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)

require 'pry'
N = gets.to_i
P = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] 

primeNumbers = []
(1..N).each do |i|
  next if i == 1

  if i == 2
    primeNumbers.push(i)
    next
  end

  judge = true
  primeNumbers.each do |number|
      if i % number == 0
        judge = false
        break
      end
  end

  primeNumbers.push(i) if judge

end

num = N
zz = []
primeNumbers.each do |pi|
  (1..10).each do |ei|
    z = pi ** ei
    if num % z == 0 && !zz.include?(z)
      num /= z
      zz << z
      # puts "p=#{pi}, e=#{ei}, z=#{z}, N=#{num}zz=#{zz}"
    end
   
  end
end

puts zz.size