Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
St000400: Ordered trees ⟶ ℤ
Values
[1,0] => [1] => [.,.] => [[]] => 1
[1,0,1,0] => [2,1] => [[.,.],.] => [[],[]] => 2
[1,1,0,0] => [1,2] => [.,[.,.]] => [[[]]] => 3
[1,0,1,0,1,0] => [3,2,1] => [[[.,.],.],.] => [[],[],[]] => 3
[1,0,1,1,0,0] => [2,3,1] => [[.,.],[.,.]] => [[],[[]]] => 4
[1,1,0,0,1,0] => [3,1,2] => [[.,[.,.]],.] => [[[]],[]] => 4
[1,1,0,1,0,0] => [2,1,3] => [[.,.],[.,.]] => [[],[[]]] => 4
[1,1,1,0,0,0] => [1,2,3] => [.,[.,[.,.]]] => [[[[]]]] => 6
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [[[[.,.],.],.],.] => [[],[],[],[]] => 4
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [[[.,.],.],[.,.]] => [[],[],[[]]] => 5
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [[[.,.],[.,.]],.] => [[],[[]],[]] => 5
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [[[.,.],.],[.,.]] => [[],[],[[]]] => 5
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => [[],[[[]]]] => 7
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [[[.,[.,.]],.],.] => [[[]],[],[]] => 5
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [[[]],[[]]] => 6
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [[[.,.],[.,.]],.] => [[],[[]],[]] => 5
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [[[.,.],.],[.,.]] => [[],[],[[]]] => 5
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => [[],[[[]]]] => 7
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[.,[.,[.,.]]],.] => [[[[]]],[]] => 7
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [[.,[.,.]],[.,.]] => [[[]],[[]]] => 6
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [[],[[[]]]] => 7
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[[[[]]]]] => 10
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [[],[],[],[],[]] => 5
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 6
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => 6
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 6
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 8
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [[[[.,.],[.,.]],.],.] => [[],[[]],[],[]] => 6
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 7
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => 6
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 6
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 8
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => 8
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 7
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 8
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 11
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.] => [[[]],[],[],[]] => 6
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => 7
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => 7
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => 7
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 9
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [[[[.,.],[.,.]],.],.] => [[],[[]],[],[]] => 6
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 7
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => 6
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 6
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 8
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => 8
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 7
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 8
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 11
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => [[[[]]],[],[]] => 8
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => 9
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => 7
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => 7
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 9
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => 8
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 7
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 8
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 11
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => [[[[[]]]],[]] => 11
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => 9
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 9
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 11
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [[[[[[]]]]]] => 15
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [[],[],[],[],[],[]] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 7
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 7
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 7
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 9
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [[],[],[[]],[],[]] => 7
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 8
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 7
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 7
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 9
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 9
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 8
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 9
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 12
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.] => [[],[[]],[],[],[]] => 7
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 8
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 8
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 8
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 10
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],.] => [[],[],[[]],[],[]] => 7
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 8
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 7
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 7
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 9
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 9
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 8
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 9
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 12
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.] => [[],[[[]]],[],[]] => 9
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 10
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 8
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 8
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 10
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 9
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 8
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 9
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 12
>>> Load all 1544 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 12
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 10
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 10
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 12
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 16
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.] => [[[]],[],[],[],[]] => 7
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 8
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [[[]],[],[[]],[]] => 8
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 8
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 10
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],.] => [[[]],[[]],[],[]] => 8
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 9
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [[[]],[],[[]],[]] => 8
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 8
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 10
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 10
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 9
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 10
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 13
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.] => [[],[[]],[],[],[]] => 7
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 8
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 8
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 8
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 10
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.] => [[],[],[[]],[],[]] => 7
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 8
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 7
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 7
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 9
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 9
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 8
