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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
typedef long long ll;

int main()
{
    ll n;
    ll ans = 0;

    scanf("%lld", &n);

    for (ll mod = 1; mod * mod <= n; mod++) {

        ll valid = n / mod;
        ll invalid = n / (mod + 1);

        while (llabs(valid - invalid) > 1) {
            ll mid = (valid + invalid) / 2;

            if (n % mid <= mod) {
                valid = mid;
            }
            else {
                invalid = mid;
            }
        }

        if (n % valid == mod) {
            ans += valid;
        }
    }

    printf("%lld\n", ans);

    return 0;
}