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: Time Limit Exceeded)

from collections import defaultdict
from math import sqrt
n = int(input())
cnt = defaultdict(int)
index = defaultdict(int)
ans = 0
flag = True

def judge_prime(i):
    cnt = 0
    for j in range(1, int(sqrt(i)) + 1):
        if i % j == 0:
            cnt += 1
    
    if cnt == 1 and i != 1:
        return True
    else:
        return False
while flag == True:
    flag = False
    if judge_prime(n):
        if cnt[n] == 0:
            ans += 1
        break
    for i in range(2, n):
        if judge_prime(i):
            j = index[i] + 1
            while 1:
                if n % (i ** j) == 0 and cnt[i ** j] == 0:
                    n //= i ** j
                    ans += 1
                    flag = True
                    cnt[i ** j] += 1
                    index[i] = j
                    break
                elif i ** j > n:
                    break 
                j += 1
        if flag:
            break
print(ans)