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.*;
import java.io.*;
 
public class Main{
  Scanner sc = new Scanner(System.in);	
 
  public void run(){
    int n = sc.nextInt();
    
    long MAX = 1234567891L;
    long posMax = -MAX;
    long posMin = MAX;
    long negMax = -MAX;
    long negMin = MAX;
    
    for(int i = 0 ;i < n ; i++){
      long x = sc.nextInt();
      long y = sc.nextInt();
      
      long pos = x+y;
      long neg = x-y;
      posMax = Math.max(posMax, pos);
      posMin = Math.min(posMin, pos);
      negMax = Math.max(negMax, neg);
      negMin = Math.min(negMin, neg);
    }
    
    System.out.println(Math.max(posMax-posMin, negMax-negMin));
  }
  public static void main(String[] args){
    Main m = new Main();
    m.run();
  }
}
