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 <iostream>
#include <string>
#include <vector>

using namespace std;
int main()
{
	int N, a, b, r, dist, di, maxr, minr;
	a = 0; b = 0; maxr = 0; minr = 0; r = 0;
	int maxxy[2] = { 0,0 };
	int minxy[2] = { 0,0 };
	cin >> N;

	cin >> a >> b;
	maxr = r;
	minr = r;
	maxxy[0] = a, maxxy[1] = b;
	minxy[0] = a; minxy[1] = b;

	for (int i = 1; i < N; i++) {
		cin >> a >> b;
		r = a + b;
		if (r > maxr) {
			maxr = r;
			maxxy[0] = a, maxxy[1] = b;
		}
		if (r < minr) {
			minr = r;
			minxy[0] = a; minxy[1] = b;
		}
	}
	cout << maxxy[0] + maxxy[1] - minxy[0] - minxy[1];
	return 0;
}