Identifier
-
Mp00010:
Binary trees
—to ordered tree: left child = left brother⟶
Ordered trees
St000679: Ordered trees ⟶ ℤ
Values
[.,.] => [[]] => 1
[.,[.,.]] => [[[]]] => 1
[[.,.],.] => [[],[]] => 1
[.,[.,[.,.]]] => [[[[]]]] => 1
[.,[[.,.],.]] => [[[],[]]] => 2
[[.,.],[.,.]] => [[],[[]]] => 1
[[.,[.,.]],.] => [[[]],[]] => 1
[[[.,.],.],.] => [[],[],[]] => 1
[.,[.,[.,[.,.]]]] => [[[[[]]]]] => 1
[.,[.,[[.,.],.]]] => [[[[],[]]]] => 2
[.,[[.,.],[.,.]]] => [[[],[[]]]] => 2
[.,[[.,[.,.]],.]] => [[[[]],[]]] => 2
[.,[[[.,.],.],.]] => [[[],[],[]]] => 2
[[.,.],[.,[.,.]]] => [[],[[[]]]] => 1
[[.,.],[[.,.],.]] => [[],[[],[]]] => 2
[[.,[.,.]],[.,.]] => [[[]],[[]]] => 1
[[[.,.],.],[.,.]] => [[],[],[[]]] => 1
[[.,[.,[.,.]]],.] => [[[[]]],[]] => 1
[[.,[[.,.],.]],.] => [[[],[]],[]] => 2
[[[.,.],[.,.]],.] => [[],[[]],[]] => 1
[[[.,[.,.]],.],.] => [[[]],[],[]] => 1
[[[[.,.],.],.],.] => [[],[],[],[]] => 1
[.,[.,[.,[.,[.,.]]]]] => [[[[[[]]]]]] => 1
[.,[.,[.,[[.,.],.]]]] => [[[[[],[]]]]] => 2
[.,[.,[[.,.],[.,.]]]] => [[[[],[[]]]]] => 2
[.,[.,[[.,[.,.]],.]]] => [[[[[]],[]]]] => 2
[.,[.,[[[.,.],.],.]]] => [[[[],[],[]]]] => 2
[.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]] => 2
[.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => 2
[.,[[.,[.,.]],[.,.]]] => [[[[]],[[]]]] => 2
[.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]] => 2
[.,[[.,[.,[.,.]]],.]] => [[[[[]]],[]]] => 2
[.,[[.,[[.,.],.]],.]] => [[[[],[]],[]]] => 2
[.,[[[.,.],[.,.]],.]] => [[[],[[]],[]]] => 2
[.,[[[.,[.,.]],.],.]] => [[[[]],[],[]]] => 2
[.,[[[[.,.],.],.],.]] => [[[],[],[],[]]] => 2
[[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 1
[[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => 2
[[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 2
[[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => 2
[[.,.],[[[.,.],.],.]] => [[],[[],[],[]]] => 2
[[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 1
[[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => 2
[[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 1
[[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => 2
[[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => 1
[[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => 2
[[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 1
[[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => 1
[[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 1
[[.,[.,[.,[.,.]]]],.] => [[[[[]]]],[]] => 1
[[.,[.,[[.,.],.]]],.] => [[[[],[]]],[]] => 2
[[.,[[.,.],[.,.]]],.] => [[[],[[]]],[]] => 2
[[.,[[.,[.,.]],.]],.] => [[[[]],[]],[]] => 2
[[.,[[[.,.],.],.]],.] => [[[],[],[]],[]] => 2
[[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => 1
[[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => 2
[[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => 1
[[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => 1
[[[.,[.,[.,.]]],.],.] => [[[[]]],[],[]] => 1
[[[.,[[.,.],.]],.],.] => [[[],[]],[],[]] => 2
[[[[.,.],[.,.]],.],.] => [[],[[]],[],[]] => 1
[[[[.,[.,.]],.],.],.] => [[[]],[],[],[]] => 1
[[[[[.,.],.],.],.],.] => [[],[],[],[],[]] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => [[[[[[[]]]]]]] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [[[[[[],[]]]]]] => 2
[.,[.,[.,[[.,.],[.,.]]]]] => [[[[[],[[]]]]]] => 2
[.,[.,[.,[[.,[.,.]],.]]]] => [[[[[[]],[]]]]] => 2
[.,[.,[.,[[[.,.],.],.]]]] => [[[[[],[],[]]]]] => 2
[.,[.,[[.,.],[.,[.,.]]]]] => [[[[],[[[]]]]]] => 2
[.,[.,[[.,.],[[.,.],.]]]] => [[[[],[[],[]]]]] => 2
[.,[.,[[.,[.,.]],[.,.]]]] => [[[[[]],[[]]]]] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [[[[],[],[[]]]]] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [[[[[[]]],[]]]] => 2
[.,[.,[[.,[[.,.],.]],.]]] => [[[[[],[]],[]]]] => 2
[.,[.,[[[.,.],[.,.]],.]]] => [[[[],[[]],[]]]] => 2
[.,[.,[[[.,[.,.]],.],.]]] => [[[[[]],[],[]]]] => 2
[.,[.,[[[[.,.],.],.],.]]] => [[[[],[],[],[]]]] => 2
[.,[[.,.],[.,[.,[.,.]]]]] => [[[],[[[[]]]]]] => 2
[.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => 2
[.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 2
[.,[[.,.],[[.,[.,.]],.]]] => [[[],[[[]],[]]]] => 2
[.,[[.,.],[[[.,.],.],.]]] => [[[],[[],[],[]]]] => 2
[.,[[.,[.,.]],[.,[.,.]]]] => [[[[]],[[[]]]]] => 2
[.,[[.,[.,.]],[[.,.],.]]] => [[[[]],[[],[]]]] => 2
[.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]] => 2
[.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]] => 2
[.,[[.,[.,[.,.]]],[.,.]]] => [[[[[]]],[[]]]] => 2
