Identifier
-
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
St000919: Binary trees ⟶ ℤ
Values
[1,0,1,0] => [1,2] => [.,[.,.]] => 0
[1,1,0,0] => [2,1] => [[.,.],.] => 1
[1,0,1,0,1,0] => [1,2,3] => [.,[.,[.,.]]] => 0
[1,0,1,1,0,0] => [1,3,2] => [.,[[.,.],.]] => 1
[1,1,0,0,1,0] => [2,1,3] => [[.,.],[.,.]] => 1
[1,1,0,1,0,0] => [2,3,1] => [[.,.],[.,.]] => 1
[1,1,1,0,0,0] => [3,1,2] => [[.,[.,.]],.] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [.,[[.,.],[.,.]]] => 1
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [.,[[.,[.,.]],.]] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[.,.],[[.,.],.]] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => 1
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [[.,.],[[.,.],.]] => 2
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [[.,[.,.]],[.,.]] => 1
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [[.,[.,.]],[.,.]] => 1
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => 1
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [[.,[.,[.,.]]],.] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [[.,.],[.,[[.,.],.]]] => 2
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [[.,.],[[.,.],[.,.]]] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [[.,.],[[.,.],[.,.]]] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [[.,.],[[.,.],[.,.]]] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
>>> Load all 1470 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [[.,.],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,1,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1,7,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,5,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,8] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,5,8,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,4,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,4,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,4,8,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,4,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,4,6,7] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,4,7,8,5] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,4,8,5,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,4,5,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,4,8,5] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,4,5] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,4,5,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,4,5,8,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,4,8,5,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,5,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,8,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,3,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,3,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,4,5,7,3,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,3,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,3,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,3,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,3,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,3,7,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,3,8,5,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,3,5] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,3,5,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,3,5,6,8] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,3,5,8,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,3,8,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,3,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,3,5,6,7] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,3,4,6,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,3,4,7,8,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,3,6,7,8,4] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,2,5,3,7,4,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,8,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,3,8,4,6,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,3,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,2,5,6,3,4,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,3,7,4,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,3,7,8,4] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,5,6,3,8,4,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,3,8,4] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,3,4] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,3,4,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,3,4,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,3,4,8,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,3,8,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,3,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,3,4,6,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,6,3,4,7,5,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,3,4,7,8,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,3,4,8,5,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,6,3,7,4,5,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,8,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,3,8,4,5,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,3,4,5,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,6,7,3,4,8,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,3,8,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,6,8,3,4,5,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,3,4,5,8,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,3,8,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,5,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,4,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,8,5,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,4,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,4,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,4,5,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,8,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,8,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,5,6,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,2,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,2,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,2,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,2,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,2,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,2,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,2,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,2,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,2,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,8,2,5,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,3,4,7,2,5,6,8] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,2,5,8,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,7,8,2,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,2,5,6,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,2,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,2,4,6,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,2,6,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,6,8,4,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,2,7,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,2,8,4,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,2,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,5,6,2,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,2,7,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,6,2,8,4,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,2,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,2,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,2,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,2,4,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,2,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,2,4,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,2,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,2,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,2,4,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,2,4,5,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,2,4,5,8,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,2,4,7,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,6,2,4,7,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,2,7,4,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,2,7,4,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,6,7,2,4,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,2,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,2,4,5,6,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,7,2,4,5,8,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,2,4,8,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,2,8,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,2,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,2,3,5,7,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,2,3,6,7,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,2,3,6,7,8,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,2,3,7,5,8,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,2,3,7,8,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,3,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,2,5,6,7,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,2,5,6,8,3,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,2,5,7,3,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,2,5,7,8,3,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,2,5,8,3,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,6,3,5,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,6,3,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,8,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,2,6,7,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,2,6,7,8,3,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,2,6,8,3,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,7,3,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,7,3,5,8,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,8,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,2,7,8,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,8,3,5,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,2,3,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,2,3,7,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,2,6,3,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,7,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,2,6,7,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,6,8,3,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,4,5,2,7,3,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,7,8,3,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,2,8,3,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,2,3,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,2,7,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,5,6,2,7,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,2,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,2,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,2,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,4,5,6,8,2,3,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,2,3,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,2,3,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,2,3,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,2,3,5,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,4,6,2,3,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,2,3,7,8,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,2,7,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,2,7,3,8,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,2,8,3,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,2,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,2,8,3,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,2,3,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,2,3,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,2,3,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,2,3,5,8,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,2,3,8,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,2,8,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,2,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,2,3,4,7,8,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,2,3,6,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2,3,6,4,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,2,3,6,7,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,3,6,7,8,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,2,3,6,8,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,5,2,3,7,4,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,2,3,7,8,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,2,3,8,4,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,6,3,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,6,3,4,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,8,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,2,6,7,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,2,6,7,8,3,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,2,6,8,3,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,7,3,4,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,7,3,4,8,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,8,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,2,7,8,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,8,3,4,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,2,3,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,2,3,4,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,6,2,3,7,8,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,5,6,2,8,3,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,2,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,2,3,8,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,5,6,7,2,8,3,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,5,6,8,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,2,3,4,8,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,5,7,2,3,8,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,2,8,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,5,7,8,2,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,2,3,4,7,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,3,4,7,8,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,2,3,4,8,5,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,2,3,7,4,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,2,3,7,8,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,6,2,3,8,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,7,3,4,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,7,3,4,8,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,8,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,2,7,8,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,8,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,2,3,4,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,2,3,4,8,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,6,7,2,3,8,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,2,8,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,2,3,4,8,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,2,3,8,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,8,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,5,8,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,3,5,6,8,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,4,6,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,4,5,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,4,8,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,6,7,4,8,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,7,4,8,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,3,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,3,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,3,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,3,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,4,6,3,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,3,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,3,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,3,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,3,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,3,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,3,6,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,3,6,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,3,6,8,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,3,7,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,8,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,3,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,3,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,3,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,3,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,5,7,3,4,6,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,3,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,3,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,3,