apps_825


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Points: 3
Time limit: 30.0s
Memory limit: 250M

Problem type
Allowed languages
Python

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----- 24

-----Sample Output----- 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.)

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