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
n = int(input())
N = n

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

yakusu = []
multi = []

i = 2
while(i <= int(math.sqrt(N))):
    
    if(n % i == 0):
        if(i in yakusu):
            multi[yakusu.index(i)] += 1
        else:
            yakusu.append(i)
            multi.append(1)
        n = int(n / i)
        continue
    
    if(n == 1):
        break
    
    i += 1

if(len(yakusu) == 0):
    yakusu.append(n)
    multi.append(1)
    
ans = 0

for j in range(len(multi)):
    h = (-1 + int(math.sqrt(1 + 8 * multi[j]))) / 2
    ans += int(h)

print(ans)