Problem:
Score : 400 points

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}

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 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

Solution in Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program ABC169_D
  integer(8)::M,O,k=2,l=1,ans=0
  integer(8),allocatable::A(:)
  double precision::N
  read(*,*)N
  O=dint(sqrt(N))
  allocate(A(0:O))
  A=0
  M=dint(N)
  do while(M>1)
     if(mod(M,k)==0) then
        A(k)=A(k)+1
        M=M/k
     else
        k=k+1
        if(k>O) then
           if(sum(A)==0) A(0)=1
           exit
        end if
     end if
  end do
  do i=0,O
     do while(A(i)-l>=0)
        ans=ans+1
        A(i)=A(i)-l
        l=l+1
     end do
     l=1
  end do
  write(*,*)ans
end program ABC169_D