Identifier
-
Mp00050:
Ordered trees
—to binary tree: right brother = right child⟶
Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
St000201: Binary trees ⟶ ℤ (values match St000196The number of occurrences of the contiguous pattern [[.,.],[.,.)
Values
[[]] => [.,.] => [.,.] => 1
[[],[]] => [.,[.,.]] => [.,[.,.]] => 1
[[[]]] => [[.,.],.] => [[.,.],.] => 1
[[],[],[]] => [.,[.,[.,.]]] => [.,[.,[.,.]]] => 1
[[],[[]]] => [.,[[.,.],.]] => [.,[[.,.],.]] => 1
[[[]],[]] => [[.,.],[.,.]] => [[.,[.,.]],.] => 1
[[[],[]]] => [[.,[.,.]],.] => [[.,.],[.,.]] => 2
[[[[]]]] => [[[.,.],.],.] => [[[.,.],.],.] => 1
[[],[],[],[]] => [.,[.,[.,[.,.]]]] => [.,[.,[.,[.,.]]]] => 1
[[],[],[[]]] => [.,[.,[[.,.],.]]] => [.,[.,[[.,.],.]]] => 1
[[],[[]],[]] => [.,[[.,.],[.,.]]] => [.,[[.,[.,.]],.]] => 1
[[],[[],[]]] => [.,[[.,[.,.]],.]] => [.,[[.,.],[.,.]]] => 2
[[],[[[]]]] => [.,[[[.,.],.],.]] => [.,[[[.,.],.],.]] => 1
[[[]],[],[]] => [[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.] => 1
[[[]],[[]]] => [[.,.],[[.,.],.]] => [[.,[[.,.],.]],.] => 1
[[[],[]],[]] => [[.,[.,.]],[.,.]] => [[.,[.,.]],[.,.]] => 2
[[[[]]],[]] => [[[.,.],.],[.,.]] => [[[.,[.,.]],.],.] => 1
[[[],[],[]]] => [[.,[.,[.,.]]],.] => [[.,.],[.,[.,.]]] => 2
[[[],[[]]]] => [[.,[[.,.],.]],.] => [[.,.],[[.,.],.]] => 2
[[[[]],[]]] => [[[.,.],[.,.]],.] => [[[.,.],[.,.]],.] => 2
[[[[],[]]]] => [[[.,[.,.]],.],.] => [[[.,.],.],[.,.]] => 2
[[[[[]]]]] => [[[[.,.],.],.],.] => [[[[.,.],.],.],.] => 1
[[],[],[],[],[]] => [.,[.,[.,[.,[.,.]]]]] => [.,[.,[.,[.,[.,.]]]]] => 1
[[],[],[],[[]]] => [.,[.,[.,[[.,.],.]]]] => [.,[.,[.,[[.,.],.]]]] => 1
[[],[],[[]],[]] => [.,[.,[[.,.],[.,.]]]] => [.,[.,[[.,[.,.]],.]]] => 1
[[],[],[[],[]]] => [.,[.,[[.,[.,.]],.]]] => [.,[.,[[.,.],[.,.]]]] => 2
[[],[],[[[]]]] => [.,[.,[[[.,.],.],.]]] => [.,[.,[[[.,.],.],.]]] => 1
[[],[[]],[],[]] => [.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]] => 1
[[],[[]],[[]]] => [.,[[.,.],[[.,.],.]]] => [.,[[.,[[.,.],.]],.]] => 1
[[],[[],[]],[]] => [.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => 2
[[],[[[]]],[]] => [.,[[[.,.],.],[.,.]]] => [.,[[[.,[.,.]],.],.]] => 1
[[],[[],[],[]]] => [.,[[.,[.,[.,.]]],.]] => [.,[[.,.],[.,[.,.]]]] => 2
[[],[[],[[]]]] => [.,[[.,[[.,.],.]],.]] => [.,[[.,.],[[.,.],.]]] => 2
[[],[[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [.,[[[.,.],[.,.]],.]] => 2
[[],[[[],[]]]] => [.,[[[.,[.,.]],.],.]] => [.,[[[.,.],.],[.,.]]] => 2
[[],[[[[]]]]] => [.,[[[[.,.],.],.],.]] => [.,[[[[.,.],.],.],.]] => 1
[[[]],[],[],[]] => [[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => 1
[[[]],[],[[]]] => [[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.] => 1
[[[]],[[]],[]] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[[[]],[[],[]]] => [[.,.],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],.] => 2
[[[]],[[[]]]] => [[.,.],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],.] => 1
[[[],[]],[],[]] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[[[[]]],[],[]] => [[[.,.],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],.] => 1
[[[],[]],[[]]] => [[.,[.,.]],[[.,.],.]] => [[.,[[.,.],.]],[.,.]] => 2
[[[[]]],[[]]] => [[[.,.],.],[[.,.],.]] => [[[.,[[.,.],.]],.],.] => 1
[[[],[],[]],[]] => [[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => 2
[[[],[[]]],[]] => [[.,[[.,.],.]],[.,.]] => [[.,[.,.]],[[.,.],.]] => 2
[[[[]],[]],[]] => [[[.,.],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],.] => 2
[[[[],[]]],[]] => [[[.,[.,.]],.],[.,.]] => [[[.,[.,.]],.],[.,.]] => 2
[[[[[]]]],[]] => [[[[.,.],.],.],[.,.]] => [[[[.,[.,.]],.],.],.] => 1
[[[],[],[],[]]] => [[.,[.,[.,[.,.]]]],.] => [[.,.],[.,[.,[.,.]]]] => 2
[[[],[],[[]]]] => [[.,[.,[[.,.],.]]],.] => [[.,.],[.,[[.,.],.]]] => 2
[[[],[[]],[]]] => [[.,[[.,.],[.,.]]],.] => [[.,.],[[.,[.,.]],.]] => 2
[[[],[[],[]]]] => [[.,[[.,[.,.]],.]],.] => [[.,.],[[.,.],[.,.]]] => 3
[[[],[[[]]]]] => [[.,[[[.,.],.],.]],.] => [[.,.],[[[.,.],.],.]] => 2
[[[[]],[],[]]] => [[[.,.],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],.] => 2
[[[[]],[[]]]] => [[[.,.],[[.,.],.]],.] => [[[.,.],[[.,.],.]],.] => 2
[[[[],[]],[]]] => [[[.,[.,.]],[.,.]],.] => [[[.,.],[.,.]],[.,.]] => 3
[[[[[]]],[]]] => [[[[.,.],.],[.,.]],.] => [[[[.,.],[.,.]],.],.] => 2
[[[[],[],[]]]] => [[[.,[.,[.,.]]],.],.] => [[[.,.],.],[.,[.,.]]] => 2
[[[[],[[]]]]] => [[[.,[[.,.],.]],.],.] => [[[.,.],.],[[.,.],.]] => 2
[[[[[]],[]]]] => [[[[.,.],[.,.]],.],.] => [[[[.,.],.],[.,.]],.] => 2
[[[[[],[]]]]] => [[[[.,[.,.]],.],.],.] => [[[[.,.],.],.],[.,.]] => 2
[[[[[[]]]]]] => [[[[[.,.],.],.],.],.] => [[[[[.,.],.],.],.],.] => 1
[[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[[],[],[],[],[[]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => 1
[[],[],[],[[]],[]] => [.,[.,[.,[[.,.],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[[],[],[],[[],[]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[[],[],[],[[[]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [.,[.,[.,[[[.,.],.],.]]]] => 1
[[],[],[[]],[],[]] => [.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[[],[],[[]],[[]]] => [.,[.,[[.,.],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],.]]] => 1
[[],[],[[],[]],[]] => [.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[[],[],[[[]]],[]] => [.,[.,[[[.,.],.],[.,.]]]] => [.,[.,[[[.,[.,.]],.],.]]] => 1
[[],[],[[],[],[]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[[],[],[[],[[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [.,[.,[[.,.],[[.,.],.]]]] => 2
[[],[],[[[]],[]]] => [.,[.,[[[.,.],[.,.]],.]]] => [.,[.,[[[.,.],[.,.]],.]]] => 2
[[],[],[[[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [.,[.,[[[.,.],.],[.,.]]]] => 2
[[],[],[[[[]]]]] => [.,[.,[[[[.,.],.],.],.]]] => [.,[.,[[[[.,.],.],.],.]]] => 1
[[],[[]],[],[],[]] => [.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[[],[[]],[],[[]]] => [.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]] => 1
[[],[[]],[[]],[]] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[[],[[]],[[],[]]] => [.,[[.,.],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],.]] => 2
[[],[[]],[[[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [.,[[.,[[[.,.],.],.]],.]] => 1
[[],[[],[]],[],[]] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[[],[[[]]],[],[]] => [.,[[[.,.],.],[.,[.,.]]]] => [.,[[[.,[.,[.,.]]],.],.]] => 1
[[],[[],[]],[[]]] => [.,[[.,[.,.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,.]]] => 2
[[],[[[]]],[[]]] => [.,[[[.,.],.],[[.,.],.]]] => [.,[[[.,[[.,.],.]],.],.]] => 1
[[],[[],[],[]],[]] => [.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[[],[[],[[]]],[]] => [.,[[.,[[.,.],.]],[.,.]]] => [.,[[.,[.,.]],[[.,.],.]]] => 2
[[],[[[]],[]],[]] => [.,[[[.,.],[.,.]],[.,.]]] => [.,[[[.,[.,.]],[.,.]],.]] => 2
[[],[[[],[]]],[]] => [.,[[[.,[.,.]],.],[.,.]]] => [.,[[[.,[.,.]],.],[.,.]]] => 2
[[],[[[[]]]],[]] => [.,[[[[.,.],.],.],[.,.]]] => [.,[[[[.,[.,.]],.],.],.]] => 1
[[],[[],[],[],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[[],[[],[],[[]]]] => [.,[[.,[.,[[.,.],.]]],.]] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[[],[[],[[]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [.,[[.,.],[[.,[.,.]],.]]] => 2