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 9
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 12
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],.] => [[],[[[]]],[],[]] => 9
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 10
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 8
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 8
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 10
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 9
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 8
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 9
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 12
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 12
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 10
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 10
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 12
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 16
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => [[[[]]],[],[],[]] => 9
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 10
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[]]],[[]],[]] => 10
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 10
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 12
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.] => [[[]],[[]],[],[]] => 8
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 9
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.] => [[[]],[],[[]],[]] => 8
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 8
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 10
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 10
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 9
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 10
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 13
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.] => [[],[[[]]],[],[]] => 9
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 10
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 8
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 8
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 10
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 9
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 8
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 9
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 12
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 12
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 10
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 10
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 12
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 16
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.] => [[[[[]]]],[],[]] => 12
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[[[]]]],[[]]] => 13
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[]]],[[]],[]] => 10
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 10
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 12
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 10
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 9
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 10
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 13
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 12
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 10
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 10
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 12
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 16
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => [[[[[[]]]]],[]] => 16
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[[[]]]],[[]]] => 13
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 12
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 13
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 16
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [[[[[[[]]]]]]] => 21
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [[],[],[],[],[],[],[]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [[],[],[],[],[],[[]]] => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [[],[],[],[],[[]],[]] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [[],[],[],[],[],[[]]] => 8
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [[],[],[],[[]],[],[]] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [[],[],[],[],[[]],[]] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [[],[],[],[],[],[[]]] => 8
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[],[],[],[[[]]],[]] => 10
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [[],[],[[]],[],[],[]] => 8
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[],[],[[]],[[]],[]] => 9
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [[],[],[],[[]],[],[]] => 8
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [[],[],[],[],[[]],[]] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [[],[],[],[],[],[[]]] => 8
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[],[],[],[[[]]],[]] => 10
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [[],[],[[[]]],[],[]] => 10
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[],[],[[]],[[]],[]] => 9
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[],[],[],[[[]]],[]] => 10
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[],[],[[[[]]]],[]] => 13
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],.] => [[],[[]],[],[],[],[]] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[],[[]],[],[],[[]]] => 9
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [[],[[]],[],[[]],[]] => 9
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[],[[]],[],[],[[]]] => 9
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [[],[[]],[[]],[],[]] => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [[],[[]],[],[[]],[]] => 9
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[],[[]],[],[],[[]]] => 9
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[],[[]],[[[]]],[]] => 11
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [[],[],[[]],[],[],[]] => 8
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[],[],[[]],[[]],[]] => 9
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [[],[],[],[[]],[],[]] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [[],[],[],[],[[]],[]] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [[],[],[],[],[],[[]]] => 8
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[],[],[],[[[]]],[]] => 10
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [[],[],[[[]]],[],[]] => 10
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[],[],[[]],[[]],[]] => 9
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[],[],[],[[[]]],[]] => 10
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[],[],[[[[]]]],[]] => 13
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [[],[[[]]],[],[],[]] => 10
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[],[[[]]],[],[[]]] => 11
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [[],[[[]]],[[]],[]] => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[],[[[]]],[],[[]]] => 11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [[],[[]],[[]],[],[]] => 9
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [[],[[]],[],[[]],[]] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[],[[]],[],[],[[]]] => 9
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[],[[]],[[[]]],[]] => 11
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [[],[],[[[]]],[],[]] => 10
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[],[],[[]],[[]],[]] => 9
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[],[],[],[[[]]],[]] => 10
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[],[],[[[[]]]],[]] => 13
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [[],[[[[]]]],[],[]] => 13
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[],[[[[]]]],[[]]] => 14
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [[],[[[]]],[[]],[]] => 11
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[],[[[]]],[],[[]]] => 11
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[],[[]],[[[]]],[]] => 11
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[],[],[[[[]]]],[]] => 13
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [[],[[[[[]]]]],[]] => 17
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[],[[[[]]]],[[]]] => 14
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[],[[[[[[]]]]]]] => 22
