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>
#include <queue>
using namespace std;
int main(){
	long long int N; cin >> N; 
	vector<long long int> D; 
	for(long long int i = 1; i * i <= N; i++){
		if(N % i == 0){
			D.push_back(i-1); 
			if(i * i != N) D.push_back(N/i-1); 
		}
	}
	long long int ans = 0; 
	for(int i = 0; i < D.size(); i++){
		if(D.at(i) == 0) continue; 
		long long int a = N / D.at(i); 
		long long int b = N % (D.at(i)); 
		if(a == b) ans += D.at(i); 
	}
	cout << ans << endl; 
}