- FindStat

Identifier

Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001735: Permutations ⟶ ℤ

Values

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

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

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

[[],[],[]] => [[[.,.],.],.] => [1,2,3] => [1,2,3] => 1

[[],[[]]] => [[.,.],[.,.]] => [1,3,2] => [1,2,3] => 1

[[[]],[]] => [[.,[.,.]],.] => [2,1,3] => [1,2,3] => 1

[[[],[]]] => [.,[[.,.],.]] => [2,3,1] => [1,2,3] => 1

[[[[]]]] => [.,[.,[.,.]]] => [3,2,1] => [1,3,2] => 2

[[],[],[],[]] => [[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => 1

[[],[],[[]]] => [[[.,.],.],[.,.]] => [1,2,4,3] => [1,2,3,4] => 1

[[],[[]],[]] => [[[.,.],[.,.]],.] => [1,3,2,4] => [1,2,3,4] => 1

[[],[[],[]]] => [[.,.],[[.,.],.]] => [1,3,4,2] => [1,2,3,4] => 1

[[],[[[]]]] => [[.,.],[.,[.,.]]] => [1,4,3,2] => [1,2,4,3] => 2

[[[]],[],[]] => [[[.,[.,.]],.],.] => [2,1,3,4] => [1,2,3,4] => 1

[[[]],[[]]] => [[.,[.,.]],[.,.]] => [2,1,4,3] => [1,2,3,4] => 1

[[[],[]],[]] => [[.,[[.,.],.]],.] => [2,3,1,4] => [1,2,3,4] => 1

[[[[]]],[]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => [1,3,2,4] => 2

[[[],[],[]]] => [.,[[[.,.],.],.]] => [2,3,4,1] => [1,2,3,4] => 1

[[[],[[]]]] => [.,[[.,.],[.,.]]] => [2,4,3,1] => [1,2,4,3] => 2

[[[[]],[]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => [1,3,4,2] => 2

[[[[],[]]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => [1,3,2,4] => 2

[[[[[]]]]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,4,2,3] => 2

[[],[],[],[],[]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => 1

[[],[],[],[[]]] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [1,2,3,4,5] => 1

[[],[],[[]],[]] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [1,2,3,4,5] => 1

[[],[],[[],[]]] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [1,2,3,4,5] => 1

[[],[],[[[]]]] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [1,2,3,5,4] => 2

[[],[[]],[],[]] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [1,2,3,4,5] => 1

[[],[[]],[[]]] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [1,2,3,4,5] => 1

[[],[[],[]],[]] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [1,2,3,4,5] => 1

[[],[[[]]],[]] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [1,2,4,3,5] => 2

[[],[[],[],[]]] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [1,2,3,4,5] => 1

[[],[[],[[]]]] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [1,2,3,5,4] => 2

[[],[[[]],[]]] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [1,2,4,5,3] => 2

[[],[[[],[]]]] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [1,2,4,3,5] => 2

[[],[[[[]]]]] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [1,2,5,3,4] => 2

[[[]],[],[],[]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [1,2,3,4,5] => 1

[[[]],[],[[]]] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [1,2,3,4,5] => 1

[[[]],[[]],[]] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [1,2,3,4,5] => 1

[[[]],[[],[]]] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [1,2,3,4,5] => 1

[[[]],[[[]]]] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [1,2,3,5,4] => 2

[[[],[]],[],[]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [1,2,3,4,5] => 1

[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [1,3,2,4,5] => 2

[[[],[]],[[]]] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [1,2,3,4,5] => 1

[[[[]]],[[]]] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [1,3,2,4,5] => 2

[[[],[],[]],[]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [1,2,3,4,5] => 1

[[[],[[]]],[]] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [1,2,4,3,5] => 2

[[[[]],[]],[]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [1,3,4,2,5] => 2

[[[[],[]]],[]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [1,3,2,4,5] => 2

[[[[[]]]],[]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [1,4,2,3,5] => 2

[[[],[],[],[]]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,2,3,4,5] => 1

[[[],[],[[]]]] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [1,2,3,5,4] => 2

[[[],[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [1,2,4,5,3] => 2

[[[],[[],[]]]] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [1,2,4,3,5] => 2

[[[],[[[]]]]] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [1,2,5,3,4] => 2

[[[[]],[],[]]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [1,3,4,5,2] => 2

[[[[]],[[]]]] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [1,3,5,2,4] => 2

[[[[],[]],[]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,3,2,4,5] => 2

[[[[[]]],[]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [1,4,5,2,3] => 2

[[[[],[],[]]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,3,5,2,4] => 2

[[[[],[[]]]]] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [1,3,4,2,5] => 2

[[[[[]],[]]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [1,4,2,3,5] => 2

[[[[[],[]]]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,4,2,5,3] => 6

[[[[[[]]]]]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,5,2,4,3] => 6

[[],[],[],[],[],[]] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1

[[],[],[],[],[[]]] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => 1

[[],[],[],[[]],[]] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => 1

[[],[],[],[[],[]]] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [1,2,3,4,5,6] => 1

[[],[],[],[[[]]]] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [1,2,3,4,6,5] => 2

[[],[],[[]],[],[]] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => 1

[[],[],[[]],[[]]] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => 1

[[],[],[[],[]],[]] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [1,2,3,4,5,6] => 1

[[],[],[[[]]],[]] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => 2

[[],[],[[],[],[]]] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [1,2,3,4,5,6] => 1

[[],[],[[],[[]]]] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [1,2,3,4,6,5] => 2

[[],[],[[[]],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [1,2,3,5,6,4] => 2

[[],[],[[[],[]]]] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [1,2,3,5,4,6] => 2

[[],[],[[[[]]]]] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => 2

[[],[[]],[],[],[]] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [1,2,3,4,5,6] => 1

[[],[[]],[],[[]]] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => 1

[[],[[]],[[]],[]] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => 1

[[],[[]],[[],[]]] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [1,2,3,4,5,6] => 1

[[],[[]],[[[]]]] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [1,2,3,4,6,5] => 2

[[],[[],[]],[],[]] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [1,2,3,4,5,6] => 1

[[],[[[]]],[],[]] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => 2

[[],[[],[]],[[]]] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [1,2,3,4,5,6] => 1

