Identifier
- St000161: Binary trees ⟶ ℤ
Values
[.,.] => 0
[.,[.,.]] => 1
[[.,.],.] => 0
[.,[.,[.,.]]] => 3
[.,[[.,.],.]] => 2
[[.,.],[.,.]] => 1
[[.,[.,.]],.] => 1
[[[.,.],.],.] => 0
[.,[.,[.,[.,.]]]] => 6
[.,[.,[[.,.],.]]] => 5
[.,[[.,.],[.,.]]] => 4
[.,[[.,[.,.]],.]] => 4
[.,[[[.,.],.],.]] => 3
[[.,.],[.,[.,.]]] => 3
[[.,.],[[.,.],.]] => 2
[[.,[.,.]],[.,.]] => 2
[[[.,.],.],[.,.]] => 1
[[.,[.,[.,.]]],.] => 3
[[.,[[.,.],.]],.] => 2
[[[.,.],[.,.]],.] => 1
[[[.,[.,.]],.],.] => 1
[[[[.,.],.],.],.] => 0
[.,[.,[.,[.,[.,.]]]]] => 10
[.,[.,[.,[[.,.],.]]]] => 9
[.,[.,[[.,.],[.,.]]]] => 8
[.,[.,[[.,[.,.]],.]]] => 8
[.,[.,[[[.,.],.],.]]] => 7
[.,[[.,.],[.,[.,.]]]] => 7
[.,[[.,.],[[.,.],.]]] => 6
[.,[[.,[.,.]],[.,.]]] => 6
[.,[[[.,.],.],[.,.]]] => 5
[.,[[.,[.,[.,.]]],.]] => 7
[.,[[.,[[.,.],.]],.]] => 6
[.,[[[.,.],[.,.]],.]] => 5
[.,[[[.,[.,.]],.],.]] => 5
[.,[[[[.,.],.],.],.]] => 4
[[.,.],[.,[.,[.,.]]]] => 6
[[.,.],[.,[[.,.],.]]] => 5
[[.,.],[[.,.],[.,.]]] => 4
[[.,.],[[.,[.,.]],.]] => 4
[[.,.],[[[.,.],.],.]] => 3
[[.,[.,.]],[.,[.,.]]] => 4
[[.,[.,.]],[[.,.],.]] => 3
[[[.,.],.],[.,[.,.]]] => 3
[[[.,.],.],[[.,.],.]] => 2
[[.,[.,[.,.]]],[.,.]] => 4
[[.,[[.,.],.]],[.,.]] => 3
[[[.,.],[.,.]],[.,.]] => 2
[[[.,[.,.]],.],[.,.]] => 2
[[[[.,.],.],.],[.,.]] => 1
[[.,[.,[.,[.,.]]]],.] => 6
[[.,[.,[[.,.],.]]],.] => 5
[[.,[[.,.],[.,.]]],.] => 4
[[.,[[.,[.,.]],.]],.] => 4
[[.,[[[.,.],.],.]],.] => 3
[[[.,.],[.,[.,.]]],.] => 3
[[[.,.],[[.,.],.]],.] => 2
[[[.,[.,.]],[.,.]],.] => 2
[[[[.,.],.],[.,.]],.] => 1
[[[.,[.,[.,.]]],.],.] => 3
[[[.,[[.,.],.]],.],.] => 2
[[[[.,.],[.,.]],.],.] => 1
[[[[.,[.,.]],.],.],.] => 1
[[[[[.,.],.],.],.],.] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[.,[.,[.,[[.,.],.]]]]] => 14
[.,[.,[.,[[.,.],[.,.]]]]] => 13
[.,[.,[.,[[.,[.,.]],.]]]] => 13
[.,[.,[.,[[[.,.],.],.]]]] => 12
[.,[.,[[.,.],[.,[.,.]]]]] => 12
[.,[.,[[.,.],[[.,.],.]]]] => 11
[.,[.,[[.,[.,.]],[.,.]]]] => 11
[.,[.,[[[.,.],.],[.,.]]]] => 10
[.,[.,[[.,[.,[.,.]]],.]]] => 12
[.,[.,[[.,[[.,.],.]],.]]] => 11
[.,[.,[[[.,.],[.,.]],.]]] => 10
[.,[.,[[[.,[.,.]],.],.]]] => 10
[.,[.,[[[[.,.],.],.],.]]] => 9
[.,[[.,.],[.,[.,[.,.]]]]] => 11
[.,[[.,.],[.,[[.,.],.]]]] => 10
[.,[[.,.],[[.,.],[.,.]]]] => 9
[.,[[.,.],[[.,[.,.]],.]]] => 9
[.,[[.,.],[[[.,.],.],.]]] => 8
[.,[[.,[.,.]],[.,[.,.]]]] => 9
[.,[[.,[.,.]],[[.,.],.]]] => 8
[.,[[[.,.],.],[.,[.,.]]]] => 8
[.,[[[.,.],.],[[.,.],.]]] => 7
[.,[[.,[.,[.,.]]],[.,.]]] => 9
[.,[[.,[[.,.],.]],[.,.]]] => 8
[.,[[[.,.],[.,.]],[.,.]]] => 7
[.,[[[.,[.,.]],.],[.,.]]] => 7
[.,[[[[.,.],.],.],[.,.]]] => 6
[.,[[.,[.,[.,[.,.]]]],.]] => 11
[.,[[.,[.,[[.,.],.]]],.]] => 10
[.,[[.,[[.,.],[.,.]]],.]] => 9
[.,[[.,[[.,[.,.]],.]],.]] => 9
[.,[[.,[[[.,.],.],.]],.]] => 8
[.,[[[.,.],[.,[.,.]]],.]] => 8
[.,[[[.,.],[[.,.],.]],.]] => 7
[.,[[[.,[.,.]],[.,.]],.]] => 7
[.,[[[[.,.],.],[.,.]],.]] => 6
>>> Load all 1008 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => 8
[.,[[[.,[[.,.],.]],.],.]] => 7
[.,[[[[.,.],[.,.]],.],.]] => 6
[.,[[[[.,[.,.]],.],.],.]] => 6
[.,[[[[[.,.],.],.],.],.]] => 5
[[.,.],[.,[.,[.,[.,.]]]]] => 10
[[.,.],[.,[.,[[.,.],.]]]] => 9
[[.,.],[.,[[.,.],[.,.]]]] => 8
[[.,.],[.,[[.,[.,.]],.]]] => 8
[[.,.],[.,[[[.,.],.],.]]] => 7
[[.,.],[[.,.],[.,[.,.]]]] => 7
[[.,.],[[.,.],[[.,.],.]]] => 6
[[.,.],[[.,[.,.]],[.,.]]] => 6
[[.,.],[[[.,.],.],[.,.]]] => 5
[[.,.],[[.,[.,[.,.]]],.]] => 7
[[.,.],[[.,[[.,.],.]],.]] => 6
[[.,.],[[[.,.],[.,.]],.]] => 5
[[.,.],[[[.,[.,.]],.],.]] => 5
[[.,.],[[[[.,.],.],.],.]] => 4
[[.,[.,.]],[.,[.,[.,.]]]] => 7
[[.,[.,.]],[.,[[.,.],.]]] => 6
[[.,[.,.]],[[.,.],[.,.]]] => 5
[[.,[.,.]],[[.,[.,.]],.]] => 5
[[.,[.,.]],[[[.,.],.],.]] => 4
[[[.,.],.],[.,[.,[.,.]]]] => 6
[[[.,.],.],[.,[[.,.],.]]] => 5
[[[.,.],.],[[.,.],[.,.]]] => 4
[[[.,.],.],[[.,[.,.]],.]] => 4
[[[.,.],.],[[[.,.],.],.]] => 3
[[.,[.,[.,.]]],[.,[.,.]]] => 6
[[.,[.,[.,.]]],[[.,.],.]] => 5
[[.,[[.,.],.]],[.,[.,.]]] => 5
[[.,[[.,.],.]],[[.,.],.]] => 4
[[[.,.],[.,.]],[.,[.,.]]] => 4
[[[.,.],[.,.]],[[.,.],.]] => 3
[[[.,[.,.]],.],[.,[.,.]]] => 4
[[[.,[.,.]],.],[[.,.],.]] => 3
[[[[.,.],.],.],[.,[.,.]]] => 3
[[[[.,.],.],.],[[.,.],.]] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => 7
[[.,[.,[[.,.],.]]],[.,.]] => 6
[[.,[[.,.],[.,.]]],[.,.]] => 5
[[.,[[.,[.,.]],.]],[.,.]] => 5
[[.,[[[.,.],.],.]],[.,.]] => 4
[[[.,.],[.,[.,.]]],[.,.]] => 4
[[[.,.],[[.,.],.]],[.,.]] => 3
[[[.,[.,.]],[.,.]],[.,.]] => 3
[[[[.,.],.],[.,.]],[.,.]] => 2
[[[.,[.,[.,.]]],.],[.,.]] => 4
[[[.,[[.,.],.]],.],[.,.]] => 3
[[[[.,.],[.,.]],.],[.,.]] => 2
[[[[.,[.,.]],.],.],[.,.]] => 2
[[[[[.,.],.],.],.],[.,.]] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => 10
[[.,[.,[.,[[.,.],.]]]],.] => 9
[[.,[.,[[.,.],[.,.]]]],.] => 8
[[.,[.,[[.,[.,.]],.]]],.] => 8
[[.,[.,[[[.,.],.],.]]],.] => 7
[[.,[[.,.],[.,[.,.]]]],.] => 7
[[.,[[.,.],[[.,.],.]]],.] => 6
[[.,[[.,[.,.]],[.,.]]],.] => 6
[[.,[[[.,.],.],[.,.]]],.] => 5
[[.,[[.,[.,[.,.]]],.]],.] => 7
[[.,[[.,[[.,.],.]],.]],.] => 6
[[.,[[[.,.],[.,.]],.]],.] => 5
[[.,[[[.,[.,.]],.],.]],.] => 5
[[.,[[[[.,.],.],.],.]],.] => 4
[[[.,.],[.,[.,[.,.]]]],.] => 6
[[[.,.],[.,[[.,.],.]]],.] => 5
[[[.,.],[[.,.],[.,.]]],.] => 4
[[[.,.],[[.,[.,.]],.]],.] => 4
[[[.,.],[[[.,.],.],.]],.] => 3
[[[.,[.,.]],[.,[.,.]]],.] => 4
[[[.,[.,.]],[[.,.],.]],.] => 3
[[[[.,.],.],[.,[.,.]]],.] => 3
[[[[.,.],.],[[.,.],.]],.] => 2
[[[.,[.,[.,.]]],[.,.]],.] => 4
[[[.,[[.,.],.]],[.,.]],.] => 3
[[[[.,.],[.,.]],[.,.]],.] => 2
[[[[.,[.,.]],.],[.,.]],.] => 2
[[[[[.,.],.],.],[.,.]],.] => 1
[[[.,[.,[.,[.,.]]]],.],.] => 6
[[[.,[.,[[.,.],.]]],.],.] => 5
[[[.,[[.,.],[.,.]]],.],.] => 4
[[[.,[[.,[.,.]],.]],.],.] => 4
[[[.,[[[.,.],.],.]],.],.] => 3
[[[[.,.],[.,[.,.]]],.],.] => 3
[[[[.,.],[[.,.],.]],.],.] => 2
[[[[.,[.,.]],[.,.]],.],.] => 2
[[[[[.,.],.],[.,.]],.],.] => 1
[[[[.,[.,[.,.]]],.],.],.] => 3
[[[[.,[[.,.],.]],.],.],.] => 2
[[[[[.,.],[.,.]],.],.],.] => 1
[[[[[.,[.,.]],.],.],.],.] => 1
[[[[[[.,.],.],.],.],.],.] => 0
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 10
[.,[[[.,.],[.,.]],[[.,.],.]]] => 9
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 11
[.,[[.,[[[.,.],.],.]],[.,.]]] => 10
[.,[[[.,.],[[.,.],.]],[.,.]]] => 9
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 9
[.,[[[[.,.],.],[.,.]],[.,.]]] => 8
[.,[[[.,[[.,.],.]],.],[.,.]]] => 9
[.,[[[[.,.],[.,.]],.],[.,.]]] => 8
[.,[[[[.,[.,.]],.],.],[.,.]]] => 8
[.,[[[[[.,.],.],.],.],[.,.]]] => 7
[.,[[.,[[[[.,.],.],.],.]],.]] => 10
[.,[[[[.,.],[.,.]],[.,.]],.]] => 8
[.,[[[[[.,.],.],.],[.,.]],.]] => 7
[.,[[[.,[[.,[.,.]],.]],.],.]] => 10
[.,[[[.,[[[.,.],.],.]],.],.]] => 9
[.,[[[[.,.],[[.,.],.]],.],.]] => 8
[.,[[[[.,[.,.]],[.,.]],.],.]] => 8
[.,[[[[[.,.],.],[.,.]],.],.]] => 7
[.,[[[[.,[.,[.,.]]],.],.],.]] => 9
[.,[[[[.,[[.,.],.]],.],.],.]] => 8
[.,[[[[[.,.],[.,.]],.],.],.]] => 7
[.,[[[[[.,[.,.]],.],.],.],.]] => 7
