- FindStat

Identifier

Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
St000204: Binary trees ⟶ ℤ

Values

[1,0] => [1] => [1] => [.,.] => 0

[1,0,1,0] => [1,2] => [1,2] => [.,[.,.]] => 0

[1,1,0,0] => [2,1] => [2,1] => [[.,.],.] => 0

[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]] => 0

[1,0,1,1,0,0] => [1,3,2] => [3,1,2] => [[.,.],[.,.]] => 0

[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [[.,.],[.,.]] => 0

[1,1,0,1,0,0] => [2,3,1] => [2,3,1] => [[.,[.,.]],.] => 1

[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => [[[.,.],.],.] => 0

[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0

[1,0,1,0,1,1,0,0] => [1,2,4,3] => [4,1,2,3] => [[.,.],[.,[.,.]]] => 0

[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1,2,4] => [[.,.],[.,[.,.]]] => 0

[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1,4,2] => [[.,.],[[.,.],.]] => 1

[1,0,1,1,1,0,0,0] => [1,4,3,2] => [4,3,1,2] => [[[.,.],.],[.,.]] => 0

[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]] => 0

[1,1,0,0,1,1,0,0] => [2,1,4,3] => [4,2,1,3] => [[[.,.],.],[.,.]] => 0

[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,3,1,4] => [[.,[.,.]],[.,.]] => 1

[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,3,4,1] => [[.,[.,[.,.]]],.] => 2

[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,2,3,1] => [[[.,.],[.,.]],.] => 1

[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]] => 0

[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => [[[.,.],[.,.]],.] => 1

[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,4,3,1] => [[.,[[.,.],.]],.] => 2

[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [[[[.,.],.],.],.] => 0

[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0

[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]] => 0

[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]] => 0

[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [4,1,2,5,3] => [[.,.],[.,[[.,.],.]]] => 1

[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [5,4,1,2,3] => [[[.,.],.],[.,[.,.]]] => 0

[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]] => 0

[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [5,3,1,2,4] => [[[.,.],.],[.,[.,.]]] => 0

[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,1,4,2,5] => [[.,.],[[.,.],[.,.]]] => 1

[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [3,1,4,5,2] => [[.,.],[[.,[.,.]],.]] => 2

[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [5,3,1,4,2] => [[[.,.],.],[[.,.],.]] => 1

[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [4,3,1,2,5] => [[[.,.],.],[.,[.,.]]] => 0

[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [4,3,1,5,2] => [[[.,.],.],[[.,.],.]] => 1

[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [5,1,3,4,2] => [[.,.],[[.,[.,.]],.]] => 2

[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [5,4,3,1,2] => [[[[.,.],.],.],[.,.]] => 0

[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => 0

[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [5,2,1,3,4] => [[[.,.],.],[.,[.,.]]] => 0

[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]] => 0

[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [4,2,1,5,3] => [[[.,.],.],[[.,.],.]] => 1

[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [5,4,2,1,3] => [[[[.,.],.],.],[.,.]] => 0

[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => 1

[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [5,2,3,1,4] => [[[.,.],[.,.]],[.,.]] => 1

[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => 2

[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 3

[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => 2

[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => 1

[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.] => 2

[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => 3

[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,4,2,3,1] => [[[[.,.],.],[.,.]],.] => 1

[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => 0

[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [5,3,2,1,4] => [[[[.,.],.],.],[.,.]] => 0

[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]] => 1

[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.] => 2

[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => 1

[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => 2

[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => 3

[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => 3

[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => 2

[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => 0

[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => [[[[.,.],.],[.,.]],.] => 1

[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [3,5,2,4,1] => [[[.,[.,.]],[.,.]],.] => 2

[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [3,5,4,2,1] => [[[.,[[.,.],.]],.],.] => 2

[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => 0

[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0

[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [5,1,2,3,6,4] => [[.,.],[.,[.,[[.,.],.]]]] => 1

[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => [[[.,.],.],[.,[.,[.,.]]]] => 0

[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [6,4,1,2,3,5] => [[[.,.],.],[.,[.,[.,.]]]] => 0

[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [4,1,2,5,3,6] => [[.,.],[.,[[.,.],[.,.]]]] => 1

