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 <cmath>
#include <iostream>
#include <string>
#include <tuple>
#include <vector>

using namespace std;
typedef long long int ll;
typedef vector<int> vi;
typedef vector<vi> vvi;

#define INF (1e9)

ll N;

int main() {
    cin >> N;
    ll ans = 0;
    for (ll i = 1; i * i <= N; i++) {
        if (N % i != 0) continue;
        if (i - 1 > N / i)
            ans += i - 1;
        if (N / i == i) continue;
        if (N / i - 1 > i)
            ans += N / i - 1;
    }

    cout << ans << endl;
    return 0;
}