[.,[[[[[[.,.],.],.],.],.],.]] => 6
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 14
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 13
[[.,.],[.,[.,[[[.,.],.],.]]]] => 12
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
[[.,.],[.,[[.,.],[[.,.],.]]]] => 11
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 11
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 12
[[.,.],[.,[[.,[[.,.],.]],.]]] => 11
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 11
[[.,.],[[[[[.,.],.],.],.],.]] => 5
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 11
[[.,[[[.,.],.],.]],[.,[.,.]]] => 6
[[[.,.],[.,[.,.]]],[.,[.,.]]] => 6
[[[.,.],[.,[.,.]]],[[.,.],.]] => 5
[[[.,[[.,.],.]],.],[.,[.,.]]] => 5
[[[[.,[.,.]],.],.],[.,[.,.]]] => 4
[[[[[.,.],.],.],.],[.,[.,.]]] => 3
[[[[[.,.],.],.],.],[[.,.],.]] => 2
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => 11
[[.,[[.,.],[.,[.,.]]]],[.,.]] => 8
[[.,[[[[.,.],.],.],.]],[.,.]] => 5
[[[.,.],[.,[[.,.],.]]],[.,.]] => 6
[[[.,.],[[.,[.,.]],.]],[.,.]] => 5
[[[.,[.,.]],[.,[.,.]]],[.,.]] => 5
[[[[.,.],.],[.,[.,.]]],[.,.]] => 4
[[[[[.,.],.],.],[.,.]],[.,.]] => 2
[[[.,[[.,[.,.]],.]],.],[.,.]] => 5
[[[.,[[[.,.],.],.]],.],[.,.]] => 4
[[[[.,.],[.,[.,.]]],.],[.,.]] => 4
[[[[.,.],[[.,.],.]],.],[.,.]] => 3
[[[[.,[.,.]],[.,.]],.],[.,.]] => 3
[[[[[.,.],.],[.,.]],.],[.,.]] => 2
[[[[.,[.,[.,.]]],.],.],[.,.]] => 4
[[[[.,[[.,.],.]],.],.],[.,.]] => 3
[[[[[.,.],[.,.]],.],.],[.,.]] => 2
[[[[[.,[.,.]],.],.],.],[.,.]] => 2
[[[[[[.,.],.],.],.],.],[.,.]] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => 15
[[.,[.,[.,[.,[[.,.],.]]]]],.] => 14
[[.,[.,[.,[[.,.],[.,.]]]]],.] => 13
[[.,[.,[.,[[.,[.,.]],.]]]],.] => 13
[[.,[.,[.,[[[.,.],.],.]]]],.] => 12
[[.,[.,[[.,.],[.,[.,.]]]]],.] => 12
[[.,[.,[[.,.],[[.,.],.]]]],.] => 11
[[.,[.,[[.,[.,.]],[.,.]]]],.] => 11
[[.,[.,[[.,[.,[.,.]]],.]]],.] => 12
[[.,[.,[[.,[[.,.],.]],.]]],.] => 11
[[.,[[.,.],[.,[.,[.,.]]]]],.] => 11
[[.,[[[.,.],[.,.]],[.,.]]],.] => 7
[[.,[[.,[.,[.,[.,.]]]],.]],.] => 11
[[[[.,.],[.,[.,.]]],[.,.]],.] => 4
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 14
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => 13
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 12
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => 12
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => 11
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => 10
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => 10
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 10
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 12
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 14
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 16
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 16
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 14
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => 12
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 12
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 10
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => 10
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => 8
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 10
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => 9
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => 8
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => 8
[.,[[[[[[[.,.],.],.],.],.],.],.]] => 7
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 20
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 19
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 18
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 18
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 12
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 12
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 12
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 11
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 10
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 12
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 10
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 8
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 8
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 8
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 12
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 12
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => 8
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 8
[[.,.],[[[[[[.,.],.],.],.],.],.]] => 6
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 12
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 12
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 10
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => 11
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => 10
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => 9
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => 10
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => 8
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => 8
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => 8
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => 7
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => 10
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => 10
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => 8
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => 8
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => 6
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => 12
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => 11
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => 10
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => 10
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => 9
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => 8
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => 8
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => 8
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 7
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => 8
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => 7
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => 6
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => 9
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => 8
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 12
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => 10
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => 8
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => 8
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => 8
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => 8
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => 6
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 9
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => 8
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 7
