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;
use std::collections::BTreeMap;

fn factors(n: i64) -> BTreeMap<i64,i64> {
    let mut result = BTreeMap::new();
    let mut ntmp = n;
    for i in 2..n + 1 {
        if i * i > n {
            break;
        }
        while ntmp % i == 0 {
            *result.entry(i).or_insert(0) += 1;
            ntmp /= i;
        }
    }
    if ntmp != 1 {
        *result.entry(ntmp).or_insert(0) += 1;
    }
    result
}

fn calc_num(count: i64) -> i64 {
    let mut ans = 0;
    let mut sum = 0;
    for i in 1..count+1 {
        if sum + i > count {
            break;
        }
        ans += 1;
        sum += i;
    }
    ans
}

fn main() {
    input! {
        n: i64,
    }
    let fs = factors(n);
    let mut ans = 0;
    for v in fs.values() {
        ans += calc_num(*v);
    }
    println!("{}", ans);
}