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],.] => [[[]],[],[],[],[],[]] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [[[]],[],[],[],[[]]] => 9
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => [[[]],[],[],[[]],[]] => 9
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [[[]],[],[],[],[[]]] => 9
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[]],[],[],[[[]]]] => 11
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],.] => [[[]],[],[[]],[],[]] => 9
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[]],[],[[]],[[]]] => 10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => [[[]],[],[],[[]],[]] => 9
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [[[]],[],[],[],[[]]] => 9
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[]],[],[],[[[]]]] => 11
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [[[]],[],[[[]]],[]] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[]],[],[[]],[[]]] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[]],[],[],[[[]]]] => 11
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[]],[],[[[[]]]]] => 14
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],.] => [[[]],[[]],[],[],[]] => 9
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [[[]],[[]],[],[[]]] => 10
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [[[]],[[]],[[]],[]] => 10
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [[[]],[[]],[],[[]]] => 10
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[]],[[]],[[[]]]] => 12
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [[[[[.,[.,.]],.],[.,.]],.],.] => [[[]],[],[[]],[],[]] => 9
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[]],[],[[]],[[]]] => 10
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => [[[]],[],[],[[]],[]] => 9
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [[[]],[],[],[],[[]]] => 9
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[]],[],[],[[[]]]] => 11
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [[[]],[],[[[]]],[]] => 11
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[]],[],[[]],[[]]] => 10
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[]],[],[],[[[]]]] => 11
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[]],[],[[[[]]]]] => 14
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [[[]],[[[]]],[],[]] => 11
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[]],[[[]]],[[]]] => 12
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [[[]],[[]],[[]],[]] => 10
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [[[]],[[]],[],[[]]] => 10
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[]],[[]],[[[]]]] => 12
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [[[]],[],[[[]]],[]] => 11
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[]],[],[[]],[[]]] => 10
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[]],[],[],[[[]]]] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[]],[],[[[[]]]]] => 14
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [[[]],[[[[]]]],[]] => 14
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[]],[[[]]],[[]]] => 12
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[]],[[]],[[[]]]] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[]],[],[[[[]]]]] => 14
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[[]],[[[[[]]]]]] => 18
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],.] => [[],[[]],[],[],[],[]] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[],[[]],[],[],[[]]] => 9
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => [[],[[]],[],[[]],[]] => 9
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[],[[]],[],[],[[]]] => 9
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],.] => [[],[[]],[[]],[],[]] => 9
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => [[],[[]],[],[[]],[]] => 9
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[],[[]],[],[],[[]]] => 9
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[],[[]],[[[]]],[]] => 11
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],.] => [[],[],[[]],[],[],[]] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[],[],[[]],[[]],[]] => 9
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],.] => [[],[],[],[[]],[],[]] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],[.,.]],.] => [[],[],[],[],[[]],[]] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [[],[],[],[],[],[[]]] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[],[],[],[[[]]],[]] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => [[],[],[[[]]],[],[]] => 10
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[],[],[[]],[[]],[]] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[],[],[],[[[]]],[]] => 10
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[],[],[[[[]]]],[]] => 13
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => [[],[[[]]],[],[],[]] => 10
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[],[[[]]],[],[[]]] => 11
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [[],[[[]]],[[]],[]] => 11
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[],[[[]]],[],[[]]] => 11
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [[[[[.,.],[.,.]],[.,.]],.],.] => [[],[[]],[[]],[],[]] => 9
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [[[[[.,.],[.,.]],.],[.,.]],.] => [[],[[]],[],[[]],[]] => 9
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[],[[]],[],[],[[]]] => 9
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[],[[]],[[[]]],[]] => 11
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => [[],[],[[[]]],[],[]] => 10
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[],[],[[]],[[]],[]] => 9
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[],[],[],[[[]]],[]] => 10
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[],[],[[[[]]]],[]] => 13
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [[],[[[[]]]],[],[]] => 13
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[],[[[[]]]],[[]]] => 14
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [[],[[[]]],[[]],[]] => 11
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[],[[[]]],[],[[]]] => 11
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[],[[]],[[[]]],[]] => 11
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[],[],[[[[]]]],[]] => 13
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [[],[[[[[]]]]],[]] => 17
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[],[[[[]]]],[[]]] => 14
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[],[[[[[[]]]]]]] => 22
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],.] => [[[[]]],[],[],[],[]] => 10
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [[[[]]],[],[],[[]]] => 11
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [[[[]]],[],[[]],[]] => 11
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [[[[]]],[],[],[[]]] => 11
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[[]]],[],[[[]]]] => 13
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [[[[]]],[[]],[],[]] => 11
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [[[[]]],[[]],[[]]] => 12
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [[[[]]],[],[[]],[]] => 11
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [[[[]]],[],[],[[]]] => 11
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[[]]],[],[[[]]]] => 13
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [[[[]]],[[[]]],[]] => 13
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [[[[]]],[[]],[[]]] => 12
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[[]]],[],[[[]]]] => 13
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[[[]]],[[[[]]]]] => 16
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],.] => [[[]],[[]],[],[],[]] => 9
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [[[]],[[]],[],[[]]] => 10
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [[[]],[[]],[[]],[]] => 10
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [[[]],[[]],[],[[]]] => 10
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[]],[[]],[[[]]]] => 12
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [[[[[.,[.,.]],.],[.,.]],.],.] => [[[]],[],[[]],[],[]] => 9
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[]],[],[[]],[[]]] => 10
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],[.,.]],.] => [[[]],[],[],[[]],[]] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,.]] => [[[]],[],[],[],[[]]] => 9
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[]],[],[],[[[]]]] => 11
