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++ (Clang 10.0.0) (judge verdict: Accepted)

#include <cmath>
#include <iostream>
using namespace std;
int main() {
    int n; cin >> n;
    int x[n], y[n];
    for (int i = 0; i < n; i++) cin >> x[i] >> y[i];

    long long ans = 0;
    for (long long s : {1, -1}) {
        long long ub = -(1LL<<60), lb = 1LL<<60;
        for (int i = 0; i < n; i++) {
            ub = max(ub, x[i] + s * y[i]);
            lb = min(lb, x[i] + s * y[i]);
        }
        ans = max(ans, ub - lb);
    }
    cout << ans << endl;
}