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => 6
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => 6
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 6
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 5
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => 4
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => 6
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => 5
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => 4
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => 6
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => 5
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => 4
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => 8
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => 8
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 5
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => 4
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => 5
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => 4
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => 5
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 4
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => 6
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => 5
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => 4
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => 5
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => 4
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => 6
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => 4
[[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 10
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => 8
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => 6
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => 6
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 5
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => 5
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => 4
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 5
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => 4
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => 4
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => 6
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => 5
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 4
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => 4
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => 2
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 7
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => 2
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => 4
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => 2
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => 4
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => 3
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => 2
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => 2
[[[[[[[.,.],.],.],.],.],.],[.,.]] => 1
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 21
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 20
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 19
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 19
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => 18
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 18
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 18
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => 12
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => 12
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => 11
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => 10
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 9
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => 12
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 12
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 12
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => 6
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 6
[[[[.,.],.],[[[[.,.],.],.],.]],.] => 4
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => 6
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 5
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => 4
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => 6
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => 4
[[[[[[.,.],.],.],.],[[.,.],.]],.] => 2
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => 2
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => 2
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => 2
[[[[[[.,.],.],.],[[.,.],.]],.],.] => 2
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => 2
[[[[[[[[.,.],.],.],.],.],.],.],.] => 0
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => 8
[[[[.,.],.],[.,.]],[[.,.],[.,[.,.]]]] => 8
[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]] => 13
[[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]] => 9
[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]] => 14
[[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]] => 9
[[[.,.],[.,.]],[[[.,.],[.,[.,.]]],.]] => 9
[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]] => 14
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],.]]] => 14
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 28
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => 2
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => 9
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => 2
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => 3
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => 9
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => 10
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 27
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 27
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 26
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 26
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 26
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 26
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => 9
[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]] => 9
[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] => 15
[[[[[.,.],.],.],[.,.]],[[.,.],[.,[.,.]]]] => 8
[.,[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]]] => 14
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 36
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 20
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => 20
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 18
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]] => 20
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]] => 20
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 16
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => 16
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 16
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 16
