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



Sample input:
24


Sample output:
3

Submission status: Runtime Error

Solution code:
def cin(): # To take limited number of inputs
    return map(int,input().split())

def cins(): # To take space sepreated strings
    return input.split()

def cino(test=False): # To take individual int input (test = False)
    if not test:
        return int(input())
    else: # To take string input (test = True)
        return input()

def cina(): # array input
  return list(map(int,input().split()))

def ssplit(): # multiple string input
    return list(input().split())

def printlist(l): # To print space seperated array
    for i in l:
        print(i,end=" ")

import math
import sys
import fractions
import random
def sieve(n):
	sqrtn = int(n**0.5)
	sieve = [True] * (n+1)
	sieve[0] = False
	sieve[1] = False
	for i in range(2, sqrtn+1):
		if sieve[i]:
			m = n//i - i
			sieve[i*i:n+1:i] = [False] * (m+1)
	return sieve
isprime=sieve(100000)
write = sys.stdout.write
def gcd(a, b):
    while b:
        a, b = b, a%b
    return a
def mr_pass(a, s, d, n):
    a_to_power = pow(a, d, n)
    if a_to_power == 1:
        return True
    for i in range(s-1):
        if a_to_power == n - 1:
            return True
        a_to_power = (a_to_power * a_to_power) % n
    return a_to_power == n - 1
def is_prime(n):
	if n<100000:
		return isprime[n]
	d = n - 1
	s = 0
	while d % 2 == 0:
		d >>= 1
		s += 1
	for repeat in range(3):
		a=random.randint(1,n-1)
		if not mr_pass(a, s, d, n):
			return False
	return True
def prime_power(n):
	power =int(math.log(n,2))
	for i in range(1,power+1):
		if i==1:m=n
		elif i==2:m=int(math.sqrt(n))
		else:m=int(round(math.exp(math.log(n)/i),0))
		if(n==(m**i) and is_prime(m)):
			return 1
	return 0

l = 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def main():
    a = cino()
    i = 0
    cnt = 0
    while(a>1):
        if a%l[i]==0:
            a = a//l[i]
            cnt += 1
        i += 1
        
    print(cnt)
        


if __name__ == '__main__':
    main()