LetSbe a set ofnpoints in the plane with distinct integerx- andycoordinates. LetTbe a complete binary tree storing the points fromSat its external nodes, such that the points are ordered left-to-right by increasingx-coordinates. For each nodevinT, letS(v) denote the subset ofSconsisting of points stored in the subtree rooted atv. For the rootrofT, definetop(r) to be the point inS=S(r) with maximumy-coordinate. For every other nodev, definetop(r) to be the point inSwith highestycoordinate inS(v) that is not also the highesty-coordinate inS(u), whereuis the parent ofvinT(if such a point exists). Such labeling turnsTinto apriority search tree. Describe a linear-time algorithm for turningTinto a priority search tree.