6 The distance between two points p1 = (x1, y1) and p2 = (x2, y2) on the plane can be defined in many different ways. We introduce the following three distances: d1(p1, p2) = |x1 − x2| + |y1 − y2| d2(p1, p2) = q (x1 − x2) 2 + (y1 − y2) 2 d3(p1, p2) = max{|x1 − x2|, |y1 − y2|} For each of these distances compute the maximum number of points that have to be checked for each point x ∈ PL ∩ Z in the nearest neighbors algorithm.