edit this statistic or download as text // json
Identifier
Values
[.,.] => 1
[.,[.,.]] => 2
[[.,.],.] => 2
[.,[.,[.,.]]] => 3
[.,[[.,.],.]] => 3
[[.,.],[.,.]] => 2
[[.,[.,.]],.] => 3
[[[.,.],.],.] => 3
[.,[.,[.,[.,.]]]] => 4
[.,[.,[[.,.],.]]] => 4
[.,[[.,.],[.,.]]] => 3
[.,[[.,[.,.]],.]] => 4
[.,[[[.,.],.],.]] => 4
[[.,.],[.,[.,.]]] => 3
[[.,.],[[.,.],.]] => 3
[[.,[.,.]],[.,.]] => 3
[[[.,.],.],[.,.]] => 3
[[.,[.,[.,.]]],.] => 4
[[.,[[.,.],.]],.] => 4
[[[.,.],[.,.]],.] => 3
[[[.,[.,.]],.],.] => 4
[[[[.,.],.],.],.] => 4
[.,[.,[.,[.,[.,.]]]]] => 5
[.,[.,[.,[[.,.],.]]]] => 5
[.,[.,[[.,.],[.,.]]]] => 4
[.,[.,[[.,[.,.]],.]]] => 5
[.,[.,[[[.,.],.],.]]] => 5
[.,[[.,.],[.,[.,.]]]] => 4
[.,[[.,.],[[.,.],.]]] => 4
[.,[[.,[.,.]],[.,.]]] => 4
[.,[[[.,.],.],[.,.]]] => 4
[.,[[.,[.,[.,.]]],.]] => 5
[.,[[.,[[.,.],.]],.]] => 5
[.,[[[.,.],[.,.]],.]] => 4
[.,[[[.,[.,.]],.],.]] => 5
[.,[[[[.,.],.],.],.]] => 5
[[.,.],[.,[.,[.,.]]]] => 4
[[.,.],[.,[[.,.],.]]] => 4
[[.,.],[[.,.],[.,.]]] => 3
[[.,.],[[.,[.,.]],.]] => 4
[[.,.],[[[.,.],.],.]] => 4
[[.,[.,.]],[.,[.,.]]] => 3
[[.,[.,.]],[[.,.],.]] => 3
[[[.,.],.],[.,[.,.]]] => 3
[[[.,.],.],[[.,.],.]] => 3
[[.,[.,[.,.]]],[.,.]] => 4
[[.,[[.,.],.]],[.,.]] => 4
[[[.,.],[.,.]],[.,.]] => 3
[[[.,[.,.]],.],[.,.]] => 4
[[[[.,.],.],.],[.,.]] => 4
[[.,[.,[.,[.,.]]]],.] => 5
[[.,[.,[[.,.],.]]],.] => 5
[[.,[[.,.],[.,.]]],.] => 4
[[.,[[.,[.,.]],.]],.] => 5
[[.,[[[.,.],.],.]],.] => 5
[[[.,.],[.,[.,.]]],.] => 4
[[[.,.],[[.,.],.]],.] => 4
[[[.,[.,.]],[.,.]],.] => 4
[[[[.,.],.],[.,.]],.] => 4
[[[.,[.,[.,.]]],.],.] => 5
[[[.,[[.,.],.]],.],.] => 5
[[[[.,.],[.,.]],.],.] => 4
[[[[.,[.,.]],.],.],.] => 5
[[[[[.,.],.],.],.],.] => 5
[.,[.,[.,[.,[.,[.,.]]]]]] => 6
[.,[.,[.,[.,[[.,.],.]]]]] => 6
[.,[.,[.,[[.,.],[.,.]]]]] => 5
[.,[.,[.,[[.,[.,.]],.]]]] => 6
[.,[.,[.,[[[.,.],.],.]]]] => 6
[.,[.,[[.,.],[.,[.,.]]]]] => 5
[.,[.,[[.,.],[[.,.],.]]]] => 5
[.,[.,[[.,[.,.]],[.,.]]]] => 5
[.,[.,[[[.,.],.],[.,.]]]] => 5
[.,[.,[[.,[.,[.,.]]],.]]] => 6
[.,[.,[[.,[[.,.],.]],.]]] => 6
[.,[.,[[[.,.],[.,.]],.]]] => 5
[.,[.,[[[.,[.,.]],.],.]]] => 6
[.,[.,[[[[.,.],.],.],.]]] => 6
[.,[[.,.],[.,[.,[.,.]]]]] => 5
[.,[[.,.],[.,[[.,.],.]]]] => 5
[.,[[.,.],[[.,.],[.,.]]]] => 4
[.,[[.,.],[[.,[.,.]],.]]] => 5
[.,[[.,.],[[[.,.],.],.]]] => 5
[.,[[.,[.,.]],[.,[.,.]]]] => 4
[.,[[.,[.,.]],[[.,.],.]]] => 4
[.,[[[.,.],.],[.,[.,.]]]] => 4
[.,[[[.,.],.],[[.,.],.]]] => 4
[.,[[.,[.,[.,.]]],[.,.]]] => 5
[.,[[.,[[.,.],.]],[.,.]]] => 5
[.,[[[.,.],[.,.]],[.,.]]] => 4
[.,[[[.,[.,.]],.],[.,.]]] => 5
[.,[[[[.,.],.],.],[.,.]]] => 5
[.,[[.,[.,[.,[.,.]]]],.]] => 6
[.,[[.,[.,[[.,.],.]]],.]] => 6
[.,[[.,[[.,.],[.,.]]],.]] => 5
[.,[[.,[[.,[.,.]],.]],.]] => 6
[.,[[.,[[[.,.],.],.]],.]] => 6
[.,[[[.,.],[.,[.,.]]],.]] => 5
[.,[[[.,.],[[.,.],.]],.]] => 5
[.,[[[.,[.,.]],[.,.]],.]] => 5
[.,[[[[.,.],.],[.,.]],.]] => 5
>>> Load all 1008 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => 6
[.,[[[.,[[.,.],.]],.],.]] => 6
[.,[[[[.,.],[.,.]],.],.]] => 5
[.,[[[[.,[.,.]],.],.],.]] => 6
[.,[[[[[.,.],.],.],.],.]] => 6
[[.,.],[.,[.,[.,[.,.]]]]] => 5
[[.,.],[.,[.,[[.,.],.]]]] => 5
[[.,.],[.,[[.,.],[.,.]]]] => 4
[[.,.],[.,[[.,[.,.]],.]]] => 5
[[.,.],[.,[[[.,.],.],.]]] => 5
[[.,.],[[.,.],[.,[.,.]]]] => 4
[[.,.],[[.,.],[[.,.],.]]] => 4
[[.,.],[[.,[.,.]],[.,.]]] => 4
[[.,.],[[[.,.],.],[.,.]]] => 4
[[.,.],[[.,[.,[.,.]]],.]] => 5
[[.,.],[[.,[[.,.],.]],.]] => 5
[[.,.],[[[.,.],[.,.]],.]] => 4
[[.,.],[[[.,[.,.]],.],.]] => 5
[[.,.],[[[[.,.],.],.],.]] => 5
[[.,[.,.]],[.,[.,[.,.]]]] => 4
[[.,[.,.]],[.,[[.,.],.]]] => 4
[[.,[.,.]],[[.,.],[.,.]]] => 3
[[.,[.,.]],[[.,[.,.]],.]] => 4
[[.,[.,.]],[[[.,.],.],.]] => 4
[[[.,.],.],[.,[.,[.,.]]]] => 4
[[[.,.],.],[.,[[.,.],.]]] => 4
[[[.,.],.],[[.,.],[.,.]]] => 3
[[[.,.],.],[[.,[.,.]],.]] => 4
[[[.,.],.],[[[.,.],.],.]] => 4
[[.,[.,[.,.]]],[.,[.,.]]] => 4
[[.,[.,[.,.]]],[[.,.],.]] => 4
[[.,[[.,.],.]],[.,[.,.]]] => 4
[[.,[[.,.],.]],[[.,.],.]] => 4
[[[.,.],[.,.]],[.,[.,.]]] => 3
[[[.,.],[.,.]],[[.,.],.]] => 3
[[[.,[.,.]],.],[.,[.,.]]] => 4
[[[.,[.,.]],.],[[.,.],.]] => 4
[[[[.,.],.],.],[.,[.,.]]] => 4
[[[[.,.],.],.],[[.,.],.]] => 4
[[.,[.,[.,[.,.]]]],[.,.]] => 5
[[.,[.,[[.,.],.]]],[.,.]] => 5
[[.,[[.,.],[.,.]]],[.,.]] => 4
[[.,[[.,[.,.]],.]],[.,.]] => 5
[[.,[[[.,.],.],.]],[.,.]] => 5
[[[.,.],[.,[.,.]]],[.,.]] => 4
[[[.,.],[[.,.],.]],[.,.]] => 4
[[[.,[.,.]],[.,.]],[.,.]] => 4
[[[[.,.],.],[.,.]],[.,.]] => 4
[[[.,[.,[.,.]]],.],[.,.]] => 5
[[[.,[[.,.],.]],.],[.,.]] => 5
[[[[.,.],[.,.]],.],[.,.]] => 4
[[[[.,[.,.]],.],.],[.,.]] => 5
[[[[[.,.],.],.],.],[.,.]] => 5
[[.,[.,[.,[.,[.,.]]]]],.] => 6
[[.,[.,[.,[[.,.],.]]]],.] => 6
[[.,[.,[[.,.],[.,.]]]],.] => 5
[[.,[.,[[.,[.,.]],.]]],.] => 6
[[.,[.,[[[.,.],.],.]]],.] => 6
[[.,[[.,.],[.,[.,.]]]],.] => 5
[[.,[[.,.],[[.,.],.]]],.] => 5
[[.,[[.,[.,.]],[.,.]]],.] => 5
[[.,[[[.,.],.],[.,.]]],.] => 5
[[.,[[.,[.,[.,.]]],.]],.] => 6
[[.,[[.,[[.,.],.]],.]],.] => 6
[[.,[[[.,.],[.,.]],.]],.] => 5
[[.,[[[.,[.,.]],.],.]],.] => 6
[[.,[[[[.,.],.],.],.]],.] => 6
[[[.,.],[.,[.,[.,.]]]],.] => 5
[[[.,.],[.,[[.,.],.]]],.] => 5
[[[.,.],[[.,.],[.,.]]],.] => 4
[[[.,.],[[.,[.,.]],.]],.] => 5
[[[.,.],[[[.,.],.],.]],.] => 5
[[[.,[.,.]],[.,[.,.]]],.] => 4
[[[.,[.,.]],[[.,.],.]],.] => 4
[[[[.,.],.],[.,[.,.]]],.] => 4
[[[[.,.],.],[[.,.],.]],.] => 4
[[[.,[.,[.,.]]],[.,.]],.] => 5
[[[.,[[.,.],.]],[.,.]],.] => 5
[[[[.,.],[.,.]],[.,.]],.] => 4
[[[[.,[.,.]],.],[.,.]],.] => 5
[[[[[.,.],.],.],[.,.]],.] => 5
[[[.,[.,[.,[.,.]]]],.],.] => 6
[[[.,[.,[[.,.],.]]],.],.] => 6
[[[.,[[.,.],[.,.]]],.],.] => 5
[[[.,[[.,[.,.]],.]],.],.] => 6
[[[.,[[[.,.],.],.]],.],.] => 6
[[[[.,.],[.,[.,.]]],.],.] => 5
[[[[.,.],[[.,.],.]],.],.] => 5
[[[[.,[.,.]],[.,.]],.],.] => 5
[[[[[.,.],.],[.,.]],.],.] => 5
[[[[.,[.,[.,.]]],.],.],.] => 6
[[[[.,[[.,.],.]],.],.],.] => 6
[[[[[.,.],[.,.]],.],.],.] => 5
[[[[[.,[.,.]],.],.],.],.] => 6
[[[[[[.,.],.],.],.],.],.] => 6
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 4
[.,[[[.,.],[.,.]],[[.,.],.]]] => 4
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 5
[.,[[.,[[[.,.],.],.]],[.,.]]] => 6
[.,[[[.,.],[[.,.],.]],[.,.]]] => 5
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 5
[.,[[[[.,.],.],[.,.]],[.,.]]] => 5
[.,[[[.,[[.,.],.]],.],[.,.]]] => 6
[.,[[[[.,.],[.,.]],.],[.,.]]] => 5
[.,[[[[.,[.,.]],.],.],[.,.]]] => 6
[.,[[[[[.,.],.],.],.],[.,.]]] => 6
[.,[[.,[[[[.,.],.],.],.]],.]] => 7
[.,[[[[.,.],[.,.]],[.,.]],.]] => 5
[.,[[[[[.,.],.],.],[.,.]],.]] => 6
[.,[[[.,[[.,[.,.]],.]],.],.]] => 7
[.,[[[.,[[[.,.],.],.]],.],.]] => 7
[.,[[[[.,.],[[.,.],.]],.],.]] => 6
[.,[[[[.,[.,.]],[.,.]],.],.]] => 6
[.,[[[[[.,.],.],[.,.]],.],.]] => 6
[.,[[[[.,[.,[.,.]]],.],.],.]] => 7
[.,[[[[.,[[.,.],.]],.],.],.]] => 7
[.,[[[[[.,.],[.,.]],.],.],.]] => 6
[.,[[[[[.,[.,.]],.],.],.],.]] => 7
[.,[[[[[[.,.],.],.],.],.],.]] => 7
