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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cassert>
#include <functional>
#include <algorithm>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
using namespace std;
using llong = long long;

llong n;
llong ans = 0;

int main() {
    cin >> n;

    llong ans = 0;
    // km + k = k(m + 1)
    for (llong i = 1; i * i <= n; i++) {
        if (n % i == 0) {
            llong d = i - 1;

            if (d != 0 && n / d == n % d) {
                ans += d;
            }

            d = n / i - 1;
            if (d != 0 && n / d == n % d) {
                ans += d;
            }
        }
    }

    cout << ans << endl;

    return 0;
}