[[],[[[]]],[[]]] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => 2

[[],[[],[],[]],[]] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [1,2,3,4,5,6] => 1

[[],[[],[[]]],[]] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [1,2,3,5,4,6] => 2

[[],[[[]],[]],[]] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [1,2,4,5,3,6] => 2

[[],[[[],[]]],[]] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [1,2,4,3,5,6] => 2

[[],[[[[]]]],[]] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => 2

[[],[[],[],[],[]]] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [1,2,3,4,5,6] => 1

[[],[[],[],[[]]]] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [1,2,3,4,6,5] => 2

[[],[[],[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [1,2,3,5,6,4] => 2

[[],[[],[[],[]]]] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [1,2,3,5,4,6] => 2

[[],[[],[[[]]]]] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [1,2,3,6,4,5] => 2

[[],[[[]],[],[]]] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [1,2,4,5,6,3] => 2

[[],[[[]],[[]]]] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [1,2,4,6,3,5] => 2

[[],[[[],[]],[]]] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [1,2,4,3,5,6] => 2

[[],[[[[]]],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [1,2,5,6,3,4] => 2

>>> Load all 588 entries. <<<

[[],[[[],[],[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [1,2,4,6,3,5] => 2

[[],[[[],[[]]]]] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [1,2,4,5,3,6] => 2

[[],[[[[]],[]]]] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [1,2,5,3,4,6] => 2

[[],[[[[],[]]]]] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [1,2,5,3,6,4] => 6

[[],[[[[[]]]]]] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => 6

[[[]],[],[],[],[]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [1,2,3,4,5,6] => 1

[[[]],[],[],[[]]] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [1,2,3,4,5,6] => 1

[[[]],[],[[]],[]] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [1,2,3,4,5,6] => 1

[[[]],[],[[],[]]] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [1,2,3,4,5,6] => 1

[[[]],[],[[[]]]] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [1,2,3,4,6,5] => 2

[[[]],[[]],[],[]] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [1,2,3,4,5,6] => 1

[[[]],[[]],[[]]] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => 1

[[[]],[[],[]],[]] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [1,2,3,4,5,6] => 1

[[[]],[[[]]],[]] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [1,2,3,5,4,6] => 2

[[[]],[[],[],[]]] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [1,2,3,4,5,6] => 1

[[[]],[[],[[]]]] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [1,2,3,4,6,5] => 2

[[[]],[[[]],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [1,2,3,5,6,4] => 2

[[[]],[[[],[]]]] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [1,2,3,5,4,6] => 2

[[[]],[[[[]]]]] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => 2

[[[],[]],[],[],[]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [1,2,3,4,5,6] => 1

[[[[]]],[],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [1,3,2,4,5,6] => 2

[[[],[]],[],[[]]] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [1,2,3,4,5,6] => 1

[[[[]]],[],[[]]] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [1,3,2,4,5,6] => 2

[[[],[]],[[]],[]] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [1,2,3,4,5,6] => 1

[[[[]]],[[]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [1,3,2,4,5,6] => 2

[[[],[]],[[],[]]] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [1,2,3,4,5,6] => 1

[[[],[]],[[[]]]] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [1,2,3,4,6,5] => 2

[[[[]]],[[],[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [1,3,2,4,5,6] => 2

[[[[]]],[[[]]]] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => 4

[[[],[],[]],[],[]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [1,2,3,4,5,6] => 1

[[[],[[]]],[],[]] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [1,2,4,3,5,6] => 2

[[[[]],[]],[],[]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [1,3,4,2,5,6] => 2

[[[[],[]]],[],[]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [1,3,2,4,5,6] => 2

[[[[[]]]],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => 2

[[[],[],[]],[[]]] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [1,2,3,4,5,6] => 1

[[[],[[]]],[[]]] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [1,2,4,3,5,6] => 2

[[[[]],[]],[[]]] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [1,3,4,2,5,6] => 2

[[[[],[]]],[[]]] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [1,3,2,4,5,6] => 2

[[[[[]]]],[[]]] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => 2

[[[],[],[],[]],[]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [1,2,3,4,5,6] => 1

[[[],[],[[]]],[]] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [1,2,3,5,4,6] => 2

[[[],[[]],[]],[]] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [1,2,4,5,3,6] => 2

[[[],[[],[]]],[]] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [1,2,4,3,5,6] => 2

[[[],[[[]]]],[]] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [1,2,5,3,4,6] => 2

[[[[]],[],[]],[]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [1,3,4,5,2,6] => 2

[[[[]],[[]]],[]] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [1,3,5,2,4,6] => 2

[[[[],[]],[]],[]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [1,3,2,4,5,6] => 2

[[[[[]]],[]],[]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [1,4,5,2,3,6] => 2

[[[[],[],[]]],[]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [1,3,5,2,4,6] => 2

[[[[],[[]]]],[]] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [1,3,4,2,5,6] => 2

[[[[[]],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [1,4,2,3,5,6] => 2

[[[[[],[]]]],[]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [1,4,2,5,3,6] => 6

[[[[[[]]]]],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => 6

[[[],[],[],[],[]]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 1

[[[],[],[],[[]]]] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [1,2,3,4,6,5] => 2

[[[],[],[[]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [1,2,3,5,6,4] => 2

[[[],[],[[],[]]]] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [1,2,3,5,4,6] => 2

[[[],[],[[[]]]]] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [1,2,3,6,4,5] => 2

[[[],[[]],[],[]]] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [1,2,4,5,6,3] => 2

[[[],[[]],[[]]]] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [1,2,4,6,3,5] => 2

[[[],[[],[]],[]]] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [1,2,4,3,5,6] => 2

[[[],[[[]]],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [1,2,5,6,3,4] => 2

[[[],[[],[],[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [1,2,4,6,3,5] => 2

[[[],[[],[[]]]]] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [1,2,4,5,3,6] => 2

[[[],[[[]],[]]]] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [1,2,5,3,4,6] => 2

[[[],[[[],[]]]]] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [1,2,5,3,6,4] => 6

[[[],[[[[]]]]]] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [1,2,6,3,5,4] => 6

