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"
	"math"
	"os"
	"strconv"
	"strings"
)

var sc = bufio.NewReaderSize(os.Stdin, 1024*1024*1)

func main() {
	N := getStdinInt()
	Nori := N
	arr := make([]bool, int(math.Sqrt(float64(N)))+1)

	// 初期化
	for i := 2; i < len(arr); i++ {
		arr[i] = true
	}
	// 素数を求める
	arr[0] = false
	arr[1] = false
	for i := 2; i < len(arr); i++ {
		if arr[i] {
			for j := i * 2; j < len(arr); j += i {
				arr[j] = false
			}
		}
	}
	// 割り切れるか判別（素因数分解）
	cnt := 0
	for i := 2; i < len(arr); i++ {
		if arr[i] && (N%i) == 0 {
			mul := i
			for {
				if N%mul == 0 {
					cnt++
					N /= mul
					mul += mul
				} else {
					break
				}
			}
			if N == 1 {
				break
			}
		}
	}

	if cnt == 0 && (Nori == 0 || Nori == 1) {
		fmt.Printf("%d\n", 0)
	} else if cnt == 0 {
		fmt.Printf("1\n")
	} else {
		fmt.Printf("%d\n", cnt)
	}
}

func getStdin() string {
	return readLine()
}
func getStdinInt() int {
	str := getStdin()
	rtn, _ := strconv.Atoi(str)
	return rtn
}
func getStdinIntArr() []int {
	str := getStdin()
	list := strings.Split(str, " ")
	rtn := make([]int, len(list))
	for idx, val := range list {
		rtn[idx], _ = strconv.Atoi(val)
	}
	return rtn
}

func getStdinIntArr64() []int64 {
	str := getStdin()
	list := strings.Split(str, " ")
	rtn := make([]int64, len(list))
	for idx, val := range list {
		rtn[idx], _ = strconv.ParseInt(val, 10, 64)
	}
	return rtn
}

func readLine() string {
	buf := make([]byte, 0, 0)
	for {
		l, p, e := sc.ReadLine()
		if e != nil {
			panic(e)
		}
		buf = append(buf, l...)
		if !p {
			break
		}
	}
	return string(buf)
}