Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00223: Permutations —runsort⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
St000568: Binary trees ⟶ ℤ
Values
[1,0,1,0] => [2,1] => [1,2] => [.,[.,.]] => 1
[1,1,0,0] => [1,2] => [1,2] => [.,[.,.]] => 1
[1,0,1,0,1,0] => [3,2,1] => [1,2,3] => [.,[.,[.,.]]] => 1
[1,0,1,1,0,0] => [2,3,1] => [1,2,3] => [.,[.,[.,.]]] => 1
[1,1,0,0,1,0] => [3,1,2] => [1,2,3] => [.,[.,[.,.]]] => 1
[1,1,0,1,0,0] => [2,1,3] => [1,3,2] => [.,[[.,.],.]] => 2
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]] => 1
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 1
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 1
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 2
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 1
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 2
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [1,4,2,3] => [.,[[.,.],[.,.]]] => 2
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [1,4,2,3] => [.,[[.,.],[.,.]]] => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 2
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [1,3,4,2] => [.,[[.,[.,.]],.]] => 2
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 1
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 2
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 2
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 2
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 2
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => 2
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => 3
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 2
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => 2
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
>>> Load all 951 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [1,5,6,2,4,3] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [1,2,6,3,5,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [1,2,7,3,5,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [1,2,7,3,5,6,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [1,2,4,6,3,5,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [1,2,6,7,3,5,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,2,4,5,7,3,6] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [1,2,4,6,7,3,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [1,4,2,3,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [1,6,2,3,5,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [1,7,2,3,5,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [1,7,2,3,5,6,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [1,4,2,3,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [1,5,2,4,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [1,5,2,4,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [1,6,2,4,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [1,7,2,4,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [1,7,2,4,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [1,6,2,5,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [1,7,2,5,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [1,6,2,5,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [1,7,2,5,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [1,7,2,6,3,5,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [1,6,2,3,5,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [1,7,2,3,5,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [1,6,2,4,5,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [1,7,2,4,5,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [1,7,2,4,6,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [1,7,2,5,6,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [1,7,2,5,6,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [1,7,2,3,5,6,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [1,7,2,4,5,6,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [1,2,6,3,5,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [1,2,7,3,5,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [1,2,7,3,5,6,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [1,3,4,2,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [1,3,5,2,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [1,3,5,2,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [1,3,6,2,4,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [1,3,6,2,4,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [1,3,7,2,4,6,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [1,6,7,2,3,5,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [1,5,6,2,4,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [1,5,7,2,4,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [1,6,7,2,4,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [1,6,7,2,5,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [1,6,7,2,5,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [1,6,7,2,3,5,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [1,6,7,2,4,5,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [1,2,4,6,3,5,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [1,2,6,7,3,5,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [1,3,4,5,2,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [1,3,4,5,2,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [1,3,4,6,2,5,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [1,3,4,7,2,5,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [1,3,4,7,2,5,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [1,3,5,6,2,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [1,3,5,7,2,4,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [1,3,6,7,2,4,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [1,3,6,7,2,4,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [1,4,5,6,2,3,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [1,4,5,7,2,3,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [1,4,6,7,2,3,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [1,4,5,6,2,3,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [1,4,5,7,2,3,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [1,4,6,7,2,3,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [1,5,6,7,2,4,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [1,2,4,5,7,3,6] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [1,2,4,6,7,3,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [1,3,4,5,6,2,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [1,3,4,5,7,2,6] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [1,3,4,6,7,2,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [1,3,5,6,7,2,4] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [1,4,5,6,7,2,3] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,4,5,6,7,2,3] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [1,3,4,5,6,7,2] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [1,2,3,4,8,5,7,6] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [1,2,3,4,6,8,5,7] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [1,2,3,8,4,5,7,6] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 3
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [1,2,3,8,4,6,7,5] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [1,2,3,5,8,4,6,7] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [1,2,8,3,4,5,7,6] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [1,2,8,3,4,5,7,6] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [1,2,8,3,7,4,5,6] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [1,2,8,3,7,4,6,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [1,2,3,8,4,5,7,6] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [1,2,4,8,3,5,6,7] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [1,2,6,7,8,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [1,2,6,7,8,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [1,2,5,6,7,8,3,4] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [1,2,5,6,7,8,3,4] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => [1,2,3,8,4,5,7,6] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 3
