Consider the two-dimensional post office location problem: given n points (x1, y1), . . . , (xn, yn) in the Cartesian plane, find a location (x, y) for a post office that minimizes 1 n n i=1(|xi − x| + |yi − y|), the average Manhattan distance from the post office to these points. Explain how this problem can be efficiently solved by the problem reduction technique, provided the post office does not have to be located at one of the input points.