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
from collections import defaultdict
N=int(input())
soinsu=defaultdict(int)
x=2
while x<=10**6:
  while N%x==0:
    soinsu[x]+=1
    N//=x
  x+=1
  
if N>1:
  soinsu[N]+=1
  
ans=0
for key in soinsu.keys():
  x=1
  while soinsu[key]>=x:
    ans+=1
    soinsu[key]-=x
    x+=1
    
print(ans)