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 
fscanf(STDIN, "%d", $N);
$n = $N; //素因数分解を行う数字 
$init = 2; //１以外の最初の素数 
$count = 0;
$result = [];
while ($n !== 1) { //$nが1になるまで繰り返す 
  $i = $init; 
  while (true) { //$iの上限を設定 
    if ($n % $i == 0 && !in_array($i, $result)) { //$nが$iで割り切れた場合 
      $result[] = $i; //$iを素因数として配列に格納 
      $n /= $i; //$nを$iで割って$nに代入。 
      break; //Whileを抜ける 
    } $i++; //$iに1をプラス 
  } 
  $count++;
  $init = $i; 
}

print_r ($count);
?>