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 <bits/stdc++.h>
#pragma GCC optimize("unroll-loops,no-stack-protector")
#pragma GCC target("sse,sse2,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define watch(x) cout << (#x) << " is " << (x) << endl
#define debug cout << "hi" << endl

using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;

const int MOD = 1e9 + 7;
const int INF32 = 1<<30;
const ll INF64 = 1LL<<60;

int main()
{
	#ifndef ONLINE_JUDGE
	freopen(".in.txt", "r", stdin);
	freopen(".out.txt", "w", stdout);
	#endif
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	int n, mini1 = INF32, mini2 = INF32, maxi1 = 0, maxi2 = 0; cin >> n;
	for(int i = 0; i < n; i++)
	{
		int x, y; cin >> x >> y;
		mini1 = min(mini1, x + y);
		maxi1 = max(maxi1, x + y);
		mini2 = min(mini2, x - y);
		maxi2 = max(maxi2, x - y);
	}
	cout << max(abs(maxi1 - mini1), abs(maxi2 - mini2));

	return 0;
}