- FindStat

Identifier

Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
St000161: Binary trees ⟶ ℤ

Values

[1,0] => [.,.] => 0

[1,0,1,0] => [[.,.],.] => 0

[1,1,0,0] => [.,[.,.]] => 1

[1,0,1,0,1,0] => [[[.,.],.],.] => 0

[1,0,1,1,0,0] => [[.,.],[.,.]] => 1

[1,1,0,0,1,0] => [[.,[.,.]],.] => 1

[1,1,0,1,0,0] => [.,[[.,.],.]] => 2

[1,1,1,0,0,0] => [.,[.,[.,.]]] => 3

[1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 0

[1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 1

[1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 1

[1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 2

[1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 3

[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] => [[.,[[.,.],.]],.] => 2

[1,1,0,1,0,1,0,0] => [.,[[[.,.],.],.]] => 3

[1,1,0,1,1,0,0,0] => [.,[[.,.],[.,.]]] => 4

[1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 3

[1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],.]] => 4

[1,1,1,0,1,0,0,0] => [.,[.,[[.,.],.]]] => 5

[1,1,1,1,0,0,0,0] => [.,[.,[.,[.,.]]]] => 6

[1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => 0

[1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => 1

[1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => 1

[1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 2

[1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => 3

[1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => 1

[1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => 2

[1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => 2

[1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => 3

[1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 4

[1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => 3

[1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => 4

[1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => 5

[1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => 6

[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] => [[.,[.,.]],[[.,.],.]] => 3

[1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => 4

[1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => 2

[1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => 3

[1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => 3

[1,1,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => 4

[1,1,0,1,0,1,1,0,0,0] => [.,[[[.,.],.],[.,.]]] => 5

[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => 4

[1,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => 5

[1,1,0,1,1,0,1,0,0,0] => [.,[[.,.],[[.,.],.]]] => 6

[1,1,0,1,1,1,0,0,0,0] => [.,[[.,.],[.,[.,.]]]] => 7

[1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => 3

[1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 4

[1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 4

[1,1,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],.],.]] => 5

[1,1,1,0,0,1,1,0,0,0] => [.,[[.,[.,.]],[.,.]]] => 6

[1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 5

[1,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,.],.]],.]] => 6

[1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => 7

[1,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,.],[.,.]]]] => 8

[1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => 6

[1,1,1,1,0,0,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => 7

[1,1,1,1,0,0,1,0,0,0] => [.,[.,[[.,[.,.]],.]]] => 8

[1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[.,.],.]]]] => 9

[1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,.]]]]] => 10

[1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => 0

[1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => 1

[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] => [[[[.,.],.],.],[[.,.],.]] => 2

[1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => 3

[1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => 1

[1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => 2

[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] => [[[.,.],.],[[[.,.],.],.]] => 3

[1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => 4

[1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => 3

[1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => 4

[1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5

[1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6

[1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => 1

[1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => 2

[1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => 2

[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] => [[[.,.],[.,.]],[.,[.,.]]] => 4

[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] => [[[.,.],[[[.,.],.],.]],.] => 3

[1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => 4

[1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => 5

[1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => 4

[1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => 5

[1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6

[1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7

[1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => 3

[1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => 4

[1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => 4

[1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => 5

[1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => 6

[1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => 5

[1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => 6

[1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 7

[1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8

>>> Load all 755 entries. <<<

[1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => 6

[1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => 7

[1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => 8

[1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 9

[1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 10

[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] => [[[.,[.,.]],.],[[.,.],.]] => 3

[1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => 4

[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] => [[[.,[.,.]],[[.,.],.]],.] => 3

[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => 4

[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => 5

[1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => 4

[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => 5

[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => 6

[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => 7

[1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => 2

[1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => 3

[1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => 3

[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => 4

[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => 5

[1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => 3

[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => 4

[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => 4

[1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => 5

[1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,.]]] => 6

[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => 5

[1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => 6

[1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 7

[1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,[.,.]]]] => 8

[1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => 4

[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => 5

[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => 5

[1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,.]],.],.]] => 6

[1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => 7

[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => 6

[1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],.]],.]] => 7

[1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => 8

[1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,.],[[.,.],[.,.]]]] => 9

[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => 7

[1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => 8

[1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => 9

[1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => 10

[1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,.]]]]] => 11

[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] => [[[.,[.,[.,.]]],.],[.,.]] => 4

