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)

# coding: utf-8


def prime_set(limit=10**5):
    """
    2020/04/10
    https://atcoder.jp/contests/abc084/tasks/abc084_d
    """

    ret = [2]
    for x in range(3, limit+1, 2):
        is_prime = True
        sqrtx = int(pow(x, 0.5))

        for p in ret:
            if p > sqrtx:
                break

            if x % p == 0:
                is_prime = False
                break

        if is_prime:
            ret.append(x)

    return ret


def main():
    N = int(input())
    N_ = N

    primes = prime_set(int(N**0.5)+1)

    # primes = prime_set(10**6)  # 1.3 sec
    # print(len(primes))  # 78498

    soinsu = {}
    for p in primes:
        if N == 1:
            break

        if N % p == 0:
            soinsu[p] = 1
            N = N // p
            while True:
                if N % p == 0:
                    soinsu[p] += 1
                    N = N // p
                else:
                    break
    
    if len(soinsu.keys()) == 0 and N_ != 1:
        soinsu[N_] = 1
    # print(soinsu)

    counts = {}
    for cnt in soinsu.values():
        if cnt not in counts:
            counts[cnt] = 1
        else:
            counts[cnt] += 1

    ans = 0
    for k, v in counts.items():
        for n in range(int((2*k+0.25)**0.5) + 1, -1, -1):
            if n*(n+1) <= 2*k < (n+1)*(n+2):
                ans += n*v
                break
    
    return ans


print(main())