- FindStat

Identifier

Mp00016: Binary trees —left-right symmetry⟶ Binary trees
St000161: Binary trees ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[.,[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],.]] => 7

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

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

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

[[[[.,.],.],[.,.]],.] => [.,[[.,.],[.,[.,.]]]] => 7

[[[.,[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],.]]] => 7

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

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

[[[[.,[.,.]],.],.],.] => [.,[.,[.,[[.,.],.]]]] => 9

[[[[[.,.],.],.],.],.] => [.,[.,[.,[.,[.,.]]]]] => 10

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[.,[[.,[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],.]],.] => 7

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

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

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

[.,[[[[.,.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => 7

>>> Load all 604 entries. <<<

[.,[[[.,[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],.]]],.] => 7

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

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

[.,[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],.] => 9

[.,[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],.] => 10

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

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

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

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

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

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

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

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

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

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

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

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

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

[[.,.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,.]] => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[[[.,.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 7

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

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

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

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

[[.,[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],.]] => 7

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

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

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

[[[[.,.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,.]]]] => 7

[[[.,[.,[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],.],.]]] => 7

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

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

[[[[.,[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],.]]]] => 9

[[[[[.,.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,.]]]]] => 10

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

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

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

[[.,[.,[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],.],.]] => 7

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

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

[[.,[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],.]] => 7

[[.,[[.,[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],.]],.]] => 7

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

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

[[.,[[.,[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],.]],.]] => 9

[[.,[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],.]] => 9

[[.,[[[.,[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],.]]],.]] => 10

[[.,[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],.]] => 11

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

[[[.,.],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[.,.]]] => 7

[[[.,.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,.]]] => 7

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

[[[.,.],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[.,.]]] => 9

[[[.,[.,.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,.],.]]] => 7

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

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

[[[[.,.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,.]]]] => 9

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

[[[.,[[.,.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,.]],.]]] => 9

[[[[.,.],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[.,.]]]] => 9

[[[[.,[.,.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,.],.]]]] => 10

[[[[[.,.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,.]]]]] => 11

[[[.,[.,[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],.],.]]] => 9

[[[.,[.,[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],.],.]]] => 10

[[[.,[[.,.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,.]],.]]] => 10

[[[.,[[.,[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],.]],.]]] => 11

[[[.,[[[.,.],.],.]],.],.] => [.,[.,[[.,[.,[.,.]]],.]]] => 12

[[[[.,.],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[.,.]]]] => 10

[[[[.,.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,.]]]] => 11

[[[[.,[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],.]]]] => 11

[[[[[.,.],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[.,.]]]]] => 12

[[[[.,[.,[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],.],.]]]] => 12

[[[[.,[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],.]]]] => 13

[[[[[.,.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,.]]]]] => 13

[[[[[.,[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],.]]]]] => 14

[[[[[[.,.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15

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

[.,[[.,[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 11

[.,[[[.,.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 7

[.,[[[[[.,.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 11

[.,[[[.,[[.,[.,.]],.]],.],.]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 11

[.,[[[.,[[[.,.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 12

[.,[[[[.,.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 11

[.,[[[[.,[.,.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => 11

[.,[[[[[.,.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 12

[.,[[[[.,[.,[.,.]]],.],.],.]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => 12

[.,[[[[.,[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 13

[.,[[[[[.,.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 13

[.,[[[[[.,[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 14

[.,[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 15

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[.,.],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 11

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

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

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

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

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

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

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

[[[[[.,.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 11

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

[[.,[[[[.,.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 11

[[[[[.,.],.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11

[[[.,[[.,[.,.]],.]],.],[.,.]] => [[.,.],[.,[[.,[[.,.],.]],.]]] => 11

[[[.,[[[.,.],.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 12

[[[[.,.],[[.,.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 11

[[[[.,[.,.]],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11

[[[[[.,.],.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12

[[[[.,[.,[.,.]]],.],.],[.,.]] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 12

[[[[.,[[.,.],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 13

[[[[[.,.],[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13

[[[[[.,[.,.]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 14

[[[[[[.,.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 15

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

[[.,[.,[.,[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],.],.],.]] => 7

[[.,[.,[.,[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],.],.],.]] => 7

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

[[.,[.,[.,[[[.,.],.],.]]]],.] => [.,[[[[.,[.,[.,.]]],.],.],.]] => 9

[[.,[.,[[.,.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,.]],.],.]] => 7

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

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

[[.,[.,[[.,[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],.]],.],.]] => 9

[[.,[.,[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],.],.]] => 10

[[.,[[.,.],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[.,.]],.]] => 7

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

[[.,[[.,[.,[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],.],.]],.]] => 10

[[[.,.],[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7

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

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

[[[.,.],[.,[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],.],[.,.]]] => 9

