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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"log"
	"os"
	"strconv"
)

func main() {
	n := readInt64()

	answer := map[int64]int64{}
	max := n
	for i := int64(2); i*i <= max; i++ {
		if n%i == 0 {
			if _, ok := answer[i]; ok {
				answer[i]++

			} else {
				answer[i] = 1
			}
			n = n / i
			// if you want to answer prime number only, you should take off the comment out below.
			// i--

			if n == 1 {
				break
			}

		}

	}

	if n != 1 {
		answer[n] = 1
	}

	count := int64(0)
	for _, v := range answer {
		count += v
	}
	fmt.Println(count)
}

var (
	scanner *bufio.Scanner
)

func init() {
	scanner = bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
}

func readInt64() int64 {
	var t string

	if scanner.Scan() {
		t = scanner.Text()
	}

	n, err := strconv.ParseInt(t, 10, 64)
	if err != nil {
		log.Fatal(err)
	}

	return n
}