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)

from itertools import accumulate


def main():
    n = int(input())
    acc = tuple(accumulate(range(1, 42)))  # 10^12 < 2^39

    def count_add(c):
        for accum_index, x in enumerate(acc):
            if c < x:
                return accum_index

    f = 2
    count = 0
    ans = 0
    while n % f == 0:
        n //= f
        count += 1
    ans += count_add(count)

    f = 3
    count = 0
    while 1:
        if n % f == 0:
            n //= f
            count += 1
            continue

        ans += count_add(count)
        f += 2
        count = 0
        if f * f > n:
            break
    if n != 1:
        ans += 1

    print(ans)


if __name__ == '__main__':
    main()