[.,[[.,[[.,.],.]],[.,.]]] => [[[[],[]],[[]]]] => 2
[.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 2
[.,[[[.,[.,.]],.],[.,.]]] => [[[[]],[],[[]]]] => 2
[.,[[[[.,.],.],.],[.,.]]] => [[[],[],[],[[]]]] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => [[[[[[]]]],[]]] => 2
[.,[[.,[.,[[.,.],.]]],.]] => [[[[[],[]]],[]]] => 2
[.,[[.,[[.,.],[.,.]]],.]] => [[[[],[[]]],[]]] => 2
[.,[[.,[[.,[.,.]],.]],.]] => [[[[[]],[]],[]]] => 2
[.,[[.,[[[.,.],.],.]],.]] => [[[[],[],[]],[]]] => 2
[.,[[[.,.],[.,[.,.]]],.]] => [[[],[[[]]],[]]] => 2
[.,[[[.,.],[[.,.],.]],.]] => [[[],[[],[]],[]]] => 2
[.,[[[.,[.,.]],[.,.]],.]] => [[[[]],[[]],[]]] => 2
[.,[[[[.,.],.],[.,.]],.]] => [[[],[],[[]],[]]] => 2
>>> Load all 1200 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [[[[[]]],[],[]]] => 2
[.,[[[.,[[.,.],.]],.],.]] => [[[[],[]],[],[]]] => 2
[.,[[[[.,.],[.,.]],.],.]] => [[[],[[]],[],[]]] => 2
[.,[[[[.,[.,.]],.],.],.]] => [[[[]],[],[],[]]] => 2
[.,[[[[[.,.],.],.],.],.]] => [[[],[],[],[],[]]] => 2
[[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 1
[[.,.],[.,[.,[[.,.],.]]]] => [[],[[[[],[]]]]] => 2
[[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 2
[[.,.],[.,[[.,[.,.]],.]]] => [[],[[[[]],[]]]] => 2
[[.,.],[.,[[[.,.],.],.]]] => [[],[[[],[],[]]]] => 2
[[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 2
[[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 2
[[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[[.,.],[[.,[.,[.,.]]],.]] => [[],[[[[]]],[]]] => 2
[[.,.],[[.,[[.,.],.]],.]] => [[],[[[],[]],[]]] => 2
[[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[[.,.],[[[.,[.,.]],.],.]] => [[],[[[]],[],[]]] => 2
[[.,.],[[[[.,.],.],.],.]] => [[],[[],[],[],[]]] => 2
[[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 1
[[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 2
[[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 2
[[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 1
[[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 2
[[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 1
[[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 2
[[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 2
[[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 1
[[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 1
[[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 1
[[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => [[[[[]]]],[[]]] => 1
[[.,[.,[[.,.],.]]],[.,.]] => [[[[],[]]],[[]]] => 2
[[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 2
[[.,[[.,[.,.]],.]],[.,.]] => [[[[]],[]],[[]]] => 2
[[.,[[[.,.],.],.]],[.,.]] => [[[],[],[]],[[]]] => 2
[[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 1
[[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 1
[[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 1
[[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 1
[[[.,[[.,.],.]],.],[.,.]] => [[[],[]],[],[[]]] => 2
[[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 1
[[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 1
[[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [[[[[[]]]]],[]] => 1
[[.,[.,[.,[[.,.],.]]]],.] => [[[[[],[]]]],[]] => 2
[[.,[.,[[.,.],[.,.]]]],.] => [[[[],[[]]]],[]] => 2
[[.,[.,[[.,[.,.]],.]]],.] => [[[[[]],[]]],[]] => 2
[[.,[.,[[[.,.],.],.]]],.] => [[[[],[],[]]],[]] => 2
[[.,[[.,.],[.,[.,.]]]],.] => [[[],[[[]]]],[]] => 2
[[.,[[.,.],[[.,.],.]]],.] => [[[],[[],[]]],[]] => 2
[[.,[[.,[.,.]],[.,.]]],.] => [[[[]],[[]]],[]] => 2
[[.,[[[.,.],.],[.,.]]],.] => [[[],[],[[]]],[]] => 2
[[.,[[.,[.,[.,.]]],.]],.] => [[[[[]]],[]],[]] => 2
[[.,[[.,[[.,.],.]],.]],.] => [[[[],[]],[]],[]] => 2
[[.,[[[.,.],[.,.]],.]],.] => [[[],[[]],[]],[]] => 2
[[.,[[[.,[.,.]],.],.]],.] => [[[[]],[],[]],[]] => 2
[[.,[[[[.,.],.],.],.]],.] => [[[],[],[],[]],[]] => 2
[[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 1
[[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => 2
[[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 2
[[[.,.],[[.,[.,.]],.]],.] => [[],[[[]],[]],[]] => 2
[[[.,.],[[[.,.],.],.]],.] => [[],[[],[],[]],[]] => 2
[[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 1
[[[.,[.,.]],[[.,.],.]],.] => [[[]],[[],[]],[]] => 2
[[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 1
[[[[.,.],.],[[.,.],.]],.] => [[],[],[[],[]],[]] => 2
[[[.,[.,[.,.]]],[.,.]],.] => [[[[]]],[[]],[]] => 1
[[[.,[[.,.],.]],[.,.]],.] => [[[],[]],[[]],[]] => 2
[[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 1
