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 <cstdio>
#include <cstdlib>
#include <algorithm>
typedef long long ll;
using namespace std;
ll ans=0,N;
void check(ll d)
{
    if(d!=0&&N/d==N%d) ans+=d;
}
int main()
{
    cin>>N;
    for(ll d=1;d*d<=N;++d)
    {
        if(d*d==N) check(d-1);
        else if(N%d==0) {check(d-1);check(N/d-1);}
    }
    cout<<ans;
    return 0;
}