Identifier
Values
[1,0] => [2,1] => [[.,.],.] => [1,1,0,0] => 1
[1,0,1,0] => [3,1,2] => [[.,[.,.]],.] => [1,1,0,1,0,0] => 1
[1,1,0,0] => [2,3,1] => [[.,.],[.,.]] => [1,1,0,0,1,0] => 2
[1,0,1,0,1,0] => [4,1,2,3] => [[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0] => [3,1,4,2] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,0] => [2,4,1,3] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0] => [4,3,1,2] => [[[.,[.,.]],.],.] => [1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [[.,[[.,[.,.]],.]],.] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
>>> Load all 374 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,1,2,5,3,7,8,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,1,8,2,4,7,5,6] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,8,2,6,7,4,5] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,7,5,2,4,8,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,8,6,2,7,4,5] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,5,2,7,8,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,1,8,7,6,2,4,5] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,1,7,5,6,2,8,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,1,4,5,6,2,3,7] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,8,3,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,6,1,5,3,8,4,7] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,3,1,2,8,4,6,7] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,4,1,2,3,5,8,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,1,2,3,8,5,7] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,4,1,2,3,7,8,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [5,8,1,2,6,3,4,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,1,2,6,3,4,5] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [5,4,1,2,6,8,3,7] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,3,1,6,2,8,5,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,4,1,5,2,3,6,7] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,3,4,1,2,5,8,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,5,4,1,2,3,6,7] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,5,4,1,2,8,3,7] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,3,4,1,8,2,6,7] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,3,4,5,1,2,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,3,4,5,1,2,8,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,1,2,3,4,5,8,6,7] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,1,2,3,9,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [7,1,2,8,3,4,5,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,1,8,9,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,7,1,2,3,4,8,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,6,1,2,3,7,8,9,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,7,8,1,2,3,4,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,8,1,2,3,4,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[] => [1] => [.,.] => [1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,1,2,3,4,5,6,7,8] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,8,1,9,2,3,4,5,6,7] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,9,8,1,2,3,4,5,6,7] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
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Description
The number of touch points (or returns) of a Dyck path.
This is the number of points, excluding the origin, where the Dyck path has height 0.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
  • a leaf is associated to the empty Dyck Word
  • a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.