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)

import bisect
import math
from typing import Dict, List, NoReturn


def factorize(n: int) -> Dict[int, int]:
    result: Dict[int, int] = {}

    for d in range(2, int(math.sqrt(n)) + 1):
        div_count: int = 0
        while n % d == 0:
            n /= d
            div_count += 1

        result[d] = div_count

        if n == 1:
            break

    return result


def reverse_sum(n: int) -> int:
    sum_of_k: List[int] = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120,
                           136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378,
                           406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820]

    return bisect.bisect_left(sum_of_k, n)


def main() -> NoReturn:
    n: int = int(input())

    factors: Dict[int, int] = factorize(n)

    answer: int = 0

    for value in factors:
        answer += reverse_sum(value)

    print(answer)


if __name__ == '__main__':
    main()