[[],[[],[[],[]]]] => [.,[[.,[[.,[.,.]],.]],.]] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[[],[[],[[[]]]]] => [.,[[.,[[[.,.],.],.]],.]] => [.,[[.,.],[[[.,.],.],.]]] => 2
[[],[[[]],[],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [.,[[[.,.],[.,[.,.]]],.]] => 2
[[],[[[]],[[]]]] => [.,[[[.,.],[[.,.],.]],.]] => [.,[[[.,.],[[.,.],.]],.]] => 2
[[],[[[],[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[.,.]]] => 3
[[],[[[[]]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [.,[[[[.,.],[.,.]],.],.]] => 2
>>> Load all 830 entries. <<<[[],[[[],[],[]]]] => [.,[[[.,[.,[.,.]]],.],.]] => [.,[[[.,.],.],[.,[.,.]]]] => 2
[[],[[[],[[]]]]] => [.,[[[.,[[.,.],.]],.],.]] => [.,[[[.,.],.],[[.,.],.]]] => 2
[[],[[[[]],[]]]] => [.,[[[[.,.],[.,.]],.],.]] => [.,[[[[.,.],.],[.,.]],.]] => 2
[[],[[[[],[]]]]] => [.,[[[[.,[.,.]],.],.],.]] => [.,[[[[.,.],.],.],[.,.]]] => 2
[[],[[[[[]]]]]] => [.,[[[[[.,.],.],.],.],.]] => [.,[[[[[.,.],.],.],.],.]] => 1
[[[]],[],[],[],[]] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[[[]],[],[],[[]]] => [[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[[[]],[],[[]],[]] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[[[]],[],[[],[]]] => [[.,.],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[[[]],[],[[[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [[.,[.,[[[.,.],.],.]]],.] => 1
[[[]],[[]],[],[]] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[[[]],[[]],[[]]] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[[[]],[[],[]],[]] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[[[]],[[[]]],[]] => [[.,.],[[[.,.],.],[.,.]]] => [[.,[[[.,[.,.]],.],.]],.] => 1
[[[]],[[],[],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[[[]],[[],[[]]]] => [[.,.],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],.] => 2
[[[]],[[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [[.,[[[.,.],[.,.]],.]],.] => 2
[[[]],[[[],[]]]] => [[.,.],[[[.,[.,.]],.],.]] => [[.,[[[.,.],.],[.,.]]],.] => 2
[[[]],[[[[]]]]] => [[.,.],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],.] => 1
[[[],[]],[],[],[]] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[[[[]]],[],[],[]] => [[[.,.],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],.] => 1
[[[],[]],[],[[]]] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[[[[]]],[],[[]]] => [[[.,.],.],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],.],.] => 1
[[[],[]],[[]],[]] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[[[[]]],[[]],[]] => [[[.,.],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],.] => 1
[[[],[]],[[],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[[[],[]],[[[]]]] => [[.,[.,.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,.]] => 2
[[[[]]],[[],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],.],.] => 2
[[[[]]],[[[]]]] => [[[.,.],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],.] => 1
[[[],[],[]],[],[]] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[[[],[[]]],[],[]] => [[.,[[.,.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[[[[]],[]],[],[]] => [[[.,.],[.,.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,.]],.] => 2
[[[[],[]]],[],[]] => [[[.,[.,.]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,.]] => 2
[[[[[]]]],[],[]] => [[[[.,.],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],.] => 1
[[[],[],[]],[[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[[[],[[]]],[[]]] => [[.,[[.,.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[.,.],.]] => 2
[[[[]],[]],[[]]] => [[[.,.],[.,.]],[[.,.],.]] => [[[.,[[.,.],.]],[.,.]],.] => 2
[[[[],[]]],[[]]] => [[[.,[.,.]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,.]] => 2
[[[[[]]]],[[]]] => [[[[.,.],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],.] => 1
[[[],[],[],[]],[]] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[[[],[],[[]]],[]] => [[.,[.,[[.,.],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[[[],[[]],[]],[]] => [[.,[[.,.],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[[[],[[],[]]],[]] => [[.,[[.,[.,.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,.]]] => 3
[[[],[[[]]]],[]] => [[.,[[[.,.],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],.]] => 2
[[[[]],[],[]],[]] => [[[.,.],[.,[.,.]]],[.,.]] => [[[.,[.,.]],[.,[.,.]]],.] => 2
[[[[]],[[]]],[]] => [[[.,.],[[.,.],.]],[.,.]] => [[[.,[.,.]],[[.,.],.]],.] => 2
[[[[],[]],[]],[]] => [[[.,[.,.]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,.]] => 3
[[[[[]]],[]],[]] => [[[[.,.],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],.] => 2
[[[[],[],[]]],[]] => [[[.,[.,[.,.]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,.]]] => 2
[[[[],[[]]]],[]] => [[[.,[[.,.],.]],.],[.,.]] => [[[.,[.,.]],.],[[.,.],.]] => 2
[[[[[]],[]]],[]] => [[[[.,.],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],.] => 2
[[[[[],[]]]],[]] => [[[[.,[.,.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,.]] => 2
[[[[[[]]]]],[]] => [[[[[.,.],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],.] => 1
[[[],[],[],[],[]]] => [[.,[.,[.,[.,[.,.]]]]],.] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[[[],[],[],[[]]]] => [[.,[.,[.,[[.,.],.]]]],.] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[[[],[],[[]],[]]] => [[.,[.,[[.,.],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[[[],[],[[],[]]]] => [[.,[.,[[.,[.,.]],.]]],.] => [[.,.],[.,[[.,.],[.,.]]]] => 3
[[[],[],[[[]]]]] => [[.,[.,[[[.,.],.],.]]],.] => [[.,.],[.,[[[.,.],.],.]]] => 2
[[[],[[]],[],[]]] => [[.,[[.,.],[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],.]] => 2
[[[],[[]],[[]]]] => [[.,[[.,.],[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],.]] => 2
[[[],[[],[]],[]]] => [[.,[[.,[.,.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,.]]] => 3
[[[],[[[]]],[]]] => [[.,[[[.,.],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],.]] => 2
[[[],[[],[],[]]]] => [[.,[[.,[.,[.,.]]],.]],.] => [[.,.],[[.,.],[.,[.,.]]]] => 3
[[[],[[],[[]]]]] => [[.,[[.,[[.,.],.]],.]],.] => [[.,.],[[.,.],[[.,.],.]]] => 3
[[[],[[[]],[]]]] => [[.,[[[.,.],[.,.]],.]],.] => [[.,.],[[[.,.],[.,.]],.]] => 3
[[[],[[[],[]]]]] => [[.,[[[.,[.,.]],.],.]],.] => [[.,.],[[[.,.],.],[.,.]]] => 3
[[[],[[[[]]]]]] => [[.,[[[[.,.],.],.],.]],.] => [[.,.],[[[[.,.],.],.],.]] => 2
[[[[]],[],[],[]]] => [[[.,.],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],.] => 2
[[[[]],[],[[]]]] => [[[.,.],[.,[[.,.],.]]],.] => [[[.,.],[.,[[.,.],.]]],.] => 2
[[[[]],[[]],[]]] => [[[.,.],[[.,.],[.,.]]],.] => [[[.,.],[[.,[.,.]],.]],.] => 2
[[[[]],[[],[]]]] => [[[.,.],[[.,[.,.]],.]],.] => [[[.,.],[[.,.],[.,.]]],.] => 3
[[[[]],[[[]]]]] => [[[.,.],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],.] => 2
[[[[],[]],[],[]]] => [[[.,[.,.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,.]] => 3
[[[[[]]],[],[]]] => [[[[.,.],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],.] => 2
[[[[],[]],[[]]]] => [[[.,[.,.]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,.]] => 3
[[[[[]]],[[]]]] => [[[[.,.],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],.] => 2
[[[[],[],[]],[]]] => [[[.,[.,[.,.]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,.]]] => 3
[[[[],[[]]],[]]] => [[[.,[[.,.],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],.]] => 3
