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>
#define ll long long
using namespace std;
int main()
{
    long long n,ans=0;
    scanf("%lld",&n);
    long long l=1,r;
    while(l<=n)
    {
        r=n/(n/l);
        ll x=l,y=r;
        while(x<=y)
        {
            ll m=x+y>>1;
            if(n/m==n%m) {ans+=m;break;}
            else if(n/m>n%m) y=m-1;
            else x=m+1;
        }
        l=r+1;
    }
    printf("%lld\n",ans);
}