Identifier
-
Mp00090:
Permutations
—cycle-as-one-line notation⟶
Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
St000252: Binary trees ⟶ ℤ
Values
[1] => [1] => [.,.] => 0
[1,2] => [1,2] => [.,[.,.]] => 0
[2,1] => [1,2] => [.,[.,.]] => 0
[1,2,3] => [1,2,3] => [.,[.,[.,.]]] => 0
[1,3,2] => [1,2,3] => [.,[.,[.,.]]] => 0
[2,1,3] => [1,2,3] => [.,[.,[.,.]]] => 0
[2,3,1] => [1,2,3] => [.,[.,[.,.]]] => 0
[3,1,2] => [1,3,2] => [.,[[.,.],.]] => 0
[3,2,1] => [1,3,2] => [.,[[.,.],.]] => 0
[1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[1,2,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[1,3,2,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[1,3,4,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[1,4,2,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 0
[1,4,3,2] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 0
[2,1,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[2,1,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[2,3,1,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[2,3,4,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[2,4,1,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 0
[2,4,3,1] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 0
[3,1,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 1
[3,1,4,2] => [1,3,4,2] => [.,[[.,[.,.]],.]] => 0
[3,2,1,4] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 1
[3,2,4,1] => [1,3,4,2] => [.,[[.,[.,.]],.]] => 0
[3,4,1,2] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 1
[3,4,2,1] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 1
[4,1,2,3] => [1,4,3,2] => [.,[[[.,.],.],.]] => 0
[4,1,3,2] => [1,4,2,3] => [.,[[.,.],[.,.]]] => 1
[4,2,1,3] => [1,4,3,2] => [.,[[[.,.],.],.]] => 0
[4,2,3,1] => [1,4,2,3] => [.,[[.,.],[.,.]]] => 1
[4,3,1,2] => [1,4,2,3] => [.,[[.,.],[.,.]]] => 1
[4,3,2,1] => [1,4,2,3] => [.,[[.,.],[.,.]]] => 1
[1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,2,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,2,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,2,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,2,5,3,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 0
[1,2,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 0
[1,3,2,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,3,2,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,3,4,2,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,3,4,5,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,3,5,2,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 0
[1,3,5,4,2] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 0
[1,4,2,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 1
[1,4,2,5,3] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => 0
[1,4,3,2,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 1
[1,4,3,5,2] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => 0
[1,4,5,2,3] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 1
[1,4,5,3,2] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 1
[1,5,2,3,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => 0
[1,5,2,4,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 1
[1,5,3,2,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => 0
[1,5,3,4,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 1
[1,5,4,2,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 1
[1,5,4,3,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 1
[2,1,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[2,1,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[2,1,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[2,1,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[2,1,5,3,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 0
[2,1,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 0
[2,3,1,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[2,3,1,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[2,3,4,1,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[2,3,4,5,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[2,3,5,1,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 0
[2,3,5,4,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 0
[2,4,1,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 1
[2,4,1,5,3] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => 0
[2,4,3,1,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 1
[2,4,3,5,1] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => 0
[2,4,5,1,3] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 1
[2,4,5,3,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 1
[2,5,1,3,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => 0
[2,5,1,4,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 1
[2,5,3,1,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => 0
[2,5,3,4,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 1
[2,5,4,1,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 1
[2,5,4,3,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 1
[3,1,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 1
[3,1,2,5,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 1
[3,1,4,2,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => 1
[3,1,4,5,2] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => 0
[3,1,5,2,4] => [1,3,5,4,2] => [.,[[.,[[.,.],.]],.]] => 0
[3,1,5,4,2] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => 1
[3,2,1,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 1
[3,2,1,5,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 1
[3,2,4,1,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => 1
[3,2,4,5,1] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => 0
[3,2,5,1,4] => [1,3,5,4,2] => [.,[[.,[[.,.],.]],.]] => 0
[3,2,5,4,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => 1
[3,4,1,2,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 1
[3,4,1,5,2] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 1
[3,4,2,1,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 1
[3,4,2,5,1] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 1
[3,4,5,1,2] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => 1
[3,4,5,2,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => 1
[3,5,1,2,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => 1
[3,5,1,4,2] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => 1
>>> Load all 873 entries. <<<[3,5,2,1,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => 1
[3,5,2,4,1] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => 1
[3,5,4,1,2] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => 1
[3,5,4,2,1] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => 1
[4,1,2,3,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => 1
[4,1,2,5,3] => [1,4,5,3,2] => [.,[[[.,[.,.]],.],.]] => 0
[4,1,3,2,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 1
[4,1,3,5,2] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 1
[4,1,5,2,3] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 1
[4,1,5,3,2] => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]] => 1
[4,2,1,3,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => 1
[4,2,1,5,3] => [1,4,5,3,2] => [.,[[[.,[.,.]],.],.]] => 0
[4,2,3,1,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 1
[4,2,3,5,1] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 1
[4,2,5,1,3] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 1
[4,2,5,3,1] => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]] => 1
[4,3,1,2,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 1
[4,3,1,5,2] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 1