[[[[.,[.,.]],.],[.,.]],.] => [[[]],[],[[]],[]] => 1
[[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 1
[[[.,[.,[.,[.,.]]]],.],.] => [[[[[]]]],[],[]] => 1
[[[.,[.,[[.,.],.]]],.],.] => [[[[],[]]],[],[]] => 2
[[[.,[[.,.],[.,.]]],.],.] => [[[],[[]]],[],[]] => 2
[[[.,[[.,[.,.]],.]],.],.] => [[[[]],[]],[],[]] => 2
[[[.,[[[.,.],.],.]],.],.] => [[[],[],[]],[],[]] => 2
[[[[.,.],[.,[.,.]]],.],.] => [[],[[[]]],[],[]] => 1
[[[[.,.],[[.,.],.]],.],.] => [[],[[],[]],[],[]] => 2
[[[[.,[.,.]],[.,.]],.],.] => [[[]],[[]],[],[]] => 1
[[[[[.,.],.],[.,.]],.],.] => [[],[],[[]],[],[]] => 1
[[[[.,[.,[.,.]]],.],.],.] => [[[[]]],[],[],[]] => 1
[[[[.,[[.,.],.]],.],.],.] => [[[],[]],[],[],[]] => 2
[[[[[.,.],[.,.]],.],.],.] => [[],[[]],[],[],[]] => 1
[[[[[.,[.,.]],.],.],.],.] => [[[]],[],[],[],[]] => 1
[[[[[[.,.],.],.],.],.],.] => [[],[],[],[],[],[]] => 1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[[]]]]]]]] => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [[[[[[[],[]]]]]]] => 2
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [[[[[[],[[]]]]]]] => 2
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [[[[[[[]],[]]]]]] => 2
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [[[[[[],[],[]]]]]] => 2
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [[[[[],[[[]]]]]]] => 2
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [[[[[],[[],[]]]]]] => 2
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [[[[[[]],[[]]]]]] => 2
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [[[[[],[],[[]]]]]] => 2
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [[[[[[[]]],[]]]]] => 2
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [[[[[[],[]],[]]]]] => 2
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [[[[[],[[]],[]]]]] => 2
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [[[[[[]],[],[]]]]] => 2
[.,[.,[.,[[[[.,.],.],.],.]]]] => [[[[[],[],[],[]]]]] => 2
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [[[[],[[[[]]]]]]] => 2
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [[[[],[[[],[]]]]]] => 2
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [[[[],[[],[[]]]]]] => 2
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [[[[],[[[]],[]]]]] => 2
[.,[.,[[.,.],[[[.,.],.],.]]]] => [[[[],[[],[],[]]]]] => 2
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [[[[[]],[[[]]]]]] => 2
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [[[[[]],[[],[]]]]] => 2
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [[[[],[],[[[]]]]]] => 2
[.,[.,[[[.,.],.],[[.,.],.]]]] => [[[[],[],[[],[]]]]] => 2
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [[[[[[]]],[[]]]]] => 2
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [[[[[],[]],[[]]]]] => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [[[[],[[]],[[]]]]] => 2
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [[[[[]],[],[[]]]]] => 2
[.,[.,[[[[.,.],.],.],[.,.]]]] => [[[[],[],[],[[]]]]] => 2
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [[[[[[[]]]],[]]]] => 2
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [[[[[[],[]]],[]]]] => 2
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [[[[[],[[]]],[]]]] => 2
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [[[[[[]],[]],[]]]] => 2
[.,[.,[[.,[[[.,.],.],.]],.]]] => [[[[[],[],[]],[]]]] => 2
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [[[[],[[[]]],[]]]] => 2
[.,[.,[[[.,.],[[.,.],.]],.]]] => [[[[],[[],[]],[]]]] => 2
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [[[[[]],[[]],[]]]] => 2
[.,[.,[[[[.,.],.],[.,.]],.]]] => [[[[],[],[[]],[]]]] => 2
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [[[[[[]]],[],[]]]] => 2
[.,[.,[[[.,[[.,.],.]],.],.]]] => [[[[[],[]],[],[]]]] => 2
[.,[.,[[[[.,.],[.,.]],.],.]]] => [[[[],[[]],[],[]]]] => 2
[.,[.,[[[[.,[.,.]],.],.],.]]] => [[[[[]],[],[],[]]]] => 2
[.,[.,[[[[[.,.],.],.],.],.]]] => [[[[],[],[],[],[]]]] => 2
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [[[],[[[[[]]]]]]] => 2
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [[[],[[[[],[]]]]]] => 2
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [[[],[[[],[[]]]]]] => 2
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [[[],[[[[]],[]]]]] => 2
[.,[[.,.],[.,[[[.,.],.],.]]]] => [[[],[[[],[],[]]]]] => 2
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [[[],[[],[[[]]]]]] => 2
[.,[[.,.],[[.,.],[[.,.],.]]]] => [[[],[[],[[],[]]]]] => 2
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [[[],[[[]],[[]]]]] => 2