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 6
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 6
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 5
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 6
[[.,.],[.,[.,[[[.,.],.],.]]]] => 6
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 5
[[.,.],[.,[[.,.],[[.,.],.]]]] => 5
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 5
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 6
[[.,.],[.,[[.,[[.,.],.]],.]]] => 6
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 5
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 6
[[.,.],[[[[[.,.],.],.],.],.]] => 6
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 5
[[.,[[[.,.],.],.]],[.,[.,.]]] => 5
[[[.,.],[.,[.,.]]],[.,[.,.]]] => 4
[[[.,.],[.,[.,.]]],[[.,.],.]] => 4
[[[.,[[.,.],.]],.],[.,[.,.]]] => 5
[[[[.,[.,.]],.],.],[.,[.,.]]] => 5
[[[[[.,.],.],.],.],[.,[.,.]]] => 5
[[[[[.,.],.],.],.],[[.,.],.]] => 5
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => 6
[[.,[[.,.],[.,[.,.]]]],[.,.]] => 5
[[.,[[[[.,.],.],.],.]],[.,.]] => 6
[[[.,.],[.,[[.,.],.]]],[.,.]] => 5
[[[.,.],[[.,[.,.]],.]],[.,.]] => 5
[[[.,[.,.]],[.,[.,.]]],[.,.]] => 4
[[[[.,.],.],[.,[.,.]]],[.,.]] => 4
[[[[[.,.],.],.],[.,.]],[.,.]] => 5
[[[.,[[.,[.,.]],.]],.],[.,.]] => 6
[[[.,[[[.,.],.],.]],.],[.,.]] => 6
[[[[.,.],[.,[.,.]]],.],[.,.]] => 5
[[[[.,.],[[.,.],.]],.],[.,.]] => 5
[[[[.,[.,.]],[.,.]],.],[.,.]] => 5
[[[[[.,.],.],[.,.]],.],[.,.]] => 5
[[[[.,[.,[.,.]]],.],.],[.,.]] => 6
[[[[.,[[.,.],.]],.],.],[.,.]] => 6
[[[[[.,.],[.,.]],.],.],[.,.]] => 5
[[[[[.,[.,.]],.],.],.],[.,.]] => 6
[[[[[[.,.],.],.],.],.],[.,.]] => 6
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => 7
[[.,[.,[.,[.,[[.,.],.]]]]],.] => 7
[[.,[.,[.,[[.,.],[.,.]]]]],.] => 6
[[.,[.,[.,[[.,[.,.]],.]]]],.] => 7
[[.,[.,[.,[[[.,.],.],.]]]],.] => 7
[[.,[.,[[.,.],[.,[.,.]]]]],.] => 6
[[.,[.,[[.,.],[[.,.],.]]]],.] => 6
[[.,[.,[[.,[.,.]],[.,.]]]],.] => 6
[[.,[.,[[.,[.,[.,.]]],.]]],.] => 7
[[.,[.,[[.,[[.,.],.]],.]]],.] => 7
[[.,[[.,.],[.,[.,[.,.]]]]],.] => 6
[[.,[[[.,.],[.,.]],[.,.]]],.] => 5
[[.,[[.,[.,[.,[.,.]]]],.]],.] => 7
[[[[.,.],[.,[.,.]]],[.,.]],.] => 5
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 5
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => 5
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 4
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => 5
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => 5
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => 5
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => 5
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 5
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 6
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 6
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 7
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 8
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 7
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => 6
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 7
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 6
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => 8
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => 7
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 8
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => 8
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => 7
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => 8
[.,[[[[[[[.,.],.],.],.],.],.],.]] => 8
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 7
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 7
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 7
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 7
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 5
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 5
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 6
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => 6
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 5
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 4
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 5
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 5
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 5
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => 5
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 5
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 5
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 6
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 6
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 7
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => 5
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 5
[[.,.],[[[[[[.,.],.],.],.],.],.]] => 7
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 5
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 5
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 6
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => 5
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => 4
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => 5
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => 4
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => 4
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => 4
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => 5
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => 5
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => 5
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => 6
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => 5
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => 5
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => 6
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => 5
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => 4
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => 5
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => 4
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => 4
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => 4
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => 4
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 4
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => 5
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => 4
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => 5
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => 4
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => 4
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => 4
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 4
[[[[.,.],.],.],[[[[.,.],.],.],.]] => 5
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 5
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => 5
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => 4
