Identifier
-
Mp00020:
Binary trees
—to Tamari-corresponding Dyck path⟶
Dyck paths
St000032: Dyck paths ⟶ ℤ
Values
[.,.] => [1,0] => 1
[.,[.,.]] => [1,1,0,0] => 2
[[.,.],.] => [1,0,1,0] => 1
[.,[.,[.,.]]] => [1,1,1,0,0,0] => 5
[.,[[.,.],.]] => [1,1,0,1,0,0] => 3
[[.,.],[.,.]] => [1,0,1,1,0,0] => 2
[[.,[.,.]],.] => [1,1,0,0,1,0] => 2
[[[.,.],.],.] => [1,0,1,0,1,0] => 1
[.,[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0] => 14
[.,[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0] => 9
[.,[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0] => 7
[.,[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0] => 7
[.,[[[.,.],.],.]] => [1,1,0,1,0,1,0,0] => 4
[[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => 5
[[.,.],[[.,.],.]] => [1,0,1,1,0,1,0,0] => 3
[[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => 4
[[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => 2
[[.,[.,[.,.]]],.] => [1,1,1,0,0,0,1,0] => 5
[[.,[[.,.],.]],.] => [1,1,0,1,0,0,1,0] => 3
[[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => 2
[[[.,[.,.]],.],.] => [1,1,0,0,1,0,1,0] => 2
[[[[.,.],.],.],.] => [1,0,1,0,1,0,1,0] => 1
[.,[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0] => 42
[.,[.,[.,[[.,.],.]]]] => [1,1,1,1,0,1,0,0,0,0] => 28
[.,[.,[[.,.],[.,.]]]] => [1,1,1,0,1,1,0,0,0,0] => 23
[.,[.,[[.,[.,.]],.]]] => [1,1,1,1,0,0,1,0,0,0] => 23
[.,[.,[[[.,.],.],.]]] => [1,1,1,0,1,0,1,0,0,0] => 14
[.,[[.,.],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,0] => 19
[.,[[.,.],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,0] => 12
[.,[[.,[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,0] => 16
[.,[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,0] => 9
[.,[[.,[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,0,0] => 19
[.,[[.,[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,0,0] => 12
[.,[[[.,.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,0] => 9
[.,[[[.,[.,.]],.],.]] => [1,1,1,0,0,1,0,1,0,0] => 9
[.,[[[[.,.],.],.],.]] => [1,1,0,1,0,1,0,1,0,0] => 5
[[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => 14
[[.,.],[.,[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0] => 9
[[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => 7
[[.,.],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => 7
[[.,.],[[[.,.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => 4
[[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => 10
[[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => 6
[[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 5
[[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => 3
[[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => 10
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0] => 6
[[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 4
[[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => 4
[[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => 2
[[.,[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,0,1,0] => 14
[[.,[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,0,1,0] => 9
[[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,0,1,0] => 7
[[.,[[.,[.,.]],.]],.] => [1,1,1,0,0,1,0,0,1,0] => 7
[[.,[[[.,.],.],.]],.] => [1,1,0,1,0,1,0,0,1,0] => 4
[[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => 5
[[[.,.],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,0] => 3
[[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => 4
[[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => 2
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,0,1,0] => 5
[[[.,[[.,.],.]],.],.] => [1,1,0,1,0,0,1,0,1,0] => 3
[[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => 2
[[[[.,[.,.]],.],.],.] => [1,1,0,0,1,0,1,0,1,0] => 2
[[[[[.,.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 132
[.,[.,[.,[.,[[.,.],.]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => 90
[.,[.,[.,[[.,.],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => 76
[.,[.,[.,[[.,[.,.]],.]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => 76
[.,[.,[.,[[[.,.],.],.]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => 48
[.,[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => 66
[.,[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => 43
[.,[.,[[.,[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => 57
[.,[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => 34
[.,[.,[[.,[.,[.,.]]],.]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => 66
[.,[.,[[.,[[.,.],.]],.]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => 43
[.,[.,[[[.,.],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => 34
[.,[.,[[[.,[.,.]],.],.]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => 34
[.,[.,[[[[.,.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => 20
[.,[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => 56
[.,[[.,.],[.,[[.,.],.]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => 37
[.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => 30
[.,[[.,.],[[.,[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => 30
[.,[[.,.],[[[.,.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => 18
[.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => 43
[.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => 27
[.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => 24
[.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => 15
[.,[[.,[.,[.,.]]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => 43
[.,[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => 27
[.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => 20
[.,[[[.,[.,.]],.],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => 20
[.,[[[[.,.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => 11
[.,[[.,[.,[.,[.,.]]]],.]] => [1,1,1,1,1,0,0,0,0,1,0,0] => 56
[.,[[.,[.,[[.,.],.]]],.]] => [1,1,1,1,0,1,0,0,0,1,0,0] => 37
[.,[[.,[[.,.],[.,.]]],.]] => [1,1,1,0,1,1,0,0,0,1,0,0] => 30
[.,[[.,[[.,[.,.]],.]],.]] => [1,1,1,1,0,0,1,0,0,1,0,0] => 30
[.,[[.,[[[.,.],.],.]],.]] => [1,1,1,0,1,0,1,0,0,1,0,0] => 18
[.,[[[.,.],[.,[.,.]]],.]] => [1,1,0,1,1,1,0,0,0,1,0,0] => 24
[.,[[[.,.],[[.,.],.]],.]] => [1,1,0,1,1,0,1,0,0,1,0,0] => 15
[.,[[[.,[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,0,0] => 20
[.,[[[[.,.],.],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,0,0] => 11
>>> Load all 1001 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,0] => 24
[.,[[[.,[[.,.],.]],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,0] => 15
[.,[[[[.,.],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,0] => 11
[.,[[[[.,[.,.]],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,0] => 11
[.,[[[[[.,.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0] => 6
[[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 42
[[.,.],[.,[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => 28
[[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => 23
[[.,.],[.,[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 23
[[.,.],[.,[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => 14
[[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 19
[[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => 12
[[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 16
[[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 9
[[.,.],[[.,[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 19
[[.,.],[[.,[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 12
[[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 9
[[.,.],[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 9
[[.,.],[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 28
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 18
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 14
[[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 14
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 8
[[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 14
[[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 9
[[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 7
[[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 7
[[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 25
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 15
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 15
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 9
[[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 6
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 10
[[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 6
[[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 28
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 18
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 14
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 14
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 8
[[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 10
[[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 6
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 8
[[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 4
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 10
[[[.,[[.,.],.]],.],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 6
[[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 4
[[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,0,1,0] => 42
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,1,1,0,1,0,0,0,0,1,0] => 28
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,1,0,1,1,0,0,0,0,1,0] => 23
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,1,1,0,0,1,0,0,0,1,0] => 23
[[.,[.,[[[.,.],.],.]]],.] => [1,1,1,0,1,0,1,0,0,0,1,0] => 14
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,0,1,0] => 19
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,0,1,0] => 12
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,0,1,0] => 16
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,0,1,1,0,0,0,1,0] => 9
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,1,1,0,0,0,1,0,0,1,0] => 19
[[.,[[.,[[.,.],.]],.]],.] => [1,1,1,0,1,0,0,1,0,0,1,0] => 12
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,0,0,1,0,0,1,0] => 9
[[.,[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,0,1,0,0,1,0] => 9
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => 14
[[[.,.],[.,[[.,.],.]]],.] => [1,0,1,1,1,0,1,0,0,0,1,0] => 9
[[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => 7
[[[.,.],[[.,[.,.]],.]],.] => [1,0,1,1,1,0,0,1,0,0,1,0] => 7
[[[.,.],[[[.,.],.],.]],.] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => 6
[[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 5
[[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => 10
[[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
[[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4
[[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0] => 14
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0] => 9
[[[.,[[.,.],[.,.]]],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0] => 7
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[[.,[[[.,.],.],.]],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => 5
[[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => 3
[[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4
[[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
