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: Wrong Answer)

n = int(input())

def func(i):
	temp = 0
	for j in range(i+2):
		temp+=j
		if(temp > i):
			break
	return j-1

i = 0
ret = 0
while n % 2 == 0:
	i += 1
	n //= 2

if(i >= 1):
	tempret = func(i)
	ret+=tempret
	print(2,i,n,tempret,ret)
f = 3
i = 0
while f * f <= n:
	if n % f == 0:
		i += 1
		n //= f
		print("bb",n,f,i,ret)
	else:
		f += 2
		if(i >= 1):
			tempret = func(i)
			ret+=tempret
			print("cc",f,i,tempret,ret)
			i = 0

if(n > 1):
	i+=1
	if(i >= 1):
		tempret = func(i)
		ret+=tempret
		print("dd",f,i,tempret,ret)

print(ret)