 [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]=>4 [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>4 [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]=>4 [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]=>4 [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>4 [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>4 [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]=>3 [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>3 [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]=>4 [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]=>4 [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>4 [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>4 [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>4 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>4 [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2 [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>3 [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>4 [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>4 [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>4 [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>4 [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>4 [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>4 [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>4 [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>4 [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]=>2 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2 [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>2 [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>2 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>2 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>2 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5 [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5 [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>4 [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>5 [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>5 [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>5 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3 [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>5 [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>5 [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>5 [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>5 [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>5 [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>5 [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3 [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>5 [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4 [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>5 [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>5 [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>5 [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>5 [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>5 [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3 [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3 [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>3 [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>3 [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>3 [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>6 [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>4 [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>4 [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>4 [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>5 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4 [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>5 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>5 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>5 [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>5 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>5 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>5 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>3 [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>6 [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>4 [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>5 [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>5 [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>5 [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>6 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>6 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>6 [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>6 [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>6 [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>6 [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>6 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>4 [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>6 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>5 [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>6 [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>6 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>6 [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>6 [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>6 [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>6 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>4 [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>4 [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>4 [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>4 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>4 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>6 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>4 [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>5 [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>5 [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>5 [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>6 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>5 [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>6 [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>6 [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>6 [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>6 [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>6 [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>6 [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>4 [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>5 [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6 [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>6 [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>6 [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>6 [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>6 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>6 [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>4 [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>4 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>4 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>4 [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>4 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>3 [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>4 [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]=>4 [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>4 [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>4 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>3 [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>4 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4 [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]=>4 [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>4 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>4 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>4 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>4 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>7 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>5 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>5 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>3
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Description
The number of natural descents for set-valued two row standard Young tableaux.
Bijections via bicolored Motzkin paths (with two restrictions, see [1]) give the following for Dyck paths.
Let $j$ be smallest integer such that $2j$ is a down step. Then $k$ is a natural descent if
  • $k-2\ge j$ and positions 2(k-1)-1,2(k-1) are a valley i.e. [0,1], or
  • $k-2\ge j$ and positions 2(k-1)-1,2(k-1) are a peak i.e. [1,0], or
  • $k-1\ge j$ and positions 2(k-1),2k-1,2k form [0,1,1], or
  • $k=j$ and positions 2k-1,2k are double down i.e. [0,0], or
  • $k < j$ and positions 2k-1,2k are a valley i.e. [0,1].
References
[1] Alexander Lazar and Svante Linusson, "Two-row Set-Valued Tableaux: Catalan$^+k$ Combinatorics", Extended abstract at FPSAC 2024.
Code
def statistic(D):
    for j in range(1, D.semilength()+1):
        if D[2*j-1] == 0:
            break
    else:
        raise ValueError
    des = []
    for k in range(1, len(D)+2):
        if k-2 >= j and D[2*(k-1)-2:2*(k-1)] == [0,1]:
            des.append(k)
        elif k-2 >= j and D[2*(k-1)-2:2*(k-1)] == [1,0]:
            des.append(k)
        elif k-1 >= j and D[2*(k-1)-1:2*k] == [0,1,1]:
            des.append(k)
        elif k == j and D[2*k-2:2*k] == [0,0]:
            des.append(k)
        elif k < j and D[2*k-2:2*k] == [0,1]:
            des.append(k)
    return len(des)
Created
Jul 25, 2024 at 16:21 by Martin Rubey
Updated
Jul 25, 2024 at 16:21 by Martin Rubey