Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
St000203: Binary trees ⟶ ℤ
Values
[1,0] => [1] => [1] => [.,.] => 1
[1,0,1,0] => [1,2] => [1,2] => [.,[.,.]] => 2
[1,1,0,0] => [2,1] => [2,1] => [[.,.],.] => 2
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]] => 3
[1,0,1,1,0,0] => [1,3,2] => [3,1,2] => [[.,.],[.,.]] => 3
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [[.,.],[.,.]] => 3
[1,1,0,1,0,0] => [2,3,1] => [2,3,1] => [[.,[.,.]],.] => 2
[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => [[[.,.],.],.] => 3
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 4
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [4,1,2,3] => [[.,.],[.,[.,.]]] => 4
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1,2,4] => [[.,.],[.,[.,.]]] => 4
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1,4,2] => [[.,.],[[.,.],.]] => 3
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [4,3,1,2] => [[[.,.],.],[.,.]] => 4
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]] => 4
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [4,2,1,3] => [[[.,.],.],[.,.]] => 4
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,3,1,4] => [[.,[.,.]],[.,.]] => 3
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,3,4,1] => [[.,[.,[.,.]]],.] => 2
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,2,3,1] => [[[.,.],[.,.]],.] => 3
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]] => 4
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => [[[.,.],[.,.]],.] => 3
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,4,3,1] => [[.,[[.,.],.]],.] => 2
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [[[[.,.],.],.],.] => 4
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]] => 5
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]] => 5
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [4,1,2,5,3] => [[.,.],[.,[[.,.],.]]] => 4
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [5,4,1,2,3] => [[[.,.],.],[.,[.,.]]] => 5
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]] => 5
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [5,3,1,2,4] => [[[.,.],.],[.,[.,.]]] => 5
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,1,4,2,5] => [[.,.],[[.,.],[.,.]]] => 4
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [3,1,4,5,2] => [[.,.],[[.,[.,.]],.]] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [5,3,1,4,2] => [[[.,.],.],[[.,.],.]] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [4,3,1,2,5] => [[[.,.],.],[.,[.,.]]] => 5
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [4,3,1,5,2] => [[[.,.],.],[[.,.],.]] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [5,1,3,4,2] => [[.,.],[[.,[.,.]],.]] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [5,4,3,1,2] => [[[[.,.],.],.],[.,.]] => 5
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => 5
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [5,2,1,3,4] => [[[.,.],.],[.,[.,.]]] => 5
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]] => 5
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [4,2,1,5,3] => [[[.,.],.],[[.,.],.]] => 4
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [5,4,2,1,3] => [[[[.,.],.],.],[.,.]] => 5
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => 4
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [5,2,3,1,4] => [[[.,.],[.,.]],[.,.]] => 4
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 2
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => 4
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.] => 3
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,4,2,3,1] => [[[[.,.],.],[.,.]],.] => 4
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => 5
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [5,3,2,1,4] => [[[[.,.],.],.],[.,.]] => 5
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]] => 4
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.] => 3
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => 4
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => 3
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => 2
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => 3
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => 5
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => [[[[.,.],.],[.,.]],.] => 4
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [3,5,2,4,1] => [[[.,[.,.]],[.,.]],.] => 3
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [3,5,4,2,1] => [[[.,[[.,.],.]],.],.] => 3
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [5,1,2,3,6,4] => [[.,.],[.,[.,[[.,.],.]]]] => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [6,4,1,2,3,5] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [4,1,2,5,3,6] => [[.,.],[.,[[.,.],[.,.]]]] => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,1,2,5,6,3] => [[.,.],[.,[[.,[.,.]],.]]] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [6,4,1,2,5,3] => [[[.,.],.],[.,[[.,.],.]]] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [5,4,1,2,6,3] => [[[.,.],.],[.,[[.,.],.]]] => 5
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [6,1,4,2,5,3] => [[.,.],[[.,.],[[.,.],.]]] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => [[[[.,.],.],.],[.,[.,.]]] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [6,3,1,2,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [5,3,1,2,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [5,3,1,2,6,4] => [[[.,.],.],[.,[[.,.],.]]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [6,5,3,1,2,4] => [[[[.,.],.],.],[.,[.,.]]] => 6
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [6,3,1,4,2,5] => [[[.,.],.],[[.,.],[.,.]]] => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [6,3,1,4,5,2] => [[[.,.],.],[[.,[.,.]],.]] => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [5,3,1,4,2,6] => [[[.,.],.],[[.,.],[.,.]]] => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [5,3,1,4,6,2] => [[[.,.],.],[[.,[.,.]],.]] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [6,1,3,4,5,2] => [[.,.],[[.,[.,[.,.]]],.]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [6,5,3,1,4,2] => [[[[.,.],.],.],[[.,.],.]] => 5
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [6,4,3,1,2,5] => [[[[.,.],.],.],[.,[.,.]]] => 6
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [4,3,1,5,2,6] => [[[.,.],.],[[.,.],[.,.]]] => 5
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,3,1,5,6,2] => [[[.,.],.],[[.,[.,.]],.]] => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [6,4,3,1,5,2] => [[[[.,.],.],.],[[.,.],.]] => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [5,1,3,4,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [5,1,3,4,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [3,1,6,4,5,2] => [[.,.],[[[.,.],[.,.]],.]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [6,5,1,3,4,2] => [[[.,.],.],[[.,[.,.]],.]] => 4
