Identifier
-
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ 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] => [1,2] => [.,[.,.]] => [.,[.,.]] => 1
[1,1,0,0] => [2,1] => [[.,.],.] => [[.,.],.] => 1
[1,0,1,0,1,0] => [1,2,3] => [.,[.,[.,.]]] => [.,[.,[.,.]]] => 1
[1,0,1,1,0,0] => [1,3,2] => [.,[[.,.],.]] => [.,[[.,.],.]] => 1
[1,1,0,0,1,0] => [2,1,3] => [[.,.],[.,.]] => [[.,[.,.]],.] => 1
[1,1,0,1,0,0] => [2,3,1] => [[.,.],[.,.]] => [[.,[.,.]],.] => 1
[1,1,1,0,0,0] => [3,1,2] => [[.,[.,.]],.] => [[.,.],[.,.]] => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [.,[.,[.,[.,.]]]] => 1
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [.,[.,[[.,.],.]]] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [.,[[.,[.,.]],.]] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [.,[[.,.],[.,.]]] => [.,[[.,[.,.]],.]] => 1
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [.,[[.,[.,.]],.]] => [.,[[.,.],[.,.]]] => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[.,.],[[.,.],.]] => [[.,[[.,.],.]],.] => 1
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.] => 1
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [[.,.],[[.,.],.]] => [[.,[[.,.],.]],.] => 1
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [[.,[.,.]],[.,.]] => [[.,[.,.]],[.,.]] => 2
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [[.,[.,.]],[.,.]] => [[.,[.,.]],[.,.]] => 2
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [[.,[.,.]],[.,.]] => 2
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [[.,[.,[.,.]]],.] => [[.,.],[.,[.,.]]] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [.,[.,[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [.,[.,[.,[[.,.],.]]]] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [.,[.,[[.,[.,.]],.]]] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => [.,[.,[[.,[.,.]],.]]] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => [.,[.,[[.,.],[.,.]]]] => 2
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [.,[[.,[[.,.],.]],.]] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => [.,[[.,[[.,.],.]],.]] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => [.,[[.,.],[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [[.,[.,.]],[[.,.],.]] => [[.,[[.,.],.]],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [[.,[.,.]],[[.,.],.]] => [[.,[[.,.],.]],[.,.]] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [[.,[.,.]],[[.,.],.]] => [[.,[[.,.],.]],[.,.]] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => [[.,.],[.,[.,[.,.]]]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],.]]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],.]]] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],.]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],.]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,.]]] => 2
>>> Load all 827 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,1,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1,7,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,4,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,2,7,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,2,8,4,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,2,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,2,4,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,2,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,2,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,2,4,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,3,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,1,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,1,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,1,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,1,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,1,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,1,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,1,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,1,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,1,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,1,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,1,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,1,6,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,1,7,3,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,1,7,8,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,1,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,1,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,4,7,1,8,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,1,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,2,5,7,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,2,7,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,5,7,2,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,1,5,7,2,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,1,5,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,1,5,7,8,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,1,2,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,1,2,4,7,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,1,2,7,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,1,2,7,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,1,2,7,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,1,7,2,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,1,7,8,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,1,2,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,1,2,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,1,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,2,3,6,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,2,3,6,7,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,2,6,3,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,2,6,3,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,2,6,7,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,2,6,7,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,6,2,3,7,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,6,2,3,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,7,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,6,7,2,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,6,7,2,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,6,7,8,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,6,1,2,3,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,1,2,7,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,1,2,7,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,1,7,2,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,6,1,7,2,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,1,7,8,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,1,2,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,1,2,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,1,2,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,1,8,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,1,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,1,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,1,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,1,7,8] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,7,8] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,8,9] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,1,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,7,8] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,9,6,8,10] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,5,7,9,10,1,2,4,6,8] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,3,6,8,5,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,3,8,5,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,4,6,9,10,1,3,5,7,8] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,4,6,8,10,12,1,3,5,7,9,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => 1
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Generating function
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Search the OEIS for these generating functions
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
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q + q^{2}$
$F_{4} = 9\ q + 5\ q^{2}$
$F_{5} = 21\ q + 21\ q^{2}$
$F_{6} = 51\ q + 78\ q^{2} + 3\ q^{3}$
$F_{7} = 127\ q + 274\ q^{2} + 28\ q^{3}$
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 $2^{n-1}$, see [2].
The number of binary tree of size $n$, at least $3$, with exactly two leaf nodes is $n(n+1)2^{n-2}$, 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 $2^{n-1}$, see [2].
The number of binary tree of size $n$, at least $3$, with exactly two leaf nodes is $n(n+1)2^{n-2}$, see [3].
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 $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
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