Identifier
- St001139: Dyck paths ⟶ ℤ
Values
[1,0,1,0] => 0
[1,1,0,0] => 1
[1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => 0
[1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => 1
[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] => 1
[1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => 0
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => 1
[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] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => 0
[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] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[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] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[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] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[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] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,2 10,3,1 31,8,3 98,27,6,1 321,88,16,4
$F_{2} = 1 + q$
$F_{3} = 3 + 2\ q$
$F_{4} = 10 + 3\ q + q^{2}$
$F_{5} = 31 + 8\ q + 3\ q^{2}$
$F_{6} = 98 + 27\ q + 6\ q^{2} + q^{3}$
$F_{7} = 321 + 88\ q + 16\ q^{2} + 4\ q^{3}$
Description
The number of occurrences of hills of size 2 in a Dyck path.
A hill of size two is a subpath beginning at height zero, consisting of two up steps followed by two down steps.
A hill of size two is a subpath beginning at height zero, consisting of two up steps followed by two down steps.
Code
def statistic(D):
return list(D.touch_composition()).count(2)
Created
Apr 09, 2018 at 14:32 by Martin Rubey
Updated
Apr 09, 2018 at 14:32 by Martin Rubey
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