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 Rust (1.15.1) (judge verdict: Accepted)

fn run() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let n: u64 = s.trim().parse().unwrap();
    let mut ans = 0;
    let mut a = 1;
    while a * a + a < n {
        if (n - a) % a == 0 {
            ans += (n - a) / a;
        }
        a += 1;
    }
    println!("{}", ans);
}

fn main() {
    run();
}