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: Wrong Answer)

def get_primes_til(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n ** .5) + 1):
        if is_prime[i]:
            for j in range(2 * i, n + 1, i):
                is_prime[j] = False
    return {i for i in range(2, n + 1) if is_prime[i]}


def factor(n):
    res = []
    for i in range(2, int(n ** .5) + 1):
        while n % i == 0:
            res.append(i)
            n //= i
    if n > 1:
        return res + [n]
    else:
        return res


primes = get_primes_til(10 ** 6)
z_candids = []
for p in primes:
    z = p
    z_candids.append(z)
    while z <= 10 ** 6:
        z *= p
        z_candids.append(z)
z_candids.sort()

N = int(input())
if len(factor(N)) == 1:
    print(1)
    exit()
cnt = 0
for z_candid in z_candids:
    if N % z_candid:
        continue
    N //= z_candid
    cnt += 1
print(cnt)