[[[[[]],[]],[]]] => [[[[.,.],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],.] => 3
[[[[[],[]]],[]]] => [[[[.,[.,.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,.]] => 3
[[[[[[]]]],[]]] => [[[[[.,.],.],.],[.,.]],.] => [[[[[.,.],[.,.]],.],.],.] => 2
[[[[],[],[],[]]]] => [[[.,[.,[.,[.,.]]]],.],.] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[[[[],[],[[]]]]] => [[[.,[.,[[.,.],.]]],.],.] => [[[.,.],.],[.,[[.,.],.]]] => 2
[[[[],[[]],[]]]] => [[[.,[[.,.],[.,.]]],.],.] => [[[.,.],.],[[.,[.,.]],.]] => 2
[[[[],[[],[]]]]] => [[[.,[[.,[.,.]],.]],.],.] => [[[.,.],.],[[.,.],[.,.]]] => 3
[[[[],[[[]]]]]] => [[[.,[[[.,.],.],.]],.],.] => [[[.,.],.],[[[.,.],.],.]] => 2
[[[[[]],[],[]]]] => [[[[.,.],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],.] => 2
[[[[[]],[[]]]]] => [[[[.,.],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],.] => 2
[[[[[],[]],[]]]] => [[[[.,[.,.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,.]] => 3
[[[[[[]]],[]]]] => [[[[[.,.],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],.] => 2
[[[[[],[],[]]]]] => [[[[.,[.,[.,.]]],.],.],.] => [[[[.,.],.],.],[.,[.,.]]] => 2
[[[[[],[[]]]]]] => [[[[.,[[.,.],.]],.],.],.] => [[[[.,.],.],.],[[.,.],.]] => 2
[[[[[[]],[]]]]] => [[[[[.,.],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],.] => 2
[[[[[[],[]]]]]] => [[[[[.,[.,.]],.],.],.],.] => [[[[[.,.],.],.],.],[.,.]] => 2
[[[[[[[]]]]]]] => [[[[[[.,.],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],.] => 1
[[],[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[[],[],[],[],[],[[]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[[],[],[],[],[[]],[]] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
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[[[]],[[[]],[],[]]] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => 2
[[[]],[[[]],[[]]]] => [[.,.],[[[.,.],[[.,.],.]],.]] => [[.,[[[.,.],[[.,.],.]],.]],.] => 2
[[[]],[[[],[]],[]]] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 3
[[[]],[[[[]]],[]]] => [[.,.],[[[[.,.],.],[.,.]],.]] => [[.,[[[[.,.],[.,.]],.],.]],.] => 2
[[[]],[[[],[],[]]]] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [[.,[[[.,.],.],[.,[.,.]]]],.] => 2
[[[]],[[[],[[]]]]] => [[.,.],[[[.,[[.,.],.]],.],.]] => [[.,[[[.,.],.],[[.,.],.]]],.] => 2
[[[]],[[[[]],[]]]] => [[.,.],[[[[.,.],[.,.]],.],.]] => [[.,[[[[.,.],.],[.,.]],.]],.] => 2
[[[]],[[[[],[]]]]] => [[.,.],[[[[.,[.,.]],.],.],.]] => [[.,[[[[.,.],.],.],[.,.]]],.] => 2
[[[]],[[[[[]]]]]] => [[.,.],[[[[[.,.],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],.]],.] => 1
[[[],[]],[],[],[],[]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[[[[]]],[],[],[],[]] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => 1
[[[],[]],[],[],[[]]] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[[[[]]],[],[],[[]]] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => 1
[[[],[]],[],[[]],[]] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[[[[]]],[],[[]],[]] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => 1
[[[],[]],[],[[],[]]] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[[[],[]],[],[[[]]]] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [[.,[.,[[[.,.],.],.]]],[.,.]] => 2
[[[[]]],[],[[],[]]] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [[[.,[.,[[.,.],[.,.]]]],.],.] => 2
[[[[]]],[],[[[]]]] => [[[.,.],.],[.,[[[.,.],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],.] => 1
[[[],[]],[[]],[],[]] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[[[[]]],[[]],[],[]] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => 1
[[[],[]],[[]],[[]]] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[[[[]]],[[]],[[]]] => [[[.,.],.],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],.],.] => 1
[[[],[]],[[],[]],[]] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[[[],[]],[[[]]],[]] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [[.,[[[.,[.,.]],.],.]],[.,.]] => 2
[[[[]]],[[],[]],[]] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [[[.,[[.,[.,.]],[.,.]]],.],.] => 2
[[[[]]],[[[]]],[]] => [[[.,.],.],[[[.,.],.],[.,.]]] => [[[.,[[[.,[.,.]],.],.]],.],.] => 1
[[[],[]],[[],[],[]]] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[[[],[]],[[],[[]]]] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],[.,.]] => 3
[[[],[]],[[[]],[]]] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [[.,[[[.,.],[.,.]],.]],[.,.]] => 3
[[[],[]],[[[],[]]]] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [[.,[[[.,.],.],[.,.]]],[.,.]] => 3
[[[],[]],[[[[]]]]] => [[.,[.,.]],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],[.,.]] => 2
[[[[]]],[[],[],[]]] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => 2
[[[[]]],[[],[[]]]] => [[[.,.],.],[[.,[[.,.],.]],.]] => [[[.,[[.,.],[[.,.],.]]],.],.] => 2
[[[[]]],[[[]],[]]] => [[[.,.],.],[[[.,.],[.,.]],.]] => [[[.,[[[.,.],[.,.]],.]],.],.] => 2
[[[[]]],[[[],[]]]] => [[[.,.],.],[[[.,[.,.]],.],.]] => [[[.,[[[.,.],.],[.,.]]],.],.] => 2
[[[[]]],[[[[]]]]] => [[[.,.],.],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],.],.] => 1
[[[],[],[]],[],[],[]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[[[],[[]]],[],[],[]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2
[[[[]],[]],[],[],[]] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => 2
[[[[],[]]],[],[],[]] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => 2
[[[[[]]]],[],[],[]] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => 1
[[[],[],[]],[],[[]]] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[[[],[[]]],[],[[]]] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[[.,.],.]] => 2
[[[[]],[]],[],[[]]] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],.] => 2
[[[[],[]]],[],[[]]] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],.],[.,.]] => 2
[[[[[]]]],[],[[]]] => [[[[.,.],.],.],[.,[[.,.],.]]] => [[[[.,[.,[[.,.],.]]],.],.],.] => 1
[[[],[],[]],[[]],[]] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[[[],[[]]],[[]],[]] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,.],.]] => 2
[[[[]],[]],[[]],[]] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[.,.]],.] => 2
[[[[],[]]],[[]],[]] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],[.,.]] => 2
[[[[[]]]],[[]],[]] => [[[[.,.],.],.],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],.],.],.] => 1
[[[],[],[]],[[],[]]] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[[[],[],[]],[[[]]]] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,[.,.]]] => 2
[[[],[[]]],[[],[]]] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],.]] => 3
[[[],[[]]],[[[]]]] => [[.,[[.,.],.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[[.,.],.]] => 2
[[[[]],[]],[[],[]]] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],[.,.]],.] => 3
[[[[]],[]],[[[]]]] => [[[.,.],[.,.]],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],[.,.]],.] => 2
[[[[],[]]],[[],[]]] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],.],[.,.]] => 3
[[[[],[]]],[[[]]]] => [[[.,[.,.]],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],[.,.]] => 2
[[[[[]]]],[[],[]]] => [[[[.,.],.],.],[[.,[.,.]],.]] => [[[[.,[[.,.],[.,.]]],.],.],.] => 2
[[[[[]]]],[[[]]]] => [[[[.,.],.],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],.],.] => 1
