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: Accepted)

package main

import "fmt"

func main() {
	var N int
	fmt.Scan(&N)
	var memo map[int]int
	memo = map[int]int{}
	sosu := true
	iti := false
	if N == 1 {
		iti = true
	}
	// fmt.Println(N)
	for i:=2; i * i <= N; i++ {
		if N % i == 0{
			target := i
			check := true
			for check {
				check = false
				for j, value := range memo {
					if target%j == 0 {
						target = target / j
						memo [j] = value + 1
						check = true
						break
					}
				}
			}
			if target != 1 {
				// fmt.Println(target)
				memo[target] = 1
				sosu = false
			}
			N = N/i
		}
	}
	target := N
	check := true
	for check {
		check = false
		// fmt.Println(memo,target)
		for j, value := range memo {
			// fmt.Println(j,value,target)
			if target%j == 0 {
				target = target / j
				memo [j] = value + 1
				check = true
				break
			}
		}
	}
	if target != 1 {
		// fmt.Println("check",target)
		memo[target] = 1
	}
	if sosu {
		if iti {
			fmt.Println(0)
		} else {
			fmt.Println(1)
		}
	} else {
		sum := 0
		for _,value := range memo {
			count := value
			for i:=1; i<=value; i++ {
				if count-i >= 0 {
					count -= i
					sum += 1
					// fmt.Println(sum,count,j)
				} else {
					break
				}
			}
		}
		fmt.Println(sum)
	}

}