Identifier
- St000394: Dyck paths ⟶ ℤ
Values
[1,0] => 0
[1,0,1,0] => 0
[1,1,0,0] => 1
[1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0] => 1
[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] => 3
[1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0] => 1
[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] => 3
[1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,0] => 1
[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] => 3
[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] => 3
[1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,0,1,0] => 2
[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] => 4
[1,1,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,1,1,0,0,0,0] => 5
[1,1,1,1,0,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,0,0] => 6
[1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => 1
[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] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => 2
[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] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => 1
[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] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => 4
[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] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => 5
[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] => 2
[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] => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => 5
>>> Load all 2245 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => 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] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => 4
[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] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => 5
[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] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => 5
[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] => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => 7
[1,1,0,1,1,0,1,1,0,0,0,0] => 6
[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] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => 7
[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] => 2
[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] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => 6
[1,1,1,0,0,1,1,1,0,0,0,0] => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => 6
[1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,1,1,0,1,0,1,0,1,0,0,0] => 8
[1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,1,1,0,1,1,0,0,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,0,1,0,0] => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,1,1,0,1,1,0,1,0,0,0,0] => 8
[1,1,1,0,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 5
[1,1,1,1,0,0,0,1,1,0,0,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,1,0,0,1,0,0,0] => 8
[1,1,1,1,0,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,0] => 4
[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] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,1,1,1,1,0,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[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] => 3
[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] => 2
[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] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => 3
[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] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[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] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5
[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] => 2
[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] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
[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] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => 3
[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] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[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] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 5
[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] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 5
[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] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 6
[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] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 7
[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] => 2
[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] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
[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] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 8
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[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] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 4
[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] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 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] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[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] => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 5
[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] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 5
[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] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 6
[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] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7
[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] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 6
[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] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 7
[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] => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 9
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 10
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[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] => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 9
[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] => 2
[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] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[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] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 9
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 9
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 9
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 10
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 11
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 9
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 10
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 6
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 7
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 7
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 10
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 9
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 11
[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] => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 9
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 11
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 4
[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] => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 9
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 10
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 10
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 12
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
[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] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 9
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[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] => 3
[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] => 2
[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] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 8
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7
[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] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 8
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 7
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 8
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 9
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 8
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 10
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 9
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 10
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[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
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 10
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 10
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 11
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 10
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 9
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 10
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 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] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 7
[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
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 6
[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] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 7
[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] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 7
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 7
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[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] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 9
[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] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => 10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 9
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 10
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 9
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => 10
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[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] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => 9
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => 11
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[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] => 7
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 10
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 12
[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] => 10
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 12
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 9
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => 7
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 9
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => 9
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => 12
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 13
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[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] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => 9
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 10
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 11
[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] => 2
[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] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 8
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 6
[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] => 6
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => 10
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 8
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 11
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => 11
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => 10
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => 10
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => 11
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => 10
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => 11
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => 12
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => 9
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => 11
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => 10
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 10
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => 11
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 9
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => 10
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => 12
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => 11
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => 12
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => 13
[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] => 12
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => 11
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => 12
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 13
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => 10
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => 10
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => 9
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 10
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => 11
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 12
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 10
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => 11
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => 12
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 13
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => 14
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 11
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 9
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 10
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 11
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 12
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 6
[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] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => 7
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => 10
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => 10
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => 11
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => 10
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => 11
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => 10
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => 9
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => 10
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => 11
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => 9
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => 11
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => 11
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 10
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 11
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 13
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => 12
[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] => 15
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 13
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 12
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => 13
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 14
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 11
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => 9
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => 11
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => 10
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => 12
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => 13
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => 11
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 12
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 13
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 14
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => 15
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 12
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 10
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 11
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 12
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 13
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 6
[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] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => 8
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => 9
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 9
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => 10
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => 11
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => 10
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => 12
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 13
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => 11
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 10
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => 11
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => 12
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => 10
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => 11
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 12
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => 11
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 13
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => 14
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => 12
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 12
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 13
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 14
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => 15
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 16
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 13
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 11
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 12