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 20
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 20
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 18
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 20
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 20
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => 14
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]] => 14
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]] => 12
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]] => 14
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => 14
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => 12
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]] => 12
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]] => 12
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]] => 12
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => 14
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]] => 14
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]] => 12
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]] => 14
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]] => 14
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => 20
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.] => 20
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.] => 18
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.] => 20
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.] => 20
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.] => 16
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.] => 16
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.] => 16
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.] => 16
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.] => 20
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.] => 20
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.] => 18
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.] => 20
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 20
[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 25
[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => 23
[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 21
[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => 21
[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => 19
[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 19
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 17
[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => 17
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => 19
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => 17
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] => 15
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => 15
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 13
[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]] => 17
[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]] => 15
[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 13
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]] => 13
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]] => 11
[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.] => 18
[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.] => 16
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]] => 11
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]] => 9
[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.] => 19
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.] => 14
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => 9
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]] => 12
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => 7
[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.] => 20
[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.] => 17
[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.] => 17
[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.] => 15
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => 12
[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]] => 16
[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]] => 14
[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]] => 12
[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]] => 10
[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]] => 13
[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]] => 10
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]] => 10
[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]] => 8
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 5
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => 2
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => 10
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 35
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => 35
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 25
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 23
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 21
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 21
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 19
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 19
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 17
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 17
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 15
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 19
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 17
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 15
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 15
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 13
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 17
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 15
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 13
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 13
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 11
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 13
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 11
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 11
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 9
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 13
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 11
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 9
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 9
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 7
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 17
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 15
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 13
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 13
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 11
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 11
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 9
