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<algorithm>
using namespace std;
 
int main()
{
  int i,j,k,n,d1[200000],d2[200000],x,y;
  cin >> n;
  for(int i=0,x,y; i<n; i++)
  {
    cin>>x>>y;
	d1[i]=(x+y);
    d2[i]=(x-y);
  }
  sort(d1,d1+n);
  sort(d2,d2+n);
  cout<<max(d1[n-1]-d1[0],d2[n-1]-d2[0])<<endl;
}