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{
    
    static final int MOD = (int)1e9 + 7;
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        long amin = (long)2e9;
        long amax = (long)-2e9;
        long bmin = (long)2e9;
        long bmax = (long)-2e9;
        for(int i=0; i<n; i++){
            long x = Integer.parseInt(sc.next());
            long y = Integer.parseInt(sc.next());
            amin = Math.min(amin, x+y);
            amax = Math.max(amax, x+y);
            bmin = Math.min(bmin, x-y);
            bmax = Math.max(bmax, x-y);
        }
        
        System.out.println(Math.max(amax-amin, bmax-bmin));
    }
    
}