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)]
use itertools::Itertools;
use proconio::{input, marker::*};
use std::cmp::*;
use std::collections::*;
use superslice::*;

fn main() {
    input! {
        n: u64,
    }

    let f = prime_factorize(n);
    let mut ans = 0;

    for (_, i) in f {
        let mut j = i;
        for k in 1..=i {
            if k <= j {
                ans += 1;
                j -= k;
            } else {
                break;
            }
        }
    }

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

fn prime_factorize(n: u64) -> Vec<(u64, u64)> {
    let mut n = n;
    let mut res = vec![];
    let mut a = 2;

    while a * a <= n {
        if n % a != 0 {
            a += 1;
            continue;
        }

        let mut count = 0;
        while n % a == 0 {
            count += 1;
            n /= a;
        }

        res.push((a, count));
        a += 1;
    }

    if n != 1 {
        res.push((n, 1));
    }

    res
}