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 (Clang 3.8.0) (judge verdict: Accepted)

#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<iostream>
#include<queue>
#include<vector>
#include <bitset>
#include<math.h>
using namespace std;
#define INF 10000000
#define MOD 1000000007
typedef long long ll;
typedef pair<ll,int> P;


int main(){
    ll N,ans=0;
    cin>>N;
    for(ll i=1;i<=1000000;i++){
        ll x=N-i;
        if(x%i!=0) continue;
        ll num=x/i;
        if(num<=i) continue;
        ans+=num;
    }
    cout<<ans<<endl;
}