Identifier
-
Mp00072:
Permutations
—binary search tree: left to right⟶
Binary trees
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
St000168: Ordered trees ⟶ ℤ
Values
[1] => [.,.] => [[]] => 0
[1,2] => [.,[.,.]] => [[[]]] => 1
[2,1] => [[.,.],.] => [[],[]] => 0
[1,2,3] => [.,[.,[.,.]]] => [[[[]]]] => 2
[1,3,2] => [.,[[.,.],.]] => [[[],[]]] => 1
[2,1,3] => [[.,.],[.,.]] => [[],[[]]] => 1
[2,3,1] => [[.,.],[.,.]] => [[],[[]]] => 1
[3,1,2] => [[.,[.,.]],.] => [[[]],[]] => 1
[3,2,1] => [[[.,.],.],.] => [[],[],[]] => 0
[1,2,3,4] => [.,[.,[.,[.,.]]]] => [[[[[]]]]] => 3
[1,2,4,3] => [.,[.,[[.,.],.]]] => [[[[],[]]]] => 2
[1,3,2,4] => [.,[[.,.],[.,.]]] => [[[],[[]]]] => 2
[1,3,4,2] => [.,[[.,.],[.,.]]] => [[[],[[]]]] => 2
[1,4,2,3] => [.,[[.,[.,.]],.]] => [[[[]],[]]] => 2
[1,4,3,2] => [.,[[[.,.],.],.]] => [[[],[],[]]] => 1
[2,1,3,4] => [[.,.],[.,[.,.]]] => [[],[[[]]]] => 2
[2,1,4,3] => [[.,.],[[.,.],.]] => [[],[[],[]]] => 1
[2,3,1,4] => [[.,.],[.,[.,.]]] => [[],[[[]]]] => 2
[2,3,4,1] => [[.,.],[.,[.,.]]] => [[],[[[]]]] => 2
[2,4,1,3] => [[.,.],[[.,.],.]] => [[],[[],[]]] => 1
[2,4,3,1] => [[.,.],[[.,.],.]] => [[],[[],[]]] => 1
[3,1,2,4] => [[.,[.,.]],[.,.]] => [[[]],[[]]] => 2
[3,1,4,2] => [[.,[.,.]],[.,.]] => [[[]],[[]]] => 2
[3,2,1,4] => [[[.,.],.],[.,.]] => [[],[],[[]]] => 1
[3,2,4,1] => [[[.,.],.],[.,.]] => [[],[],[[]]] => 1
[3,4,1,2] => [[.,[.,.]],[.,.]] => [[[]],[[]]] => 2
[3,4,2,1] => [[[.,.],.],[.,.]] => [[],[],[[]]] => 1
[4,1,2,3] => [[.,[.,[.,.]]],.] => [[[[]]],[]] => 2
[4,1,3,2] => [[.,[[.,.],.]],.] => [[[],[]],[]] => 1
[4,2,1,3] => [[[.,.],[.,.]],.] => [[],[[]],[]] => 1
[4,2,3,1] => [[[.,.],[.,.]],.] => [[],[[]],[]] => 1
[4,3,1,2] => [[[.,[.,.]],.],.] => [[[]],[],[]] => 1
[4,3,2,1] => [[[[.,.],.],.],.] => [[],[],[],[]] => 0
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [[[[[[]]]]]] => 4
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [[[[[],[]]]]] => 3
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [[[[],[[]]]]] => 3
[1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => [[[[],[[]]]]] => 3
[1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => [[[[[]],[]]]] => 3
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [[[[],[],[]]]] => 2
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]] => 3
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => 2
[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]] => 3
[1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]] => 3
[1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => 2
[1,3,5,4,2] => [.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => 2
[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => [[[[]],[[]]]] => 3
[1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]] => [[[[]],[[]]]] => 3
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]] => 2
[1,4,3,5,2] => [.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]] => 2
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [[[[]],[[]]]] => 3
[1,4,5,3,2] => [.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]] => 2
[1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => [[[[[]]],[]]] => 3
[1,5,2,4,3] => [.,[[.,[[.,.],.]],.]] => [[[[],[]],[]]] => 2
[1,5,3,2,4] => [.,[[[.,.],[.,.]],.]] => [[[],[[]],[]]] => 2
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [[[],[[]],[]]] => 2
[1,5,4,2,3] => [.,[[[.,[.,.]],.],.]] => [[[[]],[],[]]] => 2
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [[[],[],[],[]]] => 1
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 3
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => 2
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 2
[2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 2
[2,1,5,3,4] => [[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => 2
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => [[],[[],[],[]]] => 1
[2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 3
[2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => 2
[2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 3
[2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 3
[2,3,5,1,4] => [[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => 2
[2,3,5,4,1] => [[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => 2
[2,4,1,3,5] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 2
[2,4,1,5,3] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 2
[2,4,3,1,5] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 2
[2,4,3,5,1] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 2
[2,4,5,1,3] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 2
[2,4,5,3,1] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 2
[2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => 2
[2,5,1,4,3] => [[.,.],[[[.,.],.],.]] => [[],[[],[],[]]] => 1
[2,5,3,1,4] => [[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => 2
[2,5,3,4,1] => [[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => 2
[2,5,4,1,3] => [[.,.],[[[.,.],.],.]] => [[],[[],[],[]]] => 1
[2,5,4,3,1] => [[.,.],[[[.,.],.],.]] => [[],[[],[],[]]] => 1
[3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 3
[3,1,2,5,4] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => 2
[3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 3
[3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 3
[3,1,5,2,4] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => 2
[3,1,5,4,2] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => 2
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 2
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => 1
[3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 2
[3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 2
[3,2,5,1,4] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => 1
[3,2,5,4,1] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => 1
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 3
[3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 3
[3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 2
[3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 2
[3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 3
[3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 2
[3,5,1,2,4] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => 2
[3,5,1,4,2] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => 2
>>> Load all 873 entries. <<<[3,5,2,1,4] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => 1
[3,5,2,4,1] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => 1
[3,5,4,1,2] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => 2
[3,5,4,2,1] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => 1
[4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => 3
[4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => 3
[4,1,3,2,5] => [[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => 2
[4,1,3,5,2] => [[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => 2
[4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => 3
[4,1,5,3,2] => [[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => 2
