Identifier
-
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
St000396: Binary trees ⟶ ℤ
Values
[.,.] => [1] => [.,.] => 1
[.,[.,.]] => [2,1] => [[.,.],.] => 1
[[.,.],.] => [1,2] => [.,[.,.]] => 1
[.,[.,[.,.]]] => [3,2,1] => [[[.,.],.],.] => 1
[.,[[.,.],.]] => [2,3,1] => [[.,.],[.,.]] => 2
[[.,.],[.,.]] => [1,3,2] => [.,[[.,.],.]] => 1
[[.,[.,.]],.] => [2,1,3] => [[.,.],[.,.]] => 2
[[[.,.],.],.] => [1,2,3] => [.,[.,[.,.]]] => 1
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [[[[.,.],.],.],.] => 1
[.,[.,[[.,.],.]]] => [3,4,2,1] => [[[.,.],.],[.,.]] => 2
[.,[[.,.],[.,.]]] => [2,4,3,1] => [[.,.],[[.,.],.]] => 2
[.,[[.,[.,.]],.]] => [3,2,4,1] => [[[.,.],.],[.,.]] => 2
[.,[[[.,.],.],.]] => [2,3,4,1] => [[.,.],[.,[.,.]]] => 2
[[.,.],[.,[.,.]]] => [1,4,3,2] => [.,[[[.,.],.],.]] => 1
[[.,.],[[.,.],.]] => [1,3,4,2] => [.,[[.,.],[.,.]]] => 2
[[.,[.,.]],[.,.]] => [2,1,4,3] => [[.,.],[[.,.],.]] => 2
[[[.,.],.],[.,.]] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 1
[[.,[.,[.,.]]],.] => [3,2,1,4] => [[[.,.],.],[.,.]] => 2
[[.,[[.,.],.]],.] => [2,3,1,4] => [[.,.],[.,[.,.]]] => 2
[[[.,.],[.,.]],.] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 2
[[[.,[.,.]],.],.] => [2,1,3,4] => [[.,.],[.,[.,.]]] => 2
[[[[.,.],.],.],.] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 1
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => 1
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => 2
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [[[.,.],.],[[.,.],.]] => 2
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => 2
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => 2
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]] => 2
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]] => 2
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [[[.,.],.],[[.,.],.]] => 2
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]] => 2
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => 2
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => 2
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]] => 2
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => 2
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => 2
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => 1
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [.,[[[.,.],.],[.,.]]] => 2
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [.,[[.,.],[[.,.],.]]] => 2
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]] => 2
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => 2
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => 2
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => 2
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => 1
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => 2
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => 2
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => 2
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => 2
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => 2
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 1
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => 2
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => 2
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [[.,.],[[.,.],[.,.]]] => 2
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => 2
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => 2
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => 2
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => 2
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => 2
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 2
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => 2
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => 2
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 2
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => 2
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => 2
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [[[[.,.],.],.],[[.,.],.]] => 2
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => 2
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => 2
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [[[.,.],.],[[[.,.],.],.]] => 2
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [[[.,.],.],[[.,.],[.,.]]] => 2
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [[[[.,.],.],.],[[.,.],.]] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [[[.,.],.],[.,[[.,.],.]]] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]] => 2
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => 2
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [[[.,.],.],[[.,.],[.,.]]] => 2
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => 2
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]] => 2
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [[.,.],[[[.,.],.],[.,.]]] => 2
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [[.,.],[[.,.],[[.,.],.]]] => 2
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [[.,.],[[[.,.],.],[.,.]]] => 2
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [[[.,.],.],[[[.,.],.],.]] => 2
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [[[.,.],.],[[.,.],[.,.]]] => 2
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [[.,.],[.,[[[.,.],.],.]]] => 2
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [[[[.,.],.],.],[[.,.],.]] => 2
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => 2
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [[.,.],[[.,.],[[.,.],.]]] => 2
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => 2
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => 2
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => 2
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [[[.,.],.],[[.,.],[.,.]]] => 2
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => 2
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [[.,.],[[[.,.],.],[.,.]]] => 2
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => 2
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]] => 2
>>> Load all 1247 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => 2
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => 1
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [.,[[[[.,.],.],.],[.,.]]] => 2
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [.,[[[.,.],.],[[.,.],.]]] => 2
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [.,[[[[.,.],.],.],[.,.]]] => 2
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [.,[[[.,.],.],[.,[.,.]]]] => 2
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [.,[[.,.],[[[.,.],.],.]]] => 2
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]] => 2
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]] => 2
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => 2
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => 2
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [[.,.],[[[.,.],.],[.,.]]] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [[.,.],[[.,.],[[.,.],.]]] => 2
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => 2
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => 1
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [.,[.,[[[.,.],.],[.,.]]]] => 2
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]] => 2
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]] => 2
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]] => 2
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [[[.,.],.],[[.,.],[.,.]]] => 2
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => 2
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => 2
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => 2
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => 1
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => 2
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => 2
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [[.,.],[[.,.],[[.,.],.]]] => 2
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => 2
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => 2
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => 2
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 2
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => 2
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => 2
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => 2
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [[[.,.],.],[[.,.],[.,.]]] => 2
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => 2
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [[.,.],[[[.,.],.],[.,.]]] => 2
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [[[.,.],.],[[.,.],[.,.]]] => 2
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => 2
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => 2
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => 2
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => 2
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => 2
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 2
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]] => 2
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 2
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[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => 1
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[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => 2
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[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => 1
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[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
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[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => 2
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => 2
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 2
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => 2
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 2
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 2
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => 2
