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 <algorithm>
#include <climits>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <vector>

using namespace std;
constexpr long long int INF = std::numeric_limits<long long int>::max();
#define int long long int

void solve() {
  // int x;
  // cout << endl;
  int N;
  cin >> N;

  int ans = 0;
  for (int i = 1; 1 < N / i; i++) {
    if (N / i <= i) {
      break;
    }
    int a = (N / i) - 1;
    // cout << a << endl;
    if (N % a == N / a) {
      ans += a;
    }
  }

  cout << ans << endl;
}

signed main() {
  solve();
  return 0;
}