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() {
  int n;
  cin>>n;
  int plus[n];
  int x_y[n];
  int y_x[n];

  for(int i=0; i<n; i++) {
    int x,y;
    cin>>x>>y;
    plus[i] = x+y;
    x_y[i] = x-y;
    y_x[i] = y-x;
  }

  sort(plus, plus+n);
  sort(x_y, x_y+n);
  sort(y_x, y_x+n);

  int tmp1 = plus[n-1] - plus[0];
  int tmp2 = x_y[n-1] + y_x[n-1];

  cout<<max(tmp1, tmp2)<<endl;


  return 0;
}