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) {
		long INF = Long.MAX_VALUE;
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long xmax = -INF, xmin = INF, ymax = -INF, ymin = INF;
		for(int i = 0; i < N; i++) {
			int x = sc.nextInt();
			int y = sc.nextInt();
			xmax = Math.max(xmax, x+y);
			xmin = Math.min(xmin, x+y);
			ymax = Math.max(ymax, x-y);
			ymin = Math.min(ymin, x-y);
		}
		System.out.println(Math.max(xmax - xmin, ymax - ymin));
	}

}
