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>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;

#define MOD 1000000007LL

#define rep(i, n) for(ll (i) = 0LL;(i) < (ll)(n);(i)++)
#define rep2(i, s, e) for(ll (i) = (ll)(s);(i) < (ll)(e);(i)++)
#define repi(i, n) for(ll (i) = 0LL;(i) <= (ll)(n);(i)++)
#define repi2(i, s, e) for(ll (i) = (ll)(s);(i) <= (ll)(e);(i)++)
#define per(i, n) for(ll (i) = (ll)(n) - 1LL;(i) >= 0LL;(i)--)
#define per2(i, s, e) for(ll (i) = (ll)(s) - 1LL;(i) >= (ll)(e);(i)--)
#define peri(i, n) for(ll (i) = (ll)(n);(i) >= 0LL;(i)--)
#define peri2(i, s, e) for(ll (i) = (ll)(s);(i) >= (ll)(e);(i)--)
#define iter(i, it) for(auto &(i): (it))

template<typename T, typename U> ostream& operator<<(ostream &s, const pair<T, U> m) {
    cout << "(" << m.first << ", " << m.second << ")";
    return s;
}
template<typename T, typename U> ostream& operator<<(ostream &s, const map<T, U> m) {
    ll c = 0;
    cout << "{ ";
    iter(i, m) cout << i << (c++ == m.size() - 1 ? " " : ", ");
    cout << "}";
    return s;
}
template<typename T> ostream& operator<<(ostream &s, const vector<T> &v) {
    cout << "{ ";
    rep(i, v.size()) cout << v[i] << (i == v.size() - 1 ? " " : ", ");
    cout << "}";
    return s;
}
template<typename T> ostream& operator<<(ostream &s, const list<T> &v) {
    ll c = 0;
    cout << "{ ";
    iter(i, v) cout << i << (c++ == v.size() - 1 ? " " : ", ");
    cout << "}";
    return s;
}

int main(void) {
    ll N;
    cin >> N;
    ll mini = numeric_limits<ll>::max(), maxi = 0;
    rep(i, N) {
        ll x, y;
        cin >> x >> y;
        ll temp = x + y;
        mini = min(mini, temp);
        maxi = max(maxi, temp);
    }
    cout << maxi - mini << endl;
    return 0;
}