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 std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{VecDeque, HashMap, BTreeMap, HashSet, BTreeSet};
#[allow(unused_imports)]
use std::{i32, i64, i128, u32, u64, u128, f64};
#[allow(unused_imports)]
use std::io::{stdout, Write, BufWriter};
#[allow(unused_imports)]
use std::mem::{swap};
#[allow(unused_imports)]
use proconio::marker::{Isize1, Usize1, Bytes, Chars};

#[proconio::fastout]
fn main() {
    proconio::input!{
        mut n: i64,
    }
    let mut fs = HashMap::new();
    if n == 1 {
        println!("0");
        return;
    }
    for i in 2..=((n as f64).sqrt().floor() as i64 + 5) {
        while n % i == 0 {
            n /= i;
            *(fs.entry(i).or_insert(0)) += 1;
        }
        if n == 1 { break; }
    }
    if n > 1 {
        println!("1");
        return;
    }
    let mut ans = 0;
    for &c in fs.values() {
        let mut c = c;
        for i in 1.. {
            if c >= i {
                ans += 1;
                c -= i;
            } else { break; }
        }
    }
    println!("{}", ans);

}