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => 4
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => 5
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => 5
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => 5
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 4
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => 4
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 4
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => 4
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => 4
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 4
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 4
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => 4
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => 4
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => 4
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => 4
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => 5
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => 5
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => 5
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => 5
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => 6
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 4
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 4
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => 4
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => 4
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => 4
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => 5
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 5
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => 5
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => 5
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => 5
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => 5
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => 5
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => 6
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => 6
[[[[[[.,.],.],.],.],.],[[.,.],.]] => 6
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 7
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => 6
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => 4
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => 5
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 4
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => 5
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => 5
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 4
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => 4
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => 5
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => 6
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => 5
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 5
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => 5
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => 6
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 6
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => 6
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => 7
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => 6
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => 7
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => 7
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => 6
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => 7
[[[[[[[.,.],.],.],.],.],.],[.,.]] => 7
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 8
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 8
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 7
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 8
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => 8
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 7
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 8
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => 6
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => 7
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => 5
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => 6
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 6
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => 7
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 7
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 8
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => 5
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 5
[[[[.,.],.],[[[[.,.],.],.],.]],.] => 6
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => 5
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 4
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => 5
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => 5
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => 5
[[[[[[.,.],.],.],.],[[.,.],.]],.] => 6
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => 6
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => 6
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => 6
[[[[[[.,.],.],.],[[.,.],.]],.],.] => 6
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => 6
[[[[[[[[.,.],.],.],.],.],.],.],.] => 8
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => 9
[[[[.,.],.],[.,.]],[[.,.],[.,[.,.]]]] => 4
[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]] => 5
[[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]] => 4
[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]] => 5
[[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]] => 4
[[[.,.],[.,.]],[[[.,.],[.,[.,.]]],.]] => 5
[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]] => 5
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],.]]] => 5
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 9
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 8
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => 8
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => 9
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => 7
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => 8
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => 8
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => 9
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 8
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 9
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 8
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 9
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 8
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 8
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 7
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => 10
[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]] => 4
[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] => 5
[[[[[.,.],.],.],[.,.]],[[.,.],[.,[.,.]]]] => 5
[.,[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]]] => 6
