Problem 1 (4 points). Suppose we are given an instance of the Shortest st Path Problem on a directed graph G. We assume that all edge costs are positive and distinct. Let P be a minimum-cost st path for this instance. Now suppose we replace each edge cost ce by its square, ce2, thereby creating a new instance of the problem with the same graph but different costs. Consider the following statement, decide whether it is true or false. If it is true, give a short explanation. If it is false, give a counterexample. Statement: P must still be a minimum-cost st path for this new instance