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;
const int N=2e5+1000;
typedef long long ll;
int n;
ll x,y;
ll a[N],b[N];
int main()
{
  scanf("%d",&n);
  for(int i=1;i<=n;i++)
  {
    scanf("%lld %lld",&x,&y);
    a[i]=x+y;
    b[i]=x-y;
  }
  sort(a+1,a+1+n);sort(b+1,b+1+n);
  cout<<max((a[n]-a[1]),(b[n]-b[1]))<<endl;
}
