Give an example of a single directed graph in which there are three vertices x, y, and z, such that both of the following are true in your graph:

1. There is a unique shortest simple path from x to y, and this path goes through vertex z.

2. There is a unique shortest simple path from x to z, and this path goes through vertex y.

(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.)

Hint: Your graph must include a negative cycle. Find a negative cycle in your answer.