[[[],[],[],[]],[],[]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[[[],[],[[]]],[],[]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[[[],[[]],[]],[],[]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 2
[[[],[[],[]]],[],[]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[[[],[[[]]]],[],[]] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,.],.],.]] => 2
[[[[]],[],[]],[],[]] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => 2
[[[[]],[[]]],[],[]] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[[.,.],.]],.] => 2
[[[[],[]],[]],[],[]] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 3
[[[[[]]],[]],[],[]] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[[[.,[.,[.,.]]],[.,.]],.],.] => 2
[[[[],[],[]]],[],[]] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2
[[[[],[[]]]],[],[]] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[[.,.],.]] => 2
[[[[[]],[]]],[],[]] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],[.,.]],.] => 2
[[[[[],[]]]],[],[]] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 2
[[[[[[]]]]],[],[]] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[[[[.,[.,[.,.]]],.],.],.],.] => 1
[[[],[],[],[]],[[]]] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[[[],[],[[]]],[[]]] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[[.,.],.]]] => 2
[[[],[[]],[]],[[]]] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[.,.]],.]] => 2
[[[],[[],[]]],[[]]] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [[.,[[.,.],.]],[[.,.],[.,.]]] => 3
[[[],[[[]]]],[[]]] => [[.,[[[.,.],.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[[.,.],.],.]] => 2
[[[[]],[],[]],[[]]] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [[[.,[[.,.],.]],[.,[.,.]]],.] => 2
[[[[]],[[]]],[[]]] => [[[.,.],[[.,.],.]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,.],.]],.] => 2
[[[[],[]],[]],[[]]] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [[[.,[[.,.],.]],[.,.]],[.,.]] => 3
[[[[[]]],[]],[[]]] => [[[[.,.],.],[.,.]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,.]],.],.] => 2
[[[[],[],[]]],[[]]] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 2
[[[[],[[]]]],[[]]] => [[[.,[[.,.],.]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[[.,.],.]] => 2
[[[[[]],[]]],[[]]] => [[[[.,.],[.,.]],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],[.,.]],.] => 2
[[[[[],[]]]],[[]]] => [[[[.,[.,.]],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],[.,.]] => 2
[[[[[[]]]]],[[]]] => [[[[[.,.],.],.],.],[[.,.],.]] => [[[[[.,[[.,.],.]],.],.],.],.] => 1
[[[],[],[],[],[]],[]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[[[],[],[],[[]]],[]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[[[],[],[[]],[]],[]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[[[],[],[[],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 3
[[[],[],[[[]]]],[]] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [[.,[.,.]],[.,[[[.,.],.],.]]] => 2
[[[],[[]],[],[]],[]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 2
[[[],[[]],[[]]],[]] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [[.,[.,.]],[[.,[[.,.],.]],.]] => 2
[[[],[[],[]],[]],[]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[[[],[[[]]],[]],[]] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [[.,[.,.]],[[[.,[.,.]],.],.]] => 2
[[[],[[],[],[]]],[]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 3
[[[],[[],[[]]]],[]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[[[],[[[]],[]]],[]] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,.]],.]] => 3
[[[],[[[],[]]]],[]] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],[.,.]]] => 3
[[[],[[[[]]]]],[]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [[.,[.,.]],[[[[.,.],.],.],.]] => 2
[[[[]],[],[],[]],[]] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 2
[[[[]],[],[[]]],[]] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [[[.,[.,.]],[.,[[.,.],.]]],.] => 2
[[[[]],[[]],[]],[]] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [[[.,[.,.]],[[.,[.,.]],.]],.] => 2
[[[[]],[[],[]]],[]] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[.,.]]],.] => 3
[[[[]],[[[]]]],[]] => [[[.,.],[[[.,.],.],.]],[.,.]] => [[[.,[.,.]],[[[.,.],.],.]],.] => 2
[[[[],[]],[],[]],[]] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[[[[[]]],[],[]],[]] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[[[.,[.,.]],[.,[.,.]]],.],.] => 2
[[[[],[]],[[]]],[]] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [[[.,[.,.]],[[.,.],.]],[.,.]] => 3
[[[[[]]],[[]]],[]] => [[[[.,.],.],[[.,.],.]],[.,.]] => [[[[.,[.,.]],[[.,.],.]],.],.] => 2
[[[[],[],[]],[]],[]] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 3
[[[[],[[]]],[]],[]] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[[.,.],.]] => 3
[[[[[]],[]],[]],[]] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[.,.]],.] => 3
[[[[[],[]]],[]],[]] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 3
[[[[[[]]]],[]],[]] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],.],.],.] => 2
[[[[],[],[],[]]],[]] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 2
[[[[],[],[[]]]],[]] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [[[.,[.,.]],.],[.,[[.,.],.]]] => 2
[[[[],[[]],[]]],[]] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 2
[[[[],[[],[]]]],[]] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [[[.,[.,.]],.],[[.,.],[.,.]]] => 3
[[[[],[[[]]]]],[]] => [[[.,[[[.,.],.],.]],.],[.,.]] => [[[.,[.,.]],.],[[[.,.],.],.]] => 2
[[[[[]],[],[]]],[]] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 2
[[[[[]],[[]]]],[]] => [[[[.,.],[[.,.],.]],.],[.,.]] => [[[[.,[.,.]],.],[[.,.],.]],.] => 2
[[[[[],[]],[]]],[]] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 3
[[[[[[]]],[]]],[]] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[[[[.,[.,.]],.],[.,.]],.],.] => 2
[[[[[],[],[]]]],[]] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 2
[[[[[],[[]]]]],[]] => [[[[.,[[.,.],.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[[.,.],.]] => 2
[[[[[[]],[]]]],[]] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[[[[.,[.,.]],.],.],[.,.]],.] => 2
[[[[[[],[]]]]],[]] => [[[[[.,[.,.]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[.,.]] => 2
[[[[[[[]]]]]],[]] => [[[[[[.,.],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],.] => 1
[[[],[],[],[],[],[]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[[[],[],[],[],[[]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[[[],[],[],[[]],[]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[[[],[],[],[[],[]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 3
[[[],[],[],[[[]]]]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 2
[[[],[],[[]],[],[]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 2
[[[],[],[[]],[[]]]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [[.,.],[.,[[.,[[.,.],.]],.]]] => 2
[[[],[],[[],[]],[]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 3
[[[],[],[[[]]],[]]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [[.,.],[.,[[[.,[.,.]],.],.]]] => 2
[[[],[],[[],[],[]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 3
