Identifier
- St001688: Dyck paths ⟶ ℤ
Values
[1,0] => 1
[1,0,1,0] => 2
[1,1,0,0] => 4
[1,0,1,0,1,0] => 3
[1,0,1,1,0,0] => 5
[1,1,0,0,1,0] => 5
[1,1,0,1,0,0] => 8
[1,1,1,0,0,0] => 9
[1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,0] => 9
[1,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,0,1,0] => 9
[1,1,0,1,0,1,0,0] => 12
[1,1,0,1,1,0,0,0] => 13
[1,1,1,0,0,0,1,0] => 10
[1,1,1,0,0,1,0,0] => 13
[1,1,1,0,1,0,0,0] => 18
[1,1,1,1,0,0,0,0] => 16
[1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0] => 7
[1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,0] => 10
[1,0,1,0,1,1,1,0,0,0] => 11
[1,0,1,1,0,0,1,0,1,0] => 7
[1,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,0,1,0,0,1,0] => 10
[1,0,1,1,0,1,0,1,0,0] => 13
[1,0,1,1,0,1,1,0,0,0] => 14
[1,0,1,1,1,0,0,0,1,0] => 11
[1,0,1,1,1,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,0,0,0] => 19
[1,0,1,1,1,1,0,0,0,0] => 17
[1,1,0,0,1,0,1,0,1,0] => 7
[1,1,0,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,0,1,1,0,1,0,0] => 12
[1,1,0,0,1,1,1,0,0,0] => 13
[1,1,0,1,0,0,1,0,1,0] => 10
[1,1,0,1,0,0,1,1,0,0] => 12
[1,1,0,1,0,1,0,0,1,0] => 13
[1,1,0,1,0,1,0,1,0,0] => 16
[1,1,0,1,0,1,1,0,0,0] => 17
[1,1,0,1,1,0,0,0,1,0] => 14
[1,1,0,1,1,0,0,1,0,0] => 17
[1,1,0,1,1,0,1,0,0,0] => 22
[1,1,0,1,1,1,0,0,0,0] => 20
[1,1,1,0,0,0,1,0,1,0] => 11
[1,1,1,0,0,0,1,1,0,0] => 13
[1,1,1,0,0,1,0,0,1,0] => 14
[1,1,1,0,0,1,0,1,0,0] => 17
[1,1,1,0,0,1,1,0,0,0] => 18
[1,1,1,0,1,0,0,0,1,0] => 19
[1,1,1,0,1,0,0,1,0,0] => 22
[1,1,1,0,1,0,1,0,0,0] => 27
[1,1,1,0,1,1,0,0,0,0] => 25
[1,1,1,1,0,0,0,0,1,0] => 17
[1,1,1,1,0,0,0,1,0,0] => 20
[1,1,1,1,0,0,1,0,0,0] => 25
[1,1,1,1,0,1,0,0,0,0] => 32
[1,1,1,1,1,0,0,0,0,0] => 25
[1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,0,1,1,0,0,1,0] => 8
[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] => 12
[1,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,0,1,0,1,1,0,1,0,0,1,0] => 11
[1,0,1,0,1,1,0,1,0,1,0,0] => 14
[1,0,1,0,1,1,0,1,1,0,0,0] => 15
[1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,0,1,1,1,0,0,1,0,0] => 15
[1,0,1,0,1,1,1,0,1,0,0,0] => 20
[1,0,1,0,1,1,1,1,0,0,0,0] => 18
[1,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,0,1,1,0,0] => 10
[1,0,1,1,0,0,1,1,0,0,1,0] => 10
[1,0,1,1,0,0,1,1,0,1,0,0] => 13
[1,0,1,1,0,0,1,1,1,0,0,0] => 14
[1,0,1,1,0,1,0,0,1,0,1,0] => 11
[1,0,1,1,0,1,0,0,1,1,0,0] => 13
[1,0,1,1,0,1,0,1,0,0,1,0] => 14
[1,0,1,1,0,1,0,1,0,1,0,0] => 17
[1,0,1,1,0,1,0,1,1,0,0,0] => 18
[1,0,1,1,0,1,1,0,0,0,1,0] => 15
[1,0,1,1,0,1,1,0,0,1,0,0] => 18
[1,0,1,1,0,1,1,0,1,0,0,0] => 23
[1,0,1,1,0,1,1,1,0,0,0,0] => 21
[1,0,1,1,1,0,0,0,1,0,1,0] => 12
[1,0,1,1,1,0,0,0,1,1,0,0] => 14
[1,0,1,1,1,0,0,1,0,0,1,0] => 15
[1,0,1,1,1,0,0,1,0,1,0,0] => 18
[1,0,1,1,1,0,0,1,1,0,0,0] => 19
[1,0,1,1,1,0,1,0,0,0,1,0] => 20
[1,0,1,1,1,0,1,0,0,1,0,0] => 23
[1,0,1,1,1,0,1,0,1,0,0,0] => 28
[1,0,1,1,1,0,1,1,0,0,0,0] => 26
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => 18
[1,0,1,1,1,1,0,0,0,1,0,0] => 21
[1,0,1,1,1,1,0,0,1,0,0,0] => 26
[1,0,1,1,1,1,0,1,0,0,0,0] => 33
[1,0,1,1,1,1,1,0,0,0,0,0] => 26
[1,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,0,1,1,0,0] => 10
[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] => 13
[1,1,0,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,1,0,0,1,0,1,0] => 10
[1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,0,1,0,0,1,0] => 13
[1,1,0,0,1,1,0,1,0,1,0,0] => 16
[1,1,0,0,1,1,0,1,1,0,0,0] => 17
[1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,1,0,0,1,1,1,0,0,1,0,0] => 17
[1,1,0,0,1,1,1,0,1,0,0,0] => 22
[1,1,0,0,1,1,1,1,0,0,0,0] => 20
[1,1,0,1,0,0,1,0,1,0,1,0] => 11
[1,1,0,1,0,0,1,0,1,1,0,0] => 13
[1,1,0,1,0,0,1,1,0,0,1,0] => 13
[1,1,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,0,0,1,1,1,0,0,0] => 17
[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] => 16
[1,1,0,1,0,1,0,1,0,0,1,0] => 17
[1,1,0,1,0,1,0,1,0,1,0,0] => 20
[1,1,0,1,0,1,0,1,1,0,0,0] => 21
[1,1,0,1,0,1,1,0,0,0,1,0] => 18
[1,1,0,1,0,1,1,0,0,1,0,0] => 21
[1,1,0,1,0,1,1,0,1,0,0,0] => 26
[1,1,0,1,0,1,1,1,0,0,0,0] => 24
[1,1,0,1,1,0,0,0,1,0,1,0] => 15
[1,1,0,1,1,0,0,0,1,1,0,0] => 17
[1,1,0,1,1,0,0,1,0,0,1,0] => 18
[1,1,0,1,1,0,0,1,0,1,0,0] => 21
[1,1,0,1,1,0,0,1,1,0,0,0] => 22
[1,1,0,1,1,0,1,0,0,0,1,0] => 23
[1,1,0,1,1,0,1,0,0,1,0,0] => 26
[1,1,0,1,1,0,1,0,1,0,0,0] => 31
[1,1,0,1,1,0,1,1,0,0,0,0] => 29
[1,1,0,1,1,1,0,0,0,0,1,0] => 21
[1,1,0,1,1,1,0,0,0,1,0,0] => 24
[1,1,0,1,1,1,0,0,1,0,0,0] => 29
[1,1,0,1,1,1,0,1,0,0,0,0] => 36
[1,1,0,1,1,1,1,0,0,0,0,0] => 29
[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] => 14
[1,1,1,0,0,0,1,1,0,0,1,0] => 14
[1,1,1,0,0,0,1,1,0,1,0,0] => 17
[1,1,1,0,0,0,1,1,1,0,0,0] => 18
[1,1,1,0,0,1,0,0,1,0,1,0] => 15
[1,1,1,0,0,1,0,0,1,1,0,0] => 17
[1,1,1,0,0,1,0,1,0,0,1,0] => 18
[1,1,1,0,0,1,0,1,0,1,0,0] => 21
[1,1,1,0,0,1,0,1,1,0,0,0] => 22
[1,1,1,0,0,1,1,0,0,0,1,0] => 19
[1,1,1,0,0,1,1,0,0,1,0,0] => 22
[1,1,1,0,0,1,1,0,1,0,0,0] => 27
[1,1,1,0,0,1,1,1,0,0,0,0] => 25
[1,1,1,0,1,0,0,0,1,0,1,0] => 20
[1,1,1,0,1,0,0,0,1,1,0,0] => 22
[1,1,1,0,1,0,0,1,0,0,1,0] => 23
[1,1,1,0,1,0,0,1,0,1,0,0] => 26
[1,1,1,0,1,0,0,1,1,0,0,0] => 27
[1,1,1,0,1,0,1,0,0,0,1,0] => 28
[1,1,1,0,1,0,1,0,0,1,0,0] => 31
[1,1,1,0,1,0,1,0,1,0,0,0] => 36
[1,1,1,0,1,0,1,1,0,0,0,0] => 34
[1,1,1,0,1,1,0,0,0,0,1,0] => 26
[1,1,1,0,1,1,0,0,0,1,0,0] => 29
[1,1,1,0,1,1,0,0,1,0,0,0] => 34
[1,1,1,0,1,1,0,1,0,0,0,0] => 41
[1,1,1,0,1,1,1,0,0,0,0,0] => 34
[1,1,1,1,0,0,0,0,1,0,1,0] => 18
[1,1,1,1,0,0,0,0,1,1,0,0] => 20
[1,1,1,1,0,0,0,1,0,0,1,0] => 21
[1,1,1,1,0,0,0,1,0,1,0,0] => 24
[1,1,1,1,0,0,0,1,1,0,0,0] => 25
[1,1,1,1,0,0,1,0,0,0,1,0] => 26
[1,1,1,1,0,0,1,0,0,1,0,0] => 29
[1,1,1,1,0,0,1,0,1,0,0,0] => 34
[1,1,1,1,0,0,1,1,0,0,0,0] => 32
[1,1,1,1,0,1,0,0,0,0,1,0] => 33
[1,1,1,1,0,1,0,0,0,1,0,0] => 36
[1,1,1,1,0,1,0,0,1,0,0,0] => 41
[1,1,1,1,0,1,0,1,0,0,0,0] => 48
[1,1,1,1,0,1,1,0,0,0,0,0] => 41
[1,1,1,1,1,0,0,0,0,0,1,0] => 26
[1,1,1,1,1,0,0,0,0,1,0,0] => 29
[1,1,1,1,1,0,0,0,1,0,0,0] => 34
[1,1,1,1,1,0,0,1,0,0,0,0] => 41
[1,1,1,1,1,0,1,0,0,0,0,0] => 50
[1,1,1,1,1,1,0,0,0,0,0,0] => 36
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 12
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 9
[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] => 12
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 15
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 16
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 13
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 16
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 21
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 19
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 11
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 11
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 14
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 12
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 14
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 15
[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] => 19
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 16
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 19
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 24
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 22
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 13
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 15
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 16
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 19
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 20
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 21
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 24
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 29
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 27
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 19
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 22
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 27
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 34
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 27
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 11
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 11
[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] => 15
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 11
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 14
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 17
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 15
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 23
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 21
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 12
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 14
[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] => 17
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 18
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 15
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 17
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 18
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 21
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 22
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 19
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 22
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 27
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 25
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 16
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 18
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 19
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 22
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 23
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 24
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 27
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 32
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 30
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 22
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 25
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 30
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 37
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 30
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 13
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 15
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 18
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 19
[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] => 18
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 19