[[[[]],[],[],[]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [1,3,4,5,6,2] => 2

[[[[]],[],[[]]]] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [1,3,4,6,2,5] => 2

[[[[]],[[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [1,3,5,6,2,4] => 2

[[[[]],[[],[]]]] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [1,3,5,4,6,2] => 4

[[[[]],[[[]]]]] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [1,3,6,2,4,5] => 2

[[[[],[]],[],[]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,3,2,4,5,6] => 2

[[[[[]]],[],[]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [1,4,5,6,2,3] => 2

[[[[],[]],[[]]]] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [1,3,2,4,6,5] => 4

[[[[[]]],[[]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [1,4,6,2,3,5] => 2

[[[[],[],[]],[]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,3,5,6,2,4] => 2

[[[[],[[]]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [1,3,4,2,5,6] => 2

[[[[[]],[]],[]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [1,4,2,3,5,6] => 2

[[[[[],[]]],[]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,4,2,5,6,3] => 6

[[[[[[]]]],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [1,5,6,2,4,3] => 6

[[[[],[],[],[]]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,3,5,2,4,6] => 2

[[[[],[],[[]]]]] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [1,3,6,2,4,5] => 2

[[[[],[[]],[]]]] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [1,3,4,6,2,5] => 2

[[[[],[[],[]]]]] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [1,3,6,2,5,4] => 6

[[[[],[[[]]]]]] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [1,3,5,2,6,4] => 6

[[[[[]],[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [1,4,6,2,3,5] => 2

[[[[[]],[[]]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [1,4,5,2,3,6] => 2

[[[[[],[]],[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,4,6,2,5,3] => 6

[[[[[[]]],[]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [1,5,2,4,6,3] => 6

[[[[[],[],[]]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,4,3,6,2,5] => 6

[[[[[],[[]]]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [1,4,3,5,2,6] => 6

[[[[[[]],[]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [1,5,2,4,3,6] => 6

[[[[[[],[]]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,5,2,6,3,4] => 6

[[[[[[[]]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => 6

[[],[],[],[],[],[],[]] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 1

[[],[],[],[],[],[[]]] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => 1

[[],[],[],[],[[]],[]] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => 1

[[],[],[],[],[[],[]]] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [1,2,3,4,5,6,7] => 1

[[],[],[],[],[[[]]]] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [1,2,3,4,5,7,6] => 2

[[],[],[],[[]],[],[]] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => 1

[[],[],[],[[]],[[]]] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => 1

[[],[],[],[[],[]],[]] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [1,2,3,4,5,6,7] => 1

[[],[],[],[[[]]],[]] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => 2

[[],[],[],[[],[],[]]] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [1,2,3,4,5,6,7] => 1

[[],[],[],[[],[[]]]] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [1,2,3,4,5,7,6] => 2

[[],[],[],[[[]],[]]] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [1,2,3,4,6,7,5] => 2

[[],[],[],[[[],[]]]] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [1,2,3,4,6,5,7] => 2

[[],[],[],[[[[]]]]] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [1,2,3,4,7,5,6] => 2

[[],[],[[]],[],[],[]] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => 1

[[],[],[[]],[],[[]]] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => 1

[[],[],[[]],[[]],[]] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => 1

[[],[],[[]],[[],[]]] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [1,2,3,4,5,6,7] => 1

[[],[],[[]],[[[]]]] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [1,2,3,4,5,7,6] => 2

[[],[],[[],[]],[],[]] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [1,2,3,4,5,6,7] => 1

[[],[],[[[]]],[],[]] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [1,2,3,5,4,6,7] => 2

[[],[],[[],[]],[[]]] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [1,2,3,4,5,6,7] => 1

[[],[],[[[]]],[[]]] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [1,2,3,5,4,6,7] => 2

[[],[],[[],[],[]],[]] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [1,2,3,4,5,6,7] => 1

[[],[],[[],[[]]],[]] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [1,2,3,4,6,5,7] => 2

[[],[],[[[]],[]],[]] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [1,2,3,5,6,4,7] => 2

[[],[],[[[],[]]],[]] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [1,2,3,5,4,6,7] => 2

[[],[],[[[[]]]],[]] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [1,2,3,6,4,5,7] => 2

[[],[],[[],[],[],[]]] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [1,2,3,4,5,6,7] => 1

[[],[],[[],[],[[]]]] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [1,2,3,4,5,7,6] => 2

[[],[],[[],[[]],[]]] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [1,2,3,4,6,7,5] => 2

[[],[],[[],[[],[]]]] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [1,2,3,4,6,5,7] => 2

[[],[],[[],[[[]]]]] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [1,2,3,4,7,5,6] => 2

[[],[],[[[]],[],[]]] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [1,2,3,5,6,7,4] => 2

[[],[],[[[]],[[]]]] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [1,2,3,5,7,4,6] => 2

[[],[],[[[],[]],[]]] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [1,2,3,5,4,6,7] => 2

[[],[],[[[[]]],[]]] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [1,2,3,6,7,4,5] => 2

[[],[],[[[],[],[]]]] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [1,2,3,5,7,4,6] => 2

[[],[],[[[],[[]]]]] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [1,2,3,5,6,4,7] => 2

[[],[],[[[[]],[]]]] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [1,2,3,6,4,5,7] => 2

[[],[],[[[[],[]]]]] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [1,2,3,6,4,7,5] => 6

[[],[],[[[[[]]]]]] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [1,2,3,7,4,6,5] => 6

[[],[[]],[],[],[],[]] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => 1

[[],[[]],[],[],[[]]] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => 1

[[],[[]],[],[[]],[]] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => 1

[[],[[]],[],[[],[]]] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [1,2,3,4,5,6,7] => 1

[[],[[]],[],[[[]]]] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [1,2,3,4,5,7,6] => 2

[[],[[]],[[]],[],[]] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => 1

[[],[[]],[[]],[[]]] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => 1

[[],[[]],[[],[]],[]] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [1,2,3,4,5,6,7] => 1

[[],[[]],[[[]]],[]] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [1,2,3,4,6,5,7] => 2

[[],[[]],[[],[],[]]] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [1,2,3,4,5,6,7] => 1

