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();
    	int pMax = 0;
    	int pMin = Integer.MAX_VALUE;
    	int mMax = Integer.MIN_VALUE;
    	int mMin = Integer.MAX_VALUE;
    	for (int i = 0; i < n; i++) {
    	    int x = sc.nextInt();
    	    int y = sc.nextInt();
    	    pMax = Math.max(pMax, x + y);
    	    pMin = Math.min(pMin, x + y);
    	    mMax = Math.max(mMax, x - y);
    	    mMin = Math.min(mMin, x - y);
    	}
	    System.out.println(Math.max(pMax - pMin, mMax - mMin));
	}
}