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;
 

int main()
{
	ios_base::sync_with_stdio(false);
    cin.tie(NULL);
	int n;
	cin>>n;
	int m=INT_MAX,ma=INT_MIN;
	int m1=INT_MAX,ma1=INT_MIN;
	int x,y;
	for(int i=0;i<n;i++)
	{
			cin>>x>>y;
			m=min(m,x+y);
			m1=min(m1,x-y);
			ma=max(ma,x+y);
			ma1=max(ma1,x-y);
	}
	cout<<max(abs(m-ma),abs(m1-ma1))<<endl;
	return 0;
}