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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