Identifier
Values
[1,0] => [1] => [1] => [.,.] => 0
[1,0,1,0] => [1,2] => [2,1] => [[.,.],.] => 0
[1,1,0,0] => [2,1] => [1,2] => [.,[.,.]] => 1
[1,0,1,0,1,0] => [1,2,3] => [3,2,1] => [[[.,.],.],.] => 0
[1,0,1,1,0,0] => [1,3,2] => [2,3,1] => [[.,.],[.,.]] => 1
[1,1,0,0,1,0] => [2,1,3] => [3,1,2] => [[.,[.,.]],.] => 1
[1,1,0,1,0,0] => [2,3,1] => [1,3,2] => [.,[[.,.],.]] => 2
[1,1,1,0,0,0] => [3,2,1] => [1,2,3] => [.,[.,[.,.]]] => 3
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [4,3,2,1] => [[[[.,.],.],.],.] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [3,4,2,1] => [[[.,.],.],[.,.]] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [4,2,3,1] => [[[.,.],[.,.]],.] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,4,3,1] => [[.,.],[[.,.],.]] => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [2,3,4,1] => [[.,.],[.,[.,.]]] => 3
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [4,3,1,2] => [[[.,[.,.]],.],.] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [3,4,1,2] => [[.,[.,.]],[.,.]] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [4,1,3,2] => [[.,[[.,.],.]],.] => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,4,3,2] => [.,[[[.,.],.],.]] => 3
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [1,3,4,2] => [.,[[.,.],[.,.]]] => 4
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [4,1,2,3] => [[.,[.,[.,.]]],.] => 3
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [1,4,2,3] => [.,[[.,[.,.]],.]] => 4
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 4
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 6
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [5,3,4,2,1] => [[[[.,.],.],[.,.]],.] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [3,5,4,2,1] => [[[.,.],.],[[.,.],.]] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [5,4,2,3,1] => [[[[.,.],[.,.]],.],.] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [4,5,2,3,1] => [[[.,.],[.,.]],[.,.]] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => 3
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [2,5,3,4,1] => [[.,.],[[.,[.,.]],.]] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => 6
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,5,4,1,2] => [[.,[.,.]],[[.,.],.]] => 3
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => 4
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [5,4,1,3,2] => [[[.,[[.,.],.]],.],.] => 2
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [4,5,1,3,2] => [[.,[[.,.],.]],[.,.]] => 3
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [5,1,4,3,2] => [[.,[[[.,.],.],.]],.] => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => 4
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [1,4,5,3,2] => [.,[[[.,.],.],[.,.]]] => 5
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [5,1,3,4,2] => [[.,[[.,.],[.,.]]],.] => 4
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => 5
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]] => 5
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => 7
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => 3
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => 4
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [5,1,4,2,3] => [[.,[[.,[.,.]],.]],.] => 4
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [1,5,4,2,3] => [.,[[[.,[.,.]],.],.]] => 5
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 6
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [5,1,3,2,4] => [[.,[[.,.],[.,.]]],.] => 4
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [1,5,3,2,4] => [.,[[[.,.],[.,.]],.]] => 5
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => 5
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => 7
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => 6
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => 7
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => 6
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 8
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [4,6,5,3,2,1] => [[[[.,.],.],.],[[.,.],.]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [6,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],.] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [3,6,5,4,2,1] => [[[.,.],.],[[[.,.],.],.]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,5,6,4,2,1] => [[[.,.],.],[[.,.],[.,.]]] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,6,4,5,2,1] => [[[.,.],.],[[.,[.,.]],.]] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [3,5,4,6,2,1] => [[[.,.],.],[[.,.],[.,.]]] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [4,6,5,2,3,1] => [[[.,.],[.,.]],[[.,.],.]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [4,5,6,2,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [6,5,2,4,3,1] => [[[[.,.],[[.,.],.]],.],.] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [5,6,2,4,3,1] => [[[.,.],[[.,.],.]],[.,.]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [2,5,6,4,3,1] => [[.,.],[[[.,.],.],[.,.]]] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [6,2,4,5,3,1] => [[[.,.],[[.,.],[.,.]]],.] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [2,6,4,5,3,1] => [[.,.],[[[.,.],[.,.]],.]] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [2,5,4,6,3,1] => [[.,.],[[[.,.],.],[.,.]]] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [2,4,5,6,3,1] => [[.,.],[[.,.],[.,[.,.]]]] => 7
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [5,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [6,2,5,3,4,1] => [[[.,.],[[.,[.,.]],.]],.] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [2,6,5,3,4,1] => [[.,.],[[[.,[.,.]],.],.]] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [2,5,6,3,4,1] => [[.,.],[[.,[.,.]],[.,.]]] => 6
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [2,6,4,3,5,1] => [[.,.],[[[.,.],[.,.]],.]] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [2,5,4,3,6,1] => [[.,.],[[[.,.],.],[.,.]]] => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => 7
>>> Load all 460 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [2,6,3,4,5,1] => [[.,.],[[.,[.,[.,.]]],.]] => 7
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [2,5,3,4,6,1] => [[.,.],[[.,[.,.]],[.,.]]] => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]] => 8
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => 10
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [6,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],.] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [4,6,5,3,1,2] => [[[.,[.,.]],.],[[.,.],.]] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [4,5,6,3,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [6,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],.] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [6,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],.] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [3,6,5,4,1,2] => [[.,[.,.]],[[[.,.],.],.]] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,5,6,4,1,2] => [[.,[.,.]],[[.,.],[.,.]]] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [6,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],.] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,6,4,5,1,2] => [[.,[.,.]],[[.,[.,.]],.]] => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [3,5,4,6,1,2] => [[.,[.,.]],[[.,.],[.,.]]] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 7
