You notice a strange pattern on the surface of Pluto and land nearby to get a closer look. Upon closer inspection, you realize you've come across one of the famous space-warping mazes of the long-lost Pluto civilization!

Because there isn't much space on Pluto, the civilization that used to live here thrived by inventing a method for folding spacetime. Although the technology is no longer understood, mazes like this one provide a small glimpse into the daily life of an ancient Pluto citizen.

This maze is shaped like a [donut](https://en.wikipedia.org/wiki/Torus). Portals along the inner and outer edge of the donut can instantly teleport you from one side to the other. For example:

```
         A           
         A           
  #######.#########  
  #######.........#  
  #######.#######.#  
  #######.#######.#  
  #######.#######.#  
  #####  B    ###.#  
BC...##  C    ###.#  
  ##.##       ###.#  
  ##...DE  F  ###.#  
  #####    G  ###.#  
  #########.#####.#  
DE..#######...###.#  
  #.#########.###.#  
FG..#########.....#  
  ###########.#####  
             Z       
             Z       

```

This map of the maze shows solid walls (`#`) and open passages (`.`). Every maze on Pluto has a start (the open tile next to `AA`) and an end (the open tile next to `ZZ`). Mazes on Pluto also have portals; this maze has three pairs of portals: `BC`, `DE`, and `FG`. When on an open tile next to one of these labels, a single step can take you to the other tile with the same label. (You can only walk on `.` tiles; labels and empty space are not traversable.)

One path through the maze doesn't require any portals. Starting at `AA`, you could go down 1, right 8, down 12, left 4, and down 1 to reach `ZZ`, a total of 26 steps.

However, there is a shorter path: You could walk from `AA` to the inner `BC` portal (4 steps), warp to the outer `BC` portal (1 step), walk to the inner `DE` (6 steps), warp to the outer `DE` (1 step), walk to the outer `FG` (4 steps), warp to the inner `FG` (1 step), and finally walk to `ZZ` (6 steps). In total, this is only *23* steps.

Here is a larger example:

```
                   A               
                   A               
  #################.#############  
  #.#...#...................#.#.#  
  #.#.#.###.###.###.#########.#.#  
  #.#.#.......#...#.....#.#.#...#  
  #.#########.###.#####.#.#.###.#  
  #.............#.#.....#.......#  
  ###.###########.###.#####.#.#.#  
  #.....#        A   C    #.#.#.#  
  #######        S   P    #####.#  
  #.#...#                 #......VT
  #.#.#.#                 #.#####  
  #...#.#               YN....#.#  
  #.###.#                 #####.#  
DI....#.#                 #.....#  
  #####.#                 #.###.#  
ZZ......#               QG....#..AS
  ###.###                 #######  
JO..#.#.#                 #.....#  
  #.#.#.#                 ###.#.#  
  #...#..DI             BU....#..LF
  #####.#                 #.#####  
YN......#               VT..#....QG
  #.###.#                 #.###.#  
  #.#...#                 #.....#  
  ###.###    J L     J    #.#.###  
  #.....#    O F     P    #.#...#  
  #.###.#####.#.#####.#####.###.#  
  #...#.#.#...#.....#.....#.#...#  
  #.#####.###.###.#.#.#########.#  
  #...#.#.....#...#.#.#.#.....#.#  
  #.###.#####.###.###.#.#.#######  
  #.#.........#...#.............#  
  #########.###.###.#############  
           B   J   C               
           U   P   P               

```

Here, `AA` has no direct path to `ZZ`, but it does connect to `AS` and `CP`. By passing through `AS`, `QG`, `BU`, and `JO`, you can reach `ZZ` in *58* steps.

In your maze, *how many steps does it take to get from the open tile marked `AA` to the open tile marked `ZZ`?*

Your puzzle answer was `400`.

\--- Part Two ---
----------

Strangely, the exit isn't open when you reach it. Then, you remember: the ancient Plutonians were famous for building *recursive spaces*.

The marked connections in the maze aren't portals: they *physically connect* to a larger or smaller copy of the maze. Specifically, the labeled tiles around the inside edge actually connect to a smaller copy of the same maze, and the smaller copy's inner labeled tiles connect to yet a *smaller* copy, and so on.

When you enter the maze, you are at the outermost level; when at the outermost level, only the outer labels `AA` and `ZZ` function (as the start and end, respectively); all other outer labeled tiles are effectively walls. At any other level, `AA` and `ZZ` count as walls, but the other outer labeled tiles bring you one level outward.

Your goal is to find a path through the maze that brings you back to `ZZ` at the outermost level of the maze.

In the first example above, the shortest path is now the loop around the right side. If the starting level is `0`, then taking the previously-shortest path would pass through `BC` (to level `1`), `DE` (to level `2`), and `FG` (back to level `1`). Because this is not the outermost level, `ZZ` is a wall, and the only option is to go back around to `BC`, which would only send you even deeper into the recursive maze.

In the second example above, there is no path that brings you to `ZZ` at the outermost level.

