Identifier
-
Mp00061:
Permutations
—to increasing tree⟶
Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000523: Ordered trees ⟶ ℤ
Values
[1] => [.,.] => [[],[]] => 0
[1,2] => [.,[.,.]] => [[],[[],[]]] => 0
[2,1] => [[.,.],.] => [[[],[]],[]] => 0
[1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 0
[1,3,2] => [.,[[.,.],.]] => [[],[[[],[]],[]]] => 0
[2,1,3] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 1
[2,3,1] => [[.,[.,.]],.] => [[[],[[],[]]],[]] => 0
[3,1,2] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 1
[3,2,1] => [[[.,.],.],.] => [[[[],[]],[]],[]] => 0
[1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 0
[1,2,4,3] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 0
[1,3,2,4] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 1
[1,3,4,2] => [.,[[.,[.,.]],.]] => [[],[[[],[[],[]]],[]]] => 0
[1,4,2,3] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 1
[1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 0
[2,1,3,4] => [[.,.],[.,[.,.]]] => [[[],[]],[[],[[],[]]]] => 1
[2,1,4,3] => [[.,.],[[.,.],.]] => [[[],[]],[[[],[]],[]]] => 1
[2,3,1,4] => [[.,[.,.]],[.,.]] => [[[],[[],[]]],[[],[]]] => 1
[2,3,4,1] => [[.,[.,[.,.]]],.] => [[[],[[],[[],[]]]],[]] => 0
[2,4,1,3] => [[.,[.,.]],[.,.]] => [[[],[[],[]]],[[],[]]] => 1
[2,4,3,1] => [[.,[[.,.],.]],.] => [[[],[[[],[]],[]]],[]] => 0
[3,1,2,4] => [[.,.],[.,[.,.]]] => [[[],[]],[[],[[],[]]]] => 1
[3,1,4,2] => [[.,.],[[.,.],.]] => [[[],[]],[[[],[]],[]]] => 1
[3,2,1,4] => [[[.,.],.],[.,.]] => [[[[],[]],[]],[[],[]]] => 1
[3,2,4,1] => [[[.,.],[.,.]],.] => [[[[],[]],[[],[]]],[]] => 1
[3,4,1,2] => [[.,[.,.]],[.,.]] => [[[],[[],[]]],[[],[]]] => 1
[3,4,2,1] => [[[.,[.,.]],.],.] => [[[[],[[],[]]],[]],[]] => 0
[4,1,2,3] => [[.,.],[.,[.,.]]] => [[[],[]],[[],[[],[]]]] => 1
[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] => [.,[.,[.,[.,[.,.]]]]] => [[],[[],[[],[[],[[],[]]]]]] => 0
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [[],[[],[[],[[[],[]],[]]]]] => 0
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [[],[[],[[[],[]],[[],[]]]]] => 1
[1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [[],[[],[[[],[[],[]]],[]]]] => 0
[1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [[],[[],[[[],[]],[[],[]]]]] => 1
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [[],[[],[[[[],[]],[]],[]]]] => 0
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [[],[[[],[]],[[],[[],[]]]]] => 1
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [[],[[[],[]],[[[],[]],[]]]] => 1
[1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [[],[[[],[[],[]]],[[],[]]]] => 1
[1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => [[],[[[],[[],[[],[]]]],[]]] => 0
[1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => [[],[[[],[[],[]]],[[],[]]]] => 1
[1,3,5,4,2] => [.,[[.,[[.,.],.]],.]] => [[],[[[],[[[],[]],[]]],[]]] => 0
[1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [[],[[[],[]],[[],[[],[]]]]] => 1
[1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => [[],[[[],[]],[[[],[]],[]]]] => 1
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [[],[[[[],[]],[]],[[],[]]]] => 1
[1,4,3,5,2] => [.,[[[.,.],[.,.]],.]] => [[],[[[[],[]],[[],[]]],[]]] => 1
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [[],[[[],[[],[]]],[[],[]]]] => 1
[1,4,5,3,2] => [.,[[[.,[.,.]],.],.]] => [[],[[[[],[[],[]]],[]],[]]] => 0
[1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [[],[[[],[]],[[],[[],[]]]]] => 1
[1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => [[],[[[],[]],[[[],[]],[]]]] => 1
[1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => [[],[[[[],[]],[]],[[],[]]]] => 1
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [[],[[[[],[]],[[],[]]],[]]] => 1
[1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => [[],[[[[],[]],[]],[[],[]]]] => 1
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [[],[[[[[],[]],[]],[]],[]]] => 0
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [[[],[]],[[],[[],[[],[]]]]] => 1
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [[[],[]],[[],[[[],[]],[]]]] => 1
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [[[],[]],[[[],[]],[[],[]]]] => 2
[2,1,4,5,3] => [[.,.],[[.,[.,.]],.]] => [[[],[]],[[[],[[],[]]],[]]] => 1
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]] => [[[],[]],[[[],[]],[[],[]]]] => 2
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => [[[],[]],[[[[],[]],[]],[]]] => 1
[2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => [[[],[[],[]]],[[],[[],[]]]] => 1
[2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => [[[],[[],[]]],[[[],[]],[]]] => 1
[2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => [[[],[[],[[],[]]]],[[],[]]] => 1
[2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => [[[],[[],[[],[[],[]]]]],[]] => 0
[2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => [[[],[[],[[],[]]]],[[],[]]] => 1
[2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => [[[],[[],[[[],[]],[]]]],[]] => 0
[2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]] => [[[],[[],[]]],[[],[[],[]]]] => 1
[2,4,1,5,3] => [[.,[.,.]],[[.,.],.]] => [[[],[[],[]]],[[[],[]],[]]] => 1
[2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => [[[],[[[],[]],[]]],[[],[]]] => 1
[2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => [[[],[[[],[]],[[],[]]]],[]] => 1
[2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => [[[],[[],[[],[]]]],[[],[]]] => 1
[2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => [[[],[[[],[[],[]]],[]]],[]] => 0
[2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]] => [[[],[[],[]]],[[],[[],[]]]] => 1
[2,5,1,4,3] => [[.,[.,.]],[[.,.],.]] => [[[],[[],[]]],[[[],[]],[]]] => 1
[2,5,3,1,4] => [[.,[[.,.],.]],[.,.]] => [[[],[[[],[]],[]]],[[],[]]] => 1
[2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => [[[],[[[],[]],[[],[]]]],[]] => 1
[2,5,4,1,3] => [[.,[[.,.],.]],[.,.]] => [[[],[[[],[]],[]]],[[],[]]] => 1
[2,5,4,3,1] => [[.,[[[.,.],.],.]],.] => [[[],[[[[],[]],[]],[]]],[]] => 0
[3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]] => [[[],[]],[[],[[],[[],[]]]]] => 1
[3,1,2,5,4] => [[.,.],[.,[[.,.],.]]] => [[[],[]],[[],[[[],[]],[]]]] => 1
[3,1,4,2,5] => [[.,.],[[.,.],[.,.]]] => [[[],[]],[[[],[]],[[],[]]]] => 2
[3,1,4,5,2] => [[.,.],[[.,[.,.]],.]] => [[[],[]],[[[],[[],[]]],[]]] => 1
[3,1,5,2,4] => [[.,.],[[.,.],[.,.]]] => [[[],[]],[[[],[]],[[],[]]]] => 2
[3,1,5,4,2] => [[.,.],[[[.,.],.],.]] => [[[],[]],[[[[],[]],[]],[]]] => 1
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [[[[],[]],[]],[[],[[],[]]]] => 1
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [[[[],[]],[]],[[[],[]],[]]] => 1
[3,2,4,1,5] => [[[.,.],[.,.]],[.,.]] => [[[[],[]],[[],[]]],[[],[]]] => 2
[3,2,4,5,1] => [[[.,.],[.,[.,.]]],.] => [[[[],[]],[[],[[],[]]]],[]] => 1
[3,2,5,1,4] => [[[.,.],[.,.]],[.,.]] => [[[[],[]],[[],[]]],[[],[]]] => 2
[3,2,5,4,1] => [[[.,.],[[.,.],.]],.] => [[[[],[]],[[[],[]],[]]],[]] => 1
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [[[],[[],[]]],[[],[[],[]]]] => 1
[3,4,1,5,2] => [[.,[.,.]],[[.,.],.]] => [[[],[[],[]]],[[[],[]],[]]] => 1
[3,4,2,1,5] => [[[.,[.,.]],.],[.,.]] => [[[[],[[],[]]],[]],[[],[]]] => 1
[3,4,2,5,1] => [[[.,[.,.]],[.,.]],.] => [[[[],[[],[]]],[[],[]]],[]] => 1
[3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]] => [[[],[[],[[],[]]]],[[],[]]] => 1
[3,4,5,2,1] => [[[.,[.,[.,.]]],.],.] => [[[[],[[],[[],[]]]],[]],[]] => 0
[3,5,1,2,4] => [[.,[.,.]],[.,[.,.]]] => [[[],[[],[]]],[[],[[],[]]]] => 1
[3,5,1,4,2] => [[.,[.,.]],[[.,.],.]] => [[[],[[],[]]],[[[],[]],[]]] => 1
>>> Load all 873 entries. <<<[3,5,2,1,4] => [[[.,[.,.]],.],[.,.]] => [[[[],[[],[]]],[]],[[],[]]] => 1
[3,5,2,4,1] => [[[.,[.,.]],[.,.]],.] => [[[[],[[],[]]],[[],[]]],[]] => 1
[3,5,4,1,2] => [[.,[[.,.],.]],[.,.]] => [[[],[[[],[]],[]]],[[],[]]] => 1