[4,3,2,1,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 1
[4,3,2,5,1] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 1
[4,3,5,1,2] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 1
[4,3,5,2,1] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 1
[4,5,1,2,3] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => 1
[4,5,1,3,2] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => 1
[4,5,2,1,3] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => 1
[4,5,2,3,1] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => 1
[4,5,3,1,2] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => 1
[4,5,3,2,1] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => 1
[5,1,2,3,4] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => 0
[5,1,2,4,3] => [1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => 1
[5,1,3,2,4] => [1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => 1
[5,1,3,4,2] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 1
[5,1,4,2,3] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => 1
[5,1,4,3,2] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 1
[5,2,1,3,4] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => 0
[5,2,1,4,3] => [1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => 1
[5,2,3,1,4] => [1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => 1
[5,2,3,4,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 1
[5,2,4,1,3] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => 1
[5,2,4,3,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 1
[5,3,1,2,4] => [1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => 1
[5,3,1,4,2] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 1
[5,3,2,1,4] => [1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => 1
[5,3,2,4,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 1
[5,3,4,1,2] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 1
[5,3,4,2,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 1
[5,4,1,2,3] => [1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => 1
[5,4,1,3,2] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => 1
[5,4,2,1,3] => [1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => 1
[5,4,2,3,1] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => 1
[5,4,3,1,2] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => 1
[5,4,3,2,1] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,2,3,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,2,3,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,2,3,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,2,3,6,4,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[1,2,3,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[1,2,4,3,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,2,4,3,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,2,4,5,3,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,2,4,5,6,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,2,4,6,3,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[1,2,4,6,5,3] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[1,2,5,3,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,2,5,3,6,4] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 0
[1,2,5,4,3,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,2,5,4,6,3] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 0
[1,2,5,6,3,4] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,2,5,6,4,3] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,2,6,3,4,5] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => 0
[1,2,6,3,5,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,2,6,4,3,5] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => 0
[1,2,6,4,5,3] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,2,6,5,3,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,2,6,5,4,3] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,3,2,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,3,2,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,3,2,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,3,2,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,3,2,6,4,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[1,3,2,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[1,3,4,2,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,3,4,2,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,3,4,5,2,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,3,4,5,6,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,3,4,6,2,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[1,3,4,6,5,2] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[1,3,5,2,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,3,5,2,6,4] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 0
[1,3,5,4,2,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,3,5,4,6,2] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 0
[1,3,5,6,2,4] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,3,5,6,4,2] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,3,6,2,4,5] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => 0
[1,3,6,2,5,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,3,6,4,2,5] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => 0
[1,3,6,4,5,2] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,3,6,5,2,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,3,6,5,4,2] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,4,2,3,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,4,2,3,6,5] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,4,2,5,3,6] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,4,2,5,6,3] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => 0
[1,4,2,6,3,5] => [1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]] => 0
[1,4,2,6,5,3] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,4,3,2,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,4,3,2,6,5] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,4,3,5,2,6] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,4,3,5,6,2] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => 0
[1,4,3,6,2,5] => [1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]] => 0
[1,4,3,6,5,2] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,4,5,2,3,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,4,5,2,6,3] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,4,5,3,2,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,4,5,3,6,2] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,4,5,6,2,3] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,4,5,6,3,2] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,4,6,2,3,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,4,6,2,5,3] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,4,6,3,2,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,4,6,3,5,2] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,4,6,5,2,3] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,4,6,5,3,2] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,5,2,3,4,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,5,2,3,6,4] => [1,2,5,6,4,3] => [.,[.,[[[.,[.,.]],.],.]]] => 0
[1,5,2,4,3,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,5,2,4,6,3] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,5,2,6,3,4] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,5,2,6,4,3] => [1,2,5,4,6,3] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[1,5,3,2,4,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,5,3,2,6,4] => [1,2,5,6,4,3] => [.,[.,[[[.,[.,.]],.],.]]] => 0
