Identifier
- St000011: Dyck paths ⟶ ℤ
Values
[] => 0
[1,0] => 1
[1,0,1,0] => 2
[1,1,0,0] => 1
[1,0,1,0,1,0] => 3
[1,0,1,1,0,0] => 2
[1,1,0,0,1,0] => 2
[1,1,0,1,0,0] => 1
[1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0] => 3
[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] => 2
[1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0] => 3
[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] => 3
[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] => 4
[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] => 2
[1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0] => 2
[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] => 2
[1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0] => 2
[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] => 1
[1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => 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] => 3
[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] => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => 3
[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] => 3
[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
>>> Load all 1758 entries. <<<[1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => 3
[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] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => 4
[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] => 4
[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] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => 2
[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] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => 4
[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] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => 2
[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] => 2
[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] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => 2
[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] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => 3
[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] => 1
[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] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => 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] => 2
[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] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => 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] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => 2
[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] => 1
[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] => 2
[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] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => 2
[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] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3
[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] => 3
[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] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 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] => 3
[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] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[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] => 3
[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] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3
[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] => 3
[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] => 3
[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] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 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] => 3
[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] => 3
[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] => 3
[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] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[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] => 4
[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] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[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] => 4
[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] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 3
[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] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[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] => 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] => 3
[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] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
[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] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4
[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] => 4
[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] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[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] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 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] => 2
[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] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 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] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[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] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 2
[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] => 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] => 1
[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] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 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] => 2
[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] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 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] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => 2
[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] => 1
[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] => 2
[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] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[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] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[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] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[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] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[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] => 3
[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] => 3
[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] => 1
[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] => 3
[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] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1
[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] => 1
[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] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 1
[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] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[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] => 1
[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] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 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] => 2
[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] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 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] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 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] => 1
[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] => 2
[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] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 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] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 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] => 1
[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] => 3
[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] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1
[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] => 1
[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] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 1
[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] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[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] => 1
[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] => 2
[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] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[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] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[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] => 1
[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] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1
[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] => 2
[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] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[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] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3
[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
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[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
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3
[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] => 3
[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] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 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] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 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] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[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] => 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] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[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] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[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
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 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] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[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] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[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] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => 1
[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
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => 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
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => 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] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 2
[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
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => 1
[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] => 1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => 1
[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
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => 1
[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] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 2
[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] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => 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] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => 1
[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] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 1
[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] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => 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] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[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] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[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] => 2
[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] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 2
[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] => 2
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
[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] => 2
[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] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[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] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 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] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[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] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => 1
[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] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[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
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => 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] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[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] => 7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 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] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 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] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[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] => 2
[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] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[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] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 2
[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] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => 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] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 12
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 2
[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] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 2
[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] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[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] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[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] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => 1
[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
[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 13
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 14
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 15
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0] => 2
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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
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + 2\ q^{2} + q^{3}$
$F_{4} = 5\ q + 5\ q^{2} + 3\ q^{3} + q^{4}$
$F_{5} = 14\ q + 14\ q^{2} + 9\ q^{3} + 4\ q^{4} + q^{5}$
$F_{6} = 42\ q + 42\ q^{2} + 28\ q^{3} + 14\ q^{4} + 5\ q^{5} + q^{6}$
$F_{7} = 132\ q + 132\ q^{2} + 90\ q^{3} + 48\ q^{4} + 20\ q^{5} + 6\ q^{6} + q^{7}$
Description
The number of touch points (or returns) of a Dyck path.
This is the number of points, excluding the origin, where the Dyck path has height 0.
This is the number of points, excluding the origin, where the Dyck path has height 0.
Code
def statistic(x):
return x.number_of_touch_points()
Created
Sep 27, 2011 at 19:28 by Chris Berg
Updated
Dec 26, 2022 at 18:34 by Martin Rubey
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