[3,5,4,2,1] => [[[.,[[.,.],.]],.],.] => [[[[],[[[],[]],[]]],[]],[]] => 0
[4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]] => [[[],[]],[[],[[],[[],[]]]]] => 1
[4,1,2,5,3] => [[.,.],[.,[[.,.],.]]] => [[[],[]],[[],[[[],[]],[]]]] => 1
[4,1,3,2,5] => [[.,.],[[.,.],[.,.]]] => [[[],[]],[[[],[]],[[],[]]]] => 2
[4,1,3,5,2] => [[.,.],[[.,[.,.]],.]] => [[[],[]],[[[],[[],[]]],[]]] => 1
[4,1,5,2,3] => [[.,.],[[.,.],[.,.]]] => [[[],[]],[[[],[]],[[],[]]]] => 2
[4,1,5,3,2] => [[.,.],[[[.,.],.],.]] => [[[],[]],[[[[],[]],[]],[]]] => 1
[4,2,1,3,5] => [[[.,.],.],[.,[.,.]]] => [[[[],[]],[]],[[],[[],[]]]] => 1
[4,2,1,5,3] => [[[.,.],.],[[.,.],.]] => [[[[],[]],[]],[[[],[]],[]]] => 1
[4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [[[[],[]],[[],[]]],[[],[]]] => 2
[4,2,3,5,1] => [[[.,.],[.,[.,.]]],.] => [[[[],[]],[[],[[],[]]]],[]] => 1
[4,2,5,1,3] => [[[.,.],[.,.]],[.,.]] => [[[[],[]],[[],[]]],[[],[]]] => 2
[4,2,5,3,1] => [[[.,.],[[.,.],.]],.] => [[[[],[]],[[[],[]],[]]],[]] => 1
[4,3,1,2,5] => [[[.,.],.],[.,[.,.]]] => [[[[],[]],[]],[[],[[],[]]]] => 1
[4,3,1,5,2] => [[[.,.],.],[[.,.],.]] => [[[[],[]],[]],[[[],[]],[]]] => 1
[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] => [[.,[.,.]],[.,[.,.]]] => [[[],[[],[]]],[[],[[],[]]]] => 1
[4,5,1,3,2] => [[.,[.,.]],[[.,.],.]] => [[[],[[],[]]],[[[],[]],[]]] => 1
[4,5,2,1,3] => [[[.,[.,.]],.],[.,.]] => [[[[],[[],[]]],[]],[[],[]]] => 1
[4,5,2,3,1] => [[[.,[.,.]],[.,.]],.] => [[[[],[[],[]]],[[],[]]],[]] => 1
[4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [[[[],[[],[]]],[]],[[],[]]] => 1
[4,5,3,2,1] => [[[[.,[.,.]],.],.],.] => [[[[[],[[],[]]],[]],[]],[]] => 0
[5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]] => [[[],[]],[[],[[],[[],[]]]]] => 1
[5,1,2,4,3] => [[.,.],[.,[[.,.],.]]] => [[[],[]],[[],[[[],[]],[]]]] => 1
[5,1,3,2,4] => [[.,.],[[.,.],[.,.]]] => [[[],[]],[[[],[]],[[],[]]]] => 2
[5,1,3,4,2] => [[.,.],[[.,[.,.]],.]] => [[[],[]],[[[],[[],[]]],[]]] => 1
[5,1,4,2,3] => [[.,.],[[.,.],[.,.]]] => [[[],[]],[[[],[]],[[],[]]]] => 2
[5,1,4,3,2] => [[.,.],[[[.,.],.],.]] => [[[],[]],[[[[],[]],[]],[]]] => 1
[5,2,1,3,4] => [[[.,.],.],[.,[.,.]]] => [[[[],[]],[]],[[],[[],[]]]] => 1
[5,2,1,4,3] => [[[.,.],.],[[.,.],.]] => [[[[],[]],[]],[[[],[]],[]]] => 1
[5,2,3,1,4] => [[[.,.],[.,.]],[.,.]] => [[[[],[]],[[],[]]],[[],[]]] => 2
[5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [[[[],[]],[[],[[],[]]]],[]] => 1
[5,2,4,1,3] => [[[.,.],[.,.]],[.,.]] => [[[[],[]],[[],[]]],[[],[]]] => 2
[5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => [[[[],[]],[[[],[]],[]]],[]] => 1
[5,3,1,2,4] => [[[.,.],.],[.,[.,.]]] => [[[[],[]],[]],[[],[[],[]]]] => 1
[5,3,1,4,2] => [[[.,.],.],[[.,.],.]] => [[[[],[]],[]],[[[],[]],[]]] => 1
[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] => [[[.,.],.],[.,[.,.]]] => [[[[],[]],[]],[[],[[],[]]]] => 1
[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] => [.,[.,[.,[.,[.,[.,.]]]]]] => [[],[[],[[],[[],[[],[[],[]]]]]]] => 0
[1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [[],[[],[[],[[],[[[],[]],[]]]]]] => 0
[1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [[],[[],[[],[[[],[]],[[],[]]]]]] => 1
[1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => [[],[[],[[],[[[],[[],[]]],[]]]]] => 0
[1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => [[],[[],[[],[[[],[]],[[],[]]]]]] => 1
[1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => [[],[[],[[],[[[[],[]],[]],[]]]]] => 0
[1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [[],[[],[[[],[]],[[],[[],[]]]]]] => 1
[1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [[],[[],[[[],[]],[[[],[]],[]]]]] => 1
[1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [[],[[],[[[],[[],[]]],[[],[]]]]] => 1
[1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => [[],[[],[[[],[[],[[],[]]]],[]]]] => 0
[1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => [[],[[],[[[],[[],[]]],[[],[]]]]] => 1
[1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]] => [[],[[],[[[],[[[],[]],[]]],[]]]] => 0
[1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [[],[[],[[[],[]],[[],[[],[]]]]]] => 1
[1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => [[],[[],[[[],[]],[[[],[]],[]]]]] => 1
[1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => [[],[[],[[[[],[]],[]],[[],[]]]]] => 1
[1,2,5,4,6,3] => [.,[.,[[[.,.],[.,.]],.]]] => [[],[[],[[[[],[]],[[],[]]],[]]]] => 1
[1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [[],[[],[[[],[[],[]]],[[],[]]]]] => 1
[1,2,5,6,4,3] => [.,[.,[[[.,[.,.]],.],.]]] => [[],[[],[[[[],[[],[]]],[]],[]]]] => 0
[1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => [[],[[],[[[],[]],[[],[[],[]]]]]] => 1
[1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => [[],[[],[[[],[]],[[[],[]],[]]]]] => 1
[1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]] => [[],[[],[[[[],[]],[]],[[],[]]]]] => 1
[1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => [[],[[],[[[[],[]],[[],[]]],[]]]] => 1
[1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]] => [[],[[],[[[[],[]],[]],[[],[]]]]] => 1
[1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => [[],[[],[[[[[],[]],[]],[]],[]]]] => 0
[1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [[],[[[],[]],[[],[[],[[],[]]]]]] => 1
[1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [[],[[[],[]],[[],[[[],[]],[]]]]] => 1
[1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[[],[]],[[[],[]],[[],[]]]]] => 2
[1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]] => [[],[[[],[]],[[[],[[],[]]],[]]]] => 1
[1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[[],[]],[[[],[]],[[],[]]]]] => 2
[1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [[],[[[],[]],[[[[],[]],[]],[]]]] => 1
[1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [[],[[[],[[],[]]],[[],[[],[]]]]] => 1
[1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => [[],[[[],[[],[]]],[[[],[]],[]]]] => 1
[1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => [[],[[[],[[],[[],[]]]],[[],[]]]] => 1
[1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]] => [[],[[[],[[],[[],[[],[]]]]],[]]] => 0
[1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => [[],[[[],[[],[[],[]]]],[[],[]]]] => 1
[1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]] => [[],[[[],[[],[[[],[]],[]]]],[]]] => 0
[1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [[],[[[],[[],[]]],[[],[[],[]]]]] => 1
[1,3,5,2,6,4] => [.,[[.,[.,.]],[[.,.],.]]] => [[],[[[],[[],[]]],[[[],[]],[]]]] => 1
[1,3,5,4,2,6] => [.,[[.,[[.,.],.]],[.,.]]] => [[],[[[],[[[],[]],[]]],[[],[]]]] => 1
[1,3,5,4,6,2] => [.,[[.,[[.,.],[.,.]]],.]] => [[],[[[],[[[],[]],[[],[]]]],[]]] => 1
[1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [[],[[[],[[],[[],[]]]],[[],[]]]] => 1
[1,3,5,6,4,2] => [.,[[.,[[.,[.,.]],.]],.]] => [[],[[[],[[[],[[],[]]],[]]],[]]] => 0
[1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => [[],[[[],[[],[]]],[[],[[],[]]]]] => 1
[1,3,6,2,5,4] => [.,[[.,[.,.]],[[.,.],.]]] => [[],[[[],[[],[]]],[[[],[]],[]]]] => 1
[1,3,6,4,2,5] => [.,[[.,[[.,.],.]],[.,.]]] => [[],[[[],[[[],[]],[]]],[[],[]]]] => 1
[1,3,6,4,5,2] => [.,[[.,[[.,.],[.,.]]],.]] => [[],[[[],[[[],[]],[[],[]]]],[]]] => 1
[1,3,6,5,2,4] => [.,[[.,[[.,.],.]],[.,.]]] => [[],[[[],[[[],[]],[]]],[[],[]]]] => 1
[1,3,6,5,4,2] => [.,[[.,[[[.,.],.],.]],.]] => [[],[[[],[[[[],[]],[]],[]]],[]]] => 0
[1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [[],[[[],[]],[[],[[],[[],[]]]]]] => 1
[1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [[],[[[],[]],[[],[[[],[]],[]]]]] => 1
[1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[[],[]],[[[],[]],[[],[]]]]] => 2
[1,4,2,5,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => [[],[[[],[]],[[[],[[],[]]],[]]]] => 1
