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 (
	"fmt"
	"math"
)

func main() {
	var n int
	fmt.Scan(&n)

	if IsPrime(n) {
		fmt.Println(1)
		return
	}

	count := 0
	for _, cnt := range PrimeFactor(n) {
		for i := 1; i <= cnt; i++ {
			count++
			cnt -= i
		}
	}

	fmt.Println(count)
}

// generated by https://github.com/murosan/gollect

func PrimeFactor(n int) map[int]int {
	m := make(map[int]int)
	sqrt := int(math.Sqrt(float64(n)))
	for i := 2; i <= sqrt; i++ {
		for n%i == 0 {
			m[i]++
			n /= i
		}
	}
	return m
}

func IsPrime(n int) bool {
	if n == 2 {
		return true
	}
	if n < 2 || n%2 == 0 {
		return false
	}

	sqrt := int(math.Sqrt(float64(n)))
	for i := int(3); i <= sqrt; i += 2 {
		if n%i == 0 {
			return false
		}
	}

	return true
}