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
$n=trim(fgets(STDIN));
if($n==1){
  echo 0;
  exit;
}
if($n<10){
  echo ($n==6 or $n==8)?2:1;
  exit;
}
$i=2;
$l=min(pow(10,6),ceil(sqrt($n)));
while($i<=$l){
  if($n%$i==0){
    while($n%$i==0){
      $q[$i]+=1;
      $n/=$i;
    }
  }
  ++$i;
}
if(!isset($q)){
  echo 1;
  exit;
}
($n==1)?$ans=0:$ans=1;
foreach($q as $v){
  $i=1;
  while($i<=$v){
    ++$ans;
    $v-=$i;
    ++$i;
  }
}
echo $ans;