[1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[[],[]],[[[],[]],[[],[]]]]] => 2
[1,4,2,6,5,3] => [.,[[.,.],[[[.,.],.],.]]] => [[],[[[],[]],[[[[],[]],[]],[]]]] => 1
[1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => [[],[[[[],[]],[]],[[],[[],[]]]]] => 1
[1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => [[],[[[[],[]],[]],[[[],[]],[]]]] => 1
[1,4,3,5,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[[],[]],[[],[]]],[[],[]]]] => 2
[1,4,3,5,6,2] => [.,[[[.,.],[.,[.,.]]],.]] => [[],[[[[],[]],[[],[[],[]]]],[]]] => 1
[1,4,3,6,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[[],[]],[[],[]]],[[],[]]]] => 2
[1,4,3,6,5,2] => [.,[[[.,.],[[.,.],.]],.]] => [[],[[[[],[]],[[[],[]],[]]],[]]] => 1
[1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [[],[[[],[[],[]]],[[],[[],[]]]]] => 1
[1,4,5,2,6,3] => [.,[[.,[.,.]],[[.,.],.]]] => [[],[[[],[[],[]]],[[[],[]],[]]]] => 1
[1,4,5,3,2,6] => [.,[[[.,[.,.]],.],[.,.]]] => [[],[[[[],[[],[]]],[]],[[],[]]]] => 1
[1,4,5,3,6,2] => [.,[[[.,[.,.]],[.,.]],.]] => [[],[[[[],[[],[]]],[[],[]]],[]]] => 1
[1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => [[],[[[],[[],[[],[]]]],[[],[]]]] => 1
[1,4,5,6,3,2] => [.,[[[.,[.,[.,.]]],.],.]] => [[],[[[[],[[],[[],[]]]],[]],[]]] => 0
[1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => [[],[[[],[[],[]]],[[],[[],[]]]]] => 1
[1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => [[],[[[],[[],[]]],[[[],[]],[]]]] => 1
[1,4,6,3,2,5] => [.,[[[.,[.,.]],.],[.,.]]] => [[],[[[[],[[],[]]],[]],[[],[]]]] => 1
[1,4,6,3,5,2] => [.,[[[.,[.,.]],[.,.]],.]] => [[],[[[[],[[],[]]],[[],[]]],[]]] => 1
[1,4,6,5,2,3] => [.,[[.,[[.,.],.]],[.,.]]] => [[],[[[],[[[],[]],[]]],[[],[]]]] => 1
[1,4,6,5,3,2] => [.,[[[.,[[.,.],.]],.],.]] => [[],[[[[],[[[],[]],[]]],[]],[]]] => 0
[1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [[],[[[],[]],[[],[[],[[],[]]]]]] => 1
[1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => [[],[[[],[]],[[],[[[],[]],[]]]]] => 1
[1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[[],[]],[[[],[]],[[],[]]]]] => 2
[1,5,2,4,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => [[],[[[],[]],[[[],[[],[]]],[]]]] => 1
[1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[[],[]],[[[],[]],[[],[]]]]] => 2
[1,5,2,6,4,3] => [.,[[.,.],[[[.,.],.],.]]] => [[],[[[],[]],[[[[],[]],[]],[]]]] => 1
[1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]] => [[],[[[[],[]],[]],[[],[[],[]]]]] => 1
[1,5,3,2,6,4] => [.,[[[.,.],.],[[.,.],.]]] => [[],[[[[],[]],[]],[[[],[]],[]]]] => 1
[1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[[],[]],[[],[]]],[[],[]]]] => 2
[1,5,3,4,6,2] => [.,[[[.,.],[.,[.,.]]],.]] => [[],[[[[],[]],[[],[[],[]]]],[]]] => 1
[1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[[],[]],[[],[]]],[[],[]]]] => 2
[1,5,3,6,4,2] => [.,[[[.,.],[[.,.],.]],.]] => [[],[[[[],[]],[[[],[]],[]]],[]]] => 1
[1,5,4,2,3,6] => [.,[[[.,.],.],[.,[.,.]]]] => [[],[[[[],[]],[]],[[],[[],[]]]]] => 1
[1,5,4,2,6,3] => [.,[[[.,.],.],[[.,.],.]]] => [[],[[[[],[]],[]],[[[],[]],[]]]] => 1
[1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => [[],[[[[[],[]],[]],[]],[[],[]]]] => 1
[1,5,4,3,6,2] => [.,[[[[.,.],.],[.,.]],.]] => [[],[[[[[],[]],[]],[[],[]]],[]]] => 1
[1,5,4,6,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[[],[]],[[],[]]],[[],[]]]] => 2
[1,5,4,6,3,2] => [.,[[[[.,.],[.,.]],.],.]] => [[],[[[[[],[]],[[],[]]],[]],[]]] => 1
[1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => [[],[[[],[[],[]]],[[],[[],[]]]]] => 1
[1,5,6,2,4,3] => [.,[[.,[.,.]],[[.,.],.]]] => [[],[[[],[[],[]]],[[[],[]],[]]]] => 1
[1,5,6,3,2,4] => [.,[[[.,[.,.]],.],[.,.]]] => [[],[[[[],[[],[]]],[]],[[],[]]]] => 1
[1,5,6,3,4,2] => [.,[[[.,[.,.]],[.,.]],.]] => [[],[[[[],[[],[]]],[[],[]]],[]]] => 1
[1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => [[],[[[[],[[],[]]],[]],[[],[]]]] => 1
[1,5,6,4,3,2] => [.,[[[[.,[.,.]],.],.],.]] => [[],[[[[[],[[],[]]],[]],[]],[]]] => 0
[1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => [[],[[[],[]],[[],[[],[[],[]]]]]] => 1
[1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => [[],[[[],[]],[[],[[[],[]],[]]]]] => 1
[1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[[],[]],[[[],[]],[[],[]]]]] => 2
[1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]] => [[],[[[],[]],[[[],[[],[]]],[]]]] => 1
[1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[[],[]],[[[],[]],[[],[]]]]] => 2
[1,6,2,5,4,3] => [.,[[.,.],[[[.,.],.],.]]] => [[],[[[],[]],[[[[],[]],[]],[]]]] => 1
[1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]] => [[],[[[[],[]],[]],[[],[[],[]]]]] => 1
[1,6,3,2,5,4] => [.,[[[.,.],.],[[.,.],.]]] => [[],[[[[],[]],[]],[[[],[]],[]]]] => 1
[1,6,3,4,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[[],[]],[[],[]]],[[],[]]]] => 2
[1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => [[],[[[[],[]],[[],[[],[]]]],[]]] => 1
[1,6,3,5,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[[],[]],[[],[]]],[[],[]]]] => 2
[1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]] => [[],[[[[],[]],[[[],[]],[]]],[]]] => 1
[1,6,4,2,3,5] => [.,[[[.,.],.],[.,[.,.]]]] => [[],[[[[],[]],[]],[[],[[],[]]]]] => 1
[1,6,4,2,5,3] => [.,[[[.,.],.],[[.,.],.]]] => [[],[[[[],[]],[]],[[[],[]],[]]]] => 1
[1,6,4,3,2,5] => [.,[[[[.,.],.],.],[.,.]]] => [[],[[[[[],[]],[]],[]],[[],[]]]] => 1
[1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => [[],[[[[[],[]],[]],[[],[]]],[]]] => 1
[1,6,4,5,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[[],[]],[[],[]]],[[],[]]]] => 2
[1,6,4,5,3,2] => [.,[[[[.,.],[.,.]],.],.]] => [[],[[[[[],[]],[[],[]]],[]],[]]] => 1
[1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]] => [[],[[[[],[]],[]],[[],[[],[]]]]] => 1
[1,6,5,2,4,3] => [.,[[[.,.],.],[[.,.],.]]] => [[],[[[[],[]],[]],[[[],[]],[]]]] => 1
[1,6,5,3,2,4] => [.,[[[[.,.],.],.],[.,.]]] => [[],[[[[[],[]],[]],[]],[[],[]]]] => 1
[1,6,5,3,4,2] => [.,[[[[.,.],.],[.,.]],.]] => [[],[[[[[],[]],[]],[[],[]]],[]]] => 1
[1,6,5,4,2,3] => [.,[[[[.,.],.],.],[.,.]]] => [[],[[[[[],[]],[]],[]],[[],[]]]] => 1
[1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => [[],[[[[[[],[]],[]],[]],[]],[]]] => 0
[2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[],[]],[[],[[],[[],[[],[]]]]]] => 1
[2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[[],[]],[[],[[],[[[],[]],[]]]]] => 1
[2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 2
[2,1,3,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => [[[],[]],[[],[[[],[[],[]]],[]]]] => 1
[2,1,3,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 2
[2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [[[],[]],[[],[[[[],[]],[]],[]]]] => 1
[2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[2,1,4,5,3,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[2,1,4,5,6,3] => [[.,.],[[.,[.,[.,.]]],.]] => [[[],[]],[[[],[[],[[],[]]]],[]]] => 1
[2,1,4,6,3,5] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[2,1,4,6,5,3] => [[.,.],[[.,[[.,.],.]],.]] => [[[],[]],[[[],[[[],[]],[]]],[]]] => 1
[2,1,5,3,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[2,1,5,3,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[2,1,5,4,6,3] => [[.,.],[[[.,.],[.,.]],.]] => [[[],[]],[[[[],[]],[[],[]]],[]]] => 2
[2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[2,1,5,6,4,3] => [[.,.],[[[.,[.,.]],.],.]] => [[[],[]],[[[[],[[],[]]],[]],[]]] => 1
[2,1,6,3,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[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] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 1
[2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 1
[2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 1
[2,3,1,6,4,5] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[2,3,1,6,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 1
