Suppose you are evaluating a set T = {t,...,tn} of football teams. For each team ti, you have a numerical rating x > 0 of its offense and yi> 0 of its defense. We say that ti dominates another team t; if xi > xj and Yi > Yj. Given a subset T'CT, we say that ti is viable in T' if there is no team t; T' that dominates t. (a) Suppose that you have already divided T into two halves, T and T2, such that for all ti T and all tj E T2, we have x xj. Furthermore, suppose that you have already found sets S = {ti E Ti ti is viable in T} and S = {t T : ti is viable in T}. E Design a O(n)-time algorithm that uses S and S to find S = {t T: ti is viable in T}. (b) Design a O(n log n)-time algorithm to find S = {t T : t is viable in T} without making the suppositions of part (a).