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: Accepted)

use proconio::input;

fn main() {
    input! {
        n: u64,
    }
    let factorize = prime_factorize(n);
    let mut ans = 0;

    for f in &factorize {
     let mut num = 1;
     let mut add = 2;
     while num <= f.1 {
         ans += 1;
         num += add;
         add += 1;
     }   
    }

    println!("{}", ans);
}

fn prime_factorize(mut n: u64) -> Vec<(u64, u64)> {
    let mut vec = vec![];
    let mut a = 2;
    while a * a <= n {
        if n % a != 0 {
            a+=1;
            continue;
        }
        let mut ex = 0;
        while n % a == 0 {
            ex += 1;
            n /= a;
        }

        vec.push((a, ex));
        a+=1;
    }

    if n != 1 {
        vec.push((n, 1));
    }
    return vec;
}