[1,5,3,4,2,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,5,3,4,6,2] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,5,3,6,2,4] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,5,3,6,4,2] => [1,2,5,4,6,3] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[1,5,4,2,3,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,5,4,2,6,3] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,5,4,3,2,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,5,4,3,6,2] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,5,4,6,2,3] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,5,4,6,3,2] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,5,6,2,3,4] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,5,6,2,4,3] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,5,6,3,2,4] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,5,6,3,4,2] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,5,6,4,2,3] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,5,6,4,3,2] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,6,2,3,4,5] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => 0
[1,6,2,3,5,4] => [1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,6,2,4,3,5] => [1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,6,2,4,5,3] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,6,2,5,3,4] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[1,6,2,5,4,3] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,6,3,2,4,5] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => 0
[1,6,3,2,5,4] => [1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,6,3,4,2,5] => [1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,6,3,4,5,2] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,6,3,5,2,4] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[1,6,3,5,4,2] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,6,4,2,3,5] => [1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,6,4,2,5,3] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,6,4,3,2,5] => [1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,6,4,3,5,2] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,6,4,5,2,3] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,6,4,5,3,2] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,6,5,2,3,4] => [1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,6,5,2,4,3] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,6,5,3,2,4] => [1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,6,5,3,4,2] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,6,5,4,2,3] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[1,6,5,4,3,2] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,1,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,1,3,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,1,3,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,1,3,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,1,3,6,4,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[2,1,3,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[2,1,4,3,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,1,4,3,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,1,4,5,3,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,1,4,5,6,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,1,4,6,3,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[2,1,4,6,5,3] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[2,1,5,3,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,1,5,3,6,4] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 0
[2,1,5,4,3,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,1,5,4,6,3] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 0
[2,1,5,6,3,4] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,1,5,6,4,3] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,1,6,3,4,5] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => 0
[2,1,6,3,5,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,1,6,4,3,5] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => 0
[2,1,6,4,5,3] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,1,6,5,3,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,1,6,5,4,3] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,3,1,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,3,1,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,3,1,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,3,1,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,3,1,6,4,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[2,3,1,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[2,3,4,1,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,3,4,1,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,3,4,5,1,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,3,4,6,1,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[2,3,4,6,5,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[2,3,5,1,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,3,5,1,6,4] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 0
[2,3,5,4,1,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,3,5,4,6,1] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 0
[2,3,5,6,1,4] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,3,5,6,4,1] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,3,6,1,4,5] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => 0
[2,3,6,1,5,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,3,6,4,1,5] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => 0
[2,3,6,4,5,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,3,6,5,1,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,3,6,5,4,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,4,1,3,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,4,1,3,6,5] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,4,1,5,3,6] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,4,1,5,6,3] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => 0
[2,4,1,6,3,5] => [1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]] => 0
[2,4,1,6,5,3] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,4,3,1,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,4,3,1,6,5] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,4,3,5,1,6] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,4,3,5,6,1] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => 0
[2,4,3,6,1,5] => [1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]] => 0
[2,4,3,6,5,1] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,4,5,1,3,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,4,5,1,6,3] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,4,5,3,1,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,4,5,3,6,1] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,4,5,6,1,3] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,4,5,6,3,1] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,4,6,1,3,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,4,6,1,5,3] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,4,6,3,1,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,4,6,3,5,1] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,4,6,5,1,3] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,4,6,5,3,1] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,5,1,3,4,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,5,1,3,6,4] => [1,2,5,6,4,3] => [.,[.,[[[.,[.,.]],.],.]]] => 0
