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() {
	scanner := NewScanner()
	n := scanner.NextInt64()
	if n == 1 {
		fmt.Println(0)
		return
	}
	l := 10 * 10 * 10 * 10 * 10 * 10
	if int64(l) > n {
		l = int(n)
	}
	ms := make([]bool, l+1)
	count := 0
	for i := 2; i < len(ms); i++ {
		if ms[i] {
			continue
		}
		for j := i; j < len(ms); j *= i {
			ms[j] = true
			if n%int64(j) == 0 {
				n /= int64(j)
				count++
			}
		}
	}
	if count == 0 {
		// Nは素数
		fmt.Println(1)
	} else {
		fmt.Println(count)
	}
}

type Scanner struct {
	scanner *bufio.Scanner
}

func NewScanner() *Scanner {
	s := bufio.NewScanner(os.Stdin)
	s.Split(bufio.ScanWords)
	return &Scanner{s}
}

func (s *Scanner) NextWord() string {
	if !s.scanner.Scan() {
		log.Fatal("failed to find the next word")
	}
	return s.scanner.Text()
}

func (s *Scanner) NextInt() int {
	str := s.NextWord()
	i, err := strconv.Atoi(str)
	if err != nil {
		log.Fatalf("failed to parse %s to int", str)
	}
	return i
}

func (s *Scanner) NextInt64() int64 {
	str := s.NextWord()
	i, err := strconv.ParseInt(str, 10, 64)
	if err != nil {
		log.Fatalf("failed to parse %s to int64", str)
	}
	return i
}