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)

import math
N = int(input())
kazu  = []
ans = 0

def fact(n):
    a = []
    i = 1
    while n % 2 == 0:
        a.append(2 ** i)
        n //= 2
        i += 1
    f = 3
    j = 1
    while f <= math.sqrt(n) + 1:
        if n % f == 0:
            a.append(f ** j)
            n //= f
            j += 1
        else:
            f += 2
            j = 1
    if n != 1:
        a.append(n)
    return a 
"""
while a <= math.sqrt(n) + 1:
    if n % a == 0:
        kazu.append(a)
        j = 1
        while  n %   
    a += 1
"""
i = 0
kazu = fact(N)
kazu = sorted(kazu)
if len(kazu) == 0:
    ans = 0
else:
    while N > 1:
        
        N = N // kazu[i]
        i += 1
        ans += 1
        
print(ans)