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: Wrong Answer)

import java.util.Scanner

import scala.annotation.tailrec
import scala.collection.mutable

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

  def merge[A](a: Stream[A], b: Stream[A])(implicit ev$1: A => Ordered[A]): Stream[A] =
    (a.headOption, b.headOption) match {
      case (Some(x), Some(y)) if x < y => x #:: merge(a.tail, b)
      case (Some(x), Some(y)) if x > y => y #:: merge(a, b.tail)
      case (Some(x), Some(_)) => x #:: merge(a.tail, b.tail)
      case (_, None) => a
      case _ => b
    }


  def joinL[A](xs: Stream[Stream[A]])(implicit ev$1: A => Ordered[A]): Stream[A] =
    xs.head.head #:: merge(xs.head.tail, joinL(xs.tail))

  def minus[A](a: Stream[A], b: Stream[A])(implicit ev$1: A => Ordered[A]): Stream[A] =
    (a.headOption, b.headOption) match {
      case (Some(x), Some(y)) if x < y => x #:: minus(a.tail, b)
      case (Some(x), Some(y)) if x > y => minus(a, b.tail)
      case (Some(_), Some(_)) => minus(a.tail, b.tail)
      case _ => a
    }

  val primes: Stream[Long] = 2L #:: minus(Stream.iterate(3L)(_+1L),
    joinL(primes.map{p => Stream.iterate(p*p)(_+p)}))

  val a = mutable.Set.empty[Long]
  @tailrec
  def f(n: Long = N, t: Int = 1): Int = {
    val b = a.map(i => i * i)
    val zs = (primes.takeWhile(_ <= n).filter(!a.contains(_)) ++ b).filter(n % _ == 0)
    if (zs.isEmpty) t - 1
    else {
      val z = zs.head
      a += z

      val x = n / z
      val y = primes.takeWhile(_ <= x).filter(!a.contains(_)) ++ b :+ (z * z)
      if (y.exists(x % _ == 0)) f(x, t + 1)
      else t
    }
  }
  println(f())
}