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: ``` 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 ``` 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: ``` .......1.. ..1....1.. ..1....1.. .......1.. .112111211 .......... .......... .......... .......... 222111.... ``` 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?* Your puzzle answer was `6007`. \--- Part Two --- ---------- Unfortunately, considering only horizontal and vertical lines doesn't give you the full picture; you need to also consider *diagonal lines*. Because of the limits of the hydrothermal vent mapping system, the lines in your list will only ever be horizontal, vertical, or a diagonal line at exactly 45 degrees. In other words: * An entry like `1,1 -> 3,3` covers points `1,1`, `2,2`, and `3,3`. * An entry like `9,7 -> 7,9` covers points `9,7`, `8,8`, and `7,9`. Considering all lines from the above example would now produce the following diagram: ``` 1.1....11. .111...2.. ..2.1.111. ...1.2.2.. .112313211 ...1.2.... ..1...1... .1.....1.. 1.......1. 222111.... ``` You still need to determine *the number of points where at least two lines overlap*. In the above example, this is still anywhere in the diagram with a `2` or larger - now a total of `*12*` points. Consider all of the lines. *At how many points do at least two lines overlap?* Your puzzle answer was `19349`. Both parts of this puzzle are complete! They provide two gold stars: \*\* At this point, you should [return to your Advent calendar](/2021) and try another puzzle. If you still want to see it, you can [get your puzzle input](5/input).