Aerobatics - JOI 2021 How to solve?

Here’s the link to the problem in question: View problem - Aerobatics (JOI21_aerobatics) ::

Now, I’m wondering how to solve this? My current idea is that it would have something to do with building convex hull of current points than erasing them and recursively doing convex hull on the remaining points, etc. I have no way to prove idea like this works and have no way to check its correctness. Could anyone link a source to solution/editorial or provide a solution? Thanks.