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: Time Limit Exceeded)

<?php
class MyTest {
    public function run() {
        fscanf(STDIN, "%d", $a); 
        $ret = 0;
        for($i=1; $i < $a; $i++) {
            if (floor($a/$i) == $a%$i) {
                $ret += $i;
            }
        }
        echo "{$ret}\n";
    }
    
}

MyTest::run();