Identifier
Values
[1,0] => [1] => [1] => [.,.] => 1
[1,0,1,0] => [1,2] => [1,2] => [.,[.,.]] => 2
[1,1,0,0] => [2,1] => [1,2] => [.,[.,.]] => 2
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]] => 3
[1,0,1,1,0,0] => [1,3,2] => [1,2,3] => [.,[.,[.,.]]] => 3
[1,1,0,0,1,0] => [2,1,3] => [1,2,3] => [.,[.,[.,.]]] => 3
[1,1,0,1,0,0] => [2,3,1] => [1,2,3] => [.,[.,[.,.]]] => 3
[1,1,1,0,0,0] => [3,2,1] => [1,3,2] => [.,[[.,.],.]] => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 4
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 4
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 4
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 4
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 3
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 4
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 4
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 4
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 4
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 3
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 3
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [1,3,4,2] => [.,[[.,[.,.]],.]] => 2
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [1,4,2,3] => [.,[[.,.],[.,.]]] => 3
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,4,2,3] => [.,[[.,.],[.,.]]] => 3
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 4
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 4
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 4
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 4
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 5
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 4
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 4
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => 3
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 4
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 4
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 4
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 4
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => 3
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => 3
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 4
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 3
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 4
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 4
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 4
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 3
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 4
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => 4
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 5
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 5
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
>>> Load all 625 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 5
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 5
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => 5
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,5,6,2,4,3] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 4
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,2,4,5,7,3,6] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,2,4,6,3,5,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,2,4,6,7,3,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,2,6,7,3,5,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [1,2,7,3,5,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [1,2,7,3,5,6,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [1,2,4,5,7,3,6] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [1,2,4,6,3,5,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [1,2,4,6,7,3,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [1,2,6,3,5,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [1,2,6,7,3,5,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [1,2,7,3,5,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [1,2,7,3,5,6,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 5
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [1,3,4,2,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [1,3,4,5,2,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [1,3,4,5,2,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [1,3,4,5,6,2,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [1,3,4,5,6,7,2] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [1,3,4,5,7,2,6] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [1,3,4,6,2,5,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [1,3,4,6,7,2,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [1,3,4,7,2,5,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [1,3,4,7,2,5,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [1,3,5,2,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [1,3,5,2,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [1,3,5,6,2,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [1,3,5,6,7,2,4] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [1,3,5,7,2,4,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [1,3,6,2,4,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [1,3,6,7,2,4,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [1,3,6,2,4,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [1,3,6,7,2,4,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [1,3,7,2,4,6,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [1,4,2,3,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [1,4,5,6,2,3,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [1,4,5,6,7,2,3] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [1,4,5,7,2,3,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [1,4,6,7,2,3,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [1,6,2,3,5,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [1,6,7,2,3,5,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [1,7,2,3,5,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [1,7,2,3,5,6,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [1,4,2,3,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [1,4,5,6,2,3,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [1,4,5,6,7,2,3] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [1,4,5,7,2,3,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [1,4,6,2,3,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [1,4,6,7,2,3,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [1,6,2,3,5,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [1,6,7,2,3,5,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [1,7,2,3,5,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [1,7,2,3,5,6,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [1,5,2,4,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [1,5,2,4,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [1,5,6,2,4,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [1,5,6,7,2,4,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [1,5,7,2,4,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [1,6,2,4,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [1,6,7,2,4,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [1,7,2,4,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [1,7,2,4,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [1,6,2,4,5,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [1,6,7,2,4,5,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [1,7,2,4,5,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [1,7,2,4,5,6,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [1,7,2,4,6,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [1,6,2,5,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [1,6,7,2,5,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [1,7,2,5,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [1,7,2,5,6,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [1,6,2,5,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [1,6,7,2,5,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [1,7,2,5,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [1,7,2,5,6,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [1,7,2,6,3,5,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 4
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Description
The number of external nodes of a binary tree.
That is, the number of nodes that can be reached from the root by only left steps or only right steps, plus $1$ for the root node itself. A counting formula for the number of external node in all binary trees of size $n$ can be found in [1].
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.