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 9
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 7
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 11
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 9
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 7
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 7
[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[.,.]]]] => 10
[.,[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]] => 17
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 1
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => 10
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 45
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 45
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => 30
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]] => 30
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]] => 28
[[.,.],[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]] => 30
[[.,.],[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]] => 30
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]] => 26
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]] => 26
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]] => 26
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]] => 26
[[.,.],[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]] => 30
[[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]] => 30
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]] => 28
[[.,.],[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]] => 30
[[.,.],[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]] => 30
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]] => 24
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]] => 24
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]] => 22
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]] => 24
[[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]] => 24
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]] => 22
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]] => 22
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]] => 22
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]] => 22
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]] => 24
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]] => 24
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]] => 22
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]] => 24
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]] => 24
[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] => 30
[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]] => 30
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]] => 28
[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] => 30
[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] => 30
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]] => 26
[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]] => 26
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]] => 26
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]] => 26
[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]] => 30
[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] => 30
[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]] => 28
[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]] => 30
[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => 30
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 22
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => 22
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 20
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]] => 22
[[.,[[.,.],.]],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]] => 22
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 18
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => 18
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 18
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 18
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 22
[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 22
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 20
[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 22
[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 22
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]] => 18
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,[[.,.],.]],.]]] => 18
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]] => 16
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]] => 18
[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]] => 18
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]] => 18
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,[[.,.],.]],.]]] => 18
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]] => 16
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]] => 18
[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]] => 18
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]] => 18
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]] => 18
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]] => 18
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]] => 18
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]] => 16
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]] => 16
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]] => 18
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]] => 18
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]] => 18
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]] => 18
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]] => 22
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]] => 22
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]] => 20
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => 22
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]] => 22
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]] => 18
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]] => 18
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]] => 18
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]] => 18
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]] => 22
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]] => 22
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]] => 20
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]] => 22
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]] => 22
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.] => 30
[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.] => 30
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.] => 28
[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.] => 30
[[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]],.] => 30
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.] => 26
[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.] => 26
