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 REP(i,n) for (int i=0;i<(n);i++)
#define REP2(i,m,n) for (int i=m;i<(n);i++)
typedef long long ll;

ll N;

void solve() {
    cin >> N;
    vector<ll> A;

    for (ll a = 1; a * a <= N; ++a) {
        if (N % a == 0) {
            A.push_back(a);
            if (a * a != N) {
                A.push_back(N/a);
            }
        }
    }

    ll ans = 0;

    for (auto a: A) {
        ll b = (N - a) / a;
        if (b > a)
            ans += b;
    }

    cout << ans << endl;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    solve(); 
}