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.

Examples

Input

3
1 1
2 4
3 2


Output

4


Input

2
1 1
1 1


Output

0

import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    long v1 = 0;
    long v2 = Long.MAX_VALUE;
    long w1 = (-1) * Long.MAX_VALUE;
    long w2 = Long.MAX_VALUE;
    for(int i = 0; i < n; i++) {
      long x = sc.nextLong();
      long y = sc.nextLong();
      long v = x + y;
      long w = x - y;
      v1 = Math.max(v1, v);
      v2 = Math.min(v2, v);
      w1 = Math.max(w1, w);
      w2 = Math.min(w2, w);
    }
    long ans = Math.max(v1 - v2, w1 - w2);
    System.out.println(ans);
  }
}