Identifier
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
[1,0] generating graphics... => 0
[1,0,1,0] generating graphics... => 1
[1,1,0,0] generating graphics... => 0
[1,0,1,0,1,0] generating graphics... => 2
[1,0,1,1,0,0] generating graphics... => 1
[1,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,0] generating graphics... => 1
[1,1,1,0,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,0] generating graphics... => 3
[1,0,1,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0] generating graphics... => 1
[1,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,0] generating graphics... => 1
[1,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,0] generating graphics... => 1
[1,1,0,1,1,0,0,0] generating graphics... => 1
[1,1,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,0] generating graphics... => 1
[1,1,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 4
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 3
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 3
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 3
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 3
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 1
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 1
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 1
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 1
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 1
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 1
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 1
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 4
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 3
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 3
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 3
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 3
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 1
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 1
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 1
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 1
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 1
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 1
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] generating graphics... => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] generating graphics... => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] generating graphics... => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 6
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] generating graphics... => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] generating graphics... => 2
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] generating graphics... => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] generating graphics... => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] generating graphics... => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] generating graphics... => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] generating graphics... => 0
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] generating graphics... => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] generating graphics... => 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] generating graphics... => 4
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] generating graphics... => 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] generating graphics... => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] generating graphics... => 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] generating graphics... => 4
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] generating graphics... => 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] generating graphics... => 3
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 4
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] generating graphics... => 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] generating graphics... => 4
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 4
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] generating graphics... => 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] generating graphics... => 4
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 4
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] generating graphics... => 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] generating graphics... => 4
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] generating graphics... => 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] generating graphics... => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 3
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] generating graphics... => 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] generating graphics... => 4
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] generating graphics... => 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] generating graphics... => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 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] generating graphics... => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 4
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] generating graphics... => 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] generating graphics... => 4
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] generating graphics... => 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] generating graphics... => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 3
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 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] generating graphics... => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] generating graphics... => 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] generating graphics... => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] generating graphics... => 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] generating graphics... => 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] generating graphics... => 4
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] generating graphics... => 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