>>> Load all 838 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => [[[[.,.],.],.],[.,[.,.]]] => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [5,4,3,1,6,2] => [[[[.,.],.],.],[[.,.],.]] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [6,4,1,5,3,2] => [[[.,.],.],[[[.,.],.],.]] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]] => 6
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 6
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [5,2,1,3,6,4] => [[[.,.],.],[.,[[.,.],.]]] => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [6,5,2,1,3,4] => [[[[.,.],.],.],[.,[.,.]]] => 6
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [6,4,2,1,3,5] => [[[[.,.],.],.],[.,[.,.]]] => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [4,2,1,5,3,6] => [[[.,.],.],[[.,.],[.,.]]] => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [4,2,1,5,6,3] => [[[.,.],.],[[.,[.,.]],.]] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [6,4,2,1,5,3] => [[[[.,.],.],.],[[.,.],.]] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [5,4,2,1,3,6] => [[[[.,.],.],.],[.,[.,.]]] => 6
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [5,4,2,1,6,3] => [[[[.,.],.],.],[[.,.],.]] => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [6,2,4,1,5,3] => [[[.,.],[.,.]],[[.,.],.]] => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [6,5,4,2,1,3] => [[[[[.,.],.],.],.],[.,.]] => 6
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [6,2,3,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]] => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [5,2,3,1,6,4] => [[[.,.],[.,.]],[[.,.],.]] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [6,5,2,3,1,4] => [[[[.,.],.],[.,.]],[.,.]] => 5
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [6,2,3,4,1,5] => [[[.,.],[.,[.,.]]],[.,.]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => 5
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [6,4,2,3,1,5] => [[[[.,.],.],[.,.]],[.,.]] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.] => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [6,2,5,3,4,1] => [[[.,.],[[.,.],[.,.]]],.] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]] => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => [[[[.,.],.],[.,[.,.]]],.] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [4,6,2,3,5,1] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [6,2,4,5,3,1] => [[[.,.],[[.,[.,.]],.]],.] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [[[[[.,.],.],.],[.,.]],.] => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]] => 6
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]] => 6
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [5,3,2,1,6,4] => [[[[.,.],.],.],[[.,.],.]] => 5
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [6,5,3,2,1,4] => [[[[[.,.],.],.],.],[.,.]] => 6
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [6,3,2,4,1,5] => [[[[.,.],.],[.,.]],[.,.]] => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [5,3,2,4,6,1] => [[[[.,.],.],[.,[.,.]]],.] => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,6,2,4,5,1] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,5,3,2,4,1] => [[[[[.,.],.],.],[.,.]],.] => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [6,2,4,3,1,5] => [[[.,.],[[.,.],.]],[.,.]] => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [5,2,4,3,1,6] => [[[.,.],[[.,.],.]],[.,.]] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [5,2,4,3,6,1] => [[[.,.],[[.,.],[.,.]]],.] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [4,2,6,5,3,1] => [[[.,.],[[[.,.],.],.]],.] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [6,5,2,4,3,1] => [[[[.,.],.],[[.,.],.]],.] => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => 6
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [6,4,3,2,1,5] => [[[[[.,.],.],.],.],[.,.]] => 6
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]] => 5
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [[[[.,.],.],[.,[.,.]]],.] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => 5
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,5,2,4,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,5,2,4,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,2,6,4,5,1] => [[[.,.],[[.,.],[.,.]]],.] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [6,3,5,2,4,1] => [[[[.,.],[.,.]],[.,.]],.] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => [[[.,[[.,.],.]],.],[.,.]] => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => [[[.,[[.,.],.]],[.,.]],.] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [3,4,6,2,5,1] => [[[.,[.,[.,.]]],[.,.]],.] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => [[[.,[.,[[.,.],.]]],.],.] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [6,3,5,4,2,1] => [[[[.,.],[[.,.],.]],.],.] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => 6
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [[[[[.,.],.],.],[.,.]],.] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [4,6,3,2,5,1] => [[[[.,[.,.]],.],[.,.]],.] => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [4,6,3,5,2,1] => [[[[.,[.,.]],[.,.]],.],.] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => [[[.,[[[.,.],.],.]],.],.] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [6,1,2,3,4,7,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [7,5,1,2,3,4,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [5,1,2,3,6,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [5,1,2,3,6,7,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [7,5,1,2,3,6,4] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [6,5,1,2,3,7,4] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [7,1,5,2,3,6,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [7,4,1,2,3,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [6,4,1,2,3,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [6,4,1,2,3,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 6
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [7,6,4,1,2,3,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [4,1,2,5,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [7,4,1,2,5,3,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [4,1,2,5,6,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [7,4,1,2,5,6,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [6,4,1,2,5,3,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 6