[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => 4

[1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => 5

[1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 6

[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => 4

[1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => 5

[1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => 5

[1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],.],.]] => 6

[1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => 7

[1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => 6

[1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => 7

[1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => 8

[1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[.,[.,.]]]] => 9

[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => 5

[1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => 6

[1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => 6

[1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => 7

[1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],[.,.]]] => 8

[1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => 7

[1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => 8

[1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => 9

[1,1,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,.],.],[.,.]]]] => 10

[1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => 8

[1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => 9

[1,1,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => 10

[1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => 11

[1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,.]]]]] => 12

[1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => 6

[1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 7

[1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => 7

[1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => 8

[1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,.]]],[.,.]]] => 9

[1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => 8

[1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => 9

[1,1,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => 10

[1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,.]],[.,.]]]] => 11

[1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => 9

[1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => 10

[1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => 11

[1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => 12

[1,1,1,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,.]]]]] => 13

[1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => 10

[1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => 11

[1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => 12

[1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => 13

[1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => 14

[1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15

[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[.,.]] => 1

[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] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3

[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => 2

[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => 2

[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 4

[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => 2

[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => 3

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 5

[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11

[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 4

[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 4

[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 5

[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 6

[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 5

[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 6

[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11

[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12

[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 11

[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => 11

[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 12

[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13

[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 11

[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 12

[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 13

[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 14

[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 15

[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => 2

[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 4

[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 3

[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 5

[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 11

[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => 3

[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 5

[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => 4

[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => 6

[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => 5

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => 6

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => 7

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => 7

[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 8

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => 7

[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => 8

[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 7

[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => 8

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => 9

[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 10

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => 8

[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 9

[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 8

[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 11

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 4

[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => 5

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => 7

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => 8

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => 8

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 9

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => 8

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => 9

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => 9

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => 10

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => 10

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 11

[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => 11

[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 12

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => 9

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => 10

[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 11

[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 11

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => 12

[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 13

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 11

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 11

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 12

[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 13

[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 14

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 15

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => 0

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 1

[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] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 2

[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] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => 2

[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => 2

[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] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4

[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6

[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6

[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => 2

[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => 2

[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => 2

[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => 4

[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 5

[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 6

[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => 4

[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => 4

[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => 4

[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 5

[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => 6

[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 5

[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6

[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => 5

[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 6

[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => 2

[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => 2

[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => 4

[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => 5

[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => 6

[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] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => 5

[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] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => 4

[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 5

[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => 8

[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 5

[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => 6

[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => 9

[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => 4

[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] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => 4

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 6

[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8

[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 8

[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => 8

[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 8

[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 8

[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10

[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12

[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 12

[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 12

[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => 5

[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => 6

[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => 5

[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => 6

[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => 6

[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 7

[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => 8

[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 9

[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 8

[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 10

[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 11

[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 12

[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 10

[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 12

[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 12

[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 12

[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18

[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 18

[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19

[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 18

[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 19

[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 20

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21

[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] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => 4

[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => 5

[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => 6

[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 4

[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => 5

[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => 4

[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => 4

[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => 5

[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] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => 6

[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => 6

[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => 7

[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => 8

[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => 6

[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => 8

[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => 8

[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => 9

[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => 10

[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => 11

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => 6

[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => 8

[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => 8

[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => 10

[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 10

[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => 10

[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 12

[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => 10

[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 12

[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => 3

[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => 4

[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => 6

[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 7

[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => 7

[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => 8

[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => 8

[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => 8

[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => 4

[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => 6

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => 7

[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => 8

[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => 10

[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => 8

[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => 8

[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => 8

[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => 10

[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 10

[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => 11

[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 12

[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => 12

[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => 13

[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 14

[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => 8

[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => 12

[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => 12

[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => 4

[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => 6

[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => 8

[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => 9

[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => 10

[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => 10

[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => 11

[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => 12

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => 6

[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => 8

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => 8

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => 8

[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 7

[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => 8

[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 9

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 10

[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => 11

[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => 12

[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => 10

[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => 8

[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => 9

[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => 10

[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => 10

[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 12

[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 14

[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => 12

[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 12

[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 10

[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 10

[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 12

[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 12

[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 14

[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 12

[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 16

[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 18

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 16

[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => 18

[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 19

[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 18

[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 19

[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 20

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 21

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 28

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 36

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 27

[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 27

[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 45

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 35

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 26

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 26

[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 26

[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 26

[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => 35

[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 45

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => 8

[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => 9

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => 9

[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]] => 14

[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => 10

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => 9

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 1

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => 10

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => 10

[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => 2

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => 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] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => 3

