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 (1.15.1) (judge verdict: Accepted)

fn divisors(n: u64) -> Vec<u64> {
    let mut ds = Vec::<u64>::new();
    for i in 1..n {
        if i * i > n {
            break;
        }
        if n % i == 0 {
            let j = n / i;
            ds.push(i);
            if j > i {
                ds.push(j);
            }
        }
    }
    ds
}

fn main() {
    let stdin = std::io::stdin();
    let mut stdin = my::io::InputReader::new(stdin.lock());

    let N: u64 = stdin.read();
    let ds = divisors(N);
    let result: u64 = ds.iter().map(|d| d - 1).filter(|&m| m > 0 && N / m == N % m).sum();
    println!("{}", result);
}

mod my {
    pub mod io {
        use std::io::{BufRead, ErrorKind, Result};
        use std::str::{FromStr, from_utf8};
        use std::fmt::Debug;

        pub fn read_word<R: BufRead>(r: &mut R, buf: &mut Vec<u8>)
                                              -> Result<usize> {
            let mut read = 0;
            loop {
                let (done, used) = {
                    let available = match r.fill_buf() {
                        Ok(n) => n,
                        Err(ref e) if e.kind() == ErrorKind::Interrupted => continue,
                        Err(e) => return Err(e)
                    };
                    match available.iter().position(|&x| x == b'\n' || x == b' ') {
                        Some(i) => {
                            buf.extend_from_slice(&available[..i]);
                            (true, i + 1)
                        }
                        None => {
                            buf.extend_from_slice(available);
                            (false, available.len())
                        }
                    }
                };
                r.consume(used);
                read += used;
                if done || used == 0 {
                    return Ok(read);
                }
            }
        }

        pub struct InputReader<R: BufRead> {
            reader: R,
            buf: Vec<u8>,
        }

        impl<R: BufRead> InputReader<R> {
            pub fn new(reader: R) -> InputReader<R> {
                InputReader {
                    reader: reader,
                    buf: Vec::<u8>::new(),
                }
            }

            pub fn read_word(&mut self) {
                read_word(&mut self.reader, &mut self.buf);
            }
            
            pub fn read<T>(&mut self) -> T
                where T: FromStr,
                      T::Err: Debug
            {
                self.buf.clear();
                self.read_word();
                from_utf8(&self.buf).unwrap().trim().parse().unwrap()
            }
        }
    }
}