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 10
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 6
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => 7
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 6
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]] => 7
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]] => 8
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 5
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => 6
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 6
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 7
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 7
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 8
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 7
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 8
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 9
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => 5
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]] => 6
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]] => 5
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]] => 6
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => 7
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => 5
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]] => 5
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]] => 6
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]] => 6
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => 6
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]] => 7
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]] => 6
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]] => 7
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]] => 8
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => 7
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.] => 8
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.] => 7
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.] => 8
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.] => 9
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.] => 6
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.] => 7
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.] => 7
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.] => 8
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.] => 8
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.] => 9
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.] => 8
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.] => 9
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 10
[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 9
[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => 8
[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 6
[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => 8
[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => 7
[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 6
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 5
[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => 6
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => 8
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => 7
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] => 5
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => 7
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 6
[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]] => 7
[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]] => 6
[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 4
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]] => 6
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]] => 5
[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.] => 7
[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.] => 6
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]] => 6
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]] => 5
[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.] => 7
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.] => 6
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => 4
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]] => 6
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => 5
[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.] => 9
[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.] => 8
[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.] => 6
[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.] => 8
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => 7
[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]] => 6
[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]] => 5
[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]] => 5
[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]] => 4
[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]] => 8
[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]] => 7
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]] => 5
[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]] => 7
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 6
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 9
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => 9
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => 10
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 9
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 10
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => 9
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 10
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 9
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 8
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 9
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 8
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 8
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 7
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 7
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 6
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 9
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 8
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 7
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 8
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 7
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 8
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 7
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 6
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 7
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 6
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 6
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 5
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 6
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 5
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 7
