Identifier
- St000386: Dyck paths ⟶ ℤ
Values
[] => 0
[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] => 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] => 0
[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] => 1
[1,1,0,1,0,0,1,0] => 1
[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] => 1
[1,1,1,0,0,1,0,0] => 1
[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] => 0
[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] => 1
[1,0,1,1,0,1,0,0,1,0] => 1
[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] => 1
[1,0,1,1,1,0,0,1,0,0] => 1
[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] => 1
[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] => 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] => 0
[1,1,0,1,0,1,1,0,0,0] => 0
[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] => 0
[1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => 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] => 0
[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] => 1
[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] => 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] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => 1
[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] => 1
[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] => 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] => 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] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => 1
[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] => 1
[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] => 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] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => 0
>>> Load all 1628 entries. <<<[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] => 1
[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] => 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] => 1
[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] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => 2
[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] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => 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] => 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] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => 1
[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] => 1
[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] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => 1
[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] => 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] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => 1
[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] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => 1
[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] => 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] => 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] => 1
[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] => 2
[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] => 1
[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] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => 1
[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] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => 1
[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] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => 1
[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] => 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] => 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] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => 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] => 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] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => 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] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 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] => 1
[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] => 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] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[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] => 1
[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] => 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] => 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] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[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] => 1
[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] => 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] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[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] => 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] => 2
[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] => 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] => 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] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[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] => 1
[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] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[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] => 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] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[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] => 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] => 2
[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] => 1
[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] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[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] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[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] => 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] => 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] => 1
[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] => 2
[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] => 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] => 2
[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] => 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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[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] => 2
[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] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[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] => 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] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 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] => 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] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[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] => 2
[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] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[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] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[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] => 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] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[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] => 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] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1
[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] => 2
[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] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1
[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] => 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] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[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] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[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] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[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] => 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] => 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] => 1
[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] => 2
[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] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[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] => 2
[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] => 2
[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] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 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] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[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] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[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] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[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] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2
[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] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[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] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[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] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[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] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[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] => 2
[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] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[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] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[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] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[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] => 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] => 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] => 1
[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] => 2
[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] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[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] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[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] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[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] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[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] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[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] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[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] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[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] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[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] => 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] => 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] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[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] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[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] => 1
[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] => 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] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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] => 0
[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] => 1
[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] => 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] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[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] => 1
[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] => 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] => 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] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[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] => 1
[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] => 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] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[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] => 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] => 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] => 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] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[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] => 1
[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] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[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] => 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] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[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] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[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] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[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] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[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] => 1
[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] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[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] => 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] => 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] => 2
[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] => 2
[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] => 2
[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] => 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] => 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] => 2
[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] => 3
[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] => 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] => 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] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[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] => 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] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[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] => 2
[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] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[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] => 1
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[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] => 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] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[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] => 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] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1
[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] => 2
[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] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[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] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[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] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1
[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] => 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] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[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] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[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] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 2
[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] => 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] => 2
[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] => 1
[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] => 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] => 3
[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] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[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] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[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] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 1
[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] => 1
[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] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[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] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[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] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[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] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[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] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[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] => 1
[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] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[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] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[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] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[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] => 1
[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] => 2
[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] => 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] => 2
[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] => 1
[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] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1
[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] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[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] => 2
[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] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1
[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] => 1
[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] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[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] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[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] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[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] => 1
[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] => 2
[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] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[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] => 1
[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] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[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] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[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] => 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] => 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] => 1
[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] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[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] => 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] => 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] => 2
[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] => 2
[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] => 2
[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] => 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] => 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] => 2
[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] => 3
[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] => 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] => 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] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[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] => 2
[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] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[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] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[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] => 2
[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] => 3
[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] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[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] => 2
[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] => 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] => 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] => 2
[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] => 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] => 2
[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] => 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] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[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] => 2
[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] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[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] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[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] => 3
[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] => 2
[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] => 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] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 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] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[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] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 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] => 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] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[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] => 2
[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] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[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] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 5
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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:
4,1 8,6 16,24,2 32,80,20 64,240,120,5
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 6\ q$
$F_{5} = 16 + 24\ q + 2\ q^{2}$
$F_{6} = 32 + 80\ q + 20\ q^{2}$
$F_{7} = 64 + 240\ q + 120\ q^{2} + 5\ q^{3}$
Description
The number of factors DDU in a Dyck path.
References
[1] Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n, having k ddu's [here u=(1,1) and d=(1,-1)]. OEIS:A091894
Code
def statistic(D):
return len(list(Word([0,0,1]).factor_occurrences_in(Word(D))))
Created
Feb 10, 2016 at 14:31 by Martin Rubey
Updated
Jan 11, 2018 at 15:02 by Martin Rubey
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