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 Rust (1.42.0) (judge verdict: Wrong Answer)

use proconio::*;
#[allow(unused_imports)]
use proconio::marker::*;

#[fastout]
#[allow(non_snake_case)]
fn main() {
    input! {
        N: usize,
    }
    let mut v: Vec<usize> = vec![];
    let mut n = N;
    let mut count = 0;
    loop {
        let mut flag = true;
        for i in 2..((n as f64).powf(0.5) as usize) + 1 {
            if n % i == 0 {
                flag = false;
                v.push(1);
                n /= i;
                while n % i == 0 {
                    v[count] += 1;
                    n /= i;
                }
                count += 1;
            }
        }
        if flag {
            break;
        }
    }
    if v.is_empty() {
        v.push(1);
    }
    let mut count = 0;
    for &e in v.iter() {
        let mut i = 1;
        let mut e = e;
        while e >= i {
            count += 1;
            e -= i;
            i += 1;
        }
    }
    if N == 1 {
        count = 0;
    }
    println!("{}", count);
}