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 6
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 5
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 6
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 5
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 9
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 8
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 7
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 8
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 7
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 7
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 6
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 6
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 5
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 8
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 7
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 6
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 7
[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[.,.]]]] => 4
[.,[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]] => 5
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 10
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => 11
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 11
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 10
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => 7
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]] => 8
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]] => 7
[[.,.],[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]] => 8
[[.,.],[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]] => 9
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]] => 6
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]] => 7
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]] => 7
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]] => 8
[[.,.],[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]] => 8
[[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]] => 9
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]] => 8
[[.,.],[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]] => 9
[[.,.],[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]] => 10
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]] => 6
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]] => 7
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]] => 6
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]] => 7
[[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]] => 8
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]] => 6
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]] => 6
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]] => 7
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]] => 7
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]] => 7
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]] => 8
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]] => 7
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]] => 8
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]] => 9
[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] => 8
[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]] => 9
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]] => 8
[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] => 9
[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] => 10
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]] => 7
[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]] => 8
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]] => 8
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]] => 9
[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]] => 9
[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] => 10
[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]] => 9
[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]] => 10
[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => 11
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 6
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => 7
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 6
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]] => 7
[[.,[[.,.],.]],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]] => 8
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 5
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => 6
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 6
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 7
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 7
[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 8
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 7
[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 8
[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 9
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]] => 5
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,[[.,.],.]],.]]] => 6
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]] => 5
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]] => 6
[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]] => 7
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]] => 6
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,[[.,.],.]],.]]] => 6
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]] => 6
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]] => 6
[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]] => 7
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]] => 6
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]] => 6
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]] => 7
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]] => 7
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]] => 6
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]] => 6
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]] => 7
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]] => 7
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]] => 8
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]] => 8
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]] => 7
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]] => 8
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]] => 7
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => 8
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]] => 9
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]] => 6
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]] => 7
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]] => 7
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]] => 8
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]] => 8
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]] => 9
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]] => 8