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [6,4,1,2,5,7,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [7,1,4,2,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [7,6,4,1,2,5,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [7,5,4,1,2,3,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [5,4,1,2,6,3,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [5,4,1,2,6,7,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [7,5,4,1,2,6,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => 6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [6,1,4,2,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [6,1,4,2,5,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [7,1,2,4,5,6,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [7,6,1,4,2,5,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [6,5,4,1,2,7,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [5,7,4,1,2,6,3] => [[[.,[.,.]],.],[.,[[.,.],.]]] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [7,5,1,6,2,4,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [7,3,1,2,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [6,3,1,2,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [6,3,1,2,4,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 6
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [7,6,3,1,2,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [5,3,1,2,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [7,5,3,1,2,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [5,3,1,2,6,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [5,3,1,2,6,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [7,5,3,1,2,6,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => 6
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [6,5,3,1,2,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [6,5,3,1,2,7,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [7,3,5,1,2,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [7,6,5,3,1,2,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,1,4,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [7,3,1,4,2,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [6,3,1,4,2,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [6,3,1,4,2,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [7,6,3,1,4,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => 6
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [3,1,4,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [7,3,1,4,5,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [3,1,4,5,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [3,1,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [7,3,1,4,5,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [6,3,1,4,5,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [6,3,1,4,5,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [7,1,3,4,5,6,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [7,6,3,1,4,5,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [5,3,1,4,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [7,5,3,1,4,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => 6
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [5,3,1,4,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,3,1,4,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [7,5,3,1,4,6,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [6,1,3,4,5,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [6,1,3,4,5,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [3,1,7,4,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [7,6,1,3,4,5,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [6,5,3,1,4,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [6,5,3,1,4,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [5,7,3,1,4,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [7,5,1,3,6,4,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [7,6,5,3,1,4,2] => [[[[[.,.],.],.],.],[[.,.],.]] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [4,3,1,2,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [7,4,3,1,2,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [6,4,3,1,2,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [6,4,3,1,2,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [7,6,4,3,1,2,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [4,3,1,5,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [7,4,3,1,5,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => 6
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [4,3,1,5,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [4,3,1,5,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [7,4,3,1,5,6,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [6,4,3,1,5,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [6,4,3,1,5,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [4,7,3,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [7,6,4,3,1,5,2] => [[[[[.,.],.],.],.],[[.,.],.]] => 6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [5,1,3,4,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [7,5,1,3,4,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [5,1,3,4,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [5,1,3,4,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [7,5,1,3,4,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [3,1,6,4,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [3,1,6,4,5,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [3,1,4,7,5,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [7,3,1,6,4,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [6,5,1,3,4,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [6,5,1,3,4,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [7,1,5,3,4,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [7,3,1,5,6,4,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [7,6,5,1,3,4,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [5,4,3,1,2,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [7,5,4,3,1,2,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [5,4,3,1,6,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [5,4,3,1,6,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [7,5,4,3,1,6,2] => [[[[[.,.],.],.],.],[[.,.],.]] => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [4,6,3,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [4,6,3,1,5,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [4,7,1,3,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [7,4,6,3,1,5,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => 5
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [6,4,1,5,3,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => 5
