Let P be a set of points in the plane. A point p E P is Pareto-optimal if no other point in P is both above and to the right of p. The Pareto-optimal points can be connected by horizontal and vertical lines into the staircase of P, with a Pareto-optimal point at the top right corner of every step. Suppose the points in P are given in order from left to right, that is, sorted by increasing x-coordinate. Part implies that when the the input array P is not sorted, we can still compute the staircase of P in O(n log n) time. (Hopefully this algorithm is pretty obvious!) However, we can do better: Describe an algorithm to compute the the staircase of P in O(n log h) time, where h is the number of Pareto-optimal points in P.