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();
		long[] XplusY = new long[N];
		long[] XminusY = new long[N];
		for(int i=0; i<N; i++) {
			int x = sc.nextInt();
			int y = sc.nextInt();
			XplusY[i] = (long)x + y;
			XminusY[i] = (long)x - y;
		}
		
		Arrays.sort(XplusY);
		Arrays.sort(XminusY);
		
		System.out.println(Math.max(XplusY[N-1]-XplusY[0], XminusY[N-1]-XminusY[0]));
		
		sc.close();
	}
}

