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>
#define rep(i,n) for(int i=0;i<(int)n;i++)
using namespace std;
using ll = long long;
using P = pair<int, int>;

ll f(P a, P b) {
    return abs(a.first - b.first) + abs(a.second - b.second);
}

int main() {
    random_device seed_gen;
    mt19937_64 engine(seed_gen());

    ll n;
    cin >> n;
    vector<pair<ll, ll>> p(n);
    rep(i, n) cin >> p[i].first >> p[i].second;
    ll ans = 0;
    rep(i, 1e7) {
        int a = engine() % (ll)n;
        int b = engine() % (ll)n;
        ans = max(ans, f(p[a], p[b]));
     }
     cout << ans << endl;
    return 0;
}