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.] => 26
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]],.] => 26
[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.] => 30
[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.] => 30
[[.,[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]],.] => 28
[[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.] => 30
[[.,[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.] => 30
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]],.] => 24
[[.,[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]],.] => 24
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]],.] => 22
[[.,[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]],.] => 24
[[.,[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]],.] => 24
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]],.] => 22
[[.,[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]],.] => 22
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]],.] => 22
[[.,[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]],.] => 22
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]],.] => 24
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]],.] => 24
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]],.] => 22
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]],.] => 24
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]],.] => 24
[[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.] => 30
[[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.] => 30
[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],.] => 28
[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.] => 30
[[.,[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]],.] => 30
[[.,[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]],.] => 26
[[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]],.] => 26
[[.,[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]],.] => 26
[[.,[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]],.] => 26
[[.,[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]],.] => 30
[[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]],.] => 30
[[.,[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]],.] => 28
[[.,[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]],.] => 30
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => 30
[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]] => 36
[.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]] => 34
[.,[[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],.]] => 32
[.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]] => 32
[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]] => 30
[.,[[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]],.]] => 30
[.,[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]] => 28
[.,[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.]] => 28
[.,[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]] => 26
[.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]] => 30
[.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]] => 28
[.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]] => 26
[.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]] => 26
[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]] => 24
[.,[[[.,.],[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]] => 28
[.,[[[.,.],[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]] => 26
[.,[[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 24
[.,[[[.,.],[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]] => 24
[.,[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]] => 22
[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]] => 24
[.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]] => 22
[.,[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 22
[.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 20
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]] => 24
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]] => 22
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]] => 20
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[[.,.],[.,.]]]] => 20
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]] => 18
[.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]] => 28
[.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]] => 26
[.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]] => 24
[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]] => 24
[.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]] => 22
[.,[[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]] => 22
[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]] => 20
[.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]] => 20
[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]] => 18
[.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]] => 22
[.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]] => 20
[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]] => 18
[.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]] => 18
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => 16
[[.,[.,.]],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 26
[[.,[.,.]],[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => 24
[[.,[.,.]],[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 22
[[.,[.,.]],[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => 22
[[.,[.,.]],[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => 20
[[.,[.,.]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 20
[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 18
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => 18
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] => 16
[[.,[.,.]],[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => 20
[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => 18
[[.,[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] => 16
[[.,[.,.]],[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => 16
[[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 14
[[.,[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.] => 27
[[.,[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]],.] => 25
[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 16
[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.] => 23
[[.,[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.] => 21
[[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]],[.,.]] => 18
[[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]] => 16
[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 14
[[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]] => 14
[[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]] => 12
[[.,[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.]],.] => 28
