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)

use proconio::input;

fn main() {
    input! {
        mut n: u64,
    }
    let mut v = vec![];
    calc(n, &mut v);

    let mut r = 0;
    for e in v {
        r += get_count(e);
    }

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

fn calc(n: u64, v: &mut Vec<u64>) {
    let sub = |n: u64, m: u64| -> (u64, u64) {
        let mut c = 0;
        let mut r = n;
        while r % m == 0 {
            c += 1;
            r /= m;
        }
        (c, r)
    };

    let (c, n) = sub(n, 2);
    if c > 0 {
        v.push(c);
    }
    let mut m = 3;
    let mut r = n;
    while m * m <= r {
        let (c, n) = sub(r, m);
        if c > 0 {
            v.push(c);
        }
        r = n;
        m += 2;
    }
    if r > 1 {
        v.push(1);
    }
}

fn get_count(n: u64) -> u64 {
    if n <= 2 {
        1
    } else if n <= 2 + 3 {
        2
    } else if n <= 2 + 3 + 4 {
        3
    } else if n <= 2 + 3 + 4 + 5 {
        4
    } else if n <= 2 + 3 + 4 + 5 + 6 {
        5
    } else if n <= 2 + 3 + 4 + 5 + 6 + 7 {
        6
    } else if n <= 2 + 3 + 4 + 5 + 6 + 7 + 8 {
        7
    } else if n <= 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 {
        8
    } else {
        9
    }
}