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 2
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => 2
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 2
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 2
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 2
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => 2
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 2
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 2
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => 2
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => 2
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => 2
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 2
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 2
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => 2
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => 2
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 2
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => 2
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => 2
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 2
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => 2
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => 2
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]] => 2
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => 2
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => 2
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => 2
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => 2
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => 2
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 2
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 2
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 2
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => 2
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
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[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => 2
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => 2
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[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,3,6,5,4,2,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => 2
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 2
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[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 2
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[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 2
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 2
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [2,3,1,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => 2
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => 2
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,3,2,5,6,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 2
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => 2
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[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 2
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 2
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => 2
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => 2
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 2
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => 2
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[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 2
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
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[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => 2
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[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 2
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[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => 2
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 2
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[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 2
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 2
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 1
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => 2
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [2,6,7,5,4,3,1,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => 2
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [2,5,7,6,4,3,1,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => 2
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[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => 2
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[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => 2
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => 2
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,4,3,2,6,7,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => 2
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [2,1,4,3,6,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,2,4,3,6,7,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 2
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => 2
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,3,2,4,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => 2
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [2,5,4,3,1,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => 2
[[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [2,4,5,3,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 2
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [2,3,5,4,1,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 2
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 2
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => 2
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => 2
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 2
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => 2
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => 2
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,2,4,5,3,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 2
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 2
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 2
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 2
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [2,3,4,1,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => 2
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,3,4,2,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 2
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [2,4,6,5,3,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [2,4,5,6,3,1,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => 2
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [2,3,5,6,4,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [2,4,3,6,5,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => 2
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,5,6,4,3,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => 2
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,4,6,5,3,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => 2
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,5,4,6,3,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => 2
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,4,5,6,3,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => 2
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => 2
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => 2
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => 2
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,4,3,5,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => 2
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [2,1,5,6,4,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => 2
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [2,1,4,6,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => 2
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => 2
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 2
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [2,3,1,6,5,4,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => 2
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [2,3,1,5,6,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => 2
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,3,2,5,6,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => 2
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [2,4,3,1,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 2
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => 2
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => 2
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => 2
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,4,3,5,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => 2
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => 2
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => 2
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => 2
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
search for individual values
searching the database for the individual values of this statistic
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search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
3,2 4,10 5,37 6,126 7,422
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 3\ q + 2\ q^{2}$
$F_{4} = 4\ q + 10\ q^{2}$
$F_{5} = 5\ q + 37\ q^{2}$
$F_{6} = 6\ q + 126\ q^{2}$
$F_{7} = 7\ q + 422\ q^{2}$
Description
The register function (or Horton-Strahler number) of a binary tree.
This is different from the dimension of the associated poset for the tree $[[[.,.],[.,.]],[[.,.],[.,.]]]$: its register function is 3, whereas the dimension of the associated poset is 2.
This is different from the dimension of the associated poset for the tree $[[[.,.],[.,.]],[[.,.],[.,.]]]$: its register function is 3, whereas the dimension of the associated poset is 2.
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.
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.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
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