Identifier
- St001161: Dyck paths ⟶ ℤ
Values
[1,0] => 0
[1,0,1,0] => 1
[1,1,0,0] => 0
[1,0,1,0,1,0] => 3
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 2
[1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => 9
[1,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0] => 9
[1,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,0] => 7
[1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => 15
[1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0] => 11
[1,0,1,0,1,0,1,1,0,1,0,0] => 11
[1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => 12
[1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0] => 12
[1,0,1,0,1,1,0,1,0,1,0,0] => 12
[1,0,1,0,1,1,0,1,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => 13
[1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,0] => 9
[1,0,1,1,0,0,1,1,0,1,0,0] => 9
[1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => 13
[1,0,1,1,0,1,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,0] => 13
[1,0,1,1,0,1,0,1,0,1,0,0] => 13
[1,0,1,1,0,1,0,1,1,0,0,0] => 8
[1,0,1,1,0,1,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,0] => 9
[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] => 10
[1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => 10
[1,0,1,1,1,0,0,1,0,1,0,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,0,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,0] => 5
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,0,0] => 6
[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] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => 14
[1,1,0,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,0,1,1,0,0,1,0] => 10
[1,1,0,0,1,0,1,1,0,1,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => 11
[1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => 11
[1,1,0,0,1,1,0,1,0,1,0,0] => 11
[1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => 14
[1,1,0,1,0,0,1,0,1,1,0,0] => 9
[1,1,0,1,0,0,1,1,0,0,1,0] => 10
[1,1,0,1,0,0,1,1,0,1,0,0] => 10
[1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,0] => 14
[1,1,0,1,0,1,0,0,1,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,0,1,0] => 14
[1,1,0,1,0,1,0,1,0,1,0,0] => 14
[1,1,0,1,0,1,0,1,1,0,0,0] => 9
[1,1,0,1,0,1,1,0,0,0,1,0] => 10
[1,1,0,1,0,1,1,0,0,1,0,0] => 10
[1,1,0,1,0,1,1,0,1,0,0,0] => 10
[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] => 11
[1,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,0] => 11
[1,1,0,1,1,0,0,1,0,1,0,0] => 11
[1,1,0,1,1,0,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => 11
[1,1,0,1,1,0,1,0,0,1,0,0] => 11
[1,1,0,1,1,0,1,0,1,0,0,0] => 11
[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] => 7
[1,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,1,0,1,1,1,0,0,1,0,0,0] => 7
[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] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => 12
[1,1,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => 8
[1,1,1,0,0,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => 12
[1,1,1,0,0,1,0,0,1,1,0,0] => 7
[1,1,1,0,0,1,0,1,0,0,1,0] => 12
[1,1,1,0,0,1,0,1,0,1,0,0] => 12
[1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,0,1,0] => 8
[1,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => 12
[1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,0,1,0] => 12
[1,1,1,0,1,0,0,1,0,1,0,0] => 12
[1,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,1,1,0,1,0,1,0,0,0,1,0] => 12
[1,1,1,0,1,0,1,0,0,1,0,0] => 12
[1,1,1,0,1,0,1,0,1,0,0,0] => 12
[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] => 8
[1,1,1,0,1,1,0,0,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,0] => 8
[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] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => 9
[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] => 9
[1,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,1,1,1,0,0,1,0,0,1,0,0] => 9
[1,1,1,1,0,0,1,0,1,0,0,0] => 9
[1,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,1,1,0,1,0,0,0,1,0,0] => 9
[1,1,1,1,0,1,0,0,1,0,0,0] => 9
[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] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 16
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 16
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 17
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 17
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 12
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 12
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 13
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 18
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 18
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 18
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 12
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 13
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 13
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 13
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 14
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 14
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 14
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 14
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 19
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 14
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 15
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 15
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 10
[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] => 19
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 13
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 14
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 19
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 13
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 19
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 19
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 13
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 14
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 14
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 14
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 15
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 15
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 15
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 15
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 15
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 15
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 16
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 10
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 16
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 16
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 11
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 11
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 11
[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] => 16
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 16
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 16
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 16
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 16
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 16
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 12
[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] => 12
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[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] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 15
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 16
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 16
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 11
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 17
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 12
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 17
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 11
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 17
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 17
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 11
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 12
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 12
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 13
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 13
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 13
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 13
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 13
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 20
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 14
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 15
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 15
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 16
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 16
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 16
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 10
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 11
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 11
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 11
[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] => 20
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 14
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 15
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 15
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 20
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 14
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 20
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 20
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 14
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 15
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 15
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 15
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 16
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 16
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 16
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 10
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 16
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 16
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 16
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 11
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 11
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 11
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 17
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 11
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 12
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 12
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 17
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 11
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 17
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 17
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 11
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 12
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 12
[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] => 17
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 11
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 17
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 17
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 11
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 17
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 17
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 17
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 12
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 12
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 13
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 13
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 13
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 13
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 13
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 13
[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] => 13
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 13
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 8
[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] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 18
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 12
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 13
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 13
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 14
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 14
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 14
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 9
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 9
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 18
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 12
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 13
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 13
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 18
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 12
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 18
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 18
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 12
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 13
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 13
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 13
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 14
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 14
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 14
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 14
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 14
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 9
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 9
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 9
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 18
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 12
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 13
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 13
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 18
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 18
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 18
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 12
