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 <bits/stdc++.h>
using namespace std;
long long INF = 1000000000;
int main(){
  int N;
  cin >> N;
  vector<long long> x(N), y(N);
  for (int i = 0; i < N; i++){
    cin >> x[i] >> y[i];
  }
  vector<pair<long long, int>> a(N);
  for (int i = 0; i < N; i++){
    a[i] = make_pair(x[i] + y[i], i);
  }
  vector<pair<long long, int>> b(N);
  for (int i = 0; i < N; i++){
    b[i] = make_pair(x[i] - y[i], i);
  }
  sort(a.begin(), a.end());
  sort(b.begin(), b.end());
  long long ans = 0;
  int p1 = a[0].second;
  int q1 = a[N - 1].second;
  ans = max(ans, abs(x[q1] - x[p1]) + abs(y[q1] - y[p1]));
  int p2 = b[0].second;
  int q2 = b[N - 1].second;
  ans = max(ans, abs(x[q2] - x[p2]) + abs(y[q2] - y[p2]));
  cout << ans << endl;
}