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;
typedef long long ll;
typedef pair<ll, ll> P;
ll INFL = 1000000000000000010;//10^18 = 2^60
int INF = 2147483600;//10^9
ll MOD  = 1000000007;

ll N;
//約数の列挙O(√n)
vector<P> divisor(ll n){
    vector<P> res(0);
    for(ll i = 1; i * i <= n; i++){
        if(n % i == 0){
            res.push_back({n/i, i});
        }
    }
    return res;
}
void solve(){
    cin >> N;
    ll res = 0;
    vector<P> list = divisor(N);
    for(int i = 0; i < list.size(); i++){
        ll f = list.at(i).first, s = list.at(i).second;
        if(f-1 > s)res += f - 1;
    }
    cout << res << endl;
}


int main(void){
    solve();
}