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.*;
import java.math.*;
public class Main {
    public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		PrintWriter ou = new PrintWriter(System.out);
		int n = Integer.parseInt(sc.next());
		int x , y;
		int za = (int)Math.pow(10 , 9);
		int zb = -(int)Math.pow(10 , 9);
		int wa = (int)Math.pow(10 , 9);
		int wb = -(int)Math.pow(10 , 9);
		for(int i = 0 ; i < n ; i++){
			x = Integer.parseInt(sc.next());
			y = Integer.parseInt(sc.next());
			za = Math.min(x + y , za);
			zb = Math.max(x + y , zb);
			wa = Math.min(x - y , wa);
			wb = Math.max(x - y , wb);
		}
		sc.close();
		ou.println(Math.max(zb - za , wb - wa));
		ou.flush();
	}
}