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";
    
function prime(n) {
  //n未満の素数を配列で返す。
  var ps, x, flg, j;
  ps = [2, 3];
  for(x = 5; x < n; x += 2) {
    flg = 0;
    for(j = 0; ps[j] * ps[j] <= x; j++) {
      if(x % ps[j] == 0) {
        flg = 1;
        break;
      }
    }
    if(flg == 0) {
      ps.push(x);
    }
  }
  return ps;
}

const main = arg => {
    arg = arg.trim().split("\n");
    let N = parseInt(arg[0].split(" ")[0]);
    
    // 1000000までの素数全列挙、zになるうる数全列挙
    // console.log(prime(1000000).length)
    
    const primes = prime(1000000);
    const pL = primes.length;
    
    let zs = [];
    
    for(let i=0; i<pL; i++) {
        let prime = primes[i];
        zs.push(prime);
        
        while(true) {
            prime *= prime;
            
            if(prime > 100000) break;
            zs.push(prime);
        }
    }
    
    let set = [...new Set(zs)].sort((a,b)=>a-b);
    let used = {};
    const sN = set.length;
    let cnt = 0;
    let debug = 0;
    
	for(let i=0; i<sN; i++) {
            // まだ使っていないかつ、割り切れる
            if(!used[set[i]] && N % set[i] === 0) {
                N /= set[i];
                cnt++;
            }
            
            used[i] = true;
            
            if(set[i] > N) {
                console.log(cnt);
                return;
            } 
        }
    
  console.log(1)
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));