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 <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <queue>
#include <set>
#include <map>
#define rep(i, n)   for(int i = 0; i < (n); i++)
using namespace std;
typedef long long ll;

int main(){
    int n;  cin>>n;
    vector<int>a(n);
    vector<int>b(n);
    rep(i, n){
        int x,y;    cin>>x>>y;
        a[i] = x+y;
        b[i] = x-y;
    }
    sort(a.begin(), a.end());
    sort(b.begin(), b.end());
    cout << max(a[n-1]-a[0], b[n-1]-b[0]) << endl;
}