2. (25 points) Let C={C1,,Cn} be a set of n circles in R2 where each circle Ci is given as its center point qi=(xi,yi) and radius ri>0. Describe and analyze an O(nlogn) time algorithm to determine whether or not any pair of circles intersect. Note that some circles may be completely nested in one-another without intersecting. See Figure 2. Figure 2. Circles that do not intersect contrasted with some that do intersect. [Hint: Describe a plane sweep algorithm. To describe one, it suffices to explain 1) what is stored for the sweep-line status and what data structure is used, 2) what are the event points and what data structure is used for the event queue, and 3) how to check for intersections and update the sweep-line status and event queue during events. You should also explain why handling events as you do is correct.]