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [[[]],[],[[[]]],[]] => 11
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[]],[],[[]],[[]]] => 10
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[]],[],[],[[[]]]] => 11
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[]],[],[[[[]]]]] => 14
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [[[]],[[[]]],[],[]] => 11
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[]],[[[]]],[[]]] => 12
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [[[]],[[]],[[]],[]] => 10
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [[[]],[[]],[],[[]]] => 10
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[]],[[]],[[[]]]] => 12
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [[[]],[],[[[]]],[]] => 11
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[]],[],[[]],[[]]] => 10
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[]],[],[],[[[]]]] => 11
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[]],[],[[[[]]]]] => 14
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [[[]],[[[[]]]],[]] => 14
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[]],[[[]]],[[]]] => 12
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[]],[[]],[[[]]]] => 12
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[]],[],[[[[]]]]] => 14
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[[]],[[[[[]]]]]] => 18
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => [[],[[[]]],[],[],[]] => 10
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[],[[[]]],[],[[]]] => 11
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [[],[[[]]],[[]],[]] => 11
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[],[[[]]],[],[[]]] => 11
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],.],.] => [[],[[]],[[]],[],[]] => 9
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [[[[[.,.],[.,.]],.],[.,.]],.] => [[],[[]],[],[[]],[]] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[],[[]],[],[],[[]]] => 9
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[],[[]],[[[]]],[]] => 11
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => [[],[],[[[]]],[],[]] => 10
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[],[],[[]],[[]],[]] => 9
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[],[],[[]],[],[[]]] => 9
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[],[],[],[[[]]],[]] => 10
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[],[],[],[[]],[[]]] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[],[],[],[],[[[]]]] => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[],[],[[[[]]]],[]] => 13
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [[],[[[[]]]],[],[]] => 13
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[],[[[[]]]],[[]]] => 14
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [[],[[[]]],[[]],[]] => 11
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[],[[[]]],[],[[]]] => 11
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[],[[]],[[[]]],[]] => 11
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[],[],[[[[]]]],[]] => 13
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [[],[[[[[]]]]],[]] => 17
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[],[[[[]]]],[[]]] => 14
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[],[[[[[[]]]]]]] => 22
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [[[[[]]]],[],[],[]] => 13
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [[[[[]]]],[],[[]]] => 14
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [[[[[]]]],[[]],[]] => 14
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [[[[[]]]],[],[[]]] => 14
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[[[[]]]],[[[]]]] => 16
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [[[[]]],[[]],[],[]] => 11
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [[[[]]],[[]],[[]]] => 12
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [[[[]]],[],[[]],[]] => 11
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [[[[]]],[],[],[[]]] => 11
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[[]]],[],[[[]]]] => 13
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [[[[]]],[[[]]],[]] => 13
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [[[[]]],[[]],[[]]] => 12
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[[]]],[],[[[]]]] => 13
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[[[]]],[[[[]]]]] => 16
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [[[]],[[[]]],[],[]] => 11
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[]],[[[]]],[[]]] => 12
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [[[]],[[]],[[]],[]] => 10
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [[[]],[[]],[],[[]]] => 10
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[]],[[]],[[[]]]] => 12
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [[[]],[],[[[]]],[]] => 11
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[]],[],[[]],[[]]] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[]],[],[],[[[]]]] => 11
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[]],[],[[[[]]]]] => 14
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [[[]],[[[[]]]],[]] => 14
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[]],[[[]]],[[]]] => 12
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[]],[[]],[[[]]]] => 12
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[]],[],[[[[]]]]] => 14
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[[]],[[[[[]]]]]] => 18
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [[],[[[[]]]],[],[]] => 13
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[],[[[[]]]],[[]]] => 14
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [[],[[[]]],[[]],[]] => 11
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[],[[[]]],[],[[]]] => 11
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[],[[]],[[[]]],[]] => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[],[[]],[[]],[[]]] => 10
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[],[[]],[],[[[]]]] => 11
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[],[],[[[[]]]],[]] => 13
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[],[],[[[]]],[[]]] => 11
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[],[],[[]],[[[]]]] => 11
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[],[],[],[[[[]]]]] => 13
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [[],[[[[[]]]]],[]] => 17
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[],[[[[]]]],[[]]] => 14
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[],[[[[[[]]]]]]] => 22
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [[[[[[]]]]],[],[]] => 17
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[[[[[]]]]],[[]]] => 18
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [[[[[]]]],[[]],[]] => 14
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [[[[[]]]],[],[[]]] => 14
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[[[[]]]],[[[]]]] => 16
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [[[[]]],[[[]]],[]] => 13
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [[[[]]],[[]],[[]]] => 12
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[[]]],[],[[[]]]] => 13
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[[[]]],[[[[]]]]] => 16
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [[[]],[[[[]]]],[]] => 14
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[]],[[[]]],[[]]] => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[]],[[]],[[[]]]] => 12
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[]],[],[[[[]]]]] => 14
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[[]],[[[[[]]]]]] => 18
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [[],[[[[[]]]]],[]] => 17
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[],[[[[]]]],[[]]] => 14
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[],[[[]]],[[[]]]] => 13
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[],[[]],[[[[]]]]] => 14
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[],[],[[[[[]]]]]] => 17
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[],[[[[[[]]]]]]] => 22
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [[[[[[[]]]]]],[]] => 22
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[[[[[]]]]],[[]]] => 18
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[[[[]]]],[[[]]]] => 16
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[[[]]],[[[[]]]]] => 16
