Identifier
- St001034: Dyck paths ⟶ ℤ
Values
[] => 0
[1,0] => 1
[1,0,1,0] => 2
[1,1,0,0] => 2
[1,0,1,0,1,0] => 3
[1,0,1,1,0,0] => 3
[1,1,0,0,1,0] => 3
[1,1,0,1,0,0] => 3
[1,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,0] => 6
[1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,1,0,0,0] => 7
[1,1,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,0] => 8
[1,1,1,0,1,1,0,0,0,0] => 8
[1,1,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,0,1,0,0,0] => 8
[1,1,1,1,0,1,0,0,0,0] => 8
[1,1,1,1,1,0,0,0,0,0] => 9
[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] => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => 6
[1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,0,0,1,0] => 7
[1,0,1,0,1,1,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,0,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,0] => 9
>>> Load all 2181 entries. <<<[1,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,1,0,0,0] => 7
[1,1,0,0,1,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,0,1,0,1,1,0,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,0,0,1,0,1,0] => 7
[1,1,0,1,1,0,0,0,1,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,0,1,0] => 7
[1,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,1,0,1,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,1,0,0,1,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,0,0,1,0,0,0] => 9
[1,1,0,1,1,1,0,1,0,0,0,0] => 9
[1,1,0,1,1,1,1,0,0,0,0,0] => 10
[1,1,1,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => 7
[1,1,1,0,0,0,1,1,0,1,0,0] => 7
[1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,0,0,1,0,0,1,0,1,0] => 7
[1,1,1,0,0,1,0,0,1,1,0,0] => 7
[1,1,1,0,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,1,0,0,0] => 8
[1,1,1,0,0,1,1,0,0,0,1,0] => 8
[1,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,1,1,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,0,1,0,0,1,0] => 8
[1,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,1,1,0,1,0,1,0,0,0,1,0] => 9
[1,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,1,1,0,0,0,1,0,0] => 9
[1,1,1,0,1,1,0,0,1,0,0,0] => 10
[1,1,1,0,1,1,0,1,0,0,0,0] => 10
[1,1,1,0,1,1,1,0,0,0,0,0] => 11
[1,1,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,1,1,1,0,0,0,1,1,0,0,0] => 9
[1,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,1,1,1,0,0,1,0,0,1,0,0] => 9
[1,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,1,1,1,0,0,1,1,0,0,0,0] => 10
[1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,1,1,0,1,0,0,0,1,0,0] => 9
[1,1,1,1,0,1,0,0,1,0,0,0] => 10
[1,1,1,1,0,1,0,1,0,0,0,0] => 10
[1,1,1,1,0,1,1,0,0,0,0,0] => 11
[1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,0,0,0,1,0,0,0] => 11
[1,1,1,1,1,0,0,1,0,0,0,0] => 11
[1,1,1,1,1,0,1,0,0,0,0,0] => 12
[1,1,1,1,1,1,0,0,0,0,0,0] => 12
[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] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 8
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 8
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 9
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 7
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 7
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 8
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 8
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 8
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 8
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 9
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 8
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 9
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 7
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 7
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 9
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 7
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 7
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 8
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 8
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 8
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 8
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 8
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 8
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 8
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 8
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 10
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 9
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 11
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 9
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 10
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 11
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 13
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 8
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 7
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 7
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 7
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 8
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 8
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 9
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 9
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 7
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 7
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 7
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 7
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 8
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 8
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 9
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 7
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 7
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 9
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 9
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 10
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 11
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 8
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 8
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 9
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 10
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 9
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 9
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 9
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 10
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 10
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 10
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 9
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 9
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 11
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 12
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 12
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 12
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 13
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 13
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 8
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 8
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 9
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 8
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 9
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 9
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 10
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 10
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 9
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 9
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 9
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 9
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 10
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 9
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 9
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 9
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 9
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 10
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 10
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 10
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 11
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 10
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 12
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 9
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 9
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 9
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 9
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 10
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 9
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 10
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 10
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 10
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 11
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 10
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 10
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 10
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 11
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 11
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 12
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 13
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 10
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 10
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 11
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 11
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 12
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 12
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 13
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 12
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 12
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 13
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 13
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 14
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 14
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 9
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 9
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 9
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 10
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 9
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 9
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 9
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 9
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 10
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 11
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 10
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 10
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 11
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 11
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 11
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 12
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 11
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 12
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 13
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 10
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 10
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 10
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 11
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 11
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 12
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 12
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 11
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 12
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 13
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 12
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 12
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 13
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 13
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 14
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 14
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 11
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 12
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 12
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 12
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 13
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 13
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 12
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 13
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 13
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 14
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 13
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 14
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 14
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 15
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 13
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 13
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 14
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 14
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 16
[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] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 10
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 9
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 9
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 9
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 9
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 9
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 10
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 10
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 8
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 9
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 8
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 9
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 9
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 9
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 10
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 9
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 9
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 9
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 10
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 9
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 9
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 9
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 10
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 10
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 10
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 11
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 11
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 10
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 10
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 9
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 9
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 9
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 10
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 10
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 10
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 11
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 11
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 10
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 10
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 10
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 10
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 11
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 12
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 10
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 10
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 10
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 10
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 11
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 12
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 14
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 9
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 9
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 9
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 10
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 9
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 9
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 9
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 9
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 9
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 10
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 11
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 11
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 10
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 9
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 9
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 9
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 10
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 9
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 9