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]] => 9
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]] => 10
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.] => 8
[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.] => 9
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.] => 8
[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.] => 9
[[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]],.] => 10
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.] => 7
[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.] => 8
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.] => 8
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]],.] => 9
[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.] => 9
[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.] => 10
[[.,[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]],.] => 9
[[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.] => 10
[[.,[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.] => 11
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]],.] => 7
[[.,[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]],.] => 8
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]],.] => 7
[[.,[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]],.] => 8
[[.,[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]],.] => 9
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]],.] => 7
[[.,[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]],.] => 7
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]],.] => 8
[[.,[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]],.] => 8
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]],.] => 8
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]],.] => 9
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]],.] => 8
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]],.] => 9
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]],.] => 10
[[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.] => 9
[[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.] => 10
[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],.] => 9
[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.] => 10
[[.,[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]],.] => 11
[[.,[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]],.] => 8
[[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]],.] => 9
[[.,[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]],.] => 9
[[.,[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]],.] => 10
[[.,[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]],.] => 10
[[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]],.] => 11
[[.,[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]],.] => 10
[[.,[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]],.] => 11
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => 12
[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]] => 11
[.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]] => 10
[.,[[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],.]] => 8
[.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]] => 10
[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]] => 9
[.,[[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]],.]] => 8
[.,[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]] => 7
[.,[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.]] => 8
[.,[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]] => 7
[.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]] => 10
[.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]] => 9
[.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]] => 7
[.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]] => 9
[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]] => 8
[.,[[[.,.],[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]] => 8
[.,[[[.,.],[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]] => 7
[.,[[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 6
[.,[[[.,.],[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]] => 7
[.,[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]] => 6
[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]] => 6
[.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]] => 6
[.,[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 6
[.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 5
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]] => 8
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]] => 7
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]] => 5
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[[.,.],[.,.]]]] => 7
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]] => 6
[.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]] => 10
[.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]] => 9
[.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]] => 7
[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]] => 9
[.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]] => 8
[.,[[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]] => 7
[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]] => 6
[.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]] => 7
[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]] => 6
[.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]] => 9
[.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]] => 8
[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]] => 6
[.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]] => 8
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => 7
[[.,[.,.]],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 9
[[.,[.,.]],[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => 8
[[.,[.,.]],[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 6
[[.,[.,.]],[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => 8
[[.,[.,.]],[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => 7
[[.,[.,.]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 6
[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 5
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => 6
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] => 5
[[.,[.,.]],[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => 8
[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => 7
[[.,[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] => 5
[[.,[.,.]],[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => 7
[[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 6
[[.,[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.] => 9
[[.,[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]],.] => 8
[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 4
