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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

"use strict";

const main = arg => {
    const input = arg.trim().split("\n");
    const n = parseInt(input[0])

    const helper = function(num){
        let last = Math.ceil(Math.sqrt(num))+1
        for(let i = 2; i<= last; i++){
            let tmp = num
            while(tmp / i >= 1){
                tmp = tmp/i
                if(tmp === 1) return true
            }
        }
        return false
    }
    
    const get = function(num){
        let ret = [num]
        for(let i = 2; i<Math.ceil(Math.sqrt(num)); i++){
            if(helper(i)) ret.push(i)
        }
        return ret
    }

    let arr = get(n)
    let tmp = n
    let cnt = 0
    let idx = 0
    while(idx<arr.length){
        if(tmp % arr[idx] ===0){
            tmp = tmp / arr[idx]
            cnt++
        }
        idx++
    }
    return cnt
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));