[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,1,2,5,6,3] => [[.,.],[.,[[.,[.,.]],.]]] => 2

[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [6,4,1,2,5,3] => [[[.,.],.],[.,[[.,.],.]]] => 1

[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0

[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [5,4,1,2,6,3] => [[[.,.],.],[.,[[.,.],.]]] => 1

[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [6,1,4,2,5,3] => [[.,.],[[.,.],[[.,.],.]]] => 2

[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => [[[[.,.],.],.],[.,[.,.]]] => 0

[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [6,3,1,2,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => 0

[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [5,3,1,2,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0

[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [5,3,1,2,6,4] => [[[.,.],.],[.,[[.,.],.]]] => 1

[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [6,5,3,1,2,4] => [[[[.,.],.],.],[.,[.,.]]] => 0

[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1

[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [6,3,1,4,2,5] => [[[.,.],.],[[.,.],[.,.]]] => 1

[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => 2

[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => 3

[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [6,3,1,4,5,2] => [[[.,.],.],[[.,[.,.]],.]] => 2

[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [5,3,1,4,2,6] => [[[.,.],.],[[.,.],[.,.]]] => 1

[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [5,3,1,4,6,2] => [[[.,.],.],[[.,[.,.]],.]] => 2

[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [6,1,3,4,5,2] => [[.,.],[[.,[.,[.,.]]],.]] => 3

[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [6,5,3,1,4,2] => [[[[.,.],.],.],[[.,.],.]] => 1

[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0

[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [6,4,3,1,2,5] => [[[[.,.],.],.],[.,[.,.]]] => 0

[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [4,3,1,5,2,6] => [[[.,.],.],[[.,.],[.,.]]] => 1

[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,3,1,5,6,2] => [[[.,.],.],[[.,[.,.]],.]] => 2

[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [6,4,3,1,5,2] => [[[[.,.],.],.],[[.,.],.]] => 1

[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [5,1,3,4,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => 2

[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [5,1,3,4,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => 3

[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [3,1,6,4,5,2] => [[.,.],[[[.,.],[.,.]],.]] => 3

[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [6,5,1,3,4,2] => [[[.,.],.],[[.,[.,.]],.]] => 2

>>> Load all 625 entries. <<<

[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => [[[[.,.],.],.],[.,[.,.]]] => 0

[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [5,4,3,1,6,2] => [[[[.,.],.],.],[[.,.],.]] => 1

[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]] => 2

[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [6,4,1,5,3,2] => [[[.,.],.],[[[.,.],.],.]] => 2

[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]] => 0

[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0

[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => 0

[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0

[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [5,2,1,3,6,4] => [[[.,.],.],[.,[[.,.],.]]] => 1

[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [6,5,2,1,3,4] => [[[[.,.],.],.],[.,[.,.]]] => 0

[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0

[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [6,4,2,1,3,5] => [[[[.,.],.],.],[.,[.,.]]] => 0

[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [4,2,1,5,3,6] => [[[.,.],.],[[.,.],[.,.]]] => 1

[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [4,2,1,5,6,3] => [[[.,.],.],[[.,[.,.]],.]] => 2

[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [6,4,2,1,5,3] => [[[[.,.],.],.],[[.,.],.]] => 1

[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [5,4,2,1,3,6] => [[[[.,.],.],.],[.,[.,.]]] => 0

[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [5,4,2,1,6,3] => [[[[.,.],.],.],[[.,.],.]] => 1

[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [6,2,4,1,5,3] => [[[.,.],[.,.]],[[.,.],.]] => 2

[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [6,5,4,2,1,3] => [[[[[.,.],.],.],.],[.,.]] => 0

[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [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] => [6,2,3,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]] => 1

[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]] => 1

[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [5,2,3,1,6,4] => [[[.,.],[.,.]],[[.,.],.]] => 2

[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [6,5,2,3,1,4] => [[[[.,.],.],[.,.]],[.,.]] => 1

[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 2

[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [6,2,3,4,1,5] => [[[.,.],[.,[.,.]]],[.,.]] => 2

[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 3

[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 4

[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => 3

[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => 2

[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => 3

[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.] => 4

[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.] => 2

[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => 1

[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [6,4,2,3,1,5] => [[[[.,.],.],[.,.]],[.,.]] => 1