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [1,2,3,8,4,7,5,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [1,2,3,8,4,6,7,5] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [1,2,3,7,8,4,6,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [1,2,3,5,7,8,4,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [1,2,3,6,7,8,4,5] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [1,2,3,6,7,8,4,5] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [1,4,2,3,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [1,4,2,3,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [1,4,2,3,5,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [1,4,2,3,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [1,6,2,3,4,5,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [1,7,2,3,4,5,6,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [1,8,2,3,4,5,7,6] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [1,8,2,3,4,7,5,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [1,7,2,3,4,5,6,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [1,8,2,3,5,4,6,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [1,8,2,3,6,4,5,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [1,4,2,3,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [1,4,2,3,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [1,4,2,3,5,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [1,4,2,3,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [1,4,2,3,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [1,6,2,3,4,5,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [1,8,2,3,4,7,5,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [1,5,2,4,3,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [1,5,2,4,3,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 3
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [1,8,2,4,3,5,6,7] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [1,6,2,5,3,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [1,8,2,5,3,4,6,7] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 3
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [1,8,2,7,3,4,5,6] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [1,8,2,7,3,6,4,5] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [1,8,2,3,4,5,7,6] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [1,8,2,3,6,4,5,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [1,8,2,6,7,3,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 3
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [1,8,2,4,5,6,7,3] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [1,2,4,3,5,8,6,7] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [1,2,5,3,4,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [1,2,5,3,4,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [1,2,7,3,4,5,6,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [1,2,5,3,4,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [1,2,5,3,4,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [1,2,7,3,4,5,6,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [1,2,7,3,4,5,6,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [1,3,4,2,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [1,3,4,2,5,7,8,6] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [1,3,4,2,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [1,3,5,2,4,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [1,3,5,2,4,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [1,3,6,2,4,5,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [1,3,7,2,4,5,6,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [1,3,8,2,4,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [1,3,8,2,4,5,7,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [1,3,8,2,4,6,5,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [1,3,8,2,4,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [1,3,8,2,4,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [1,5,6,2,3,4,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [1,5,6,2,3,4,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [1,5,8,2,3,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [1,7,8,2,3,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [1,4,7,2,3,5,6,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [1,4,7,2,3,5,6,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [1,5,6,2,3,4,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [1,7,8,2,3,5,6,4] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [1,7,8,2,3,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [1,2,3,7,4,5,6,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [1,2,3,8,4,7,5,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [1,2,3,8,4,6,7,5] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => 3
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [1,2,4,8,3,5,6,7] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [1,2,5,8,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [1,2,7,8,3,4,5,6] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [1,2,7,8,3,4,6,5] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [1,2,5,6,3,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [1,2,7,8,3,4,5,6] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [1,2,7,8,3,6,4,5] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [1,3,4,5,2,6,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [1,3,4,5,2,6,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [1,3,4,6,2,5,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [1,3,4,6,2,5,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [1,3,4,7,2,5,6,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [1,3,4,8,2,5,6,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [1,3,5,6,2,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [1,3,5,7,2,4,6,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [1,3,7,8,2,4,5,6] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [1,4,5,6,2,3,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [1,4,5,6,2,3,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [1,4,7,8,2,3,5,6] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [1,5,6,7,2,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [1,5,6,8,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [1,5,7,8,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [1,6,7,8,2,3,4,5] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [1,6,7,8,2,3,4,5] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [1,5,6,7,2,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [1,6,7,8,2,3,4,5] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [1,6,7,8,2,3,4,5] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [1,2,3,4,7,5,6,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [1,2,3,4,7,5,6,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [1,2,3,4,8,5,7,6] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => 3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [1,2,3,7,8,4,5,6] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [1,2,4,6,8,3,5,7] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [1,2,5,7,8,3,4,6] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [1,3,4,5,6,2,7,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [1,4,5,6,7,2,3,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [1,5,6,7,8,2,3,4] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [1,4,5,6,7,2,3,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [1,4,5,7,8,2,3,6] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [1,5,6,7,8,2,4,3] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [1,5,6,7,8,2,3,4] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [1,2,3,4,6,8,5,7] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [1,2,3,5,7,8,4,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [1,2,4,5,6,8,3,7] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [1,2,5,6,7,8,3,4] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [1,3,4,5,6,7,2,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [1,3,4,5,6,8,2,7] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [1,4,5,6,7,8,2,3] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,25,1 32,89,11 64,290,74,1
$F_{2} = 2\ q$
$F_{3} = 4\ q + q^{2}$
$F_{4} = 8\ q + 6\ q^{2}$
$F_{5} = 16\ q + 25\ q^{2} + q^{3}$
$F_{6} = 32\ q + 89\ q^{2} + 11\ q^{3}$
$F_{7} = 64\ q + 290\ q^{2} + 74\ q^{3} + q^{4}$
Description
The hook number of a binary tree.
A hook of a binary tree is a vertex together with is left- and its right-most branch. Then there is a unique decomposition of the tree into hooks and the hook number is the number of hooks in this decomposition.
A hook of a binary tree is a vertex together with is left- and its right-most branch. Then there is a unique decomposition of the tree into hooks and the hook number is the number of hooks in this decomposition.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
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