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 22
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 23
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 20
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 23
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 28
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 26
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 21
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 23
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 24
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 27
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 28
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 29
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 32
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 37
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 35
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 27
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 30
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 35
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 42
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 35
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 19
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 21
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 22
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 25
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 26
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 27
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 30
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 35
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 33
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 34
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 37
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 42
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 49
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 42
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 27
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 30
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 35
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 42
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 51
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 37
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 11
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 11
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 14
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 11
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 13
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 14
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 17
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 18
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 18
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 23
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 21
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 11
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 13
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 16
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 17
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 14
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 16
[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] => 20
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 21
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 18
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 21
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 26
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 24
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 15
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 17
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 18
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 21
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 22
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 23
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 26
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 31
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 29
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 21
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 24
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 29
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 36
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 29
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 12
[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] => 14
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 17
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 18
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 14
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 16
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 17
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 20
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 21
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 18
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 21
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 26
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 24
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 15
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 17
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 17
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 20
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 21
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 18
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 20
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 21
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 24
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 25
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 22
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 25
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 30
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 28
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 19
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 21
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 22
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 25
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 26
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 27
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 30
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 35
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 33
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 25
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 28
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 33
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 40
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 33
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 16
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 18
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 18
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 21
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 22
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 19
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 21
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 22
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 25
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 26
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 23
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 26
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 31
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 29
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 24
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 26
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 27
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 30
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 31
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 32
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 35
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 40
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 38
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 30
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 33
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 38
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 45
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 38
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 22
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 24
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 25
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 28
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 29
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 30
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 33
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 38
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 36
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 37
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 40
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 45
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 52
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 45
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 30
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 33
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 38
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 45
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 54
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 40
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 13
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 15
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 15
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 18
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 19
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 15
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 17
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 18
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 21
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 22
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 19
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 22
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 27
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 25
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 18