[4,2,1,3,5] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 2
[4,2,1,5,3] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 2
[4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 2
[4,2,3,5,1] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 2
[4,2,5,1,3] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 2
[4,2,5,3,1] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 2
[4,3,1,2,5] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => 2
[4,3,1,5,2] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => 2
[4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 1
[4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 1
[4,3,5,1,2] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => 2
[4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 1
[4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => 3
[4,5,1,3,2] => [[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => 2
[4,5,2,1,3] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 2
[4,5,2,3,1] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 2
[4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => 2
[4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 1
[5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => [[[[[]]]],[]] => 3
[5,1,2,4,3] => [[.,[.,[[.,.],.]]],.] => [[[[],[]]],[]] => 2
[5,1,3,2,4] => [[.,[[.,.],[.,.]]],.] => [[[],[[]]],[]] => 2
[5,1,3,4,2] => [[.,[[.,.],[.,.]]],.] => [[[],[[]]],[]] => 2
[5,1,4,2,3] => [[.,[[.,[.,.]],.]],.] => [[[[]],[]],[]] => 2
[5,1,4,3,2] => [[.,[[[.,.],.],.]],.] => [[[],[],[]],[]] => 1
[5,2,1,3,4] => [[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => 2
[5,2,1,4,3] => [[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => 1
[5,2,3,1,4] => [[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => 2
[5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => 2
[5,2,4,1,3] => [[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => 1
[5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => 1
[5,3,1,2,4] => [[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => 2
[5,3,1,4,2] => [[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => 2
[5,3,2,1,4] => [[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => 1
[5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => 1
[5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => 2
[5,3,4,2,1] => [[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => 1
[5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => [[[[]]],[],[]] => 2
[5,4,1,3,2] => [[[.,[[.,.],.]],.],.] => [[[],[]],[],[]] => 1
[5,4,2,1,3] => [[[[.,.],[.,.]],.],.] => [[],[[]],[],[]] => 1
[5,4,2,3,1] => [[[[.,.],[.,.]],.],.] => [[],[[]],[],[]] => 1
[5,4,3,1,2] => [[[[.,[.,.]],.],.],.] => [[[]],[],[],[]] => 1
[5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [[],[],[],[],[]] => 0
[1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [[[[[[[]]]]]]] => 5
[1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [[[[[[],[]]]]]] => 4
[1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [[[[[],[[]]]]]] => 4
[1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => [[[[[],[[]]]]]] => 4
[1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => [[[[[[]],[]]]]] => 4
[1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => [[[[[],[],[]]]]] => 3
[1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [[[[],[[[]]]]]] => 4
[1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [[[[],[[],[]]]]] => 3
[1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [[[[],[[[]]]]]] => 4
[1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => [[[[],[[[]]]]]] => 4
[1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => [[[[],[[],[]]]]] => 3
[1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]] => [[[[],[[],[]]]]] => 3
[1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [[[[[]],[[]]]]] => 4
[1,2,5,3,6,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [[[[[]],[[]]]]] => 4
[1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => [[[[],[],[[]]]]] => 3
[1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]] => [[[[],[],[[]]]]] => 3
[1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [[[[[]],[[]]]]] => 4
[1,2,5,6,4,3] => [.,[.,[[[.,.],.],[.,.]]]] => [[[[],[],[[]]]]] => 3
[1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => [[[[[[]]],[]]]] => 4
[1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]] => [[[[[],[]],[]]]] => 3
[1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]] => [[[[],[[]],[]]]] => 3
[1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => [[[[],[[]],[]]]] => 3
[1,2,6,5,3,4] => [.,[.,[[[.,[.,.]],.],.]]] => [[[[[]],[],[]]]] => 3
[1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => [[[[],[],[],[]]]] => 2
[1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [[[],[[[[]]]]]] => 4
[1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => 3
[1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 3
[1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 3
[1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => [[[],[[[]],[]]]] => 3
[1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [[[],[[],[],[]]]] => 2
[1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [[[],[[[[]]]]]] => 4
[1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => 3
[1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [[[],[[[[]]]]]] => 4
[1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => [[[],[[[[]]]]]] => 4
[1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => 3
[1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => 3
[1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 3
[1,3,5,2,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 3
[1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 3
[1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 3
[1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 3
[1,3,5,6,4,2] => [.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 3
[1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => [[[],[[[]],[]]]] => 3
[1,3,6,2,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [[[],[[],[],[]]]] => 2
[1,3,6,4,2,5] => [.,[[.,.],[[.,[.,.]],.]]] => [[[],[[[]],[]]]] => 3
[1,3,6,4,5,2] => [.,[[.,.],[[.,[.,.]],.]]] => [[[],[[[]],[]]]] => 3
[1,3,6,5,2,4] => [.,[[.,.],[[[.,.],.],.]]] => [[[],[[],[],[]]]] => 2
[1,3,6,5,4,2] => [.,[[.,.],[[[.,.],.],.]]] => [[[],[[],[],[]]]] => 2
[1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [[[[]],[[[]]]]] => 4
[1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => [[[[]],[[],[]]]] => 3
[1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [[[[]],[[[]]]]] => 4
[1,4,2,5,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [[[[]],[[[]]]]] => 4
[1,4,2,6,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => [[[[]],[[],[]]]] => 3
[1,4,2,6,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => [[[[]],[[],[]]]] => 3
[1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]] => 3
[1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]] => 2
