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 <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <queue>
#include <string>
#include <set>
#include <cstdint>
#include <numeric>
#define INF 1000000000
#define LLINF 2000000000000000000
#define MOD 1000000007
using namespace std;
#define FOR(i,a,b) for(int i=a;i<b;i++)
#define LOOP(i,N) for(int i=0;i<N;i++)
#define LOOP1(i,N) for(int i=1;i<=N;i++)
typedef pair<int,int> P;
typedef pair<int,pair<int,int> > PP;
#define int long long

signed main(){
  int n;
  cin >> n;
  int a[n], b[n];
  int xt,yt,xb,yb;
  LOOP(i,n){
    cin >> a[i] >> b[i];

    if(i==0){
      xt = xb = a[i]+b[i];
      yt = yb = b[i]-a[i];
    }else{
      int x = a[i] + b[i];
      int y = b[i] - a[i];

      if(xt < x){
        xt = x;
      }
      if(xb > x){
        xb = x;
      }
      if(yt < y){
        yt = y;
      }if(yb > y){
        yb = y;
      }
    }
  }
  int ans = xt-xb;
  if(ans < yt-yb){
    cout << yt-yb << endl;
  }else{
    cout << ans << endl;
  }
  printf("%lld,%lld,%lld,%lld\n", xt,xb,yt,yb);
}