Problem Statement

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}

Sample Input 1

24

Sample Output 1

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.)

Sample Input 2

1

Sample Output 2

0

We cannot apply the operation at all.

Sample Input 3

64

Sample Output 3

3

We can apply the operation three times by, for example, making the following choices:

• Choose z=2 (=2^1). (Now we have N=32.)
• Choose z=4 (=2^2). (Now we have N=8.)
• Choose z=8 (=2^3). (Now we have N=1.)

Sample Input 4

1000000007

Sample Output 4

1

We can apply the operation once by, for example, making the following choice:

• z=1000000007 (=1000000007^1). (Now we have N=1.)

Sample Input 5

997764507000

Sample Output 5

7