Identifier
-
Mp00029:
Dyck paths
—to binary tree: left tree, up step, right tree, down step⟶
Binary trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
St000974: Ordered trees ⟶ ℤ
Values
[1,0] => [.,.] => [[]] => 1
[1,0,1,0] => [[.,.],.] => [[[]]] => 2
[1,1,0,0] => [.,[.,.]] => [[],[]] => 0
[1,0,1,0,1,0] => [[[.,.],.],.] => [[[[]]]] => 3
[1,0,1,1,0,0] => [[.,.],[.,.]] => [[[]],[]] => 0
[1,1,0,0,1,0] => [[.,[.,.]],.] => [[[],[]]] => 1
[1,1,0,1,0,0] => [.,[[.,.],.]] => [[],[[]]] => 0
[1,1,1,0,0,0] => [.,[.,[.,.]]] => [[],[],[]] => 0
[1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => [[[[[]]]]] => 4
[1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => [[[[]]],[]] => 0
[1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => [[[[]],[]]] => 1
[1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => [[[]],[[]]] => 0
[1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => [[[]],[],[]] => 0
[1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => [[[[],[]]]] => 2
[1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => [[[],[]],[]] => 0
[1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => [[[],[[]]]] => 1
[1,1,0,1,0,1,0,0] => [.,[[[.,.],.],.]] => [[],[[[]]]] => 0
[1,1,0,1,1,0,0,0] => [.,[[.,.],[.,.]]] => [[],[[]],[]] => 0
[1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => [[[],[],[]]] => 1
[1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],.]] => [[],[[],[]]] => 0
[1,1,1,0,1,0,0,0] => [.,[.,[[.,.],.]]] => [[],[],[[]]] => 0
[1,1,1,1,0,0,0,0] => [.,[.,[.,[.,.]]]] => [[],[],[],[]] => 0
[1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => [[[[[[]]]]]] => 5
[1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => [[[[[]]]],[]] => 0
[1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => [[[[[]]],[]]] => 1
[1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => [[[[]]],[[]]] => 0
[1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => [[[[]]],[],[]] => 0
[1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => [[[[[]],[]]]] => 2
[1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => [[[[]],[]],[]] => 0
[1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => [[[[]],[[]]]] => 1
[1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => [[[]],[[[]]]] => 0
[1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => [[[]],[[]],[]] => 0
[1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => [[[[]],[],[]]] => 1
[1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => [[[]],[[],[]]] => 0
[1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => [[[]],[],[[]]] => 0
[1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => [[[]],[],[],[]] => 0
[1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => [[[[[],[]]]]] => 3
[1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => [[[[],[]]],[]] => 0
[1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => [[[[],[]],[]]] => 1
[1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => [[[],[]],[[]]] => 0
[1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => [[[],[]],[],[]] => 0
[1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => [[[[],[[]]]]] => 2
[1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => [[[],[[]]],[]] => 0
[1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => [[[],[[[]]]]] => 1
[1,1,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => [[],[[[[]]]]] => 0
[1,1,0,1,0,1,1,0,0,0] => [.,[[[.,.],.],[.,.]]] => [[],[[[]]],[]] => 0
[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => [[[],[[]],[]]] => 1
[1,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => [[],[[[]],[]]] => 0
[1,1,0,1,1,0,1,0,0,0] => [.,[[.,.],[[.,.],.]]] => [[],[[]],[[]]] => 0
[1,1,0,1,1,1,0,0,0,0] => [.,[[.,.],[.,[.,.]]]] => [[],[[]],[],[]] => 0
[1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => [[[[],[],[]]]] => 2
[1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => [[[],[],[]],[]] => 0
[1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => [[[],[[],[]]]] => 1
[1,1,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],.],.]] => [[],[[[],[]]]] => 0
[1,1,1,0,0,1,1,0,0,0] => [.,[[.,[.,.]],[.,.]]] => [[],[[],[]],[]] => 0
[1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => [[[],[],[[]]]] => 1
[1,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,.],.]],.]] => [[],[[],[[]]]] => 0
[1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => [[],[],[[[]]]] => 0
[1,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,.],[.,.]]]] => [[],[],[[]],[]] => 0
[1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => [[[],[],[],[]]] => 1
[1,1,1,1,0,0,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => [[],[[],[],[]]] => 0
[1,1,1,1,0,0,1,0,0,0] => [.,[.,[[.,[.,.]],.]]] => [[],[],[[],[]]] => 0
[1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[.,.],.]]]] => [[],[],[],[[]]] => 0
[1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,.]]]]] => [[],[],[],[],[]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => [[[[[[[]]]]]]] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => [[[[[[]]]]],[]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => [[[[[[]]]],[]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [[[[[]]]],[[]]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[]]]],[],[]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => [[[[[[]]],[]]]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[]]],[]],[]] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => [[[[[]]],[[]]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => [[[[]]],[[[]]]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => [[[[]]],[[]],[]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => [[[[[]]],[],[]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => [[[[]]],[[],[]]] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [[[[]]],[],[[]]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[]]],[],[],[]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => [[[[[[]],[]]]]] => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => [[[[[]],[]]],[]] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => [[[[[]],[]],[]]] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [[[[]],[]],[[]]] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