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 std::io::Read;

fn input() -> i64 {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    iter.next().unwrap().parse().unwrap()
}

fn prime_factorization(mut n:i64) -> Vec<(i64,i32)>{
    let mut i:i64 = 2;
    let mut res = Vec::<(i64,i32)>::new();
    while i*i<=n {
        if n%i==0{
            let mut cnt = 0;
            while n%i==0{
                n/=i;
                cnt+=1;
            }
            res.push((i,cnt))
        }
        i+=1;
    }
    if n>1 {
        res.push((n,1));
    }
    res
}

fn main() {
    let n = input();
    let pf = prime_factorization(n);
    let mut res = 0;
    for (_,mut cnt) in pf {
        let mut i = 1;
        while i<=cnt {
            res+=1;
            cnt-=i;
            i+=1;
        }
    }
    println!("{}",res);
}