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],.] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [5,6,4,1,3,2] => [[[.,[[.,.],.]],.],[.,.]] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [6,4,5,1,3,2] => [[[.,[[.,.],.]],[.,.]],.] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [4,6,5,1,3,2] => [[.,[[.,.],.]],[[.,.],.]] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [4,5,6,1,3,2] => [[.,[[.,.],.]],[.,[.,.]]] => 5
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => [[[.,[[[.,.],.],.]],.],.] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [5,6,1,4,3,2] => [[.,[[[.,.],.],.]],[.,.]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],.] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [1,5,6,4,3,2] => [.,[[[[.,.],.],.],[.,.]]] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [6,1,4,5,3,2] => [[.,[[[.,.],.],[.,.]]],.] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [1,6,4,5,3,2] => [.,[[[[.,.],.],[.,.]],.]] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [1,5,4,6,3,2] => [.,[[[[.,.],.],.],[.,.]]] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [1,4,5,6,3,2] => [.,[[[.,.],.],[.,[.,.]]]] => 8
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [6,5,1,3,4,2] => [[[.,[[.,.],[.,.]]],.],.] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [5,6,1,3,4,2] => [[.,[[.,.],[.,.]]],[.,.]] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [6,1,5,3,4,2] => [[.,[[[.,.],[.,.]],.]],.] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [1,6,5,3,4,2] => [.,[[[[.,.],[.,.]],.],.]] => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [1,5,6,3,4,2] => [.,[[[.,.],[.,.]],[.,.]]] => 7
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [6,1,4,3,5,2] => [[.,[[[.,.],.],[.,.]]],.] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]] => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => 8
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [6,1,3,4,5,2] => [[.,[[.,.],[.,[.,.]]]],.] => 7
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => 8
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [1,5,3,4,6,2] => [.,[[[.,.],[.,.]],[.,.]]] => 7
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]] => 9
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [5,6,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [6,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [4,6,5,1,2,3] => [[.,[.,[.,.]]],[[.,.],.]] => 5
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 6
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [6,5,1,4,2,3] => [[[.,[[.,[.,.]],.]],.],.] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [5,6,1,4,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [6,1,5,4,2,3] => [[.,[[[.,[.,.]],.],.]],.] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [1,6,5,4,2,3] => [.,[[[[.,[.,.]],.],.],.]] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => 7
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [6,1,4,5,2,3] => [[.,[[.,[.,.]],[.,.]]],.] => 6
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,6,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],.]] => 7
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [1,5,4,6,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => 7
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 9
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [6,5,1,3,2,4] => [[[.,[[.,.],[.,.]]],.],.] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [5,6,1,3,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [6,1,5,3,2,4] => [[.,[[[.,.],[.,.]],.]],.] => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [1,6,5,3,2,4] => [.,[[[[.,.],[.,.]],.],.]] => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [1,5,6,3,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 7
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [6,1,4,3,2,5] => [[.,[[[.,.],.],[.,.]]],.] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [1,6,4,3,2,5] => [.,[[[[.,.],.],[.,.]],.]] => 6
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => 8
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [6,1,3,4,2,5] => [[.,[[.,.],[.,[.,.]]]],.] => 7
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [1,6,3,4,2,5] => [.,[[[.,.],[.,[.,.]]],.]] => 8
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 7
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]] => 9
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.] => 6
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 7
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [6,1,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],.] => 7
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,6,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],.]] => 8
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 9
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [6,1,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],.] => 6
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,6,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],.]] => 7
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [1,5,4,2,3,6] => [.,[[[.,[.,.]],.],[.,.]]] => 7
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 9
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [6,1,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],.] => 8
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [1,6,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],.]] => 9
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]] => 8
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 10
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => 10
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 11
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 9
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 11
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [5,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [6,7,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [6,7,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [6,7,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [6,7,5,2,4,3,1] => [[[[.,.],[[.,.],.]],.],[.,.]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [2,7,6,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],.]] => 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [2,4,5,6,7,3,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [6,7,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [7,5,6,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [5,7,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [5,6,7,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [6,7,2,5,3,4,1] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [2,4,5,6,3,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [2,3,5,6,4,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [2,7,3,4,5,6,1] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 11
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [2,3,6,4,5,7,1] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 11
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [2,3,5,4,6,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 15
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [5,6,7,4,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [6,7,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [3,4,5,6,7,1,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 11
