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 <bits/stdc++.h>
using namespace std;

const int N = 1100000;

int main() {
#ifdef Hwang_Baek_I
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w", stdout);
#endif
	ios::sync_with_stdio(0);
	cin.tie(0); cout.tie(0);
	long long n; cin >> n;
	set<long long> S;
	for (int i = 1; (long long)i * i <= n; i++) {
		if (n % i) continue;
		long long m, k;
		m = i - 1, k = n / i;
		if (m > k) S.insert(m);
		m = n / i - 1, k = i;
		if (m > k) S.insert(m);
	}
	long long ans = 0;
	for (long long t : S) ans += t;
	cout << ans << endl;
	return 0;
}