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 <string>
#include <functional>
#include <algorithm>
#include <math.h>

using namespace std;

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

	long long cnt = 0;
	for (int i = 1; i < sqrt(n); i++)
	{
		if (n % i == 0)
		{
			if (i != 1)
			{
				if (n / (i - 1) == n % (i - 1))
					cnt += i - 1;
			}
			if (n / (n / i - 1) == n % (n / i - 1))
				cnt += n/i - 1;
		}
	}

	cout << cnt << endl;

	return 0;
}