Identifier
-
Mp00072:
Permutations
—binary search tree: left to right⟶
Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
St001169: Dyck paths ⟶ ℤ (values match St000015The number of peaks of a Dyck path., St000053The number of valleys of the Dyck path., St001068Number of torsionless simple modules in the corresponding Nakayama algebra.)
Values
[1] => [.,.] => [1,0] => 0
[1,2] => [.,[.,.]] => [1,0,1,0] => 1
[2,1] => [[.,.],.] => [1,1,0,0] => 0
[1,2,3] => [.,[.,[.,.]]] => [1,0,1,0,1,0] => 2
[1,3,2] => [.,[[.,.],.]] => [1,0,1,1,0,0] => 1
[2,1,3] => [[.,.],[.,.]] => [1,1,0,0,1,0] => 1
[2,3,1] => [[.,.],[.,.]] => [1,1,0,0,1,0] => 1
[3,1,2] => [[.,[.,.]],.] => [1,1,0,1,0,0] => 1
[3,2,1] => [[[.,.],.],.] => [1,1,1,0,0,0] => 0
[1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 3
[1,2,4,3] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 2
[1,3,2,4] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => 2
[1,3,4,2] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => 2
[1,4,2,3] => [.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => 2
[1,4,3,2] => [.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => 1
[2,1,3,4] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 2
[2,1,4,3] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 1
[2,3,1,4] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 2
[2,3,4,1] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 2
[2,4,1,3] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 1
[2,4,3,1] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 1
[3,1,2,4] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 2
[3,1,4,2] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 2
[3,2,1,4] => [[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => 1
[3,2,4,1] => [[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => 1
[3,4,1,2] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 2
[3,4,2,1] => [[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => 1
[4,1,2,3] => [[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => 2
[4,1,3,2] => [[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => 1
[4,2,1,3] => [[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => 1
[4,2,3,1] => [[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => 1
[4,3,1,2] => [[[.,[.,.]],.],.] => [1,1,1,0,1,0,0,0] => 1
[4,3,2,1] => [[[[.,.],.],.],.] => [1,1,1,1,0,0,0,0] => 0
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 3
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => 3
[1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => 3
[1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,3,5,4,2] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 3
[1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 3
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,4,3,5,2] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 3
[1,4,5,3,2] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => 3
[1,5,2,4,3] => [.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => 2
[1,5,3,2,4] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,5,4,2,3] => [.,[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 3
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,1,5,3,4] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 3
[2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 3
[2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 3
[2,3,5,1,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,3,5,4,1] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,4,1,3,5] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,4,1,5,3] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,4,3,1,5] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,4,3,5,1] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,4,5,1,3] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,4,5,3,1] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,5,1,4,3] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,5,3,1,4] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,5,3,4,1] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,5,4,1,3] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,5,4,3,1] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,1,2,5,4] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
[3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,1,5,2,4] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
[3,1,5,4,2] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,2,5,1,4] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,2,5,4,1] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,5,1,2,4] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
[3,5,1,4,2] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
>>> Load all 873 entries. <<<[3,5,2,1,4] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,5,2,4,1] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,5,4,1,2] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
[3,5,4,2,1] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => 1
[4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 3
[4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 3
[4,1,3,2,5] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => 2
[4,1,3,5,2] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => 2
[4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 3
[4,1,5,3,2] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => 2
[4,2,1,3,5] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 2
[4,2,1,5,3] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 2
[4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 2
[4,2,3,5,1] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 2
[4,2,5,1,3] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 2
[4,2,5,3,1] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 2
[4,3,1,2,5] => [[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => 2
[4,3,1,5,2] => [[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => 2
[4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => 1
[4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => 1
[4,3,5,1,2] => [[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => 2
[4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => 1
[4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 3
[4,5,1,3,2] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => 2
[4,5,2,1,3] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 2
[4,5,2,3,1] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 2
[4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => 2
[4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => 1
[5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => 3
[5,1,2,4,3] => [[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => 2
[5,1,3,2,4] => [[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => 2
[5,1,3,4,2] => [[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => 2
[5,1,4,2,3] => [[.,[[.,[.,.]],.]],.] => [1,1,0,1,1,0,1,0,0,0] => 2
[5,1,4,3,2] => [[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => 1
[5,2,1,3,4] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,1,4,3] => [[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => 1
[5,2,3,1,4] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,4,1,3] => [[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => 1
[5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => 1
[5,3,1,2,4] => [[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => 2
[5,3,1,4,2] => [[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => 2
[5,3,2,1,4] => [[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => 1
[5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => 1
[5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => 2
[5,3,4,2,1] => [[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => 1
[5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => 2
[5,4,1,3,2] => [[[.,[[.,.],.]],.],.] => [1,1,1,0,1,1,0,0,0,0] => 1
[5,4,2,1,3] => [[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => 1
[5,4,2,3,1] => [[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => 1
[5,4,3,1,2] => [[[[.,[.,.]],.],.],.] => [1,1,1,1,0,1,0,0,0,0] => 1
[5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,2,5,3,6,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,2,5,6,4,3] => [.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,2,6,5,3,4] => [.,[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,3,5,2,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,3,5,6,4,2] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,3,6,2,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,3,6,4,2,5] => [.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,3,6,4,5,2] => [.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,3,6,5,2,4] => [.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,3,6,5,4,2] => [.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,4,2,5,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,4,2,6,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,4,2,6,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,4,3,6,2,5] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,4,5,2,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,4,5,6,3,2] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,4,6,3,2,5] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,4,6,3,5,2] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,4,6,5,2,3] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,4,6,5,3,2] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,5,2,3,6,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,5,2,4,6,3] => [.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,5,2,6,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,5,2,6,4,3] => [.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,5,3,2,4,6] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,5,3,2,6,4] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,5,3,4,6,2] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,5,3,6,4,2] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,5,4,2,3,6] => [.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,5,4,2,6,3] => [.