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 divisors(n: usize) -> Vec<usize> {
    let mut d = vec![];
    for i in 1.. {
        if i * i > n {
            break;
        }
        if n % i == 0 {
            d.push(i);
            if i != n / i {
                d.push(n / i);
            }
        }
    }
    d.sort();
    d
}

fn main() {
    input! {
        n: usize,
    };
    let mut ans = 0;
    for &d_i in divisors(n).iter() {
        if d_i == 1 {
            continue;
        }
        if n % (d_i - 1) == n / (d_i - 1) {
            ans += d_i - 1;
        }
    }
    println!("{}", ans);
}