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)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};
fn main() {
    input! {//
        n:usize,
    }
    let divisors = divisor(n);

    let mut ans = 0;
    for &m in divisors.iter() {
        let x = n / m;
        // m*x = n
        if m > 1 && (m - 1) > x {
            ans += m - 1;
        }
    }
    println!("{}", ans);
}
pub fn divisor(n: usize) -> Vec<usize> {
    let mut res = Vec::new();
    for i in (1..).take_while(|x| x * x <= n) {
        if n % i == 0 {
            res.push(i);
            if i != n / i {
                res.push(n / i);
            }
        }
    }
    res.sort();
    res
}