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 q,x,y;
long long mx1=INT_MIN,mx2=INT_MIN,mn1=INT_MAX,mn2=INT_MAX;
int main()
{
    cin >> q;
    while(q--)
    {   cin>>x>>y;
        if(y+x>mx1)mx1=y+x;
        if(y-x>mx2)mx2=y-x;
        if(y+x<mn1)mn1=y+x;
        if(y-x<mn2)mn2=y-x;
    }
    cout<< max(abs(mx1-mn1), abs(mx2-mn2));
}
 