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 <iostream>
#include <algorithm>
#include <vector>
#include <cmath>
#include <string>
#include <map>
#include <set>
#include <queue>

#define ll long long
#define REP(i,n) for(int i = 0; i < (n); ++i)
#define PI 3.141592653589
#define MOD 1000000007

using namespace std;

template<typename T> T gcd(T a, T b){ return (a % b)? gcd(b, a%b) : b; }
template<typename T> T lcm(T a, T b){ return a * b / gcd(a, b); }

ll f(int d, pair<ll, ll> x){
    if(d == 0) return x.first - x.second;
    return x.first + x.second;
}

int main(void){
    int n;
    cin >> n;
    pair<ll, ll> r[n];
    REP(i,n){
        cin >> r[i].first >> r[i].second;
    }

    ll ans = -1;
    REP(d,2){
        ll M = -1, m = (ll)3*10e9;
        REP(i,n){
            M = max(f(d, r[i]), M);
            m = min(f(d, r[i]), m);
        }
        ans = max(ans, M-m);
    }
    cout << ans << endl;
    
    return 0;
}