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [6,7,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],[.,.]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [5,6,7,4,1,3,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [6,7,5,1,4,3,2] => [[[.,[[[.,.],.],.]],.],[.,.]] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [5,6,7,1,4,3,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [6,7,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],[.,.]] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [1,6,7,5,4,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [1,7,5,6,4,3,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [1,6,5,7,4,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [1,7,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [1,6,7,4,5,3,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [1,7,5,4,6,3,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [1,6,5,4,7,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [1,6,4,5,7,3,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [1,7,6,5,3,4,2] => [.,[[[[[.,.],[.,.]],.],.],.]] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [1,6,7,5,3,4,2] => [.,[[[[.,.],[.,.]],.],[.,.]]] => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [7,1,5,6,3,4,2] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [1,7,5,6,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [1,6,5,7,3,4,2] => [.,[[[[.,.],[.,.]],.],[.,.]]] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [1,5,6,7,3,4,2] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 10
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [1,7,6,4,3,5,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [1,6,7,4,3,5,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [1,7,5,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [1,6,4,5,3,7,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [6,7,1,3,4,5,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 8
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [7,1,5,3,4,6,2] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 7
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [1,7,5,3,4,6,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [1,6,5,3,4,7,2] => [.,[[[[.,.],[.,.]],.],[.,.]]] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [1,5,6,3,4,7,2] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 10
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [1,6,3,5,4,7,2] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 9
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [7,1,3,4,5,6,2] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 11
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [6,7,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [6,7,5,1,4,2,3] => [[[.,[[.,[.,.]],.]],.],[.,.]] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [1,7,6,5,4,2,3] => [.,[[[[[.,[.,.]],.],.],.],.]] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [1,6,7,5,4,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [1,6,5,7,4,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]] => 8
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [1,7,6,4,5,2,3] => [.,[[[[.,[.,.]],[.,.]],.],.]] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [1,6,7,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 9
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [1,6,5,4,7,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [1,6,4,5,7,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [1,7,6,5,3,2,4] => [.,[[[[[.,.],[.,.]],.],.],.]] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [1,6,7,5,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => 8
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [7,1,5,6,3,2,4] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 7
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [1,7,5,6,3,2,4] => [.,[[[[.,.],[.,.]],[.,.]],.]] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [1,6,5,7,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [1,5,6,7,3,2,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 10
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [1,7,6,4,3,2,5] => [.,[[[[[.,.],.],[.,.]],.],.]] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [1,6,7,4,3,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,7,5,4,3,2,6] => [.,[[[[[.,.],.],.],[.,.]],.]] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [1,6,4,5,3,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [6,7,1,3,4,2,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [7,1,5,3,4,2,6] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [1,7,5,3,4,2,6] => [.,[[[[.,.],[.,.]],[.,.]],.]] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [1,6,5,3,4,2,7] => [.,[[[[.,.],[.,.]],.],[.,.]]] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [1,5,6,3,4,2,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 10
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [1,6,3,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 9
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [7,1,3,4,5,2,6] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 11
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [1,7,6,5,2,3,4] => [.,[[[[.,[.,[.,.]]],.],.],.]] => 9
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [1,7,6,4,2,3,5] => [.,[[[[.,[.,.]],[.,.]],.],.]] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [1,6,7,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [1,6,5,4,2,3,7] => [.,[[[[.,[.,.]],.],.],[.,.]]] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [1,6,4,5,2,3,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 9
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [1,6,7,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 11
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [1,6,5,2,4,3,7] => [.,[[[.,[[.,.],.]],.],[.,.]]] => 9
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [1,6,2,5,4,3,7] => [.,[[.,[[[.,.],.],.]],[.,.]]] => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [7,1,2,4,5,3,6] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 12
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [1,6,2,4,5,3,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [6,7,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 11
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [7,1,6,2,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 11
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [7,1,2,5,3,4,6] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 11
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [7,1,2,4,3,5,6] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 12
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [1,6,2,4,3,5,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 11
