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: Wrong Answer)

require "prime"
require "set"

# @param num [Integer]
# @return Integer
def divisors(num)
  (1..Math.sqrt(num).floor).map do |divisor|
    next unless num % divisor == 0

    quotient = num / divisor
    quotient == divisor ? [divisor] : [divisor, quotient]
  end.compact.flatten.sort
end

n = gets.to_i
divs = divisors(n)

ans = 0
prime_divs = Prime.prime_division(n).to_h
divs.each do |d|
  next if d == 1

  ds = Prime.prime_division(d)
  flg = true
  ds.each do |prime_num, exponent|
    unless prime_divs.key?(prime_num) && prime_divs[prime_num] >= exponent
      flg = false
      break
    end
  end

  next unless flg

  ds.each do |prime_num, exponent|
    prime_divs[prime_num] -= exponent
  end

  ans += 1
  n /= d
end

puts ans