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.Scanner;

public class Main {
	// Shojin
	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in)) {
			int n = sc.nextInt();
			long plusMax = 0;
			long plusMin = Long.MAX_VALUE;
			long minusMax = 0;
			long minusMin = Long.MAX_VALUE;
			for (int i = 0; i < n; i++) {
				long x = sc.nextLong();
				long y = sc.nextLong();
				plusMax = Math.max(plusMax, x + y);
				plusMin = Math.min(plusMin, x + y);
				minusMax = Math.max(minusMax, y - x);
				minusMin = Math.min(minusMin, y - x);
			}
			System.out.println(Math.max(plusMax - plusMin, minusMax - minusMin));
		}
	}
}