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()
{
    int n ;
    cin>>n;
   vector<int >x,y;int a,b;
    for (int i = 0;i<n;i++)
    {
    cin>>a>>b;
    x.push_back(a+b);
    y.push_back(a-b);
    }
    
    sort(x.begin(),x.end());
    sort(y.begin(),y.end());
    
    cout<<max(x[n-1]-x[0],y[n-1]-y[0]);
    return 0;
}