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [7,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [6,8,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [7,8,5,6,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [8,5,7,6,4,3,2,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [7,8,6,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [8,6,7,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [8,7,4,6,5,3,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [4,8,7,6,5,3,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [4,7,5,6,8,3,2,1] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [7,8,6,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [8,6,7,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [8,7,5,6,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [5,8,7,6,3,4,2,1] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [5,7,8,6,3,4,2,1] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => [5,7,6,8,3,4,2,1] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [6,8,7,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [8,3,7,6,5,4,2,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [6,8,7,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [6,7,8,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [7,8,6,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [8,6,7,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [5,8,7,6,4,2,3,1] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [5,7,8,6,4,2,3,1] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [5,7,6,8,4,2,3,1] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [6,7,8,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [8,4,7,6,5,2,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => 4
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [4,6,7,8,5,2,3,1] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [7,8,4,5,6,2,3,1] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,7,5,6,4,8] => [8,4,6,5,7,2,3,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 5
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [4,6,7,5,8,2,3,1] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [7,8,5,6,2,4,3,1] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [8,5,7,6,2,4,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [2,8,7,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,8,6,5,7,2] => [2,7,5,6,8,4,3,1] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 8
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [2,7,8,5,4,6,3,1] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [2,7,6,4,5,8,3,1] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 8
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [6,7,8,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => 6
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [7,8,5,6,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [5,8,7,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [5,8,6,7,2,3,4,1] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 7
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [5,6,7,8,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 9
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [2,7,6,8,5,3,4,1] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 8
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [2,7,6,5,8,3,4,1] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 8
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [2,5,7,6,8,3,4,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 11
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,5,3,4,7,6,8,2] => [2,8,6,7,4,3,5,1] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => [2,7,6,8,4,3,5,1] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,8,3,4,6,5,7,2] => [2,7,5,6,4,3,8,1] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [2,7,6,4,5,3,8,1] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,8,3,6,5,7,4,2] => [2,4,7,5,6,3,8,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 12
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [2,7,6,5,3,4,8,1] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [2,3,4,6,5,7,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [7,8,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [5,8,7,6,4,3,1,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [6,8,7,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [6,7,8,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [7,8,4,6,5,3,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [6,8,7,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [6,7,8,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [5,8,6,7,3,4,1,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [3,8,7,6,5,4,1,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [3,7,6,8,5,4,1,2] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => 7
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [7,8,3,5,6,4,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [3,7,5,6,8,4,1,2] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => 8
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [7,8,3,6,4,5,1,2] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [3,8,6,7,4,5,1,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [3,7,6,8,4,5,1,2] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => 8
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [7,8,3,5,4,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => 6
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [3,7,5,6,4,8,1,2] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => 8
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [3,5,7,6,4,8,1,2] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => 10
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [3,6,7,4,5,8,1,2] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => 10
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [3,8,4,6,5,7,1,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [7,8,6,5,4,1,3,2] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [6,8,7,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [4,8,7,6,5,1,3,2] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => 6
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [4,7,8,6,5,1,3,2] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [4,8,6,7,5,1,3,2] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,8,6,7,4] => [4,7,6,8,5,1,3,2] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 7
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [4,7,8,5,6,1,3,2] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => 8
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,7,5,6,8,4] => [4,8,6,5,7,1,3,2] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => 7
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [4,7,6,5,8,1,3,2] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 7
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,8,6,5,7,4] => [4,7,5,6,8,1,3,2] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [7,8,6,5,1,4,3,2] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [5,8,7,6,1,4,3,2] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [1,8,7,6,4,5,3,2] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => 8
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [5,7,8,6,1,3,4,2] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => 8
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [5,8,6,7,1,3,4,2] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [1,8,7,6,5,3,4,2] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [1,7,8,5,6,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 10
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,3,8,6,7,5,1] => [1,5,7,6,8,3,4,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 12