[[[[.,[[.,.],.]],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[[[[[.,[.,.]],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
[[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 429
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 297
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 255
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 255
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 165
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 227
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 151
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 199
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 123
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 227
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 151
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 123
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 123
[.,[.,[.,[[[[.,.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 75
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 202
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 136
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 113
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 113
[.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 70
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 161
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 104
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 95
[.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 61
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 161
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 104
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 81
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 81
[.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 47
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 202
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 136
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 113
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 113
[.,[.,[[.,[[[.,.],.],.]],.]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 70
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 95
[.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 61
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 81
[.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 47
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 95
[.,[.,[[[.,[[.,.],.]],.],.]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 61
[.,[.,[[[[.,.],[.,.]],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 47
[.,[.,[[[[.,[.,.]],.],.],.]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 47
[.,[.,[[[[[.,.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 27
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 174
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 118
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 99
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 99
[.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 62
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 85
[.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 55
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 73
[.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 43
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 85
[.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 55
[.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 43
[.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 43
[.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 25
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 126
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 83
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 67
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 67
[.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 40
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 70
[.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 46
[.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 37
[.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 37
[.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 22
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 115
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 72
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 72
[.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 45
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 53
[.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 33
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 53
[.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 33
[.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 29
[.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 18
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 126
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 83
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 67
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 67
[.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 40
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 53
[.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 33
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 44
[.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 24
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 53
[.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 33
[.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 24
[.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 24
[.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 13
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 174
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 118
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 99
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 99
[.,[[.,[.,[[[.,.],.],.]]],.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 62
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 85
[.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 55
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 73
[.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 43
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 85
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 55
[.,[[.,[[[.,.],[.,.]],.]],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 43
[.,[[.,[[[.,[.,.]],.],.]],.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 43
[.,[[.,[[[[.,.],.],.],.]],.]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 25
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 70
[.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 46
[.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 37
[.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 37
[.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 22
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 53
[.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 33
[.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 29
[.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 18
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 53
[.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 33
[.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 24
[.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 24
[.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 13
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 70
[.,[[[.,[.,[[.,.],.]]],.],.]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 46
[.,[[[.,[[.,.],[.,.]]],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 37
[.,[[[.,[[.,[.,.]],.]],.],.]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 37
[.,[[[.,[[[.,.],.],.]],.],.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 22
[.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 29
[.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 18
[.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 24
[.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 13
[.,[[[[.,[.,[.,.]]],.],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 29
[.,[[[[.,[[.,.],.]],.],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 18
[.,[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 13
[.,[[[[[.,[.,.]],.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 13
[.,[[[[[[.,.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 132
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 90
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 76
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 76
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 48
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 66
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 43
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 57
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 34
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 66
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 43
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 34
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 34
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 20
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 56
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 37
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 30
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 30
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 18
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 43
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 27
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 24
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 15
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 43
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 27
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 20
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 20
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 11
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 56
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 37
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 30
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 30
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 18
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 24
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 15
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 20
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 11
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 24
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 15
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 11
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 11
[[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 84
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 56
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 46
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 46
[[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 28
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 38
[[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 24
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 32
[[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 18
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 38
[[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 24
[[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 18
