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)

import math
import sys

def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]

n = int(input())

if n <= 1:
    print(0)
    sys.exit()

yakusu = set(make_divisors(n))
yakusu.discard(1)

sosu = set([min(yakusu)])
tansaku = set(yakusu)
kari = set(tansaku)



while 1:
    for var in tansaku:
        if var % max(sosu) == 0:
            kari.discard(var)
    tansaku = set(kari)
    if len(tansaku) == 0:
        break
    sosu.add(min(tansaku))
sosu = sosu | tansaku

i = 1
j = 0
kari = set(sosu)

while n != 1:
    for var in sosu:
        if n % (var ** i) == 0:
            n = n / (var ** i)
            j += 1
        else:
            kari.discard(var)
    sosu = set(kari)

    i += 1
    if i > 1000:
        break

print(j)