Identifier
- St000013: Dyck paths ⟶ ℤ (values match St000442The maximal area to the right of an up step of a Dyck path.)
Values
[] => 0
[1,0] => 1
[1,0,1,0] => 1
[1,1,0,0] => 2
[1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => 2
[1,1,0,0,1,0] => 2
[1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0] => 1
[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] => 3
[1,1,0,0,1,0,1,0] => 2
[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] => 2
[1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0] => 1
[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] => 3
[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] => 3
[1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0] => 2
[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] => 2
[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] => 4
[1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => 1
[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] => 3
[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] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => 3
[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] => 4
[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] => 3
[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] => 3
[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] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => 3
[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] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => 3
[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] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => 3
>>> Load all 1915 entries. <<<[1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => 2
[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] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => 2
[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] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => 2
[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] => 2
[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] => 4
[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] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => 3
[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] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => 3
[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] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => 3
[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] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => 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] => 5
[1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => 4
[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] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[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] => 3
[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] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[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] => 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] => 3
[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] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[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] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[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] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[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] => 3
[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] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[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] => 4
[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] => 3
[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] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[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] => 3
[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] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[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] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 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] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[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] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[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] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[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] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[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] => 4
[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] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[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] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[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] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[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] => 4
[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] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 5
[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] => 4
[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] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 5
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[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] => 3
[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] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 3
[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] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[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] => 3
[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] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 3
[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] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[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] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[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] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 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] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3
[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] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[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] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[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] => 5
[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] => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 6
[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] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 4
[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] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[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] => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[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] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[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] => 3
[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] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[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] => 5
[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
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[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] => 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] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[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] => 3
[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] => 4
[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] => 4
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 4
[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] => 4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[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
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[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
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[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] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[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] => 3
[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] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 5
[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] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[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] => 4
[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] => 4
[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] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 5
[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
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[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] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[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] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[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] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[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] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 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] => 4
[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] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 5
[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
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[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] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[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] => 3
[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] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[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] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => 6
[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] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 5
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 5
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => 5
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 6
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[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] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[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] => 3
[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] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 3
[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] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[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] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => 5
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => 5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => 5
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => 5
[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] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 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
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => 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] => 6
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 6
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => 5
[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] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 5
[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] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 6
[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] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 7
[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] => 7
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => 7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 6
[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] => 6
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 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
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 6
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 7
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 7
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => 6
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => 7
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => 7
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => 7
[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
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 7
[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] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[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
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[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] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[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] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[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] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[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] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[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] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[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] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[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] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[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] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => 5
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[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] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[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] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => 4
[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] => 3
[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] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 5
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 8
[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] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[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
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[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] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => 7
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 7
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[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] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[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] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[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] => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 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] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 5
[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] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 8
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => 8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 8
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[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] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => 9
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 11
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 9
[1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 8
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => 11
[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
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[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] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[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] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 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] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 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] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 5
[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] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[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] => 5
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 5
[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] => 5
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 5
[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] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 4
[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] => 5
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 6
[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] => 5
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 5
[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] => 6
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => 11
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[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] => 12
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0] => 11
[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
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => 7
[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] => 13
[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
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 10
[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] => 14
[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] => 1
[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] => 15
[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 13
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => 15
[1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] => 24
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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 1,3,1 1,7,5,1 1,15,18,7,1 1,31,57,33,9,1 1,63,169,132,52,11,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 3\ q^{2} + q^{3}$
$F_{4} = q + 7\ q^{2} + 5\ q^{3} + q^{4}$
$F_{5} = q + 15\ q^{2} + 18\ q^{3} + 7\ q^{4} + q^{5}$
$F_{6} = q + 31\ q^{2} + 57\ q^{3} + 33\ q^{4} + 9\ q^{5} + q^{6}$
$F_{7} = q + 63\ q^{2} + 169\ q^{3} + 132\ q^{4} + 52\ q^{5} + 11\ q^{6} + q^{7}$
Description
The height of a Dyck path.
The height of a Dyck path $D$ of semilength $n$ is defined as the maximal height of a peak of $D$. The height of $D$ at position $i$ is the number of up-steps minus the number of down-steps before position $i$.
The height of a Dyck path $D$ of semilength $n$ is defined as the maximal height of a peak of $D$. The height of $D$ at position $i$ is the number of up-steps minus the number of down-steps before position $i$.
Code
def statistic(x):
return x.height()
Created
Sep 27, 2011 at 19:30 by Chris Berg
Updated
Feb 13, 2024 at 15:15 by Martin Rubey
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