[1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]] => 3
[1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]] => 3
[1,4,3,6,2,5] => [.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]] => 2
[1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]] => 2
[1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [[[[]],[[[]]]]] => 4
[1,4,5,2,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [[[[]],[[[]]]]] => 4
[1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]] => 3
[1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]] => 3
[1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [[[[]],[[[]]]]] => 4
[1,4,5,6,3,2] => [.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]] => 3
[1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => [[[[]],[[],[]]]] => 3
[1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => [[[[]],[[],[]]]] => 3
[1,4,6,3,2,5] => [.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]] => 2
[1,4,6,3,5,2] => [.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]] => 2
[1,4,6,5,2,3] => [.,[[.,[.,.]],[[.,.],.]]] => [[[[]],[[],[]]]] => 3
[1,4,6,5,3,2] => [.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]] => 2
[1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => [[[[[]]],[[]]]] => 4
[1,5,2,3,6,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [[[[[]]],[[]]]] => 4
[1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]] => [[[[],[]],[[]]]] => 3
[1,5,2,4,6,3] => [.,[[.,[[.,.],.]],[.,.]]] => [[[[],[]],[[]]]] => 3
[1,5,2,6,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [[[[[]]],[[]]]] => 4
[1,5,2,6,4,3] => [.,[[.,[[.,.],.]],[.,.]]] => [[[[],[]],[[]]]] => 3
[1,5,3,2,4,6] => [.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 3
[1,5,3,2,6,4] => [.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 3
[1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 3
[1,5,3,4,6,2] => [.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 3
[1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 3
[1,5,3,6,4,2] => [.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 3
[1,5,4,2,3,6] => [.,[[[.,[.,.]],.],[.,.]]] => [[[[]],[],[[]]]] => 3
[1,5,4,2,6,3] => [.,[[[.,[.,.]],.],[.,.]]] => [[[[]],[],[[]]]] => 3
[1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => [[[],[],[],[[]]]] => 2
[1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]] => [[[],[],[],[[]]]] => 2
[1,5,4,6,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => [[[[]],[],[[]]]] => 3
[1,5,4,6,3,2] => [.,[[[[.,.],.],.],[.,.]]] => [[[],[],[],[[]]]] => 2
[1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [[[[[]]],[[]]]] => 4
[1,5,6,2,4,3] => [.,[[.,[[.,.],.]],[.,.]]] => [[[[],[]],[[]]]] => 3
[1,5,6,3,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 3
[1,5,6,3,4,2] => [.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 3
[1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => [[[[]],[],[[]]]] => 3
[1,5,6,4,3,2] => [.,[[[[.,.],.],.],[.,.]]] => [[[],[],[],[[]]]] => 2
[1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => [[[[[[]]]],[]]] => 4
[1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]] => [[[[[],[]]],[]]] => 3
[1,6,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],.]] => [[[[],[[]]],[]]] => 3
[1,6,2,4,5,3] => [.,[[.,[[.,.],[.,.]]],.]] => [[[[],[[]]],[]]] => 3
[1,6,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],.]] => [[[[[]],[]],[]]] => 3
[1,6,2,5,4,3] => [.,[[.,[[[.,.],.],.]],.]] => [[[[],[],[]],[]]] => 2
[1,6,3,2,4,5] => [.,[[[.,.],[.,[.,.]]],.]] => [[[],[[[]]],[]]] => 3
[1,6,3,2,5,4] => [.,[[[.,.],[[.,.],.]],.]] => [[[],[[],[]],[]]] => 2
[1,6,3,4,2,5] => [.,[[[.,.],[.,[.,.]]],.]] => [[[],[[[]]],[]]] => 3
[1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => [[[],[[[]]],[]]] => 3
[1,6,3,5,2,4] => [.,[[[.,.],[[.,.],.]],.]] => [[[],[[],[]],[]]] => 2
[1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]] => [[[],[[],[]],[]]] => 2
[1,6,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],.]] => [[[[]],[[]],[]]] => 3
[1,6,4,2,5,3] => [.,[[[.,[.,.]],[.,.]],.]] => [[[[]],[[]],[]]] => 3
[1,6,4,3,2,5] => [.,[[[[.,.],.],[.,.]],.]] => [[[],[],[[]],[]]] => 2
[1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => [[[],[],[[]],[]]] => 2
[1,6,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],.]] => [[[[]],[[]],[]]] => 3
[1,6,4,5,3,2] => [.,[[[[.,.],.],[.,.]],.]] => [[[],[],[[]],[]]] => 2
[1,6,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],.]] => [[[[[]]],[],[]]] => 3
[1,6,5,2,4,3] => [.,[[[.,[[.,.],.]],.],.]] => [[[[],[]],[],[]]] => 2
[1,6,5,3,2,4] => [.,[[[[.,.],[.,.]],.],.]] => [[[],[[]],[],[]]] => 2
[1,6,5,3,4,2] => [.,[[[[.,.],[.,.]],.],.]] => [[[],[[]],[],[]]] => 2
[1,6,5,4,2,3] => [.,[[[[.,[.,.]],.],.],.]] => [[[[]],[],[],[]]] => 2
[1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => [[[],[],[],[],[]]] => 1
[2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 4
[2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[],[[[[],[]]]]] => 3
[2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 3
[2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 3
[2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [[],[[[[]],[]]]] => 3
[2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [[],[[[],[],[]]]] => 2
[2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,1,4,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,1,4,6,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,1,5,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,1,5,6,4,3] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [[],[[[[]]],[]]] => 3
[2,1,6,3,5,4] => [[.,.],[[.,[[.,.],.]],.]] => [[],[[[],[]],[]]] => 2
[2,1,6,4,3,5] => [[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[2,1,6,5,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [[],[[[]],[],[]]] => 2
[2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [[],[[],[],[],[]]] => 1
[2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 4
[2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[],[[[[],[]]]]] => 3
[2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 3
[2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 3
[2,3,1,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [[],[[[[]],[]]]] => 3
[2,3,1,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [[],[[[],[],[]]]] => 2
[2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 4
[2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[],[[[[],[]]]]] => 3
[2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 4
[2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 4
[2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[],[[[[],[]]]]] => 3
[2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]] => [[],[[[[],[]]]]] => 3
[2,3,5,1,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 3
[2,3,5,1,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 3
[2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 3
[2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 3
[2,3,5,6,1,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 3
