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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

def divisor(x):
    ret = []
    for i in range(1, int(x ** 0.5) + 1):
        if x % i == 0:
            ret.append(i)
            ret.append(x // i)
    return sorted(list(set(ret)))

def prime_factor(n):
    ass = []
    for i in range(2, int(n ** 0.5) + 1):
        while n % i == 0:
            ass.append(i)
            n = n // i
    if n != 1:
        ass.append(n)
    return len(set(ass))==1

n = int(input())

div = divisor(n)[1:]

l=[]
for i in div:
    if prime_factor(i):
        l.append(i)

ans = 0
for i in div:
    if n % i == 0:
        ans += 1
        n //= i
 
print(ans)