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 mut divs = vec![];

    for i in 2..=(n as f64).sqrt().ceil() as usize {
        if n % i == 0 {
            divs.push(i-1);
            divs.push(n/i-1);
        }
    }
    divs.push(n-1);

    let mut sum = 0;

    for div in divs {
        if div == 0 {
            continue;
        }
        if n / div == n % div {
            sum += div;
        }
    }

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