[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => 2

[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => 3

[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.] => 2

[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 3

[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 4

[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => 4

[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [6,2,5,3,4,1] => [[[.,.],[[.,.],[.,.]]],.] => 3

[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]] => 1

[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => [[[[.,.],.],[.,[.,.]]],.] => 2

[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [4,6,2,3,5,1] => [[[.,[.,.]],[.,[.,.]]],.] => 3

[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [6,2,4,5,3,1] => [[[.,.],[[.,[.,.]],.]],.] => 3

[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [[[[[.,.],.],.],[.,.]],.] => 1

[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0

[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]] => 0

[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]] => 0

[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [5,3,2,1,6,4] => [[[[.,.],.],.],[[.,.],.]] => 1

[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [6,5,3,2,1,4] => [[[[[.,.],.],.],.],[.,.]] => 0

[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => 1

[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [6,3,2,4,1,5] => [[[[.,.],.],[.,.]],[.,.]] => 1

[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => 2

[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => 3

[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => 2

[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => 1

[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [5,3,2,4,6,1] => [[[[.,.],.],[.,[.,.]]],.] => 2

[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,6,2,4,5,1] => [[[.,[.,.]],[.,[.,.]]],.] => 3

[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,5,3,2,4,1] => [[[[[.,.],.],.],[.,.]],.] => 1

[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => 2

[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [6,2,4,3,1,5] => [[[.,.],[[.,.],.]],[.,.]] => 2

[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 3

[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 4

[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.] => 3

[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => 3

[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 4

[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 4

[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.] => 3

[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [5,2,4,3,1,6] => [[[.,.],[[.,.],.]],[.,.]] => 2

[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [5,2,4,3,6,1] => [[[.,.],[[.,.],[.,.]]],.] => 3

[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.] => 4

[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [4,2,6,5,3,1] => [[[.,.],[[[.,.],.],.]],.] => 3

[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [6,5,2,4,3,1] => [[[[.,.],.],[[.,.],.]],.] => 2

[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => 0

[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [6,4,3,2,1,5] => [[[[[.,.],.],.],.],[.,.]] => 0

[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]] => 1

[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [[[[.,.],.],[.,[.,.]]],.] => 2

[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => 1

[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,5,2,4,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => 2

[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,5,2,4,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => 3

[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,2,6,4,5,1] => [[[.,.],[[.,.],[.,.]]],.] => 3

[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [6,3,5,2,4,1] => [[[[.,.],[.,.]],[.,.]],.] => 2

[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => [[[.,[[.,.],.]],.],[.,.]] => 2

[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => [[[.,[[.,.],.]],[.,.]],.] => 3

[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [3,4,6,2,5,1] => [[[.,[.,[.,.]]],[.,.]],.] => 3

[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => [[[.,[.,[[.,.],.]]],.],.] => 3

[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [6,3,5,4,2,1] => [[[[.,.],[[.,.],.]],.],.] => 2

[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => 0

[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [[[[[.,.],.],.],[.,.]],.] => 1

[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [4,6,3,2,5,1] => [[[[.,[.,.]],.],[.,.]],.] => 2

[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [4,6,3,5,2,1] => [[[[.,[.,.]],[.,.]],.],.] => 2

[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => [[[.,[[[.,.],.],.]],.],.] => 3

[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => 0

[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0

[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0

[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0

[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [6,1,2,3,4,7,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 1

[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0

[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [7,5,1,2,3,4,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [5,1,2,3,6,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1

[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [5,1,2,3,6,7,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2

[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [7,5,1,2,3,6,4] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 1

[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [6,5,1,2,3,7,4] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 1

[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [7,1,5,2,3,6,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2

[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0

[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [7,4,1,2,3,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [6,4,1,2,3,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [6,4,1,2,3,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 1

[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [7,6,4,1,2,3,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [4,1,2,5,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1

[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [7,4,1,2,5,3,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 1

[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2

[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [4,1,2,5,6,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 3

[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [7,4,1,2,5,6,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 2

[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [6,4,1,2,5,3,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 1

[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [6,4,1,2,5,7,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 2

[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [7,1,4,2,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3

