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: usize
    }

    let v = factor(n);

    let mut count = 0;
    for &(_,m) in v.iter() {
        let mut rest = m;
        for i in 1..64 {
            if rest < i {
                break;
            }
            count += 1;
            rest -= i;
        }
    }

    println!("{}",count)
}

fn factor(n: usize) -> Vec<(usize, usize)> {
    let mut n = n;
    let mut ret = vec![];
    let ps = primes((n as f64).sqrt() as usize + 2);
    for p in ps {
        let mut cnt = 0;
        while n % p == 0 {
            n /= p;
            cnt += 1;
        }
        if cnt > 0 {
            ret.push((p, cnt));
        }
    }
    if n > 1 {
        ret.push((n, 1));
    }
    ret
}

fn primes(n: usize) -> Vec<usize> {
    let mut tbl = vec![true; n];
    let mut ps = vec![];
    tbl[0] = false;
    tbl[1] = false;
    for i in 2..n {
        if tbl[i] {
            ps.push(i);
            let mut j = i + i;
            while j < n {
                tbl[j] = false;
                j += i;
            }
        }
    }
    ps
}