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: Accepted)

<?php
fscanf(STDIN, "%d", $N);
$divs = [];
$sqrt = sqrt($N);
for ($i = 2; $i < $sqrt; $i++) {
    while(true) {
        if ($N % $i === 0) {
            !isset($divs[$i]) ? $divs[$i] = 1 : $divs[$i]++;
            $N /= $i;
        } else {
            break;
        }
    }
}
if (isPrime($N)) {
    !isset($divs[$N]) ? $divs[$N] = 1 : $divs[$N]++;
}
$ans = 0;
foreach ($divs as $k => $v) {
    $a = 1;
    while(true) {
        if ($v >= $a) {
            $v -= $a;
            $ans++;
            $a++;
        } else {
            break;
        }
    }
}

printf("%d", $ans);

function isPrime($x) {
    $bool = true;
    if ($x === 1) {
        return false;
    }
    for ($i = 2; $i <= sqrt($x); $i++) {
        if ($x % $i === 0) {
            $bool = false;
            break;
        }
    }
    return $bool;
}