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)

N = gets.to_i

require 'prime'

primes = []
limit = (N ** 0.5).to_i + 1
Prime.each(limit).each{|prime|
  primes.push(prime)
}
if Prime.prime?(N) then
  primes.push(N)
end

power = []
for i in 1..primes.length do
  power[i-1] = 0
end
num = N
for i in 1..primes.length do
  while num % primes[i-1] == 0 do
    power[i-1] += 1
    num /= primes[i-1]
  end
end

accu = []
for i in 1..10 do
  accu.push(i * (i+1) / 2)
end

ans = 0
for i in 1..primes.length do
  div_num = 0
  for j in 1..15 do
    if power[i-1] >= accu[j-1] then
      div_num += 1
    else
      break
    end
  end
  ans += div_num
end

print ans