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [6,4,1,5,3,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [7,1,4,5,3,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,7,1,5,6,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [7,6,4,1,5,3,2] => [[[[.,.],.],.],[[[.,.],.],.]] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [6,5,4,3,1,2,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [6,5,4,3,1,7,2] => [[[[[.,.],.],.],.],[[.,.],.]] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [5,7,4,3,1,6,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [5,7,4,6,1,3,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [7,6,1,4,5,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [6,2,1,3,4,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 6
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [7,6,2,1,3,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [7,5,2,1,3,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [5,2,1,3,6,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 6
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [5,2,1,3,6,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [7,5,2,1,3,6,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => 6
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [6,5,2,1,3,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [6,5,2,1,3,7,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => 6
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [7,2,5,1,3,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [7,6,5,2,1,3,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [7,4,2,1,3,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [6,4,2,1,3,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [6,4,2,1,3,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [7,6,4,2,1,3,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [4,2,1,5,3,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 6
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [7,4,2,1,5,3,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => 6
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [4,2,1,5,6,3,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [4,2,1,5,6,7,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [7,4,2,1,5,6,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [6,4,2,1,5,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [6,4,2,1,5,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [7,2,4,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [7,6,4,2,1,5,3] => [[[[[.,.],.],.],.],[[.,.],.]] => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [5,4,2,1,3,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [7,5,4,2,1,3,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [5,4,2,1,6,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [5,4,2,1,6,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [7,5,4,2,1,6,3] => [[[[[.,.],.],.],.],[[.,.],.]] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [6,2,4,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [6,2,4,1,5,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [7,2,1,4,5,6,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [7,6,2,4,1,5,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [6,5,4,2,1,3,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [6,5,4,2,1,7,3] => [[[[[.,.],.],.],.],[[.,.],.]] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [5,7,4,2,1,6,3] => [[[[.,[.,.]],.],.],[[.,.],.]] => 5
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [7,5,2,6,1,4,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [7,6,5,4,2,1,3] => [[[[[[.,.],.],.],.],.],[.,.]] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [7,2,3,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [6,2,3,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 6
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [6,2,3,1,4,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [7,6,2,3,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [5,2,3,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [7,5,2,3,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [5,2,3,1,6,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [5,2,3,1,6,7,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [7,5,2,3,1,6,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [6,5,2,3,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [6,5,2,3,1,7,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [7,2,5,3,1,6,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [7,6,5,2,3,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [6,2,3,4,1,7,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [7,6,2,3,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [2,7,3,4,5,6,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [7,5,2,3,4,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [7,5,2,3,4,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [2,6,3,4,5,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [2,6,3,4,5,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [2,3,7,4,5,6,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [7,2,6,3,4,5,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [6,5,2,3,4,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [5,7,2,3,4,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [7,2,5,3,6,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,6,5,2,3,4,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 6
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [7,4,2,3,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [6,4,2,3,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [6,4,2,3,1,7,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [7,6,4,2,3,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [7,4,2,3,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [7,4,2,3,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [6,4,2,3,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [4,7,2,3,5,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,6,4,2,3,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [2,5,3,4,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [7,2,5,3,4,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [2,5,3,4,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [2,5,3,4,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [7,2,5,3,4,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [2,3,6,4,5,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [2,3,6,4,5,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [2,3,4,7,5,6,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [7,2,3,6,4,5,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [6,2,5,3,4,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [6,2,5,3,4,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [2,7,5,3,4,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [7,2,