Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
St001161: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [.,.] => [1,0] => 0
[1,0,1,0] => [2,1] => [[.,.],.] => [1,0,1,0] => 1
[1,1,0,0] => [1,2] => [.,[.,.]] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [3,2,1] => [[[.,.],.],.] => [1,0,1,0,1,0] => 3
[1,0,1,1,0,0] => [2,3,1] => [[.,.],[.,.]] => [1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => [3,1,2] => [[.,[.,.]],.] => [1,1,0,0,1,0] => 2
[1,1,0,1,0,0] => [2,1,3] => [[.,.],[.,.]] => [1,0,1,1,0,0] => 1
[1,1,1,0,0,0] => [1,2,3] => [.,[.,[.,.]]] => [1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [[[[.,.],.],.],.] => [1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [[[.,[.,.]],.],.] => [1,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[.,[.,[.,.]]],.] => [1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.] => [1,1,0,0,1,0,1,0,1,0] => 9
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => 5
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0] => 15
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 11
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => 12
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 11
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => [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] => [6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => 13
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => 12
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 11
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => 10
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
>>> Load all 1520 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0] => 14
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => 10
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => 11
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => 10
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [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] => [6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => 13
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => 12
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 11
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => 10
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0] => 12
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => 8
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => 11
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => 10
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 9
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => 10
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0] => 9
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 16
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 16
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 16
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [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] => [7,6,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 19
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 18
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 16
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 17
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [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] => [7,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 19
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 18
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 18
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 12
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 13
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 12
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 14
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 13
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 12
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 17
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 13
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 15
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 14
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 13
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 12
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 13
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 28
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 22
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 23
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 22
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 24
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 23
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 22
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 25
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 24
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 23
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 22
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [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] => [8,7,6,5,4,2,3,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 26
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 25
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 24
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 23
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 22
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 23
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 19
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 14
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 27
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 21
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 21
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 23
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 24
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 21
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 20
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 15
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 26
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 25
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 24
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 23
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 22
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 23
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 19
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 14
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 24
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 23
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 21
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 20
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 12
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 15
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 12
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 23
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 19
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,1,5,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 14
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 20
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 15
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 19
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 14
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 14
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,1,1 1,3,2,4,2,1,1 1,4,3,8,6,6,6,4,2,1,1 1,5,4,13,11,14,19,15,15,10,11,6,4,2,1,1 1,6,5,19,17,24,39,37,41,40,45,35,35,24,20,16,11,6,4,2,1,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + q^{2} + q^{3}$
$F_{4} = 1 + 3\ q + 2\ q^{2} + 4\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{5} = 1 + 4\ q + 3\ q^{2} + 8\ q^{3} + 6\ q^{4} + 6\ q^{5} + 6\ q^{6} + 4\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$
$F_{6} = 1 + 5\ q + 4\ q^{2} + 13\ q^{3} + 11\ q^{4} + 14\ q^{5} + 19\ q^{6} + 15\ q^{7} + 15\ q^{8} + 10\ q^{9} + 11\ q^{10} + 6\ q^{11} + 4\ q^{12} + 2\ q^{13} + q^{14} + q^{15}$
$F_{7} = 1 + 6\ q + 5\ q^{2} + 19\ q^{3} + 17\ q^{4} + 24\ q^{5} + 39\ q^{6} + 37\ q^{7} + 41\ q^{8} + 40\ q^{9} + 45\ q^{10} + 35\ q^{11} + 35\ q^{12} + 24\ q^{13} + 20\ q^{14} + 16\ q^{15} + 11\ q^{16} + 6\ q^{17} + 4\ q^{18} + 2\ q^{19} + q^{20} + q^{21}$
Description
The major index north count of a Dyck path.
The descent set $\operatorname{des}(D)$ of a Dyck path $D = D_1 \cdots D_{2n}$ with $D_i \in \{N,E\}$ is given by all indices $i$ such that $D_i = E$ and $D_{i+1} = N$. This is, the positions of the valleys of $D$.
The major index of a Dyck path is then the sum of the positions of the valleys, $\sum_{i \in \operatorname{des}(D)} i$, see St000027The major index of a Dyck path..
The major index north count is given by $\sum_{i \in \operatorname{des}(D)} \#\{ j \leq i \mid D_j = N\}$.
The descent set $\operatorname{des}(D)$ of a Dyck path $D = D_1 \cdots D_{2n}$ with $D_i \in \{N,E\}$ is given by all indices $i$ such that $D_i = E$ and $D_{i+1} = N$. This is, the positions of the valleys of $D$.
The major index of a Dyck path is then the sum of the positions of the valleys, $\sum_{i \in \operatorname{des}(D)} i$, see St000027The major index of a Dyck path..
The major index north count is given by $\sum_{i \in \operatorname{des}(D)} \#\{ j \leq i \mid D_j = N\}$.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
The bijection is defined recursively as follows:
- a leaf is associated with an empty Dyck path,
- a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.
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