So I was studying this infamous ICPC ECNA 2023 geo problem ([https://codeforces.me/gym/104757/problem/C](https://codeforces.me/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...↵
↵
![ ](https://zhtluo.com/img/cf/ecna-2023/1.png)↵
![ ](https://zhtluo.com/img/cf/ecna-2023/2.png)↵
![ ](https://zhtluo.com/img/cf/ecna-2023/3.png)↵
![ ](https://zhtluo.com/img/cf/ecna-2023/4.png)↵
↵
So now I am stumped. What is the correct solution for this problem? Does it even exist?
↵
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...↵
↵
![ ](https://zhtluo.com/img/cf/ecna-2023/1.png)↵
![ ](https://zhtluo.com/img/cf/ecna-2023/2.png)↵
![ ](https://zhtluo.com/img/cf/ecna-2023/3.png)↵
![ ](https://zhtluo.com/img/cf/ecna-2023/4.png)↵
↵
So now I am stumped. What is the correct solution for this problem? Does it even exist?