So I was studying this infamous ICPC ECNA 2023 geo problem (https://mirror.codeforces.com/gym/104757/problem/C)...

I tried to read the judge's solutions here (https://raw.githubusercontent.com/icpc/na-ecna-archive/main/2023-2024/convexhullextension.zip) from this site (https://na.icpc.global/2022-23/regionals/ecna/ecna-archive-2022-23/) but they don't really make sense to me.

So I came up with this test case:

```
5
-999 999
-998 -998
999 -999
998 999
0 1000
```

And I tried to run it on the solutions. It turns out that the solutions don't agree with each other...

So now I am stumped. What is the correct solution for this problem? Does it even exist?