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;

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0); cout.tie(0);
	long long N; cin >> N;
	long long q = 1;
	while(q * q <= N) ++ q;
	long long ans = 0;
	for(long long m = 1; N / m > q; ++ m) {
		if(N % m == N / m) ans += m;
	}
	for(; q >= 1; -- q) {
		long long m = (N - q) / q;
		if(m && N % m == N / m) ans += m;
	}
	cout << ans;
	return 0;
}