3,5,6,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [7,6,2,5,3,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,4,2,3,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [7,5,4,2,3,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [5,4,2,3,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [5,4,2,3,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [7,5,4,2,3,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,6,2,3,5,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,6,2,3,5,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,2,7,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [7,4,6,2,3,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [6,2,4,5,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [6,2,4,5,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [2,7,4,5,3,6,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,2,7,5,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [7,6,2,4,5,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,5,4,2,3,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [6,5,4,2,3,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [5,7,4,2,3,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [5,7,4,2,6,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,6,5,4,2,3,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [7,3,2,1,4,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [6,3,2,1,4,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [6,3,2,1,4,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => 6
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [7,6,3,2,1,4,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [5,3,2,1,4,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [7,5,3,2,1,4,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [5,3,2,1,6,4,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 6
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [5,3,2,1,6,7,4] => [[[[.,.],.],.],[[.,[.,.]],.]] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [7,5,3,2,1,6,4] => [[[[[.,.],.],.],.],[[.,.],.]] => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [6,5,3,2,1,4,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [6,5,3,2,1,7,4] => [[[[[.,.],.],.],.],[[.,.],.]] => 6
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [7,3,5,2,1,6,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],.],.],.],[.,.]] => 7
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 6
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [6,3,2,4,1,7,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [7,6,3,2,4,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => 6
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [3,7,2,4,5,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,6,3,2,4,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [7,5,3,2,4,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [7,5,3,2,4,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 5
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [3,6,2,4,5,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [3,6,2,4,5,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [3,2,7,4,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [7,3,6,2,4,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,5,3,2,4,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 6
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [6,5,3,2,4,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [5,7,3,2,4,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [7,3,5,2,6,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [2,4,3,1,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [7,2,4,3,1,5,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [6,2,4,3,1,5,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [6,2,4,3,1,7,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [7,6,2,4,3,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [2,4,3,5,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [7,2,4,3,5,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [2,4,3,5,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [7,2,4,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [6,2,4,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [6,2,4,3,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [2,7,4,3,5,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [7,6,2,4,3,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [2,3,5,4,1,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [7,2,3,5,4,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [2,3,5,4,6,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [2,3,5,4,6,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [7,2,3,5,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [2,3,4,6,5,1,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,6,5,7,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [2,3,4,5,7,6,1] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [6,2,3,5,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [6,2,3,5,4,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [2,7,3,5,4,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [5,2,3,7,6,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [7,6,2,3,5,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [5,2,4,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [7,5,2,4,3,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => 5
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [5,2,4,3,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [5,2,4,3,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [7,5,2,4,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [2,6,4,3,5,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [2,6,4,3,5,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [2,4,7,3,5,6,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [7,2,6,4,3,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [4,2,6,5,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [4,2,6,5,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [4,2,5,7,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,2,5,7,6,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [7,4,2,6,5,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [6,5,2,4,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [6,5,2,4,3,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [5,7,2,4,3,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [7,2,5,4,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [7,2,4,6,5,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [7,6,5,2,4,3,1] => [[[[[.,.],.],.],[[.,.],.]],.] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [6,4,3,2,1,7,5] => [[[[[.,.],.],.],.],[[.,.],.]] => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],.],.],[.,.]] => 7