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,3,4,7,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,3,4,8,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,3,7,8,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,8,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,3,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,3,4,5,8,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,3,4,8,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,8,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,7,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,4,5,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,8,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,4,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,4,5,8,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,8,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,5,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,8,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,1,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,1,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,1,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,1,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,1,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,1,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,1,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,1,8,5,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,1,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,1,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,1,5,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,1,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,1,5,8,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,1,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,1,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,1,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,1,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,4,8,6,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,1,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,3,5,1,6,8,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,1,8,4,6,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,1,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,1,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,1,7,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,1,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,1,8,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,1,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,1,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,1,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,1,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,1,4,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,1,4,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,1,8,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,1,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,1,4,6,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,1,4,5,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,1,4,5,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,6,1,4,7,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,1,4,7,8,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,1,4,8,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,1,8,4,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,1,8,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,1,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,1,4,5,6,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,1,4,5,8,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,1,4,8,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,7,8,1,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,4,1,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,1,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,1,3,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,1,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,1,3,8,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,3,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,3,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,8,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,1,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,1,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,1,5,6,8,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,1,5,8,3,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,1,6,3,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,1,6,7,8,3,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,1,6,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,1,7,3,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,1,7,8,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,1,8,3,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,1,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,1,3,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,1,3,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,4,5,1,6,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,1,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,1,6,8,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,4,5,1,7,3,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,1,7,8,3,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,1,8,3,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,1,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,4,5,6,1,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,1,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,1,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,1,8,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,1,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,1,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,1,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,1,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,4,5,7,1,8,3,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,1,3,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,1,3,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,1,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,4,6,1,3,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,1,7,3,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,1,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,1,3,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,1,3,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,1,3,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,4,7,1,8,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,1,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,1,3,4,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,1,3,6,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,1,3,6,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,1,3,6,8,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,1,3,7,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,1,3,7,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,1,3,8,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,1,6,3,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,5,1,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,1,6,7,3,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,1,6,7,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,5,1,6,8,3,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,1,7,3,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,1,7,8,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,1,8,3,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,1,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,5,6,1,3,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,1,3,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,5,6,1,3,8,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,1,7,3,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,1,7,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,1,3,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,1,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,1,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,1,3,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,5,7,1,3,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,5,7,1,8,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,5,7,8,1,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,1,3,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,6,1,3,4,5,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,1,3,4,5,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1,3,4,7,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,1,3,4,7,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,1,3,4,8,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,6,1,3,7,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,1,3,7,8,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,1,3,8,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,6,1,7,3,4,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,1,7,3,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,6,1,7,3,8,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,1,7,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,1,8,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,1,3,4,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,6,7,1,3,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,6,7,1,3,8,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,1,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,1,3,4,5,6,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,1,3,4,5,8,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,1,3,8,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,1,8,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,2,4,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,2,4,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,4,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,4,6,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,4,6,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,4,6,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,2,4,7,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,2,4,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,6,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,5,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,2,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,2,6,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,2,6,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,2,6,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,7,5,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,8,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,5,2,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,6,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,6,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,4,5,7,2,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,4,5,7,8,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,4,5,8,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,4,6,2,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,4,6,2,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,4,6,7,2,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,4,6,7,8,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,4,6,8,2,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,4,7,2,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4,8,2,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,2,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,5,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,1,5,6,2,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,1,5,6,7,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,1,5,6,7,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,4,1,2,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,4,1,2,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,1,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,4,1,2,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,4,1,2,6,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,1,2,6,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,1,2,6,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,4,1,2,7,5,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,1,2,7,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,1,2,8,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,6,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,1,5,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,1,5,6,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,1,5,7,2,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,1,5,7,8,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,1,5,8,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,1,6,2,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,2,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,1,6,7,2,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,1,6,7,2,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,4,1,6,7,8,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,4,1,6,8,2,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,1,8,2,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,1,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,1,2,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,1,2,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,1,2,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,1,6,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,1,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,1,7,8,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,1,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,1,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,1,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,1,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,1,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,1,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,1,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,1,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,1,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,5,7,1,2,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,1,2,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,1,8,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,1,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,1,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,1,2,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,1,2,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,1,2,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,1,7,2,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,1,7,8,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,4,6,7,1,2,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,1,2,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,1,8,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,1,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,1,2,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,1,2,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,1,8,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,1,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,1,2,4,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,1,2,6,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,1,2,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,5,1,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,5,1,6,7,2,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,1,6,7,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,5,6,1,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,1,2,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,1,2,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,1,7,2,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,1,7,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,1,2,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,1,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,1,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,1,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
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Generating function
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Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,4 1,11,2 1,26,15 1,57,69,5 1,120,252,56
F2=1+q
F3=1+4 q
F4=1+11 q+2 q2
F5=1+26 q+15 q2
F6=1+57 q+69 q2+5 q3
F7=1+120 q+252 q2+56 q3
Description
The number of maximal left branches of a binary tree.
A maximal left branch of a binary tree is an inclusion wise maximal path which consists of left edges only. This statistic records the number of distinct maximal left branches in the tree.
A maximal left branch of a binary tree is an inclusion wise maximal path which consists of left edges only. This statistic records the number of distinct maximal left branches in the tree.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength n in an n×n square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength n in an n×n square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
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