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 <cmath>
#include <string>
#include <vector>
#include <iostream>
#include <algorithm>
#include <functional>
using namespace std;
const int mod = 1000000007;
int main() {
	int N;
	cin >> N;
	vector<int> X(N), Y(N);
	for (int i = 0; i < N; ++i) {
		cin >> X[i] >> Y[i];
		int xa = X[i] + Y[i];
		int xb = X[i] - Y[i];
		X[i] = xa; Y[i] = xb;
	}
	int xl = *min_element(X.begin(), X.end());
	int xr = *max_element(X.begin(), X.end());
	int yl = *min_element(Y.begin(), Y.end());
	int yr = *max_element(Y.begin(), Y.end());
	cout << max(xr - xl, yr - yl) << endl;
	return 0;
}