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [4,7,3,2,5,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [3,5,2,4,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [7,3,5,2,4,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,5,2,4,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [7,3,5,2,4,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [3,2,6,4,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,6,4,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [3,2,4,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [7,3,2,6,4,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [6,3,5,2,4,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [6,3,5,2,4,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [3,7,5,2,4,6,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [7,3,2,5,6,4,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [7,6,3,5,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [3,5,4,2,1,6,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 5
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [7,3,5,4,2,1,6] => [[[[.,.],[[.,.],.]],.],[.,.]] => 5
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [3,5,4,2,6,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [3,5,4,2,6,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [7,3,5,4,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [3,4,6,2,5,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [3,4,6,2,5,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [3,4,2,7,5,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [7,3,4,6,2,5,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [3,4,6,5,2,1,7] => [[[.,[.,[[.,.],.]]],.],[.,.]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [3,4,6,5,2,7,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [3,4,5,7,2,6,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [3,4,5,7,6,2,1] => [[[.,[.,[.,[[.,.],.]]]],.],.] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [7,3,4,6,5,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [6,3,5,4,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [6,3,5,4,2,7,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [3,7,5,4,2,6,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [3,7,5,4,6,2,1] => [[[.,[[[.,.],.],[.,.]]],.],.] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [3,7,4,6,5,2,1] => [[[.,[[.,.],[[.,.],.]]],.],.] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [7,6,3,5,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],.],[.,.]] => 7
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [4,6,3,2,5,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [4,6,3,2,5,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [4,3,7,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [7,4,6,3,2,5,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [4,6,3,5,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [4,6,3,5,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [4,3,7,5,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [4,3,7,5,6,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [7,4,6,3,5,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [3,6,5,4,2,1,7] => [[[.,[[[.,.],.],.]],.],[.,.]] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,6,5,4,2,7,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [3,5,7,4,2,6,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,5,7,4,6,2,1] => [[[.,[[.,[.,.]],[.,.]]],.],.] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [3,4,7,6,5,2,1] => [[[.,[.,[[[.,.],.],.]]],.],.] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [7,3,6,5,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [5,7,4,3,2,6,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [5,7,4,3,6,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [4,7,6,3,5,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [4,7,6,5,3,2,1] => [[[[.,[[[.,.],.],.]],.],.],.] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [7,1,2,3,4,5,8,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [6,1,2,3,4,7,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [6,1,2,3,4,7,8,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [5,1,2,3,6,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [5,1,2,3,6,7,8,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 8
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,7,5,6,3,8] => [7,1,4,2,5,6,3,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 5
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [8,7,6,1,4,2,5,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => [8,5,7,4,1,2,6,3] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [6,8,5,4,1,2,7,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 8
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [8,7,3,5,1,2,6,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [6,8,5,3,1,2,7,4] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [8,6,3,1,4,2,7,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [7,6,3,1,4,2,8,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [6,5,3,1,4,7,2,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [6,8,5,3,1,7,4,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => 5
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [8,7,6,5,3,1,4,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [6,4,3,1,5,7,2,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [8,4,6,3,1,7,5,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => 5
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [8,7,6,4,3,1,5,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [8,7,5,1,3,4,2,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,3,4,6,2,7,8] => [5,1,3,4,6,2,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => [7,6,5,1,3,4,2,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [5,4,3,1,6,7,2,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [8,7,5,4,3,1,6,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,7,4,5,6,3,2,8] => [4,7,1,5,6,3,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [8,6,5,4,3,1,7,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7,5,4,6,3,8,2] => [5,7,4,6,1,3,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => 4
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [8,5,7,4,6,1,3,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [7,6,5,4,3,1,8,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [6,8,5,4,7,1,3,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 5
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [8,7,5,1,6,4,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 5
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [8,7,6,5,4,3,1,2] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 8