[.,[[.,.],[[[.,.],.],[.,.]]]] => [[[],[[],[],[[]]]]] => 2
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [[[],[[[[]]],[]]]] => 2
[.,[[.,.],[[.,[[.,.],.]],.]]] => [[[],[[[],[]],[]]]] => 2
[.,[[.,.],[[[.,.],[.,.]],.]]] => [[[],[[],[[]],[]]]] => 2
[.,[[.,.],[[[.,[.,.]],.],.]]] => [[[],[[[]],[],[]]]] => 2
[.,[[.,.],[[[[.,.],.],.],.]]] => [[[],[[],[],[],[]]]] => 2
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [[[[]],[[[[]]]]]] => 2
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [[[[]],[[[],[]]]]] => 2
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [[[[]],[[],[[]]]]] => 2
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [[[[]],[[[]],[]]]] => 2
[.,[[.,[.,.]],[[[.,.],.],.]]] => [[[[]],[[],[],[]]]] => 2
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [[[],[],[[[[]]]]]] => 2
[.,[[[.,.],.],[.,[[.,.],.]]]] => [[[],[],[[[],[]]]]] => 2
[.,[[[.,.],.],[[.,.],[.,.]]]] => [[[],[],[[],[[]]]]] => 2
[.,[[[.,.],.],[[.,[.,.]],.]]] => [[[],[],[[[]],[]]]] => 2
[.,[[[.,.],.],[[[.,.],.],.]]] => [[[],[],[[],[],[]]]] => 2
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [[[[[]]],[[[]]]]] => 2
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [[[[[]]],[[],[]]]] => 2
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [[[[],[]],[[[]]]]] => 2
[.,[[.,[[.,.],.]],[[.,.],.]]] => [[[[],[]],[[],[]]]] => 3
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [[[],[[]],[[[]]]]] => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => [[[],[[]],[[],[]]]] => 2
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [[[[]],[],[[[]]]]] => 2
[.,[[[.,[.,.]],.],[[.,.],.]]] => [[[[]],[],[[],[]]]] => 2
[.,[[[[.,.],.],.],[.,[.,.]]]] => [[[],[],[],[[[]]]]] => 2
[.,[[[[.,.],.],.],[[.,.],.]]] => [[[],[],[],[[],[]]]] => 2
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [[[[[[]]]],[[]]]] => 2
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [[[[[],[]]],[[]]]] => 2
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [[[[],[[]]],[[]]]] => 2
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [[[[[]],[]],[[]]]] => 2
[.,[[.,[[[.,.],.],.]],[.,.]]] => [[[[],[],[]],[[]]]] => 2
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [[[],[[[]]],[[]]]] => 2
[.,[[[.,.],[[.,.],.]],[.,.]]] => [[[],[[],[]],[[]]]] => 2
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [[[[]],[[]],[[]]]] => 2
[.,[[[[.,.],.],[.,.]],[.,.]]] => [[[],[],[[]],[[]]]] => 2
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [[[[[]]],[],[[]]]] => 2
[.,[[[.,[[.,.],.]],.],[.,.]]] => [[[[],[]],[],[[]]]] => 2
[.,[[[[.,.],[.,.]],.],[.,.]]] => [[[],[[]],[],[[]]]] => 2
[.,[[[[.,[.,.]],.],.],[.,.]]] => [[[[]],[],[],[[]]]] => 2
[.,[[[[[.,.],.],.],.],[.,.]]] => [[[],[],[],[],[[]]]] => 2
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [[[[[[[]]]]],[]]] => 2
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [[[[[[],[]]]],[]]] => 2
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [[[[[],[[]]]],[]]] => 2
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [[[[[[]],[]]],[]]] => 2
[.,[[.,[.,[[[.,.],.],.]]],.]] => [[[[[],[],[]]],[]]] => 2
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [[[[],[[[]]]],[]]] => 2
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[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [[],[[[],[],[],[]]],[]] => 2
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [[],[[],[[[[]]]]],[]] => 2
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [[],[[],[[[],[]]]],[]] => 2
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [[],[[],[[],[[]]]],[]] => 2
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [[],[[],[[[]],[]]],[]] => 2
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [[],[[],[[],[],[]]],[]] => 2
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [[],[[[]],[[[]]]],[]] => 2
[[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [[],[[[]],[[],[]]],[]] => 2
[[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [[],[[],[],[[[]]]],[]] => 2
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [[],[[],[],[[],[]]],[]] => 2
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [[],[[[[]]],[[]]],[]] => 2
[[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [[],[[[],[]],[[]]],[]] => 2
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [[],[[],[[]],[[]]],[]] => 2
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [[],[[[]],[],[[]]],[]] => 2
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [[],[[],[],[],[[]]],[]] => 2
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [[],[[[[[]]]],[]],[]] => 2