[2,3,5,6,4,1] => [[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 3
[2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [[],[[[[]],[]]]] => 3
[2,3,6,1,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [[],[[[],[],[]]]] => 2
[2,3,6,4,1,5] => [[.,.],[.,[[.,[.,.]],.]]] => [[],[[[[]],[]]]] => 3
[2,3,6,4,5,1] => [[.,.],[.,[[.,[.,.]],.]]] => [[],[[[[]],[]]]] => 3
[2,3,6,5,1,4] => [[.,.],[.,[[[.,.],.],.]]] => [[],[[[],[],[]]]] => 2
[2,3,6,5,4,1] => [[.,.],[.,[[[.,.],.],.]]] => [[],[[[],[],[]]]] => 2
[2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,1,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,1,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,1,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,1,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,1,6,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,3,1,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,3,1,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,3,6,1,5] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,3,6,5,1] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,5,1,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,5,1,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,5,3,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,5,6,1,3] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,5,6,3,1] => [[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 3
[2,4,6,1,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,6,1,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,6,3,1,5] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,6,3,5,1] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,6,5,1,3] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,4,6,5,3,1] => [[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,1,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,1,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,1,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,1,6,4,3] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,3,1,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,3,1,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,3,4,1,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,3,4,6,1] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,3,6,1,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,3,6,4,1] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,4,1,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,4,1,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,4,3,1,6] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,4,3,6,1] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,4,6,1,3] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,4,6,3,1] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,6,1,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,6,1,4,3] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,6,3,1,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,6,3,4,1] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 3
[2,5,6,4,1,3] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,5,6,4,3,1] => [[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [[],[[[[]]],[]]] => 3
[2,6,1,3,5,4] => [[.,.],[[.,[[.,.],.]],.]] => [[],[[[],[]],[]]] => 2
[2,6,1,4,3,5] => [[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[2,6,1,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[2,6,1,5,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [[],[[[]],[],[]]] => 2
[2,6,1,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [[],[[],[],[],[]]] => 1
[2,6,3,1,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [[],[[[[]]],[]]] => 3
[2,6,3,1,5,4] => [[.,.],[[.,[[.,.],.]],.]] => [[],[[[],[]],[]]] => 2
[2,6,3,4,1,5] => [[.,.],[[.,[.,[.,.]]],.]] => [[],[[[[]]],[]]] => 3
[2,6,3,4,5,1] => [[.,.],[[.,[.,[.,.]]],.]] => [[],[[[[]]],[]]] => 3
[2,6,3,5,1,4] => [[.,.],[[.,[[.,.],.]],.]] => [[],[[[],[]],[]]] => 2
[2,6,3,5,4,1] => [[.,.],[[.,[[.,.],.]],.]] => [[],[[[],[]],[]]] => 2
[2,6,4,1,3,5] => [[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[2,6,4,1,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[2,6,4,3,1,5] => [[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[2,6,4,3,5,1] => [[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[2,6,4,5,1,3] => [[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[2,6,4,5,3,1] => [[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[2,6,5,1,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [[],[[[]],[],[]]] => 2
[2,6,5,1,4,3] => [[.,.],[[[[.,.],.],.],.]] => [[],[[],[],[],[]]] => 1
[2,6,5,3,1,4] => [[.,.],[[[.,[.,.]],.],.]] => [[],[[[]],[],[]]] => 2
[2,6,5,3,4,1] => [[.,.],[[[.,[.,.]],.],.]] => [[],[[[]],[],[]]] => 2
[2,6,5,4,1,3] => [[.,.],[[[[.,.],.],.],.]] => [[],[[],[],[],[]]] => 1
[2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]] => [[],[[],[],[],[]]] => 1
[3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 4
[3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 3
[3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,1,2,5,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 3
[3,1,2,6,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[3,1,4,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 4
[3,1,4,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 3
[3,1,4,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 4
[3,1,4,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 4
[3,1,4,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 3
[3,1,4,6,5,2] => [[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 3
[3,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,1,5,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,1,5,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,1,5,4,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,1,5,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,1,5,6,4,2] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,1,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 3
[3,1,6,2,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[3,1,6,4,2,5] => [[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 3
[3,1,6,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 3
[3,1,6,5,2,4] => [[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[3,1,6,5,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,2,1,5,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,2,1,6,4,5] => [[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 1
[3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[3,2,4,6,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[3,2,5,1,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,2,5,1,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,2,5,4,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,2,5,6,1,4] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,2,5,6,4,1] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,2,6,1,4,5] => [[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[3,2,6,1,5,4] => [[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 1
