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 = intval(fgets(STDIN));
$sum = 0;
foreach(divisor($N) as $div){
    $div--;
    if($div == 0)continue;
    if($N % $div == floor($N/$div)){
        $sum+=$div;
    }
}
echo $sum;

function divisor($n){
    for($i = ceil(sqrt($n)); $i >= 1; $i--){
        if($n % $i == 0){
            $f[] = $i;
            $f[] = $n / $i;
        }
    }
    sort($f);
    return array_unique($f);
}