[[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 18
[[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 10
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 42
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 28
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 23
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 23
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 14
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 19
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 12
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 16
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 9
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 19
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 12
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 9
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 9
[[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 70
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 45
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 35
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 35
[[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 20
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 42
[[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 27
[[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 21
[[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 21
[[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 12
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 28
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 18
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 14
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 14
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 8
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 28
[[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 18
[[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 14
[[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 14
[[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 8
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 14
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 9
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 7
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 7
[[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 70
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 42
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 45
[[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 27
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 35
[[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 21
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 35
[[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 21
[[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 20
[[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 12
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 25
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 15
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 15
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 9
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 20
[[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 12
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 6
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 25
[[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 15
[[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 15
[[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 9
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 10
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 6
[[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 10
[[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 6
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 84
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 56
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 46
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 46
[[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 28
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 38
[[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 24
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 32
[[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 18
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 38
[[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 24
[[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 18
[[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 18
[[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 10
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 28
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 18
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 14
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 14
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 8
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 20
[[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 12
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 10
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 6
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 20
[[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 12
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 8
[[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 8
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 28
[[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 18
[[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 14
[[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 14
[[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 6
[[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 8
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 10
[[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 6
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
[[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 132
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 90
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 76
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 76
[[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 48
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 66
[[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 43
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 57
[[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 34
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 66
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 43
[[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 34
[[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 34
[[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 20
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 56
[[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 37
[[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 30
[[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 30
[[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 18
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 43
[[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 27
[[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 24
[[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 15
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 43
[[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 27
[[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 20
[[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 20
[[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 11
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 56
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 37
[[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 30
[[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 30
[[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 18
[[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 24
[[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 15
[[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 20
[[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 11
[[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 24
[[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 15
[[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 11
[[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 11
[[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 42
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 28
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 23
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 23
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 14
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 19
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 12
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 16
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 9
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 19
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 12
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 9
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 9
[[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 28
[[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 18
[[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 14
[[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 14
[[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 8
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 14
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 9
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 7
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 7
[[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 25
[[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 15
[[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 15
[[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 9
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 6
[[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 10
[[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 6
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5
[[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 28
[[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 18
[[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 14
[[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 14
[[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 10
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 6
[[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 8
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 10
[[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 6
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4
[[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 42
[[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 28
[[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 23
[[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 23
[[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 14
[[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 19
[[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 12
[[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 16
[[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 9
[[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 19
[[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 12
[[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 9
