Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

3
1 1
2 4
3 2

Sample Output 1

4

The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.

Sample Input 2

2
1 1
1 1

Sample Output 2

0

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
using namespace std;
using ll = long long;

int main() {
  ll n;
  cin >> n;
  ll ppmax = -1e10, ppmin = 1e10;
  ll pmmax = -1e10, pmmin = 1e10;
  for (int i = 0; i < n; i++) {
    ll x, y;
    cin >> x >> y;
    ppmax = max(ppmax, x + y);
    ppmin = min(ppmin, x + y);
    pmmax = max(pmmax, x - y);
    pmmin = min(pmmin, x - y);
  }
  cout << max(ppmax - ppmin, pmmax - pmmin) << endl;
}