[[.,[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.] => 26
[[.,[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]],.] => 21
[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.] => 19
[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[.,.],[.,.]]],.]] => 14
[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]] => 12
[[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.],[.,.]] => 19
[[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]] => 17
[[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]] => 12
[[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]] => 10
[[.,[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]],.] => 29
[[.,[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]],.] => 24
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.] => 19
[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.] => 22
[[.,[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]],.] => 17
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]] => 14
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]] => 12
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]] => 15
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => 10
[[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.],[.,.]] => 20
[[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.],[.,.]] => 15
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => 10
[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]],[.,.]] => 13
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => 8
[[.,[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]],.] => 30
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]],.] => 27
[[.,[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]],.] => 27
[[.,[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]],.] => 25
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]],.] => 22
[[.,[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]],.] => 26
[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.] => 24
[[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.] => 22
[[.,[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]],.] => 20
[[.,[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]],.] => 23
[[.,[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]],.] => 20
[[.,[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]],.] => 20
[[.,[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]],.] => 18
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => 15
[[[.,.],[.,.]],[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]] => 25
[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]] => 23
[[[.,[.,.]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.] => 18
[[[.,.],[.,.]],[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]] => 21
[[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]] => 19
[[[.,[[.,.],[.,.]]],.],[.,[[.,[[.,.],[.,.]]],.]]] => 19
[[[.,[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]] => 17
[[[[.,.],[.,.]],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]] => 17
[[[[.,.],[.,.]],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]] => 15
[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,[[.,.],[.,.]]]] => 17
[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[.,.],[.,.]]]] => 15
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]] => 13
[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,[[.,.],[.,.]]]] => 13
[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[[.,.],[.,.]]]] => 11
[[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.],[.,.]] => 21
[[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.],[.,.]] => 18
[[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.],[.,.]] => 18
[[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.],[.,.]] => 16
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.],[.,.]] => 13
[[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]],[.,.]] => 17
[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]],[.,.]] => 15
[[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[.,.]] => 13
[[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]],[.,.]] => 11
[[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]],[.,.]] => 14
[[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]],[.,.]] => 11
[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],[.,.]] => 11
[[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]],[.,.]] => 9
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 6
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => 36
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]] => 34
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => 32
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]] => 32
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]] => 30
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => 30
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]] => 28
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => 28
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => 26
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]] => 30
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => 28
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => 26
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => 26
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => 24
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 28
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 26
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 24
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 24
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 22
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => 24
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => 22
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 22
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 20
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => 24
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => 22
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 20
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => 20
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 18
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => 28
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => 26
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => 24
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => 24
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => 22
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 22
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 20
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => 20
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 18
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => 22
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => 20