[[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [[],[[[[],[]]],[]],[]] => 2
[[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [[],[[[],[[]]],[]],[]] => 2
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [[],[[[[]],[]],[]],[]] => 2
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [[],[[[],[],[]],[]],[]] => 2
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [[],[[],[[[]]],[]],[]] => 2
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [[],[[],[[],[]],[]],[]] => 2
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [[],[[[]],[[]],[]],[]] => 2
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [[],[[],[],[[]],[]],[]] => 2
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [[],[[[[]]],[],[]],[]] => 2
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [[],[[[],[]],[],[]],[]] => 2
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [[],[[],[[]],[],[]],[]] => 2
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [[],[[[]],[],[],[]],[]] => 2
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [[],[[],[],[],[],[]],[]] => 2
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[]],[[[[[]]]]],[]] => 1
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [[[]],[[[[],[]]]],[]] => 2
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [[[]],[[[],[[]]]],[]] => 2
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [[[]],[[[[]],[]]],[]] => 2
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [[[]],[[[],[],[]]],[]] => 2
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [[[]],[[],[[[]]]],[]] => 2
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [[[]],[[],[[],[]]],[]] => 2
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [[[]],[[[]],[[]]],[]] => 2
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [[[]],[[],[],[[]]],[]] => 2
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [[[]],[[[[]]],[]],[]] => 2
[[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [[[]],[[[],[]],[]],[]] => 2
[[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [[[]],[[],[[]],[]],[]] => 2
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [[[]],[[[]],[],[]],[]] => 2
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [[[]],[[],[],[],[]],[]] => 2
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 1
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [[],[],[[[[],[]]]],[]] => 2
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [[],[],[[[],[[]]]],[]] => 2
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [[],[],[[[[]],[]]],[]] => 2
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [[],[],[[[],[],[]]],[]] => 2
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [[],[],[[],[[[]]]],[]] => 2
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [[],[],[[],[[],[]]],[]] => 2
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [[],[],[[[]],[[]]],[]] => 2
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [[],[],[[],[],[[]]],[]] => 2
[[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [[],[],[[[[]]],[]],[]] => 2
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [[],[],[[[],[]],[]],[]] => 2
[[[[.,.],.],[[[.,.],[.,.]],.]],.] => [[],[],[[],[[]],[]],[]] => 2
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [[],[],[[[]],[],[]],[]] => 2
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [[],[],[[],[],[],[]],[]] => 2
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 1
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [[],[[]],[[[],[]]],[]] => 2
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [[],[[]],[[],[[]]],[]] => 2
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [[],[[]],[[[]],[]],[]] => 2
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [[],[[]],[[],[],[]],[]] => 2
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [[[]],[],[[[[]]]],[]] => 1
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [[[]],[],[[[],[]]],[]] => 2
[[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [[[]],[],[[],[[]]],[]] => 2
[[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [[[]],[],[[[]],[]],[]] => 2
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [[[]],[],[[],[],[]],[]] => 2
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 1
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [[],[],[],[[[],[]]],[]] => 2
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [[],[],[],[[],[[]]],[]] => 2
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [[],[],[],[[[]],[]],[]] => 2
