Identifier
-
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
St000683: Dyck paths ⟶ ℤ
Values
[1,0,1,0] => [1,2] => [.,[.,.]] => [1,0,1,0] => 0
[1,1,0,0] => [2,1] => [[.,.],.] => [1,1,0,0] => 1
[1,0,1,0,1,0] => [1,2,3] => [.,[.,[.,.]]] => [1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => [1,3,2] => [.,[[.,.],.]] => [1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => [2,1,3] => [[.,.],[.,.]] => [1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => [2,3,1] => [[.,[.,.]],.] => [1,1,0,1,0,0] => 0
[1,1,1,0,0,0] => [3,1,2] => [[.,.],[.,.]] => [1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
>>> Load all 1470 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,1,2,4,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,1,2,3,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,1,2,7,3,4] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1,7,2,3,4,5] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 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] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 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] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 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] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 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] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,5,7] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 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] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 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] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,4,7] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,4,6,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,4,8,6] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,4,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,4,6,7] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,4,7,8,5] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 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] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 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] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,4,8,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 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] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,4,8,5,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,4,5,6] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 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] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 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] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,6,7] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,3,7] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,3,6,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,4,5,7,3,8,6] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,3,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,3,6,7] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,3,5,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,3,5,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,3,7,5,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,3,8,5,7] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,3,5,7] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,3,5,6,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,3,5,8,6] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,3,8,5,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,3,5,6] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,3,5,6,7] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,3,4,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 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] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 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] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,3,6,7,8,4] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,3,8,4,6,7] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,2,5,6,3,4,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,3,7,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 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] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,5,6,3,8,4,7] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,3,8,4] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,3,4,7] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,3,4,6,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,3,4,8,6] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,3,8,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,3,4,6] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,3,4,7,8,5] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 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] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 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] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,8,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 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] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,6,7,3,4,8,5] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 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] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 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] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,6,8,3,4,5,7] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,3,8,4,5,6] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,3,4,5,6] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 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] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,5,7] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,4,6,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,4,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,4,6,7] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,8,5,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,4,8,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 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] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,6,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,8,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,5,6,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,6,7] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,2,7] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,2,6,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,2,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,2,6,7] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,2,5,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,2,5,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,2,7,5,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,2,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,2,8,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,8,2,5,7] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,3,4,7,2,5,6,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,2,5,8,6] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,7,8,2,5,6] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,2,5,6,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,2,4,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,2,4,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,2,6,7,4,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,6,8,4,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,2,7,4,6,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,8,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,2,8,4,6,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,2,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,5,6,2,4,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,6,2,8,4,7] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,2,4,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,2,8,4] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,2,4] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,2,4,7] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,2,4,6,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,2,4,8,6] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,2,8,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,2,4,6] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,2,4,6,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,2,4,5,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,2,4,5,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,2,7,4,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,2,7,4,8,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,6,7,2,4,8,5] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,2,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,2,4,5,6,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,7,2,4,5,8,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,2,4,8,5,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,2,8,4,5,6] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,2,4,5,6] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 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] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,2,3,6,7,8,5] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,2,3,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,3,6,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,8,6,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,2,5,6,7,3,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 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] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 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] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 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] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,2,5,8,3,6,7] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,6,3,5,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,8,5,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,2,6,7,8,3,5] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,2,6,8,3,5,7] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,7,3,5,6,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,8,5,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,2,7,8,3,5,6] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,8,3,5,6,7] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,2,3,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,2,3,7,8,6] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,2,6,3,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 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] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,2,6,7,8,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,6,8,3,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,4,5,2,7,3,6,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,8,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,2,8,3,6,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,2,3,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,2,7,3,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 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] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,2,3,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,2,8,3] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 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] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,4,5,6,8,2,3,7] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,2,3,6,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,2,3,8,6] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,2,3,6] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,2,3,5,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,4,6,2,3,5,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,2,3,7,8,5] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,2,7,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,2,7,3,8,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,2,8,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,2,3,5,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,2,8,3,5] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,2,3,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,2,3,5,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,2,3,5,6,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,2,3,5,8,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,2,3,8,5,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,2,8,3,5,6] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,2,3,5,6] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 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] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2,3,6,4,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,2,3,6,7,4,8] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 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] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,5,2,3,7,4,6,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,2,3,7,8,4,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,2,3,8,4,6,7] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,6,3,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,8,4,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,2,6,7,3,4,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 