[]],[]],[],[]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => [[[[[]],[[]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => [[[[]],[[]]],[]] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => [[[[]],[[[]]]]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => [[[]],[[[[]]]]] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => [[[]],[[[]]],[]] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => [[[[]],[[]],[]]] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => [[[]],[[[]],[]]] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => [[[]],[[]],[[]]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => [[[]],[[]],[],[]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => [[[[[]],[],[]]]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[]],[],[]],[]] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => [[[[]],[[],[]]]] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => [[[]],[[[],[]]]] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => [[[]],[[],[]],[]] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => [[[[]],[],[[]]]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => [[[]],[[],[[]]]] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [[[]],[],[[[]]]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => [[[]],[],[[]],[]] => 0
>>> Load all 1262 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => [[[[]],[],[],[]]] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => [[[]],[[],[],[]]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => [[[]],[],[[],[]]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [[[]],[],[],[[]]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[]],[],[],[],[]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => [[[[[[],[]]]]]] => 4
[1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => [[[[[],[]]]],[]] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => [[[[[],[]]],[]]] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[]]],[[]]] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[]]],[],[]] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => [[[[[],[]],[]]]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[]],[]],[]] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => [[[[],[]],[[]]]] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[]],[[[]]]] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[]],[[]],[]] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => [[[[],[]],[],[]]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[]],[[],[]]] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[]],[],[[]]] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[]],[],[],[]] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => [[[[[],[[]]]]]] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => [[[[],[[]]]],[]] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => [[[[],[[]]],[]]] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[]]],[[]]] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[]]],[],[]] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => [[[[],[[[]]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[[[]]]],[]] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => [[[],[[[[]]]]]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => [[],[[[[[]]]]]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,.]]] => [[],[[[[]]]],[]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => [[[],[[[]]],[]]] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => [[],[[[[]]],[]]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],.],[[.,.],.]]] => [[],[[[]]],[[]]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,[.,.]]]] => [[],[[[]]],[],[]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => [[[[],[[]],[]]]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]],[]],[]] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => [[[],[[[]],[]]]] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,.]],.],.]] => [[],[[[[]],[]]]] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[]],[]],[]] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => [[[],[[]],[[]]]] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],.]],.]] => [[],[[[]],[[]]]] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => [[],[[]],[[[]]]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[]],[[]],[]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => [[[],[[]],[],[]]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => [[],[[[]],[],[]]] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => [[],[[]],[[],[]]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [[],[[]],[],[[]]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,.]]]]] => [[],[[]],[],[],[]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => [[[[[],[],[]]]]] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[],[],[]]],[]] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[],[],[]],[]]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[],[]],[[]]] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[],[]],[],[]] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => [[[[],[[],[]]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => [[[],[[],[]]],[]] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => [[[],[[[],[]]]]] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],.],.]] => [[],[[[[],[]]]]] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => [[],[[[],[]]],[]] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => [[[],[[],[]],[]]] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => [[],[[[],[]],[]]] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => [[],[[],[]],[[]]] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[.,[.,.]]]] => [[],[[],[]],[],[]] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => [[[[],[],[[]]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => [[[],[],[[]]],[]] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => [[[],[[],[[]]]]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => [[],[[[],[[]]]]] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],[.,.]]] => [[],[[],[[]]],[]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => [[[],[],[[[]]]]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => [[],[[],[[[]]]]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [[],[],[[[[]]]]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,.],.],[.,.]]]] => [[],[],[[[]]],[]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => [[[],[],[[]],[]]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => [[],[[],[[]],[]]] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => [[],[],[[[]],[]]] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => [[],[],[[]],[[]]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,.]]]]] => [[],[],[[]],[],[]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => [[[[],[],[],[]]]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[],[],[],[]],[]] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => [[[],[[],[],[]]]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => [[],[[[],[],[]]]] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,.]]],[.,.]]] => [[],[[],[],[]],[]] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => [[[],[],[[],[]]]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => [[],[[],[[],[]]]] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => [[],[],[[[],[]]]] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,.]],[.,.]]]] => [[],[],[[],[]],[]] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => [[[],[],[],[[]]]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => [[],[[],[],[[]]]] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => [[],[],[[],[[]]]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => [[],[],[],[[[]]]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,.]]]]] => [[],[],[],[[]],[]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [[[],[],[],[],[]]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => [[],[[],[],[],[]]] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => [[],[],[[],[],[]]] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => [[],[],[],[[],[]]] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [[],[],[],[],[[]]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [[],[],[],[],[],[]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],.] => [[[[[[[[]]]]]]]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[.,.]] => [[[[[[[]]]]]],[]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],.] => [[[[[[[]]]]],[]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => [[[[[[]]]]],[[]]] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[[[[[]]]]],[],[]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],[.,.]],.],.] => [[[[[[[]]]],[]]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[[[[[]]]],[]],[]] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[.,.],.],.],[[.,.],.]],.] => [[[[[[]]]],[[]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => [[[[[]]]],[[[]]]] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => [[[[[]]]],[[]],[]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[[[[[]]]],[],[]]] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => [[[[[]]]],[[],[]]] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => [[[[[]]]],[],[[]]] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[[[[]]]],[],[],[]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],.],.],.] => [[[[[[[]]],[]]]]] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[[[[[]]],[]]],[]] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[[[[[]]],[]],[]]] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => [[[[[]]],[]],[[]]] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[[[[]]],[]],[],[]] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[.,.],.],[[.,.],.]],.],.] => [[[[[[]]],[[]]]]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => [[[[[]]],[[]]],[]] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[.,.],.],.]],.] => [[[[[]]],[[[]]]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => [[[[]]],[[[[]]]]] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => [[[[]]],[[[]]],[]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => [[[[[]]],[[]],[]]] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => [[[[]]],[[[]],[]]] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => [[[[]]],[[]],[[]]] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [[[[]]],[[]],[],[]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[.,.]]],.],.] => [[[[[[]]],[],[]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[[[[]]],[],[]],[]] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => [[[[[]]],[[],[]]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => [[[[]]],[[[],[]]]] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [[[[]]],[[],[]],[]] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => [[[[[]]],[],[[]]]] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => [[[[]]],[[],[[]]]] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => [[[[]]],[],[[[]]]] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [[[[]]],[],[[]],[]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[[[[]]],[],[],[]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [[[[]]],[[],[],[]]] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [[[[]]],[],[[],[]]] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [[[[]]],[],[],[[]]] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[[[]]],[],[],[],[]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,.]],.],.],.],.] => [[[[[[[]],[]]]]]] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[[[[[]],[]]]],[]] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,.]],.] => [[[[[[]],[]]],[]]] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => [[[[[]],[]]],[[]]] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[[[[]],[]]],[],[]] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,.]],[.,.]],.],.] => [[[[[[]],[]],[]]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[[[[]],[]],[]],[]] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],.]],.] => [[[[[]],[]],[[]]]] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => [[[[]],[]],[[[]]]] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [[[[]],[]],[[]],[]] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[[[[]],[]],[],[]]] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [[[[]],[]],[[],[]]] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [[[[]],[]],[],[[]]] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[[[]],[]],[],[],[]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[[.,.],.]],.],.],.] => [[[[[[]],[[]]]]]] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => [[[[[]],[[]]]],[]] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,.]],.] => [[[[[]],[[]]],[]]] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => [[[[]],[[]]],[[]]] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [[[[]],[[]]],[],[]] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[.,.],.],.]],.],.] => [[[[[]],[[[]]]]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => [[[[]],[[[]]]],[]] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,.],.],.],.]],.] => [[[[]],[[[[]]]]]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => [[[]],[[[[[]]]]]] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => [[[]],[[[[]]]],[]] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,.],.],[.,.]]],.] => [[[[]],[[[]]],[]]] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => [[[]],[[[[]]],[]]] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => [[[]],[[[]]],[[]]] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [[[]],[[[]]],[],[]] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[.,.]]],.],.] => [[[[[]],[[]],[]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [[[[]],[[]],[]],[]] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],[.,.]],.]],.] => [[[[]],[[[]],[]]]] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => [[[]],[[[[]],[]]]] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [[[]],[[[]],[]],[]] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],.]]],.] => [[[[]],[[]],[[]]]] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => [[[]],[[[]],[[]]]] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => [[[]],[[]],[[[]]]] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[[]],[[]],[[]],[]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [[[[]],[[]],[],[]]] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [[[]],[[[]],[],[]]] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[[]],[[]],[[],[]]] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[[]],[[]],[],[[]]] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[[]],[[]],[],[],[]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,.]]],.],.],.] => [[[[[[]],[],[]]]]] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[[[[]],[],[]]],[]] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [[[[[]],[],[]],[]]] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [[[[]],[],[]],[[]]] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[[[]],[],[]],[],[]] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,[.,.]],.]],.],.] => [[[[[]],[[],[]]]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [[[[]],[[],[]]],[]] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => [[[[]],[[[],[]]]]] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => [[[]],[[[[],[]]]]] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [[[]],[[[],[]]],[]] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [[[[]],[[],[]],[]]] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [[[]],[[[],[]],[]]] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[[]],[[],[]],[[]]] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[[]],[[],[]],[],[]] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[[.,.],.]]],.],.] => [[[[[]],[],[[]]]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [[[[]],[],[[]]],[]] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],.]],.] => [[[[]],[[],[[]]]]] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => [[[]],[[[],[[]]]]] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [[[]],[[],[[]]],[]] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],.],.]]],.] => [[[[]],[],[[[]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => [[[]],[[],[[[]]]]] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => [[[]],[],[[[[]]]]] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [[[]],[],[[[]]],[]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [[[[]],[],[[]],[]]] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [[[]],[[],[[]],[]]] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [[[]],[],[[[]],[]]] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[[]],[],[[]],[[]]] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[[]],[],[[]],[],[]] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [[[[[]],[],[],[]]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[[[]],[],[],[]],[]] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [[[[]],[[],[],[]]]] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [[[]],[[[],[],[]]]] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[[]],[[],[],[]],[]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [[[[]],[],[[],[]]]] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [[[]],[[],[[],[]]]] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [[[]],[],[[[],[]]]] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[[]],[],[[],[]],[]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [[[[]],[],[],[[]]]] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [[[]],[[],[],[[]]]] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [[[]],[],[[],[[]]]] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [[[]],[],[],[[[]]]] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[[]],[],[],[[]],[]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [[[[]],[],[],[],[]]] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [[[]],[[],[],[],[]]] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [[[]],[],[[],[],[]]] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[[]],[],[],[[],[]]] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[[]],[],[],[],[[]]] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[[]],[],[],[],[],[]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],.] => [[[[[[[],[]]]]]]] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => [[[[[[],[]]]]],[]] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => [[[[[[],[]]]],[]]] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => [[[[[],[]]]],[[]]] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