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)

use std::io::Read;
use std::io::{stdout, BufWriter, Write};

fn main() {
    let mut buf = String::new();

    // stdinから全てbufに読み込む
    std::io::stdin().read_to_string(&mut buf).unwrap();

    // 読み込んだ文字列をスペースで分解する
    let mut iter = buf.split_whitespace();

    // about n
    let n: u64 = iter.next().unwrap().parse().unwrap();

    // ans
    let mut ans: u64 = 0;
    
    let mut q = 1;
    while q * q < n {
        if n / q > 0 && n % q == 0 {
            let m = n / q - 1;
            if n / m == n % m {
                ans += m;
            }
        }
        q += 1;
    }

    // 出力
    let out = stdout();
    let mut out = BufWriter::new(out.lock());
    writeln!(out, "{}", ans).unwrap();
}