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::cmp::*;
use std::io::*;

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();

    // n // m == n % m
    // (n - n % m ) / m == n % m
    // n - n % m == m * (n % m)
    // n == (m + 1) * (n % m)

    let mut i = 1;
    let mut ans = 0;
    while i * i <= n {
        if n % i == 0 {
            if i > 1 && i * (n % (i - 1)) == n {
                ans += i - 1;
            }
            if n / i != i {
                if n / i > 1 && (n / i) * (n % (n / i - 1)) == n {
                    ans += n / i - 1;
                }
            }
        }
        i += 1;
    }
    println!("{}", ans);
}