Identifier
-
Mp00049:
Ordered trees
—to binary tree: left brother = left child⟶
Binary trees
St000396: Binary 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
[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => 1
[[[],[]],[[]]] => [[.,[[.,.],.]],[.,.]] => 2
[[[[]]],[[]]] => [[.,[.,[.,.]]],[.,.]] => 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
[[[[]]],[],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => 1
[[[],[]],[],[[]]] => [[[.,[[.,.],.]],.],[.,.]] => 2
[[[[]]],[],[[]]] => [[[.,[.,[.,.]]],.],[.,.]] => 2
[[[],[]],[[]],[]] => [[[.,[[.,.],.]],[.,.]],.] => 2
[[[[]]],[[]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => 2
[[[],[]],[[],[]]] => [[.,[[.,.],.]],[[.,.],.]] => 2
[[[],[]],[[[]]]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[[[[]]],[[],[]]] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[[[[]]],[[[]]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[[[],[],[]],[],[]] => [[[.,[[[.,.],.],.]],.],.] => 1
[[[],[[]]],[],[]] => [[[.,[[.,.],[.,.]]],.],.] => 2
[[[[]],[]],[],[]] => [[[.,[[.,[.,.]],.]],.],.] => 1
[[[[],[]]],[],[]] => [[[.,[.,[[.,.],.]]],.],.] => 1
[[[[[]]]],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => 1
[[[],[],[]],[[]]] => [[.,[[[.,.],.],.]],[.,.]] => 2
[[[],[[]]],[[]]] => [[.,[[.,.],[.,.]]],[.,.]] => 2
[[[[]],[]],[[]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[[[[],[]]],[[]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[[[[[]]]],[[]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 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
[[[[[]]],[],[]]] => [.,[[[.,[.,[.,.]]],.],.]] => 1
[[[[],[]],[[]]]] => [.,[[.,[[.,.],.]],[.,.]]] => 2
[[[[[]]],[[]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 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
[[],[[]],[[],[[]]]] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 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
[[],[[],[[],[]]],[]] => [[[.,.],[[.,.],[[.,.],.]]],.] => 2
[[],[[],[[[]]]],[]] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 2
[[],[[[]],[],[]],[]] => [[[.,.],[[[.,[.,.]],.],.]],.] => 2
[[],[[[]],[[]]],[]] => [[[.,.],[[.,[.,.]],[.,.]]],.] => 2
[[],[[[],[]],[]],[]] => [[[.,.],[[.,[[.,.],.]],.]],.] => 2
[[],[[[[]]],[]],[]] => [[[.,.],[[.,[.,[.,.]]],.]],.] => 2
[[],[[[],[],[]]],[]] => [[[.,.],[.,[[[.,.],.],.]]],.] => 2
[[],[[[],[[]]]],[]] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 2
[[],[[[[]],[]]],[]] => [[[.,.],[.,[[.,[.,.]],.]]],.] => 2
[[],[[[[],[]]]],[]] => [[[.,.],[.,[.,[[.,.],.]]]],.] => 2
[[],[[[[[]]]]],[]] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 2
[[],[[],[],[],[],[]]] => [[.,.],[[[[[.,.],.],.],.],.]] => 2
[[],[[],[],[],[[]]]] => [[.,.],[[[[.,.],.],.],[.,.]]] => 2
[[],[[],[],[[]],[]]] => [[.,.],[[[[.,.],.],[.,.]],.]] => 2
[[],[[],[],[[],[]]]] => [[.,.],[[[.,.],.],[[.,.],.]]] => 2
[[],[[],[],[[[]]]]] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[],[[],[[]],[],[]]] => [[.,.],[[[[.,.],[.,.]],.],.]] => 2
[[],[[],[[]],[[]]]] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 2
[[],[[],[[],[]],[]]] => [[.,.],[[[.,.],[[.,.],.]],.]] => 2
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[[],[[],[[],[[]]]]] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
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[[[[],[],[[]],[]],[]]] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => 2
[[[[],[],[[],[]]],[]]] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => 2
[[[[],[],[[[]]]],[]]] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => 2
[[[[],[[]],[],[]],[]]] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => 2
[[[[],[[]],[[]]],[]]] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 2
[[[[],[[],[]],[]],[]]] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => 2
[[[[],[[[]]],[]],[]]] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => 2
[[[[],[[],[],[]]],[]]] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => 2
[[[[],[[],[[]]]],[]]] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => 2
[[[[],[[[]],[]]],[]]] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => 2
[[[[],[[[],[]]]],[]]] => [.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => 2
[[[[],[[[[]]]]],[]]] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => 2
[[[[[]],[],[],[]],[]]] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => 1
[[[[[]],[],[[]]],[]]] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => 2
[[[[[]],[[]],[]],[]]] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 2
[[[[[]],[[],[]]],[]]] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => 2
[[[[[]],[[[]]]],[]]] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => 2
[[[[[],[]],[],[]],[]]] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => 1
[[[[[[]]],[],[]],[]]] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => 1
[[[[[],[]],[[]]],[]]] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => 2
