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 Scala (2.13.1) (judge verdict: Wrong Answer)

object Main extends App{
    val n = io.StdIn.readLong
    
    if (n == 1) println(0)
    else if (n == 2) println(1)
    else {
        
        val divisors = (3 to n.toInt by 2).filter(n % _ == 0)
        
        if (divisors.length == 1) println(1)
        else {
            
            def rec(acc: Long, index: Int, count: Int): Int = {
                if (divisors.length-1 < index) count
                else if (acc % divisors(index) == 0) rec(acc/divisors(index), index+1, count+1)
                else rec(acc, index+1, count)
            }
            
            val output = rec(n, 0, 0)
            println(output)
            
        }
    }
}