[2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 1
[2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 1
[2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[],[[],[[],[[],[]]]]],[[],[]]] => 1
[2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => [[[],[[],[[],[[],[[],[]]]]]],[]] => 0
[2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[],[[],[[],[[],[]]]]],[[],[]]] => 1
[2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => [[[],[[],[[],[[[],[]],[]]]]],[]] => 0
[2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 1
[2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 1
[2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => [[[],[[],[[[],[]],[]]]],[[],[]]] => 1
[2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => [[[],[[],[[[],[]],[[],[]]]]],[]] => 1
[2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[],[[],[[],[[],[]]]]],[[],[]]] => 1
[2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => [[[],[[],[[[],[[],[]]],[]]]],[]] => 0
[2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 1
[2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 1
[2,3,6,4,1,5] => [[.,[.,[[.,.],.]]],[.,.]] => [[[],[[],[[[],[]],[]]]],[[],[]]] => 1
[2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => [[[],[[],[[[],[]],[[],[]]]]],[]] => 1
[2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]] => [[[],[[],[[[],[]],[]]]],[[],[]]] => 1
[2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => [[[],[[],[[[[],[]],[]],[]]]],[]] => 0
[2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 1
[2,4,1,3,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 1
[2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 1
[2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[2,4,1,6,5,3] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 1
[2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 1
[2,4,3,1,6,5] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 1
[2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 2
[2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => [[[],[[[],[]],[[],[[],[]]]]],[]] => 1
[2,4,3,6,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 2
[2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => [[[],[[[],[]],[[[],[]],[]]]],[]] => 1
[2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 1
[2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 1
[2,4,5,3,1,6] => [[.,[[.,[.,.]],.]],[.,.]] => [[[],[[[],[[],[]]],[]]],[[],[]]] => 1
[2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => [[[],[[[],[[],[]]],[[],[]]]],[]] => 1
[2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[],[[],[[],[[],[]]]]],[[],[]]] => 1
[2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => [[[],[[[],[[],[[],[]]]],[]]],[]] => 0
[2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 1
[2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 1
[2,4,6,3,1,5] => [[.,[[.,[.,.]],.]],[.,.]] => [[[],[[[],[[],[]]],[]]],[[],[]]] => 1
[2,4,6,3,5,1] => [[.,[[.,[.,.]],[.,.]]],.] => [[[],[[[],[[],[]]],[[],[]]]],[]] => 1
[2,4,6,5,1,3] => [[.,[.,[[.,.],.]]],[.,.]] => [[[],[[],[[[],[]],[]]]],[[],[]]] => 1
[2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.] => [[[],[[[],[[[],[]],[]]],[]]],[]] => 0
[2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 1
[2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 1
[2,5,1,4,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[2,5,1,4,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 1
[2,5,1,6,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[2,5,1,6,4,3] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 1
[2,5,3,1,4,6] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 1
[2,5,3,1,6,4] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 1
[2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 2
[2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => [[[],[[[],[]],[[],[[],[]]]]],[]] => 1
[2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 2
[2,5,3,6,4,1] => [[.,[[.,.],[[.,.],.]]],.] => [[[],[[[],[]],[[[],[]],[]]]],[]] => 1
[2,5,4,1,3,6] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 1
[2,5,4,1,6,3] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 1
[2,5,4,3,1,6] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[[[[],[]],[]],[]]],[[],[]]] => 1
[2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => [[[],[[[[],[]],[]],[[],[]]]],[]] => 1
[2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 2
[2,5,4,6,3,1] => [[.,[[[.,.],[.,.]],.]],.] => [[[],[[[[],[]],[[],[]]],[]]],[]] => 1
[2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 1
[2,5,6,1,4,3] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 1
[2,5,6,3,1,4] => [[.,[[.,[.,.]],.]],[.,.]] => [[[],[[[],[[],[]]],[]]],[[],[]]] => 1
[2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.] => [[[],[[[],[[],[]]],[[],[]]]],[]] => 1
[2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]] => [[[],[[[],[[],[]]],[]]],[[],[]]] => 1
[2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.] => [[[],[[[[],[[],[]]],[]],[]]],[]] => 0
[2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 1
[2,6,1,3,5,4] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 1
[2,6,1,4,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[2,6,1,4,5,3] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 1
[2,6,1,5,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[2,6,1,5,4,3] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 1
[2,6,3,1,4,5] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 1
[2,6,3,1,5,4] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 1
[2,6,3,4,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 2
[2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.] => [[[],[[[],[]],[[],[[],[]]]]],[]] => 1
[2,6,3,5,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 2
[2,6,3,5,4,1] => [[.,[[.,.],[[.,.],.]]],.] => [[[],[[[],[]],[[[],[]],[]]]],[]] => 1
[2,6,4,1,3,5] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 1
[2,6,4,1,5,3] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 1
[2,6,4,3,1,5] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[[[[],[]],[]],[]]],[[],[]]] => 1
[2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.] => [[[],[[[[],[]],[]],[[],[]]]],[]] => 1
[2,6,4,5,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 2
[2,6,4,5,3,1] => [[.,[[[.,.],[.,.]],.]],.] => [[[],[[[[],[]],[[],[]]],[]]],[]] => 1
[2,6,5,1,3,4] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 1
[2,6,5,1,4,3] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 1
[2,6,5,3,1,4] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[[[[],[]],[]],[]]],[[],[]]] => 1
[2,6,5,3,4,1] => [[.,[[[.,.],.],[.,.]]],.] => [[[],[[[[],[]],[]],[[],[]]]],[]] => 1
[2,6,5,4,1,3] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[[[[],[]],[]],[]]],[[],[]]] => 1
[2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.] => [[[],[[[[[],[]],[]],[]],[]]],[]] => 0
[3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[],[]],[[],[[],[[],[[],[]]]]]] => 1
[3,1,2,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[[],[]],[[],[[],[[[],[]],[]]]]] => 1
[3,1,2,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 2
[3,1,2,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => [[[],[]],[[],[[[],[[],[]]],[]]]] => 1
[3,1,2,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 2
[3,1,2,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [[[],[]],[[],[[[[],[]],[]],[]]]] => 1
[3,1,4,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[3,1,4,2,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[3,1,4,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[3,1,4,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => [[[],[]],[[[],[[],[[],[]]]],[]]] => 1
[3,1,4,6,2,5] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[3,1,4,6,5,2] => [[.,.],[[.,[[.,.],.]],.]] => [[[],[]],[[[],[[[],[]],[]]],[]]] => 1
