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Identifier
  • St000306: Dyck paths ⟶ ℤ (values match St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: )
Values
=>
Cc0005;cc-rep
[1,0]=>0 [1,0,1,0]=>1 [1,1,0,0]=>0 [1,0,1,0,1,0]=>2 [1,0,1,1,0,0]=>1 [1,1,0,0,1,0]=>1 [1,1,0,1,0,0]=>1 [1,1,1,0,0,0]=>0 [1,0,1,0,1,0,1,0]=>3 [1,0,1,0,1,1,0,0]=>2 [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]=>1 [1,1,0,0,1,0,1,0]=>2 [1,1,0,0,1,1,0,0]=>1 [1,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,0]=>1 [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]=>0 [1,0,1,0,1,0,1,0,1,0]=>4 [1,0,1,0,1,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,0]=>3 [1,0,1,0,1,1,0,1,0,0]=>3 [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]=>2 [1,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,1,1,0,0,1,0,0]=>2 [1,0,1,1,1,0,1,0,0,0]=>2 [1,0,1,1,1,1,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0]=>3 [1,1,0,0,1,0,1,1,0,0]=>2 [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]=>1 [1,1,0,1,0,0,1,0,1,0]=>3 [1,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,1,0,0]=>2 [1,1,0,1,0,1,1,0,0,0]=>1 [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]=>1 [1,1,0,1,1,1,0,0,0,0]=>1 [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]=>1 [1,1,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,0,0,1,0]=>2 [1,1,1,0,1,0,0,1,0,0]=>1 [1,1,1,0,1,0,1,0,0,0]=>1 [1,1,1,0,1,1,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,0]=>1 [1,1,1,1,0,0,0,1,0,0]=>1 [1,1,1,1,0,0,1,0,0,0]=>1 [1,1,1,1,0,1,0,0,0,0]=>1 [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]=>4 [1,0,1,0,1,0,1,1,0,0,1,0]=>4 [1,0,1,0,1,0,1,1,0,1,0,0]=>4 [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]=>4 [1,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,0]=>4 [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]=>2 [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]=>2 [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]=>3 [1,0,1,1,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,0]=>3 [1,0,1,1,0,1,1,0,0,1,0,0]=>3 [1,0,1,1,0,1,1,0,1,0,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,0]=>2 [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]=>2 [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]=>2 [1,0,1,1,1,0,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,1,0,0,0,1,0]=>3 [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]=>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]=>1 [1,1,0,0,1,0,1,0,1,0,1,0]=>4 [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]=>2 [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]=>3 [1,1,0,0,1,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,0,0,1,0]=>2 [1,1,0,0,1,1,1,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,1,1,0,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,0,1,0]=>4 [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]=>3 [1,1,0,1,0,0,1,1,0,1,0,0]=>3 [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]=>3 [1,1,0,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,1,0,1,0,0]=>2 [1,1,0,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,0,1,1,0,0,0,1,0]=>2 [1,1,0,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,1,0,1,1,1,0,0,0,0]=>1 [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]=>2 [1,1,0,1,1,0,0,1,1,0,0,0]=>2 [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]=>1 [1,1,0,1,1,1,0,0,0,0,1,0]=>2 [1,1,0,1,1,1,0,0,0,1,0,0]=>2 [1,1,0,1,1,1,0,0,1,0,0,0]=>2 [1,1,0,1,1,1,0,1,0,0,0,0]=>1 [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]=>2 [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]=>1 [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]=>2 [1,1,1,0,0,1,0,1,0,1,0,0]=>2 [1,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,1,1,0,0,1,1,0,0,0,1,0]=>2 [1,1,1,0,0,1,1,0,0,1,0,0]=>2 [1,1,1,0,0,1,1,0,1,0,0,0]=>1 [1,1,1,0,0,1,1,1,0,0,0,0]=>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]=>2 [1,1,1,0,1,0,0,1,0,1,0,0]=>2 [1,1,1,0,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,1,0,0,0,1,0]=>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]=>1 [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]=>1 [1,1,1,0,1,1,0,1,0,0,0,0]=>1 [1,1,1,0,1,1,1,0,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,0,1,0]=>2 [1,1,1,1,0,0,0,0,1,1,0,0]=>1 [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]=>1 [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]=>2 [1,1,1,1,0,0,1,0,0,1,0,0]=>1 [1,1,1,1,0,0,1,0,1,0,0,0]=>1 [1,1,1,1,0,0,1,1,0,0,0,0]=>1 [1,1,1,1,0,1,0,0,0,0,1,0]=>2 [1,1,1,1,0,1,0,0,0,1,0,0]=>1 [1,1,1,1,0,1,0,0,1,0,0,0]=>1 [1,1,1,1,0,1,0,1,0,0,0,0]=>1 [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]=>0 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>5 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>4 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>5 [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 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>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 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>5 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>4 [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]=>3 [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 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>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 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>3 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>3 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3 [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]=>4 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>3 [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]=>4 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>4 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>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]=>2 [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]=>4 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>4 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>4 [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]=>2 [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 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>2 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2 [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]=>5 [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]=>3 [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]=>3 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3 [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]=>4 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>3 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>2 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>3 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>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]=>2 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>5 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>3 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3 [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]=>3 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3 [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]=>2 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>4 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2 [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 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2 [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]=>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 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>2 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1 [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]=>4 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>2 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>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]=>3 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>2 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>2 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>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]=>3 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>2 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>2 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>2 [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 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2 [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]=>2 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>1 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>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]=>1 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>1 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>2 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>2 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>1 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>2 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>2 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>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]=>1 [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]=>2 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2 [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 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>2 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1 [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]=>1 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>1 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1 [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]=>1 [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]=>1 [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]=>1 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>1 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>1 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1 [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]=>1 [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]=>1 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>5 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>5 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>5 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>5 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>5 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4 [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>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]=>2 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>5 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>5 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>4 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>5 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>2 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3 [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]=>3 [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2 [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 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>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]=>1 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>6 [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]=>4 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4 [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>4 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2 [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2 [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>2 [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>5 [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>5 [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>4 [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>4 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3 [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2 [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3 [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3 [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>4 [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>5 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3 [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2 [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2 [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1 [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>5 [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>4 [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>4 [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>2 [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>3 [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>3 [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>2 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>3 [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>4 [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>2 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2 [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>2 [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>2 [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>1 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>3 [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>2 [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>2 [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>1 [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>2 [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>2 [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>2 [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>1 [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>1 [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>2 [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>2 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>1 [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>2 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>2 [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>2 [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>2 [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>1 [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>2 [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>1 [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>2 [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>2 [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>2 [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>1 [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>1 [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>2 [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>1 [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>1 [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>2 [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>1 [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>2 [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>2 [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>2 [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>1 [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>1 [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>1 [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>2 [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>1 [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>1 [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>1 [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>1 [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>0 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>1 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>2 [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>2 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>2 [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>2 [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>2 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>1 [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>2 [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2 [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>2 [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>2 [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>2 [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2 [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>4 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>4 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>4 [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>2 [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>1 [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>1 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2 [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>2 [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>1 [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>7 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>7 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>6 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>6 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6 [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>6 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>3 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>2 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>6 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>6 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>4 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>6 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>4 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>4 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>4 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>4 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>4 [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>4 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>4 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>1 [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>2 [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>2 [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>2 [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>2 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>1 [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>1 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>2 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>2 [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>2 [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>2 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>8 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>4 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>4 [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>3 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>3 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>7 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>0 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>4 [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>7 [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>1 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>3 [1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>3 [1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>3 [1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>3 [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3 [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>3 [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>3 [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>3 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>1 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>4 [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>4 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>1 [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>9 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>9 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9 [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>1 [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>1 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3 [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>0 [1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>1 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>1 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>3 [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>3 [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>3 [1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>3 [1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>3 [1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>3 [1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>3 [1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>4 [1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>4 [1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>4 [1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>4 [1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>4 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>3 [1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>3 [1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>3 [1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>3 [1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>4 [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>4 [1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>3 [1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>4 [1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>3 [1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>3 [1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>4 [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>3 [1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>4 [1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4 [1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4 [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4 [1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4 [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>4 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>4 [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>3 [1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>3 [1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>4 [1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>3 [1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>4 [1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>4 [1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>3 [1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>3 [1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>3 [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>3
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Description
The bounce count of a Dyck path.
For a Dyck path $D$ of length $2n$, this is the number of point $(i,i)$ for $1 \leq i < n$ that are touching points of the bounce path of $D$.
References
[1] Loehr, N. A. Permutation statistics and the $q$, $t$-Catalan sequence MathSciNet:2101036
Code
def statistic(D):
    return len(D.bounce_path().touch_points())-1
Created
Dec 02, 2015 at 15:27 by Christian Stump
Updated
Jan 29, 2020 at 14:06 by Christian Stump