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: Wrong Answer)

#include<iostream>
#include<cstring>
#include<math.h>
#include<algorithm>
#include<queue>
#include<list>
#include<vector>

#define rep(i,a,b) for(int i=a;i<b;i++)

using namespace std;


vector<long long> divisors(int n) {
    vector<long long> res;
    for(int i = 1; i*i <= n; ++i) {
        if(n % i != 0) continue;
        res.push_back(i);
        if(n/i == i) continue; // 上の行で追加済み。
        res.push_back(n/i);
    }
    return res;
}


int main(){

    unsigned long long n;
    cin >> n;

    unsigned long long ans = 0;
    vector<long long>vec = divisors(n);

    for(int i=0;i<vec.size();i++){
        if(vec[i]*vec[i]>=n)ans += vec[i]-1;
    }

    cout << ans << endl;
}