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 <vector>
#include <algorithm>
using namespace std;

int main(void){
    int N, xbuf, ybuf;
    int zmax, zmin, wmax, wmin;
    cin >> N;
    for(int i=0; i<N; i++){
        cin >> xbuf >> ybuf;
        if(i==0){
            zmax = xbuf + ybuf;
            zmin = zmax;
            wmax = xbuf - ybuf;
            wmin = wmax;
        }else{
            zmax = max(zmax, xbuf + ybuf);
            zmin = min(zmin, xbuf + ybuf);
            wmax = max(wmax, xbuf - ybuf);
            wmin = min(wmin, xbuf - ybuf);
        }
    }
    cout << max(zmax - zmin, wmax - wmin);
    return 0;
}