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)

n = int(input())


def Pf(n):
    l = {}
    if n == 1:
        return 0
    else:
        i = 2
        tnp = 0
        while n > 1 and i < int(n**0.5)+1:
            if n % i == 0:
                tnp += 1
                n //= i
            else:
                l[i] = tnp
                tnp = 0
                i += 1
        l[i] = tnp
        return l


def f(x):  # 何個取り出せるか
    if x == 0:
        return 0
    elif 1 <= x <= 2:
        return 1
    elif 3 <= x <= 5:
        return 2
    elif 6 <= x <= 9:
        return 3
    elif 10 <= x <= 14:
        return 4
    elif 15 <= x <= 20:
        return 5
    elif 21 <= x <= 27:
        return 6
    elif 28 <= x <= 35:
        return 7
    else:
        return 8


if n == 1:
    print(0)
    quit()

info = Pf(n).values()
# print(info)
ans = 0
for i in info:
    ans += f(i)

print(ans)