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[[]],[[[[[]]]]]] => 18
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[],[[[[[[]]]]]]] => 22
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[[]]]]]]]] => 28
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [[],[],[],[],[],[],[],[]] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [[],[],[],[],[],[],[[]]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [[],[],[],[],[],[[]],[]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [[],[],[],[],[],[],[[]]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [[],[],[],[],[[]],[],[]] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [[],[],[],[],[],[[]],[]] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [[],[],[],[],[],[],[[]]] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [[],[],[],[[]],[],[],[]] => 9
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [[],[],[],[],[[]],[],[]] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [[],[],[],[],[],[[]],[]] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [[],[],[],[],[],[],[[]]] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[],[],[],[[[]]],[],[]] => 11
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [[],[],[[]],[],[],[],[]] => 9
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 10
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 10
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 12
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [[],[],[],[[]],[],[],[]] => 9
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [[],[],[],[],[[]],[],[]] => 9
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [[],[],[],[],[],[[]],[]] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [[],[],[],[],[],[],[[]]] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[],[],[],[[[]]],[],[]] => 11
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [[],[],[[[]]],[],[],[]] => 11
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 12
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 10
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[],[],[],[[[]]],[],[]] => 11
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [[],[],[[[[]]]],[],[]] => 14
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 12
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [[],[[]],[],[],[],[],[]] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[],[[]],[],[],[[]],[]] => 10
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [[],[[]],[],[[]],[],[]] => 10
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[],[[]],[],[],[[]],[]] => 10
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[],[[]],[],[[[]]],[]] => 12
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [[],[[]],[[]],[],[],[]] => 10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[],[[]],[[]],[[]],[]] => 11
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [[],[[]],[],[[]],[],[]] => 10
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[],[[]],[],[],[[]],[]] => 10
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[],[[]],[],[[[]]],[]] => 12
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [[],[[]],[[[]]],[],[]] => 12
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[],[[]],[[]],[[]],[]] => 11
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [[],[],[[]],[],[],[],[]] => 9
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 10
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 10
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 10
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 12
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [[],[],[],[[]],[],[],[]] => 9
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [[],[],[],[],[[]],[],[]] => 9
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [[],[],[],[],[],[[]],[]] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [[],[],[],[],[],[],[[]]] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [[],[],[[[]]],[],[],[]] => 11
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 12
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 10
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 10
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 12
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[],[],[],[[[]]],[],[]] => 11
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 12
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [[],[[[]]],[],[],[],[]] => 11
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[],[[[]]],[],[[]],[]] => 12
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [[],[[[]]],[[]],[],[]] => 12
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[],[[[]]],[],[[]],[]] => 12
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 14
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [[],[[]],[],[[]],[],[]] => 10
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[],[[]],[],[],[[]],[]] => 10
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [[],[],[[[]]],[],[],[]] => 11
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 12
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 10
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 10
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[],[],[],[[[]]],[],[]] => 11
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 12
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [[],[[[[]]]],[],[],[]] => 14
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[],[[[[]]]],[],[[]]] => 15
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [[],[[[[]]]],[[]],[]] => 15
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[],[[[[]]]],[],[[]]] => 15
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[],[[]],[[]],[[]],[]] => 11
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[],[[]],[],[[[]]],[]] => 12
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [[],[[[[[]]]]],[],[]] => 18
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [[],[[[[]]]],[[]],[]] => 15
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[],[[[[]]]],[],[[]]] => 15
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [[],[[[[[[]]]]]],[]] => 23
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[],[[[[[[[]]]]]]]] => 29
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [[[]],[],[],[],[],[],[]] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[]],[],[],[],[],[[]]] => 10
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [[[]],[],[],[],[[]],[]] => 10
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[]],[],[],[],[],[[]]] => 10
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[]],[],[],[],[[[]]]] => 12
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [[[]],[],[],[[]],[],[]] => 10
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[]],[],[],[[]],[[]]] => 11
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [[[]],[],[],[],[[]],[]] => 10
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[]],[],[],[],[],[[]]] => 10
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[]],[],[],[],[[[]]]] => 12
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[]],[],[],[[]],[[]]] => 11
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[]],[],[],[],[[[]]]] => 12
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [[[]],[],[[]],[],[],[]] => 10
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [[[]],[],[[]],[],[[]]] => 11
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [[[]],[],[[]],[[]],[]] => 11
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [[[]],[],[],[[]],[],[]] => 10
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[]],[],[],[],[],[[]]] => 10
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [[[]],[],[],[[[]]],[]] => 12
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[]],[],[],[[]],[[]]] => 11
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[]],[],[],[],[[[]]]] => 12
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[[]],[],[[[]]],[[]]] => 13
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [[[]],[],[[]],[[]],[]] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [[[]],[],[[]],[],[[]]] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [[[]],[],[],[[[]]],[]] => 12
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[]],[],[],[],[[[]]]] => 12
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[]],[],[[[[[]]]]]] => 19
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [[[]],[[]],[],[],[],[]] => 10
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[[]],[[]],[],[],[[]]] => 11