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] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 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] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,7,3,4,6,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,2,7,8,3,4,6] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,8,3,4,6,7] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,2,3,4,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,6,2,3,7,8,4] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,5,6,2,8,3,4,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,2,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,2,3,8,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 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] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 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] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,5,6,8,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,2,3,4,8,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,5,7,2,3,8,4,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,2,8,3,4,6] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,5,7,8,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 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] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,3,4,7,8,5] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 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] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 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] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,2,3,7,8,4,5] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 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] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,7,3,4,8,5] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,8,4,5] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,2,7,8,3,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 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] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,2,3,4,8,5] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 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] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 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] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 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] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 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] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,2,3,4,8,5,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,2,3,8,4,5,6] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,8,3,4,5,6] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 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] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 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] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 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] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 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] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 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] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 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] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 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] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,4,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,4,5,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 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] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 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] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 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] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,7,4,8,5,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,4,5,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 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] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 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] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,5,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,3,7] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,3,8,6] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,3,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,3,5,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,5,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,4,6,3,7,5,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,3,7,8,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,3,8,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,3,8,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,3,5] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,3,5,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,3,5,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,3,5,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,3,5,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,3,6,7,4,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 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] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,3,7,8,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,8,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 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] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,4,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,3,8,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,3,4,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,5,7,3,4,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,3,4,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,3,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,3,4,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 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] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 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] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,3,7,8,4,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 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] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 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] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,3,4,5,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,3,4,8,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,8,4,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,3,4,5,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,7,5,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,5,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,4,5,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,4,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,4,1,3,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,1,3,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,1,3,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,1,3,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,1,3,8,5,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,3,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,1,6,3,5,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,1,8,3,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,1,3,4,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,1,3,6,4,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,1,3,6,7,8,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,1,3,6,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,1,3,7,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,1,3,7,8,4,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,1,3,8,4,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,1,8,3,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,6,1,3,4,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,1,3,4,5,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1,3,4,7,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,1,3,4,7,8,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,1,3,4,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,6,1,3,7,4,8,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,1,3,8,4,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,6,1,7,3,4,5,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,1,8,3,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,1,3,4,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,1,3,4,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,1,3,8,4,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,1,8,3,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 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] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 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] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 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] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,4,6,7,8,5] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 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] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,2,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,6,7,4,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,5,6,7,8,4] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,1,2,5,6,8,4,7] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,2,5,7,4,8,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,2,5,8,4,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,2,6,4,7,8,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,2,6,7,4,8,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,1,2,6,7,8,4,5] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,1,2,6,8,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,2,7,4,8,5,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,2,7,8,4,5,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 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] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,2,5,7,8,6] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 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] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,2,6,7,5,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 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] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,7,5,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,2,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 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] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,2,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 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] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 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] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,6,2,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 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] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 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] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,4,5,7,2,8,6] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,4,5,8,2,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,5,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,4,6,2,7,8,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,4,6,2,8,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,4,6,7,2,8,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,4,6,8,2,5,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,4,7,2,5,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 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] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,5,2,4,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,2,6,7,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,2,6,8,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,2,7,8,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,8,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,5,6,2,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,1,5,6,2,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 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] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,1,5,6,2,8,4,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 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] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,1,5,6,8,2,4,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,5,7,2,4,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,1,5,7,2,4,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,1,5,7,2,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,1,5,7,8,2,4,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,1,5,8,2,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,6,2,4,5,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,6,2,4,7,5,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,6,2,4,7,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,6,2,4,8,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,6,7,2,4,5,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,1,6,7,2,8,4,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,1,6,8,2,4,5,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,7,2,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,7,2,4,5,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,8,4,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,7,8,2,4,5,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 