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)

# D - Div Game
from collections import defaultdict
from math import sqrt
from typing import ValuesView


def prime_factorize_indices(n: int) -> ValuesView[int]:
    """Prime factorization of n (trial division)."""
    if n < 1:
        raise ValueError

    prime_factors = defaultdict(int)
    while n % 2 == 0:
        n //= 2
        prime_factors[2] += 1

    for i in range(3, int(sqrt(n)) + 1, 2):
        while n % i == 0:
            n //= i
            prime_factors[i] += 1
        if n == 1:
            break

    if n > 2:  # n is prime
        prime_factors[n] += 1

    return prime_factors.values()


def main():
    N = int(input())
    calc = lambda n: int((sqrt(8 * n + 1) - 1) / 2)
    print(sum(calc(e) for e in prime_factorize_indices(N)))


if __name__ == "__main__":
    main()