[3,1,5,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[3,1,5,2,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[3,1,5,4,2,6] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[3,1,5,4,6,2] => [[.,.],[[[.,.],[.,.]],.]] => [[[],[]],[[[[],[]],[[],[]]],[]]] => 2
[3,1,5,6,2,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[3,1,5,6,4,2] => [[.,.],[[[.,[.,.]],.],.]] => [[[],[]],[[[[],[[],[]]],[]],[]]] => 1
[3,1,6,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[3,1,6,2,5,4] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[3,1,6,4,2,5] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[3,1,6,4,5,2] => [[.,.],[[[.,.],[.,.]],.]] => [[[],[]],[[[[],[]],[[],[]]],[]]] => 2
[3,1,6,5,2,4] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[3,1,6,5,4,2] => [[.,.],[[[[.,.],.],.],.]] => [[[],[]],[[[[[],[]],[]],[]],[]]] => 1
[3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 1
[3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 1
[3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[3,2,1,5,6,4] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 1
[3,2,1,6,4,5] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 1
[3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[3,2,4,1,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [[[[],[]],[[],[[],[[],[]]]]],[]] => 1
[3,2,4,6,1,5] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[3,2,4,6,5,1] => [[[.,.],[.,[[.,.],.]]],.] => [[[[],[]],[[],[[[],[]],[]]]],[]] => 1
[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] => [[[.,.],[[.,[.,.]],.]],.] => [[[[],[]],[[[],[[],[]]],[]]],[]] => 1
[3,2,6,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[3,2,6,1,5,4] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[3,2,6,4,1,5] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 2
[3,2,6,4,5,1] => [[[.,.],[[.,.],[.,.]]],.] => [[[[],[]],[[[],[]],[[],[]]]],[]] => 2
[3,2,6,5,1,4] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 2
[3,2,6,5,4,1] => [[[.,.],[[[.,.],.],.]],.] => [[[[],[]],[[[[],[]],[]],[]]],[]] => 1
[3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 1
[3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 1
[3,4,1,5,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[3,4,1,5,6,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 1
[3,4,1,6,2,5] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[3,4,1,6,5,2] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 1
[3,4,2,1,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 1
[3,4,2,1,6,5] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 1
[3,4,2,5,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[3,4,2,5,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => [[[[],[[],[]]],[[],[[],[]]]],[]] => 1
[3,4,2,6,1,5] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[3,4,2,6,5,1] => [[[.,[.,.]],[[.,.],.]],.] => [[[[],[[],[]]],[[[],[]],[]]],[]] => 1
[3,4,5,1,2,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 1
[3,4,5,1,6,2] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 1
[3,4,5,2,1,6] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[],[[],[[],[]]]],[]],[[],[]]] => 1
[3,4,5,2,6,1] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[],[[],[[],[]]]],[[],[]]],[]] => 1
[3,4,5,6,1,2] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[],[[],[[],[[],[]]]]],[[],[]]] => 1
[3,4,5,6,2,1] => [[[.,[.,[.,[.,.]]]],.],.] => [[[[],[[],[[],[[],[]]]]],[]],[]] => 0
[3,4,6,1,2,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 1
[3,4,6,1,5,2] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 1
[3,4,6,2,1,5] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[],[[],[[],[]]]],[]],[[],[]]] => 1
[3,4,6,2,5,1] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[],[[],[[],[]]]],[[],[]]],[]] => 1
[3,4,6,5,1,2] => [[.,[.,[[.,.],.]]],[.,.]] => [[[],[[],[[[],[]],[]]]],[[],[]]] => 1
[3,4,6,5,2,1] => [[[.,[.,[[.,.],.]]],.],.] => [[[[],[[],[[[],[]],[]]]],[]],[]] => 0
[3,5,1,2,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 1
[3,5,1,2,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 1
[3,5,1,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[3,5,1,4,6,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 1
[3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[3,5,1,6,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 1
[3,5,2,1,4,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 1
[3,5,2,1,6,4] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 1
[3,5,2,4,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[3,5,2,4,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => [[[[],[[],[]]],[[],[[],[]]]],[]] => 1
[3,5,2,6,1,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[3,5,2,6,4,1] => [[[.,[.,.]],[[.,.],.]],.] => [[[[],[[],[]]],[[[],[]],[]]],[]] => 1
[3,5,4,1,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 1
[3,5,4,1,6,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 1
[3,5,4,2,1,6] => [[[.,[[.,.],.]],.],[.,.]] => [[[[],[[[],[]],[]]],[]],[[],[]]] => 1
[3,5,4,2,6,1] => [[[.,[[.,.],.]],[.,.]],.] => [[[[],[[[],[]],[]]],[[],[]]],[]] => 1
[3,5,4,6,1,2] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 2
[3,5,4,6,2,1] => [[[.,[[.,.],[.,.]]],.],.] => [[[[],[[[],[]],[[],[]]]],[]],[]] => 1
[3,5,6,1,2,4] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 1
[3,5,6,1,4,2] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 1
[3,5,6,2,1,4] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[],[[],[[],[]]]],[]],[[],[]]] => 1
[3,5,6,2,4,1] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[],[[],[[],[]]]],[[],[]]],[]] => 1
[3,5,6,4,1,2] => [[.,[[.,[.,.]],.]],[.,.]] => [[[],[[[],[[],[]]],[]]],[[],[]]] => 1
[3,5,6,4,2,1] => [[[.,[[.,[.,.]],.]],.],.] => [[[[],[[[],[[],[]]],[]]],[]],[]] => 0
[3,6,1,2,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 1
[3,6,1,2,5,4] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 1
[3,6,1,4,2,5] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[3,6,1,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 1
[3,6,1,5,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[3,6,1,5,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 1
[3,6,2,1,4,5] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 1
[3,6,2,1,5,4] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 1
[3,6,2,4,1,5] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[3,6,2,4,5,1] => [[[.,[.,.]],[.,[.,.]]],.] => [[[[],[[],[]]],[[],[[],[]]]],[]] => 1
[3,6,2,5,1,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[3,6,2,5,4,1] => [[[.,[.,.]],[[.,.],.]],.] => [[[[],[[],[]]],[[[],[]],[]]],[]] => 1
[3,6,4,1,2,5] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 1
[3,6,4,1,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 1
[3,6,4,2,1,5] => [[[.,[[.,.],.]],.],[.,.]] => [[[[],[[[],[]],[]]],[]],[[],[]]] => 1
[3,6,4,2,5,1] => [[[.,[[.,.],.]],[.,.]],.] => [[[[],[[[],[]],[]]],[[],[]]],[]] => 1
[3,6,4,5,1,2] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 2
[3,6,4,5,2,1] => [[[.,[[.,.],[.,.]]],.],.] => [[[[],[[[],[]],[[],[]]]],[]],[]] => 1
[3,6,5,1,2,4] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 1
[3,6,5,1,4,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 1
[3,6,5,2,1,4] => [[[.,[[.,.],.]],.],[.,.]] => [[[[],[[[],[]],[]]],[]],[[],[]]] => 1
[3,6,5,2,4,1] => [[[.,[[.,.],.]],[.,.]],.] => [[[[],[[[],[]],[]]],[[],[]]],[]] => 1
[3,6,5,4,1,2] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[[[[],[]],[]],[]]],[[],[]]] => 1
[3,6,5,4,2,1] => [[[.,[[[.,.],.],.]],.],.] => [[[[],[[[[],[]],[]],[]]],[]],[]] => 0
[4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[],[]],[[],[[],[[],[[],[]]]]]] => 1
[4,1,2,3,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[[],[]],[[],[[],[[[],[]],[]]]]] => 1
