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;
#define ll long long
#define ld long double 
#define foi(a,n) for(int i = a; i < n; i++)
#define ee 1000000007
#define pb push_back

ll fast(ll base, ll power, ll mod=ee){
    ll ans =1;
    base%=mod;
    while(power){
        if(power&1){
            ans*=base;
            ans%=mod;
        }
        base*=base;
        base%=mod;
        power>>=1;
    }
    return ans;
}

void solve() {
    ll n;
    cin >> n;
    vector<pair<int, int>> v(n);
    for(auto &x: v){
		cin >> x.first >> x.second;
	}
	int mx1 = -ee, mx2 = -ee, mx3 = -ee, mx4 = -ee, mn1 = ee, mn2 = ee, mn3 = ee, mn4 = ee;
	for(int i = 0; i < n; i++){
		mx1 = max(mx1, v[i].first + v[i].second);
		mn1 = min(mn1, v[i].first + v[i].second);
		mx2 = max(mx2, v[i].first - v[i].second);
		mn2 = min(mn2, v[i].first - v[i].second);
	}
	cout << max(mx1-mn1, mx2 - mn2);
}

int main() {
	ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    int t = 1;
    //~ cin >> t;
    while(t--){
		solve();
		//~ cout << '\n';
	}
}