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 Python (3.8.2) (judge verdict: Accepted)

def main():
    
    import collections

    N = int(input())

    def factorization(num):
        factorize = []
        while (num % 2 == 0):
            num //= 2
            factorize.append(2)
        
        division = 3
        
        while (division * division <= num):
            
            if (num % division == 0):
                factorize.append(division)
                num //= division
            else:
                division += 2
            
        if (num != 1):
            factorize.append(num)
        
        return (factorize)
    
    def count_div(n):
        cnt = 0
        sub = 0
        
        while (n > 0):
            sub += 1
            n -= sub
            if (n >= 0):
                cnt += 1

        return(cnt)

    facts = factorization(N)
    CTR_facts = collections.Counter(facts).most_common()
    
    ans = 0
    
    for i in range(len(CTR_facts)):
        v = CTR_facts[i][1]
        
        tmp = count_div(v)
        ans += tmp
    
    print(ans)


if __name__ == '__main__':
    main()