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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
using namespace std;
using ll = long long;
using P = pair<int, int>;

int main() {
  ll n;
  cin >> n;

  vector<ll> div;
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      div.push_back(i);
      if (i != n / i) div.push_back(n / i);
    }
  }

  ll ans = 0;
  for (auto x : div) {
    ll m = n / x - 1;
    if (m == 0) continue;
    if (n / m == n % m) ans += m;
  }
  cout << ans << endl;
  return 0;
}