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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

double distance (double x1, double x2, double y1, double y2) {
  return abs(x1 - x2) + abs(y1 - y2);
}

int main () {
  ll N;
  cin >> N;

  vector<ll> x(N);
  vector<ll> y(N);

  ll sumx = 0;
  ll sumy = 0;
  for (ll i = 0; i < N; i++) {
    cin >> x[i] >> y[i];
    sumx += x[i];
    sumy += y[i];
  }
  double cx = sumx / N;
  double cy = sumy / N;

  double far = 0;
  ll farIndex = -1;
  for (ll i = 0; i < N; i++) {
    double dist = distance(cx, x[i], cy, y[i]);
    if (far <= dist) {
      far = dist;
      farIndex = i;
    }
  }

  ll ans = 0;
  for (ll i = 0; i < N; i++) {
    ll dist = distance(x[farIndex], x[i], y[farIndex], y[i]);
    if (ans < dist) {
      ans = dist;
    }
  }

  cout << ans << endl;
}