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 = 1e6+100;
typedef long long ll;
vector<ll> fac;
int main(){
	ll n;
	cin>>n;
	if(n==1){
		puts("0");
		return 0;
	}
	for(ll i=2;i*i<=n;i++){
		if(n%i==0){
			if(i*i==n) fac.push_back(i);
			else{
				fac.push_back(i);
				fac.push_back(n/i);
			}
		}
	}
	fac.push_back(n); 
	ll ans=0;
	for(auto x:fac){
		if(n/(x)==(ll)(n/(x-1))) ans+=(x-1);
	}
	cout<<ans<<endl;
	return 0;
}