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;
#define REP(i, n) for(int i=0; i<(int)(n); i++)
int main(){
long N, ans=0; cin >> N; long a, b, x[N], y[N], minX=1e10, minY=1e10, maxX=-1e10, maxY=-1e10;
REP(i, N){ 
  cin >> a >> b; x[i]=a-b; y[i]=a+b;
  minX=min(minX, x[i]);minY=min(minY, y[i]);
  maxX=max(maxX, x[i]);maxY=max(maxY, y[i]);
}
ans=max(maxX-minX, maxY-minY);
cout << abs(ans) << "\n";
}