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [1,5,6,7,8,3,4,2] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 14
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [1,8,7,6,4,3,5,2] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [1,7,8,5,3,4,6,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 10
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [1,5,6,7,3,4,8,2] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 14
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [7,8,6,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [6,7,8,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => 6
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [4,7,8,6,5,1,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => 8
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [4,7,6,5,8,1,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => 8
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [4,6,7,5,8,1,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => 10
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [4,5,7,6,8,1,2,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => 11
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [7,8,5,6,1,4,2,3] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => 6
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [5,7,8,6,1,4,2,3] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => 8
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [5,8,6,7,1,4,2,3] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => 8
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [5,7,6,8,1,4,2,3] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [1,8,7,6,5,4,2,3] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => 8
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [7,8,6,1,4,5,2,3] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 7
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [7,8,1,6,4,5,2,3] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [8,1,6,7,4,5,2,3] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 9
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [1,8,6,7,4,5,2,3] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [8,1,6,4,5,7,2,3] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 9
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,7,5,4,6,8,1] => [1,8,6,4,5,7,2,3] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 10
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [8,1,4,6,5,7,2,3] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => 11
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [5,7,8,6,1,3,2,4] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => 8
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [5,8,6,7,1,3,2,4] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => 8
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [5,7,6,8,1,3,2,4] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [1,8,7,6,5,3,2,4] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => 8
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => [1,5,6,7,8,3,2,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 14
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [1,8,7,6,4,3,2,5] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,2,4,3,5,8,7,1] => [1,7,8,5,3,4,2,6] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 10
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8,2,4,3,7,6,5,1] => [1,5,6,7,3,4,2,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 14
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 12
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [1,8,7,6,5,2,3,4] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 10
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [7,8,6,1,4,2,3,5] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 7
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [7,8,1,6,4,2,3,5] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [8,1,6,7,4,2,3,5] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 9
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,3,2,4,7,6,8,1] => [1,8,6,7,4,2,3,5] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 10
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [8,1,6,4,5,2,3,7] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 9
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,3,2,5,4,6,8,1] => [1,8,6,4,5,2,3,7] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 10
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,3,4,2,6,8,7,1] => [1,7,8,6,2,4,3,5] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 12
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [1,7,6,8,2,4,3,5] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 12
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [1,7,6,2,4,5,3,8] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 12
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,4,3,5,2,7,1,8] => [8,1,7,2,5,3,4,6] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [1,8,6,2,5,3,4,7] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 12
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [1,7,6,2,4,3,5,8] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [1,8,2,6,4,3,5,7] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 14
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [8,1,2,3,5,4,6,7] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 18
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 21
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 28
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [2,3,4,5,6,7,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,8,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 36
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [2,3,4,5,6,7,8,9,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 45
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 45
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,2,3] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => [1,9,8,7,6,5,3,2,4] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [8,9,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [10,11,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [1,10,9,8,7,6,5,4,2,3] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [1,11,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [8,9,7,6,5,4,2,3,1] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [8,9,7,6,5,4,3,1,2] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [9,10,8,7,6,5,4,3,1,2] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [9,10,7,8,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [8,9,7,6,5,4,1,3,2] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,9,8,1,10] => [10,1,8,9,6,7,4,5,2,3] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => 12
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,3,4,1,2] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 6
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Description
The sum of the sizes of the right subtrees of a binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the $312$-avoiding permutation corresponding to the binary tree.
It is also the sum of all heights $j$ of the coordinates $(i,j)$ of the Dyck path corresponding to the binary tree.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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..