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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;
#define ll long long

vector<long long> divisor;

int calculateDivisor(long long N) {
    for (long long i = 1; i * i < N; ++i) {
        if (N % i == 0) {
            divisor.push_back(i);
        }
    }
    return 0;
}

long long solve(long long N) {
    long long M = divisor.size();
    long long ans;
    for (long long i = 1; i < M; ++i) {
        long long num = divisor[i] - 1;
        long long quotient = num / i;
        long long remainder = num % i;
        if (quotient == remainder) {
            ans += i;
        }
    }
    return ans;
}


int main() {

    long long N;
    cin >> N;
    long long ans;
    calculateDivisor(N);
    ans = solve(N);
    cout << ans << endl;

    return 0;
}