[[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[[[.,[[[[.,.],.],.],.]],.],.] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 14
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 9
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 7
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 10
[[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 6
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5
[[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 10
[[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 6
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 14
[[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 9
[[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 7
[[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 7
[[[[.,[[[.,.],.],.]],.],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[[[[[.,.],[[.,.],.]],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[[[[[.,[[.,.],.]],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[[[[[[.,[.,.]],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[[[[[[[.,.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 202
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 136
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 113
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 113
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 70
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 95
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 61
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 81
[[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 47
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 95
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 61
[[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 47
[[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 47
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 47
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 27
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 174
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 118
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 99
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 99
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 62
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 85
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 55
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 73
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 43
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 85
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 55
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 43
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 43
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 25
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 126
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 83
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 67
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 67
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 40
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 70
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 46
[[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 37
[[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 37
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 22
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 115
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 72
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 72
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 45
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 53
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 33
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 53
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 33
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 29
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 18
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 67
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 67
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 40
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 53
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 33
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 44
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 24
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 53
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 33
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 24
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 24
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 13
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 85
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 55
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 43
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 43
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 43
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 25
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 70
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 46
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 37
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 37
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 22
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 53
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 33
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 29
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 18
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 53
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 33
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 24
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 24
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 13
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 37
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 37
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 22
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 29
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 18
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 24
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 13
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 29
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 18
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 13
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 13
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 132
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 90
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 76
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 76
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 48
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 66
[[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 43
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 57
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 34
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 66
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 43
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 34
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 34
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 20
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 56
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 37
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 30
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 30
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 18
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 43
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 27
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 24
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 15
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 43
[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 27
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 20
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 20
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 11
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 56
[[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 37
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 30
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 30
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 18
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 24
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 15
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 20
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 11
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 24
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 15
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 11
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 11
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 84
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 56
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 46
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 46
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 28
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 38
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 24
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 32
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 18
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 38
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 24
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 18
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 18
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 10
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 42
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 28
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 23
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 23
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 14
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 19
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 12
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 16
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 9
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 19
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 12
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 9
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 9
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 70
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 45
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 35
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 35
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 20
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 42
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 27
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 21
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 21
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 12
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 28
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 18
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 14
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 14
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 8
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 28
