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
i = 2
ans = 0
while i*i <= NN:
  if N%i==0:
    j = 0
    while N%i==0:
      N /= i
      j+=1
    k = 1
    while j>0:
      if j - k < 0: break
      ans += 1
#      print(i,ans,j,k)
      j -= k
      k += 1
  i += 1
if N != 1:
  ans += 1
print(ans)


