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() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << setprecision(20) << fixed;
  int N; cin >> N;
  vector<long long> z, w;
  for(int i = 0; i < N; i++){  
    int x, y; cin >> x >> y;
    z.push_back(x+y);
    w.push_back(x-y);
  }
  sort(z.begin(), z.end());
  sort(w.begin(), w.end());
  cout << max(z[N-1] - z[0], w[N-1] - w[0]) <<endl;
}