[[[],[]]]],[],[]] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[.,.]],.],.] => [[[[[[],[]]],[]]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[[[],[]]],[]],[]] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],.]],.] => [[[[[],[]]],[[]]]] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => [[[[],[]]],[[[]]]] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [[[[],[]]],[[]],[]] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [[[[[],[]]],[],[]]] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [[[[],[]]],[[],[]]] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [[[[],[]]],[],[[]]] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[[],[]]],[],[],[]] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => [[[[[[],[]],[]]]]] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [[[[[],[]],[]]],[]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [[[[[],[]],[]],[]]] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [[[[],[]],[]],[[]]] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[[],[]],[]],[],[]] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[.,.],.]],.],.] => [[[[[],[]],[[]]]]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [[[[],[]],[[]]],[]] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => [[[[],[]],[[[]]]]] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => [[[],[]],[[[[]]]]] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [[[],[]],[[[]]],[]] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [[[[],[]],[[]],[]]] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [[[],[]],[[[]],[]]] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[[],[]],[[]],[[]]] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[[],[]],[[]],[],[]] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [[[[[],[]],[],[]]]] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[[],[]],[],[]],[]] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [[[[],[]],[[],[]]]] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [[[],[]],[[[],[]]]] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[[],[]],[[],[]],[]] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [[[[],[]],[],[[]]]] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [[[],[]],[[],[[]]]] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [[[],[]],[],[[[]]]] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[[],[]],[],[[]],[]] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [[[[],[]],[],[],[]]] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[[],[]],[[],[],[]]] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[[],[]],[],[[],[]]] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[[],[]],[],[],[[]]] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[[],[]],[],[],[],[]] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,.],.]],.],.],.],.] => [[[[[[],[[]]]]]]] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => [[[[[],[[]]]]],[]] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => [[[[[],[[]]]],[]]] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => [[[[],[[]]]],[[]]] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [[[[],[[]]]],[],[]] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],.]],[.,.]],.],.] => [[[[[],[[]]],[]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [[[[],[[]]],[]],[]] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => [[[[],[[]]],[[]]]] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => [[[],[[]]],[[[]]]] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [[[],[[]]],[[]],[]] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [[[[],[[]]],[],[]]] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [[[],[[]]],[[],[]]] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [[[],[[]]],[],[[]]] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [[[],[[]]],[],[],[]] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],.],.]],.],.],.] => [[[[[],[[[]]]]]]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => [[[[],[[[]]]]],[]] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => [[[[],[[[]]]],[]]] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => [[[],[[[]]]],[[]]] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [[[],[[[]]]],[],[]] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],.]],.],.] => [[[[],[[[[]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => [[[],[[[[]]]]],[]] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],.],.],.],.]],.] => [[[],[[[[[]]]]]]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => [[],[[[[[[]]]]]]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => [[],[[[[[]]]]],[]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => [[[],[[[[]]]],[]]] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => [[],[[[[[]]]],[]]] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => [[],[[[[]]]],[[]]] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [[],[[[[]]]],[],[]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => [[[[],[[[]]],[]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [[[],[[[]]],[]],[]] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => [[[],[[[[]]],[]]]] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => [[],[[[[[]]],[]]]] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [[],[[[[]]],[]],[]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => [[[],[[[]]],[[]]]] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => [[],[[[[]]],[[]]]] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => [[],[[[]]],[[[]]]] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [[],[[[]]],[[]],[]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [[[],[[[]]],[],[]]] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [[],[[[[]]],[],[]]] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [[],[[[]]],[[],[]]] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [[],[[[]]],[],[[]]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [[],[[[]]],[],[],[]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => [[[[[],[[]],[]]]]] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [[[[],[[]],[]]],[]] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [[[[],[[]],[]],[]]] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [[[],[[