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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

import math
import collections

n = int(input())

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

ans = 0

factor = []
tmp = n
for i in range(2 , int(-(-n**0.5//1))+1):
    if tmp % i == 0:
        cnt = 0
        while tmp % i == 0:
            cnt += 1
            tmp //= i
        factor.append([i , cnt])

if tmp != 1:
    factor.append([tmp , 1])
if factor == []:
    factor.append([n , 1])
        
s = collections.Counter(factor)


s = list(s.values())

for i in s:
    j = 1
    while True:
        i -= j
        if i < 0:
            break
        j += 1
        ans += 1

print(ans)