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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int inf=1e9; 
int main()
{
	int n;
	ll a=-inf,b=inf,c=-inf,d=inf;
	scanf("%d",&n);
	ll x,y;
	for(int i=1;i<=n;i++)
	{
		scanf("%lld%lld",&x,&y);
		a=max(x+y,a);
		b=min(x+y,b);
		c=max(x-y,c);
		d=min(x-y,d);
	}
	printf("%lld",max(a-b,c-d));
}