[3,2,6,4,1,5] => [[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[3,2,6,4,5,1] => [[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[3,2,6,5,1,4] => [[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 1
[3,2,6,5,4,1] => [[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 1
[3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 4
[3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 3
[3,4,1,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 4
[3,4,1,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 4
[3,4,1,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 3
[3,4,1,6,5,2] => [[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 3
[3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[3,4,2,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[3,4,2,6,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[3,4,2,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 4
[3,4,5,1,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 4
[3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 4
[3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[3,4,6,1,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 3
[3,4,6,1,5,2] => [[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 3
[3,4,6,2,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[3,4,6,2,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[3,4,6,5,1,2] => [[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 3
[3,4,6,5,2,1] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 2
[3,5,1,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,1,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,1,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,1,4,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,1,6,4,2] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,2,1,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,2,1,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,2,4,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,2,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,2,6,1,4] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,2,6,4,1] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,4,1,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,4,1,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,4,2,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,4,2,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,4,6,1,2] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,4,6,2,1] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,6,1,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,6,1,4,2] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,6,2,1,4] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,6,2,4,1] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,5,6,4,1,2] => [[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 3
[3,5,6,4,2,1] => [[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 2
[3,6,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 3
[3,6,1,2,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[3,6,1,4,2,5] => [[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 3
[3,6,1,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 3
[3,6,1,5,2,4] => [[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[3,6,1,5,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[3,6,2,1,4,5] => [[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[3,6,2,1,5,4] => [[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 1
[3,6,2,4,1,5] => [[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[3,6,2,4,5,1] => [[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[3,6,2,5,1,4] => [[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 1
[3,6,2,5,4,1] => [[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 1
[3,6,4,1,2,5] => [[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 3
[3,6,4,1,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 3
[3,6,4,2,1,5] => [[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[3,6,4,2,5,1] => [[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[3,6,4,5,1,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 3
[3,6,4,5,2,1] => [[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 2
[3,6,5,1,2,4] => [[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[3,6,5,1,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[3,6,5,2,1,4] => [[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 1
[3,6,5,2,4,1] => [[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 1
[3,6,5,4,1,2] => [[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[3,6,5,4,2,1] => [[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 1
[4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 4
[4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 3
[4,1,2,5,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 4
[4,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 4
[4,1,2,6,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 3
[4,1,2,6,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 3
[4,1,3,2,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 3
[4,1,3,2,6,5] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[4,1,3,5,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 3
[4,1,3,5,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 3
[4,1,3,6,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[4,1,3,6,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[4,1,5,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 4
[4,1,5,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 4
[4,1,5,3,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 3
[4,1,5,3,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 3
[4,1,5,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 4
[4,1,5,6,3,2] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 3
[4,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 3
[4,1,6,2,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 3
[4,1,6,3,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[4,1,6,3,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[4,1,6,5,2,3] => [[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 3
[4,1,6,5,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,1,3,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,1,5,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,1,5,6,3] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,1,6,3,5] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,1,6,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,3,6,1,5] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,3,6,5,1] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,5,1,6,3] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,5,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,5,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,5,6,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,5,6,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,2,6,1,3,5] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,6,1,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,6,3,1,5] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,6,3,5,1] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,6,5,1,3] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,2,6,5,3,1] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[4,3,1,2,6,5] => [[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[4,3,1,5,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[4,3,1,5,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[4,3,1,6,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[4,3,1,6,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 2
