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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
$n = (int)trim(fgets(STDIN));

$max = (int)ceil(sqrt($n));
$sum = 0;
for ($i=1; $i <= $max; $i++) { 
	if ($n % $i === 0) {
		$m = (int)($n/$i)-1;
		// echo $i . ': ' . $m . PHP_EOL;
		if ($m > 0 && (int)($n/$m) === $n%$m) {
			$sum += $m;
		}
	}
}
echo $sum;