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<iostream>
#include<algorithm>
using namespace std;
int main()
{
  int n,i,x,y,pa,pi,ma,mi;
  cin >> n;
  cin >> x >> y;
  pa=x+y;
  pi=x+y;
  ma=y-x;
  mi=y-x;
  for(i=1;i<n;i++){
    cin >> x >> y;
    pa=max(pa,x+y);
    pi=min(pi,x+y);
    ma=max(ma,y-x);
    mi=min(mi,y-x);
  }
  cout << max(pa-pi,ma-mi) << endl;
  return 0;
}