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)

use proconio::input;

fn main() {
	input!(n: usize);

	let mut nn = n;
	let mut fact: Vec<(usize, usize)> = Vec::new();

	fn factor_sub(n: usize, m: usize) -> (usize, usize) {
        let mut c = 0;
        let mut x = n;
        while x % m == 0 {
            c += 1;
            x /= m;
        }
        (c, x)
    }

    let (c, n) = factor_sub(n, 2);
    if c > 0 {
		fact.push((2,c));
		 //print!("({},{})", 2, c); 
	}
    let mut x = 3;
    let mut m = n;
    while x * x <= m {
        let (c, n) = factor_sub(m, x);
        if c > 0 {
			fact.push((x,c));
			//print!("({},{})", x, c);
		}
        m = n;
        x += 2;
    }
    if m > 1 {
		fact.push((m,1));
		//print!("({},{})", m, 1);
	}

	let mut z: Vec<usize> = Vec::new();
	for i in fact {
		for j in 0..(i.1) {
			z.push(i.0.pow((j+1) as u32));
		}
	}
	z.sort();
	z.dedup();

	let mut count: usize = 0;
	loop {
		if z.len() == count {
			break;
		}
	//		println!("nn={}", nn);
		nn /= z[count];
		if nn == 0 {
			break;
		}
		count += 1;
	}
	println!("{}", count);
//	println!("{}", z.len());
//	println!("{:?}", z);
}