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)

#!/usr/bin/env python3


def main():
    from collections import deque

    def prime_factorization_list(n: int):
        """
        入力された整数nを素因数分解し，素因数が列挙されたリストで返却
        Parameters
        ----------
        n : int
            素因数分解したい整数
        Returns
        -------
        prime_factorization_lst : lst
            [素因数]の形で素因数が列挙された素因数分解結果
        """
        fct = []  # prime factor
        b = 2     # base factor
        while b * b <= n:
            while n % b == 0:
                n //= b
                fct.append(b)
            b += 1
        if n > 1:
            fct.append(n)
        return fct

    N = int(input())

    q = deque(prime_factorization_list(N))
    memo = []
    while q:
        p = q.popleft()
        res = p
        while res in memo and q:
            can = q.popleft()
            if can == p:
                res *= can
            else:
                res = can
                break
        if res not in memo:
            memo.append(res)
    print(len(memo))


if __name__ == '__main__':
    main()