[4,1,2,5,3,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 2
[4,1,2,5,6,3] => [[.,.],[.,[[.,[.,.]],.]]] => [[[],[]],[[],[[[],[[],[]]],[]]]] => 1
[4,1,2,6,3,5] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 2
[4,1,2,6,5,3] => [[.,.],[.,[[[.,.],.],.]]] => [[[],[]],[[],[[[[],[]],[]],[]]]] => 1
[4,1,3,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[4,1,3,2,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[4,1,3,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[4,1,3,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => [[[],[]],[[[],[[],[[],[]]]],[]]] => 1
[4,1,3,6,2,5] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[4,1,3,6,5,2] => [[.,.],[[.,[[.,.],.]],.]] => [[[],[]],[[[],[[[],[]],[]]],[]]] => 1
[4,1,5,2,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[4,1,5,2,6,3] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[4,1,5,3,2,6] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[4,1,5,3,6,2] => [[.,.],[[[.,.],[.,.]],.]] => [[[],[]],[[[[],[]],[[],[]]],[]]] => 2
[4,1,5,6,2,3] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[4,1,5,6,3,2] => [[.,.],[[[.,[.,.]],.],.]] => [[[],[]],[[[[],[[],[]]],[]],[]]] => 1
[4,1,6,2,3,5] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[4,1,6,2,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[4,1,6,3,2,5] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[4,1,6,3,5,2] => [[.,.],[[[.,.],[.,.]],.]] => [[[],[]],[[[[],[]],[[],[]]],[]]] => 2
[4,1,6,5,2,3] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[4,1,6,5,3,2] => [[.,.],[[[[.,.],.],.],.]] => [[[],[]],[[[[[],[]],[]],[]],[]]] => 1
[4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 1
[4,2,1,3,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 1
[4,2,1,5,3,6] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[4,2,1,5,6,3] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 1
[4,2,1,6,3,5] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[4,2,1,6,5,3] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 1
[4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [[[[],[]],[[],[[],[[],[]]]]],[]] => 1
[4,2,3,6,1,5] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[4,2,3,6,5,1] => [[[.,.],[.,[[.,.],.]]],.] => [[[[],[]],[[],[[[],[]],[]]]],[]] => 1
[4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[4,2,5,1,6,3] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[4,2,5,3,1,6] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 2
[4,2,5,3,6,1] => [[[.,.],[[.,.],[.,.]]],.] => [[[[],[]],[[[],[]],[[],[]]]],[]] => 2
[4,2,5,6,1,3] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[4,2,5,6,3,1] => [[[.,.],[[.,[.,.]],.]],.] => [[[[],[]],[[[],[[],[]]],[]]],[]] => 1
[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] => [[[.,.],[[[.,.],.],.]],.] => [[[[],[]],[[[[],[]],[]],[]]],[]] => 1
[4,3,1,2,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 1
[4,3,1,2,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 1
[4,3,1,5,2,6] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[4,3,1,5,6,2] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 1
[4,3,1,6,2,5] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[4,3,1,6,5,2] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 1
[4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 1
[4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => [[[[[],[]],[]],[]],[[[],[]],[]]] => 1
[4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[4,3,2,5,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [[[[[],[]],[]],[[],[[],[]]]],[]] => 1
[4,3,2,6,1,5] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[4,3,2,6,5,1] => [[[[.,.],.],[[.,.],.]],.] => [[[[[],[]],[]],[[[],[]],[]]],[]] => 1
[4,3,5,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[4,3,5,1,6,2] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[4,3,5,2,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [[[[[],[]],[[],[]]],[]],[[],[]]] => 2
[4,3,5,2,6,1] => [[[[.,.],[.,.]],[.,.]],.] => [[[[[],[]],[[],[]]],[[],[]]],[]] => 2
[4,3,5,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[4,3,5,6,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [[[[[],[]],[[],[[],[]]]],[]],[]] => 1
[4,3,6,1,2,5] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[4,3,6,1,5,2] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[4,3,6,2,1,5] => [[[[.,.],[.,.]],.],[.,.]] => [[[[[],[]],[[],[]]],[]],[[],[]]] => 2
[4,3,6,2,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [[[[[],[]],[[],[]]],[[],[]]],[]] => 2
[4,3,6,5,1,2] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 2
[4,3,6,5,2,1] => [[[[.,.],[[.,.],.]],.],.] => [[[[[],[]],[[[],[]],[]]],[]],[]] => 1
[4,5,1,2,3,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 1
[4,5,1,2,6,3] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 1
[4,5,1,3,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[4,5,1,3,6,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 1
[4,5,1,6,2,3] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[4,5,1,6,3,2] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 1
[4,5,2,1,3,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 1
[4,5,2,1,6,3] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 1
[4,5,2,3,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[4,5,2,3,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => [[[[],[[],[]]],[[],[[],[]]]],[]] => 1
[4,5,2,6,1,3] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[4,5,2,6,3,1] => [[[.,[.,.]],[[.,.],.]],.] => [[[[],[[],[]]],[[[],[]],[]]],[]] => 1
[4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 1
[4,5,3,1,6,2] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 1
[4,5,3,2,1,6] => [[[[.,[.,.]],.],.],[.,.]] => [[[[[],[[],[]]],[]],[]],[[],[]]] => 1
[4,5,3,2,6,1] => [[[[.,[.,.]],.],[.,.]],.] => [[[[[],[[],[]]],[]],[[],[]]],[]] => 1
[4,5,3,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[4,5,3,6,2,1] => [[[[.,[.,.]],[.,.]],.],.] => [[[[[],[[],[]]],[[],[]]],[]],[]] => 1
[4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 1
[4,5,6,1,3,2] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 1
[4,5,6,2,1,3] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[],[[],[[],[]]]],[]],[[],[]]] => 1
[4,5,6,2,3,1] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[],[[],[[],[]]]],[[],[]]],[]] => 1
[4,5,6,3,1,2] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[],[[],[[],[]]]],[]],[[],[]]] => 1
[4,5,6,3,2,1] => [[[[.,[.,[.,.]]],.],.],.] => [[[[[],[[],[[],[]]]],[]],[]],[]] => 0
[4,6,1,2,3,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 1
[4,6,1,2,5,3] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 1
[4,6,1,3,2,5] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[4,6,1,3,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 1
[4,6,1,5,2,3] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[4,6,1,5,3,2] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 1
[4,6,2,1,3,5] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 1
[4,6,2,1,5,3] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 1
[4,6,2,3,1,5] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[4,6,2,3,5,1] => [[[.,[.,.]],[.,[.,.]]],.] => [[[[],[[],[]]],[[],[[],[]]]],[]] => 1
[4,6,2,5,1,3] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[4,6,2,5,3,1] => [[[.,[.,.]],[[.,.],.]],.] => [[[[],[[],[]]],[[[],[]],[]]],[]] => 1
[4,6,3,1,2,5] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 1
[4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 1
[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] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 1
[4,6,5,1,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 1
[4,6,5,2,1,3] => [[[.,[[.,.],.]],.],[.,.]] => [[[[],[[[],[]],[]]],[]],[[],[]]] => 1
[4,6,5,2,3,1] => [[[.,[[.,.],.]],[.,.]],.] => [[[[],[[[],[]],[]]],[[],[]]],[]] => 1
