You fly into the asteroid belt and reach the Ceres monitoring station. The Elves here have an emergency: they're having trouble tracking all of the asteroids and can't be sure they're safe.

The Elves would like to build a new monitoring station in a nearby area of space; they hand you a map of all of the asteroids in that region (your puzzle input).

The map indicates whether each position is empty (`.`) or contains an asteroid (`#`). The asteroids are much smaller than they appear on the map, and every asteroid is exactly in the center of its marked position. The asteroids can be described with `X,Y` coordinates where `X` is the distance from the left edge and `Y` is the distance from the top edge (so the top-left corner is `0,0` and the position immediately to its right is `1,0`).

Your job is to figure out which asteroid would be the best place to build a *new monitoring station*. A monitoring station can *detect* any asteroid to which it has *direct line of sight* - that is, there cannot be another asteroid *exactly* between them. This line of sight can be at any angle, not just lines aligned to the grid or diagonally. The *best* location is the asteroid that can *detect* the largest number of other asteroids.

For example, consider the following map:

```
.#..#
.....
#####
....#
...##

```

The best location for a new monitoring station on this map is the highlighted asteroid at `3,4` because it can detect `8` asteroids, more than any other location. (The only asteroid it cannot detect is the one at `1,0`; its view of this asteroid is blocked by the asteroid at `2,2`.) All other asteroids are worse locations; they can detect `7` or fewer other asteroids. Here is the number of other asteroids a monitoring station on each asteroid could detect:

```
.7..7
.....
67775
....7
...87

```

Here is an asteroid (`#`) and some examples of the ways its line of sight might be blocked. If there were another asteroid at the location of a capital letter, the locations marked with the corresponding lowercase letter would be blocked and could not be detected:

```
#.........
...A......
...B..a...
.EDCG....a
..F.c.b...
.....c....
..efd.c.gb
.......c..
....f...c.
...e..d..c

```

Here are some larger examples:

* Best is `5,8` with `33` other asteroids detected:

  ```
  ......#.#.
  #..#.#....
  ..#######.
  .#.#.###..
  .#..#.....
  ..#....#.#
  #..#....#.
  .##.#..###
  ##...#..#.
  .#....####

  ```

* Best is `1,2` with `35` other asteroids detected:

  ```
  #.#...#.#.
  .###....#.
  .#....#...
  ##.#.#.#.#
  ....#.#.#.
  .##..###.#
  ..#...##..
  ..##....##
  ......#...
  .####.###.

  ```

* Best is `6,3` with `41` other asteroids detected:

  ```
  .#..#..###
  ####.###.#
  ....###.#.
  ..###.##.#
  ##.##.#.#.
  ....###..#
  ..#.#..#.#
  #..#.#.###
  .##...##.#
  .....#.#..

  ```

* Best is `11,13` with `210` other asteroids detected:

  ```
  .#..##.###...#######
  ##.############..##.
  .#.######.########.#
  .###.#######.####.#.
  #####.##.#.##.###.##
  ..#####..#.#########
  ####################
  #.####....###.#.#.##
  ##.#################
  #####.##.###..####..
  ..######..##.#######
  ####.##.####...##..#
  .#####..#.######.###
  ##...#.##########...
  #.##########.#######
  .####.#.###.###.#.##
  ....##.##.###..#####
  .#.#.###########.###
  #.#.#.#####.####.###
  ###.##.####.##.#..##

  ```

Find the best location for a new monitoring station. *How many other asteroids can be detected from that location?*

Your puzzle answer was `263`.

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

Once you give them the coordinates, the Elves quickly deploy an Instant Monitoring Station to the location and discover the worst: there are simply too many asteroids.

The only solution is *complete vaporization by giant laser*.

Fortunately, in addition to an asteroid scanner, the new monitoring station also comes equipped with a giant rotating laser perfect for vaporizing asteroids. The laser starts by pointing *up* and always rotates *clockwise*, vaporizing any asteroid it hits.

If multiple asteroids are *exactly* in line with the station, the laser only has enough power to vaporize *one* of them before continuing its rotation. In other words, the same asteroids that can be *detected* can be vaporized, but if vaporizing one asteroid makes another one detectable, the newly-detected asteroid won't be vaporized until the laser has returned to the same position by rotating a full 360 degrees.

For example, consider the following map, where the asteroid with the new monitoring station (and laser) is marked `X`:

```
.#....#####...#..
##...##.#####..##
##...#...#.#####.
..#.....X...###..
..#.#.....#....##

```

The first nine asteroids to get vaporized, in order, would be:

```
.#....###24...#..
##...##.13#67..9#
##...#...5.8####.
..#.....X...###..
..#.#.....#....##

```

Note that some asteroids (the ones behind the asteroids marked `1`, `5`, and `7`) won't have a chance to be vaporized until the next full rotation. The laser continues rotating; the next nine to be vaporized are:

```
.#....###.....#..
##...##...#.....#
##...#......1234.
..#.....X...5##..
..#.9.....8....76

```

The next nine to be vaporized are then:

```
.8....###.....#..
56...9#...#.....#
34...7...........
..2.....X....##..
..1..............

```

Finally, the laser completes its first full rotation (`1` through `3`), a second rotation (`4` through `8`), and vaporizes the last asteroid (`9`) partway through its third rotation:

```
......234.....6..
......1...5.....7
.................
........X....89..
.................

```

In the large example above (the one with the best monitoring station location at `11,13`):

* The 1st asteroid to be vaporized is at `11,12`.
* The 2nd asteroid to be vaporized is at `12,1`.
* The 3rd asteroid to be vaporized is at `12,2`.
* The 10th asteroid to be vaporized is at `12,8`.
* The 20th asteroid to be vaporized is at `16,0`.
* The 50th asteroid to be vaporized is at `16,9`.
* The 100th asteroid to be vaporized is at `10,16`.
* The 199th asteroid to be vaporized is at `9,6`.
* *The 200th asteroid to be vaporized is at `8,2`.*
* The 201st asteroid to be vaporized is at `10,9`.
* The 299th and final asteroid to be vaporized is at `11,1`.

The Elves are placing bets on which will be the *200th* asteroid to be vaporized. Win the bet by determining which asteroid that will be; *what do you get if you multiply its X coordinate by `100` and then add its Y coordinate?* (For example, `8,2` becomes *`802`*.)

Your puzzle answer was `1110`.

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](10/input).