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)

#[allow(unused_imports)]
use proconio::{
    fastout, input,
    marker::{Bytes, Chars, Isize1, Usize1},
};

#[allow(unused_macros)]
macro_rules! echo {
    ($($e:expr),+) => ( { $(println!("{}", $e))+ } );
}

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
}

fn main() {
    input! {
        n: usize,
    }

    if n == 1 {
        echo!(0);
        return;
    }

    let mut n = n;

    let ps = primes(1_000_010);
    let mut ks = vec![];
    let mut is_prime = true;

    for p in ps {
        if n % p != 0 {
            continue;
        } else {
            is_prime = false;
            let mut cnt = 0;
            let mut divided_n = n;
            while divided_n % p == 0 {
                cnt += 1;
                divided_n /= p;
            }
            n = divided_n;
            ks.push(cnt);
        }
    }

    if is_prime {
        echo!(1);
        return;
    }

    let mut result = 0;

    for k in ks {
        if k >= 45 {
            result += 9;
        } else if k >= 36 {
            result += 8;
        } else if k >= 28 {
            result += 7;
        } else if k >= 21 {
            result += 6;
        } else if k >= 15 {
            result += 5;
        } else if k >= 10 {
            result += 4;
        } else if k >= 6 {
            result += 3;
        } else if k >= 3 {
            result += 2;
        } else {
            result += 1;
        }
    }

    echo!(result);
}