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)

mod prime_number {

use std::iter::Iterator;

pub struct PrimeFactorization {
    n: usize,
    cur: usize,
    limit: usize,
}

///素因数分解
impl PrimeFactorization {
    ///素因数を計算するイテレータを返す。
    pub fn calc(n: usize) -> PrimeFactorization {
        PrimeFactorization {
            n: n,
            cur: 1,
            limit: (n as f64).sqrt() as usize + 1,
        }
    }
}

impl Iterator for PrimeFactorization {
    type Item = usize;
    fn next(&mut self) -> Option<Self::Item> {
        loop {
            if self.cur == 0 || self.cur > self.n {
                return None;
            }

            self.cur += 1;

            if self.cur > self.limit {
                if self.n != 1 {
                    self.cur = 0;
                    return Some(self.n);
                }
                return None;
            }
            if self.n % self.cur == 0 {
                self.n /= self.cur;
                self.cur -= 1;
                return Some(self.cur + 1);
            }
        }
    }
}

}

use proconio::{
   fastout, input,
   marker::{Bytes, Chars, Isize1, Usize1},
};

use prime_number::*;
use std::collections::HashMap;

#[fastout]
fn main() {
   input! {
      mut n:usize
   }

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

   let mut v = PrimeFactorization::calc(n).collect::<Vec<_>>();
   let mut map = HashMap::new();
   for i in v {
      *map.entry(i).or_insert(0) += 1;
   }
   let mut ans = 0;
   for (_, mut x) in map {
      let mut k = 1;
      loop {
         if x < k {
            break;
         }
         x -= k;
         ans += 1;
         k += 1;
      }
   }
   println!("{}", ans);
}