Here is a more interesting example:

```
             Z L X W       C                 
             Z P Q B       K                 
  ###########.#.#.#.#######.###############  
  #...#.......#.#.......#.#.......#.#.#...#  
  ###.#.#.#.#.#.#.#.###.#.#.#######.#.#.###  
  #.#...#.#.#...#.#.#...#...#...#.#.......#  
  #.###.#######.###.###.#.###.###.#.#######  
  #...#.......#.#...#...#.............#...#  
  #.#########.#######.#.#######.#######.###  
  #...#.#    F       R I       Z    #.#.#.#  
  #.###.#    D       E C       H    #.#.#.#  
  #.#...#                           #...#.#  
  #.###.#                           #.###.#  
  #.#....OA                       WB..#.#..ZH
  #.###.#                           #.#.#.#  
CJ......#                           #.....#  
  #######                           #######  
  #.#....CK                         #......IC
  #.###.#                           #.###.#  
  #.....#                           #...#.#  
  ###.###                           #.#.#.#  
XF....#.#                         RF..#.#.#  
  #####.#                           #######  
  #......CJ                       NM..#...#  
  ###.#.#                           #.###.#  
RE....#.#                           #......RF
  ###.###        X   X       L      #.#.#.#  
  #.....#        F   Q       P      #.#.#.#  
  ###.###########.###.#######.#########.###  
  #.....#...#.....#.......#...#.....#.#...#  
  #####.#.###.#######.#######.###.###.#.#.#  
  #.......#.......#.#.#.#.#...#...#...#.#.#  
  #####.###.#####.#.#.#.#.###.###.#.###.###  
  #.......#.....#.#...#...............#...#  
  #############.#.#.###.###################  
               A O F   N                     
               A A D   M                     

```

One shortest path through the maze is the following:

* Walk from `AA` to `XF` (16 steps)
* Recurse into level 1 through `XF` (1 step)
* Walk from `XF` to `CK` (10 steps)
* Recurse into level 2 through `CK` (1 step)
* Walk from `CK` to `ZH` (14 steps)
* Recurse into level 3 through `ZH` (1 step)
* Walk from `ZH` to `WB` (10 steps)
* Recurse into level 4 through `WB` (1 step)
* Walk from `WB` to `IC` (10 steps)
* Recurse into level 5 through `IC` (1 step)
* Walk from `IC` to `RF` (10 steps)
* Recurse into level 6 through `RF` (1 step)
* Walk from `RF` to `NM` (8 steps)
* Recurse into level 7 through `NM` (1 step)
* Walk from `NM` to `LP` (12 steps)
* Recurse into level 8 through `LP` (1 step)
* Walk from `LP` to `FD` (24 steps)
* Recurse into level 9 through `FD` (1 step)
* Walk from `FD` to `XQ` (8 steps)
* Recurse into level 10 through `XQ` (1 step)
* Walk from `XQ` to `WB` (4 steps)
* Return to level 9 through `WB` (1 step)
* Walk from `WB` to `ZH` (10 steps)
* Return to level 8 through `ZH` (1 step)
* Walk from `ZH` to `CK` (14 steps)
* Return to level 7 through `CK` (1 step)
* Walk from `CK` to `XF` (10 steps)
* Return to level 6 through `XF` (1 step)
* Walk from `XF` to `OA` (14 steps)
* Return to level 5 through `OA` (1 step)
* Walk from `OA` to `CJ` (8 steps)
* Return to level 4 through `CJ` (1 step)
* Walk from `CJ` to `RE` (8 steps)
* Return to level 3 through `RE` (1 step)
* Walk from `RE` to `IC` (4 steps)
* Recurse into level 4 through `IC` (1 step)
* Walk from `IC` to `RF` (10 steps)
* Recurse into level 5 through `RF` (1 step)
* Walk from `RF` to `NM` (8 steps)
* Recurse into level 6 through `NM` (1 step)
* Walk from `NM` to `LP` (12 steps)
* Recurse into level 7 through `LP` (1 step)
* Walk from `LP` to `FD` (24 steps)
* Recurse into level 8 through `FD` (1 step)
* Walk from `FD` to `XQ` (8 steps)
* Recurse into level 9 through `XQ` (1 step)
* Walk from `XQ` to `WB` (4 steps)
* Return to level 8 through `WB` (1 step)
* Walk from `WB` to `ZH` (10 steps)
* Return to level 7 through `ZH` (1 step)
* Walk from `ZH` to `CK` (14 steps)
* Return to level 6 through `CK` (1 step)
* Walk from `CK` to `XF` (10 steps)
* Return to level 5 through `XF` (1 step)
* Walk from `XF` to `OA` (14 steps)
* Return to level 4 through `OA` (1 step)
* Walk from `OA` to `CJ` (8 steps)
* Return to level 3 through `CJ` (1 step)
* Walk from `CJ` to `RE` (8 steps)
* Return to level 2 through `RE` (1 step)
* Walk from `RE` to `XQ` (14 steps)
* Return to level 1 through `XQ` (1 step)
* Walk from `XQ` to `FD` (8 steps)
* Return to level 0 through `FD` (1 step)
* Walk from `FD` to `ZZ` (18 steps)

This path takes a total of *396* steps to move from `AA` at the outermost layer to `ZZ` at the outermost layer.

In your maze, when accounting for recursion, *how many steps does it take to get from the open tile marked `AA` to the open tile marked `ZZ`, both at the outermost layer?*

Your puzzle answer was `4986`.

Both parts of this puzzle are complete! They provide two gold stars: \*\*

At this point, you should [return to your Advent calendar](/2019) and try another puzzle.

If you still want to see it, you can [get your puzzle input](20/input).