]],[]],[[]]] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [[[],[[]],[]],[],[]] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => [[[[],[[[]],[]]]]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [[[],[[[]],[]]],[]] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => [[[],[[[[]],[]]]]] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => [[],[[[[[]],[]]]]] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [[],[[[[]],[]]],[]] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [[[],[[[]],[]],[]]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [[],[[[[]],[]],[]]] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [[],[[[]],[]],[[]]] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [[],[[[]],[]],[],[]] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],.]]],.],.] => [[[[],[[]],[[]]]]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [[[],[[]],[[]]],[]] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => [[[],[[[]],[[]]]]] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => [[],[[[[]],[[]]]]] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [[],[[[]],[[]]],[]] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => [[[],[[]],[[[]]]]] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => [[],[[[]],[[[]]]]] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => [[],[[]],[[[[]]]]] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [[],[[]],[[[]]],[]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [[[],[[]],[[]],[]]] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [[],[[[]],[[]],[]]] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [[],[[]],[[[]],[]]] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [[],[[]],[[]],[[]]] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [[],[[]],[[]],[],[]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [[[[],[[]],[],[]]]] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [[[],[[]],[],[]],[]] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [[[],[[[]],[],[]]]] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [[],[[[[]],[],[]]]] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [[],[[[]],[],[]],[]] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [[[],[[]],[[],[]]]] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [[],[[[]],[[],[]]]] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [[],[[]],[[[],[]]]] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [[],[[]],[[],[]],[]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [[[],[[]],[],[[]]]] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [[],[[[]],[],[[]]]] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [[],[[]],[[],[[]]]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [[],[[]],[],[[[]]]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [[],[[]],[],[[]],[]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [[[],[[]],[],[],[]]] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [[],[[[]],[],[],[]]] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [[],[[]],[[],[],[]]] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [[],[[]],[],[[],[]]] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [[],[[]],[],[],[[]]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [[],[[]],[],[],[],[]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => [[[[[[],[],[]]]]]] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [[[[[],[],[]]]],[]] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [[[[[],[],[]]],[]]] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [[[[],[],[]]],[[]]] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[[],[],[]]],[],[]] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [[[[[],[],[]],[]]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [[[[],[],[]],[]],[]] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [[[[],[],[]],[[]]]] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [[[],[],[]],[[[]]]] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[[],[],[]],[[]],[]] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [[[[],[],[]],[],[]]] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[[],[],[]],[[],[]]] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[[],[],[]],[],[[]]] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[[],[],[]],[],[],[]] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => [[[[[],[[],[]]]]]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [[[[],[[],[]]]],[]] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [[[[],[[],[]]],[]]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [[[],[[],[]]],[[]]] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [[[],[[],[]]],[],[]] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => [[[[],[[[],[]]]]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [[[],[[[],[]]]],[]] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => [[[],[[[[],[]]]]]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => [[],[[[[[],[]]]]]] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [[],[[[[],[]]]],[]] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [[[],[[[],[]]],[]]] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [[],[[[[],[]]],[]]] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [[],[[[],[]]],[[]]] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [[],[[[],[]]],[],[]] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [[[[],[[],[]],[]]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [[[],[[],[]],[]],[]] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [[[],[[[],[]],[]]]] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [[],[[[[],[]],[]]]] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [[],[[[],[]],[]],[]] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [[[],[[],[]],[[]]]] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [[],[[[],[]],[[]]]] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [[],[[],[]],[[[]]]] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [[],[[],[]],[[]],[]] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [[[],[[],[]],[],[]]] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [[],[[[],[]],[],[]]] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [[],[[],[]],[[],[]]] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [[],[[],[]],[],[[]]] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [[],[[],[]],[],[],[]] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => [[[[[],[],[[]]]]]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [[[[],[],[[]]]],[]] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [[[[],[],[[]]],[]]] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [[[],[],[[]]],[[]]] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [[[],[],[[]]],[],[]] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => [[[[],[[],[[]]]]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [[[],[[],[[]]]],[]] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => [[[],[[[],[[]]]]]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => [[],[[[[],[[]]]]]] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [[],[[[],[[]]]],[]] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [[[],[[],[[]]],[]]] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [[],[[[],[[]]],[]]] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [[],[[],[[]]],[[]]] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [[],[[],[[]]],[],[]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => [[[[],[],[[[]]]]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [[[],[],[[[]]]],[]] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => [[[],[[],[[[]]]]]] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => [[],[[[],[[[]]]]]] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [[],[[],[[[]]]],[]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => [[[],[],[[[[]]]]]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => [[],[[],[[[[]]]]]] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => [[],[],[[[[[]]]]]] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [[],[],[[[[]]]],[]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [[[],[],[[[]]],[]]] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [[],[[],[[[]]],[]]] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [[],[],[[[[]]],[]]] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [[],[],[[[]]],[[]]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [[],[],[[[]]],[],[]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [[[[],[],[[]],[]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [[[],[],[[]],[]],[]] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [[[],[[],[[]],[]]]] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [[],[[[],[[]],[]]]] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [[],[[],[[]],[]],[]] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [[[],[],[[[]],[]]]] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [[],[[],[[[]],[]]]] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [[],[],[[[[]],[]]]] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [[],[],[[[]],[]],[]] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [[[],[],[[]],[[]]]] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [[],[[],[[]],[[]]]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [[],[],[[[]],[[]]]] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [[],[],[[]],[[[]]]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [[],[],[[]],[[]],[]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [[[],[],[[]],[],[]]] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [[],[[],[[]],[],[]]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [[],[],[[[]],[],[]]] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [[],[],[[]],[[],[]]] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [[],[],[[]],[],[[]]] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [[],[],[[]],[],[],[]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [[[[[],[],[],[]]]]] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [[[[],[],[],[]]],[]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [[[[],[],[],[]],[]]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[[],[],[],[]],[[]]] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[[],[],[],[]],[],[]] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [[[[],[[],[],[]]]]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [[[],[[],[],[]]],[]] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [[[],[[[],[],[]]]]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [[],[[[[],[],[]]]]] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [[],[[[],[],[]]],[]] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [[[],[[],[],[]],[]]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [[],[[[],[],[]],[]]] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [[],[[],[],[]],[[]]] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [[],[[],[],[]],[],[]] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [[[[],[],[[],[]]]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [[[],[],[[],[]]],[]] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [[[],[[],[[],[]]]]] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [[],[[[],[[],[]]]]] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [[],[[],[[],[]]],[]] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [[[],[],[[[],[]]]]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [[],[[],[[[],[]]]]] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [[],[],[[[[],[]]]]] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [[],[],[[[],[]]],[]] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [[[],[],[[],[]],[]]] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [[],[[],[[],[]],[]]] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [[],[],[[[],[]],[]]] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [[],[],[[],[]],[[]]] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [[],[],[[],[]],[],[]] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [[[[],[],[],[[]]]]] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [[[],[],[],[[]]],[]] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [[[],[[],[],[[]]]]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [[],[[[],[],[[]]]]] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [[],[[],[],[[]]],[]] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [[[],[],[[],[[]]]]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [[],[[],[[],[[]]]]] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [[],[],[[[],[[]]]]] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [[],[],[[],[[]]],[]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [[[],[],[],[[[]]]]] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [[],[[],[],[[[]]]]] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [[],[],[[],[[[]]]]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [[],[],[],[[[[]]]]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [[],[],[],[[[]]],[]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [[[],[],[],[[]],[]]] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [[],[[],[],[[]],[]]] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [[],[],[[],[[]],[]]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [[],[],[],[[[]],[]]] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [[],[],[],[[]],[[]]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [[],[],[],[[]],[],[]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [[[[],[],[],[],[]]]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[[],[],[],[],[]],[]] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [[[],[[],[],[],[]]]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [[],[[[],[],[],[]]]] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [[],[[],[],[],[]],[]] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [[[],[],[[],[],[]]]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [[],[[],[[],[],[]]]] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [[],[],[[[],[],[]]]] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [[],[],[[],[],[]],[]] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [[[],[],[],[[],[]]]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [[],[[],[],[[],[]]]] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [[],[],[[],[[],[]]]] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [[],[],[],[[[],[]]]] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [[],[],[],[[],[]],[]] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [[[],[],[],[],[[]]]] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [[],[[],[],[],[[]]]] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [[],[],[[],[],[[]]]] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [[],[],[],[[],[[]]]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [[],[],[],[],[[[]]]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [[],[],[],[],[[]],[]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [[[],[],[],[],[],[]]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [[],[[],[],[],[],[]]] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [[],[],[[],[],[],[]]] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [[],[],[],[[],[],[]]] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [[],[],[],[],[[],[]]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [[],[],[],[],[],[[]]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [[],[],[],[],[],[],[]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [[[[[[[[]]]]]]],[]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[[[[[[]]],[]]]],[]] => 0
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [[[[]]],[],[[]],[[]]] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [[[[]]],[],[[]],[],[]] => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [[[[]]],[],[],[[[]]]] => 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [[[[]]],[],[],[[]],[]] => 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [[[[]]],[],[],[[],[]]] => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [[[[]]],[],[],[],[[]]] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[]]],[],[],[],[],[]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[[[[[[]],[]]]]],[]] => 0
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[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [[[]],[[[[]]]],[],[]] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [[[]],[[[[[]]],[]]]] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [[[]],[[[[]]],[]],[]] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [[[]],[[[[]]],[[]]]] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [[[]],[[[]]],[[[]]]] => 0
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [[[]],[[[]]],[[]],[]] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [[[]],[[[[]]],[],[]]] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [[[]],[[[]]],[[],[]]] => 0
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [[[]],[[[]]],[],[[]]] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [[[]],[[[]]],[],[],[]] => 0
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[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [[[]],[[[]],[[]]],[]] => 0
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[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => [[],[[[],[[[[],[]],[]],[]]],[]]] => 0
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[],[[[[],[]],[[[],[]],[]]],[]]] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [[],[[[[[],[]],[[],[]]],[]],[]]] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => [[],[[[[],[[[],[]],[]]],[]],[]]] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => [[],[[[[[],[[],[]]],[]],[]],[]]] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[],[[[[[[],[]],[]],[]],[]],[]]] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,0,1 3,1,0,1 9,3,1,0,1 28,9,3,1,0,1 90,28,9,3,1,0,1 297,90,28,9,3,1,0,1
$F_{1} = q$
$F_{2} = 1 + q^{2}$
$F_{3} = 3 + q + q^{3}$
$F_{4} = 9 + 3\ q + q^{2} + q^{4}$
$F_{5} = 28 + 9\ q + 3\ q^{2} + q^{3} + q^{5}$
$F_{6} = 90 + 28\ q + 9\ q^{2} + 3\ q^{3} + q^{4} + q^{6}$
$F_{7} = 297 + 90\ q + 28\ q^{2} + 9\ q^{3} + 3\ q^{4} + q^{5} + q^{7}$
Description
The length of the trunk of an ordered tree.
This is the length of the path from the root to the first vertex which has not exactly one child.
This is the length of the path from the root to the first vertex which has not exactly one child.
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
to ordered tree: right child = right brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the right child of $y$, $x$ becomes the right brother of $y$,
- if $x$ is the left child of $y$, $x$ becomes the first child of $y$.
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