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 s  = new Scanner(System.in);
          	int n = s.nextInt();
          	int max = 0;
          	int[] Xs = new int[n];
          	int[] Ys = new int[n];
          	int[] sums = new int[n];
          	int[] diffs = new int[n];
          	for(int i = 0;i<n;i++){
            	Xs[i] = s.nextInt();
              	Ys[i] = s.nextInt();
              	sums[i] = Xs[i]+Ys[i];
              	diffs[i] = Xs[i]-Ys[i];
            }
          Arrays.sort(sums);
          Arrays.sort(diffs);
          int res1 = sums[n-1]-sums[0];
          int res2 = diffs[n-1] - diffs[0];
          System.out.println(Math.max(res1,res2));
        }
    }