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;
  vector<long long> x45, y45;
  for ( int i = 0; i < n; i++ ) {
    long long x, y;
    cin >> x >> y;
    x45.push_back(x+y);
    y45.push_back(x-y);
  }
  
  sort(x45.begin(), x45.end());
  sort(y45.begin(), y45.end());
  
  cout << max(x45[n-1]-x45[0], y45[n-1]-y45[0]) << endl;
  return 0;
}