[2,5,1,4,3,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,5,1,4,6,3] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,5,1,6,3,4] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,5,1,6,4,3] => [1,2,5,4,6,3] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[2,5,3,1,4,6] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,5,3,1,6,4] => [1,2,5,6,4,3] => [.,[.,[[[.,[.,.]],.],.]]] => 0
[2,5,3,4,1,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,5,3,4,6,1] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,5,3,6,1,4] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,5,3,6,4,1] => [1,2,5,4,6,3] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[2,5,4,1,3,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,5,4,1,6,3] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,5,4,3,1,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,5,4,3,6,1] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[2,5,4,6,1,3] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,5,4,6,3,1] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,5,6,1,3,4] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,5,6,1,4,3] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,5,6,3,1,4] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,5,6,3,4,1] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,5,6,4,1,3] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,5,6,4,3,1] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,6,1,3,4,5] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => 0
[2,6,1,3,5,4] => [1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,6,1,4,3,5] => [1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,6,1,4,5,3] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,6,1,5,3,4] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[2,6,1,5,4,3] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,6,3,1,4,5] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => 0
[2,6,3,1,5,4] => [1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,6,3,4,1,5] => [1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,6,3,4,5,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,6,3,5,1,4] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[2,6,3,5,4,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,6,4,1,3,5] => [1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,6,4,1,5,3] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,6,4,3,1,5] => [1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,6,4,3,5,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,6,4,5,1,3] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,6,4,5,3,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[2,6,5,1,3,4] => [1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,6,5,1,4,3] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,6,5,3,1,4] => [1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[2,6,5,3,4,1] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,6,5,4,1,3] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[2,6,5,4,3,1] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 1
[3,1,2,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,1,2,4,6,5] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,1,2,5,4,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,1,2,5,6,4] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,1,2,6,4,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[3,1,2,6,5,4] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[3,1,4,2,5,6] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,1,4,2,6,5] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,1,4,5,2,6] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,1,4,5,6,2] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]] => 0
[3,1,4,6,2,5] => [1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]] => 0
[3,1,4,6,5,2] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,1,5,2,4,6] => [1,3,5,4,2,6] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,1,5,2,6,4] => [1,3,5,6,4,2] => [.,[[.,[[.,[.,.]],.]],.]] => 0
[3,1,5,4,2,6] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,1,5,4,6,2] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,1,5,6,2,4] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,1,5,6,4,2] => [1,3,5,4,6,2] => [.,[[.,[[.,.],[.,.]]],.]] => 1
[3,1,6,2,4,5] => [1,3,6,5,4,2] => [.,[[.,[[[.,.],.],.]],.]] => 0
[3,1,6,2,5,4] => [1,3,6,4,2,5] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,1,6,4,2,5] => [1,3,6,5,2,4] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,1,6,4,5,2] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,1,6,5,2,4] => [1,3,6,4,5,2] => [.,[[.,[[.,.],[.,.]]],.]] => 1
[3,1,6,5,4,2] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,2,1,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,2,1,4,6,5] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,2,1,5,4,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,2,1,5,6,4] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,2,1,6,4,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[3,2,1,6,5,4] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[3,2,4,1,5,6] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,2,4,1,6,5] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,2,4,5,1,6] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,2,4,5,6,1] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]] => 0
[3,2,4,6,1,5] => [1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]] => 0
[3,2,4,6,5,1] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,2,5,1,4,6] => [1,3,5,4,2,6] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,2,5,1,6,4] => [1,3,5,6,4,2] => [.,[[.,[[.,[.,.]],.]],.]] => 0
[3,2,5,4,1,6] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,2,5,4,6,1] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,2,5,6,1,4] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,2,5,6,4,1] => [1,3,5,4,6,2] => [.,[[.,[[.,.],[.,.]]],.]] => 1
[3,2,6,1,4,5] => [1,3,6,5,4,2] => [.,[[.,[[[.,.],.],.]],.]] => 0
[3,2,6,1,5,4] => [1,3,6,4,2,5] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,2,6,4,1,5] => [1,3,6,5,2,4] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,2,6,4,5,1] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,2,6,5,1,4] => [1,3,6,4,5,2] => [.,[[.,[[.,.],[.,.]]],.]] => 1
[3,2,6,5,4,1] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,4,1,2,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,4,1,2,6,5] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,4,1,5,2,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,4,1,5,6,2] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,4,1,6,2,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[3,4,1,6,5,2] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[3,4,2,1,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,4,2,1,6,5] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,4,2,5,1,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,4,2,5,6,1] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[3,4,2,6,1,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[3,4,2,6,5,1] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[3,4,5,1,2,6] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,4,5,1,6,2] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,4,5,2,1,6] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,4,5,2,6,1] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,4,5,6,1,2] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,4,5,6,2,1] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,4,6,1,2,5] => [1,3,6,5,2,4] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,4,6