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;
using ll = long long;


/*  
    
*/

void test_case(){
    int n; cin >> n;
    int x[n],y[n];
    for(int i =0; i <n;i++)
        cin >> x[i] >> y[i];
    int p[4][2];
    for(int i = 0; i < 4; i++){
        p[i][0] = x[0];
        p[i][1] = y[0];
    }
    
    
    
    for(int i = 1; i < n; i++){
        int u = x[i] , v = y[i];
        if( (-u - v)  > ( -p[0][0] - p[0][1]) ){
            p[0][0] = u;
            p[0][1] = v;
        }
        
        if( (-u + v)  > ( -p[1][0] + p[1][1] ) ){
            p[1][0] = u;
            p[1][1] = v;
        }
        
        if( (u - v)  > ( p[2][0] - p[2][1] ) ){
            p[2][0] = u;
            p[2][1] = v;
        }
        
        if( u + v > p[3][0] + p[3][1]){
            p[3][0] = u;
            p[3][1] = v;
        }
    
    
    }
    
    ll res = 0;
    for(int i = 0; i <4; i++){
        for(int j = 0; j < 4; j++){
            if(i != j)
                res = max(res, ll(abs(p[i][0]-p[j][0])) + ll(abs(p[i][1] -p[j][1] )) );
        }
    }
    
    cout << res << endl;
    
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int t; t = 1;
    //~ cin >> t;
    while(t--)
        test_case();
    return 0;
}