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,5,4,6,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,5,4,6,3,2] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,5,6,2,4,3] => [.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,5,6,3,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,5,6,3,4,2] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,5,6,4,3,2] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,6,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,6,2,4,5,3] => [.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,6,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,6,2,5,4,3] => [.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,6,3,2,4,5] => [.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,6,3,2,5,4] => [.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,6,3,4,2,5] => [.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,6,3,5,2,4] => [.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,6,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,6,4,2,5,3] => [.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,6,4,3,2,5] => [.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,6,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,6,4,5,3,2] => [.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,6,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,6,5,2,4,3] => [.,[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,6,5,3,2,4] => [.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,6,5,3,4,2] => [.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,6,5,4,2,3] => [.,[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,1,4,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,1,4,6,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,1,5,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,1,5,6,4,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[2,1,6,3,5,4] => [[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[2,1,6,4,3,5] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,1,6,5,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,3,1,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[2,3,1,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[2,3,5,1,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,3,5,1,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,3,5,6,1,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,3,5,6,4,1] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[2,3,6,1,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[2,3,6,4,1,5] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[2,3,6,4,5,1] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[2,3,6,5,1,4] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[2,3,6,5,4,1] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,1,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,1,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,1,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,1,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,1,6,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,3,1,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,3,1,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,3,6,1,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,3,6,5,1] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,5,1,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,5,1,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,5,3,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,5,6,1,3] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,5,6,3,1] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,4,6,1,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,6,1,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,6,3,1,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,6,3,5,1] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,6,5,1,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,4,6,5,3,1] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,1,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,1,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,1,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,1,6,4,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,3,1,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,3,1,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,3,4,1,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,3,4,6,1] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,3,6,1,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,3,6,4,1] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,4,1,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,4,1,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,4,3,1,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,4,3,6,1] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,4,6,1,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,4,6,3,1] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,6,1,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,6,1,4,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,6,3,1,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,6,3,4,1] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,5,6,4,1,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,6,4,3,1] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[2,6,1,3,5,4] => [[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[2,6,1,4,3,5] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,6,1,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,6,1,5,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[2,6,1,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,6,3,1,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[2,6,3,1,5,4] => [[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[2,6,3,4,1,5] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[2,6,3,4,5,1] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[2,6,3,5,1,4] => [[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[2,6,3,5,4,1] => [[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[2,6,4,1,3,5] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,6,4,1,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,6,4,3,1,5] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,6,4,3,5,1] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,6,4,5,1,3] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,6,4,5,3,1] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,6,5,1,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[2,6,5,1,4,3] => [[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,6,5,3,1,4] => [[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[2,6,5,3,4,1] => [[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[2,6,5,4,1,3] => [[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,2,5,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,1,2,6,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,1,4,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[3,1,4,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,1,4,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[3,1,4,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[3,1,4,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,1,4,6,5,2] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,5,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,5,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,5,4,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,5,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,5,6,4,2] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,1,6,2,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,1,6,4,2,5] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,1,6,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,1,6,5,2,4] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,1,6,5,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,2,1,5,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,2,1,6,4,5] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,2,4,6,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,2,5,1,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,2,5,1,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,2,5,4,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,2,5,6,1,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,2,5,6,4,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,2,6,1,4,5] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,2,6,1,5,4] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,6,4,1,5] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,2,6,4,5,1] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,2,6,5,1,4] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,6,5,4,1] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,4,1,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[3,4,1,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[3,4,1,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,4,1,6,5,2] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,4,2,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,4,2,6,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,4,2,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[3,4,5,1,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,4,6,1,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,4,6,1,5,2] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,4,6,2,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,4,6,2,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,4,6,5,1,2] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,4,6,5,2,1] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,5,1,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,1,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,1,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,1,4,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,1,6,4,2] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,2,1,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,2,1,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,2,4,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,2,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,2,6,1,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,2,6,4,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