,1,5,2] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,4,6,2,1,5] => [1,3,6,5,2,4] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,4,6,2,5,1] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,4,6,5,1,2] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,4,6,5,2,1] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,5,1,2,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,5,1,2,6,4] => [1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[3,5,1,4,2,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,5,1,4,6,2] => [1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[3,5,1,6,2,4] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,5,1,6,4,2] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,5,2,1,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,5,2,1,6,4] => [1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[3,5,2,4,1,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,5,2,4,6,1] => [1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[3,5,2,6,1,4] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,5,2,6,4,1] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,5,4,1,2,6] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,5,4,1,6,2] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,5,4,2,1,6] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,5,4,2,6,1] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[3,5,4,6,1,2] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,5,4,6,2,1] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,5,6,1,2,4] => [1,3,6,4,2,5] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,5,6,1,4,2] => [1,3,6,2,5,4] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,5,6,2,1,4] => [1,3,6,4,2,5] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,5,6,2,4,1] => [1,3,6,2,5,4] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,5,6,4,1,2] => [1,3,6,2,5,4] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,5,6,4,2,1] => [1,3,6,2,5,4] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,6,1,2,4,5] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => 1
[3,6,1,2,5,4] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,6,1,4,2,5] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => 1
[3,6,1,4,5,2] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,6,1,5,2,4] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,6,1,5,4,2] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,6,2,1,4,5] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => 1
[3,6,2,1,5,4] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,6,2,4,1,5] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => 1
[3,6,2,4,5,1] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,6,2,5,1,4] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,6,2,5,4,1] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[3,6,4,1,2,5] => [1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,6,4,1,5,2] => [1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,6,4,2,1,5] => [1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,6,4,2,5,1] => [1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,6,4,5,1,2] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,6,4,5,2,1] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[3,6,5,1,2,4] => [1,3,5,2,6,4] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,6,5,1,4,2] => [1,3,5,4,2,6] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,6,5,2,1,4] => [1,3,5,2,6,4] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,6,5,2,4,1] => [1,3,5,4,2,6] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[3,6,5,4,1,2] => [1,3,5,2,6,4] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[3,6,5,4,2,1] => [1,3,5,2,6,4] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[4,1,2,3,5,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[4,1,2,3,6,5] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[4,1,2,5,3,6] => [1,4,5,3,2,6] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[4,1,2,5,6,3] => [1,4,5,6,3,2] => [.,[[[.,[.,[.,.]]],.],.]] => 0
[4,1,2,6,3,5] => [1,4,6,5,3,2] => [.,[[[.,[[.,.],.]],.],.]] => 0
[4,1,2,6,5,3] => [1,4,6,3,2,5] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[4,1,3,2,5,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,1,3,2,6,5] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,1,3,5,2,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,1,3,5,6,2] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[4,1,3,6,2,5] => [1,4,6,5,2,3] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[4,1,3,6,5,2] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,1,5,2,3,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,1,5,2,6,3] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,1,5,3,2,6] => [1,4,3,5,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[4,1,5,3,6,2] => [1,4,3,5,6,2] => [.,[[[.,.],[.,[.,.]]],.]] => 1
[4,1,5,6,2,3] => [1,4,6,3,5,2] => [.,[[[.,[.,.]],[.,.]],.]] => 1
[4,1,5,6,3,2] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,1,6,2,3,5] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[4,1,6,2,5,3] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[4,1,6,3,2,5] => [1,4,3,6,5,2] => [.,[[[.,.],[[.,.],.]],.]] => 1
[4,1,6,3,5,2] => [1,4,3,6,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[4,1,6,5,2,3] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,1,6,5,3,2] => [1,4,5,3,6,2] => [.,[[[.,[.,.]],[.,.]],.]] => 1
[4,2,1,3,5,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[4,2,1,3,6,5] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[4,2,1,5,3,6] => [1,4,5,3,2,6] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[4,2,1,5,6,3] => [1,4,5,6,3,2] => [.,[[[.,[.,[.,.]]],.],.]] => 0
[4,2,1,6,3,5] => [1,4,6,5,3,2] => [.,[[[.,[[.,.],.]],.],.]] => 0
[4,2,1,6,5,3] => [1,4,6,3,2,5] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[4,2,3,1,5,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,2,3,1,6,5] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,2,3,5,1,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,2,3,5,6,1] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[4,2,3,6,1,5] => [1,4,6,5,2,3] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[4,2,3,6,5,1] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,2,5,1,3,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,2,5,1,6,3] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,2,5,3,1,6] => [1,4,3,5,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[4,2,5,3,6,1] => [1,4,3,5,6,2] => [.,[[[.,.],[.,[.,.]]],.]] => 1
[4,2,5,6,1,3] => [1,4,6,3,5,2] => [.,[[[.,[.,.]],[.,.]],.]] => 1
[4,2,5,6,3,1] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,2,6,1,3,5] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[4,2,6,1,5,3] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[4,2,6,3,1,5] => [1,4,3,6,5,2] => [.,[[[.,.],[[.,.],.]],.]] => 1
[4,2,6,3,5,1] => [1,4,3,6,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[4,2,6,5,1,3] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,2,6,5,3,1] => [1,4,5,3,6,2] => [.,[[[.,[.,.]],[.,.]],.]] => 1
[4,3,1,2,5,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,3,1,2,6,5] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,3,1,5,2,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,3,1,5,6,2] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[4,3,1,6,2,5] => [1,4,6,5,2,3] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[4,3,1,6,5,2] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,3,2,1,5,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,3,2,1,6,5] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,3,2,5,1,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,3,2,5,6,1] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[4,3,2,6,1,5] => [1,4,6,5,2,3] => [.,[[.,[[.,.],.]],[.,.]]] => 1