[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.] => 8
[[.,[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.] => 7
[[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]],[.,.]] => 8
[[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]] => 7
[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 4
[[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]] => 7
[[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]] => 6
[[.,[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.]],.] => 9
[[.,[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.] => 8
[[.,[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]],.] => 8
[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.] => 7
[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[.,.],[.,.]]],.]] => 5
[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]] => 4
[[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.],[.,.]] => 8
[[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]] => 7
[[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]] => 7
[[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]] => 6
[[.,[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]],.] => 9
[[.,[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]],.] => 8
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.] => 6
[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.] => 8
[[.,[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]],.] => 7
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]] => 6
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]] => 5
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]] => 6
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => 5
[[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.],[.,.]] => 8
[[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.],[.,.]] => 7
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => 5
[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]],[.,.]] => 7
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => 6
[[.,[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]],.] => 11
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]],.] => 10
[[.,[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]],.] => 8
[[.,[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]],.] => 10
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]],.] => 9
[[.,[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]],.] => 8
[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.] => 7
[[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.] => 7
[[.,[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]],.] => 6
[[.,[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]],.] => 10
[[.,[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]],.] => 9
[[.,[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]],.] => 7
[[.,[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]],.] => 9
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => 8
[[[.,.],[.,.]],[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]] => 8
[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]] => 7
[[[.,[.,.]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.] => 6
[[[.,.],[.,.]],[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]] => 7
[[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]] => 6
[[[.,[[.,.],[.,.]]],.],[.,[[.,[[.,.],[.,.]]],.]]] => 6
[[[.,[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]] => 5
[[[[.,.],[.,.]],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]] => 6
[[[[.,.],[.,.]],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]] => 5
[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,[[.,.],[.,.]]]] => 7
[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[.,.],[.,.]]]] => 6
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]] => 5
[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,[[.,.],[.,.]]]] => 6
[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[[.,.],[.,.]]]] => 5
[[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.],[.,.]] => 10
[[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.],[.,.]] => 9
[[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.],[.,.]] => 7
[[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.],[.,.]] => 9
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.],[.,.]] => 8
[[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]],[.,.]] => 7
[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]],[.,.]] => 6
[[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[.,.]] => 6
[[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]],[.,.]] => 5
[[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]],[.,.]] => 9
[[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]],[.,.]] => 8
[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],[.,.]] => 6
[[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]],[.,.]] => 8
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 7
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => 12
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]] => 11
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => 10
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]] => 11
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]] => 10
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => 10
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]] => 9
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => 9
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => 8
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]] => 11
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => 10
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => 9
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => 10
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => 9
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 10
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 9
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 8
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 9
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 8
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => 8
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => 7
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 8
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 7
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => 9
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => 8
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 7
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => 8
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 7
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => 11
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => 10
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => 9