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 10
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 9
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 9
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 10
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 10
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 11
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 11
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 10
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 9
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 10
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 10
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 10
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 10
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 11
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 11
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 10
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 10
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 10
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 11
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 11
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 12
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 11
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 12
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 11
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 11
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 12
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 13
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 14
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 9
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 9
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 9
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 9
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 9
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 9
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 11
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 11
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 9
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 9
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 9
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 9
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 10
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 11
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 11
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 11
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 11
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 13
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 10
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 10
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 10
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 11
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 10
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 10
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 10
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 11
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 11
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 11
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 13
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 14
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 11
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 13
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 14
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 13
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 14
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 14
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 15
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 15
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 10
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 10
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 10
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 10
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 10
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 10
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 10
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 11
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 11
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 11
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 14
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 14
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 13
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 14
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 14
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 15
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 15
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 13
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 15
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 15
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 15
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 16
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 16
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 14
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 15
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 15
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 16
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 16
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 17
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 9
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 9
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 10
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 9
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 9
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 10
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 10
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 12
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 8
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 9
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 9
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 10
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 9
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 9
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 9
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 10
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 10
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 10
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 10
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 11
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 11
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 10
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 10
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 11
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 9
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 9
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 9
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 9
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 9
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 9
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 9
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 10
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 10
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 11
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 11
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 11
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 11
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 11
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 11
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 11
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 11
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 12
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 14
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 9
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 9
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 9
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 10
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => 9
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => 9
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => 11
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 12
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => 10
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => 10
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 10
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => 10
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => 10
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => 11
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => 10
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => 10
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => 11
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => 10
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => 10
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => 11
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => 12
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 14
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => 9
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => 9
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => 10
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => 10
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => 11
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 11
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => 11
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => 12
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => 13
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => 10
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 10
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 10
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => 11
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => 12
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => 12
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => 13
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 12
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => 15
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => 15
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => 10
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => 10
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => 11
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => 11
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => 12
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => 11
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 14
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 15
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 15
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 12
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => 15
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 15
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => 15
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 16
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 16
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => 14
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 14
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 15
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => 15
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 16
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 16
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 17
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => 11
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => 12
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => 12
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 12
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 13
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 11
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 9
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => 10
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => 10
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => 11
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => 10
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => 11
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => 11
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => 13
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 10
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => 11
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 11
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 12
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => 11
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => 12
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => 13
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => 15
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 10
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => 10
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 12
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 12
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 10
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 10
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 10
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 12
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 11
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => 11
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 11
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 11
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 11
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 12
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => 13
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 13
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 13
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 14
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => 14
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => 14
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => 15
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 12
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => 14
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 13
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => 14
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => 14
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => 15
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => 15
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => 15
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => 16
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => 16
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 12
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => 14
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 14
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => 14
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 15
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => 12
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => 13
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => 15
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => 15
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => 15
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 16
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => 16
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 13
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 13
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => 15
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => 15
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 14
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => 15
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 15
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 16
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => 15
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => 16
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 16
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => 17
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 17
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => 15
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 16
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 16
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 17
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 17
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 18
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 10
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => 10
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 12
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 12
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => 10
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => 10
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => 10
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 10
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => 11
