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 which you learn whether the jar is too large, too small, or an exact match for the lid. The differences in size between pairs of jars or lids are too small to see by eye, so you cannot compare the sizes of two jars or two lids directly. You are to match each jar to each lid, with the assumption that no two jars or two lids are of the same size, and that every jar in one box has a corresponding lid in the other box. Give a randomized O(n log n) expected time algorithm for this problem.