,4,1,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,4,1,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,4,2,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,4,2,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,4,6,1,2] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,4,6,2,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,6,1,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,6,1,4,2] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,6,2,1,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,6,2,4,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,6,4,1,2] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,5,6,4,2,1] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,6,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,6,1,2,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,6,1,4,2,5] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,6,1,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,6,1,5,2,4] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,6,1,5,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,6,2,1,4,5] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,6,2,1,5,4] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,6,2,4,1,5] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,6,2,4,5,1] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,6,2,5,1,4] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,6,2,5,4,1] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,6,4,1,2,5] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,6,4,1,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,6,4,2,1,5] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,6,4,2,5,1] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,6,4,5,1,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,6,4,5,2,1] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,6,5,1,2,4] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,6,5,1,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,6,5,2,1,4] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,6,5,2,4,1] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,6,5,4,1,2] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,6,5,4,2,1] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[4,1,2,5,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[4,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[4,1,2,6,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[4,1,2,6,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[4,1,3,2,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,1,3,2,6,5] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,1,3,5,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,1,3,5,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,1,3,6,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,1,3,6,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,1,5,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[4,1,5,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[4,1,5,3,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,1,5,3,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,1,5,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[4,1,5,6,3,2] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[4,1,6,2,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[4,1,6,3,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,1,6,3,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,1,6,5,2,3] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[4,1,6,5,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,1,3,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,1,5,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,1,5,6,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,1,6,3,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,1,6,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,3,6,1,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,3,6,5,1] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,5,1,6,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,5,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,5,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,5,6,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,5,6,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,6,1,3,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,6,1,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,6,3,1,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,6,3,5,1] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,6,5,1,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,2,6,5,3,1] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,3,1,2,6,5] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,3,1,5,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,3,1,5,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,3,1,6,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,3,1,6,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,3,2,6,1,5] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,3,2,6,5,1] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,3,5,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,3,5,1,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,3,5,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,3,6,1,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,3,6,1,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,3,6,2,1,5] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,3,6,2,5,1] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,3,6,5,1,2] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,3,6,5,2,1] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[4,5,1,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[4,5,1,3,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,5,1,3,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,5,1,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[4,5,1,6,3,2] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,5,2,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,5,2,1,6,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,5,2,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,5,2,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,5,2,6,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,5,2,6,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,5,3,1,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,5,3,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[4,5,6,1,3,2] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,5,6,2,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,5,6,2,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,5,6,3,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,6,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[4,6,1,2,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[4,6,1,3,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,6,1,3,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,6,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[4,6,1,5,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,6,2,1,3,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,6,2,1,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,6,2,3,1,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,6,2,3,5,1] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,6,2,5,1,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,6,2,5,3,1] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,6,3,1,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,6,3,2,1,5] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,6,3,2,5,1] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,6,3,5,1,2] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,6,3,5,2,1] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,6,5,1,2,3] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[4,6,5,1,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,6,5,2,1,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,6,5,2,3,1] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,6,5,3,1,2] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,6,5,3,2,1] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[5,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[5,1,2,4,3,6] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[5,1,2,4,6,3] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[5,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[5,1,2,6,4,3] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[5,1,3,2,4,6] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[5,1,3,2,6,4] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[5,1,3,4,2,6] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[5,1,3,4,6,2] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[5,1,3,6,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[5,1,3,6,4,2] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[5,1,4,2,3,6] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[5,1,4,2,6,3] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[5,1,4,3,2,6] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[5,1,4,3,6,2] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[5,1,4,6,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[5,1,4,6,3,2] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[5,1,6,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[5,1,6,2,4,3] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[5,1,6,3,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[5,1,6,3,4,2] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[5,1,6,4,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[5,1,6,4,3,2] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,1,3,6,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,1,4,3,6] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,1,4,6,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,1,6,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,1,6,4,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,3,1,6,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,3,6,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,4,1,3,6] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,4,1,6,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