[4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 1
[4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 2
[4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 2
[4,3,2,6,1,5] => [[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 1
[4,3,2,6,5,1] => [[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 1
[4,3,5,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[4,3,5,1,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 2
[4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 2
[4,3,5,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 2
[4,3,6,1,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[4,3,6,1,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[4,3,6,2,1,5] => [[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 1
[4,3,6,2,5,1] => [[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 1
[4,3,6,5,1,2] => [[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[4,3,6,5,2,1] => [[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 1
[4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 4
[4,5,1,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 4
[4,5,1,3,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 3
[4,5,1,3,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 3
[4,5,1,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 4
[4,5,1,6,3,2] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 3
[4,5,2,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,5,2,1,6,3] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,5,2,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,5,2,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,5,2,6,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,5,2,6,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[4,5,3,1,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 2
[4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 2
[4,5,3,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 2
[4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 4
[4,5,6,1,3,2] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 3
[4,5,6,2,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,5,6,2,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[4,5,6,3,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 2
[4,6,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 3
[4,6,1,2,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 3
[4,6,1,3,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[4,6,1,3,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[4,6,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 3
[4,6,1,5,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[4,6,2,1,3,5] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,6,2,1,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,6,2,3,1,5] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,6,2,3,5,1] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,6,2,5,1,3] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,6,2,5,3,1] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,6,3,1,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[4,6,3,2,1,5] => [[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 1
[4,6,3,2,5,1] => [[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 1
[4,6,3,5,1,2] => [[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[4,6,3,5,2,1] => [[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 1
[4,6,5,1,2,3] => [[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 3
[4,6,5,1,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[4,6,5,2,1,3] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,6,5,2,3,1] => [[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 2
[4,6,5,3,1,2] => [[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 2
[4,6,5,3,2,1] => [[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 1
[5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[[[]]]],[[]]] => 4
[5,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[[[]]]],[[]]] => 4
[5,1,2,4,3,6] => [[.,[.,[[.,.],.]]],[.,.]] => [[[[],[]]],[[]]] => 3
[5,1,2,4,6,3] => [[.,[.,[[.,.],.]]],[.,.]] => [[[[],[]]],[[]]] => 3
[5,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[[[]]]],[[]]] => 4
[5,1,2,6,4,3] => [[.,[.,[[.,.],.]]],[.,.]] => [[[[],[]]],[[]]] => 3
[5,1,3,2,4,6] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 3
[5,1,3,2,6,4] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 3
[5,1,3,4,2,6] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 3
[5,1,3,4,6,2] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 3
[5,1,3,6,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 3
[5,1,3,6,4,2] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 3
[5,1,4,2,3,6] => [[.,[[.,[.,.]],.]],[.,.]] => [[[[]],[]],[[]]] => 3
[5,1,4,2,6,3] => [[.,[[.,[.,.]],.]],[.,.]] => [[[[]],[]],[[]]] => 3
[5,1,4,3,2,6] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[],[]],[[]]] => 2
[5,1,4,3,6,2] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[],[]],[[]]] => 2
[5,1,4,6,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => [[[[]],[]],[[]]] => 3
[5,1,4,6,3,2] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[],[]],[[]]] => 2
[5,1,6,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[[[]]]],[[]]] => 4
[5,1,6,2,4,3] => [[.,[.,[[.,.],.]]],[.,.]] => [[[[],[]]],[[]]] => 3
[5,1,6,3,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 3
[5,1,6,3,4,2] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 3
[5,1,6,4,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => [[[[]],[]],[[]]] => 3
[5,1,6,4,3,2] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[],[]],[[]]] => 2