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 18
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 21
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 22
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 19
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 21
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 22
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 25
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 26
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 23
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 26
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 31
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 29
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 20
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 22
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 23
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 26
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 27
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 28
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 31
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 36
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 34
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 26
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 29
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 34
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 41
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 34
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 21
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 23
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 23
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 26
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 27
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 24
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 26
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 27
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 30
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 31
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 28
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 31
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 36
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 34
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 29
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 31
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 32
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 35
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 36
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 37
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 40
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 45
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 43
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 35
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 38
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 43
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 50
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 43
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 27
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 29
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 30
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 33
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 34
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 35
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 38
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 43
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 41
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 42
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 45
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 50
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 57
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 50
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 35
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 38
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 43
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 50
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 59
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 45
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 19
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 21
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 21
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 24
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 25
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 22
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 24
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 25
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 28
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 29
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 26
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 29
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 34
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 32
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 27
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 29
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 30
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 33
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 34
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 35
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 38
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 43
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 41
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 33
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 36
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 41
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 48
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 41
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 34
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 36
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 37
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 40
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 41
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 42
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 45
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 50
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 48
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 49
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 52
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 57
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 64
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 57
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 42
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 45
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 50
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 57
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 66
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 52
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 27
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 29
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 30
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 33
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 34
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 35
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 38
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 43
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 41
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 42
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 45
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 50
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 57
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 50
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 51
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 54
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 59
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 66
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 75
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 61
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 37
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 40
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 45
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 52
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 61
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 72
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 49
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 13
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 12
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 13
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 16
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 17
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 14
[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] => 22
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 20
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 12
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 15
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 16
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 13
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 15
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 16
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 19
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 20
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 17
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 20
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 25
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 23
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 16
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 17
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 20
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 21
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 22
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 25
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 30
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 28
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 20
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 23
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 28
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 35
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 28
