(Challenge) Delete DAG

You are given a directed acyclic graph with $N$ vertices (numbered $1$ through $N$) and $M$ edges. You want to destroy it all! To destroy the graph, you should delete all of its vertices. In one step, you are allowed to delete at most two vertices; you may only delete a vertex when there is no edge from it to another (not yet deleted) vertex. You may not delete two vertices when there is an ed