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

[[[.,.],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 9

[[[.,.],[[.,[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 9

[[[.,.],[[.,[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],.]],[.,.]]] => 10

[[[.,.],[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 11

[[[.,[.,.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,.],.]]] => 9

[[[[.,.],.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 10

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 12

[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 12

[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => 12

[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 9

[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => 10

[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => 11

[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => 12

[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => 12

[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 18

[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 18

[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => 18

[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 19

[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 19

[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 20

[.,[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 21

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

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

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

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

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

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

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

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

[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 10

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 7

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

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

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

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

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

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

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

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

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

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

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

[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => 10

[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 9

[[[[.,.],.],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 12

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

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

[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => 7

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

[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 7

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

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

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

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

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

[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => 9

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

[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => 10

[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => 10

[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => 9

[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => 11

[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => 12

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

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

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

[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => 10

[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => 10

[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => 7

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

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

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

[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => 10

[[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => 9

[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => 10

[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => 11

[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 10

[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 12

[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 12

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

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

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

[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 12

[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 12

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

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

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

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

[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 10

[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 12

[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 10

[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 11

[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 12

[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10

[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 12

[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 12

[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12

[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 18

[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18

[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 18

[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 19

[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19

[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 20

[[[[[[[.,.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21

[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => 7

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

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

[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => 9

[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 10

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

[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => 10

[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 10

[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 12

[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => 12

[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 14

[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 16

[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 16

[[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 14

[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 12

[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 10

[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => 10

[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => 10

[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => 11

[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => 12

[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 12

[[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => 13

[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 14

[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 28

[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 36

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

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

[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => 9

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

[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 7

[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]] => [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 11

[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 13

[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 13

[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 15

[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 17

[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 13

[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 13

[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 17

[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 13

[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 17

[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 19

[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 17

[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 17

[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 19

[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.] => [.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 19

[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.] => [.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 23

[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 25

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

[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] => [[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => 20

[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]] => [[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => 18

[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 18

[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 20

[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] => [[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => 22

[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => 22

[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]] => [[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => 24

[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => 26

[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 18

[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.] => [.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => 24

[[.,[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]],.] => [.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => 24

[[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.] => [.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => 26

[[.,[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.] => [.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => 28

[[.,[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]],.] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => 24

[[.,[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => 22

[[.,[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => 24

[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 24

[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 24

[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 26

[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 28

[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.] => [.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => 28

[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => 36

[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 20

[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => 30

[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28

[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36

[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 27

[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 27

[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 45

[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => 35

[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 26

[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 26

[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 26

[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 26

[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 35

[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 45

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

[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => 9

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

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

[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => 10

[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => 10

[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => 10

[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => 9

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

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

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

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

[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 20

[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.] => 20

[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.] => 20

[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.] => 20

[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.] => 18

[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.] => 20

[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => 20

[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]] => 14

[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]] => 14

[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]] => 14

[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => 14

[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]] => 12

[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]] => 12

[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => 14

[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]] => 14

[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]] => 14

[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 20

[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 20

[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 20

[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 16

[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => 16

[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 16

[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => 20

[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.] => 30

[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],.] => 28

[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.] => 30

[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.] => 30

[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.] => 30

[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.] => 30

[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.] => 26

[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.] => 26

[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.] => 26

[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.] => 30

[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.] => 28

[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.] => 30

[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.] => 30

[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => 22

[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]] => 20

[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]] => 22

[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]] => 22

[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]] => 18

[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]] => 18

[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]] => 18

[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]] => 18

[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 22

[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 20

[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 22

[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 22

[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => 18

[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => [[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => 30

[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => [[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] => 30

[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] => 30

[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]] => 28

[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]] => 30

[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] => 30

[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]] => 24

[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]] => 24

[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]] => 22

[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]] => 22

[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]] => 24

[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]] => 24

[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]] => 22

[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]] => 24

[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]] => 24

[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]] => 30

[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]] => 26

[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]] => 30

[[[[.,.],[.,.]],[[.,.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]] => 13

[[[[.,.],.],[.,.]],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]] => 9

[[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]] => 9

[[[[.,.],[.,.]],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]] => 14

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

[[[[.,.],.],[.,.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]] => 9

[[.,[[[.,.],.],[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],[.,[.,.]]],.]] => 9

[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 25

[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 13

[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => 9

[.,[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.] => 20

[.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.] => 17

[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]] => [[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.] => 15

[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => 12

[[.,[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]] => 36

[[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.] => [.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]] => 24

[.,[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => 15

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searching the database for the individual values of this statistic

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searching the database for statistics with the same generating function

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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

left-right symmetry

Description

Return the left-right symmetrized tree of a binary tree.