Identifier
-
Mp00029:
Dyck paths
—to binary tree: left tree, up step, right tree, down step⟶
Binary trees
St000201: Binary trees ⟶ ℤ (values match St000196The number of occurrences of the contiguous pattern [[.,.],[.,.)
Values
[1,0] => [.,.] => 1
[1,0,1,0] => [[.,.],.] => 1
[1,1,0,0] => [.,[.,.]] => 1
[1,0,1,0,1,0] => [[[.,.],.],.] => 1
[1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,0,0,1,0] => [[.,[.,.]],.] => 1
[1,1,0,1,0,0] => [.,[[.,.],.]] => 1
[1,1,1,0,0,0] => [.,[.,[.,.]]] => 1
[1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 1
[1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 2
[1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 2
[1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 2
[1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 2
[1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => 1
[1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 2
[1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 1
[1,1,0,1,0,1,0,0] => [.,[[[.,.],.],.]] => 1
[1,1,0,1,1,0,0,0] => [.,[[.,.],[.,.]]] => 2
[1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 1
[1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],.]] => 1
[1,1,1,0,1,0,0,0] => [.,[.,[[.,.],.]]] => 1
[1,1,1,1,0,0,0,0] => [.,[.,[.,[.,.]]]] => 1
[1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => 1
[1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => 2
[1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => 2
[1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 2
[1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => 2
[1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => 2
[1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => 3
[1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => 2
[1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => 2
[1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 3
[1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => 2
[1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => 2
[1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => 2
[1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => 1
[1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => 2
[1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => 2
[1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => 1
[1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => 2
[1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => 1
[1,1,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => 1
[1,1,0,1,0,1,1,0,0,0] => [.,[[[.,.],.],[.,.]]] => 2
[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => 2
[1,1,0,1,1,0,1,0,0,0] => [.,[[.,.],[[.,.],.]]] => 2
[1,1,0,1,1,1,0,0,0,0] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => 1
[1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 1
[1,1,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],.],.]] => 1
[1,1,1,0,0,1,1,0,0,0] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 1
[1,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,.],.]],.]] => 1
[1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => 1
[1,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,.],[.,.]]]] => 2
[1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => 1
[1,1,1,1,0,0,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => 1
[1,1,1,1,0,0,1,0,0,0] => [.,[.,[[.,[.,.]],.]]] => 1
[1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[.,.],.]]]] => 1
[1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => 2
[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] => [[[[.,.],.],[.,.]],[.,.]] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => 3
[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] => [[[.,.],[[.,.],.]],[.,.]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => 3
[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] => [[[.,.],[.,[.,.]]],[.,.]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => 3
>>> Load all 1106 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => 2
[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] => [[[.,[.,.]],[.,.]],[.,.]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => 2
[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] => [.,[[[[[.,.],.],.],.],.]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,.]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,[.,.]]]] => 2
[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] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,.]],.],.]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],.]],.]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[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] => [.,[[[[.,[.,.]],.],.],.]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[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] => [.,[[[.,[[.,.],.]],.],.]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],[.,.]]] => 2
[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] => [.,[[.,[[[.,.],.],.]],.]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,.],.],[.,.]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[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] => [.,[[[.,[.,[.,.]]],.],.]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[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] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[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] => [.,[[.,[.,[[.,.],.]]],.]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[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] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],.] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[.,.]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],.] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 2
[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] => [[[[[.,.],.],.],[.,.]],[.,.]] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[.,.],.],.],[[.,.],.]],.] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],.],.],.] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,.]],[.,.]],.] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 3
[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] => [[[[.,.],.],[[.,.],.]],[.,.]] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[.,.],.],.]],.] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 3
[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] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,.]],.],.],.],.] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,.]],.] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,.]],[.,.]],.],.] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],.]],.] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[[.,.],.]],.],.],.] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,.]],.] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 3
[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] => [[[.,.],[[[.,.],.],.]],[.,.]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,.],.],.],.]],.] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,.],.],[.,.]]],.] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[.,.]]],.],.] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],[.,.]],.]],.] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],.]]],.] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,.]]],.],.],.] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 3
[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] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,.]]],.] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 3
[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] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],.]],.] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],.],.]]],.] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 3
[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] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 2
[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] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],.]],.] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 3
[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] => [[[.,[.,.]],[[.,.],.]],[.,.]] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 3
[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] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,.],.]],.],.],.],.] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 2
[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] => [[[.,[[.,.],.]],[.,.]],[.,.]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],.],.]],.],.],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],.]],.],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => 2
[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] => [.,[[[[[[.,.],.],.],.],.],.]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => 2
[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] => [[.,[[[.,.],.],[.,.]]],[.,.]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[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] => [[.,[[[.,.],[.,.]],.]],[.,.]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 3
[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] => [[.,[[.,.],[[.,.],.]]],[.,.]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[.,.]],.]]] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[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] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],.]]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2
[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] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => 2
[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] => [.,[[[[[.,[.,.]],.],.],.],.]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => 2
[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] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[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] => [.,[[[[.,[[.,.],.]],.],.],.]] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[.,.],.]]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => 2
[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] => [.,[[[.,[[[.,.],.],.]],.],.]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => 2
[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] => [.,[[.,[[[[.,.],.],.],.]],.]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],.],[.,.]],.]]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2
[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] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],.]]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],.]]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[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] => [.,[[[[.,[.,[.,.]]],.],.],.]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[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] => [.,[[[.,[[.,[.,.]],.]],.],.]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[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] => [.,[[.,[[[.,[.,.]],.],.]],.]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[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] => [.,[[[.,[.,[[.,.],.]]],.],.]] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[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] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[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] => [.,[[.,[.,[[[.,.],.],.]]],.]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[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] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[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] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[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] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[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] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[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] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 4
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 4
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 3
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => 4
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => 4
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => 3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 3
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => 2
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 5
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 3
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 4
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => 6
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]] => 5
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]] => 5
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]] => 5
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]] => 5
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]] => 5
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]] => 4
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]] => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]] => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]] => 3
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] => 5
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]] => 4
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]] => 4
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] => 4
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]] => 4
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]] => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]] => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]] => 3
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]] => 4
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] => 3
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]] => 3
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 5
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 4
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 3
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]] => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]] => 5
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]] => 4
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]] => 4
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => 4
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]] => 4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]] => 3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]] => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 4
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 3
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => 5
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => 4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => 3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 3
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 3
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 3
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => 4
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => 3
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => 3
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]] => 3
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 3
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 4
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => 4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => 3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => 5
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]] => 5
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]] => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => 3
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 16,24,2 32,80,20 64,240,120,5
F1=q
F2=2 q
F3=4 q+q2
F4=8 q+6 q2
F5=16 q+24 q2+2 q3
F6=32 q+80 q2+20 q3
F7=64 q+240 q2+120 q3+5 q4
Description
The number of leaf nodes in a binary tree.
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size n, at least 1, with exactly one leaf node for is 2n−1, see [2].
The number of binary tree of size n, at least 3, with exactly two leaf nodes is n(n+1)2n−2, see [3].
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size n, at least 1, with exactly one leaf node for is 2n−1, see [2].
The number of binary tree of size n, at least 3, with exactly two leaf nodes is n(n+1)2n−2, see [3].
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 L1R0 for Dyck paths L,R of respective semilengths n1,n2 with n1+n2=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 L1R0 for Dyck paths L,R of respective semilengths n1,n2 with n1+n2=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.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!