[[],[[]],[[],[[]]]] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [1,2,3,4,5,7,6] => 2

[[],[[]],[[[]],[]]] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [1,2,3,4,6,7,5] => 2

[[],[[]],[[[],[]]]] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [1,2,3,4,6,5,7] => 2

[[],[[]],[[[[]]]]] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [1,2,3,4,7,5,6] => 2

[[],[[],[]],[],[],[]] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [1,2,3,4,5,6,7] => 1

[[],[[[]]],[],[],[]] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [1,2,4,3,5,6,7] => 2

[[],[[],[]],[],[[]]] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [1,2,3,4,5,6,7] => 1

[[],[[[]]],[],[[]]] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [1,2,4,3,5,6,7] => 2

[[],[[],[]],[[]],[]] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [1,2,3,4,5,6,7] => 1

[[],[[[]]],[[]],[]] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [1,2,4,3,5,6,7] => 2

[[],[[],[]],[[],[]]] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [1,2,3,4,5,6,7] => 1

[[],[[],[]],[[[]]]] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [1,2,3,4,5,7,6] => 2

[[],[[[]]],[[],[]]] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [1,2,4,3,5,6,7] => 2

[[],[[[]]],[[[]]]] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [1,2,4,3,5,7,6] => 4

[[],[[],[],[]],[],[]] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [1,2,3,4,5,6,7] => 1

[[],[[],[[]]],[],[]] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [1,2,3,5,4,6,7] => 2

[[],[[[]],[]],[],[]] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [1,2,4,5,3,6,7] => 2

[[],[[[],[]]],[],[]] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [1,2,4,3,5,6,7] => 2

[[],[[[[]]]],[],[]] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [1,2,5,3,4,6,7] => 2

[[],[[],[],[]],[[]]] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [1,2,3,4,5,6,7] => 1

[[],[[],[[]]],[[]]] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [1,2,3,5,4,6,7] => 2

[[],[[[]],[]],[[]]] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [1,2,4,5,3,6,7] => 2

[[],[[[],[]]],[[]]] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [1,2,4,3,5,6,7] => 2

[[],[[[[]]]],[[]]] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [1,2,5,3,4,6,7] => 2

[[],[[],[],[],[]],[]] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [1,2,3,4,5,6,7] => 1

[[],[[],[],[[]]],[]] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [1,2,3,4,6,5,7] => 2

[[],[[],[[]],[]],[]] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [1,2,3,5,6,4,7] => 2

[[],[[],[[],[]]],[]] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [1,2,3,5,4,6,7] => 2

[[],[[],[[[]]]],[]] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [1,2,3,6,4,5,7] => 2

[[],[[[]],[],[]],[]] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [1,2,4,5,6,3,7] => 2

[[],[[[]],[[]]],[]] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [1,2,4,6,3,5,7] => 2

[[],[[[],[]],[]],[]] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [1,2,4,3,5,6,7] => 2

[[],[[[[]]],[]],[]] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [1,2,5,6,3,4,7] => 2

[[],[[[],[],[]]],[]] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [1,2,4,6,3,5,7] => 2

[[],[[[],[[]]]],[]] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [1,2,4,5,3,6,7] => 2

[[],[[[[]],[]]],[]] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [1,2,5,3,4,6,7] => 2

[[],[[[[],[]]]],[]] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [1,2,5,3,6,4,7] => 6

[[],[[[[[]]]]],[]] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => 6

[[],[[],[],[],[],[]]] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [1,2,3,4,5,6,7] => 1

[[],[[],[],[],[[]]]] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [1,2,3,4,5,7,6] => 2

[[],[[],[],[[]],[]]] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [1,2,3,4,6,7,5] => 2

[[],[[],[],[[],[]]]] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [1,2,3,4,6,5,7] => 2

[[],[[],[],[[[]]]]] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [1,2,3,4,7,5,6] => 2

[[],[[],[[]],[],[]]] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [1,2,3,5,6,7,4] => 2

[[],[[],[[]],[[]]]] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [1,2,3,5,7,4,6] => 2

[[],[[],[[],[]],[]]] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [1,2,3,5,4,6,7] => 2

[[],[[],[[[]]],[]]] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [1,2,3,6,7,4,5] => 2

[[],[[],[[],[],[]]]] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [1,2,3,5,7,4,6] => 2

[[],[[],[[],[[]]]]] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [1,2,3,5,6,4,7] => 2

[[],[[],[[[]],[]]]] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [1,2,3,6,4,5,7] => 2

[[],[[],[[[],[]]]]] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [1,2,3,6,4,7,5] => 6

[[],[[],[[[[]]]]]] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [1,2,3,7,4,6,5] => 6

[[],[[[]],[],[],[]]] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [1,2,4,5,6,7,3] => 2

[[],[[[]],[],[[]]]] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [1,2,4,5,7,3,6] => 2

[[],[[[]],[[]],[]]] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [1,2,4,6,7,3,5] => 2

[[],[[[]],[[],[]]]] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [1,2,4,6,5,7,3] => 4

[[],[[[]],[[[]]]]] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [1,2,4,7,3,5,6] => 2

[[],[[[],[]],[],[]]] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [1,2,4,3,5,6,7] => 2

[[],[[[[]]],[],[]]] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [1,2,5,6,7,3,4] => 2

[[],[[[],[]],[[]]]] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [1,2,4,3,5,7,6] => 4

[[],[[[[]]],[[]]]] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [1,2,5,7,3,4,6] => 2

[[],[[[],[],[]],[]]] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [1,2,4,6,7,3,5] => 2

[[],[[[],[[]]],[]]] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [1,2,4,5,3,6,7] => 2

[[],[[[[]],[]],[]]] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [1,2,5,3,4,6,7] => 2

[[],[[[[],[]]],[]]] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [1,2,5,3,6,7,4] => 6

[[],[[[[[]]]],[]]] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [1,2,6,7,3,5,4] => 6

[[],[[[],[],[],[]]]] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [1,2,4,6,3,5,7] => 2

[[],[[[],[],[[]]]]] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [1,2,4,7,3,5,6] => 2

[[],[[[],[[]],[]]]] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [1,2,4,5,7,3,6] => 2