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => 10
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => 9
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 9
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 8
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => 8
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 7
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => 10
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => 9
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 8
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => 9
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => 8
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 10
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 9
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 8
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 9
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 8
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 8
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 7
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 7
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 6
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 9
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 8
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 7
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 8
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 7
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 8
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 7
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 6
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 7
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 6
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 8
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 7
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 6
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 7
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 6
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => 7
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => 7
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 6
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 6
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 6
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 5
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 6
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 6
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 6
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 5
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => 9
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => 8
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 7
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => 8
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 7
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 7
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 6
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 6
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 5
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => 8
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 7
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 6
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 7
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 6
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => 11
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => 10
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => 9
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => 10
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => 9
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 9
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 8
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => 8
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 7
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => 10
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => 9
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 8
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => 9
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => 8
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 9
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 8
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 7
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 8
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 7
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 7
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 6
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 7
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 6
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => 8
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 7
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 6
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 7
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 6
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => 10
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => 9
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 8
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => 9
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => 8
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 8
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 7
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 7
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 6
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => 9
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => 8
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 7
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => 8
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Description
The depth or height of a binary tree.
The depth (or height) of a binary tree is the maximal depth (or height) of one of its vertices.
The height of a vertex is the number of edges on the longest path between that node and a leaf. The depth of a vertex is the number of edges from the vertex to the root.
See [1] and [2] for this terminology.
The depth (or height) of a tree $T$ can be recursively defined: $\operatorname{depth}(T) = 0$ if $T$ is empty and
$$\operatorname{depth}(T) = 1 + max(\operatorname{depth}(L),\operatorname{depth}(R))$$
if $T$ is nonempty with left and right subtrees $L$ and $R$, respectively.
The upper and lower bounds on the depth of a binary tree $T$ of size $n$ are $log_2(n) \leq \operatorname{depth}(T) \leq n$.
References
[1] wikipedia:Tree (data_structure)
[2] Depth and height of tree
Code
def statistic(t):
    return t.depth()
Created
Mar 25, 2013 at 11:09 by Viviane Pons
Updated
Jan 17, 2018 at 23:05 by Martin Rubey