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: Accepted)

#include<bits/stdc++.h>
using namespace std;
constexpr int64_t mod=1e9+7;

int main()
{
  int64_t n;
  cin>>n;
  
  
  //divisor n
  std::vector<int64_t> div;
  for (int64_t i = 1; i*i < n; ++i)
  {
    if(n%i==0){
      div.push_back(n/i);
    }
  }

  int64_t ans=0;
  for(auto&& e: div) {
    e-=1;
    if(n%e==(n-n%e)/e){
      ans+=e;
    }
  }
  cout<<ans;
}