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 mx1, mx2, mn1, mn2;
  mx1 = mx2 = INT_MIN; mn1 = mn2 = INT_MAX;
  //cout << mx << " " << mn;
  for(int i = 0; i < n; ++i) {
    int x, y;
    cin >> x >> y;
    mx1 = max(mx1, x + y);
    mn1 = min(mn1, x + y);
    mx2 = max(mx2, x - y);
    mn2 = min(mn2, x - y);
  }
  cout << max(abs(mx1 - mn1), abs(mx2 - mn2));
  return 0;
}