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 Scala (2.13.1) (judge verdict: Time Limit Exceeded)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n = sc.nextLong()

  def factorize(n: Long): List[Long] = {
    if (n == 1) {
      Nil
    } else {
      var i = 2
      var d = 0
      while (i*i <= n && d == 0) {
        if (n % i == 0) d = i
        i += 1
      }
      if (d == 0) List(n) else d::factorize(n/d)
    }
  }

  val factorMap = factorize(n).groupBy(identity).view.mapValues(_.length).toMap
  val counts = factorMap.map{ case (p, k) =>
    var rest = k
    var e = 1
    var ans = 0
    while (e <= rest) {
      ans += 1
      rest -= e
      e += 1
    }
    ans
  }

  println(counts.sum)
}