Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
St001733: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [.,.] => [1,0] => 1
[1,0,1,0] => [1,2] => [.,[.,.]] => [1,0,1,0] => 2
[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] => 3
[1,0,1,1,0,0] => [1,3,2] => [.,[[.,.],.]] => [1,0,1,1,0,0] => 2
[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] => 2
[1,1,1,0,0,0] => [3,2,1] => [[[.,.],.],.] => [1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => 2
[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] => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [[[[.,.],.],.],.] => [1,1,1,1,0,0,0,0] => 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] => 5
[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] => 4
[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] => 3
[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] => 4
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => 3
[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] => 2
[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] => 3
[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] => 3
[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] => 4
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => 2
[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] => 3
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => 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] => 2
[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] => 3
[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] => 3
[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] => 4
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0] => 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] => 6
[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] => 5
[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] => 4
[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] => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => 2
[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] => 3
[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] => 3
[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] => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
>>> Load all 1011 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 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] => 3
[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] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 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] => 2
[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] => 3
[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] => 3
[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] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0] => 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] => 7
[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] => 6
[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] => 5
[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] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[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] => 4
[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] => 5
[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] => 5
[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] => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[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] => 4
[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] => 5
[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] => 5
[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] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[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] => 2
[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] => 3
[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] => 3
[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] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[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] => 4
[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] => 5
[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] => 5
[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] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [.,[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[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] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 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] => 3
[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] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 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] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 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] => 2
[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] => 3
[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] => 3
[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] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 4
[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] => 4
[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] => 5
[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] => 5
[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] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 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] => 8
[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] => 7
[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] => 6
[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] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[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] => 5
[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] => 6
[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] => 6
[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] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[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] => 4
[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] => 5
[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] => 5
[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] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[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] => 5
[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] => 6
[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] => 6
[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] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[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] => 4
[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] => 5
[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] => 5
[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] => 6
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[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] => 4
[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] => 5
[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] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[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] => 5
[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] => 6
[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] => 6
[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] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => [.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,7,5,4,6,8,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[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] => 2
[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] => 3
[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] => 3
[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] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => 3
[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] => 4
[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] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
[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] => 4
[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] => 5
[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] => 5
[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] => 6
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[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] => 3
[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] => 4
[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] => 4
[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] => 5
[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] => 5
[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] => 5
[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] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[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] => 4
[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] => 5
[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] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 5
[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] => 5
[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] => 6
[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] => 6
[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] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,3,5,6,7,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,8,4,5,6,3,7,2] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [.,[[[[.,.],[[[.,.],.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[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] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[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] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 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] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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] => 4
[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] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 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] => 3
[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] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[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] => 5
[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] => 5
[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] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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] => 2
[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] => 3
[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] => 3
[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] => 4
[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] => 4
[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] => 4
[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] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,2,1 5,5,3,1 13,15,9,4,1 35,47,30,14,5,1 98,149,104,51,20,6,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + 2\ q^{2} + q^{3}$
$F_{4} = 5\ q + 5\ q^{2} + 3\ q^{3} + q^{4}$
$F_{5} = 13\ q + 15\ q^{2} + 9\ q^{3} + 4\ q^{4} + q^{5}$
$F_{6} = 35\ q + 47\ q^{2} + 30\ q^{3} + 14\ q^{4} + 5\ q^{5} + q^{6}$
$F_{7} = 98\ q + 149\ q^{2} + 104\ q^{3} + 51\ q^{4} + 20\ q^{5} + 6\ q^{6} + q^{7}$
Description
The number of weak left to right maxima of a Dyck path.
A weak left to right maximum is a peak whose height is larger than or equal to the height of all peaks to its
left.
A weak left to right maximum is a peak whose height is larger than or equal to the height of all peaks to its
left.
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 increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
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