Problem:
Score : 400 points

Problem Statement

Given is a positive integer N. Consider repeatedly applying the operation below on N:

First, choose a positive integer z satisfying all of the conditions below:

z can be represented as z=p^e, where p is a prime number and e is a positive integer;

z divides N;

z is different from all integers chosen in previous operations.

Then, replace N with N/z.

Find the maximum number of times the operation can be applied.

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 maximum number of times the operation can be applied.

Sample Input 1

24

Sample Output 1

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=12.)

Choose z=3 (=3^1). (Now we have N=4.)

Choose z=4 (=2^2). (Now we have N=1.)

Sample Input 2

1

Sample Output 2

0

We cannot apply the operation at all.

Sample Input 3

64

Sample Output 3

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=32.)

Choose z=4 (=2^2). (Now we have N=8.)

Choose z=8 (=2^3). (Now we have N=1.)

Sample Input 4

1000000007

Sample Output 4

1

We can apply the operation once by, for example, making the following choice:

z=1000000007 (=1000000007^1). (Now we have N=1.)

Sample Input 5

997764507000

Sample Output 5

7

Solution in PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
$N = (int)fgets(STDIN);
if ($N === 1) {
    echo 0;
    return;
}

$sqrt_N = (int)sqrt($N) + 1;

$map_of_prime = [];
for ($i = 2; $i < $sqrt_N; $i++) {
    $map_of_prime[$i] = 0;
    while ($N % $i === 0) {
        $map_of_prime[$i] += 1;
        $N = $N / $i;
    }
}

$ans = 0;
foreach ($map_of_prime as $prime) {
    if ($prime > 0) {
        $i = 1;
        while ($prime >= $i) {
            $ans += 1;
            $prime -= $i;
            $i += 1;
        }
    }
}

echo $ans ? $ans : 1;