[[],[[[],[[],[]]]]] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [1,2,4,7,3,6,5] => 6

[[],[[[],[[[]]]]]] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [1,2,4,6,3,7,5] => 6

[[],[[[[]],[],[]]]] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [1,2,5,7,3,4,6] => 2

[[],[[[[]],[[]]]]] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [1,2,5,6,3,4,7] => 2

[[],[[[[],[]],[]]]] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [1,2,5,7,3,6,4] => 6

[[],[[[[[]]],[]]]] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [1,2,6,3,5,7,4] => 6

[[],[[[[],[],[]]]]] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [1,2,5,4,7,3,6] => 6

[[],[[[[],[[]]]]]] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [1,2,5,4,6,3,7] => 6

[[],[[[[[]],[]]]]] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [1,2,6,3,5,4,7] => 6

[[],[[[[[],[]]]]]] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [1,2,6,3,7,4,5] => 6

[[],[[[[[[]]]]]]] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [1,2,7,3,6,4,5] => 6

[[[]],[],[],[],[],[]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => 1

[[[]],[],[],[],[[]]] => [[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => 1

[[[]],[],[],[[]],[]] => [[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => 1

[[[]],[],[],[[],[]]] => [[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [1,2,3,4,5,6,7] => 1

[[[]],[],[],[[[]]]] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [1,2,3,4,5,7,6] => 2

[[[]],[],[[]],[],[]] => [[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => 1

[[[]],[],[[]],[[]]] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => 1

[[[]],[],[[],[]],[]] => [[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [1,2,3,4,5,6,7] => 1

[[[]],[],[[[]]],[]] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [1,2,3,4,6,5,7] => 2

[[[]],[],[[],[],[]]] => [[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [1,2,3,4,5,6,7] => 1

[[[]],[],[[],[[]]]] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [1,2,3,4,5,7,6] => 2

[[[]],[],[[[]],[]]] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [1,2,3,4,6,7,5] => 2

[[[]],[],[[[],[]]]] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [1,2,3,4,6,5,7] => 2

[[[]],[],[[[[]]]]] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [1,2,3,4,7,5,6] => 2

[[[]],[[]],[],[],[]] => [[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => 1

[[[]],[[]],[],[[]]] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => 1

[[[]],[[]],[[]],[]] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => 1

[[[]],[[]],[[],[]]] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [1,2,3,4,5,6,7] => 1

[[[]],[[]],[[[]]]] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [1,2,3,4,5,7,6] => 2

[[[]],[[],[]],[],[]] => [[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [1,2,3,4,5,6,7] => 1

[[[]],[[[]]],[],[]] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [1,2,3,5,4,6,7] => 2

[[[]],[[],[]],[[]]] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [1,2,3,4,5,6,7] => 1

[[[]],[[[]]],[[]]] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [1,2,3,5,4,6,7] => 2

[[[]],[[],[],[]],[]] => [[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [1,2,3,4,5,6,7] => 1

[[[]],[[],[[]]],[]] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [1,2,3,4,6,5,7] => 2

[[[]],[[[]],[]],[]] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [1,2,3,5,6,4,7] => 2

[[[]],[[[],[]]],[]] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [1,2,3,5,4,6,7] => 2

[[[]],[[[[]]]],[]] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [1,2,3,6,4,5,7] => 2

[[[]],[[],[],[],[]]] => [[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [1,2,3,4,5,6,7] => 1

[[[]],[[],[],[[]]]] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [1,2,3,4,5,7,6] => 2

[[[]],[[],[[]],[]]] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [1,2,3,4,6,7,5] => 2

[[[]],[[],[[],[]]]] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [1,2,3,4,6,5,7] => 2

[[[]],[[],[[[]]]]] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [1,2,3,4,7,5,6] => 2

[[[]],[[[]],[],[]]] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [1,2,3,5,6,7,4] => 2

[[[]],[[[]],[[]]]] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [1,2,3,5,7,4,6] => 2

[[[]],[[[],[]],[]]] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [1,2,3,5,4,6,7] => 2

[[[]],[[[[]]],[]]] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [1,2,3,6,7,4,5] => 2

[[[]],[[[],[],[]]]] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [1,2,3,5,7,4,6] => 2

[[[]],[[[],[[]]]]] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [1,2,3,5,6,4,7] => 2

[[[]],[[[[]],[]]]] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [1,2,3,6,4,5,7] => 2

[[[]],[[[[],[]]]]] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [1,2,3,6,4,7,5] => 6

[[[]],[[[[[]]]]]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [1,2,3,7,4,6,5] => 6

[[[],[]],[],[],[],[]] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => 1

[[[[]]],[],[],[],[]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [1,3,2,4,5,6,7] => 2

[[[],[]],[],[],[[]]] => [[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => 1

[[[[]]],[],[],[[]]] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [1,3,2,4,5,6,7] => 2

[[[],[]],[],[[]],[]] => [[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => 1

[[[[]]],[],[[]],[]] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [1,3,2,4,5,6,7] => 2

[[[],[]],[],[[],[]]] => [[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => 1

[[[],[]],[],[[[]]]] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [1,2,3,4,5,7,6] => 2

[[[[]]],[],[[],[]]] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [1,3,2,4,5,6,7] => 2

[[[[]]],[],[[[]]]] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [1,3,2,4,5,7,6] => 4

[[[],[]],[[]],[],[]] => [[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => 1

[[[[]]],[[]],[],[]] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [1,3,2,4,5,6,7] => 2

[[[],[]],[[]],[[]]] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => 1

[[[[]]],[[]],[[]]] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [1,3,2,4,5,6,7] => 2

[[[],[]],[[],[]],[]] => [[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => 1

[[[],[]],[[[]]],[]] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [1,2,3,4,6,5,7] => 2

[[[[]]],[[],[]],[]] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [1,3,2,4,5,6,7] => 2

[[[[]]],[[[]]],[]] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [1,3,2,4,6,5,7] => 4

[[[],[]],[[],[],[]]] => [[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => 1

[[[],[]],[[],[[]]]] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [1,2,3,4,5,7,6] => 2

[[[],[]],[[[]],[]]] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [1,2,3,4,6,7,5] => 2