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 13
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 13
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 13
[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] => 18
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 18
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 18
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 12
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 18
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 18
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 18
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 13
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 13
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 13
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 14
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 14
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 14
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 14
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 14
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 14
[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] => 14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 14
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 14
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 9
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 9
[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] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 15
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 10
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 15
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 9
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 15
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 15
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 9
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 10
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 10
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 15
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 9
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 15
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 15
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 9
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 15
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 15
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 15
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 10
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 10
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 15
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 15
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 15
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 9
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 15
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 15
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 15
[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] => 15
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 15
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 15
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 9
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 10
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 10
[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] => 10
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 11
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 11
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 11
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11
[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] => 11
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 28
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 22
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 22
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 23
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 23
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 23
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 16
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 17
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 17
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 24
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 18
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 24
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 17
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 24
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 24
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 17
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 18
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 18
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 19
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 19
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 12
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 19
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 19
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 19
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 12
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 13
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 13
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 13
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 25
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 19
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 20
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 20
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 13
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 14
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 14
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 25
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 18
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 19
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 19
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 12
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 25
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 18
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 25
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 25
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 18
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 19
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 19
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 19
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 12
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 20
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 13
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 20
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 20
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 13
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 20
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 20
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 20
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 13
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 14
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 14
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 14
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 14
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 15
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 21
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 14
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 21
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 21
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 14
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 15
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 15
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 15
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 21
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 14
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 21
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 21
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 14
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 21
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 21
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 21
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 14
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 15
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 15
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 15
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 15
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 16
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 16
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 16
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 16
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 16
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 16
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 16
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 16
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 16
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 9
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 26
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 20
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 21
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 21
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 14
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 15
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 15
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 16
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 22
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 15
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 22
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 22
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 15
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 16
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 16
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 16
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 17
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 17
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 17
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 17
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 17
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 10
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 11
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 26
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 19
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 20
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 20
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 13
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 21
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 14
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 21
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 21
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 14
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 15
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 15
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 15
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 26
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 19
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 20
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 20
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 13
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 26
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 19
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 26
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 26
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 19
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 20
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 20
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 20
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 13
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 21
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 14
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 21
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 21
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 14
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 21
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 21
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 21
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 14
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 15
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 15
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 15
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 15
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 22
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 15
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 16
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 16
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 22
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 15
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 22
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 22
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 15
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 16
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 16
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 16
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 22
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 15
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 22
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 22
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 15
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 22
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 22
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 22
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 15
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 16
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 16
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 16
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 17
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 17