[4,3,2,6,5,1] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,3,5,1,2,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,3,5,1,6,2] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,3,5,2,1,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,3,5,2,6,1] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[4,3,5,6,1,2] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,3,5,6,2,1] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,3,6,1,2,5] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[4,3,6,1,5,2] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[4,3,6,2,1,5] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[4,3,6,2,5,1] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[4,3,6,5,1,2] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,3,6,5,2,1] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[4,5,1,2,3,6] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,5,1,2,6,3] => [1,4,2,5,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[4,5,1,3,2,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[4,5,1,3,6,2] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[4,5,1,6,2,3] => [1,4,6,3,2,5] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[4,5,1,6,3,2] => [1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[4,5,2,1,3,6] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,5,2,1,6,3] => [1,4,2,5,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[4,5,2,3,1,6] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[4,5,2,3,6,1] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[4,5,2,6,1,3] => [1,4,6,3,2,5] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[4,5,2,6,3,1] => [1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[4,5,3,1,2,6] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,5,3,1,6,2] => [1,4,2,5,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[4,5,3,2,1,6] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,5,3,2,6,1] => [1,4,2,5,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[4,5,3,6,1,2] => [1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[4,5,3,6,2,1] => [1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[4,5,6,1,2,3] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,5,6,1,3,2] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,5,6,2,1,3] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,5,6,2,3,1] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,5,6,3,1,2] => [1,4,3,6,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[4,5,6,3,2,1] => [1,4,3,6,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[4,6,1,2,3,5] => [1,4,2,6,5,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[4,6,1,2,5,3] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,6,1,3,2,5] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => 1
[4,6,1,3,5,2] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => 1
[4,6,1,5,2,3] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[4,6,1,5,3,2] => [1,4,5,3,2,6] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[4,6,2,1,3,5] => [1,4,2,6,5,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[4,6,2,1,5,3] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,6,2,3,1,5] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => 1
[4,6,2,3,5,1] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => 1
[4,6,2,5,1,3] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[4,6,2,5,3,1] => [1,4,5,3,2,6] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[4,6,3,1,2,5] => [1,4,2,6,5,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[4,6,3,1,5,2] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,6,3,2,1,5] => [1,4,2,6,5,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[4,6,3,2,5,1] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,6,3,5,1,2] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[4,6,3,5,2,1] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[4,6,5,1,2,3] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,6,5,1,3,2] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,6,5,2,1,3] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,6,5,2,3,1] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[4,6,5,3,1,2] => [1,4,3,5,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[4,6,5,3,2,1] => [1,4,3,5,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,1,2,3,4,6] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => 1
[5,1,2,3,6,4] => [1,5,6,4,3,2] => [.,[[[[.,[.,.]],.],.],.]] => 0
[5,1,2,4,3,6] => [1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,1,2,4,6,3] => [1,5,6,3,2,4] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[5,1,2,6,3,4] => [1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,1,2,6,4,3] => [1,5,4,6,3,2] => [.,[[[[.,.],[.,.]],.],.]] => 1
[5,1,3,2,4,6] => [1,5,4,2,3,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,1,3,2,6,4] => [1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[5,1,3,4,2,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,1,3,4,6,2] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[5,1,3,6,2,4] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,1,3,6,4,2] => [1,5,4,6,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,1,4,2,3,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,1,4,2,6,3] => [1,5,6,3,4,2] => [.,[[[.,[.,.]],[.,.]],.]] => 1
[5,1,4,3,2,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,1,4,3,6,2] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[5,1,4,6,2,3] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,1,4,6,3,2] => [1,5,3,4,6,2] => [.,[[[.,.],[.,[.,.]]],.]] => 1
[5,1,6,2,3,4] => [1,5,3,6,4,2] => [.,[[[.,.],[[.,.],.]],.]] => 1
[5,1,6,2,4,3] => [1,5,4,2,3,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,1,6,3,2,4] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[5,1,6,3,4,2] => [1,5,4,3,6,2] => [.,[[[[.,.],.],[.,.]],.]] => 1
[5,1,6,4,2,3] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[5,1,6,4,3,2] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,2,1,3,4,6] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => 1
[5,2,1,3,6,4] => [1,5,6,4,3,2] => [.,[[[[.,[.,.]],.],.],.]] => 0
[5,2,1,4,3,6] => [1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,2,1,4,6,3] => [1,5,6,3,2,4] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[5,2,1,6,3,4] => [1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,2,1,6,4,3] => [1,5,4,6,3,2] => [.,[[[[.,.],[.,.]],.],.]] => 1
[5,2,3,1,4,6] => [1,5,4,2,3,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,2,3,1,6,4] => [1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[5,2,3,4,1,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,2,3,4,6,1] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[5,2,3,6,1,4] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,2,3,6,4,1] => [1,5,4,6,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,2,4,1,3,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,2,4,1,6,3] => [1,5,6,3,4,2] => [.,[[[.,[.,.]],[.,.]],.]] => 1
[5,2,4,3,1,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,2,4,3,6,1] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[5,2,4,6,1,3] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,2,4,6,3,1] => [1,5,3,4,6,2] => [.,[[[.,.],[.,[.,.]]],.]] => 1
[5,2,6,1,3,4] => [1,5,3,6,4,2] => [.,[[[.,.],[[.,.],.]],.]] => 1
