3. (15 points) Finding the topological order: By implementation of the decrease-and-conquer technique: repeatedly, identify in a remaining digraph a source, which is a vertex with no incoming edges, and delete it along with all the edges outgoing from it. The order in which the vertices are deleted yields a solution to the topological sorting problem. The key step here is to find the source, is it possible that a nonempty dag have no sources? Prove your claim. (hint: use a proof by contradiction)