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;
const int64_t INF = (1LL << 62);

int main()
{
  int64_t N, x, y;
  cin >> N;
  int64_t mis = INF, mas = -INF, mid = INF, mad = -INF;
  for (int i = 0; i < N; i++)
  {
    cin >> x >> y;
    mis = min(mis, x + y);
    mas = max(mas, x + y);
    mid = min(mid, x - y);
    mad = max(mad, x - y);
  }
  cout << max(mas - mis, mad - mid) << endl;
}
