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 std::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

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

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();

    let divisors = enumerate_divisors(n);
    let mut ans: usize = 0;
    for d in divisors {
        if d == 1 {
            continue;
        }
        let d = d - 1;
        if n / d == n % d {
            ans += d;
        }
    }
    ans.to_string()
}

fn enumerate_divisors(n: usize) -> Vec<usize> {
    let mut divisors = Vec::new();

    let mut i = 1;
    while i * i <= n {
        if n % i == 0 {
            divisors.push(i);
            if n / i != i {
                divisors.push(n / i);
            }
        }
        i += 1;
    }
    divisors.sort();
    return divisors;
}