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)

#![allow(unused_imports)]
#![allow(dead_code)]
use datastructure::*;
use grapth::*;
use input_scanner::*;
use math::*;
use string_algorithm::*;
use util::*;

use std::cmp;
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, LinkedList, VecDeque};

fn main() {
    let mut scan = Scanner::new();
    let n: u64 = scan.next();
    let pf = prime_factor(n);

    let mut ans = 0;
    for (_v, mut c) in pf {
        let mut i = 1;
        while i <= c {
            c -= i;
            i += 1;
        }
        ans += i - 1;
    }

    println!("{}", ans);
}

mod datastructure {}
mod grapth {}
mod math {
    pub fn prime_factor(mut n: u64) -> Vec<(u64, usize)> {
        let mut res: Vec<(u64, usize)> = vec![];
        let mut i: u64 = 2;
        while i * i <= n {
            let mut c: usize = 0;
            while n % i == 0 {
                n /= i;
                c += 1;
            }
            if 0 < c {
                res.push((i, c));
            }
            i += 1;
        }
        if 1 < n {
            res.push((n, 1));
        }
        res
    }
}
mod string_algorithm {}
mod util {}
mod input_scanner {
    pub struct Scanner {
        bytes: Vec<u8>,
        begin: usize,
        end: usize,
    }

    impl Scanner {
        pub fn new() -> Self {
            use std::io::Read;
            let mut buffer: Vec<u8> = Vec::new();
            std::io::stdin().read_to_end(&mut buffer).unwrap();
            let end = (0..buffer.len())
                .find(|i| buffer[*i].is_ascii_whitespace())
                .unwrap_or(buffer.len());
            Scanner {
                bytes: buffer,
                begin: 0,
                end: end,
            }
        }
        pub fn next<T: std::str::FromStr>(&mut self) -> T {
            let s: &str =
                unsafe { std::str::from_utf8_unchecked(&self.bytes[self.begin..self.end]) };
            let ret: T = s.parse::<T>().ok().expect("Parse error.");
            self.skip();
            ret
        }
        pub fn next_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
            (0..n).map(|_| self.next()).collect()
        }
        pub fn next_word(&mut self) -> Vec<u8> {
            let r = Vec::from(&self.bytes[self.begin..self.end]);
            self.skip();
            r
        }
        fn skip(&mut self) {
            self.begin = (self.end..self.bytes.len())
                .find(|i| !self.bytes[*i].is_ascii_whitespace())
                .unwrap_or(self.bytes.len());
            self.end = (self.begin..self.bytes.len())
                .find(|i| self.bytes[*i].is_ascii_whitespace())
                .unwrap_or(self.bytes.len());
        }
    }
}