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 <bits/stdc++.h>
using namespace std;
static const long long MOD=1000000007;

int main(){
  long long n;
  cin>>n;
  long long temp=1;
  long long def=1;
  long long def2=1;
  for(int i=0;i<n;i++){
    temp*=10;
    temp%=MOD;
    def*=9;
    def%=MOD;
    def2*=8;
    def2%=MOD;
  }
  
  if(n<2){
    cout<<0<<endl;
    return 0;
  }
      
  cout<<temp-def*2+def2<<endl;
    
  
  
  return 0;
}