Let S be a set of n points in the plane with distinct integer x- and y-coordinates. Let T be a complete binary tree storing the points from S at its external nodes, such that the points are ordered left to right by increasing x-coordinates. For each node v in T, let S(v) denote the subset of S consisting of points stored in the subtree rooted at v. For the root r of T, define top(r) to be the point in S = S(r) with maximal y-coordinate. For every other node v, define top(r) to be the point in S with highest y-coordinate in S(v) that is not also the highest y-coordinate in S(u), where u is the parent of v in T (if such a point exists). Such labeling turns T into a priority search tree. Describe a linear-time algorithm for turning T into a priority search tree. Implement this approach.