[[[],[]],[[[],[]]]] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [1,2,3,4,6,5,7] => 2

[[[],[]],[[[[]]]]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [1,2,3,4,7,5,6] => 2

[[[[]]],[[],[],[]]] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [1,3,2,4,5,6,7] => 2

[[[[]]],[[],[[]]]] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [1,3,2,4,5,7,6] => 4

[[[[]]],[[[]],[]]] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [1,3,2,4,6,7,5] => 4

[[[[]]],[[[],[]]]] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [1,3,2,4,6,5,7] => 4

[[[[]]],[[[[]]]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [1,3,2,4,7,5,6] => 4

[[[],[],[]],[],[],[]] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => 1

[[[],[[]]],[],[],[]] => [[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [1,2,4,3,5,6,7] => 2

[[[[]],[]],[],[],[]] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [1,3,4,2,5,6,7] => 2

[[[[],[]]],[],[],[]] => [[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [1,3,2,4,5,6,7] => 2

[[[[[]]]],[],[],[]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [1,4,2,3,5,6,7] => 2

[[[],[],[]],[],[[]]] => [[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => 1

[[[],[[]]],[],[[]]] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [1,2,4,3,5,6,7] => 2

[[[[]],[]],[],[[]]] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [1,3,4,2,5,6,7] => 2

[[[[],[]]],[],[[]]] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [1,3,2,4,5,6,7] => 2

[[[[[]]]],[],[[]]] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [1,4,2,3,5,6,7] => 2

[[[],[],[]],[[]],[]] => [[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => 1

[[[],[[]]],[[]],[]] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [1,2,4,3,5,6,7] => 2

[[[[]],[]],[[]],[]] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [1,3,4,2,5,6,7] => 2

[[[[],[]]],[[]],[]] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [1,3,2,4,5,6,7] => 2

[[[[[]]]],[[]],[]] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [1,4,2,3,5,6,7] => 2

[[[],[],[]],[[],[]]] => [[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => 1

[[[],[],[]],[[[]]]] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [1,2,3,4,5,7,6] => 2

[[[],[[]]],[[],[]]] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [1,2,4,3,5,6,7] => 2

[[[],[[]]],[[[]]]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [1,2,4,3,5,7,6] => 4

[[[[]],[]],[[],[]]] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [1,3,4,2,5,6,7] => 2

[[[[]],[]],[[[]]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [1,3,4,2,5,7,6] => 4

[[[[],[]]],[[],[]]] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [1,3,2,4,5,6,7] => 2

[[[[],[]]],[[[]]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [1,3,2,4,5,7,6] => 4

[[[[[]]]],[[],[]]] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [1,4,2,3,5,6,7] => 2

[[[[[]]]],[[[]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [1,4,2,3,5,7,6] => 4

[[[],[],[],[]],[],[]] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => 1

[[[],[],[[]]],[],[]] => [[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [1,2,3,5,4,6,7] => 2

[[[],[[]],[]],[],[]] => [[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [1,2,4,5,3,6,7] => 2

[[[],[[],[]]],[],[]] => [[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [1,2,4,3,5,6,7] => 2

[[[],[[[]]]],[],[]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [1,2,5,3,4,6,7] => 2

[[[[]],[],[]],[],[]] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [1,3,4,5,2,6,7] => 2

[[[[]],[[]]],[],[]] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [1,3,5,2,4,6,7] => 2

[[[[],[]],[]],[],[]] => [[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [1,3,2,4,5,6,7] => 2

[[[[[]]],[]],[],[]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [1,4,5,2,3,6,7] => 2

[[[[],[],[]]],[],[]] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [1,3,5,2,4,6,7] => 2

[[[[],[[]]]],[],[]] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [1,3,4,2,5,6,7] => 2

[[[[[]],[]]],[],[]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [1,4,2,3,5,6,7] => 2

[[[[[],[]]]],[],[]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [1,4,2,5,3,6,7] => 6

[[[],[],[],[]],[[]]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => 1

[[[],[],[[]]],[[]]] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [1,2,3,5,4,6,7] => 2

[[[],[[]],[]],[[]]] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [1,2,4,5,3,6,7] => 2

[[[],[[],[]]],[[]]] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [1,2,4,3,5,6,7] => 2

[[[],[[[]]]],[[]]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [1,2,5,3,4,6,7] => 2

[[[[]],[],[]],[[]]] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [1,3,4,5,2,6,7] => 2

[[[[]],[[]]],[[]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [1,3,5,2,4,6,7] => 2

[[[[],[]],[]],[[]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [1,3,2,4,5,6,7] => 2

[[[[[]]],[]],[[]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [1,4,5,2,3,6,7] => 2

[[[[],[],[]]],[[]]] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [1,3,5,2,4,6,7] => 2

[[[[],[[]]]],[[]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [1,3,4,2,5,6,7] => 2

[[[[[]],[]]],[[]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [1,4,2,3,5,6,7] => 2

[[[[[],[]]]],[[]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [1,4,2,5,3,6,7] => 6

[[[],[],[],[],[]],[]] => [[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => 1

[[[],[],[],[[]]],[]] => [[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [1,2,3,4,6,5,7] => 2

[[[],[],[[]],[]],[]] => [[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [1,2,3,5,6,4,7] => 2

[[[],[],[[],[]]],[]] => [[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [1,2,3,5,4,6,7] => 2

[[[],[],[[[]]]],[]] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [1,2,3,6,4,5,7] => 2

[[[],[[]],[],[]],[]] => [[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [1,2,4,5,6,3,7] => 2

[[[],[[]],[[]]],[]] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [1,2,4,6,3,5,7] => 2

[[[],[[],[]],[]],[]] => [[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [1,2,4,3,5,6,7] => 2

[[[],[[[]]],[]],[]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [1,2,5,6,3,4,7] => 2

[[[],[[],[],[]]],[]] => [[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [1,2,4,6,3,5,7] => 2

[[[],[[],[[]]]],[]] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [1,2,4,5,3,6,7] => 2

[[[],[[[]],[]]],[]] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [1,2,5,3,4,6,7] => 2

[[[],[[[],[]]]],[]] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [1,2,5,3,6,4,7] => 6

