Identifier
- St001584: Dyck paths ⟶ ℤ
Values
[1,0] => 0
[1,0,1,0] => 0
[1,1,0,0] => 0
[1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => 0
[1,1,0,0,1,0] => 0
[1,1,0,1,0,0] => 1
[1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0] => 2
[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] => 0
[1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0] => 3
[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] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => 1
[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] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => 1
[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] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => 0
[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] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => 1
[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] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => 1
[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] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => 2
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => 3
[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] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => 0
[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] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => 1
[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] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => 1
[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] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => 1
[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] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => 1
[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] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => 2
[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] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,0] => 4
[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] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[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] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[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] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[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] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[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] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[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] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[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] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[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] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[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] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[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] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[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] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[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] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[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] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[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] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[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] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 1
[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] => 2
[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] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2
[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] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[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] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[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] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[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] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[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] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 5
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[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] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[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] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[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] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[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] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[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] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[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] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 6
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 6
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 6
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 6
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 5
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 6
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 6
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[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] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[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] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 6
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 6
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 7
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 4
[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] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 5
[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] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[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] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[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] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[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] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[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] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[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] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[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] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[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] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[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] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[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] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[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] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[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] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[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] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[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] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 5
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 5
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[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] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 4
[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] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[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] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 1
[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] => 2
[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] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[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] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2
[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] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[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] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[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] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[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] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[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] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[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] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[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] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[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] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[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] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[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] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 6
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[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] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[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] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 6
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[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] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 7
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 8
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 4
[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] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 5
[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] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[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] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 1
[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] => 2
[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] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[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] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[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] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => 0
[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] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[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] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2
[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] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[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] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[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] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 5
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[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] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[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] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[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] => 3
[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] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[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] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[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] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 5
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[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] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[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] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 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:
4,1 8,4,2 16,12,9,4,1 32,32,30,20,12,4,2 64,80,88,73,56,34,20,9,4,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 4\ q + 2\ q^{2}$
$F_{5} = 16 + 12\ q + 9\ q^{2} + 4\ q^{3} + q^{4}$
$F_{6} = 32 + 32\ q + 30\ q^{2} + 20\ q^{3} + 12\ q^{4} + 4\ q^{5} + 2\ q^{6}$
$F_{7} = 64 + 80\ q + 88\ q^{2} + 73\ q^{3} + 56\ q^{4} + 34\ q^{5} + 20\ q^{6} + 9\ q^{7} + 4\ q^{8} + q^{9}$
Description
The area statistic between a Dyck path and its bounce path.
The bounce path Mp00099bounce path is weakly below a given Dyck path and this statistic records the number of boxes between the two paths.
The bounce path Mp00099bounce path is weakly below a given Dyck path and this statistic records the number of boxes between the two paths.
Code
def statistic(D):
return D.area() - D.bounce_path().area()
Created
Aug 20, 2020 at 10:13 by Christian Stump
Updated
Aug 20, 2020 at 10:13 by Christian Stump
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