(Challenge) Dynamic Hull

There are $N$ points in a plane (numbered $1$ through $N$). For each valid $i$, the coordinates of the $i$-th point are $(X_i,Y_i)$. We want to remove all the points one by one; you should choose the order in which they are removed. Whenever a point is removed, we compute the area of the convex hull of the remaining points. Then, we define a *penalty* $P$ as twice the sum of all these areas. It