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'

n = gets.to_i

div = Prime.prime_division(n)
div_map = div.to_h

num = div_map.keys
count = div_map.values.sum

result = 0
before_result = 0

(1..100).each{ |i|
	num.repeated_combination(i).each{ |c|
		c_h = c.each_with_object(Hash.new(0)){ |x, h| h[x] += 1}
		
		flag = true
		
		c_h.each{ |k,v|
			if div_map[k] < v then
				flag = false
				break
			end
		}
		
		if flag then
			c_h.each{ |k,v|
				div_map[k] -= v
			}
			
			count -= i
			result += 1
			
			if count < i then
				puts result
				exit
			end
		end
	}

	if before_result == result then
		break
	else
		before_result = result
	end

	num = div_map.select{|k,v| v > 0}.keys
}

puts result