[[[],[],[[],[[]]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[[[],[],[[[]],[]]]] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [[.,.],[.,[[[.,.],[.,.]],.]]] => 3
[[[],[],[[[],[]]]]] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [[.,.],[.,[[[.,.],.],[.,.]]]] => 3
[[[],[],[[[[]]]]]] => [[.,[.,[[[[.,.],.],.],.]]],.] => [[.,.],[.,[[[[.,.],.],.],.]]] => 2
[[[],[[]],[],[],[]]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 2
[[[],[[]],[],[[]]]] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [[.,.],[[.,[.,[[.,.],.]]],.]] => 2
[[[],[[]],[[]],[]]] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [[.,.],[[.,[[.,[.,.]],.]],.]] => 2
[[[],[[]],[[],[]]]] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [[.,.],[[.,[[.,.],[.,.]]],.]] => 3
[[[],[[]],[[[]]]]] => [[.,[[.,.],[[[.,.],.],.]]],.] => [[.,.],[[.,[[[.,.],.],.]],.]] => 2
[[[],[[],[]],[],[]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[[[],[[[]]],[],[]]] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [[.,.],[[[.,[.,[.,.]]],.],.]] => 2
[[[],[[],[]],[[]]]] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],[.,.]]] => 3
[[[],[[[]]],[[]]]] => [[.,[[[.,.],.],[[.,.],.]]],.] => [[.,.],[[[.,[[.,.],.]],.],.]] => 2
[[[],[[],[],[]],[]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 3
[[[],[[],[[]]],[]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[[[],[[[]],[]],[]]] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[.,.]],.]] => 3
[[[],[[[],[]]],[]]] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],[.,.]]] => 3
[[[],[[[[]]]],[]]] => [[.,[[[[.,.],.],.],[.,.]]],.] => [[.,.],[[[[.,[.,.]],.],.],.]] => 2
[[[],[[],[],[],[]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 3
[[[],[[],[],[[]]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[[[],[[],[[]],[]]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[[[],[[],[[],[]]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 4
[[[],[[],[[[]]]]]] => [[.,[[.,[[[.,.],.],.]],.]],.] => [[.,.],[[.,.],[[[.,.],.],.]]] => 3
[[[],[[[]],[],[]]]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 3
[[[],[[[]],[[]]]]] => [[.,[[[.,.],[[.,.],.]],.]],.] => [[.,.],[[[.,.],[[.,.],.]],.]] => 3
[[[],[[[],[]],[]]]] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 4
[[[],[[[[]]],[]]]] => [[.,[[[[.,.],.],[.,.]],.]],.] => [[.,.],[[[[.,.],[.,.]],.],.]] => 3
[[[],[[[],[],[]]]]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 3
[[[],[[[],[[]]]]]] => [[.,[[[.,[[.,.],.]],.],.]],.] => [[.,.],[[[.,.],.],[[.,.],.]]] => 3
[[[],[[[[]],[]]]]] => [[.,[[[[.,.],[.,.]],.],.]],.] => [[.,.],[[[[.,.],.],[.,.]],.]] => 3
[[[],[[[[],[]]]]]] => [[.,[[[[.,[.,.]],.],.],.]],.] => [[.,.],[[[[.,.],.],.],[.,.]]] => 3
[[[],[[[[[]]]]]]] => [[.,[[[[[.,.],.],.],.],.]],.] => [[.,.],[[[[[.,.],.],.],.],.]] => 2
[[[[]],[],[],[],[]]] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 2
[[[[]],[],[],[[]]]] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [[[.,.],[.,[.,[[.,.],.]]]],.] => 2
[[[[]],[],[[]],[]]] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [[[.,.],[.,[[.,[.,.]],.]]],.] => 2
[[[[]],[],[[],[]]]] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 3
[[[[]],[],[[[]]]]] => [[[.,.],[.,[[[.,.],.],.]]],.] => [[[.,.],[.,[[[.,.],.],.]]],.] => 2
[[[[]],[[]],[],[]]] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [[[.,.],[[.,[.,[.,.]]],.]],.] => 2
[[[[]],[[]],[[]]]] => [[[.,.],[[.,.],[[.,.],.]]],.] => [[[.,.],[[.,[[.,.],.]],.]],.] => 2
[[[[]],[[],[]],[]]] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[.,.]]],.] => 3
[[[[]],[[[]]],[]]] => [[[.,.],[[[.,.],.],[.,.]]],.] => [[[.,.],[[[.,[.,.]],.],.]],.] => 2
[[[[]],[[],[],[]]]] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[[[[]],[[],[[]]]]] => [[[.,.],[[.,[[.,.],.]],.]],.] => [[[.,.],[[.,.],[[.,.],.]]],.] => 3
[[[[]],[[[]],[]]]] => [[[.,.],[[[.,.],[.,.]],.]],.] => [[[.,.],[[[.,.],[.,.]],.]],.] => 3
[[[[]],[[[],[]]]]] => [[[.,.],[[[.,[.,.]],.],.]],.] => [[[.,.],[[[.,.],.],[.,.]]],.] => 3
[[[[]],[[[[]]]]]] => [[[.,.],[[[[.,.],.],.],.]],.] => [[[.,.],[[[[.,.],.],.],.]],.] => 2
[[[[],[]],[],[],[]]] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[[[[[]]],[],[],[]]] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[[[.,.],[.,[.,[.,.]]]],.],.] => 2
[[[[],[]],[],[[]]]] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 3
[[[[[]]],[],[[]]]] => [[[[.,.],.],[.,[[.,.],.]]],.] => [[[[.,.],[.,[[.,.],.]]],.],.] => 2
[[[[],[]],[[]],[]]] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 3
[[[[[]]],[[]],[]]] => [[[[.,.],.],[[.,.],[.,.]]],.] => [[[[.,.],[[.,[.,.]],.]],.],.] => 2
[[[[],[]],[[],[]]]] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[[[[],[]],[[[]]]]] => [[[.,[.,.]],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],[.,.]] => 3
[[[[[]]],[[],[]]]] => [[[[.,.],.],[[.,[.,.]],.]],.] => [[[[.,.],[[.,.],[.,.]]],.],.] => 3
[[[[[]]],[[[]]]]] => [[[[.,.],.],[[[.,.],.],.]],.] => [[[[.,.],[[[.,.],.],.]],.],.] => 2
[[[[],[],[]],[],[]]] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 3
[[[[],[[]]],[],[]]] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 3
[[[[[]],[]],[],[]]] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 3
[[[[[],[]]],[],[]]] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 3
[[[[[[]]]],[],[]]] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[[[[.,.],[.,[.,.]]],.],.],.] => 2
[[[[],[],[]],[[]]]] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 3
[[[[],[[]]],[[]]]] => [[[.,[[.,.],.]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[[.,.],.]] => 3
[[[[[]],[]],[[]]]] => [[[[.,.],[.,.]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[.,.]],.] => 3
[[[[[],[]]],[[]]]] => [[[[.,[.,.]],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],[.,.]] => 3
[[[[[[]]]],[[]]]] => [[[[[.,.],.],.],[[.,.],.]],.] => [[[[[.,.],[[.,.],.]],.],.],.] => 2
[[[[],[],[],[]],[]]] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 3
[[[[],[],[[]]],[]]] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 3
[[[[],[[]],[]],[]]] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 3
[[[[],[[],[]]],[]]] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 4
[[[[],[[[]]]],[]]] => [[[.,[[[.,.],.],.]],[.,.]],.] => [[[.,.],[.,.]],[[[.,.],.],.]] => 3
[[[[[]],[],[]],[]]] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[[[[[]],[[]]],[]]] => [[[[.,.],[[.,.],.]],[.,.]],.] => [[[[.,.],[.,.]],[[.,.],.]],.] => 3
[[[[[],[]],[]],[]]] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 4
[[[[[[]]],[]],[]]] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[[[[.,.],[.,.]],[.,.]],.],.] => 3
[[[[[],[],[]]],[]]] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 3
[[[[[],[[]]]],[]]] => [[[[.,[[.,.],.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[[.,.],.]] => 3
[[[[[[]],[]]],[]]] => [[[[[.,.],[.,.]],.],[.,.]],.] => [[[[[.,.],[.,.]],.],[.,.]],.] => 3
[[[[[[],[]]]],[]]] => [[[[[.,[.,.]],.],.],[.,.]],.] => [[[[[.,.],[.,.]],.],.],[.,.]] => 3
[[[[[[[]]]]],[]]] => [[[[[[.,.],.],.],.],[.,.]],.] => [[[[[[.,.],[.,.]],.],.],.],.] => 2
[[[[],[],[],[],[]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[[[],[],[],[[]]]]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 2
[[[[],[],[[]],[]]]] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 2
[[[[],[],[[],[]]]]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 3
