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)

N = gets.chomp.to_i


# 素数で割っていってカウントする
# ルートNまでの素数をまず列挙する
# それで順番に悪のを繰り返す
# それをハッシュにいれておく
# 最後に足す
# 2が3回とかだったらまた別の計算方法をする？

def fetch_prime_list(max)
  table = Array.new(max + 1,true)
  prime_list = []

  (2..max).each do |num|
    if table[num] == true
      prime_list << num
      k = num * num
      while k <= max
        table[k] = false
        k += num
      end
    end
  end
  return prime_list
end

pl = fetch_prime_list(Math.sqrt(N))

th = Math.sqrt(N)

p_list = []
p_list.push(pl)
p_list.flatten!

pl.each do |p|
  tmp = p
  while 1
    break if tmp*p > th

    tmp *= p

    p_list << tmp
  end
end

ans = 0
num = N
p_list.sort.each do |pi|
  # p pi
  # p num
  if num % pi == 0
    ans += 1
    num /= pi
  end
end

if num > th
  ans += 1
end

p ans