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 'prime'

n = gets.chomp.to_i

if n == 1
  puts 0
  exit
end

prime_division = Prime.prime_division(n)
powers = prime_division.map(&:last).sort

def initialize_hash(powers)
  h = {}

  max = powers.last
  n = 1
  sum = 0
  while sum < max
    sum = n * (n + 1) / 2
    h[n] = sum
    n += 1
  end

  h
end

h = initialize_hash(powers)
h_values = h.values.sort.reverse

def calc_h(h, h_values, power)
  return h.key(power) if h.has_value?(power)

  greatest_value_less_than_power = h_values.find { |x| x < power }
  raise unless greatest_value_less_than_power

  h.key(greatest_value_less_than_power)
end

results = powers.map { |power| calc_h(h, h_values, power) }

puts results.sum