[5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,1,3,6,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,1,4,3,6] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,1,4,6,3] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,1,6,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,1,6,4,3] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,3,1,6,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,3,6,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,4,1,3,6] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,4,1,6,3] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,4,3,1,6] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,4,3,6,1] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,4,6,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,4,6,3,1] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,6,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,6,1,4,3] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,6,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,6,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,2,6,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,2,6,4,3,1] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,1,2,6,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,1,4,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,1,4,6,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,1,6,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,1,6,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,2,1,6,4] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,2,4,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,2,6,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,2,6,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,4,2,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,4,2,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,4,6,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,6,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,6,1,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,6,2,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,6,2,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,3,6,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,3,6,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 3
[5,4,1,2,6,3] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 3
[5,4,1,3,2,6] => [[[.,[[.,.],.]],.],[.,.]] => [[[],[]],[],[[]]] => 2
[5,4,1,3,6,2] => [[[.,[[.,.],.]],.],[.,.]] => [[[],[]],[],[[]]] => 2
[5,4,1,6,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 3
[5,4,1,6,3,2] => [[[.,[[.,.],.]],.],[.,.]] => [[[],[]],[],[[]]] => 2
[5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 2
[5,4,2,1,6,3] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 2
[5,4,2,3,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 2
[5,4,2,3,6,1] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 2
[5,4,2,6,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 2
[5,4,2,6,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 2
[5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 2
[5,4,3,1,6,2] => [[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 2
[5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 1
[5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 1
[5,4,3,6,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 2
[5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 1
[5,4,6,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 3
[5,4,6,1,3,2] => [[[.,[[.,.],.]],.],[.,.]] => [[[],[]],[],[[]]] => 2
[5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 2
[5,4,6,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 2
[5,4,6,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 2
[5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 1
[5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[[[]]]],[[]]] => 4
[5,6,1,2,4,3] => [[.,[.,[[.,.],.]]],[.,.]] => [[[[],[]]],[[]]] => 3
[5,6,1,3,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 3
[5,6,1,3,4,2] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 3
[5,6,1,4,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => [[[[]],[]],[[]]] => 3
[5,6,1,4,3,2] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[],[]],[[]]] => 2
[5,6,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,6,2,1,4,3] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,6,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[5,6,2,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,6,2,4,3,1] => [[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 2
[5,6,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,6,3,1,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,6,3,2,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,6,3,2,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[5,6,3,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 2
[5,6,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 3
[5,6,4,1,3,2] => [[[.,[[.,.],.]],.],[.,.]] => [[[],[]],[],[[]]] => 2
[5,6,4,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 2
[5,6,4,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 2
[5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 2
[5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 1
[6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => [[[[[[]]]]],[]] => 4
[6,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],.] => [[[[[],[]]]],[]] => 3
[6,1,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],.] => [[[[],[[]]]],[]] => 3
[6,1,2,4,5,3] => [[.,[.,[[.,.],[.,.]]]],.] => [[[[],[[]]]],[]] => 3
[6,1,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],.] => [[[[[]],[]]],[]] => 3
[6,1,2,5,4,3] => [[.,[.,[[[.,.],.],.]]],.] => [[[[],[],[]]],[]] => 2
[6,1,3,2,4,5] => [[.,[[.,.],[.,[.,.]]]],.] => [[[],[[[]]]],[]] => 3
[6,1,3,2,5,4] => [[.,[[.,.],[[.,.],.]]],.] => [[[],[[],[]]],[]] => 2
[6,1,3,4,2,5] => [[.,[[.,.],[.,[.,.]]]],.] => [[[],[[[]]]],[]] => 3
[6,1,3,4,5,2] => [[.,[[.,.],[.,[.,.]]]],.] => [[[],[[[]]]],[]] => 3
[6,1,3,5,2,4] => [[.,[[.,.],[[.,.],.]]],.] => [[[],[[],[]]],[]] => 2
[6,1,3,5,4,2] => [[.,[[.,.],[[.,.],.]]],.] => [[[],[[],[]]],[]] => 2
[6,1,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],.] => [[[[]],[[]]],[]] => 3
[6,1,4,2,5,3] => [[.,[[.,[.,.]],[.,.]]],.] => [[[[]],[[]]],[]] => 3
[6,1,4,3,2,5] => [[.,[[[.,.],.],[.,.]]],.] => [[[],[],[[]]],[]] => 2
[6,1,4,3,5,2] => [[.,[[[.,.],.],[.,.]]],.] => [[[],[],[[]]],[]] => 2
[6,1,4,5,2,3] => [[.,[[.,[.,.]],[.,.]]],.] => [[[[]],[[]]],[]] => 3
[6,1,4,5,3,2] => [[.,[[[.,.],.],[.,.]]],.] => [[[],[],[[]]],[]] => 2
[6,1,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],.] => [[[[[]]],[]],[]] => 3
[6,1,5,2,4,3] => [[.,[[.,[[.,.],.]],.]],.] => [[[[],[]],[]],[]] => 2
[6,1,5,3,2,4] => [[.,[[[.,.],[.,.]],.]],.] => [[[],[[]],[]],[]] => 2
[6,1,5,3,4,2] => [[.,[[[.,.],[.,.]],.]],.] => [[[],[[]],[]],[]] => 2
[6,1,5,4,2,3] => [[.,[[[.,[.,.]],.],.]],.] => [[[[]],[],[]],[]] => 2
[6,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],.] => [[[],[],[],[]],[]] => 1
[6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 3
[6,2,1,3,5,4] => [[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => 2
[6,2,1,4,3,5] => [[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 2
[6,2,1,4,5,3] => [[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 2
[6,2,1,5,3,4] => [[[.,.],[[.,[.,.]],.]],.] => [[],[[[]],[]],[]] => 2
[6,2,1,5,4,3] => [[[.,.],[[[.,.],.],.]],.] => [[],[[],[],[]],[]] => 1
[6,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 3
[6,2,3,1,5,4] => [[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => 2
[6,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 3
[6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 3
[6,2,3,5,1,4] => [[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => 2
[6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => 2