[[[[],[],[[[]]]]]] => [[[.,[.,[[[.,.],.],.]]],.],.] => [[[.,.],.],[.,[[[.,.],.],.]]] => 2
[[[[],[[]],[],[]]]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 2
[[[[],[[]],[[]]]]] => [[[.,[[.,.],[[.,.],.]]],.],.] => [[[.,.],.],[[.,[[.,.],.]],.]] => 2
[[[[],[[],[]],[]]]] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 3
[[[[],[[[]]],[]]]] => [[[.,[[[.,.],.],[.,.]]],.],.] => [[[.,.],.],[[[.,[.,.]],.],.]] => 2
[[[[],[[],[],[]]]]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 3
[[[[],[[],[[]]]]]] => [[[.,[[.,[[.,.],.]],.]],.],.] => [[[.,.],.],[[.,.],[[.,.],.]]] => 3
[[[[],[[[]],[]]]]] => [[[.,[[[.,.],[.,.]],.]],.],.] => [[[.,.],.],[[[.,.],[.,.]],.]] => 3
[[[[],[[[],[]]]]]] => [[[.,[[[.,[.,.]],.],.]],.],.] => [[[.,.],.],[[[.,.],.],[.,.]]] => 3
[[[[],[[[[]]]]]]] => [[[.,[[[[.,.],.],.],.]],.],.] => [[[.,.],.],[[[[.,.],.],.],.]] => 2
[[[[[]],[],[],[]]]] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 2
[[[[[]],[],[[]]]]] => [[[[.,.],[.,[[.,.],.]]],.],.] => [[[[.,.],.],[.,[[.,.],.]]],.] => 2
[[[[[]],[[]],[]]]] => [[[[.,.],[[.,.],[.,.]]],.],.] => [[[[.,.],.],[[.,[.,.]],.]],.] => 2
[[[[[]],[[],[]]]]] => [[[[.,.],[[.,[.,.]],.]],.],.] => [[[[.,.],.],[[.,.],[.,.]]],.] => 3
[[[[[]],[[[]]]]]] => [[[[.,.],[[[.,.],.],.]],.],.] => [[[[.,.],.],[[[.,.],.],.]],.] => 2
[[[[[],[]],[],[]]]] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 3
[[[[[[]]],[],[]]]] => [[[[[.,.],.],[.,[.,.]]],.],.] => [[[[[.,.],.],[.,[.,.]]],.],.] => 2
[[[[[],[]],[[]]]]] => [[[[.,[.,.]],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],[.,.]] => 3
[[[[[[]]],[[]]]]] => [[[[[.,.],.],[[.,.],.]],.],.] => [[[[[.,.],.],[[.,.],.]],.],.] => 2
[[[[[],[],[]],[]]]] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 3
[[[[[],[[]]],[]]]] => [[[[.,[[.,.],.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[[.,.],.]] => 3
[[[[[[]],[]],[]]]] => [[[[[.,.],[.,.]],[.,.]],.],.] => [[[[[.,.],.],[.,.]],[.,.]],.] => 3
[[[[[[],[]]],[]]]] => [[[[[.,[.,.]],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],[.,.]] => 3
[[[[[[[]]]],[]]]] => [[[[[[.,.],.],.],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],.],.],.] => 2
[[[[[],[],[],[]]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[[[[],[],[[]]]]]] => [[[[.,[.,[[.,.],.]]],.],.],.] => [[[[.,.],.],.],[.,[[.,.],.]]] => 2
[[[[[],[[]],[]]]]] => [[[[.,[[.,.],[.,.]]],.],.],.] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2
[[[[[],[[],[]]]]]] => [[[[.,[[.,[.,.]],.]],.],.],.] => [[[[.,.],.],.],[[.,.],[.,.]]] => 3
[[[[[],[[[]]]]]]] => [[[[.,[[[.,.],.],.]],.],.],.] => [[[[.,.],.],.],[[[.,.],.],.]] => 2
[[[[[[]],[],[]]]]] => [[[[[.,.],[.,[.,.]]],.],.],.] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[[[[[[]],[[]]]]]] => [[[[[.,.],[[.,.],.]],.],.],.] => [[[[[.,.],.],.],[[.,.],.]],.] => 2
[[[[[[],[]],[]]]]] => [[[[[.,[.,.]],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],[.,.]] => 3
[[[[[[[]]],[]]]]] => [[[[[[.,.],.],[.,.]],.],.],.] => [[[[[[.,.],.],.],[.,.]],.],.] => 2
[[[[[[],[],[]]]]]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [[[[[.,.],.],.],.],[.,[.,.]]] => 2
[[[[[[],[[]]]]]]] => [[[[[.,[[.,.],.]],.],.],.],.] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
[[[[[[[]],[]]]]]] => [[[[[[.,.],[.,.]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,.]],.] => 2
[[[[[[[],[]]]]]]] => [[[[[[.,[.,.]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[.,.]] => 2
[[[[[[[[]]]]]]]] => [[[[[[[.,.],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],.] => 1
[[],[[]],[[]],[[]],[]] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[[],[[]],[[]],[[],[]]] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[[],[[]],[[[]],[]],[]] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 2
[[],[[]],[[[],[]],[]]] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 3
[[],[[[]],[]],[[]],[]] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 2
[[],[[[],[]]],[[],[]]] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 3
[[],[[[[]]]],[[[]]]] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => 1
[[],[[[[[]]]]],[],[]] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 1
[[],[[[[[]]]]],[[]]] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => 1
[[],[[[]],[[]],[]],[]] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => 2
[[],[[[[]],[]],[]],[]] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 3
[[],[[[[[[]]]]]],[]] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => 1
[[],[[[],[],[],[]],[]]] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 3
[[],[[[],[],[[]]],[]]] => [.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => 3
[[],[[[],[[]],[]],[]]] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => 3
[[],[[[],[[],[]]],[]]] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 4
[[],[[[],[[[]]]],[]]] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => 3
[[],[[[[],[]],[]],[]]] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 4
[[],[[[[],[[]]]],[]]] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => 3
[[],[[[[[[]]]]],[]]] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => 2
[[],[[[[],[[]]],[]]]] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => 3
[[],[[[[[[]]]],[]]]] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => 2
[[],[[[[[[[]]]]]]]] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => 1
[[[]],[],[],[],[],[],[]] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[[[]],[],[],[],[],[[]]] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[[[]],[],[],[],[[]],[]] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[[[]],[],[],[],[[],[]]] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[[[]],[],[],[],[[[]]]] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => 1
[[[]],[],[],[[]],[],[]] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[[[]],[],[],[[],[],[]]] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[[[]],[[]],[[]],[[]]] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[[[]],[[]],[[],[]],[]] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[[[]],[[]],[[],[[]]]] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => 2
[[[]],[[],[[]]],[[]]] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => 2
[[[]],[[],[[],[]]],[]] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => 3
[[[]],[[[],[]],[]],[]] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 3
[[[]],[[],[[]],[[]]]] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => 2
[[[]],[[],[[],[[]]]]] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => 3
[[[],[]],[[]],[[]],[]] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[[[],[]],[[[]],[]],[]] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => 3
[[[],[[]]],[[]],[[]]] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => 2
[[[[],[]]],[[],[]],[]] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 3
[[[],[[]]],[[],[[]]]] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => 3
[[[],[],[],[]],[],[],[]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[[[],[],[[]]],[],[[]]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => 2
[[[],[[]],[]],[[]],[]] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => 2
[[[],[[],[]]],[[]],[]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => 3