[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [7,6,4,1,2,5,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [7,5,4,1,2,3,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [5,4,1,2,6,3,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 1

[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [5,4,1,2,6,7,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 2

[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [7,5,4,1,2,6,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [6,1,4,2,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2

[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [6,1,4,2,5,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3

[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [7,1,2,4,5,6,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 3

[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [7,6,1,4,2,5,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => 2

[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [6,5,4,1,2,7,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [5,7,4,1,2,6,3] => [[[.,[.,.]],.],[.,[[.,.],.]]] => 2

[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [7,5,1,6,2,4,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => 2

[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0

[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [7,3,1,2,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [6,3,1,2,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [6,3,1,2,4,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 1

[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [7,6,3,1,2,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [5,3,1,2,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [7,5,3,1,2,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [5,3,1,2,6,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 1

[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [5,3,1,2,6,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 2

[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [7,5,3,1,2,6,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [6,5,3,1,2,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [6,5,3,1,2,7,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [7,3,5,1,2,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 2

[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [7,6,5,3,1,2,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,1,4,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1

[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [7,3,1,4,2,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 1

[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [6,3,1,4,2,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 1

[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [6,3,1,4,2,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => 2

[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [7,6,3,1,4,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [3,1,4,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2

[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [7,3,1,4,5,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [3,1,4,5,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [3,1,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 4

[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [7,3,1,4,5,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [6,3,1,4,5,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [6,3,1,4,5,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [7,1,3,4,5,6,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 4

[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [7,6,3,1,4,5,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [5,3,1,4,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 1

[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [7,5,3,1,4,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [5,3,1,4,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,3,1,4,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [7,5,3,1,4,6,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [6,1,3,4,5,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3

[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [6,1,3,4,5,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 4

[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [3,1,7,4,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 4

[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [7,6,1,3,4,5,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [6,5,3,1,4,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [6,5,3,1,4,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [5,7,3,1,4,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 3

[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [7,5,1,3,6,4,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => 3

[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [7,6,5,3,1,4,2] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [4,3,1,2,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [7,4,3,1,2,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [6,4,3,1,2,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [6,4,3,1,2,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [7,6,4,3,1,2,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [4,3,1,5,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 1

[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [7,4,3,1,5,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [4,3,1,5,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [4,3,1,5,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [7,4,3,1,5,6,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [6,4,3,1,5,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [6,4,3,1,5,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [4,7,3,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 3

[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [7,6,4,3,1,5,2] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [5,1,3,4,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2

[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [7,5,1,3,4,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [5,1,3,4,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3

[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [5,1,3,4,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 4

[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [7,5,1,3,4,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [3,1,6,4,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 3

[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [3,1,6,4,5,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 4

[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [3,1,4,7,5,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => 4

[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [7,3,1,6,4,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => 3

[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [6,5,1,3,4,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [6,5,1,3,4,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [7,1,5,3,4,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 4

[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [7,3,1,5,6,4,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => 3

[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [7,6,5,1,3,4,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [5,4,3,1,2,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [7,5,4,3,1,2,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [5,4,3,1,6,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [5,4,3,1,6,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [7,5,4,3,1,6,2] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [4,6,3,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => 2

[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [4,6,3,1,5,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 3

[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [4,7,1,3,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 4

[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [7,4,6,3,1,5,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => 2

[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [6,4,1,5,3,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => 2

[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [6,4,1,5,3,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => 3

[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [7,1,4,5,3,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => 4

[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,7,1,5,6,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => 4

[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [7,6,4,1,5,3,2] => [[[[.,.],.],.],[[[.,.],.],.]] => 2

[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [6,5,4,3,1,2,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [6,5,4,3,1,7,2] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [5,7,4,3,1,6,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => 2

[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [5,7,4,6,1,3,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => 3

[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [7,6,1,4,5,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => 3

[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]] => 0

[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0

[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [6,2,1,3,4,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 1

[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [7,6,2,1,3,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [7,5,2,1,3,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [5,2,1,3,6,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 1

[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [5,2,1,3,6,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 2

[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [7,5,2,1,3,6,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [6,5,2,1,3,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [6,5,2,1,3,7,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [7,2,5,1,3,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 2