[4,6,5,3,1,2] => [[[.,[[.,.],.]],.],[.,.]] => [[[[],[[[],[]],[]]],[]],[[],[]]] => 1
[4,6,5,3,2,1] => [[[[.,[[.,.],.]],.],.],.] => [[[[[],[[[],[]],[]]],[]],[]],[]] => 0
[5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[],[]],[[],[[],[[],[[],[]]]]]] => 1
[5,1,2,3,6,4] => [[.,.],[.,[.,[[.,.],.]]]] => [[[],[]],[[],[[],[[[],[]],[]]]]] => 1
[5,1,2,4,3,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 2
[5,1,2,4,6,3] => [[.,.],[.,[[.,[.,.]],.]]] => [[[],[]],[[],[[[],[[],[]]],[]]]] => 1
[5,1,2,6,3,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 2
[5,1,2,6,4,3] => [[.,.],[.,[[[.,.],.],.]]] => [[[],[]],[[],[[[[],[]],[]],[]]]] => 1
[5,1,3,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[5,1,3,2,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[5,1,3,4,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[5,1,3,4,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => [[[],[]],[[[],[[],[[],[]]]],[]]] => 1
[5,1,3,6,2,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[5,1,3,6,4,2] => [[.,.],[[.,[[.,.],.]],.]] => [[[],[]],[[[],[[[],[]],[]]],[]]] => 1
[5,1,4,2,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[5,1,4,2,6,3] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[5,1,4,3,2,6] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[5,1,4,3,6,2] => [[.,.],[[[.,.],[.,.]],.]] => [[[],[]],[[[[],[]],[[],[]]],[]]] => 2
[5,1,4,6,2,3] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[5,1,4,6,3,2] => [[.,.],[[[.,[.,.]],.],.]] => [[[],[]],[[[[],[[],[]]],[]],[]]] => 1
[5,1,6,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[5,1,6,2,4,3] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[5,1,6,3,2,4] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[5,1,6,3,4,2] => [[.,.],[[[.,.],[.,.]],.]] => [[[],[]],[[[[],[]],[[],[]]],[]]] => 2
[5,1,6,4,2,3] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[5,1,6,4,3,2] => [[.,.],[[[[.,.],.],.],.]] => [[[],[]],[[[[[],[]],[]],[]],[]]] => 1
[5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 1
[5,2,1,3,6,4] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 1
[5,2,1,4,3,6] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[5,2,1,4,6,3] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 1
[5,2,1,6,3,4] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[5,2,1,6,4,3] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 1
[5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[5,2,3,1,6,4] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [[[[],[]],[[],[[],[[],[]]]]],[]] => 1
[5,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[5,2,3,6,4,1] => [[[.,.],[.,[[.,.],.]]],.] => [[[[],[]],[[],[[[],[]],[]]]],[]] => 1
[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] => [[[.,.],[[.,[.,.]],.]],.] => [[[[],[]],[[[],[[],[]]],[]]],[]] => 1
[5,2,6,1,3,4] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[5,2,6,1,4,3] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[5,2,6,3,1,4] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 2
[5,2,6,3,4,1] => [[[.,.],[[.,.],[.,.]]],.] => [[[[],[]],[[[],[]],[[],[]]]],[]] => 2
[5,2,6,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 2
[5,2,6,4,3,1] => [[[.,.],[[[.,.],.],.]],.] => [[[[],[]],[[[[],[]],[]],[]]],[]] => 1
[5,3,1,2,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 1
[5,3,1,2,6,4] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 1
[5,3,1,4,2,6] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[5,3,1,4,6,2] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 1
[5,3,1,6,2,4] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[5,3,1,6,4,2] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 1
[5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 1
[5,3,2,1,6,4] => [[[[.,.],.],.],[[.,.],.]] => [[[[[],[]],[]],[]],[[[],[]],[]]] => 1
[5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[5,3,2,4,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [[[[[],[]],[]],[[],[[],[]]]],[]] => 1
[5,3,2,6,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[5,3,2,6,4,1] => [[[[.,.],.],[[.,.],.]],.] => [[[[[],[]],[]],[[[],[]],[]]],[]] => 1
[5,3,4,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[5,3,4,1,6,2] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[5,3,4,2,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [[[[[],[]],[[],[]]],[]],[[],[]]] => 2
[5,3,4,2,6,1] => [[[[.,.],[.,.]],[.,.]],.] => [[[[[],[]],[[],[]]],[[],[]]],[]] => 2
[5,3,4,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[5,3,4,6,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [[[[[],[]],[[],[[],[]]]],[]],[]] => 1
[5,3,6,1,2,4] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[5,3,6,1,4,2] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[5,3,6,2,1,4] => [[[[.,.],[.,.]],.],[.,.]] => [[[[[],[]],[[],[]]],[]],[[],[]]] => 2
[5,3,6,2,4,1] => [[[[.,.],[.,.]],[.,.]],.] => [[[[[],[]],[[],[]]],[[],[]]],[]] => 2
[5,3,6,4,1,2] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 2
[5,3,6,4,2,1] => [[[[.,.],[[.,.],.]],.],.] => [[[[[],[]],[[[],[]],[]]],[]],[]] => 1
[5,4,1,2,3,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 1
[5,4,1,2,6,3] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 1
[5,4,1,3,2,6] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[5,4,1,3,6,2] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 1
[5,4,1,6,2,3] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[5,4,1,6,3,2] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 1
[5,4,2,1,3,6] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 1
[5,4,2,1,6,3] => [[[[.,.],.],.],[[.,.],.]] => [[[[[],[]],[]],[]],[[[],[]],[]]] => 1
[5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[5,4,2,3,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [[[[[],[]],[]],[[],[[],[]]]],[]] => 1
[5,4,2,6,1,3] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[5,4,2,6,3,1] => [[[[.,.],.],[[.,.],.]],.] => [[[[[],[]],[]],[[[],[]],[]]],[]] => 1
[5,4,3,1,2,6] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 1
[5,4,3,1,6,2] => [[[[.,.],.],.],[[.,.],.]] => [[[[[],[]],[]],[]],[[[],[]],[]]] => 1
[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] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[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] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 1
[5,6,1,2,4,3] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 1
[5,6,1,3,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[5,6,1,3,4,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 1
[5,6,1,4,2,3] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 2
[5,6,1,4,3,2] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 1
[5,6,2,1,3,4] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 1
[5,6,2,1,4,3] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 1
[5,6,2,3,1,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[5,6,2,3,4,1] => [[[.,[.,.]],[.,[.,.]]],.] => [[[[],[[],[]]],[[],[[],[]]]],[]] => 1
[5,6,2,4,1,3] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[5,6,2,4,3,1] => [[[.,[.,.]],[[.,.],.]],.] => [[[[],[[],[]]],[[[],[]],[]]],[]] => 1
[5,6,3,1,2,4] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 1
[5,6,3,1,4,2] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 1
[5,6,3,2,1,4] => [[[[.,[.,.]],.],.],[.,.]] => [[[[[],[[],[]]],[]],[]],[[],[]]] => 1
[5,6,3,2,4,1] => [[[[.,[.,.]],.],[.,.]],.] => [[[[[],[[],[]]],[]],[[],[]]],[]] => 1
[5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 2
[5,6,3,4,2,1] => [[[[.,[.,.]],[.,.]],.],.] => [[[[[],[[],[]]],[[],[]]],[]],[]] => 1
[5,6,4,1,2,3] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 1
[5,6,4,1,3,2] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 1
[5,6,4,2,1,3] => [[[[.,[.,.]],.],.],[.,.]] => [[[[[],[[],[]]],[]],[]],[[],[]]] => 1
[5,6,4,2,3,1] => [[[[.,[.,.]],.],[.,.]],.] => [[[[[],[[],[]]],[]],[[],[]]],[]] => 1