,4,3,1,6] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,4,3,6,1] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,4,6,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,4,6,3,1] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,6,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,6,1,4,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,6,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,6,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,2,6,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,6,4,3,1] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,1,2,6,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,1,4,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,1,4,6,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,1,6,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,1,6,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,2,1,6,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,2,4,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,2,6,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,2,6,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,4,2,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,4,2,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,4,6,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,6,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,6,1,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,6,2,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,6,2,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,3,6,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,3,6,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[5,4,1,2,6,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[5,4,1,3,2,6] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[5,4,1,3,6,2] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[5,4,1,6,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[5,4,1,6,3,2] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,4,2,1,6,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,4,2,3,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,4,2,3,6,1] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,4,2,6,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,4,2,6,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[5,4,3,1,6,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[5,4,3,6,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[5,4,6,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[5,4,6,1,3,2] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,4,6,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,4,6,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[5,6,1,2,4,3] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[5,6,1,3,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[5,6,1,3,4,2] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[5,6,1,4,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[5,6,1,4,3,2] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[5,6,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,6,2,1,4,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,6,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,6,2,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,6,2,4,3,1] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,6,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,6,3,1,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,6,3,2,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,6,3,2,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,6,3,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,6,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[5,6,4,1,3,2] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[5,6,4,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,6,4,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => 4
[6,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => 3
[6,1,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => 3
[6,1,2,4,5,3] => [[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => 3
[6,1,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0] => 3
[6,1,2,5,4,3] => [[.,[.,[[[.,.],.],.]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[6,1,3,2,4,5] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3
[6,1,3,2,5,4] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => 2
[6,1,3,4,2,5] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3
[6,1,3,4,5,2] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3
[6,1,3,5,2,4] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => 2
[6,1,3,5,4,2] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => 2
[6,1,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3
[6,1,4,2,5,3] => [[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3
[6,1,4,3,2,5] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[6,1,4,3,5,2] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[6,1,4,5,2,3] => [[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3
[6,1,4,5,3,2] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[6,1,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,0,0] => 3
[6,1,5,2,4,3] => [[.,[[.,[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[6,1,5,3,2,4] => [[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[6,1,5,3,4,2] => [[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[6,1,5,4,2,3] => [[.,[[[.,[.,.]],.],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[6,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,2,1,3,5,4] => [[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[6,2,1,4,3,5] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[6,2,1,4,5,3] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[6,2,1,5,3,4] => [[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[6,2,1,5,4,3] => [[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[6,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,2,3,1,5,4] => [[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[6,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,2,3,5,1,4] => [[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[6,2,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[6,2,4,1,5,3] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[6,2,4,3,1,5] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[6,2,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[6,2,4,5,3,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[6,2,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[6,2,5,1,4,3] => [[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[6,2,5,3,1,4] => [[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[6,2,5,3,4,1] => [[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[6,2,5,4,1,3] => [[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[6,3,1,2,5,4] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[6,3,1,4,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[6,3,1,4,5,2] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[6,3,1,5,2,4] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[6,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,2,1,5,4] => [[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[6,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,2,5,1,4] => [[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[6,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[6,3,4,1,5,2] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[6,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[6,3,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[6,3,5,2,1,4] => [[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[6,3,5,2,4,1] => [[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[6,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[6,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[6,4,1,2,5,3] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[6,4,1,3,2,5] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[6,4,1,3,5,2] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[6,4,1,5,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[6,4,1,5,3,2] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[6,4,2,1,5,3] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[6,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[6,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[6,4,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[6,4,2,5,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,3,1,5,2] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[6,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[6,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[6,4,5,1,3,2] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[6,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[6,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[6,5,1,2,4,3] => [[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[6,5,1,3,2,4] => [[[.,[[.,.],[.,.]]],.],.] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2
[6,5,1,3,4,2] => [[[.,[[.,.],[.,.]]],.],.] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2
[6,5,1,4,2,3] => [[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[6,5,1,4,3,2] => [[[.,[[[.,.],.],.]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[6,5,2,1,4,3] => [[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[6,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[6,5,2,4,1,3] => [[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[6,5,2,4,3,1] => [[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[6,5,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[6,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[6,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[6,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],.] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,4,1 1,11,11,1 1,26,66,26,1 1,57,302,302,57,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 4\ q + q^{2}$
$F_{4} = 1 + 11\ q + 11\ q^{2} + q^{3}$
$F_{5} = 1 + 26\ q + 66\ q^{2} + 26\ q^{3} + q^{4}$
$F_{6} = 1 + 57\ q + 302\ q^{2} + 302\ q^{3} + 57\ q^{4} + q^{5}$
Description
Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
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