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[[]],[[]],[],[],[[]]] => 11
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[]],[[]],[],[[[]]]] => 13
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [[[]],[[]],[[]],[],[]] => 11
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]],[[]]] => 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] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [[[]],[[]],[],[[]],[]] => 11
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[[]],[[]],[],[],[[]]] => 11
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[]],[[]],[],[[[]]]] => 13
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[]],[[]],[[[]]],[]] => 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] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]],[[]]] => 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] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[]],[[]],[],[[[]]]] => 13
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[]],[[]],[[[[]]]]] => 16
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[]],[],[],[[]],[[]]] => 11
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [[[]],[],[],[],[[]],[]] => 10
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[]],[],[],[],[],[[]]] => 10
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[]],[],[],[[]],[[]]] => 11
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [[[]],[],[[[]]],[],[]] => 12
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[[]],[],[[[]]],[[]]] => 13
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [[[]],[],[],[[[]]],[]] => 12
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[]],[],[],[[]],[[]]] => 11
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[]],[],[],[],[[[]]]] => 12
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[]],[],[[[[[]]]]]] => 19
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [[[]],[[[]]],[],[],[]] => 12
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [[[]],[[[]]],[],[[]]] => 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] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[]],[[[]]],[[]],[]] => 13
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]],[[]]] => 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] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[[]],[[]],[],[],[[]]] => 11
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [[[]],[],[[[]]],[],[]] => 12
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[[]],[],[[[]]],[[]]] => 13
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [[[]],[],[[]],[],[[]]] => 11
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [[[]],[],[],[[[]]],[]] => 12
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[]],[],[],[[]],[[]]] => 11
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[]],[],[],[],[[[]]]] => 12
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[[]],[],[[[]]],[[]]] => 13
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[]],[],[[[[[]]]]]] => 19
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [[[]],[[[[]]]],[],[]] => 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] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[]],[[[[]]]],[[]]] => 16
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [[[]],[[[]]],[],[[]]] => 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] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[]],[[]],[[[]]],[]] => 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] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]],[[]]] => 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] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[]],[[]],[[[[]]]]] => 16
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [[[]],[],[[[[]]]],[]] => 15
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[]],[],[[[[[]]]]]] => 19
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[]],[[[[[]]]]],[]] => 19
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[]],[[[[]]]],[[]]] => 16
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[]],[[[]]],[[[]]]] => 15
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[]],[[]],[[[[]]]]] => 16
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[]],[],[[[[[]]]]]] => 19
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[]],[[[[[[]]]]]]] => 24
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [[],[[]],[],[],[],[],[]] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[],[[]],[],[],[[]],[]] => 10
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [[],[[]],[],[[]],[],[]] => 10
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [[],[[]],[[]],[],[],[]] => 10
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [[],[],[[]],[],[],[],[]] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 10
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 10
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 10
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 12
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [[],[],[],[[]],[],[],[]] => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [[],[],[],[],[[]],[],[]] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [[],[],[],[],[],[[]],[]] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [[],[],[],[],[],[],[[]]] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[],[],[],[[[]]],[],[]] => 11
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [[],[],[[[]]],[],[],[]] => 11
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 10
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 10
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 12
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [[],[],[[[[]]]],[],[]] => 14
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [[],[[[]]],[],[],[],[]] => 11
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[],[[[]]],[],[[]],[]] => 12
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [[],[[[]]],[[]],[],[]] => 12
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[],[[[]]],[],[[]],[]] => 12
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 14
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [[],[[]],[[]],[],[],[]] => 10
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[],[[]],[],[],[[]],[]] => 10
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[],[[]],[],[[[]]],[]] => 12
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [[],[[]],[[[]]],[],[]] => 12
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [[],[],[[[]]],[],[],[]] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 12
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 10
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 10
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[],[],[],[[[]]],[],[]] => 11
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [[],[],[[[[]]]],[],[]] => 14
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [[],[[[[]]]],[],[],[]] => 14
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [[],[[[[]]]],[[]],[]] => 15
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[],[[[[]]]],[],[[]]] => 15
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[],[[[]]],[],[[]],[]] => 12
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 14
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[],[[]],[[]],[[]],[]] => 11
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[],[[]],[],[[[]]],[]] => 12
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 12
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 12
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [[],[[[[[]]]]],[],[]] => 18
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[],[[[[]]]],[],[[]]] => 15
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 14
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [[],[[[[[[]]]]]],[]] => 23
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[],[[[[[[[]]]]]]]] => 29
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [[[[]]],[],[],[],[],[]] => 11
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[[[]]],[],[],[],[[]]] => 12
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[[[]]],[],[],[],[[]]] => 12
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[]]],[],[],[[[]]]] => 14
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[[[]]],[],[[]],[[]]] => 13
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [[[[]]],[],[],[[]],[]] => 12
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[[[]]],[],[],[],[[]]] => 12
