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)

#[allow(unused_macros)]
macro_rules! invec {
    ( $t:ty ) => {{
        let mut s = String::new();
        match std::io::stdin().read_line(&mut s) {
            Ok(0) => Vec::<$t>::new(),
            Ok(n) => s.trim().split_whitespace().map(|s| s.parse::<$t>().unwrap()).collect::<Vec<$t>>(),
            Err(_) => Vec::<$t>::new(),
        }
    }}
}

#[allow(unused_macros)]
macro_rules! input {
    ( $($t:ty),* ) => {{
        let mut s = String::new();
        std::io::stdin().read_line(&mut s);
        let mut splits = s.trim().split_whitespace();
        ($(
            {
                 splits.next().unwrap().parse::<$t>().unwrap()
            },
        )*)
    }}
}

fn divisors(n: u64) -> Vec<u64> {
    let mut res = vec![];

    for i in (1..(((n as f64).sqrt().floor() as u64) + 1)).rev() {
        if n % i == 0 {
            res.insert(0, i);
            if i != n / i {
                res.push(n / i);
            }
        }
    }

    return res;
}

#[allow(unused_must_use)]
#[allow(unused_variables)]
fn solve() {
    let (n, ) = input!(u64);

    let divisors = divisors(n);
    let mut total = 0;

    for div in &divisors[1..divisors.len()] {
        let candidate = div - 1;
        if n / candidate == n % candidate {
            total += candidate;
        }
    }

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

fn main() {
    solve();
}