[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 13

[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 20

[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 18

[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 16

[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 16

[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 16

[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 20

[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 20

[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 18

[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 20

[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 20

[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => 14

[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]] => 12

[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]] => 14

[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => 14

[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => 12

[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]] => 12

[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]] => 12

[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]] => 12

[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => 14

[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]] => 14

[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]] => 12

[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]] => 14

[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]] => 14

[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 20

[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => 30

[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]] => 28

[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]] => 26

[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]] => 26

[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]] => 26

[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]] => 24

[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]] => 22

[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]] => 22

[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]] => 22

[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]] => 24

[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]] => 24

[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]] => 22

[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]] => 24

[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]] => 24

[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] => 30

[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]] => 30

[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]] => 28

[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] => 30

[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] => 30

[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]] => 26

[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]] => 26

[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]] => 26

[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]] => 26

[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]] => 30

[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] => 30

[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]] => 28

[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]] => 30

[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => 30

[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 22

[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 20

[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 18

[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 18

[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 18

[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 22

[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 22

[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 20

[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 22

[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 22

[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]] => 18

[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]] => 16

[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]] => 18

[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]] => 18

[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]] => 18

[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]] => 16

[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]] => 18

[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]] => 18

[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]] => 18

[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]] => 18

[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]] => 18

[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]] => 18

[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]] => 16

[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]] => 16

[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]] => 18

[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]] => 18

[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]] => 18

[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]] => 18

[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]] => 22

[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]] => 22

[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]] => 20

[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => 22

[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]] => 22

[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]] => 18

[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]] => 18

[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]] => 18

[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]] => 18

[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]] => 22

[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]] => 22

[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]] => 20

[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]] => 22

[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]] => 22

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 7

[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 9

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 11

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 13

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => 12

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 7

[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 9

[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 11

[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 11

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 7

[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 11

[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 13

[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 15

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 17

[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 7

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 9

[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 13

[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 9

[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 11

[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 13

[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 17

[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 13

[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 15

[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 19

[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 21

[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 21

[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 23

[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 15

[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 17

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 25

[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 17

[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 19

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 9

[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 13

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 9

[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 11

[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 13

[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 15

[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 17

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 19

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 11

[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 15

[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] => [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => 8

[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => 12

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 8

[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => 10

[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 12

[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 14

[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => 16

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => 18

[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 8

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 10

[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => 14

[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 10

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => 12

[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 12

[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 14

[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => 18

[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 14

[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 16

[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => 20

[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => 22

[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => 22

[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => 24

[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 16

[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 18

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => 26

[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 18

[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 20

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 8

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 10

[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => 14

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 10

[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 12

[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 14

[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 16

[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => 18

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => 20

[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 10

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 12

[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => 16

[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 12

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => 14

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 12

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 14

[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => 18

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 14

[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 16

[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 18

[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 20

[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => 22

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => 24

[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 14

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 16

[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => 20

[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 16

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 18

[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 20

[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 22

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]] => 30

[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 22

[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 24

[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 22

[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 24

[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]] => 32

[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 24

[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 26

[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => 24

[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => 26

[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => 26

[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => 28

[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]] => 34

[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => 36

[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => 26

[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]] => 28

[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => 28

[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]] => 30

[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 16

[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 18

[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => 22

[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 18

[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 20

[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 26

[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 28

[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => 30

[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => 32

[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 18

[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 20

[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => 24

[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 20

[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 22

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 8

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 10

[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => 14

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 10

[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 12

[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 14

[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 16

[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => 18

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => 20

[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 10

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 12

[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => 16

[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 12

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 14

[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 14

[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 16

[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => 20

[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 16

[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 18

[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => 22

[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => 24

[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => 24

[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => 26

[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 18

[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 20

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => 28

[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 20

[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 22

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 10

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 12

[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => 16

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 12

[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 14

[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 16

[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 18

[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => 20

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => 22

[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 12

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 14

[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => 18

[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 14

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => 16

[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => 7

[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => 19

[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]] => 11

[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => 17

[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => 19

[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]] => 24

[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]] => 24

[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 25

[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => 23

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$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 1 + 2\ q + q^{2} + q^{3}$

$F_{4} = 1 + 3\ q + 3\ q^{2} + 3\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$

$F_{5} = 1 + 4\ q + 6\ q^{2} + 7\ q^{3} + 7\ q^{4} + 5\ q^{5} + 5\ q^{6} + 3\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$

$F_{6} = 1 + 5\ q + 10\ q^{2} + 14\ q^{3} + 17\ q^{4} + 16\ q^{5} + 16\ q^{6} + 14\ q^{7} + 11\ q^{8} + 9\ q^{9} + 7\ q^{10} + 5\ q^{11} + 3\ q^{12} + 2\ q^{13} + q^{14} + q^{15}$

Description

The sum of the sizes of the right subtrees of a binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the

$312$ -avoiding permutation corresponding to the binary tree.
It is also the sum of all heights

$j$ of the coordinates

$(i,j)$ of the Dyck path corresponding to the binary tree.

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.