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 12
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 15
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 16
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 12
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 14
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 15
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 18
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 19
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 16
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 19
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 24
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 22
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 13
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 15
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 15
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 18
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 19
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 16
[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] => 19
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 22
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 23
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 20
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 23
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 28
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 26
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 17
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 19
[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] => 23
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 24
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 25
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 28
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 33
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 31
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 23
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 26
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 31
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 38
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 31
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 14
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 16
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 16
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 19
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 20
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 17
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 19
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 20
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 23
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 24
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 21
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 24
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 29
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 27
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 22
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 24
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 25
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 28
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 29
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 30
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 33
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 38
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 36
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 28
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 31
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 36
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 43
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 36
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 20
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 22
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 23
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 26
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 27
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 28
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 31
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 36
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 34
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 35
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 38
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 43
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 50
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 43
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 28
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 31
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 36
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 43
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 52
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 38
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 12
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 12
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 15
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 16
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 12
[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] => 15
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 18
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 19
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 19
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 24
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 22
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 12
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 14
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 17
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 18
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 15
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 17
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 18
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 21
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 22
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 19
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 22
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 27
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 25
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 16
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 19
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 22
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 23
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 24
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 27
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 32
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 30
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 22
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 25
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 30
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 37
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 30
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 13
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 15
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 15
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 18
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 19
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 15
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 17
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 18
[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] => 22
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 19
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 22
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 27
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 25
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 18
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 21
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 22
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 19
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 21
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 22
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 25
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 26
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 23
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 26
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 31
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 29
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 20
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 22
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 23
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 26
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 27
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 28
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 31
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 36
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 34
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 26
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 29
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 34
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 41
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 34
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 17
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 19
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 19
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 22
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 23
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 20
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 22
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 23
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 26
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 27
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 24
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 27
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 32
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 30
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 25
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 27
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 28
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 31
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 32
