Identifier
- St000932: Dyck paths ⟶ ℤ (values match St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra., St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless.)
Values
[1,0,1,0] => 1
[1,1,0,0] => 0
[1,0,1,0,1,0] => 2
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 0
[1,1,0,1,0,0] => 1
[1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0] => 1
[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] => 2
[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] => 0
[1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0] => 1
[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] => 2
[1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0] => 1
[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] => 1
[1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => 1
[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] => 1
[1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => 3
[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] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => 2
[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] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => 3
[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] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => 2
[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] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => 2
[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] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => 1
[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
[1,0,1,1,1,1,0,0,0,0,1,0] => 1
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => 3
[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] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => 2
[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] => 1
[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] => 2
[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] => 0
[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] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => 2
[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] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => 3
[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] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => 2
[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] => 2
[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] => 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] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => 0
[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] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => 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] => 1
[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] => 2
[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] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => 1
[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] => 0
[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] => 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] => 1
[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] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => 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] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[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] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[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] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[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] => 3
[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] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[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] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[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] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[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] => 2
[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] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3
[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] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[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] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[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] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[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] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[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] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[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] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3
[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] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[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] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[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] => 2
[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] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[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] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[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] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 2
[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] => 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] => 1
[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] => 0
[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] => 0
[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] => 2
[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] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0
[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] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[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] => 3
[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] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[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] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 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] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2
[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] => 2
[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] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[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] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 3
[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] => 3
[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] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[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] => 2
[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] => 1
[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] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[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] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[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] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[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] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[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] => 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] => 2
[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] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[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] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 1
[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] => 2
[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] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[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] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2
[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] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0
[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] => 1
[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] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[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] => 1
[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] => 3
[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] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[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] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[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] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[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] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[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] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[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] => 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] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0
[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] => 2
[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] => 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] => 1
[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] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0
[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] => 1
[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] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[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] => 1
[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] => 2
[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] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[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] => 0
[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] => 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] => 1
[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] => 1
[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] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 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] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
[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] => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[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] => 3
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3
[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] => 4
[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] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[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] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[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] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[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] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[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] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2
[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] => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[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] => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[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] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[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] => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[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] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[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] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[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] => 2
[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] => 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] => 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] => 2
[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] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[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] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 4
[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] => 5
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3
[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] => 4
[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] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[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] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 2
[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] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 3
[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] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2
[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] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 3
[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] => 4
[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] => 5
[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] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 2
[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] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 4
[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] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3
[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] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[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] => 4
[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] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[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] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1
[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] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[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] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[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] => 3
[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] => 4
[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] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[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] => 3
[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] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 4
[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] => 4
[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] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3
[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] => 3
[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] => 2
[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] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[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] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 3
[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] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[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] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[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] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[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] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[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] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[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] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[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] => 3
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[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] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[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] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[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] => 2
[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] => 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] => 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] => 2
[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] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[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] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[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] => 2
[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] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[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] => 3
[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] => 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] => 3
[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] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[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] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[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] => 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] => 2
[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] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[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] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0
[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] => 2
[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] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0
[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] => 0
[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] => 1
[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] => 2
[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] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => 2
[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] => 2
[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] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 0
[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] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0
[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] => 0
[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] => 2
[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] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[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] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[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] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[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] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
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Generating function
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Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,2,1 4,6,3,1 9,16,12,4,1 21,45,40,20,5,1 51,126,135,80,30,6,1
$F_{2} = 1 + q$
$F_{3} = 2 + 2\ q + q^{2}$
$F_{4} = 4 + 6\ q + 3\ q^{2} + q^{3}$
$F_{5} = 9 + 16\ q + 12\ q^{2} + 4\ q^{3} + q^{4}$
$F_{6} = 21 + 45\ q + 40\ q^{2} + 20\ q^{3} + 5\ q^{4} + q^{5}$
$F_{7} = 51 + 126\ q + 135\ q^{2} + 80\ q^{3} + 30\ q^{4} + 6\ q^{5} + q^{6}$
Description
The number of occurrences of the pattern UDU in a Dyck path.
The number of Dyck paths with statistic value 0 are counted by the Motzkin numbers [1].
The number of Dyck paths with statistic value 0 are counted by the Motzkin numbers [1].
References
[1] Motzkin numbers: number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle. OEIS:A001006
Code
def statistic(D):
return sum(1 for i in range(len(D)-2) if D[i:i+3] == [1,0,1])
Created
Aug 09, 2017 at 14:30 by Christian Stump
Updated
Aug 09, 2017 at 14:30 by Christian Stump
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