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
#include <stdio.h>
#include <algorithm>
int x[200010],y[200010];
int main()
{
	int a;
	scanf("%d",&a);
	for(int i=1;i<=a;i++)
	{
		int b,c;
		scanf("%d%d",&b,&c);
		x[i] = b-c;
		y[i] = b+c;
	}
	std::sort(x+1,x+a+1);
	std::sort(y+1,y+a+1);
	long long int s1 = x[a]-x[1];
	long long int s2 = y[a]-y[1];
	printf("%lld",s1>s2?s1:s2);
}