[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [7,6,5,2,1,3,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [7,4,2,1,3,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [6,4,2,1,3,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [6,4,2,1,3,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [7,6,4,2,1,3,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [4,2,1,5,3,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 1

[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [7,4,2,1,5,3,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [4,2,1,5,6,3,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [4,2,1,5,6,7,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [7,4,2,1,5,6,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [6,4,2,1,5,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [6,4,2,1,5,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [7,2,4,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 3

[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [7,6,4,2,1,5,3] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [5,4,2,1,3,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [7,5,4,2,1,3,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [5,4,2,1,6,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [5,4,2,1,6,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [7,5,4,2,1,6,3] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [6,2,4,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 2

[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [6,2,4,1,5,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 3

[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [7,2,1,4,5,6,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [7,6,2,4,1,5,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => 2

[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [6,5,4,2,1,3,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [6,5,4,2,1,7,3] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [5,7,4,2,1,6,3] => [[[[.,[.,.]],.],.],[[.,.],.]] => 2

[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [7,5,2,6,1,4,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => 2

[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [7,6,5,4,2,1,3] => [[[[[[.,.],.],.],.],.],[.,.]] => 0

[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1

[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [7,2,3,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1

[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [6,2,3,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1

[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [6,2,3,1,4,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 2

[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [7,6,2,3,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [5,2,3,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1

[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [7,5,2,3,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [5,2,3,1,6,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 2

[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [5,2,3,1,6,7,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 3

[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [7,5,2,3,1,6,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => 2

[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [6,5,2,3,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [6,5,2,3,1,7,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => 2

[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [7,2,5,3,1,6,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => 3

[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [7,6,5,2,3,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1

[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2

[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2

[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2

[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [6,2,3,4,1,7,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 3

[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [7,6,2,3,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2

[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3

[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3

[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 4

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 5

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 4

[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 4

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [2,7,3,4,5,6,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 5

[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3

[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2

[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [7,5,2,3,4,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2

[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 4

[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [7,5,2,3,4,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3

[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [2,6,3,4,5,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 4

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [2,6,3,4,5,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 5

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [2,3,7,4,5,6,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 5

[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [7,2,6,3,4,5,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 4

[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [6,5,2,3,4,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [5,7,2,3,4,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 4

[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [7,2,5,3,6,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => 4

[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,6,5,2,3,4,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2

[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1

[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [7,4,2,3,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [6,4,2,3,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [6,4,2,3,1,7,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => 2

[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [7,6,4,2,3,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1

[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2

[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [7,4,2,3,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2

[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 4

[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [7,4,2,3,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3

[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2

[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [6,4,2,3,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [4,7,2,3,5,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 4

[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,6,4,2,3,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2

[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [2,5,3,4,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3

[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [7,2,5,3,4,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 3

[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [2,5,3,4,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 4

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [2,5,3,4,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 5

[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [7,2,5,3,4,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 4

[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [2,3,6,4,5,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 4

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [2,3,6,4,5,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 5

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [2,3,4,7,5,6,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 5

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [7,2,3,6,4,5,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 4

[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [6,2,5,3,4,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 3

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [6,2,5,3,4,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 4

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [2,7,5,3,4,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => 5

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [7,2,3,5,6,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => 4

[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [7,6,2,5,3,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => 3

[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,4,2,3,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [7,5,4,2,3,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1

[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [5,4,2,3,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [5,4,2,3,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3

[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [7,5,4,2,3,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2

[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,6,2,3,5,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3

[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,6,2,3,5,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 4

[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,2,7,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 4

[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [7,4,6,2,3,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3

[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [6,2,4,5,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 3

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [6,2,4,5,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => 4

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [2,7,4,5,3,6,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 5

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,2,7,5,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => 4

[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [7,6,2,4,5,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => 3

[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,5,4,2,3,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1

[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [6,5,4,2,3,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2

[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [5,7,4,2,3,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 3

[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [5,7,4,2,6,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => 3

[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => 4

[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,6,5,4,2,3,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 1

[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [7,3,2,1,4,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [6,3,2,1,4,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [6,3,2,1,4,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [7,6,3,2,1,4,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [5,3,2,1,4,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [7,5,3,2,1,4,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [5,3,2,1,6,4,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [5,3,2,1,6,7,4] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [7,5,3,2,1,6,4] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [6,5,3,2,1,4,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [6,5,3,2,1,7,4] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [7,3,5,2,1,6,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => 2