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [8,7,2,5,1,3,6,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 6
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [8,6,2,7,1,3,5,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [8,4,6,2,1,3,7,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => 6
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [8,4,2,1,5,6,3,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,6,3,8] => [7,4,2,1,5,6,3,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [8,7,6,4,2,1,5,3] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [5,4,2,1,6,7,3,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,4,5,3,7,8] => [6,2,4,1,5,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [8,6,2,4,1,5,3,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [8,6,5,4,2,1,7,3] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [5,8,2,4,1,6,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [8,2,5,6,1,4,7,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [7,6,5,4,2,1,8,3] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [6,8,5,7,2,1,4,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => 5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [8,7,2,5,6,1,4,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [8,7,6,5,4,2,1,3] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,4,7,8,6] => [7,5,2,3,1,4,8,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 6
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,6,4,8,7] => [8,5,2,3,1,6,4,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 6
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [8,2,3,5,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,8,6,5,7,4] => [6,8,5,2,3,1,7,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 5
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [8,6,2,7,3,1,5,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => 5
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [8,7,6,5,2,3,1,4] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [7,2,3,4,1,5,8,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [8,7,2,3,4,1,5,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [8,6,2,3,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [6,2,3,4,1,7,8,5] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [8,6,2,3,4,1,7,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [7,6,2,3,4,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [7,6,2,3,4,1,8,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [8,5,2,3,4,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [7,5,2,3,4,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [2,3,4,8,5,6,7,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [6,5,2,3,4,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [8,4,6,2,3,1,7,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => 5
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [8,7,6,4,2,3,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [8,4,2,3,5,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [7,4,2,3,5,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,3,8,6,7,5,1] => [8,4,6,2,3,7,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,7,3,4,5,6,8,1] => [2,3,4,7,5,6,8,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [2,3,4,5,8,6,7,1] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => [7,6,2,5,3,4,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [8,4,6,2,3,5,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,7,4,3,6,5,1,8] => [7,4,6,2,3,5,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 5
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [8,4,2,6,3,7,5,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,4,5,3,1,8,7] => [8,6,2,4,5,3,1,7] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => 5
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,6,4,5,3,8,7,1] => [8,6,2,4,5,3,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => [7,6,2,4,5,3,1,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [7,6,2,4,5,3,8,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [8,6,5,4,2,3,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,5,4,6,3,7,1] => [5,4,8,2,6,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [7,6,5,4,2,3,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [8,3,6,2,1,4,7,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => 6
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [8,7,5,3,2,1,6,4] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [8,6,5,3,2,1,7,4] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => [7,3,5,2,1,6,4,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [7,6,5,3,2,1,8,4] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 8
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [8,3,6,2,4,1,7,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => 5
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [8,7,6,3,2,4,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [3,2,4,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,2,4,5,1,7,8,6] => [7,3,2,4,5,1,8,6] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 5
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [8,7,5,3,2,4,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [8,3,6,2,4,5,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [8,6,5,3,2,4,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [7,3,5,2,6,4,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [7,3,5,2,6,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,6,5,3,2,4,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [8,3,7,5,2,6,4,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => 4
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [8,6,2,4,3,1,7,5] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => 5
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [7,6,2,4,3,1,8,5] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [8,7,2,4,3,5,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 5
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,2,3,6,5,1,8,7] => [8,6,2,4,3,5,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [4,2,3,7,6,5,1,8] => [7,6,2,4,3,5,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [2,3,4,6,5,7,8,1] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,3,4,5,7,6,8,1] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,8,7,1] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [8,5,2,4,3,6,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 5
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2,4,5,3,1,8,7] => [8,4,2,6,5,3,1,7] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => 5
