2. (a) Give an example of a single directed graph in which there are three vertices r, y, and z, such that both of the following are true in your graph: There is a unique shortest simple path from r to y, and this path goes through vertex z. (Recall that a simple path is a path that does not have any repeated edges or vertices. Your answer should specify the weights on each edge of your graph.) (b) In order to answer part (a) correctly, your graph must include a negative cycle. Find a negative cycle in your answer to pari (a)