Problem 1. Consider the following scheduling problem. The input is a set of n requests R = {r1, r2, ..., rn}, where request ri = (si, fi) represents the interval for a class that meets from time si to time fi. We want to find an assignment of classes to lecture halls that uses the fewest number of lecture halls in which all requests are granted and no two classes can use a lecture hall at the same time. Provide a counterexample that the following algorithm will not find an optimal solution. Assign as many classes as possible to the first lecture hall (using the activity scheduling algorithm discussed in class), and then assign as many classes as possible to the second lecture hall, etc. Justify your answer. (either provide a counter example or a justification of correctness.)