[5,2,6,1,4,3] => [1,5,4,2,3,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,2,6,3,1,4] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[5,2,6,3,4,1] => [1,5,4,3,6,2] => [.,[[[[.,.],.],[.,.]],.]] => 1
[5,2,6,4,1,3] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[5,2,6,4,3,1] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,3,1,2,4,6] => [1,5,4,2,3,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,3,1,2,6,4] => [1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[5,3,1,4,2,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,3,1,4,6,2] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[5,3,1,6,2,4] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,3,1,6,4,2] => [1,5,4,6,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,3,2,1,4,6] => [1,5,4,2,3,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,3,2,1,6,4] => [1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[5,3,2,4,1,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,3,2,4,6,1] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[5,3,2,6,1,4] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,3,2,6,4,1] => [1,5,4,6,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,3,4,1,2,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,3,4,1,6,2] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[5,3,4,2,1,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,3,4,2,6,1] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[5,3,4,6,1,2] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,3,4,6,2,1] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[5,3,6,1,2,4] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[5,3,6,1,4,2] => [1,5,4,2,3,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,3,6,2,1,4] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[5,3,6,2,4,1] => [1,5,4,2,3,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,3,6,4,1,2] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[5,3,6,4,2,1] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[5,4,1,2,3,6] => [1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,4,1,2,6,3] => [1,5,6,3,2,4] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[5,4,1,3,2,6] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,4,1,3,6,2] => [1,5,6,2,4,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[5,4,1,6,2,3] => [1,5,2,4,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[5,4,1,6,3,2] => [1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,4,2,1,3,6] => [1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,4,2,1,6,3] => [1,5,6,3,2,4] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[5,4,2,3,1,6] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,4,2,3,6,1] => [1,5,6,2,4,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[5,4,2,6,1,3] => [1,5,2,4,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[5,4,2,6,3,1] => [1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[5,4,3,1,2,6] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,4,3,1,6,2] => [1,5,6,2,4,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[5,4,3,2,1,6] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,4,3,2,6,1] => [1,5,6,2,4,3] => [.,[[.,[.,.]],[[.,.],.]]] => 1
[5,4,3,6,1,2] => [1,5,2,4,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[5,4,3,6,2,1] => [1,5,2,4,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[5,4,6,1,2,3] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,4,6,1,3,2] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,4,6,2,1,3] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,4,6,2,3,1] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,4,6,3,1,2] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,4,6,3,2,1] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,6,1,2,3,4] => [1,5,3,2,6,4] => [.,[[[.,.],.],[[.,.],.]]] => 1
[5,6,1,2,4,3] => [1,5,4,2,6,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[5,6,1,3,2,4] => [1,5,2,6,4,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[5,6,1,3,4,2] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => 1
[5,6,1,4,2,3] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,6,1,4,3,2] => [1,5,3,2,6,4] => [.,[[[.,.],.],[[.,.],.]]] => 1
[5,6,2,1,3,4] => [1,5,3,2,6,4] => [.,[[[.,.],.],[[.,.],.]]] => 1
[5,6,2,1,4,3] => [1,5,4,2,6,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[5,6,2,3,1,4] => [1,5,2,6,4,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[5,6,2,3,4,1] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => 1
[5,6,2,4,1,3] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,6,2,4,3,1] => [1,5,3,2,6,4] => [.,[[[.,.],.],[[.,.],.]]] => 1
[5,6,3,1,2,4] => [1,5,2,6,4,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[5,6,3,1,4,2] => [1,5,4,2,6,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[5,6,3,2,1,4] => [1,5,2,6,4,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[5,6,3,2,4,1] => [1,5,4,2,6,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[5,6,3,4,1,2] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,6,3,4,2,1] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,6,4,1,2,3] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,6,4,1,3,2] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,6,4,2,1,3] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,6,4,2,3,1] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[5,6,4,3,1,2] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[5,6,4,3,2,1] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,1,2,3,4,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => 0
[6,1,2,3,5,4] => [1,6,4,3,2,5] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,1,2,4,3,5] => [1,6,5,3,2,4] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,1,2,4,5,3] => [1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,1,2,5,3,4] => [1,6,4,5,3,2] => [.,[[[[.,.],[.,.]],.],.]] => 1
[6,1,2,5,4,3] => [1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,1,3,2,4,5] => [1,6,5,4,2,3] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,1,3,2,5,4] => [1,6,4,2,3,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,1,3,4,2,5] => [1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,1,3,4,5,2] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,1,3,5,2,4] => [1,6,4,5,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,1,3,5,4,2] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,1,4,2,3,5] => [1,6,5,3,4,2] => [.,[[[[.,.],.],[.,.]],.]] => 1
[6,1,4,2,5,3] => [1,6,3,4,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,1,4,3,2,5] => [1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,1,4,3,5,2] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,1,4,5,2,3] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => 1
[6,1,4,5,3,2] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,1,5,2,3,4] => [1,6,4,2,3,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,1,5,2,4,3] => [1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]] => 1
[6,1,5,3,2,4] => [1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => 1
[6,1,5,3,4,2] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[6,1,5,4,2,3] => [1,6,3,5,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,1,5,4,3,2] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[6,2,1,3,4,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => 0
[6,2,1,3,5,4] => [1,6,4,3,2,5] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,2,1,4,3,5] => [1,6,5,3,2,4] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,2,1,4,5,3] => [1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,2,1,5,3,4] => [1,6,4,5,3,2] => [.,[[[[.,.],[.,.]],.],.]] => 1