[[[],[[[[]]]]],[]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [1,2,6,3,5,4,7] => 6

[[[[]],[],[],[]],[]] => [[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [1,3,4,5,6,2,7] => 2

[[[[]],[],[[]]],[]] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [1,3,4,6,2,5,7] => 2

[[[[]],[[]],[]],[]] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [1,3,5,6,2,4,7] => 2

[[[[]],[[],[]]],[]] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [1,3,5,4,6,2,7] => 6

[[[[]],[[[]]]],[]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [1,3,6,2,4,5,7] => 2

[[[[],[]],[],[]],[]] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [1,3,2,4,5,6,7] => 2

[[[[[]]],[],[]],[]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [1,4,5,6,2,3,7] => 2

[[[[],[]],[[]]],[]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [1,3,2,4,6,5,7] => 4

[[[[[]]],[[]]],[]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [1,4,6,2,3,5,7] => 2

[[[[],[],[]],[]],[]] => [[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [1,3,5,6,2,4,7] => 2

[[[[],[[]]],[]],[]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [1,3,4,2,5,6,7] => 2

[[[[[]],[]],[]],[]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [1,4,2,3,5,6,7] => 2

[[[[[],[]]],[]],[]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [1,4,2,5,6,3,7] => 6

[[[[],[],[],[]]],[]] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [1,3,5,2,4,6,7] => 2

[[[[],[],[[]]]],[]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [1,3,6,2,4,5,7] => 2

[[[[],[[]],[]]],[]] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [1,3,4,6,2,5,7] => 2

[[[[],[[],[]]]],[]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [1,3,6,2,5,4,7] => 6

[[[[],[[[]]]]],[]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [1,3,5,2,6,4,7] => 6

[[[[[]],[],[]]],[]] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [1,4,6,2,3,5,7] => 2

[[[[[]],[[]]]],[]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [1,4,5,2,3,6,7] => 2

[[[[[],[]],[]]],[]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [1,4,6,2,5,3,7] => 6

[[[[[],[],[]]]],[]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [1,4,3,6,2,5,7] => 6

[[[[[],[[]]]]],[]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [1,4,3,5,2,6,7] => 6

[[[],[],[],[],[],[]]] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => 1

[[[],[],[],[],[[]]]] => [.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => 2

[[[],[],[],[[]],[]]] => [.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [1,2,3,4,6,7,5] => 2

[[[],[],[],[[],[]]]] => [.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [1,2,3,4,6,5,7] => 2

[[[],[],[],[[[]]]]] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [1,2,3,4,7,5,6] => 2

[[[],[],[[]],[],[]]] => [.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [1,2,3,5,6,7,4] => 2

[[[],[],[[]],[[]]]] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [1,2,3,5,7,4,6] => 2

[[[],[],[[],[]],[]]] => [.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [1,2,3,5,4,6,7] => 2

[[[],[],[[[]]],[]]] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [1,2,3,6,7,4,5] => 2

[[[],[],[[],[],[]]]] => [.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [1,2,3,5,7,4,6] => 2

[[[],[],[[],[[]]]]] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [1,2,3,5,6,4,7] => 2

[[[],[],[[[]],[]]]] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [1,2,3,6,4,5,7] => 2

[[[],[],[[[],[]]]]] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [1,2,3,6,4,7,5] => 6

[[[],[],[[[[]]]]]] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [1,2,3,7,4,6,5] => 6

[[[],[[]],[],[],[]]] => [.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [1,2,4,5,6,7,3] => 2

[[[],[[]],[],[[]]]] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [1,2,4,5,7,3,6] => 2

[[[],[[]],[[]],[]]] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [1,2,4,6,7,3,5] => 2

[[[],[[]],[[],[]]]] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [1,2,4,6,5,7,3] => 4

[[[],[[]],[[[]]]]] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [1,2,4,7,3,5,6] => 2

[[[],[[],[]],[],[]]] => [.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [1,2,4,3,5,6,7] => 2

[[[],[[[]]],[],[]]] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [1,2,5,6,7,3,4] => 2

[[[],[[],[]],[[]]]] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [1,2,4,3,5,7,6] => 4

[[[],[[[]]],[[]]]] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [1,2,5,7,3,4,6] => 2

[[[],[[],[],[]],[]]] => [.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [1,2,4,6,7,3,5] => 2

[[[],[[],[[]]],[]]] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [1,2,4,5,3,6,7] => 2

[[[],[[[]],[]],[]]] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [1,2,5,3,4,6,7] => 2

[[[],[[[],[]]],[]]] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [1,2,5,3,6,7,4] => 6

[[[],[[[[]]]],[]]] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [1,2,6,7,3,5,4] => 6

[[[],[[],[],[],[]]]] => [.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [1,2,4,6,3,5,7] => 2

[[[],[[],[],[[]]]]] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [1,2,4,7,3,5,6] => 2

[[[],[[],[[]],[]]]] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [1,2,4,5,7,3,6] => 2

[[[],[[],[[],[]]]]] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [1,2,4,7,3,6,5] => 6

[[[],[[],[[[]]]]]] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [1,2,4,6,3,7,5] => 6

[[[],[[[]],[],[]]]] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [1,2,5,7,3,4,6] => 2

[[[],[[[]],[[]]]]] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [1,2,5,6,3,4,7] => 2

[[[],[[[],[]],[]]]] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [1,2,5,7,3,6,4] => 6

[[[],[[[[]]],[]]]] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [1,2,6,3,5,7,4] => 6

[[[],[[[],[],[]]]]] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [1,2,5,4,7,3,6] => 6

[[[],[[[],[[]]]]]] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [1,2,5,4,6,3,7] => 6

[[[],[[[[]],[]]]]] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [1,2,6,3,5,4,7] => 6

[[[],[[[[],[]]]]]] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [1,2,6,3,7,4,5] => 6

[[[],[[[[[]]]]]]] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [1,2,7,3,6,4,5] => 6

[[[[]],[],[],[],[]]] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [1,3,4,5,6,7,2] => 2

[[[[]],[],[],[[]]]] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [1,3,4,5,7,2,6] => 2

[[[[]],[],[[]],[]]] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [1,3,4,6,7,2,5] => 2

