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

# 階差数列
# 2 ** 45 > 10 ** 12 (nの最大値)だから45まで用意
arr = [1, 3, 6, 10, 15, 21, 28, 36, 45]

# 素因数分解
# pdは[[p1, p1の指数], [p2, p2の指数], ... ]のような形
pd = n.prime_division

# n = p1^e1 * p2^e2 * ... のようにしたとき
# p1^1), p1^2, ... でnを順番に割っていきたい
result = 0
pd.each do |(p, exp)|
  # 階差数列を利用して exp -> p^iでnを順番に割れる個数に変換
  # ex) exp = 7 なら p^1, p^2, p^3 の3回で割れる. p^4では割れない
  result += arr.index{|a| a > exp}
end

puts result