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,x,y,maxp=-2000000000,maxd=-2000000000,minp=2000000000,mind=2000000000;
    cin>>n;
    for (int i=0;i<n;i++)
    {
        cin>>x>>y;
        maxp=max(maxp,x+y);
        minp=min(minp,x+y);
        maxd=max(maxd,x-y);
        mind=min(mind,x-y);
    }
    cout<<max(maxp-minp,maxd-mind);
    return 0;
}