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [8,4,2,5,7,3,6,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [6,5,2,4,3,7,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 5
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [8,5,7,2,4,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [8,7,6,5,2,4,3,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => 6
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [8,6,4,3,2,1,7,5] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [7,6,4,3,2,1,8,5] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 8
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [8,7,4,3,2,5,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [4,3,2,5,6,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [8,3,5,2,4,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [7,3,5,2,4,1,6,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,3,2,4,1,7,8,6] => [7,3,5,2,4,1,8,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [7,3,5,2,4,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,3,2,4,5,1,8,7] => [8,3,2,6,4,5,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 5
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [7,3,2,5,6,4,8,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [8,7,6,3,5,2,4,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [7,3,5,4,2,1,8,6] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => 5
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [7,3,5,4,2,6,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 5
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [8,3,4,2,5,7,6,1] => [8,3,4,2,7,5,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [6,3,5,4,2,7,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [8,7,6,3,5,4,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [7,5,4,3,2,1,8,6] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [8,7,5,4,3,2,1,6] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 8
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [8,5,4,3,2,6,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [4,6,3,2,5,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1,8] => [4,3,7,2,5,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 5
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [8,7,4,6,3,2,5,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,4,3,5,2,7,1,8] => [4,6,3,5,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [4,3,7,5,2,6,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [8,7,4,6,3,5,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => 6
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [3,5,7,4,2,6,1,8] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [8,5,7,4,3,2,6,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [4,7,6,5,3,2,1,8] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,1,2] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 10
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 11
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [11,10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 11
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [9,7,6,5,4,3,2,1,8] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 9
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [9,8,7,6,5,4,2,1,3] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [10,8,7,6,5,4,3,2,1,9] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 10
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,4,2,1,3] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,9,3,4,5,6,7,8,1] => [2,3,4,5,6,9,7,8,1] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [2,3,4,5,6,8,7,9,1] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,9,8,1] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [8,1,2,3,4,5,6,9,7] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [7,1,2,3,4,5,8,9,6] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [9,1,2,3,4,5,6,7,10,8] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [7,1,2,3,4,5,6,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 9
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 9
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 9
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [9,8,7,6,5,3,2,1,4] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 9
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [9,8,7,6,4,3,2,1,5] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 9
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [9,8,7,5,4,3,2,1,6] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [9,8,6,5,4,3,2,1,7] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 10
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 10
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 10
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [10,9,8,7,6,5,3,2,1,4] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 10
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [10,9,8,7,6,4,3,2,1,5] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 10
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [10,9,8,7,5,4,3,2,1,6] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 10
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [10,9,8,6,5,4,3,2,1,7] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [10,9,7,6,5,4,3,2,1,8] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,10,9,1] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [11,9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 11
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [7,1,2,3,4,5,8,6,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 11
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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:
1,4 2,4,8 4,10,12,16 8,26,34,32,32 17,71,98,99,80,64
$F_{1} = q$
$F_{2} = 2\ q^{2}$
$F_{3} = q^{2} + 4\ q^{3}$
$F_{4} = 2\ q^{2} + 4\ q^{3} + 8\ q^{4}$
$F_{5} = 4\ q^{2} + 10\ q^{3} + 12\ q^{4} + 16\ q^{5}$
$F_{6} = 8\ q^{2} + 26\ q^{3} + 34\ q^{4} + 32\ q^{5} + 32\ q^{6}$
$F_{7} = 17\ q^{2} + 71\ q^{3} + 98\ q^{4} + 99\ q^{5} + 80\ q^{6} + 64\ q^{7}$
Description
The number of external nodes of a binary tree.
That is, the number of nodes that can be reached from the root by only left steps or only right steps, plus $1$ for the root node itself. A counting formula for the number of external node in all binary trees of size $n$ can be found in [1].
That is, the number of nodes that can be reached from the root by only left steps or only right steps, plus $1$ for the root node itself. A counting formula for the number of external node in all binary trees of size $n$ can be found in [1].
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
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