B"You are given n points on the plane. The polygon formed from all the n points is strictly convex, that is, the polygon is convex, and there are no three collinear points (i.e. lying in the same straight line). The points are numbered from 1 to n , in clockwise order. We define the distance between two points p_1 = (x_1, y_1) and p_2 = (x_2, y_2) as their Manhattan distance: d(p_1, p_2) = |x_1 - x_2| + |y_1 - y_2|. Furthermore, we define the perimeter of a polygon, as the sum of Manhattan distances between all adjacent pairs of points on it; if the points on the polygon are ordered as p_1, p_2, ldots, p_k (k geq 3) , then the perimeter of the polygon is d(p_1, p_2) + d(p_2, p_3) + ldots + d(p_k, p_1) . For some parameter k , let's consider all the polygons that can be formed from the given set of points, having any k vertices, such that the polygon is not self-intersecting. For each such polygon, let's consider its perimeter. Over all such perimeters, we define f(k) to be the maximal perimeter. Please note, when checking whether a polygon is self-intersecting, that the edges of a polygon are still drawn as straight lines. For instance, in the following pictures: In the middle polygon, the order of points ( p_1, p_3, p_2, p_4 ) is not valid, since it is a self-intersecting polygon. The right polygon (whose edges resemble the Manhattan distance) has the same order and is not self-intersecting, but we consider edges as straight lines. The correct way to draw this polygon is ( p_1, p_2, p_3, p_4 ), which is the left polygon. Your task is to compute f(3), f(4), ldots, f(n) . In other words, find the maximum possible perimeter for each possible number of points (i.e. 3 to n ). The first line contains a single integer n ( 3 <= q n <= q 3 cdot 10^5 ) -- the number of points. Each of the next n lines contains two integers x_i and y_"...