In several computational geometry problems involving distances defined by a set, S, of n points in the plane, it is often useful to first know what is the largest distance between a pair of points in S, which is known as the diameter of S. Another way to define the diameter of such a set, S, is as the largest distance between two parallel lines, L₁ and L₂, such that all the points of S are either on one of these lines or between them. Suppose, then, that your are given such a set, S. Describe an O(n log n)-time algorithm for computing the diameter of S.