Problem:
Score : 500 points

Problem Statement

Snuke received a positive integer N from Takahashi.
A positive integer m is called a favorite number when the following condition is satisfied:

The quotient and remainder of N divided by m are equal, that is, \lfloor \frac{N}{m} \rfloor = N \bmod m holds.

Find all favorite numbers and print the sum of those.

Constraints

All values in input are integers.

1 \leq N \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

8

Sample Output 1

10

There are two favorite numbers: 3 and 7. Print the sum of these, 10.

Sample Input 2

1000000000000

Sample Output 2

2499686339916

Watch out for overflow.

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

int main(){
  long long n;
  cin >> n;
  vector<int> data(1,0);
  long long quotient,remainder;
  
  for(long long i=1; i<n; i++){
    quotient = n/i;
    remainder = n%i;
    
    if(quotient == remainder){
      data.push_back(i);
    }
  }
  
  long long sum;
  
  for(long long i=1; i<data.size(); i++){
    sum += data.at(i);
  }
  
  cout << sum << endl;
  
}