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[]]],[],[],[[[]]]] => 14
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[[[]]],[],[[]],[[]]] => 13
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[]]],[],[],[[[]]]] => 14
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [[[[]]],[],[[]],[],[]] => 12
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[[[]]],[],[[]],[[]]] => 13
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [[[[]]],[],[],[[]],[]] => 12
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[[[]]],[],[],[],[[]]] => 12
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[]]],[],[],[[[]]]] => 14
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[[[]]],[],[[]],[[]]] => 13
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[]]],[],[],[[[]]]] => 14
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[[[]]],[],[[]],[[]]] => 13
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[]]],[],[],[[[]]]] => 14
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [[[]],[[]],[],[],[],[]] => 10
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[[]],[[]],[],[],[[]]] => 11
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [[[]],[[]],[],[[]],[]] => 11
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[[]],[[]],[],[],[[]]] => 11
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [[[]],[[]],[[]],[],[]] => 11
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]],[[]]] => 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] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [[[]],[[]],[],[[]],[]] => 11
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[[]],[[]],[],[],[[]]] => 11
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[]],[[]],[],[[[]]]] => 13
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]],[[]]] => 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] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[]],[[]],[],[[[]]]] => 13
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[]],[[]],[[[[]]]]] => 16
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [[[]],[],[[]],[],[],[]] => 10
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [[[]],[],[],[[]],[],[]] => 10
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[]],[],[],[[]],[[]]] => 11
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [[[]],[],[],[],[[]],[]] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[]],[],[],[],[],[[]]] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[]],[],[],[],[[[]]]] => 12
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[]],[],[],[[]],[[]]] => 11
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [[[]],[],[[]],[[]],[]] => 11
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [[[]],[],[[]],[],[[]]] => 11
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[]],[],[[[[[]]]]]] => 19
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [[[]],[[[]]],[],[],[]] => 12
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [[[]],[[[]]],[],[[]]] => 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] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[]],[[[]]],[[]],[]] => 13
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[]],[[[]]],[[[]]]] => 15
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [[[]],[[]],[[]],[],[]] => 11
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [[[]],[[]],[],[[]],[]] => 11
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[[]],[[]],[],[],[[]]] => 11
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[]],[[]],[[[]]],[]] => 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] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[]],[[]],[],[[[]]]] => 13
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [[[]],[],[],[[[]]],[]] => 12
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[]],[],[],[],[[[]]]] => 12
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [[[]],[],[[[[]]]],[]] => 15
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [[[]],[[[[]]]],[],[]] => 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] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[]],[[[[]]]],[[]]] => 16
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[]],[[[]]],[[]],[]] => 13
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[]],[[[]]],[[[]]]] => 15
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[]],[[]],[[[]]],[]] => 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] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[]],[[]],[[[[]]]]] => 16
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [[[]],[],[[[[]]]],[]] => 15
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[]],[[[[[]]]]],[]] => 19
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[]],[[[]]],[[[]]]] => 15
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[]],[],[[[[[]]]]]] => 19
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[]],[[[[[[]]]]]]] => 24
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [[],[[[]]],[],[],[],[]] => 11
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [[],[[[]]],[[]],[],[]] => 12
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[],[[[]]],[],[[]],[]] => 12
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 14
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [[],[[]],[[]],[],[],[]] => 10
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[],[[]],[[]],[[]],[]] => 11
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[],[[]],[],[],[[]],[]] => 10
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[],[[]],[],[],[],[[]]] => 10
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[],[[]],[],[[[]]],[]] => 12
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [[],[],[[[]]],[],[],[]] => 11
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 12
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 10
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 10
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[],[],[[]],[],[],[[]]] => 10
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 12
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[],[],[],[[[]]],[],[]] => 11
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 10
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[],[],[],[[]],[],[[]]] => 10
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[],[],[],[],[[]],[[]]] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[],[],[],[],[],[[[]]]] => 11
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [[],[],[[[[]]]],[],[]] => 14
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 12
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [[],[[[[]]]],[],[],[]] => 14
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[],[[[[]]]],[],[[]]] => 15
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [[],[[[[]]]],[[]],[]] => 15
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[],[[[[]]]],[],[[]]] => 15
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[],[[[]]],[],[[]],[]] => 12
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 14
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[],[[]],[[]],[[]],[]] => 11
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,1,5,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[],[[]],[],[[]],[[]]] => 11
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [[],[],[[[[]]]],[],[]] => 14
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [[],[[[[[]]]]],[],[]] => 18
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [[],[[[[]]]],[[]],[]] => 15
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[],[[[[]]]],[],[[]]] => 15
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 14
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [[],[[[[[[]]]]]],[]] => 23
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[],[[[[[[[]]]]]]]] => 29
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [[[[]]],[],[[]],[],[]] => 12
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[[[]]],[],[[]],[[]]] => 13
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [[[[]]],[],[],[[]],[]] => 12
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[[[]]],[],[],[],[[]]] => 12
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [[[]],[[[]]],[],[],[]] => 12
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [[[]],[[[]]],[],[[]]] => 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] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[]],[[[]]],[[]],[]] => 13