[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],.],.],.],[.,.]] => 0

[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1

[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [6,3,2,4,1,7,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => 2

[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [7,6,3,2,4,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1

[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2

[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2

[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 4

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3

[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [3,7,2,4,5,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 4

[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,6,3,2,4,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2

[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [7,5,3,2,4,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1

[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [7,5,3,2,4,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2

[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [3,6,2,4,5,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [3,6,2,4,5,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 4

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [3,2,7,4,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 4

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [7,3,6,2,4,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3

[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,5,3,2,4,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [6,5,3,2,4,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [5,7,3,2,4,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 3

[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [7,3,5,2,6,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => 3

[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 1

[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [2,4,3,1,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2

[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [7,2,4,3,1,5,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 2

[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [6,2,4,3,1,5,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 2

[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [6,2,4,3,1,7,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => 3

[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [7,6,2,4,3,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => 2

[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [2,4,3,5,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3

[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [7,2,4,3,5,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 3

[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [2,4,3,5,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 4

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 5

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [7,2,4,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 4

[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [6,2,4,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 3

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [6,2,4,3,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 4

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [2,7,4,3,5,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => 5

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [7,6,2,4,3,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => 3

[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [2,3,5,4,1,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 3

[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [7,2,3,5,4,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 3

[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [2,3,5,4,6,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 4

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [2,3,5,4,6,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 5

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [7,2,3,5,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 4

[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [2,3,4,6,5,1,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 4

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,6,5,7,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 5

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [2,3,4,5,7,6,1] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 5

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => 4

[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [6,2,3,5,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 3

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [6,2,3,5,4,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 4

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [2,7,3,5,4,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => 5

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [5,2,3,7,6,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => 4

[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [7,6,2,3,5,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => 3

[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [5,2,4,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 2

[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [7,5,2,4,3,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => 2

[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [5,2,4,3,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 3

[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [5,2,4,3,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 4

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [7,5,2,4,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => 3

[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [2,6,4,3,5,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => 4

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [2,6,4,3,5,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => 5

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [2,4,7,3,5,6,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 5

[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [7,2,6,4,3,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => 4

[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [4,2,6,5,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => 3

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [4,2,6,5,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => 4

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [4,2,5,7,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => 4

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,2,5,7,6,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => 4

[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [7,4,2,6,5,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => 3

[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [6,5,2,4,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => 2

[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [6,5,2,4,3,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => 3

[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [5,7,2,4,3,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => 4

[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [7,2,5,4,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => 4

[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [7,2,4,6,5,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => 4

[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [7,6,5,2,4,3,1] => [[[[[.,.],.],.],[[.,.],.]],.] => 2

[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0

[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [6,4,3,2,1,7,5] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],.],.],[.,.]] => 0

[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1

[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2

[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [4,7,3,2,5,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 3

[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 1

[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [3,5,2,4,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2

[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [7,3,5,2,4,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2

[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,5,2,4,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 4

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [7,3,5,2,4,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3

[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [3,2,6,4,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 3

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,6,4,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 4

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [3,2,4,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 4

[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [7,3,2,6,4,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => 3

[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [6,3,5,2,4,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2

[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [6,3,5,2,4,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [3,7,5,2,4,6,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => 4

[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [7,3,2,5,6,4,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => 3

[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [7,6,3,5,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => 2

[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [3,5,4,2,1,6,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 2

[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [7,3,5,4,2,1,6] => [[[[.,.],[[.,.],.]],.],[.,.]] => 2

[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [3,5,4,2,6,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => 3

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [3,5,4,2,6,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => 4

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [7,3,5,4,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => 3

[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [3,4,6,2,5,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 3

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [3,4,6,2,5,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => 4

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [3,4,2,7,5,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => 4

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [7,3,4,6,2,5,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 3

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [3,4,6,5,2,1,7] => [[[.,[.,[[.,.],.]]],.],[.,.]] => 3

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [3,4,6,5,2,7,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => 4

