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 Ruby (2.7.1) (judge verdict: Runtime Error)

struct Int
  
  def prime_factor : Hash(Int64, Int64)
    return Hash{1_i64 => 1_i64} if 1 == self
    n = self.to_i64
    res = Hash(Int64, Int64).new(0_i64);
      (2_i64).upto((self**0.5).to_i64) do |i|
      while n % i == 0
        res[i] += 1_i64
        n = (n / i).to_i64
      end
    end
    res[n] = 1_i64 if n != 1
    res
  end
end

n = gets.to_s.to_i64
 
ans = 0
d = n.prime_factor
 
d.each do |(k, v)|
  
  i = 1
  while v >= i
    v -= i
    i += 1
    ans += 1
  end
end
 
puts ans