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: Time Limit Exceeded)

<?php

$n = (int)fgets(STDIN);

//素数判定関数
function is_prime($n) {
    if ($n < 2) {
        return false;
    } else if ($n == 2) {
        return true;
    }

    if ($n % 2 == 0) {
        return false;
    }

    for ($i = 3; $i * $i <= $n; $i += 2) {
        if ($n % $i == 0) {
            return false;
        }
    }
    return true;
}

$p = 1;
$c = 1;
$hoge = 0;
$hokan = [];
while (1) {
    if ($p == $n) {
        break;
    }

    $p = $p + 1;
    if (is_prime($p)) {
    } else {
        continue;
    }

    while (1) {
        $z = pow($p, $c);
        if ($z > $n) {
            $flag = 1;
            break;
        }
        if ($n % $z == 0) {
            if (in_array($z, $hokan)) {
                $c++;
                continue;
            } else {
                $hokan[] = $z;
            }
            $hoge = $hoge + 1;
            break;
        }
        $c++;
    }

    if (isset($flag) && $flag === 1) {
        $flag = 0;
        $c = 1;
        continue;
    }

    $n = $n / $z;
    $p = 1;
    $c = 1;
}

echo $hoge;