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 <bits/stdc++.h>
using namespace std;
#ifdef __DEBUG__
    void debug_out() { cerr << endl; } 
    template <typename Head, typename... Tail>
    void debug_out(Head H, Tail... T) {cerr << " " << H; debug_out(T...);}
    #define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
    #define debug(...) 
#endif

using ll = long long int;
using ull = unsigned long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

int dx[]={1, 0, -1, 0, 1,-1, 1,-1};
int dy[]={0, 1, 0, -1, 1, 1,-1,-1};
const int INT_INF = (int)(2e9);
const ll  LL_INF = (ll)(2e18);

inline void fast_io() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); };
template<typename T, typename S> inline ostream& operator<<(ostream& os, const pair<T, S> p) { cout << "[" << p.first << ";" << p.second << "]"; return os; }
template<typename T, typename S> inline ostream& operator<<(ostream& os, const map<T, S> p) { for (auto el : p) cout << "[" << el.first << ";" << el.second << "]"; return os; }
template<typename T> inline ostream& operator<<(ostream& os, const vector<T>& v) { for (auto el : v) cout << el << " "; return os; }
template<typename T> inline ostream& operator<<(ostream& os, const deque<T>& v) { for (auto el : v) cout << el << " "; return os; }
template<typename T> inline ostream& operator<<(ostream& os, const set<T>& v) { for (auto el : v) cout << el << " "; return os; }
template<typename T> inline vector<T> fetch_vec(int sz) { vector<T> ret(sz); for (auto& elem : ret) cin >> elem; return ret; }

int N;
vector<pll> P;
inline void input(){
    fast_io();
    cin >> N;
    for (int i = 0; i < N; i++)
    {
        ll x,y; cin >> x >> y;
        P.emplace_back(x+y,x-y);
    }
}

void chmax(ll &a, ll b){if(a<b) a=b;};

inline int solve(){
    ll ans = 0;
    sort(P.begin(),P.end());
    chmax(ans, abs(P[0].first - P[N-1].first));
    auto cmp_sec = [](pll a, pll b){return a.second < b.second;};
    sort(P.begin(),P.end(),cmp_sec);
    chmax(ans, abs(P[0].second - P[N-1].second));
    cout << ans << endl;
    return 0;
}   

int main()
{
    input();
    solve();
    return 0;
}