How many piers does a harbor master need for accommodating six cruise ships S₁, · · ·, S₆ with expected dates of arrival A and departure D in July, (A, D) = (10, 13), (13, 15), (16, 18), (14, 17), (12, 15), (16, 18), (14, 17), respectively, if each pier can accommodate only one ship, arrival being at 6 am and departures at 11 pm? Join S_i and S_j by an edge if their intervals overlap. Then color vertices.