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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
    input! {
        n: usize,
    }
    let v = enum_divisors(n);
    let mut ans = 0;

    for &nv in &v {
        let num = nv - 1;
        if num != 0 && n / num == n % num {
            ans += num;
        }
    }

    println!("{}", ans);
}

fn enum_divisors(n: usize) -> Vec<usize> {
    let mut res = vec![];
    let mut i = 1;
    while i * i <= n {
        if n % i == 0 {
            res.push(i);
            if n / i != i {
                res.push(n / i);
            }
        }
        i += 1;
    }
    res.sort();
    res
}