You are given two boxes: one box filled with mason jars of different sizes, and another box filled with corresponding screw top lids. You can test whether a given jar and lid are a match, from which1 you learn whether the jar is too large, too small, or an exact match for the lid. The differences insize between pairs of jars or lids are too small to see by eye, so you cannot compare the sizes oftwo jars or two lids directly. You are to match each jar to each lid, with the assumption that notwo jars or two lids are of the same size, and that every jar in one box has a corresponding lid inthe other box. Give a randomized O(nlogn) expected time algorithm for this problem.