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. Suppose we are given an instance of the Shortest s - t Path Problem on a directed graph G. We assume that all edge costs are positive and distinct. Let P be a minimum-cost s - t path for this instance. Now suppose we replace each edge cost c_e by its square, c_e^2, thereby creating a new instance of the problem with the same graph but different costs. True or false? P must still be a minimum-cost s - t path for this new instance