Identifier
Values
[1,0,1,0] => [2,1] => [[.,.],.] => [1,2] => 0
[1,1,0,0] => [1,2] => [.,[.,.]] => [2,1] => 0
[1,0,1,0,1,0] => [2,1,3] => [[.,.],[.,.]] => [1,3,2] => 0
[1,0,1,1,0,0] => [2,3,1] => [[.,[.,.]],.] => [2,1,3] => 1
[1,1,0,0,1,0] => [3,1,2] => [[.,.],[.,.]] => [1,3,2] => 0
[1,1,0,1,0,0] => [1,3,2] => [.,[[.,.],.]] => [2,3,1] => 0
[1,1,1,0,0,0] => [1,2,3] => [.,[.,[.,.]]] => [3,2,1] => 0
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [[.,.],[[.,.],.]] => [1,3,4,2] => 0
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 1
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 0
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 1
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [[.,.],[[.,.],.]] => [1,3,4,2] => 0
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 1
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 0
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [2,4,3,1] => 0
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 0
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [.,[[.,.],[.,.]]] => [2,4,3,1] => 0
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 0
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 1
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 1
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 0
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 0
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 1
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 0
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 0
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 1
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 0
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 0
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 0
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 1
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 0
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 0
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 0
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 0
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 0
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 0
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 0
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 0
>>> Load all 260 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 0
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Description
The number of inner valleys of a permutation.
The number of valleys including the boundary is St000099The number of valleys of a permutation, including the boundary..
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.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
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.