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => 11
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => 12
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => 11
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => 12
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => 12
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => 13
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => 14
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => 11
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => 12
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => 13
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => 14
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => 14
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => 14
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => 15
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => 14
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => 14
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => 14
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => 14
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => 15
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => 15
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => 15
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => 16
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => 16
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 12
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 12
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => 14
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 14
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 15
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 12
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 12
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => 14
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => 13
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 14
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 15
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 14
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 15
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => 15
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 16
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 16
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 13
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => 15
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => 15
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => 15
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => 15
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => 16
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 15
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 16
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 16
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => 17
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 17
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 15
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 16
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 16
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 17
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 17
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 18
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 12
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 12
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 13
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => 12
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => 12
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => 12
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => 13
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => 13
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => 14
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => 14
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => 13
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 13
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 15
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => 15
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 14
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 15
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => 15
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 16
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 13
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => 15
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => 15
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => 15
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => 16
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 15
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => 15
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 16
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => 16
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => 17
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 17
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 14
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => 15
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 16
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => 16
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 15
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 16
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => 17
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 16
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 16
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 17
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => 17
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 18
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 18
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 16
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 16
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 17
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 17
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 18
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 18
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 19
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 14
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 14
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => 14
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => 14
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => 15
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => 15
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => 15
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 16
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => 16
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 15
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 15
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => 16
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 17
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 16
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 16
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 17
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 17
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 18
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 18
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 16
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 16
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => 17
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 17
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 18
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 18
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 19
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 17
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 17
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 18
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 18
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 19
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 19
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 20
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 20
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 21
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 21
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 21
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 21
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 20
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 20
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 20
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 20
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 20
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 19
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 19
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 19
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => 18
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 18
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 18
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 19
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 18
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 18
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 18
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 17
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 17
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 18
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 17
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 17
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 17
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 17
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 13
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 10
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 13
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 13
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 14
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => 12
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 14
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 14
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 14
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 15
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 13
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 15
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 15
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 16
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 20
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 19
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 20
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 18
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 20
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 20
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 21
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 21
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 15
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 16
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 17
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 20
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 22
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 16
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => 16
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 16
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => 16
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 17
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => 20
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => 22
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => 17
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => 17
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => 17
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 21
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => 22
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => 20
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => 22
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 23
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => 23
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => 21
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => 21
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => 21
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => 19
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => 22
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 20
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 22
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 23
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => 23
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => 20
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 20
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => 22
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => 22
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 21
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 24
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 24
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 21
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 22
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => 22
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => 23
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => 23
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 24
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 24
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 25
[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] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 10
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 10
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 11
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 11
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 12
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 12
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 13
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 13
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 13
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 14
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 14
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 15
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 10
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 15
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 16
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 11
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 15
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 13
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 15
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 15
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 16
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 9
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 15
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 14
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 13
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 12
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 11
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => 15
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => 13
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => 11
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 14
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 14
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 15
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => 14
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => 16
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 15
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 11
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 12
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 14
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 16
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 15
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => 15
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => 14
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => 15
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => 15
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 16
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 10
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => 11
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => 12
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => 13
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => 11
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => 11
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 10
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 15
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 15
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 14
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 14
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 14
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 14
