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: Accepted)

import java.util.Scanner
import math.sqrt

object Main extends App {
  def readALine(c:Int, ac:List[Int]):List[Int] =
    if (c > 0) readALine(c-1, sc.nextInt::ac) else ac.reverse
  def readLines(r:Int, c:Int, ac:List[List[Int]]):List[List[Int]] =
    if (r > 0) readLines(r-1, c, readALine(c, Nil)::ac) else ac.reverse
  val sc = new Scanner(System.in)
  val N = sc.nextLong

  def factorize(n:Long):List[(Long, Long)] = {
    def makePrimeLike():(()=>Long) = {
      val primes:Array[Long] = Array(2,3,5,7,11,13,17,19,23,29)
      var num = 0
      () => {
        if (num < 10) { num +=1; primes(num-1)}
        else if ((num & 1) == 1) { num +=1; (num>>1)*6 -1} else {num +=1; (num>>1)*6 +1} 
      }      
    }
    val generator = makePrimeLike()

    def iter(n:Long, ac:List[(Long, Long)]):List[(Long, Long)] = {
      def isDivided(n:Long, d:Long):Boolean = n == (n/d)*d
      def iterDev(n:Long, d:Long, c:Long):(Long, Long, Long) =
        if (isDivided(n, d)) iterDev(n/d, d, c+1) else (n, d, c)
      
      val div = generator()

      if (n == 1) ac
      else if (n < div*div) (n, 1L)::ac 
      else {
        val (q, d, c) = iterDev(n, div, 0)
        if (c > 0) iter(q, (d, c)::ac) else iter(q, ac)
      }
    }
    iter(n, Nil)    
  }

  def solver(n:Long):Long = {
    val factor = factorize(n)
    factor.map((t) => t match { case (a, x) => ((sqrt(8*x+1)-1)/2).toLong }).sum 
  }

  println(solver(N))

}