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 main():
    import sys
    from math import log
    input = sys.stdin.readline
    sys.setrecursionlimit(10**6)
    N = int(input())
    prime = [True for i in range(int(N**.5)+1)]
    max_ = int(N ** .5) + 1
    ans = 0
    if N == 1:
        print(0)
        exit()

    for p in range(2, max_):
        if not prime[p]:
            continue
        for q in range(p, max_, p):
            prime[q] = False
        if N % p != 0:
            continue
        # print('p = {}'.format(p))
        t = 1
        p_ = p
        while N % p_ == 0:
            t += 1
            p_ *= p
        if N % p_ > 0:
            t -= 1
        l, r = 0, 10 ** 6
        # print('t = {}'.format(t))
        while l + 1 < r:
            m = (l + r) // 2
            if m * (m + 1) // 2 <= t:
                l = m
            else:
                r = m
        # print('ans += {}'.format(l))
        ans += l
    if ans == 0:
        ans = 1
    print(ans)

if __name__ == '__main__':
    main()