[[[[],[]],[]],[[]],[]] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => 3
[[[],[[]],[]],[[],[]]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => 3
[[[],[[],[]]],[[],[]]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => 4
[[[],[[[]]]],[[[]]]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => 2
[[[[[],[]]]],[[[]]]] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => 2
[[[],[],[],[[]]],[],[]] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => 2
[[[],[],[[],[]]],[],[]] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => 3
[[[],[],[[[]]]],[],[]] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => 2
[[[],[[],[],[]]],[],[]] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => 3
[[[],[[],[[]]]],[],[]] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => 3
[[[],[[[],[]]]],[],[]] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => 3
[[[[[],[],[]]]],[],[]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => 2
[[[[[[],[]]]]],[],[]] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => 2
[[[],[[]],[[]]],[[]]] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => 2
[[[],[[],[]],[]],[[]]] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => 3
[[[],[[],[[]]]],[[]]] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => 3
[[[],[[[]],[]]],[[]]] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => 3
[[[],[[[],[]]]],[[]]] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 3
[[[],[[[[]]]]],[[]]] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => 2
[[[[[],[[]]]]],[[]]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => 2
[[[[[[],[]]]]],[[]]] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => 2
[[[],[],[[],[]],[]],[]] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 3
[[[],[],[[],[[]]]],[]] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[[[],[],[[[[]]]]],[]] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 2
[[[],[[]],[[]],[]],[]] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => 2
[[[],[[]],[[],[]]],[]] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => 3
[[[],[[],[],[]],[]],[]] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => 3
[[[],[[[]],[]],[]],[]] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => 3
[[[],[[[],[]]],[]],[]] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => 3
[[[],[[],[],[[]]]],[]] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => 3
[[[],[[],[[],[]]]],[]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => 4
[[[],[[],[[[]]]]],[]] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => 3
[[[],[[[]],[[]]]],[]] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => 3
[[[],[[[],[]],[]]],[]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => 4
[[[],[[[],[[]]]]],[]] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => 3
[[[],[[[[],[]]]]],[]] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => 3
[[[],[[[[[]]]]]],[]] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => 2
[[[[],[]],[[]],[]],[]] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => 3
[[[[],[]],[[],[]]],[]] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => 4
[[[[],[[]],[]],[]],[]] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => 3
[[[[[],[]],[]],[]],[]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => 4
[[[[[],[],[]]],[]],[]] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => 3
[[[[[],[[]]]],[]],[]] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => 3
[[[[[],[]],[[]]]],[]] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => 3
[[[[[],[],[]],[]]],[]] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => 3
[[[[[],[[]]],[]]],[]] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 3
[[[[[],[],[[]]]]],[]] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => 2
[[[[[],[[],[]]]]],[]] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => 3
[[[[[],[[[]]]]]],[]] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => 2
[[[[[[[],[]]]]]],[]] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => 2
[[[],[],[],[],[],[],[]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[],[],[],[],[],[[]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[[[],[],[],[],[[]],[]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[[[],[],[],[],[[],[]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 3
[[[],[],[],[],[[[]]]]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 2
[[[],[],[],[[]],[],[]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[[[],[],[],[[],[],[]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 3
[[[],[[]],[[]],[[]]]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 2
[[[],[[]],[[],[[]]]]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 3
[[[],[[],[],[]],[],[]]] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[[[],[[],[[]]],[[]]]] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 3
[[[],[[],[],[[]]],[]]] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[[[],[[],[[],[]]],[]]] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 4
[[[],[[],[[[]]]],[]]] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 3
[[[],[[[[],[]]]],[]]] => [[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 3
[[[],[[],[[]],[[]]]]] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 3
[[[],[[],[[],[]],[]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 4
[[[],[[],[[],[[]]]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[[[],[[],[[[[]]]]]]] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 3
[[[],[[[[]],[]],[]]]] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 4
[[[],[[[[],[]]],[]]]] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 4
[[[],[[[[]],[[]]]]]] => [[.,[[[[.,.],[[.,.],.]],.],.]],.] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => 3
[[[],[[[[],[]],[]]]]] => [[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 4
[[[],[[[[],[[]]]]]]] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 3
[[[],[[[[[[]]]]]]]] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 2
[[[[],[],[],[]],[],[]]] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 3
[[[[],[],[[]]],[],[]]] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => 3
[[[[],[[]],[]],[],[]]] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 3
[[[[],[[[]]]],[],[]]] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => 3
[[[[[]],[],[]],[],[]]] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => 3
[[[[[],[]],[]],[],[]]] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => 4
[[[[[],[],[]]],[],[]]] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => 3
[[[[[],[[]]]],[],[]]] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => 3
[[[[[]],[[]]],[[]]]] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => 3
[[[[[],[]],[]],[[]]]] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 4
[[[[[],[[]]]],[[]]]] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => 3
[[[[],[],[[],[]]],[]]] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => 4
[[[[],[[],[],[]]],[]]] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => 4
[[[[[]],[],[[]]],[]]] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => 3
[[[[[]],[[],[]]],[]]] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 4
[[[[[]],[[[]]]],[]]] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => 3