[[[[]],[],[[],[]]]] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [1,3,4,6,5,7,2] => 4

[[[[]],[],[[[]]]]] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [1,3,4,7,2,5,6] => 2

[[[[]],[[]],[],[]]] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [1,3,5,6,7,2,4] => 2

[[[[]],[[]],[[]]]] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [1,3,5,7,2,4,6] => 2

[[[[]],[[],[]],[]]] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [1,3,5,4,6,7,2] => 4

[[[[]],[[[]]],[]]] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [1,3,6,7,2,4,5] => 2

[[[[]],[[],[],[]]]] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [1,3,5,7,2,4,6] => 2

[[[[]],[[],[[]]]]] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [1,3,5,6,4,7,2] => 4

[[[[]],[[[]],[]]]] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [1,3,6,4,5,7,2] => 4

[[[[]],[[[],[]]]]] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [1,3,6,4,7,2,5] => 6

[[[[]],[[[[]]]]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [1,3,7,2,4,6,5] => 6

[[[[],[]],[],[],[]]] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [1,3,2,4,5,6,7] => 2

[[[[[]]],[],[],[]]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [1,4,5,6,7,2,3] => 2

[[[[],[]],[],[[]]]] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [1,3,2,4,5,7,6] => 4

[[[[[]]],[],[[]]]] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [1,4,5,7,2,3,6] => 2

[[[[],[]],[[]],[]]] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [1,3,2,4,6,7,5] => 4

[[[[],[]],[[],[]]]] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [1,3,2,4,6,5,7] => 4

[[[[],[]],[[[]]]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [1,3,2,4,7,5,6] => 4

[[[[],[],[]],[],[]]] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [1,3,5,6,7,2,4] => 2

[[[[],[[]]],[],[]]] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [1,3,4,2,5,6,7] => 2

[[[[[]],[]],[],[]]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [1,4,2,3,5,6,7] => 2

[[[[[],[]]],[],[]]] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [1,4,2,5,6,7,3] => 6

[[[[],[],[]],[[]]]] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [1,3,5,7,2,4,6] => 2

[[[[],[[]]],[[]]]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [1,3,4,2,5,7,6] => 4

[[[[[]],[]],[[]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [1,4,2,3,5,7,6] => 4

[[[[[],[]]],[[]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [1,4,2,5,7,3,6] => 6

[[[[],[],[],[]],[]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [1,3,5,2,4,6,7] => 2

[[[[],[],[[]]],[]]] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [1,3,6,7,2,4,5] => 2

[[[[],[[]],[]],[]]] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [1,3,4,6,7,2,5] => 2

[[[[],[[],[]]],[]]] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [1,3,6,7,2,5,4] => 6

[[[[],[[[]]]],[]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [1,3,5,2,6,7,4] => 6

[[[[[]],[[]]],[]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [1,4,5,2,3,6,7] => 2

[[[[[],[],[]]],[]]] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [1,4,3,6,7,2,5] => 6

[[[[[],[[]]]],[]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [1,4,3,5,2,6,7] => 6

[[[[],[],[],[],[]]]] => [.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [1,3,5,7,2,4,6] => 2

[[[[],[],[],[[]]]]] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [1,3,5,6,2,4,7] => 2

[[[[],[],[[]],[]]]] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [1,3,6,2,4,5,7] => 2

[[[[],[],[[],[]]]]] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [1,3,6,2,4,7,5] => 6

[[[[],[],[[[]]]]]] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [1,3,7,2,4,6,5] => 6

[[[[],[[]],[],[]]]] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [1,3,4,6,2,5,7] => 2

[[[[],[[]],[[]]]]] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [1,3,4,7,2,5,6] => 2

[[[[],[[],[]],[]]]] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [1,3,6,2,5,7,4] => 6

[[[[],[[[]]],[]]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [1,3,5,7,2,6,4] => 6

[[[[],[[],[],[]]]]] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [1,3,6,2,5,4,7] => 6

[[[[],[[],[[]]]]]] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [1,3,7,2,5,4,6] => 6

[[[[],[[[]],[]]]]] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [1,3,5,4,7,2,6] => 6

[[[[],[[[],[]]]]]] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [1,3,7,2,6,4,5] => 6

[[[[],[[[[]]]]]]] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [1,3,6,2,7,4,5] => 6

[[[[[]],[],[],[]]]] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [1,4,6,2,3,5,7] => 2

[[[[[]],[[]],[]]]] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [1,4,5,7,2,3,6] => 2

[[[[[]],[[[]]]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [1,4,6,2,3,7,5] => 6

[[[[[],[]],[],[]]]] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [1,4,6,2,5,7,3] => 6

[[[[[],[],[]],[]]]] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [1,4,3,6,2,5,7] => 6

[[[[[],[[]]],[]]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [1,4,3,5,7,2,6] => 6

[[[[[],[],[[]]]]]] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [1,4,6,2,5,3,7] => 6

[[[[[],[[],[]]]]]] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [1,4,5,3,7,2,6] => 6

[[[[[],[[[]]]]]]] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [1,4,5,3,6,2,7] => 6

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

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$F_{2} = q$

$F_{3} = 2\ q$

$F_{4} = 4\ q + q^{2}$

$F_{5} = 8\ q + 6\ q^{2}$

$F_{6} = 16\ q + 24\ q^{2} + 2\ q^{6}$

$F_{7} = 32\ q + 80\ q^{2} + 3\ q^{4} + 17\ q^{6}$

Description

The number of permutations with the same set of runs.
For example, the set of runs of

$4132$ is

$\{(13), (2), (4)\}$ . The only other permutation with this set of runs is

$4213$ , so the statistic equals

$2$ for these two permutations.

Map

to binary tree: left brother = left child

Description

Return a binary tree of size

$n-1$ (where

$n$ is the size of

$t$ , and where

$t$ is an ordered tree) by the following recursive rule:
- if

$x$ is the left brother of

$y$ in

$t$ , then

$x$ becomes the left child of

$y$ ;
- if

$x$ is the last child of

$y$ in

$t$ , then

$x$ becomes the right child of

$y$ ,
and removing the root of

$t$ .

Map

cycle-as-one-line notation

Description

Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.

Map

to 312-avoiding permutation

Description

Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.