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()
{

    long long n,m,i,j,k,a,b,e=-999999999999999,f=99999999999999,g=-9999999999999999,h=99999999999999;

    scanf("%lld",&n);

    for(i=1;i<=n;i++)
    {

        scanf("%lld %lld",&a,&b);

        if(a+b>e)e=a+b;
        if(a+b<f)f=a+b;

        if(a-b>g)g=a-b;
        if(a-b<h)h=a-b;

    }

    printf("%lld\n",max(e-f,g-h));



    return 0;
}
