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>
using namespace std;
int x[200010],y[200010],n,cmax,cmin=1999999999+10,dmax,dmin=1999999999+10,mx=999999999+1;
int main()
{
    int i;
    cin>>n;
    for(i=1;i<=n;i++)
    {
        cin>>x[i]>>y[i];
        cmax=max(cmax,x[i]+y[i]);
        cmin=min(cmin,x[i]+y[i]);
        dmax=max(dmax,x[i]+mx-y[i]);
        dmin=min(dmin,x[i]+mx-y[i]);
    }
    cout<<max(cmax-cmin,dmax-dmin);
    cin>>i;
}
    
