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! {
        n:i64,
    }
    let cnt_vec = scan_prime(n);
    let ret = sum_cnt(cnt_vec);
    println!("{}", ret)
}

fn scan_prime(mut target: i64) -> Vec<i64> {
    let mut cnt_vec = vec![];
    if target != 1 {
        for i in 2.. {
            let mut cnt = 0;
            if i * i > target {
                if target != 1 {
                    cnt_vec.push(1);
                }
                break;
            }
            while target % i == 0 {
                target /= i;
                cnt += 1;
            }
            if cnt != 0 {
                cnt_vec.push(cnt);
            }
        }
    }
    cnt_vec
}

fn sum_cnt(cnt_vec: Vec<i64>) -> i64 {
    let ret: i64 = cnt_vec.into_iter().fold(0i64, |acc, x| {
        let mut cnt = 0;
        let mut sum = x;
        while sum > 0 {
            cnt += 1;
            sum -= cnt + 1;
        }
        acc + cnt
    });
    ret
}

#[test]
fn test_scan_prime() {
    assert_eq!(scan_prime(64), vec![6]);
    assert_eq!(scan_prime(997764507000), vec![3, 3, 3, 2]);
}

#[test]
fn test_sum_cnt() {
    assert_eq!(sum_cnt(vec![0]), 0);
    assert_eq!(sum_cnt(vec![1]), 1);
    assert_eq!(sum_cnt(vec![2]), 1);
    assert_eq!(sum_cnt(vec![3]), 2);
    assert_eq!(sum_cnt(vec![4]), 2);
    assert_eq!(sum_cnt(vec![5]), 2);
    assert_eq!(sum_cnt(vec![6]), 3);
    assert_eq!(sum_cnt(vec![6]), 3);
    assert_eq!(sum_cnt(vec![3, 3, 3, 2]), 7);
}