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 Perl (5.26.1) (judge verdict: Wrong Answer)

my $N=<>;chomp $N;
my $ans=0;
my $num = $N;
for(my $i=2;$i<=(sqrt($N)+1);$i++){
    print "$i $num\n";
    my $count = 0;
    my $sre =1;
    while(){
        if(($num % $i)==0 ){
           $num = $num /$i;
           $count++;
           if( $count == $sre){
             $ans++;
             $sre++;
             $count =0;
           }
        }else{
            last;
        }
    }
    #print "$i $num\n";
    if($num == 1){last;}
}
if($N>1&&$ans==0){$ans=1;}
print "$ans";