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 26
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 26
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 25
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 25
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 25
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 25
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 25
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => 22
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 22
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 22
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 22
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 22
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 22
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 22
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 22
[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] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 14
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 17
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 17
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 17
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 19
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 10
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 19
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 11
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 20
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 12
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 18
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 14
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 18
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 16
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 18
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 19
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 20
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 30
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 10
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 24
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => 24
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 19
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 19
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 11
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => 29
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 29
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 28
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => 28
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 26
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 26
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 25
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 30
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => 29
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => 28
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 28
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 27
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 27
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 17
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 10
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 13
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 12
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 22
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 13
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 14
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 16
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 17
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 18
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => 27
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => 27
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => 28
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => 28
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => 29
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => 25
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 25
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 13
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 14
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 13
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 12
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 11
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 16
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 18
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 13
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 14
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 15
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 16
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 17
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 18
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 18
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 18
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 18
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 16
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 16
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 18
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 16
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 18
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 18
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 14
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 14
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 14
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 18
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 18
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 16
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 18
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 18
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 16
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 16
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 16
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 16
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 18
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 18
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 16
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 18
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 18
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 17
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 28
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 25
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => 25
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => 25
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 25
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 25
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 18
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 18
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 31
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 31
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 11
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 27
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 27
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 11
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => 35
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 35
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 31
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 35
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => 31
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 31
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 13
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 14
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 15
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 16
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 17
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 18
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 19
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 20
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 36
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 27
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 31
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 27
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 23
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 23
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 24
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 24
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 24
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 24
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 24
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 22
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 22
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 22
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 22
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 24
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 24
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 24
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 24
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 24
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 22
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 22
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 20
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 22
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 22
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 20
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 20
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 20
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 20
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 22
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 22
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 20
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 22
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 22
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 24
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 24
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 24
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 24
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 24
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 22
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 22
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 22
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 22
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 24
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 24
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 24
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 24
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 24
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 20
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 20
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 18
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 20
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 20
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 18
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 18
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 18
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 18
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 20
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 20
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 18
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 20
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 20
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 18
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 18
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 18
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 18
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 18
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 18
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 18
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 18
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 18
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 18
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 18
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 18
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 18
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 18
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 18
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 20
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 20
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 18
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 20
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 20
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 18
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 18
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 18
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 18
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 20
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 20
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 18
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 20
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 20
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 24
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 24
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 24
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 24
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 24
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 22
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 22
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 22
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 22
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 24
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 24
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 24
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 24
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 24
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 22
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 22
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 20
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 22
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 22
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 20
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 20
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 20
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 20
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 22
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 22
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 20
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 22
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 22
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 24
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 24
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 24
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 24
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 24
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 22
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 22
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 22
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 22
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 24
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 24
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 24
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 24
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 24
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => 37
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 37
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Generating function
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Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,4,2 16,12,9,4,1 32,32,30,20,12,4,2 64,80,88,73,56,34,20,9,4,1
$F_{1} = q$
$F_{2} = 2\ q^{2}$
$F_{3} = 4\ q^{3} + q^{4}$
$F_{4} = 8\ q^{4} + 4\ q^{5} + 2\ q^{6}$
$F_{5} = 16\ q^{5} + 12\ q^{6} + 9\ q^{7} + 4\ q^{8} + q^{9}$
$F_{6} = 32\ q^{6} + 32\ q^{7} + 30\ q^{8} + 20\ q^{9} + 12\ q^{10} + 4\ q^{11} + 2\ q^{12}$
$F_{7} = 64\ q^{7} + 80\ q^{8} + 88\ q^{9} + 73\ q^{10} + 56\ q^{11} + 34\ q^{12} + 20\ q^{13} + 9\ q^{14} + 4\ q^{15} + q^{16}$
Description
The area of the parallelogram polyomino associated with the Dyck path.
The (bivariate) generating function is given in [1].
The (bivariate) generating function is given in [1].
References
[1] Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n such that the sum of the height of the peaks is k (n>=0; n<=k<=floor((n+1)^2/4)). OEIS:A129183
Code
# depends on https://trac.sagemath.org/ticket/16110
def statistic(D):
return ParallelogramPolyomino.from_dyck_word(D).area()
Created
Nov 06, 2017 at 10:53 by Martin Rubey
Updated
Feb 05, 2022 at 21:55 by Martin Rubey
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