Identifier
Values
[1,0] => [1] => [.,.] => 0
[1,0,1,0] => [2,1] => [[.,.],.] => 0
[1,1,0,0] => [1,2] => [.,[.,.]] => 0
[1,0,1,0,1,0] => [2,1,3] => [[.,.],[.,.]] => 0
[1,0,1,1,0,0] => [2,3,1] => [[.,.],[.,.]] => 0
[1,1,0,0,1,0] => [3,1,2] => [[.,[.,.]],.] => 1
[1,1,0,1,0,0] => [1,3,2] => [.,[[.,.],.]] => 1
[1,1,1,0,0,0] => [1,2,3] => [.,[.,[.,.]]] => 0
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [[.,.],[[.,.],.]] => 1
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [[.,.],[[.,.],.]] => 1
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => 0
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => 0
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => 0
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [[.,[.,.]],[.,.]] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => 1
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [[.,[.,.]],[.,.]] => 1
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 1
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [.,[[.,.],[.,.]]] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[.,[.,[.,.]]],.] => 2
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [.,[[.,[.,.]],.]] => 2
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => 1
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [[.,.],[[.,.],[.,.]]] => 1
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => 1
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [[.,.],[[.,.],[.,.]]] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [[.,.],[[.,.],[.,.]]] => 1
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]] => 2
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => 2
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => 1
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [[.,.],[.,[[.,.],.]]] => 1
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => 0
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => 0
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => 0
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => 0
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => 2
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => 2
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => 1
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => 3
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => 3
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => 2
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [[.,.],[[.,.],[[.,.],.]]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]] => 1
>>> Load all 625 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,5,6,7,1,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,5,1,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,1,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,6,1,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0
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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
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
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.