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<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
int main()
{
	int n,x,y;
	int maxn=-1e11,maxx=1e11,minx=-1e11,minn=1e11;
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>x>>y,maxn=max(x+y,maxn),maxx=min(x+y,maxx),minx=max(x-y,minx),minn=min(x-y,minn);
	cout<<max(maxn-maxx,minx-minn)<<endl;	
	return 0;
}
