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++ (Clang 10.0.0) (judge verdict: Accepted)

#include <iostream>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <cmath>
#define rep(i, n) for(int i = 0; i < (n); i++)
using namespace std;
using P = pair<int, int>;
long mod = (long) 1e9 + 7;

long MAX(long x, long y){
    if(x > y){
        return x;
    } else {
        return y;
    }
}

long MIN(long x, long y){
    if(x < y){
        return x;
    } else {
        return x;
    }
}

int main(){
    
    long n, xmin, xmax, ymin, ymax, ans;
    cin >> n;
    vector<long> x(n,0), y(n,0), z(n,0), w(n,0);
    rep(i,n) cin >> x[i] >> y[i];
    
    xmin = x[0];
    xmax = x[0];
    ymin = y[0];
    ymax = y[0];
    rep(i,n){
        xmin = MIN(xmin, x[i]);
        xmax = MAX(xmax, x[i]);
        ymin = MIN(ymin, y[i]);
        ymax = MAX(ymax, y[i]);
    }

    rep(i,n) z[i] = x[i] - xmin + y[i] - ymin;
    rep(i,n) w[i] = x[i] - xmin + ymax - y[i];
    sort(z.begin(), z.end());
    sort(w.begin(), w.end());

    ans = MAX((z[n-1] - z[0]), (w[n-1] - w[0]));

    cout << ans << "\n";
    
    return 0;
}