[6,2,1,5,4,3] => [1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,2,3,1,4,5] => [1,6,5,4,2,3] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,2,3,1,5,4] => [1,6,4,2,3,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,2,3,4,1,5] => [1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,2,3,4,5,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,2,3,5,1,4] => [1,6,4,5,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,2,3,5,4,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,2,4,1,3,5] => [1,6,5,3,4,2] => [.,[[[[.,.],.],[.,.]],.]] => 1
[6,2,4,1,5,3] => [1,6,3,4,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,2,4,3,1,5] => [1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,2,4,3,5,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,2,4,5,1,3] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => 1
[6,2,4,5,3,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,2,5,1,3,4] => [1,6,4,2,3,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,2,5,1,4,3] => [1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]] => 1
[6,2,5,3,1,4] => [1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => 1
[6,2,5,3,4,1] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[6,2,5,4,1,3] => [1,6,3,5,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,2,5,4,3,1] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[6,3,1,2,4,5] => [1,6,5,4,2,3] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,3,1,2,5,4] => [1,6,4,2,3,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,3,1,4,2,5] => [1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,3,1,4,5,2] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,3,1,5,2,4] => [1,6,4,5,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,3,1,5,4,2] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,3,2,1,4,5] => [1,6,5,4,2,3] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,3,2,1,5,4] => [1,6,4,2,3,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,3,2,4,1,5] => [1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,3,2,4,5,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,3,2,5,1,4] => [1,6,4,5,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,3,2,5,4,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,3,4,1,2,5] => [1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,3,4,1,5,2] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,3,4,2,1,5] => [1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,3,4,2,5,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,3,4,5,1,2] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,3,4,5,2,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[6,3,5,1,2,4] => [1,6,4,2,3,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,3,5,1,4,2] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[6,3,5,2,1,4] => [1,6,4,2,3,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,3,5,2,4,1] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[6,3,5,4,1,2] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[6,3,5,4,2,1] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[6,4,1,2,3,5] => [1,6,5,3,2,4] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,4,1,2,5,3] => [1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,4,1,3,2,5] => [1,6,5,2,4,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,4,1,3,5,2] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,4,1,5,2,3] => [1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,4,1,5,3,2] => [1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[6,4,2,1,3,5] => [1,6,5,3,2,4] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,4,2,1,5,3] => [1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,4,2,3,1,5] => [1,6,5,2,4,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,4,2,3,5,1] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,4,2,5,1,3] => [1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[6,4,2,5,3,1] => [1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[6,4,3,1,2,5] => [1,6,5,2,4,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,4,3,1,5,2] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,4,3,2,1,5] => [1,6,5,2,4,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,4,3,2,5,1] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,4,3,5,1,2] => [1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[6,4,3,5,2,1] => [1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[6,4,5,1,2,3] => [1,6,3,5,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,4,5,1,3,2] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,4,5,2,1,3] => [1,6,3,5,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,4,5,2,3,1] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,4,5,3,1,2] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,4,5,3,2,1] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,5,1,2,3,4] => [1,6,4,2,5,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,5,1,2,4,3] => [1,6,3,2,5,4] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,5,1,3,2,4] => [1,6,4,3,2,5] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,5,1,3,4,2] => [1,6,2,5,4,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[6,5,1,4,2,3] => [1,6,3,2,5,4] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,5,1,4,3,2] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,5,2,1,3,4] => [1,6,4,2,5,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,5,2,1,4,3] => [1,6,3,2,5,4] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,5,2,3,1,4] => [1,6,4,3,2,5] => [.,[[[[.,.],.],.],[.,.]]] => 1
[6,5,2,3,4,1] => [1,6,2,5,4,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[6,5,2,4,1,3] => [1,6,3,2,5,4] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,5,2,4,3,1] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,5,3,1,2,4] => [1,6,4,2,5,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,5,3,1,4,2] => [1,6,2,5,4,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[6,5,3,2,1,4] => [1,6,4,2,5,3] => [.,[[[.,.],.],[[.,.],.]]] => 1
[6,5,3,2,4,1] => [1,6,2,5,4,3] => [.,[[.,.],[[[.,.],.],.]]] => 1
[6,5,3,4,1,2] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,5,3,4,2,1] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,5,4,1,2,3] => [1,6,3,4,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,5,4,1,3,2] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,5,4,2,1,3] => [1,6,3,4,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[6,5,4,2,3,1] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,5,4,3,1,2] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[6,5,4,3,2,1] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
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searching the database for the individual values of this statistic
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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:
16,8 40,80 96,528,96
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 6$
$F_{4} = 16 + 8\ q$
$F_{5} = 40 + 80\ q$
$F_{6} = 96 + 528\ q + 96\ q^{2}$
Description
The number of nodes of degree 3 of a binary tree.
Equivalently, the number of internal triangles in the associated triangulation of an $(n+2)$-gon.
Equivalently, the number of internal triangles in the associated triangulation of an $(n+2)$-gon.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
to 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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