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()
{
	long long int mini=INT_MAX,maxi=0,mini1=INT_MAX,maxi1=INT_MIN,n;
  cin>>n;
  for(int i=0;i<n;i++)
  {
    long long int c,d;
    cin>>c>>d;
    mini=min(mini,c+d);
    maxi=max(maxi,c+d);
    mini1=min(mini1,c-d);
    maxi1=max(maxi1,c-d);
  }
  cout<<max(maxi-mini,maxi1-mini1);

	return 0;
}