[[[[[],[]],[],[]],[]]] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 4
[[[[[],[]],[[]]],[]]] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => 4
[[[[[],[],[]],[]],[]]] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => 4
[[[[[],[[]]],[]],[]]] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => 4
[[[[[],[],[[]]]],[]]] => [[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => 3
[[[[[],[[],[]]]],[]]] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => 4
[[[[[],[[[]]]]],[]]] => [[[[.,[[[.,.],.],.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => 3
[[[[[[[]],[]]]],[]]] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => 3
[[[[[[[],[]]]]],[]]] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => 3
[[[[[]],[[],[]],[]]]] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 3
[[[[[]],[[],[[]]]]]] => [[[[.,.],[[.,[[.,.],.]],.]],.],.] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => 3
[[[[[]],[[[[]]]]]]] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => 2
[[[[[],[]],[[]],[]]]] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => 3
[[[[[],[]],[[],[]]]]] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 4
[[[[[],[]],[[[]]]]]] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => 3
[[[[[],[],[]],[],[]]]] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 3
[[[[[],[[]]],[],[]]]] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 3
[[[[[],[[]]],[[]]]]] => [[[[.,[[.,.],.]],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => 3
[[[[[],[],[[]]],[]]]] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 3
[[[[[],[[],[]]],[]]]] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 4
[[[[[],[[[]]]],[]]]] => [[[[.,[[[.,.],.],.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => 3
[[[[[[[]]],[]],[]]]] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => 3
[[[[[[[]],[]]],[]]]] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => 3
[[[[[[[],[]]]],[]]]] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => 3
[[[[[],[[],[]],[]]]]] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 3
[[[[[],[[],[[]]]]]]] => [[[[.,[[.,[[.,.],.]],.]],.],.],.] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 3
[[[[[],[[[[]]]]]]]] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 2
[[[[[[[]]],[[]]]]]] => [[[[[[.,.],.],[[.,.],.]],.],.],.] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => 2
[[[[[[[]],[]],[]]]]] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => 3
[[[[[[[],[]]],[]]]]] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => 3
[[[[[[[]],[[]]]]]]] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => 2
[[[[[[[],[]],[]]]]]] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 3
[[[[[[[],[[]]]]]]]] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
[[[[[[[[],[]]]]]]]] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 2
[[[[[[[[[]]]]]]]]] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],.],.] => 1
[[],[[[],[[[],[]],[]]],[]]] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 5
[[],[[[[],[]],[[],[]]],[]]] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] => 5
[[],[[[[],[[],[]]],[]],[]]] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] => 5
[[],[[[[[],[]],[]],[]],[]]] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 5
[[[],[[[],[[],[]]],[]]],[]] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 5
[[[],[[[[],[]],[]],[]]],[]] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]] => 5
[[[[],[]],[[[],[]],[]]],[]] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]] => 5
[[[[],[[],[]]],[[],[]]],[]] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => 5
[[[[[],[]],[]],[[],[]]],[]] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => 5
[[[[[[],[]],[]],[]],[]],[]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 5
[[],[[[],[[[[],[]],[]],[]]],[]]] => [.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]] => 6
[[],[[[[],[]],[[[],[]],[]]],[]]] => [.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]] => 6
[[],[[[[],[[],[]]],[[],[]]],[]]] => [.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => [.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]] => 6
[[],[[[[[],[]],[]],[[],[]]],[]]] => [.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]] => 6
[[],[[[[],[[[],[]],[]]],[]],[]]] => [.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => [.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 6
[[],[[[[[],[]],[[],[]]],[]],[]]] => [.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]] => 6
[[],[[[[[],[[],[]]],[]],[]],[]]] => [.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]] => 6
[[],[[[[[[],[]],[]],[]],[]],[]]] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => 6
[[[],[[[],[[],[]]],[]]],[[],[]]] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 6
[[[],[[[],[[[],[]],[]]],[]]],[]] => [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 6
[[[],[[[[],[]],[[],[]]],[]]],[]] => [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] => 6
[[[],[[[[],[[],[]]],[]],[]]],[]] => [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] => 6
[[[],[[[[[],[]],[]],[]],[]]],[]] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 6
[[[[],[]],[[[[],[]],[]],[]]],[]] => [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]] => 6
[[[[],[[],[]]],[[[],[]],[]]],[]] => [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]] => 6
[[[[[],[]],[]],[[[],[]],[]]],[]] => [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]] => 6
[[[[],[[[],[]],[]]],[[],[]]],[]] => [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]] => 6
[[[[[],[]],[[],[]]],[[],[]]],[]] => [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => 6
[[[[[],[[],[]]],[]],[[],[]]],[]] => [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => 6
[[[[[[],[]],[]],[]],[[],[]]],[]] => [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => 6
[[[[],[[[],[[],[]]],[]]],[]],[]] => [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 6
[[[[[[[],[]],[]],[]],[]],[]],[]] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 6
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,24,2 32,80,20 64,240,120,5
$F_{2} = q$
$F_{3} = 2\ q$
$F_{4} = 4\ q + q^{2}$
$F_{5} = 8\ q + 6\ q^{2}$
$F_{6} = 16\ q + 24\ q^{2} + 2\ q^{3}$
$F_{7} = 32\ q + 80\ q^{2} + 20\ q^{3}$
$F_{8} = 64\ q + 240\ q^{2} + 120\ q^{3} + 5\ q^{4}$
Description
The number of leaf nodes in a binary tree.
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size $n$, at least $1$, with exactly one leaf node for is $2^{n-1}$, see [2].
The number of binary tree of size $n$, at least $3$, with exactly two leaf nodes is $n(n+1)2^{n-2}$, see [3].
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size $n$, at least $1$, with exactly one leaf node for is $2^{n-1}$, see [2].
The number of binary tree of size $n$, at least $3$, with exactly two leaf nodes is $n(n+1)2^{n-2}$, see [3].
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
Map
to binary tree: right brother = right child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of an ordered tree $t$) obtained from $t$ by the following recursive rule:
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.
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