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [[],[],[],[[],[],[]],[]] => 2
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 1
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [[],[[[]]],[[],[]],[]] => 2
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [[],[[],[]],[[[]]],[]] => 2
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [[],[[],[]],[[],[]],[]] => 2
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[]],[[]],[[[]]],[]] => 1
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [[[]],[[]],[[],[]],[]] => 2
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 1
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [[],[],[[]],[[],[]],[]] => 2
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[],[[]],[],[[[]]],[]] => 1
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [[],[[]],[],[[],[]],[]] => 2
[[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [[[]],[],[],[[[]]],[]] => 1
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [[[]],[],[],[[],[]],[]] => 2
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 1
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [[],[],[],[],[[],[]],[]] => 2
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [[],[[[[]]]],[[]],[]] => 1
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [[],[[[],[]]],[[]],[]] => 2
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [[],[[],[[]]],[[]],[]] => 2
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [[],[[[]],[]],[[]],[]] => 2
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [[],[[],[],[]],[[]],[]] => 2
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[]],[[[]]],[[]],[]] => 1
[[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [[[]],[[],[]],[[]],[]] => 2
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 1
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [[],[],[[],[]],[[]],[]] => 2
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[],[[]],[[]],[[]],[]] => 1
[[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [[[]],[],[[]],[[]],[]] => 1
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 1
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[],[[[]]],[],[[]],[]] => 1
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [[],[[],[]],[],[[]],[]] => 2
[[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [[[]],[[]],[],[[]],[]] => 1
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 1
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [[[[]]],[],[],[[]],[]] => 1
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [[[],[]],[],[],[[]],[]] => 2
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[],[[]],[],[],[[]],[]] => 1
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [[[]],[],[],[],[[]],[]] => 1
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [[],[],[],[],[],[[]],[]] => 1
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [[],[[[[[]]]]],[],[]] => 1
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [[],[[[[],[]]]],[],[]] => 2
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [[],[[[],[[]]]],[],[]] => 2
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [[],[[[[]],[]]],[],[]] => 2
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [[],[[[],[],[]]],[],[]] => 2
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [[],[[],[[[]]]],[],[]] => 2
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [[],[[],[[],[]]],[],[]] => 2
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [[],[[[]],[[]]],[],[]] => 2
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [[],[[],[],[[]]],[],[]] => 2
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [[],[[[[]]],[]],[],[]] => 2
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [[],[[[],[]],[]],[],[]] => 2
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [[],[[],[[]],[]],[],[]] => 2
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [[],[[[]],[],[]],[],[]] => 2
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [[],[[],[],[],[]],[],[]] => 2
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [[[]],[[[[]]]],[],[]] => 1
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [[[]],[[[],[]]],[],[]] => 2
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [[[]],[[],[[]]],[],[]] => 2
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [[[]],[[[]],[]],[],[]] => 2
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [[[]],[[],[],[]],[],[]] => 2
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [[],[],[[[[]]]],[],[]] => 1
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [[],[],[[[],[]]],[],[]] => 2
