Identifier
-
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
St000201: Binary trees ⟶ ℤ (values match St000196The number of occurrences of the contiguous pattern [[.,.],[.,.)
Values
[1,0] => [1] => [.,.] => [.,.] => 1
[1,0,1,0] => [2,1] => [[.,.],.] => [[.,.],.] => 1
[1,1,0,0] => [1,2] => [.,[.,.]] => [.,[.,.]] => 1
[1,0,1,0,1,0] => [2,3,1] => [[.,[.,.]],.] => [[.,.],[.,.]] => 2
[1,0,1,1,0,0] => [2,1,3] => [[.,.],[.,.]] => [[.,[.,.]],.] => 1
[1,1,0,0,1,0] => [1,3,2] => [.,[[.,.],.]] => [.,[[.,.],.]] => 1
[1,1,0,1,0,0] => [3,1,2] => [[.,.],[.,.]] => [[.,[.,.]],.] => 1
[1,1,1,0,0,0] => [1,2,3] => [.,[.,[.,.]]] => [.,[.,[.,.]]] => 1
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [[.,[.,[.,.]]],.] => [[.,.],[.,[.,.]]] => 2
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [[.,[.,.]],[.,.]] => [[.,[.,.]],[.,.]] => 2
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [[.,.],[[.,.],.]] => [[.,[[.,.],.]],.] => 1
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [[.,[.,.]],[.,.]] => [[.,[.,.]],[.,.]] => 2
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.] => 1
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [.,[[.,[.,.]],.]] => [.,[[.,.],[.,.]]] => 2
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [.,[[.,[.,.]],.]] => 1
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [[.,.],[[.,.],.]] => [[.,[[.,.],.]],.] => 1
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [[.,[.,.]],[.,.]] => 2
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.] => 1
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [.,[.,[[.,.],.]]] => 1
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [.,[[.,.],[.,.]]] => [.,[[.,[.,.]],.]] => 1
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [.,[.,[.,[.,.]]]] => 1
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => [[.,.],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => 2
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => [[.,[[.,.],.]],[.,.]] => 2
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => 2
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [[.,.],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],.] => 2
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [[.,[.,.]],[[.,.],.]] => [[.,[[.,.],.]],[.,.]] => 2
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => 2
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.] => 1
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [.,[[.,[[.,.],.]],.]] => 1
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]] => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [[.,.],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [[.,[.,.]],[[.,.],.]] => [[.,[[.,.],.]],[.,.]] => 2
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.] => 1
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => 1
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [.,[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [.,[.,[[.,[.,.]],.]]] => 1
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => [.,[[.,[[.,.],.]],.]] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => 1
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [.,[.,[.,[[.,.],.]]]] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [.,[.,[[.,[.,.]],.]]] => 1
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]] => 1
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [[.,.],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
>>> Load all 834 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,.]]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],.]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [.,[[.,[.,.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,.]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],.]]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],.]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,.]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [[.,.],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],.]]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,8,1,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,6,7,5,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,7,3,8,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,1,5,3,6,7,4,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,1,5,3,6,8,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,5,3,7,8,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,1,6,3,7,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,6,3,7,8,4,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,6,1,7,3,8,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,4,2,6,7,5,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,4,2,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,2,8,6,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,6,2,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,5,2,6,8,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,7,8,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,2,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [4,5,1,7,2,8,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [4,6,1,7,2,8,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [6,1,2,3,7,4,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,8,5,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,8,4,5,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,9,7,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,8,6,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,8,9,6] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,9,7,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,9,6,8] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,9,6,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,9,6,10,8] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,8,6,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => 1
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,10,7,9] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,10,7,9] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,10,7,9] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,5,8,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,7,2,8,3,9,4,10,5,6] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,8,2,9,3,10,4,11,5,12,6,7] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,10,7,12,9,11] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,7,3,8,4,9,5,10,6] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,8,3,9,4,10,5,11,6,12,7] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [3,1,4,2,9,5,10,6,11,7,12,8] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,8,3,9,5,10,7] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,7,2,8,3,9,4,10,6] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 9,5 21,21 51,78,3 127,274,28
F1=q
F2=2 q
F3=4 q+q2
F4=9 q+5 q2
F5=21 q+21 q2
F6=51 q+78 q2+3 q3
F7=127 q+274 q2+28 q3
Description
The number of leaf nodes in a binary tree.
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size n, at least 1, with exactly one leaf node for is 2n−1, see [2].
The number of binary tree of size n, at least 3, with exactly two leaf nodes is n(n+1)2n−2, see [3].
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size n, at least 1, with exactly one leaf node for is 2n−1, see [2].
The number of binary tree of size n, at least 3, with exactly two leaf nodes is n(n+1)2n−2, see [3].
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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 σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−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 σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−1(1) to the trees L and R, respectively.
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees T1,T2,T3 on its left border, it becomes T3,T2,T1 where same symmetry has been applied to T1,T2,T3.
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