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: Time Limit Exceeded)

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

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	int N;
	cin >> N;
	vector<int[2]> v(N);
	int ans = 0;
	for (int i = 0; i < N; i++) {
		cin >> v[i][0] >> v[i][1];
	}
	for (int i = 0; i < N - 1; i++) {
		for (int j = i + 1; j < N; j++) {
			int d = abs(v[i][0] - v[j][0]) + abs(v[i][1] - v[j][1]);
			if (d > ans) {
				ans = d;
			}
		}
	}
	cout << ans << "\n";
	return 0;
}