Problem:
Score : 500 points

Problem Statement

There are N points on the 2D plane, i-th of which is located on (x_i, y_i).
There can be multiple points that share the same coordinate.
What is the maximum possible Manhattan distance between two distinct points?

Here, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq x_i,y_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the answer.

Sample Input 1

3
1 1
2 4
3 2

Sample Output 1

4

The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.

Sample Input 2

2
1 1
1 1

Sample Output 2

0

Solution in Scala (2.13.1) (judge verdict: Accepted)

object Main extends App {
  val sc = new java.util.Scanner(System.in);
  val n = sc.nextInt();
  val xys = Array.fill(n)((sc.nextInt, sc.nextInt));
  val xys2 = xys.map { case (x, y) => (x + y, x - y) }
  val x_min = xys2.map(_._1).min;
  val x_max = xys2.map(_._1).max;
  val y_min = xys2.map(_._2).min;
  val y_max = xys2.map(_._2).max;
  val answer = (x_max - x_min) max (y_max - y_min);
  println(answer);
}