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 prime_factorization(n: usize) -> std::collections::BTreeMap<usize, usize> {
    let mut p = std::collections::BTreeMap::new();
    if n < 2 {
        return p;
    }
    let mut n = n; // shadowing
    for i in 2.. {
        if i * i > n {
            break;
        }
        while n % i == 0 {
            *p.entry(i).or_insert(0) += 1;
            n /= i;
        }
    }
    if n != 1 {
        *p.entry(n).or_insert(0) += 1;
    }
    p
}

fn main() {
    input! {
        n: u64,
    };
    let pq = prime_factorization(n as usize);
    let mut count = 0;
    for (&_, &q_i) in pq.iter() {
        let mut c = 0;
        for i in 1.. {
            c += i;
            if c > q_i {
                break;
            }
            count += 1;
        }
    }
    let ans = count;
    println!("{}", ans);
}