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [3,4,5,7,2,6,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => 4

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [3,4,5,7,6,2,1] => [[[.,[.,[.,[[.,.],.]]]],.],.] => 4

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [7,3,4,6,5,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => 3

[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [6,3,5,4,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]] => 2

[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [6,3,5,4,2,7,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => 3

[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [3,7,5,4,2,6,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => 4

[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [3,7,5,4,6,2,1] => [[[.,[[[.,.],.],[.,.]]],.],.] => 4

[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [3,7,4,6,5,2,1] => [[[.,[[.,.],[[.,.],.]]],.],.] => 4

[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [7,6,3,5,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => 2

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],.],[.,.]] => 0

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 1

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [4,6,3,2,5,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [4,6,3,2,5,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 3

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [4,3,7,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3

[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [7,4,6,3,2,5,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => 2

[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [4,6,3,5,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 2

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [4,6,3,5,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => 3

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [4,3,7,5,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => 3

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [4,3,7,5,6,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => 3

[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [7,4,6,3,5,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => 2

[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [3,6,5,4,2,1,7] => [[[.,[[[.,.],.],.]],.],[.,.]] => 3

[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,6,5,4,2,7,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => 4

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [3,5,7,4,2,6,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => 4

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,5,7,4,6,2,1] => [[[.,[[.,[.,.]],[.,.]]],.],.] => 4

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [3,4,7,6,5,2,1] => [[[.,[.,[[[.,.],.],.]]],.],.] => 4

[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [7,3,6,5,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => 3

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => 0

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 1

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [5,7,4,3,2,6,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => 2

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [5,7,4,3,6,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => 2

[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [4,7,6,3,5,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.] => 3

[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [4,7,6,5,3,2,1] => [[[[.,[[[.,.],.],.]],.],.],.] => 3

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => 0

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$F_{1} = 1$

$F_{2} = 2$

$F_{3} = 4 + q$

$F_{4} = 8 + 4\ q + 2\ q^{2}$

$F_{5} = 16 + 12\ q + 10\ q^{2} + 4\ q^{3}$

$F_{6} = 32 + 32\ q + 34\ q^{2} + 26\ q^{3} + 8\ q^{4}$

$F_{7} = 64 + 80\ q + 99\ q^{2} + 98\ q^{3} + 71\ q^{4} + 17\ q^{5}$

Description

The number of internal nodes of a binary tree.
That is, the total number of nodes of the tree minus St000203The number of external nodes of a binary tree.. A counting formula for the total number of internal nodes across all binary trees of size

$n$ is given in [1]. This is equivalent to the number of internal triangles in all triangulations of an

$(n+1)$ -gon.

Map

to non-crossing permutation

Description

Sends a Dyck path

$D$ with valley at positions

$\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation

$\pi$ having descents

$\{i_1,\ldots,i_k\}$ and whose inverse has descents

$\{j_1,\ldots,j_k\}$ .
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to

$n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..

Map

to increasing tree

Description

Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length

$0$ to the empty tree, and sending a permutation

$\sigma$ of length

$n \geq 1$ to a root node with two subtrees

$L$ and

$R$ by splitting

$\sigma$ at the index

$\sigma^{-1}(1)$ , normalizing both sides again to permutations and sending the permutations on the left and on the right of

$\sigma^{-1}(1)$ to the trees

$L$ and

$R$ , respectively.

Map

Foata bijection

Description

Sends a permutation to its image under the Foata bijection.
The Foata bijection

$\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word

$w_1 w_2 ... w_n$ , compute the image inductively by starting with

$\phi(w_1) = w_1$ .
At the

$i$ -th step, if

$\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$ , define

$\phi(w_1 w_2 ... w_i w_{i+1})$ by placing

$w_{i+1}$ on the end of the word

$v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.

If $w_{i+1} \geq v_i$ , place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$ .
If $w_{i+1} < v_i$ , place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$ .

In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute

$\phi([1,4,2,5,3])$ , the sequence of words is

$1$
$|1|4 \to 14$
$|14|2 \to 412$
$|4|1|2|5 \to 4125$
$|4|125|3 \to 45123.$

In total, this gives

$\phi([1,4,2,5,3]) = [4,5,1,2,3]$ .
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).