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;
long long n,a1=1e9,a2=-1e9,b1=1e9,b2=-1e9;
int main()
{
	scanf("%lld",&n);
	for(int i=1;i<=n;i++)
	{
		long long a,b;
		scanf("%lld%lld",&a,&b);
		long long x=a+b,y=a-b;
		a1=min(a1,x);
		a2=max(a2,x);
		b1=min(b1,y);
		b2=max(b2,y);
	}
	printf("%lld\n",max(a2-a1,b2-b1));
	return 0;
}