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)

import math
from sys import exit

n=int(input())
primes = {}
i = 2
ans = 0
square = math.floor(math.sqrt(n))

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

while True:
    if n % i == 0:
        if i not in primes.keys():
            primes[i] = 1
        else:
            primes[i] += 1
        n = n // i
    elif n == 1 or i >= square:
        break
    else:
        if i == 2:
            i += 1
        else:
            i += 2
        continue

if len(primes) == 0:
    print(1)
    exit()

for k,v in primes.items():
    base = v * 2
    root = math.floor(math.sqrt(base))
    if root * (root + 1) > base:
        root -= 1
    ans += root

print(ans)