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
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The bounce count of a Dyck path.
For a Dyck path $D$ of length $2n$, this is the number of points $(i,i)$ for $1 \leq i < n$ that are touching points of the bounce path of $D$.
For a Dyck path $D$ of length $2n$, this is the number of points $(i,i)$ 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
Oct 17, 2024 at 16:23 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!