[5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [[[[[],[[],[]]],[]],[]],[[],[]]] => 1
[5,6,4,3,2,1] => [[[[[.,[.,.]],.],.],.],.] => [[[[[[],[[],[]]],[]],[]],[]],[]] => 0
[6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[],[]],[[],[[],[[],[[],[]]]]]] => 1
[6,1,2,3,5,4] => [[.,.],[.,[.,[[.,.],.]]]] => [[[],[]],[[],[[],[[[],[]],[]]]]] => 1
[6,1,2,4,3,5] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 2
[6,1,2,4,5,3] => [[.,.],[.,[[.,[.,.]],.]]] => [[[],[]],[[],[[[],[[],[]]],[]]]] => 1
[6,1,2,5,3,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 2
[6,1,2,5,4,3] => [[.,.],[.,[[[.,.],.],.]]] => [[[],[]],[[],[[[[],[]],[]],[]]]] => 1
[6,1,3,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[6,1,3,2,5,4] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[6,1,3,4,2,5] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[6,1,3,4,5,2] => [[.,.],[[.,[.,[.,.]]],.]] => [[[],[]],[[[],[[],[[],[]]]],[]]] => 1
[6,1,3,5,2,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[6,1,3,5,4,2] => [[.,.],[[.,[[.,.],.]],.]] => [[[],[]],[[[],[[[],[]],[]]],[]]] => 1
[6,1,4,2,3,5] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[6,1,4,2,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 2
[6,1,4,3,2,5] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 2
[6,1,4,3,5,2] => [[.,.],[[[.,.],[.,.]],.]] => [[[],[]],[[[[],[]],[[],[]]],[]]] => 2
[6,1,4,5,2,3] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 2
[6,1,4,5,3,2] => [[.,.],[[[.,[.,.]],.],.]] => [[[],[]],[[[[],[[],[]]],[]],[]]] => 1
[6,1,5,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 2
[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] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 1
[6,2,1,3,5,4] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 1
[6,2,1,4,3,5] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[6,2,1,4,5,3] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 1
[6,2,1,5,3,4] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[6,2,1,5,4,3] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 1
[6,2,3,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[6,2,3,1,5,4] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[6,2,3,4,1,5] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [[[[],[]],[[],[[],[[],[]]]]],[]] => 1
[6,2,3,5,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.] => [[[[],[]],[[],[[[],[]],[]]]],[]] => 1
[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] => [[[.,.],[[.,[.,.]],.]],.] => [[[[],[]],[[[],[[],[]]],[]]],[]] => 1
[6,2,5,1,3,4] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[6,2,5,1,4,3] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[6,2,5,3,1,4] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 2
[6,2,5,3,4,1] => [[[.,.],[[.,.],[.,.]]],.] => [[[[],[]],[[[],[]],[[],[]]]],[]] => 2
[6,2,5,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 2
[6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.] => [[[[],[]],[[[[],[]],[]],[]]],[]] => 1
[6,3,1,2,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 1
[6,3,1,2,5,4] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 1
[6,3,1,4,2,5] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[6,3,1,4,5,2] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 1
[6,3,1,5,2,4] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[6,3,1,5,4,2] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 1
[6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 1
[6,3,2,1,5,4] => [[[[.,.],.],.],[[.,.],.]] => [[[[[],[]],[]],[]],[[[],[]],[]]] => 1
[6,3,2,4,1,5] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [[[[[],[]],[]],[[],[[],[]]]],[]] => 1
[6,3,2,5,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.] => [[[[[],[]],[]],[[[],[]],[]]],[]] => 1
[6,3,4,1,2,5] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[6,3,4,1,5,2] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[6,3,4,2,1,5] => [[[[.,.],[.,.]],.],[.,.]] => [[[[[],[]],[[],[]]],[]],[[],[]]] => 2
[6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [[[[[],[]],[[],[]]],[[],[]]],[]] => 2
[6,3,4,5,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 2
[6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [[[[[],[]],[[],[[],[]]]],[]],[]] => 1
[6,3,5,1,2,4] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[6,3,5,1,4,2] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 2
[6,3,5,2,1,4] => [[[[.,.],[.,.]],.],[.,.]] => [[[[[],[]],[[],[]]],[]],[[],[]]] => 2
[6,3,5,2,4,1] => [[[[.,.],[.,.]],[.,.]],.] => [[[[[],[]],[[],[]]],[[],[]]],[]] => 2
[6,3,5,4,1,2] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 2
[6,3,5,4,2,1] => [[[[.,.],[[.,.],.]],.],.] => [[[[[],[]],[[[],[]],[]]],[]],[]] => 1
[6,4,1,2,3,5] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 1
[6,4,1,2,5,3] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 1
[6,4,1,3,2,5] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[6,4,1,3,5,2] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 1
[6,4,1,5,2,3] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[6,4,1,5,3,2] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 1
[6,4,2,1,3,5] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 1
[6,4,2,1,5,3] => [[[[.,.],.],.],[[.,.],.]] => [[[[[],[]],[]],[]],[[[],[]],[]]] => 1
[6,4,2,3,1,5] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [[[[[],[]],[]],[[],[[],[]]]],[]] => 1
[6,4,2,5,1,3] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[6,4,2,5,3,1] => [[[[.,.],.],[[.,.],.]],.] => [[[[[],[]],[]],[[[],[]],[]]],[]] => 1
[6,4,3,1,2,5] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 1
[6,4,3,1,5,2] => [[[[.,.],.],.],[[.,.],.]] => [[[[[],[]],[]],[]],[[[],[]],[]]] => 1
[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] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 2
[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] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 1
[6,5,1,2,4,3] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 1
[6,5,1,3,2,4] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[6,5,1,3,4,2] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 1
[6,5,1,4,2,3] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 2
[6,5,1,4,3,2] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 1
[6,5,2,1,3,4] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 1
[6,5,2,1,4,3] => [[[[.,.],.],.],[[.,.],.]] => [[[[[],[]],[]],[]],[[[],[]],[]]] => 1
[6,5,2,3,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.] => [[[[[],[]],[]],[[],[[],[]]]],[]] => 1
[6,5,2,4,1,3] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 2
[6,5,2,4,3,1] => [[[[.,.],.],[[.,.],.]],.] => [[[[[],[]],[]],[[[],[]],[]]],[]] => 1
[6,5,3,1,2,4] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 1
[6,5,3,1,4,2] => [[[[.,.],.],.],[[.,.],.]] => [[[[[],[]],[]],[]],[[[],[]],[]]] => 1
[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] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 1
[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:
4,2 8,16 16,88,16 32,416,272
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + 2\ q$
$F_{4} = 8 + 16\ q$
$F_{5} = 16 + 88\ q + 16\ q^{2}$
$F_{6} = 32 + 416\ q + 272\ q^{2}$
Description
The number of 2-protected nodes of a rooted tree.
This is the number of nodes with minimal distance two to a leaf. The number of trees with no 2-protected nodes is oeis:A143363.
This is the number of nodes with minimal distance two to a leaf. The number of trees with no 2-protected nodes is oeis:A143363.
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to complete tree
Description
Return the same tree seen as an ordered tree. By default, leaves are transformed into actual nodes.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
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