[[[[[[]]],[[]]],[]]] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => 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
[[[[[]],[],[],[],[]]]] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => 1
[[[[[]],[],[],[[]]]]] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => 2
[[[[[]],[],[[]],[]]]] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => 2
[[[[[]],[],[[],[]]]]] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => 2
[[[[[]],[],[[[]]]]]] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => 2
[[[[[]],[[]],[],[]]]] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => 2
[[[[[]],[[]],[[]]]]] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => 2
[[[[[]],[[],[]],[]]]] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => 2
[[[[[]],[[[]]],[]]]] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => 2
[[[[[]],[[],[],[]]]]] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => 2
[[[[[]],[[],[[]]]]]] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 2
[[[[[]],[[[]],[]]]]] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => 2
[[[[[]],[[[],[]]]]]] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => 2
[[[[[]],[[[[]]]]]]] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 2
[[[[[],[]],[],[],[]]]] => [.,[.,[[[[.,[[.,.],.]],.],.],.]]] => 1
[[[[[[]]],[],[],[]]]] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => 1
[[[[[],[]],[],[[]]]]] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => 2
[[[[[[]]],[],[[]]]]] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => 2
[[[[[],[]],[[]],[]]]] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => 2
[[[[[[]]],[[]],[]]]] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => 2
[[[[[],[]],[[],[]]]]] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => 2
[[[[[],[]],[[[]]]]]] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => 2
[[[[[[]]],[[],[]]]]] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => 2
[[[[[[]]],[[[]]]]]] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 2
[[[[[],[],[]],[],[]]]] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]] => 1
[[[[[],[[]]],[],[]]]] => [.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => 2
[[[[[[]],[]],[],[]]]] => [.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => 1
[[[[[[],[]]],[],[]]]] => [.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => 1
[[[[[[[]]]],[],[]]]] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => 1
[[[[[],[],[]],[[]]]]] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => 2
[[[[[],[[]]],[[]]]]] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => 2
[[[[[[]],[]],[[]]]]] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => 2
[[[[[[],[]]],[[]]]]] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => 2
[[[[[[[]]]],[[]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 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
[[[[[[[]]],[],[]]]]] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => 1
[[[[[[],[]],[[]]]]]] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => 2
[[[[[[[]]],[[]]]]]] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 2
[[[[[[],[],[]],[]]]]] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => 1
[[[[[[],[[]]],[]]]]] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => 2
[[[[[[[]],[]],[]]]]] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => 1
[[[[[[[],[]]],[]]]]] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => 1
[[[[[[[[]]]],[]]]]] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => 1
[[[[[[],[],[],[]]]]]] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => 1
[[[[[[],[],[[]]]]]]] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => 2
[[[[[[],[[]],[]]]]]] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => 2
[[[[[[],[[],[]]]]]]] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => 2
[[[[[[],[[[]]]]]]]] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[[[[[[[]],[],[]]]]]] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => 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
$F_{2} = q$
$F_{3} = 2\ q$
$F_{4} = 4\ q + q^{2}$
$F_{5} = 8\ q + 6\ q^{2}$
$F_{6} = 16\ q + 26\ q^{2}$
$F_{7} = 32\ q + 100\ q^{2}$
$F_{8} = 64\ q + 364\ q^{2} + q^{3}$
Description
The register function (or Horton-Strahler number) of a binary tree.
This is different from the dimension of the associated poset for the tree $[[[.,.],[.,.]],[[.,.],[.,.]]]$: its register function is 3, whereas the dimension of the associated poset is 2.
This is different from the dimension of the associated poset for the tree $[[[.,.],[.,.]],[[.,.],[.,.]]]$: its register function is 3, whereas the dimension of the associated poset is 2.
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
searching the database
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or
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