Convex Hulk

Hulk has a set of distinct points $P$ in the 2D plane. His signature move is $Hulk$ $Smash$. He performed $Hulk$ $Smash$ on the set $P$ which caused the points to change, and so he obtained a new set of points $P'$. More formally, $Hulk$ $Smash$ makes the new set $P'$ in the following way: - Initially, let $P'$ be empty. - For every $P_i$ and $P_j$ such that $1 \le i \lt j \le N$ , add the mid po