Suppose you are hired as a consultant to a professor, Dr. Bob Loblaw, from the Sociology department. He is asking that you build him a software system that can maintain a set, P, of people from a country, Phishnonia, that he is studying. People in Phishnonia are free to come and go as they please, so Dr. Bob Loblaw is asking that your system support fast insertions and deletions. In addition, he is also interested in doing queries that respectively return the mean and median ages of the people in P. His thesis is that if the median age is much smaller than the mean, then the Phishnonia is ripe for revolution, for it implies that there are a disproportionate number of young people. Describe a scheme for maintaining P that can support median and mean age queries, subject to insertions and removals, with each of these operations running in at most O(log n) time, where n is the number of people in P.