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 33
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 36
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 41
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 39
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 31
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 34
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 39
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 46
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 39
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 23
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 25
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 26
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 29
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 30
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 31
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 34
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 39
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 37
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 38
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 41
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 46
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 53
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 46
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 31
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 34
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 39
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 46
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 55
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 41
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 14
[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] => 16
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 19
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 20
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 16
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 18
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 19
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 22
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 23
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 20
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 23
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 28
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 26
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 17
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 19
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 19
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 22
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 23
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 20
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 22
[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] => 26
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 27
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 24
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 27
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 32
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 30
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 21
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 23
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 24
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 27
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 28
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 29
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 32
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 37
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 35
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 27
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 30
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 35
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 42
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 35
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 22
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 24
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 24
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 27
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 28
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 25
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 27
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 28
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 31
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 32
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 29
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 32
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 37
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 35
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 30
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 32
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 33
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 36
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 37
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 38
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 41
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 46
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 44
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 36
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 39
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 44
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 51
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 44
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 28
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 30
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 31
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 34
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 35
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 36
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 39
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 44
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 42
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 43
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 46
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 51
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 58
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 51
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 36
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 39
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 44
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 51
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 60
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 46
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 20
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 22
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 22
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 25
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 26
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 23
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 25
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 26
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 29
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 30
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 27
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 30
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 35
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 33
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 28
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 30
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 31
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 34
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 35
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 36
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 39
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 44
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 42
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 34
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 37
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 42
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 49
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 42
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 35
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 37
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 38
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 41
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 42
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 43
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 46
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 51
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 49
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 50
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 53
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 58
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 65
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 58
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 43
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 46
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 51
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 58
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 67
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 53
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 28
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 30
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 31
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 34
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 35
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 36
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 39
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 44
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 42
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 43
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 46
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 51
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 58
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 51
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 52
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 55
