Added manhattan question (for medium difficulty padding)

Author: TianLangHin

competition/manhattan/.gitignore

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+/target

competition/manhattan/Cargo.lock

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+[package]
+name = "manhattan"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]
+rand = "0.9.1"
+rand_chacha = "0.9.0"

competition/manhattan/Cargo.toml

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+---toml
+[fuzz]
+exec = ["cargo", "run", "--release", "--", "generate"]
+env = {}
+
+[judge]
+exec = ["cargo", "run", "--release", "--quiet", "--", "validate"]
+
+[problem]
+points = 15
+difficulty = 2
+---
+
+# 🧭 Manhattan Courier
+
+As you open your eyes in the morning,
+you grumble as you throw your alarm clock on the ground,
+lamenting the hard day of work ahead at your day job.
+That job, of course, is being a courier in the busy city of Manhattan.
+
+While of course this job is simple enough for some, for you it gets even worse.
+You're not just any old courier, you're a courier in a multiverse!
+That's right, every day, your boss dispatches you to the city of Manhattan
+in some particular multiverse, which means that at the start of every day,
+you get a different map over which you will have to navigate.
+
+There is something peculiar about these alternate reality Manhattans that you have learnt, though.
+1. These buildings are scattered throughout a three-dimensional space,
+   meaning a good amount of them are straight up floating.
+2. All modes of transportation to and from different buildings are incapable of travelling
+   diagonally, meaning that the cost of moving from one city to another can never be less
+   than the [Manhattan distance](https://en.wikipedia.org/wiki/Taxicab_geometry)
+   (i.e., sum of absolute differences of coordinates) between their locations.
+   For example, the Manhattan distance between `(1, 2, 3)` and `(6, 5, 4)`
+   is `|1-6| + |2-5| + |3-4| = 5 + 3 + 1 = 9`.
+
+Of course, being the Employee of the Year two years in a row,
+you're known for being efficient and always finding the shortest path
+to get from one place to another.
+As you get ready for work, a colleague of yours poses you a challenge.
+In addition to a new Manhattan map, they give you the names of two buildings in the map.
+You are asked to find the
+**cost of the shortest path from the first given building to the second one**.
+
+In this case, the "shortest path" refers to the path that incurs the least total cost.
+A cost is incurred every single time you move from one building to another.
+
+## Example
+
+Consider the following input prompt.
+```
+aaa eee
+aaa(0, 0, 0): bbb(4), ccc(5)
+bbb(0, 1, 1): aaa(3), ccc(2), eee(10)
+ccc(0, 2, 2): ddd(3)
+ddd(1, 3, 1): bbb(4), eee(5)
+eee(2, 4, 3): ccc(8)
+```
+All paths in the city are *directed*.
+That is, from the above, moving from building `aaa` to `bbb` has a cost of 4,
+while from building `bbb` to `aaa` has a cost of 3.
+Also, in the above, your colleague has challenged you to finding the cost of
+the shortest path from building `aaa` to `eee`,
+which happens to be **13**
+(to `ccc` with cost 5, then to `ddd` with cost 3, then finally to `eee` with cost 5).
+
+## Input
+
+Your input will consist of a series of lines as per the example above.
+The first line contains two space-separated names:
+the first being the building you start at, and the second being the building you end at.
+
+The rest of the lines are in the format of:
+```
+<building name>(<location coordinates>): [<building name>(<cost>)] ...
+```
+
+For example, in the above, `aaa(0, 0, 0): bbb(4), ccc(5)` means that
+from building `aaa`, which is located at point `(0, 0, 0)`,
+moving to building `bbb` will incur a cost of 4,
+and moving to building `ccc` will incur a cost of 5.
+
+## Output
+
+Your output will be a single integer, representing the cost of the shortest path
+from the given start building to the given end building.
+
+In the above example, it will be a single integer as follows.
+```
+13
+```