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 primeFactorization(x int) map[int]int {
	ret := make(map[int]int)
	for i := 2; i*i <= x; i++ {
		for x%i == 0 {
			x /= i
			ret[i] += 1
		}
	}
	if x > 1 {
		ret[x] += 1
	}
	return ret
}

func main() {
	var N int
	fmt.Scan(&N)
	p_counts := primeFactorization(N)

	A := make([]int, 15)
	A[0] = 0
	for i := 1; i < 15; i++ {
		A[i] = A[i-1] + i
	}

	s := 0
	for _, c := range p_counts {
		for i := 1; i < 15; i++ {
			if c < A[i] {
				s += i - 1
				break
			}
		}
	}
	fmt.Println(s)
}