Identifier
- St000439: Dyck paths ⟶ ℤ (values match St000025The number of initial rises of a Dyck path.)
Values
[1,0] => 2
[1,0,1,0] => 2
[1,1,0,0] => 3
[1,0,1,0,1,0] => 2
[1,0,1,1,0,0] => 2
[1,1,0,0,1,0] => 3
[1,1,0,1,0,0] => 3
[1,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0] => 2
[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] => 2
[1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => 2
[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] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => 2
[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] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => 2
>>> Load all 1627 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => 2
[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] => 2
[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] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => 3
[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] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => 3
[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] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => 3
[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] => 3
[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] => 3
[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] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,1,0,0,0] => 5
[1,1,1,1,0,0,1,1,0,0,0,0] => 5
[1,1,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[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] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[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] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 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] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[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] => 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] => 2
[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] => 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] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 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] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[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] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[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] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[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] => 3
[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] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[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] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[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] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[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] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[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] => 3
[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] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[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] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[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] => 3
[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] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[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] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[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] => 3
[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] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[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] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[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] => 3
[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] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 3
[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] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 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] => 3
[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] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3
[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] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[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] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 4
[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] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[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] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[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] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[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] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2
[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] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[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] => 2
[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] => 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] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[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] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2
[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] => 2
[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] => 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] => 2
[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] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 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] => 2
[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] => 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] => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[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] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2
[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] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 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] => 2
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2
[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] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2
[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] => 2
[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] => 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] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 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] => 2
[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] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[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] => 2
[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] => 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] => 2
[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] => 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] => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 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] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[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] => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 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] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[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] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 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] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 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] => 2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 2
[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] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 2
[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] => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[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] => 3
[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] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[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] => 3
[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] => 3
[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] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[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] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[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] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[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] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[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] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 3
[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] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[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] => 3
[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] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[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] => 3
[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] => 3
[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] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3
[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] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[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] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[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] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[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] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[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] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
[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] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 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] => 3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 4
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 5
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 7
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 7
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 7
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 7
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 7
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 4
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 9
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 2
[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] => 2
[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] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 9
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[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] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 3
[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] => 4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[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] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[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] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 2
[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] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[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] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 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] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[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] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 3
[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] => 4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 3
[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] => 3
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 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] => 3
[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] => 3
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 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] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 4
[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] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 4
[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] => 5
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 7
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,2,1 5,5,3,1 14,14,9,4,1 42,42,28,14,5,1 132,132,90,48,20,6,1
$F_{1} = q^{2}$
$F_{2} = q^{2} + q^{3}$
$F_{3} = 2\ q^{2} + 2\ q^{3} + q^{4}$
$F_{4} = 5\ q^{2} + 5\ q^{3} + 3\ q^{4} + q^{5}$
$F_{5} = 14\ q^{2} + 14\ q^{3} + 9\ q^{4} + 4\ q^{5} + q^{6}$
$F_{6} = 42\ q^{2} + 42\ q^{3} + 28\ q^{4} + 14\ q^{5} + 5\ q^{6} + q^{7}$
$F_{7} = 132\ q^{2} + 132\ q^{3} + 90\ q^{4} + 48\ q^{5} + 20\ q^{6} + 6\ q^{7} + q^{8}$
Description
The position of the first down step of a Dyck path.
Code
def statistic(D):
return D.index(0)+1
Created
Feb 28, 2016 at 08:51 by Christian Stump
Updated
Dec 12, 2018 at 23:54 by Martin Rubey
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