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 18
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => 18
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => 16
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 26
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 24
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 22
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 22
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 20
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 20
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 18
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 18
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 16
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 20
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 18
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 16
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 16
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 14
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 20
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 18
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 16
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 16
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 14
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 18
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 16
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 14
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 14
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 12
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => 18
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => 16
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 16
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 14
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 14
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 12
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 14
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 12
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 12
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 10
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => 20
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => 18
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 16
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => 16
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 14
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 14
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 12
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 12
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 10
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => 14
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 12
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 10
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 10
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 8
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => 26
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => 24
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => 22
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => 22
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => 20
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 20
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 18
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => 18
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 16
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => 20
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => 18
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 16
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => 16
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => 14
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 18
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 16
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 14
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 14
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 12
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 14
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 12
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 12
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 10
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => 14
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 12
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 10
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 10
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 8
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => 18
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => 16
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 14
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => 14
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => 12
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 12
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 10
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 10
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 8
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => 12
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => 10
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 8
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => 8
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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 1,2,1,1 1,3,3,3,2,1,1 1,4,6,7,7,5,5,3,2,1,1 1,5,10,14,17,16,16,14,11,9,7,5,3,2,1,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + q^{2} + q^{3}$
$F_{4} = 1 + 3\ q + 3\ q^{2} + 3\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{5} = 1 + 4\ q + 6\ q^{2} + 7\ q^{3} + 7\ q^{4} + 5\ q^{5} + 5\ q^{6} + 3\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$
$F_{6} = 1 + 5\ q + 10\ q^{2} + 14\ q^{3} + 17\ q^{4} + 16\ q^{5} + 16\ q^{6} + 14\ q^{7} + 11\ q^{8} + 9\ q^{9} + 7\ q^{10} + 5\ q^{11} + 3\ q^{12} + 2\ q^{13} + q^{14} + q^{15}$
Description
The sum of the sizes of the right subtrees of a binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the $312$-avoiding permutation corresponding to the binary tree.
It is also the sum of all heights $j$ of the coordinates $(i,j)$ of the Dyck path corresponding to the binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the $312$-avoiding permutation corresponding to the binary tree.
It is also the sum of all heights $j$ of the coordinates $(i,j)$ of the Dyck path corresponding to the binary tree.
Code
def statistic(t):
if not t:
return 0
return statistic(t[0]) + statistic(t[1]) + t[1].node_number()
Created
Sep 20, 2013 at 14:03 by Viviane Pons
Updated
Jan 12, 2018 at 12:45 by Christian Stump
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