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;
 
#define REP(i,n) for(int i=0;i<(n);++i)
#define ll long long
const long long INF = 1LL<<60;
const long long mod = 1e9 + 7;
using Graph = vector<vector<int>>;

int main(){
    int N;
    cin >> N;
    vector<pair<int,int>> A(N);
    REP(i,N) cin >> A[i].first >> A[i].second;

    ll masum = 0;
    ll misum = mod;
    REP(i,N){
        ll s = A[i].first + A[i].second;
        masum = max(masum,s);
        misum = min(misum,s);
    }
    cout << masum - misum << endl;
}