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [[[]],[[[]]],[],[[]]] => 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] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[]],[[[]]],[[[]]]] => 15
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [[[]],[[]],[[]],[],[]] => 11
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]],[[]]] => 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] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[]],[[]],[[[]]],[]] => 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] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[]],[[]],[[[[]]]]] => 16
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[[]],[],[[[]]],[[]]] => 13
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [[[]],[],[[]],[[]],[]] => 11
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [[[]],[],[[]],[],[[]]] => 11
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[]],[],[],[[]],[[]]] => 11
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[]],[],[],[],[[[]]]] => 12
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [[[]],[[[[]]]],[],[]] => 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] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[]],[[[[]]]],[[]]] => 16
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[]],[[[]]],[[]],[]] => 13
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[]],[[[]]],[[[]]]] => 15
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[]],[[]],[[[]]],[]] => 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] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[]],[[]],[[[[]]]]] => 16
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[]],[[[[[]]]]],[]] => 19
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[]],[],[[[[[]]]]]] => 19
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[]],[[[[[[]]]]]]] => 24
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [[],[[[[]]]],[],[],[]] => 14
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[],[[[[]]]],[],[[]]] => 15
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [[],[[[[]]]],[[]],[]] => 15
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [[],[[[]]],[[]],[],[]] => 12
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[],[[[]]],[],[[]],[]] => 12
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[],[[[]]],[],[],[[]]] => 12
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[],[[[]]],[],[[[]]]] => 14
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 14
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [[],[[]],[[[]]],[],[]] => 12
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[],[[]],[[]],[[]],[]] => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[],[[]],[[]],[],[[]]] => 11
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[],[[]],[],[[[]]],[]] => 12
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[],[[]],[],[],[[[]]]] => 12
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[],[[]],[[[]]],[[]]] => 13
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [[],[],[[[[]]]],[],[]] => 14
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 12
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[],[],[[[]]],[],[[]]] => 12
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 12
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[],[],[[]],[[]],[[]]] => 11
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[],[],[[]],[],[[[]]]] => 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] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [[],[],[],[[[[]]]],[]] => 14
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[],[],[],[[[]]],[[]]] => 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] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[],[],[],[[]],[[[]]]] => 12
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[],[],[],[],[[[[]]]]] => 14
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[],[],[[[]]],[[[]]]] => 14
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [[],[[[[[]]]]],[],[]] => 18
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[],[[[[]]]],[],[[]]] => 15
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[],[[[]]],[[]],[[]]] => 13
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [[],[[[[[[]]]]]],[]] => 23
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[],[[[[[[[]]]]]]]] => 29
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[]]],[],[],[[[]]]] => 14
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[]],[[[[]]]],[[]]] => 16
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[]],[[[]]],[[[]]]] => 15
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[]],[[]],[[[]]],[]] => 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] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]],[[]]] => 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] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[[]],[],[[[]]],[[]]] => 13
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[]],[],[[]],[[[]]]] => 13
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[]],[],[],[[[[]]]]] => 15
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[]],[[[[[]]]]],[]] => 19
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[]],[[[[]]]],[[]]] => 16
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[]],[],[[[[[]]]]]] => 19
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[]],[[[[[[]]]]]]] => 24
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [[],[[[[[]]]]],[],[]] => 18
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 14
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[],[[]],[[[[]]]],[]] => 15
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[],[[]],[[]],[[[]]]] => 13
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[],[[]],[],[[[[]]]]] => 15
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 18
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[],[],[[[[]]]],[[]]] => 15
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[],[],[[]],[[[[]]]]] => 15
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[],[],[],[[[[[]]]]]] => 18
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [[],[[[[[[]]]]]],[]] => 23
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[],[[[[]]]],[[[]]]] => 17
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[],[[[[[[[]]]]]]]] => 29
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[]],[[[[[]]]]],[]] => 19
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[]],[[[[]]]],[[]]] => 16
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[]],[[[]]],[[[]]]] => 15
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[]],[[]],[[[[]]]]] => 16
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[]],[],[[[[[]]]]]] => 19
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[]],[[[[[[]]]]]]] => 24
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [[],[[[[[[]]]]]],[]] => 23
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[],[[[[[]]]]],[[]]] => 19
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[],[[[]]],[[[[]]]]] => 17
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[],[[]],[[[[[]]]]]] => 19
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[],[],[[[[[[]]]]]]] => 23
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[],[[[[[[[]]]]]]]] => 29
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[]],[[[[[[]]]]]]] => 24
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[],[[[[[[[]]]]]]]] => 29
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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 1,3,0,1 1,6,2,4,0,0,1 1,10,10,10,5,0,5,0,0,0,1 1,15,30,25,30,0,18,6,0,0,6,0,0,0,0,1 1,21,70,70,105,21,56,42,0,7,21,7,0,0,0,7,0,0,0,0,0,1
F1=q
F2=q2+q3
F3=q3+3 q4+q6
F4=q4+6 q5+2 q6+4 q7+q10
F5=q5+10 q6+10 q7+10 q8+5 q9+5 q11+q15
F6=q6+15 q7+30 q8+25 q9+30 q10+18 q12+6 q13+6 q16+q21
F7=q7+21 q8+70 q9+70 q10+105 q11+21 q12+56 q13+42 q14+7 q16+21 q17+7 q18+7 q22+q28
Description
The path length of an ordered tree.
This is the sum of the lengths of all paths from the root to a node, see Section 2.3.4.5 of [1].
This is the sum of the lengths of all paths from the root to a node, see Section 2.3.4.5 of [1].
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 ordered tree: left child = left brother
Description
Return an ordered tree of size n+1 by the following recursive rule:
- if x is the left child of y, x becomes the left brother of y,
- if x is the right child of y, x becomes the last child of y.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
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