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 17
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 17
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 17
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 17
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 17
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 17
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 17
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 17
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 11
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 11
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 23
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 17
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 18
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 18
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 12
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 12
[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] => 23
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 16
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 17
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 17
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 23
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 16
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 23
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 23
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 16
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 17
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 17
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 18
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 18
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 18
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 18
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 18
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 18
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 23
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 16
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 17
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 17
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 23
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 16
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 23
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 23
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 16
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 23
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 16
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 23
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 23
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 16
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 23
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 23
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 23
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 16
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 17
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 17
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 17
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 18
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 18
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 18
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 18
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 18
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 18
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 18
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 18
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 18
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 18
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 12
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 12
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 19
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 13
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 19
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 19
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 19
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 12
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 13
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 13
[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] => 19
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 19
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 19
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 19
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 19
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 19
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 19
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 19
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 19
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 19
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 19
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 19
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 19
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 19
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 19
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 19
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 13
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 14
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 14
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 14
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 14
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 14
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 14
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 14
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 14
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8
[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] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 27
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 21
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 21
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 22
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 22
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 15
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 16
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 16
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 23
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 17
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 23
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 16
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 23
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 23
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 16
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 17
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 17
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 17
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 18
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 18
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 18
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 18
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 18
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 12
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 12
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 12
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 12
[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] => 24
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 18
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 19
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 19
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 12
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 13
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 13
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 24
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 17
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 18
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 18
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 11
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 24
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 17
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 24
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 24
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 17
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 18
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 18
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 18
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 11
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 19
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 19
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 19
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 12
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 19
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 19
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 19
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 13
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 13
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 13
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 13
[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] => 20
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 20
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 13
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 20
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 20
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 13
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 14
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 14
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 14
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 20
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 13
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 20
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 20
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 13
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 20
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 20
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 20
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 13
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 14
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 14
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 14
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 14
[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] => 15
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 15
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 15
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 15
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 15
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 15
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 15
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 15
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 15
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 15
[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] => 9
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 9
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 9
[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] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 27
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 20
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 21
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 21
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 22
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 22
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 22
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 15
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 16
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 16
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 9
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,2,1 1,1,2,4,2,3,1 1,1,2,4,6,6,6,8,3,4,1 1,1,2,4,6,11,10,15,15,19,14,11,13,4,5,1 1,1,2,4,6,11,16,20,24,35,35,45,40,41,37,39,24,17,19,5,6,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + q + 2\ q^{2} + q^{3}$
$F_{4} = 1 + q + 2\ q^{2} + 4\ q^{3} + 2\ q^{4} + 3\ q^{5} + q^{6}$
$F_{5} = 1 + q + 2\ q^{2} + 4\ q^{3} + 6\ q^{4} + 6\ q^{5} + 6\ q^{6} + 8\ q^{7} + 3\ q^{8} + 4\ q^{9} + q^{10}$
$F_{6} = 1 + q + 2\ q^{2} + 4\ q^{3} + 6\ q^{4} + 11\ q^{5} + 10\ q^{6} + 15\ q^{7} + 15\ q^{8} + 19\ q^{9} + 14\ q^{10} + 11\ q^{11} + 13\ q^{12} + 4\ q^{13} + 5\ q^{14} + q^{15}$
$F_{7} = 1 + q + 2\ q^{2} + 4\ q^{3} + 6\ q^{4} + 11\ q^{5} + 16\ q^{6} + 20\ q^{7} + 24\ q^{8} + 35\ q^{9} + 35\ q^{10} + 45\ q^{11} + 40\ q^{12} + 41\ q^{13} + 37\ q^{14} + 39\ q^{15} + 24\ q^{16} + 17\ q^{17} + 19\ q^{18} + 5\ q^{19} + 6\ q^{20} + q^{21}$
Description
The major index north count of a Dyck path.
The descent set $\operatorname{des}(D)$ of a Dyck path $D = D_1 \cdots D_{2n}$ with $D_i \in \{N,E\}$ is given by all indices $i$ such that $D_i = E$ and $D_{i+1} = N$. This is, the positions of the valleys of $D$.
The major index of a Dyck path is then the sum of the positions of the valleys, $\sum_{i \in \operatorname{des}(D)} i$, see St000027The major index of a Dyck path..
The major index north count is given by $\sum_{i \in \operatorname{des}(D)} \#\{ j \leq i \mid D_j = N\}$.
The descent set $\operatorname{des}(D)$ of a Dyck path $D = D_1 \cdots D_{2n}$ with $D_i \in \{N,E\}$ is given by all indices $i$ such that $D_i = E$ and $D_{i+1} = N$. This is, the positions of the valleys of $D$.
The major index of a Dyck path is then the sum of the positions of the valleys, $\sum_{i \in \operatorname{des}(D)} i$, see St000027The major index of a Dyck path..
The major index north count is given by $\sum_{i \in \operatorname{des}(D)} \#\{ j \leq i \mid D_j = N\}$.
References
[1] Stump, C. On bijections between $231$-avoiding permutations and Dyck paths MathSciNet:2734176
Code
def statistic(D):
vals = D.valleys()
return sum(1 for d in vals for i in range(d+1) if D[i] == 1)
Created
Apr 25, 2018 at 11:56 by Christian Stump
Updated
Apr 25, 2018 at 11:56 by Christian Stump
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