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.

Examples

Input

24


Output

3


Input

1


Output

0


Input

64


Output

3


Input

1000000007


Output

1


Input

997764507000


Output

7
N=int(input())
nn=N
import math
sq=round(math.sqrt(N))+1

i=2
ans=0
count1=0
count2=1
while sq>=i:
    if nn%i==0:
        nn//=i
        count1+=1
        if count1==count2:
            ans+=1
            count2+=1
            count1=0
    else:
        i+=1
        count1=0
        count2=1

if nn>sq:
    ans+=1

print(ans)