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;

#define int long long

#define REP(i, n) for (int(i) = 0; (i) < (n); (i)++)
#define rep(i, n) for (int(i) = 0; (i) < (n); (i)++)

#ifdef DBG
#define log(item) cout << #item << " " << item << endl
#else
#define log(item)
#endif

typedef vector<int> VI;
typedef pair<int, int> PII;

//-------------------

int ans = 0;

signed main(){
    int N;
    cin >> N;

    int ans = 0;

    for(int i = 1; i * i <= N; i++){
        if(N % i == 0){
            int m = N / i;
            m--;
            if(m > i){
                ans += m;
            }
        }
    }

    cout << ans << endl;

    return 0;
}