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: Accepted)

require 'set'

def main(str)
  n = str.to_i
  return 0 if n == 1
  factors = Hash.new(0)
  (2..(n**0.5).to_i).each do |p|
    loop do
      break unless n % p == 0
      n /= p
      factors[p] += 1
    end
  end
  factors[n] += 1 if n > 1
  # puts "#{str} #{factors}"
  ans = 0
  factors.each do |_, x|
    i = 1
    loop do
      break if x < i
      x -= i
      i += 1
      ans += 1
    end
  end
  ans
end

unless ENV["TEST"]
  puts(main($stdin.read.chomp))
  exit(0)
end

require 'minitest/autorun'

class TestA < Minitest::Test
  def test_main
    assert_equal(3, main("24"))
    assert_equal(0, main("1"))
    assert_equal(3, main("64"))
    assert_equal(1, main("1000000007"))
    assert_equal(7, main("997764507000"))
    assert_equal(1, main("2"))
    assert_equal(1, main("3"))
    assert_equal(1, main("4"))
    assert_equal(1, main("5"))
    assert_equal(2, main("6"))
  end
end