(Challenge) 300 IQ Ants

There are $N$ ants (numbered $1$ through $N$) in a plane. For simplicity, we will represent the ants by points. For each valid $i$, initially, the position of the $i$-th ant is $(X_i,Y_i)$. Ada wants to gather all ants at a single point. In order to do that, she wants to give instructions to the ants. In each instruction: - First, Ada chooses a simple convex polygon with $M$ vertices (numbered $1