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;
long long n, a[200005], b[200005], c[200005], d[200005];
int main(){
       cin>>n;
       for(long long i=1; i<=n; i++){
              cin>>a[i]>>b[i];
              c[i]=a[i]+b[i];
              d[i]=(a[i]-b[i]);
       }
       sort(c+1, c+n+1);
       sort(d+1, d+n+1);
       cout<<max(c[n]-c[1], d[n]-d[1]);
       return 0;
}