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 60
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 67
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 76
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 62
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 38
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 41
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 46
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 53
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 62
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 73
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 50
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 12
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 12
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 15
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 16
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 12
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 15
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 18
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 19
[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] => 19
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 24
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 22
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 12
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 14
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 14
[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] => 18
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 15
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 17
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 18
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 21
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 22
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 19
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 22
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 27
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 25
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 16
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 18
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 19
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 22
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 23
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 24
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 27
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 32
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 30
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 22
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 25
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 30
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 37
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 30
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 12
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 14
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 17
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 18
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 14
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 16
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 17
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 20
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 21
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 18
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 21
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 26
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 24
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 15
[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] => 17
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 20
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 21
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 18
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 20
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 21
[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] => 25
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 22
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 25
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 30
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 28
[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] => 21
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 22
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 25
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 26
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 27
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 30
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 35
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 33
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 25
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 28
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 33
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 40
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 33
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 18
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 18
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 21
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 22
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 19
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 21
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 22
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 25
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 26
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 23
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 26
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 31
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 29
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 24
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 26
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 27
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 30
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 31
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 32
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 35
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 40
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 38
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 30
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 33
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 38
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 45
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 38
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 22
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 24
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 25
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 28
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 29
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 30
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 33
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 38
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 36
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 37
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 40
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 45
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 52
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 45
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 30
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 33
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 38
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 45
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 54
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 40
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 13
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 15
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 18
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 19
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 15
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 17
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 18
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 21
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 22
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 19
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 22
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 27
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 25
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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:
1,0,1 1,0,2,0,0,1,1 1,0,3,0,1,2,2,0,1,2,0,0,1,0,1 1,0,4,0,3,3,3,2,4,4,0,1,5,1,2,2,0,2,0,0,3,0,1,0,0,0,0,1 1,0,5,0,6,4,5,6,9,6,3,8,10,2,6,8,5,4,3,2,9,2,2,6,0,2,1,2,5,0,4,0,0,0,0,4,0,0,0,0,0,0,1,0,1
$F_{1} = q$
$F_{2} = q^{2} + q^{4}$
$F_{3} = q^{3} + 2\ q^{5} + q^{8} + q^{9}$
$F_{4} = q^{4} + 3\ q^{6} + q^{8} + 2\ q^{9} + 2\ q^{10} + q^{12} + 2\ q^{13} + q^{16} + q^{18}$
$F_{5} = q^{5} + 4\ q^{7} + 3\ q^{9} + 3\ q^{10} + 3\ q^{11} + 2\ q^{12} + 4\ q^{13} + 4\ q^{14} + q^{16} + 5\ q^{17} + q^{18} + 2\ q^{19} + 2\ q^{20} + 2\ q^{22} + 3\ q^{25} + q^{27} + q^{32}$
$F_{6} = q^{6} + 5\ q^{8} + 6\ q^{10} + 4\ q^{11} + 5\ q^{12} + 6\ q^{13} + 9\ q^{14} + 6\ q^{15} + 3\ q^{16} + 8\ q^{17} + 10\ q^{18} + 2\ q^{19} + 6\ q^{20} + 8\ q^{21} + 5\ q^{22} + 4\ q^{23} + 3\ q^{24} + 2\ q^{25} + 9\ q^{26} + 2\ q^{27} + 2\ q^{28} + 6\ q^{29} + 2\ q^{31} + q^{32} + 2\ q^{33} + 5\ q^{34} + 4\ q^{36} + 4\ q^{41} + q^{48} + q^{50}$
$F_{7} = q^{7} + 6\ q^{9} + 10\ q^{11} + 5\ q^{12} + 9\ q^{13} + 12\ q^{14} + 16\ q^{15} + 11\ q^{16} + 12\ q^{17} + 21\ q^{18} + 16\ q^{19} + 7\ q^{20} + 24\ q^{21} + 20\ q^{22} + 12\ q^{23} + 13\ q^{24} + 13\ q^{25} + 16\ q^{26} + 18\ q^{27} + 8\ q^{28} + 15\ q^{29} + 16\ q^{30} + 8\ q^{31} + 5\ q^{32} + 11\ q^{33} + 11\ q^{34} + 13\ q^{35} + 7\ q^{36} + 8\ q^{37} + 10\ q^{38} + 7\ q^{40} + 7\ q^{41} + 8\ q^{42} + 7\ q^{43} + 11\ q^{45} + 2\ q^{48} + 3\ q^{49} + 8\ q^{50} + 2\ q^{51} + 4\ q^{52} + 2\ q^{54} + 5\ q^{57} + 2\ q^{59} + 2\ q^{61} + q^{64} + 2\ q^{66} + q^{72} + q^{75}$
Description
The sum of the squares of the heights of the peaks of a Dyck path.
References
[1] a(n) = (2n+1)!/n!^2. OEIS:A002457
Code
def statistic(D):
H = D.heights()
return sum(H[p+1]^2 for p in D.peaks())
Created
Feb 25, 2021 at 12:40 by Martin Rubey
Updated
Feb 25, 2021 at 12:40 by Martin Rubey
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