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] => [3,2,1] => [[[.,.],.],.] => 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] => [2,1,3] => [[.,.],[.,.]] => 0
[1,1,1,0,0,0] => [1,2,3] => [.,[.,[.,.]]] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [[[[.,.],.],.],.] => 0
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [[[.,.],.],[.,.]] => 0
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [[[.,.],[.,.]],.] => 1
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [[[.,.],.],[.,.]] => 0
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => 0
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [[[.,[.,.]],.],.] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => 1
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [[[.,.],[.,.]],.] => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [[[.,.],.],[.,.]] => 0
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => 0
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[.,[.,[.,.]]],.] => 2
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [[.,[.,.]],[.,.]] => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => 0
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => 0
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [[[[.,.],.],[.,.]],.] => 1
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => 0
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => 0
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [[[[.,.],[.,.]],.],.] => 1
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [[[.,.],[.,.]],[.,.]] => 1
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => 1
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => 0
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => 0
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => 2
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [[[.,.],[.,.]],[.,.]] => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => 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] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.] => 1
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => 1
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => 2
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [[[.,[.,.]],.],[.,.]] => 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] => [5,4,2,1,3] => [[[[.,.],[.,.]],.],.] => 1
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [[[.,.],[.,.]],[.,.]] => 1
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [[[[.,.],.],[.,.]],.] => 1
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => 0
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => 0
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [[[.,.],[.,[.,.]]],.] => 2
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => 1
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => 0
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => 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] => [5,3,1,2,4] => [[[.,[.,.]],[.,.]],.] => 2
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [[[.,[.,.]],.],[.,.]] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [[[.,.],[.,[.,.]]],.] => 2
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [[[.,.],[.,.]],[.,.]] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => 0
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => 0
[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] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => 0
[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] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [[[[.,.],.],[.,.]],[.,.]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],.] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [[[[.,.],.],[.,.]],[.,.]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [[[[.,.],.],[.,.]],[.,.]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],.] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [[[[.,.],[.,.]],.],[.,.]] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[[[.,.],.],[.,.]],[.,.]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => 0
>>> Load all 625 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => 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] => [6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],.] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],.] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],.] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [[[[.,[.,.]],.],.],[.,.]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => 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] => [6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],.] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [[[[.,.],.],[.,.]],[.,.]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],.] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [[[[.,.],.],[.,.]],[.,.]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],.] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],.] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [[[[.,.],[.,.]],.],[.,.]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],.] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => 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] => [6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.] => 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] => [6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[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] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[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] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],.] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],.] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],.],.] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[.,.]] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 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] => [7,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],.] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],.] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],.] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [[[[[.,[.,.]],.],[.,.]],.],.] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],.] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 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] => [7,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],.] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],.] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],.] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [[[[[.,.],.],[.,.]],[.,.]],.] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],.] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],[.,.]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [[[[[.,.],[.,.]],[.,.]],.],.] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [[[[[.,.],[.,.]],.],[.,.]],.] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],.] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [[[[.,[.,[.,.]]],[.,.]],.],.] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 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] => [7,6,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],.] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],.] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [[[[[.,[.,.]],.],[.,.]],.],.] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],[.,.]],.] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,.]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [[[[.,[.,.]],[.,[.,.]]],.],.] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [[[[.,[.,.]],[.,.]],[.,.]],.] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],.],.] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [[[[[.,.],[.,.]],.],[.,.]],.] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],.] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => 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] => [7,6,4,1,2,3,5] => [[[[.,[.,[.,.]]],[.,.]],.],.] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [[[[.,[.,[.,.]]],.],[.,.]],.] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],.] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [[[[.,[.,.]],[.,.]],[.,.]],.] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => 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] => [7,5,1,2,3,4,6] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[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] => [6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
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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
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
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.