[6,2,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 2
[6,2,4,1,5,3] => [[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 2
[6,2,4,3,1,5] => [[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 2
[6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 2
[6,2,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 2
[6,2,4,5,3,1] => [[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 2
[6,2,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],.] => [[],[[[]],[]],[]] => 2
[6,2,5,1,4,3] => [[[.,.],[[[.,.],.],.]],.] => [[],[[],[],[]],[]] => 1
[6,2,5,3,1,4] => [[[.,.],[[.,[.,.]],.]],.] => [[],[[[]],[]],[]] => 2
[6,2,5,3,4,1] => [[[.,.],[[.,[.,.]],.]],.] => [[],[[[]],[]],[]] => 2
[6,2,5,4,1,3] => [[[.,.],[[[.,.],.],.]],.] => [[],[[],[],[]],[]] => 1
[6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.] => [[],[[],[],[]],[]] => 1
[6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 3
[6,3,1,2,5,4] => [[[.,[.,.]],[[.,.],.]],.] => [[[]],[[],[]],[]] => 2
[6,3,1,4,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 3
[6,3,1,4,5,2] => [[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 3
[6,3,1,5,2,4] => [[[.,[.,.]],[[.,.],.]],.] => [[[]],[[],[]],[]] => 2
[6,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],.] => [[[]],[[],[]],[]] => 2
[6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 2
[6,3,2,1,5,4] => [[[[.,.],.],[[.,.],.]],.] => [[],[],[[],[]],[]] => 1
[6,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 2
[6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 2
[6,3,2,5,1,4] => [[[[.,.],.],[[.,.],.]],.] => [[],[],[[],[]],[]] => 1
[6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.] => [[],[],[[],[]],[]] => 1
[6,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 3
[6,3,4,1,5,2] => [[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 3
[6,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 2
[6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 2
[6,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 3
[6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 2
[6,3,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],.] => [[[]],[[],[]],[]] => 2
[6,3,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],.] => [[[]],[[],[]],[]] => 2
[6,3,5,2,1,4] => [[[[.,.],.],[[.,.],.]],.] => [[],[],[[],[]],[]] => 1
[6,3,5,2,4,1] => [[[[.,.],.],[[.,.],.]],.] => [[],[],[[],[]],[]] => 1
[6,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],.] => [[[]],[[],[]],[]] => 2
[6,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],.] => [[],[],[[],[]],[]] => 1
[6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[]]],[[]],[]] => 3
[6,4,1,2,5,3] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[]]],[[]],[]] => 3
[6,4,1,3,2,5] => [[[.,[[.,.],.]],[.,.]],.] => [[[],[]],[[]],[]] => 2
[6,4,1,3,5,2] => [[[.,[[.,.],.]],[.,.]],.] => [[[],[]],[[]],[]] => 2
[6,4,1,5,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[]]],[[]],[]] => 3
[6,4,1,5,3,2] => [[[.,[[.,.],.]],[.,.]],.] => [[[],[]],[[]],[]] => 2
[6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 2
[6,4,2,1,5,3] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 2
[6,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 2
[6,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 2
[6,4,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 2
[6,4,2,5,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 2
[6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.] => [[[]],[],[[]],[]] => 2
[6,4,3,1,5,2] => [[[[.,[.,.]],.],[.,.]],.] => [[[]],[],[[]],[]] => 2
[6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 1
[6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 1
[6,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [[[]],[],[[]],[]] => 2
[6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 1
[6,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[]]],[[]],[]] => 3
[6,4,5,1,3,2] => [[[.,[[.,.],.]],[.,.]],.] => [[[],[]],[[]],[]] => 2
[6,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 2
[6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 2
[6,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [[[]],[],[[]],[]] => 2
[6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 1
[6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.] => [[[[[]]]],[],[]] => 3
[6,5,1,2,4,3] => [[[.,[.,[[.,.],.]]],.],.] => [[[[],[]]],[],[]] => 2
[6,5,1,3,2,4] => [[[.,[[.,.],[.,.]]],.],.] => [[[],[[]]],[],[]] => 2
[6,5,1,3,4,2] => [[[.,[[.,.],[.,.]]],.],.] => [[[],[[]]],[],[]] => 2
[6,5,1,4,2,3] => [[[.,[[.,[.,.]],.]],.],.] => [[[[]],[]],[],[]] => 2
[6,5,1,4,3,2] => [[[.,[[[.,.],.],.]],.],.] => [[[],[],[]],[],[]] => 1
[6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.] => [[],[[[]]],[],[]] => 2
[6,5,2,1,4,3] => [[[[.,.],[[.,.],.]],.],.] => [[],[[],[]],[],[]] => 1
[6,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],.] => [[],[[[]]],[],[]] => 2
[6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.] => [[],[[[]]],[],[]] => 2
[6,5,2,4,1,3] => [[[[.,.],[[.,.],.]],.],.] => [[],[[],[]],[],[]] => 1
[6,5,2,4,3,1] => [[[[.,.],[[.,.],.]],.],.] => [[],[[],[]],[],[]] => 1
[6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.] => [[[]],[[]],[],[]] => 2
[6,5,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],.] => [[[]],[[]],[],[]] => 2
[6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.] => [[],[],[[]],[],[]] => 1
[6,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],.] => [[],[],[[]],[],[]] => 1
[6,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],.] => [[[]],[[]],[],[]] => 2
[6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [[],[],[[]],[],[]] => 1
[6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => [[[[]]],[],[],[]] => 2
[6,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],.] => [[[],[]],[],[],[]] => 1
[6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.] => [[],[[]],[],[],[]] => 1
[6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.] => [[],[[]],[],[],[]] => 1
[6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.] => [[[]],[],[],[],[]] => 1
[6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [[],[],[],[],[],[]] => 0
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Generating function
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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:
1,1 1,4,1 1,11,11,1 1,26,66,26,1 1,57,302,302,57,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 4\ q + q^{2}$
$F_{4} = 1 + 11\ q + 11\ q^{2} + q^{3}$
$F_{5} = 1 + 26\ q + 66\ q^{2} + 26\ q^{3} + q^{4}$
$F_{6} = 1 + 57\ q + 302\ q^{2} + 302\ q^{3} + 57\ q^{4} + q^{5}$
Description
The number of internal nodes of an ordered tree.
A node is internal if it is neither the root nor a leaf.
A node is internal if it is neither the root nor a leaf.
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
- if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
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.
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