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] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,4,1,2,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,4,1,2,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,1,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,4,1,2,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,4,1,2,6,7,5,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,1,2,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,1,2,6,8,5,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,4,1,2,7,5,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,1,2,7,5,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,1,2,8,5,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,1,8,2,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,1,2,4,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,1,2,4,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,1,2,4,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,1,2,4,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,1,2,4,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,1,2,6,7,8,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,1,2,6,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,1,2,7,4,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,1,2,7,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,1,2,7,8,4,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,5,1,2,8,4,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,5,1,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,1,7,2,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,5,1,8,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,1,2,4,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,1,2,4,5,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,1,2,4,7,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,1,2,4,7,8,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,1,2,4,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,1,2,7,4,8,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,1,2,7,8,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,1,2,8,4,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,1,8,2,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,1,2,4,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,7,1,2,4,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,1,2,4,8,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,1,2,8,4,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,1,8,2,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,3,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,3,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,3,5,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,3,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,3,6,7,5,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,3,6,7,8,5] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,3,6,8,5,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,3,7,5,8,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,1,2,3,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,2,5,3,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,5,3,7,8,6] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,2,5,3,8,6,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,2,5,6,3,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,2,5,6,3,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,6,7,3,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,2,5,6,8,3,7] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,5,7,3,8,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,5,7,8,3,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,2,5,8,3,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,1,2,6,3,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,1,2,6,3,7,8,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,1,2,6,3,8,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,1,2,6,7,3,8,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,7,3,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,1,2,7,3,5,8,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,1,2,7,8,3,5,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,2,8,3,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,5,2,3,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,5,2,3,7,8,6] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,5,2,3,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,2,6,7,8,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,2,6,8,3,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,7,3,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,2,7,8,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,8,3,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,5,6,2,3,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,5,6,2,3,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,5,6,2,8,3,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,5,6,7,2,8,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,8,2,3] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,5,6,8,2,3,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,5,7,2,8,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,1,6,2,3,5,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,1,6,2,3,7,5,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,1,6,2,3,7,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,1,6,2,3,8,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,7,3,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,8,3,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,1,6,7,2,3,5,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,1,6,7,2,3,8,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,1,6,7,8,2,3,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,1,6,8,2,3,5,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,1,7,2,3,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,1,7,2,3,5,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,1,7,2,3,8,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,8,3,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,1,7,8,2,3,5,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,1,2,3,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,1,2,3,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,1,2,3,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,5,1,2,6,7,3,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,1,2,6,7,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,1,2,6,8,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,1,2,7,3,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,5,1,2,7,3,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,5,1,2,7,8,3,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,1,2,8,3,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,5,1,6,2,3,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,1,8,2,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,6,1,2,3,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,6,1,2,3,7,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,1,2,3,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,6,1,2,7,8,3,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,1,2,8,3,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,1,7,2,3,5,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,1,8,2,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,1,2,3,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,1,2,3,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,1,2,3,8,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,1,2,8,3,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,1,8,2,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,4,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,4,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,2,3,6,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,2,3,6,7,4,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2,3,6,8,4,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,1,2,3,7,4,8,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,1,2,3,7,8,4,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,1,2,3,8,4,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,2,6,3,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2,6,3,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,2,6,3,7,8,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2,6,3,8,4,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,4,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,2,6,7,3,8,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,2,6,7,8,3,4] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2,6,8,3,4,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,1,2,7,3,4,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,1,2,7,3,4,8,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,1,2,7,3,8,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,1,2,7,8,3,4,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,1,2,8,3,4,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,6,2,3,4,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,6,2,3,7,4,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,6,2,3,7,8,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,6,2,3,8,4,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,7,3,4,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,8,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,8,3,4,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,6,7,2,3,8,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,6,7,2,8,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,6,7,8,2,3,4] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,1,7,2,3,4,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,1,7,2,3,8,4,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,8,3,4,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,1,7,8,2,3,4,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,6,1,2,3,7,8,4] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,8,4,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,1,2,7,3,8,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,1,2,7,8,3,4] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,1,2,8,3,4,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,1,7,2,3,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,1,8,2,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,1,2,3,4,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,1,2,3,4,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,1,2,3,8,4,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,1,2,8,3,4,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,1,8,2,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,2,3,4,7,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,2,3,4,7,8,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2,3,4,8,5,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,2,3,7,4,8,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,2,3,7,8,4,5] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,1,2,3,8,4,5,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,2,7,3,4,5,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,2,7,3,4,8,5] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,2,7,3,8,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,2,7,8,3,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2,8,3,4,5,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,7,2,3,4,5,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,7,2,3,4,8,5] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,7,2,3,8,4,5] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,7,2,8,3,4,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,7,8,2,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,1,2,3,4,5,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,1,2,3,4,8,5] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,1,2,3,8,4,5] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,1,2,8,3,4,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,1,8,2,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,8,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,8,5,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1,2,3,8,4,5,6] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1,2,8,3,4,5,6] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,3 6,6,2 17,15,10 46,51,30,5 128,175,91,35
$F_{2} = 1 + q$
$F_{3} = 2 + 3\ q$
$F_{4} = 6 + 6\ q + 2\ q^{2}$
$F_{5} = 17 + 15\ q + 10\ q^{2}$
$F_{6} = 46 + 51\ q + 30\ q^{2} + 5\ q^{3}$
$F_{7} = 128 + 175\ q + 91\ q^{2} + 35\ q^{3}$
Description
The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ 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 $n\times n$ 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.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
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