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 18
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 14
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 14
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 8
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 14
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 9
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 7
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 7
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 70
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 42
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 45
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 27
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 35
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 21
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 35
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 21
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 20
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 12
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 25
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 15
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 15
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 9
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 20
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 12
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 6
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 25
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 15
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 15
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 9
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 10
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 6
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 10
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 6
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 46
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 46
[[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 28
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 38
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 24
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 32
[[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 18
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 38
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 24
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 18
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 18
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 10
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 28
[[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 18
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 14
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 14
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 8
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 20
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 12
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 10
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 6
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 20
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 12
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 8
[[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 8
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 28
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 18
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 14
[[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 14
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 6
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 8
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 10
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 6
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 66
[[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 43
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 34
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 34
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 34
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 20
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 56
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 37
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 30
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 30
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 18
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 43
[[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 27
[[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 24
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 15
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 43
[[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 27
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 20
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 20
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 11
[[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 30
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 30
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 18
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 24
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 15
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 20
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 11
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 24
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 15
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 11
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 11
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 42
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 28
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 23
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 23
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 14
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 19
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 12
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 16
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 9
[[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 19
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 12
[[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 9
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 9
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 28
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 18
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 14
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 14
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 8
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 14
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 9
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 7
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 7
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 25
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 15
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 15
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 9
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 6
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 10
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 6
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 28
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 18
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 14
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 14
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 10
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 6
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 8
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 10
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 6
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 23
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 23
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 14
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 19
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 12
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 16
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 9
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 19
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 12
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 9
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 14
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 9
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 7
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 10
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 6
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 10
[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 6
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 14
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 9
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 7
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 7
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
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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 1,2,1,0,1 1,3,2,2,2,0,2,0,1,0,0,0,0,1 1,4,3,5,4,2,4,0,5,2,0,2,0,3,0,1,0,0,2,0,0,0,2,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 2\ q^{2} + q^{3} + q^{5}$
$F_{4} = q + 3\ q^{2} + 2\ q^{3} + 2\ q^{4} + 2\ q^{5} + 2\ q^{7} + q^{9} + q^{14}$
$F_{5} = q + 4\ q^{2} + 3\ q^{3} + 5\ q^{4} + 4\ q^{5} + 2\ q^{6} + 4\ q^{7} + 5\ q^{9} + 2\ q^{10} + 2\ q^{12} + 3\ q^{14} + q^{16} + 2\ q^{19} + 2\ q^{23} + q^{28} + q^{42}$
$F_{6} = q + 5\ q^{2} + 4\ q^{3} + 9\ q^{4} + 6\ q^{5} + 7\ q^{6} + 6\ q^{7} + 3\ q^{8} + 10\ q^{9} + 6\ q^{10} + 4\ q^{11} + 4\ q^{12} + 9\ q^{14} + 5\ q^{15} + 2\ q^{16} + 4\ q^{18} + 4\ q^{19} + 4\ q^{20} + 4\ q^{23} + 3\ q^{24} + q^{25} + 2\ q^{27} + 4\ q^{28} + 4\ q^{30} + 3\ q^{34} + 2\ q^{37} + 2\ q^{42} + 4\ q^{43} + q^{48} + 2\ q^{56} + q^{57} + 2\ q^{66} + 2\ q^{76} + q^{90} + q^{132}$
$F_{7} = q + 6\ q^{2} + 5\ q^{3} + 14\ q^{4} + 8\ q^{5} + 14\ q^{6} + 9\ q^{7} + 10\ q^{8} + 16\ q^{9} + 14\ q^{10} + 8\ q^{11} + 11\ q^{12} + 5\ q^{13} + 19\ q^{14} + 12\ q^{15} + 3\ q^{16} + 20\ q^{18} + 6\ q^{19} + 13\ q^{20} + 4\ q^{21} + 3\ q^{22} + 6\ q^{23} + 16\ q^{24} + 5\ q^{25} + 7\ q^{27} + 11\ q^{28} + 4\ q^{29} + 8\ q^{30} + 2\ q^{32} + 6\ q^{33} + 6\ q^{34} + 4\ q^{35} + 10\ q^{37} + 4\ q^{38} + 2\ q^{40} + 5\ q^{42} + 14\ q^{43} + q^{44} + 3\ q^{45} + 7\ q^{46} + 4\ q^{47} + 2\ q^{48} + 6\ q^{53} + 4\ q^{55} + 6\ q^{56} + 2\ q^{57} + 3\ q^{61} + 2\ q^{62} + 4\ q^{66} + 4\ q^{67} + 7\ q^{70} + 2\ q^{72} + 2\ q^{73} + q^{75} + 4\ q^{76} + 3\ q^{81} + 2\ q^{83} + 2\ q^{84} + 4\ q^{85} + 2\ q^{90} + 3\ q^{95} + 4\ q^{99} + 2\ q^{104} + 4\ q^{113} + q^{115} + 2\ q^{118} + 3\ q^{123} + 2\ q^{126} + 2\ q^{132} + 2\ q^{136} + 2\ q^{151} + 2\ q^{161} + q^{165} + 2\ q^{174} + q^{199} + 2\ q^{202} + 2\ q^{227} + 2\ q^{255} + q^{297} + q^{429}$
Description
The number of elements smaller than the given Dyck path in the Tamari Order.
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
The bijection is defined recursively as follows:
- a leaf is associated with an empty Dyck path,
- a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.
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