https://adventofcode.com/2021/day/5

## \--- Day 5: Hydrothermal Venture ---

You come across a field of [hydrothermal
vents](https://en.wikipedia.org/wiki/Hydrothermal_vent) on the ocean floor!
These vents constantly produce large, opaque clouds, so it would be best to
avoid them if possible.

They tend to form in _lines_ ; the submarine helpfully produces a list of
nearby lines of vents (your puzzle input) for you to review. For example:

[code]

    0,9 -> 5,9
    8,0 -> 0,8
    9,4 -> 3,4
    2,2 -> 2,1
    7,0 -> 7,4
    6,4 -> 2,0
    0,9 -> 2,9
    3,4 -> 1,4
    0,0 -> 8,8
    5,5 -> 8,2
    
[/code]

Each line of vents is given as a line segment in the format `x1,y1 -> x2,y2`
where `x1`,`y1` are the coordinates of one end the line segment and `x2`,`y2`
are the coordinates of the other end. These line segments include the points
at both ends. In other words:

  * An entry like `1,1 -> 1,3` covers points `1,1`, `1,2`, and `1,3`.
  * An entry like `9,7 -> 7,7` covers points `9,7`, `8,7`, and `7,7`.

For now, _only consider horizontal and vertical lines_ : lines where either
`x1 = x2` or `y1 = y2`.

So, the horizontal and vertical lines from the above list would produce the
following diagram:

[code]

    .......1..
    ..1....1..
    ..1....1..
    .......1..
    .112111211
    ..........
    ..........
    ..........
    ..........
    222111....
    
[/code]

In this diagram, the top left corner is `0,0` and the bottom right corner is
`9,9`. Each position is shown as _the number of lines which cover that point_
or `.` if no line covers that point. The top-left pair of `1`s, for example,
comes from `2,2 -> 2,1`; the very bottom row is formed by the overlapping
lines `0,9 -> 5,9` and `0,9 -> 2,9`.

To avoid the most dangerous areas, you need to determine _the number of points
where at least two lines overlap_. In the above example, this is anywhere in
the diagram with a `2` or larger - a total of `_5_` points.

Consider only horizontal and vertical lines. _At how many points do at least
two lines overlap?_