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 PHP (7.4.4) (judge verdict: Accepted)

<?php
list($n) = ints();
$i = 1;
$ans = 0;
while (true) {
    $m = intdiv($n - $i,  $i);
    if ($m <= $i) break;
    if (($n - $i) % $i === 0) $ans += $m;
    $i++;
}
echo $ans;
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}