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Identifier
Values
=>
Cc0005;cc-rep
[1,0]=>2 [1,0,1,0]=>3 [1,1,0,0]=>2 [1,0,1,0,1,0]=>4 [1,0,1,1,0,0]=>3 [1,1,0,0,1,0]=>2 [1,1,0,1,0,0]=>3 [1,1,1,0,0,0]=>2 [1,0,1,0,1,0,1,0]=>5 [1,0,1,0,1,1,0,0]=>4 [1,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,0]=>4 [1,0,1,1,1,0,0,0]=>3 [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]=>4 [1,1,0,1,0,1,0,0]=>4 [1,1,0,1,1,0,0,0]=>3 [1,1,1,0,0,0,1,0]=>2 [1,1,1,0,0,1,0,0]=>2 [1,1,1,0,1,0,0,0]=>3 [1,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,0,1,0,1,0]=>6 [1,0,1,0,1,0,1,1,0,0]=>5 [1,0,1,0,1,1,0,0,1,0]=>4 [1,0,1,0,1,1,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,0,1,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,1,0,0,0]=>4 [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]=>4 [1,0,1,1,1,1,0,0,0,0]=>3 [1,1,0,0,1,0,1,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,1,1,0,0,0]=>2 [1,1,0,1,0,0,1,0,1,0]=>5 [1,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,1,0,1,0,1,0,0]=>4 [1,1,0,1,0,1,1,0,0,0]=>4 [1,1,0,1,1,0,0,0,1,0]=>3 [1,1,0,1,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,1,1,0,0,0,0]=>3 [1,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,0]=>3 [1,1,1,0,0,1,1,0,0,0]=>2 [1,1,1,0,1,0,0,0,1,0]=>4 [1,1,1,0,1,0,0,1,0,0]=>4 [1,1,1,0,1,0,1,0,0,0]=>4 [1,1,1,0,1,1,0,0,0,0]=>3 [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]=>3 [1,1,1,1,1,0,0,0,0,0]=>2 [1,0,1,0,1,0,1,0,1,0,1,0]=>7 [1,0,1,0,1,0,1,0,1,1,0,0]=>6 [1,0,1,0,1,0,1,1,0,0,1,0]=>5 [1,0,1,0,1,0,1,1,0,1,0,0]=>6 [1,0,1,0,1,0,1,1,1,0,0,0]=>5 [1,0,1,0,1,1,0,0,1,0,1,0]=>4 [1,0,1,0,1,1,0,0,1,1,0,0]=>4 [1,0,1,0,1,1,0,1,0,0,1,0]=>6 [1,0,1,0,1,1,0,1,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,1,0,0,0,0]=>4 [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]=>3 [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]=>6 [1,0,1,1,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,0,0]=>5 [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]=>5 [1,0,1,1,0,1,1,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,1,0,0,0,0]=>4 [1,0,1,1,1,0,0,0,1,0,1,0]=>3 [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]=>3 [1,0,1,1,1,0,0,1,0,1,0,0]=>3 [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]=>5 [1,0,1,1,1,0,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,1,0,0,0]=>5 [1,0,1,1,1,0,1,1,0,0,0,0]=>4 [1,0,1,1,1,1,0,0,0,0,1,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,1,1,1,0,0,0,0,0]=>3 [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]=>4 [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]=>4 [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]=>3 [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]=>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]=>3 [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]=>3 [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]=>6 [1,1,0,1,0,0,1,0,1,1,0,0]=>5 [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]=>5 [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]=>6 [1,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,1,0,1,0,1,0,1,0,0,1,0]=>4 [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]=>4 [1,1,0,1,0,1,1,0,0,0,1,0]=>4 [1,1,0,1,0,1,1,0,0,1,0,0]=>5 [1,1,0,1,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,1,0,0,0,0]=>4 [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]=>3 [1,1,0,1,1,0,0,1,0,0,1,0]=>5 [1,1,0,1,1,0,0,1,0,1,0,0]=>5 [1,1,0,1,1,0,0,1,1,0,0,0]=>4 [1,1,0,1,1,0,1,0,0,0,1,0]=>5 [1,1,0,1,1,0,1,0,0,1,0,0]=>5 [1,1,0,1,1,0,1,0,1,0,0,0]=>4 [1,1,0,1,1,0,1,1,0,0,0,0]=>4 [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]=>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]=>3 [1,1,1,0,0,0,1,0,1,0,1,0]=>4 [1,1,1,0,0,0,1,0,1,1,0,0]=>3 [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]=>3 [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]=>4 [1,1,1,0,0,1,0,0,1,1,0,0]=>3 [1,1,1,0,0,1,0,1,0,0,1,0]=>4 [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]=>2 [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]=>2 [1,1,1,0,1,0,0,0,1,0,1,0]=>5 [1,1,1,0,1,0,0,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,1,0,0,1,0]=>5 [1,1,1,0,1,0,0,1,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,0,0]=>4 [1,1,1,0,1,0,1,0,0,0,1,0]=>5 [1,1,1,0,1,0,1,0,0,1,0,0]=>4 [1,1,1,0,1,0,1,0,1,0,0,0]=>4 [1,1,1,0,1,0,1,1,0,0,0,0]=>4 [1,1,1,0,1,1,0,0,0,0,1,0]=>3 [1,1,1,0,1,1,0,0,0,1,0,0]=>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]=>3 [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]=>2 [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]=>2 [1,1,1,1,1,0,0,0,0,1,0,0]=>2 [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]=>2 [1,1,1,1,1,0,1,0,0,0,0,0]=>3 [1,1,1,1,1,1,0,0,0,0,0,0]=>2 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>7 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>6 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>7 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>6 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>5 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>5 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>7 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>6 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>5 [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]=>4 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>4 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>4 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>7 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>6 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>5 [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]=>4 [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]=>6 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>6 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>5 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>5 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>4 [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]=>4 [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]=>4 [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]=>3 [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]=>3 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>3 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3 [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]=>7 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>6 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>5 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>6 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>7 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>6 [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]=>6 [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]=>6 [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]=>5 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>4 [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]=>6 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>6 [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]=>6 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>5 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>5 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>4 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>4 [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]=>3 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3 [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]=>4 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>3 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>3 [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]=>6 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6 [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]=>6 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>5 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>5 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>5 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>5 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>4 [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]=>3 [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]=>3 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>5 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>5 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>5 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>5 [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]=>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]=>4 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>3 [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]=>5 [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]=>5 [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]=>3 [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]=>5 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>5 [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]=>3 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3 [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]=>3 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>4 [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]=>2 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3 [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]=>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]=>4 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>4 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>4 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4 [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]=>3 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>2 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>3 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>4 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>4 [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]=>2 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>2 [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]=>2 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>7 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>6 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>6 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>4 [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]=>6 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>6 [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]=>4 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>4 [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]=>4 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>7 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>6 [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]=>6 [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]=>5 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>4 [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]=>5 [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]=>5 [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]=>4 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>6 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>6 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>5 [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]=>5 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>4 [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]=>5 [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]=>4 [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]=>3 [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]=>6 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>5 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>6 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>5 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>5 [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]=>5 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>5 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>6 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>5 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>6 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>5 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>5 [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]=>5 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>5 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>4 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>4 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>5 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>5 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>4 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>3 [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]=>3 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>3 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>3 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>5 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>5 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>5 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>4 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>5 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>5 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>5 [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]=>4 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>3 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>3 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>4 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>4 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>3 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>5 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>4 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>3 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>4 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>3 [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]=>4 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>4 [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]=>2 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>2 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>3 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>2 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>5 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4 [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]=>4 [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]=>5 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>4 [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]=>3 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>3 [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]=>3 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>3 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>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]=>3 [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]=>3 [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]=>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]=>3 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>3 [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]=>6 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>5 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>4 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>5 [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]=>6 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>5 [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]=>5 [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]=>5 [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]=>4 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>6 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>5 [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]=>5 [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]=>5 [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]=>4 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>4 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>5 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>4 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>4 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>4 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>3 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>3 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>5 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>5 [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]=>5 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>5 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>4 [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]=>5 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>5 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>4 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>4 [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]=>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]=>4 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>4 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>4 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>3 [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]=>3 [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]=>3 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>2 [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]=>3 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>3 [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]=>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]=>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]=>3 [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]=>4 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3 [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]=>2 [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]=>2 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>5 [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]=>5 [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]=>5 [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]=>4 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>5 [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]=>4 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>3 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>4 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>4 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>4 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>4 [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]=>3 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>3 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>3 [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]=>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]=>3 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>3 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>3 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>3 [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]=>4 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>4 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>4 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>4 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>4 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>3 [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]=>3 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>2
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Description
The global dimension of the cyclic Nakayama algebra obtained from the linear Nakayama algebra corresponding to a Dyck path.
We make a cyclic Nakayama algebra out of the linear Nakayama algebra (corresponding to the Dyck path) with Kupisch series $[c_0,c_1,\ldots,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. Then we calculate the global dimension of that cyclic Nakayama algebra.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
Code
def kupisch(D):
    DR = D.reverse()
    H = DR.heights()
    return [1 + H[i] for i, s in enumerate(DR) if s == 0] + [1]

def lnak_to_cnak(L):
    """Convert LNakayama Kupisch series to CNakayama: set last entry to first + 1."""
    K = list(L)
    K[-1] = K[0] + 1
    return K

def gldim_from_kupisch(L):
    n = len(L)
    def f(x, y):
        c = (x + y) % n
        if c == 0: c = n
        z = (x + 1) % n
        if z == 0: z = n
        return (c, L[z - 1] - y)
    temp = [[(i, 1)] for i in range(n)]
    for i in range(n):
        for _ in range(2 * n + 2):
            temp[i].append(f(temp[i][-1][0], temp[i][-1][1]))
    temp3 = []
    for i in range(n):
        zeros = [j + 1 for j in range(len(temp[i])) if temp[i][j][1] == 0]
        if zeros:
            temp3.append(min(zeros))
        else:
            return "inf"
    return max(temp3) - 2

def statistic(D):
    return gldim_from_kupisch(lnak_to_cnak(kupisch(D)))
Created
Sep 03, 2017 at 14:54 by Rene Marczinzik
Updated
Mar 11, 2026 at 18:29 by Nupur Jain