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 13
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 14
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 5
[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] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => 8
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 9
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 9
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => 10
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 11
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 11
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 12
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 13
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => 12
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 13
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 14
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
[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] => 8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 9
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 11
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 11
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 13
[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] => 16
[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] => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 11
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 11
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 10
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => 9
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => 13
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => 10
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 12
[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] => 10
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 12
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 16
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 11
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 16
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 12
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 11
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 12
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 13
[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] => 8
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 13
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 15
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 10
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => 10
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 15
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => 15
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 18
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 16
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => 12
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => 15
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => 12
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 17
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => 15
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => 14
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 16
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => 17
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => 14
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => 12
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => 16
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 12
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 17
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 12
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 13
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 18
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 13
[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] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 13
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 14
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[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] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 10
[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] => 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] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 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] => 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] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 5
[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] => 1
[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
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 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] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 7
[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] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[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] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 12
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[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] => 11
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 11
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => 10
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[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] => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 8
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => 8
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 7
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 7
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 14
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 14
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 13
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 18
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => 20
[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] => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 13
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[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] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 15
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 18
[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] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 9
[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] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 21
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => 21
[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] => 9
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 19
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => 19
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 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] => 15
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => 14
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => 13
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 12
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 11
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[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] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 11
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 20
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 17
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 19
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 21
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => 11
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => 13
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => 14
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => 19
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 19
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 14
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 14
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 13
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 14
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 14
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 13
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 14
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 14
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 10
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 11
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 10
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 11
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 14
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 14
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 13
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 14
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 14
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 12
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 12
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 14
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 14
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 13
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 14
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 14
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 20
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => 14
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => 14
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 14
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 14
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => 25
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 10
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => 16
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => 15
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0] => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[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] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 25
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 25
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => 17
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 17
[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] => 18
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => 17
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 17
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 16
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 17
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 18
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 10
[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] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 20
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 7
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0] => 12
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => 10
[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
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 20
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 20
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 19
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 20
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 20
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 20
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 20
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 19
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 20
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 20
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 16
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 16
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 20
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 20
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 19
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 20
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 20
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 20
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 20
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 19
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 20
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 20
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 16
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 16
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 15
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 16
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 16
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 16
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 16
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 15
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 16
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 16
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 13
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 13
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 13
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 13
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 15
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 16
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 15
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 20
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 20
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 19
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 20
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 20
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 18
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 18
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 18
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 18
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 20
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 20
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 19
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 20
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 20
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 17
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 17
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 16
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 17
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 17
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 16
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 16
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 16
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 16
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 17
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 17
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 16
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 17
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 17
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 20
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 20
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 19
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 20
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 20
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 18
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 18
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 18
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 18
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 20
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 20
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 19
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 20
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 20
[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] => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 8
[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] => 11
[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] => 17
[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
[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] => 6
[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] => 42
[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] => 12
[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
[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] => 12
[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] => 13
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[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] => 14
[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] => 63
[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] => 28
[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] => 21
[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] => 42
[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] => 12
[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] => 15
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => 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] => 171
[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] => 27
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
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:
1,1 1,2,2 1,3,5,4,1 1,4,9,12,10,4,2 1,5,14,25,31,26,16,9,4,1 1,6,20,44,70,82,74,54,38,22,12,4,2
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + 2\ q^{2}$
$F_{4} = 1 + 3\ q + 5\ q^{2} + 4\ q^{3} + q^{4}$
$F_{5} = 1 + 4\ q + 9\ q^{2} + 12\ q^{3} + 10\ q^{4} + 4\ q^{5} + 2\ q^{6}$
$F_{6} = 1 + 5\ q + 14\ q^{2} + 25\ q^{3} + 31\ q^{4} + 26\ q^{5} + 16\ q^{6} + 9\ q^{7} + 4\ q^{8} + q^{9}$
$F_{7} = 1 + 6\ q + 20\ q^{2} + 44\ q^{3} + 70\ q^{4} + 82\ q^{5} + 74\ q^{6} + 54\ q^{7} + 38\ q^{8} + 22\ q^{9} + 12\ q^{10} + 4\ q^{11} + 2\ q^{12}$
Description
The sum of the heights of the peaks of a Dyck path minus the number of peaks.
References
[1] Feinberg, G., Lee, K.-H. Homogeneous representations of Type A KLR-algebras and Dyck paths arXiv:1505.04075
[2] Cheng, S.-E., Elizalde, S., Kasraoui, A., Sagan, B. Inversion polynomials for 321-avoiding permutations arXiv:1112.6014
[2] Cheng, S.-E., Elizalde, S., Kasraoui, A., Sagan, B. Inversion polynomials for 321-avoiding permutations arXiv:1112.6014
Code
def statistic(D):
heights = D.heights()
return sum(heights[i+1]-1 for i in D.peaks())
Created
Feb 17, 2016 at 20:41 by Christian Stump
Updated
Dec 30, 2023 at 12:12 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!