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [[],[],[[],[[]]],[],[]] => 2
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [[],[],[[[]],[]],[],[]] => 2
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [[],[],[[],[],[]],[],[]] => 2
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [[],[[]],[[[]]],[],[]] => 1
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [[],[[]],[[],[]],[],[]] => 2
[[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [[[]],[],[[[]]],[],[]] => 1
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [[[]],[],[[],[]],[],[]] => 2
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[],[],[],[[[]]],[],[]] => 1
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [[],[],[],[[],[]],[],[]] => 2
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [[],[[[]]],[[]],[],[]] => 1
[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [[],[[],[]],[[]],[],[]] => 2
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [[[]],[[]],[[]],[],[]] => 1
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 1
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [[[[]]],[],[[]],[],[]] => 1
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [[[],[]],[],[[]],[],[]] => 2
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [[],[[]],[],[[]],[],[]] => 1
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [[[]],[],[],[[]],[],[]] => 1
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [[],[],[],[],[[]],[],[]] => 1
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [[],[[[[]]]],[],[],[]] => 1
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [[],[[[],[]]],[],[],[]] => 2
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [[],[[],[[]]],[],[],[]] => 2
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [[],[[[]],[]],[],[],[]] => 2
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [[],[[],[],[]],[],[],[]] => 2
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [[[]],[[[]]],[],[],[]] => 1
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [[[]],[[],[]],[],[],[]] => 2
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [[],[],[[[]]],[],[],[]] => 1
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [[],[],[[],[]],[],[],[]] => 2
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [[],[[]],[[]],[],[],[]] => 1
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [[[]],[],[[]],[],[],[]] => 1
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [[],[],[],[[]],[],[],[]] => 1
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [[],[[[]]],[],[],[],[]] => 1
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [[],[[],[]],[],[],[],[]] => 2
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [[[]],[[]],[],[],[],[]] => 1
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [[],[],[[]],[],[],[],[]] => 1
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [[[[]]],[],[],[],[],[]] => 1
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [[[],[]],[],[],[],[],[]] => 2
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [[],[[]],[],[],[],[],[]] => 1
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [[[]],[],[],[],[],[],[]] => 1
[[[[[[[[.,.],.],.],.],.],.],.],.] => [[],[],[],[],[],[],[],[]] => 1
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,26 32,100 64,364,1
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q + q^{2}$
$F_{4} = 8\ q + 6\ q^{2}$
$F_{5} = 16\ q + 26\ q^{2}$
$F_{6} = 32\ q + 100\ q^{2}$
$F_{7} = 64\ q + 364\ q^{2} + q^{3}$
Description
The pruning number of an ordered tree.
A hanging branch of an ordered tree is a proper factor of the form $[^r]^r$ for some $r\geq 1$. A hanging branch is a maximal hanging branch if it is not a proper factor of another hanging branch.
A pruning of an ordered tree is the act of deleting all its maximal hanging branches. The pruning order of an ordered tree is the number of prunings required to reduce it to $[]$.
A hanging branch of an ordered tree is a proper factor of the form $[^r]^r$ for some $r\geq 1$. A hanging branch is a maximal hanging branch if it is not a proper factor of another hanging branch.
A pruning of an ordered tree is the act of deleting all its maximal hanging branches. The pruning order of an ordered tree is the number of prunings required to reduce it to $[]$.
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
- if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
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