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)

function Main(input) {
  input = input.split("\n");
  var N = parseInt(input[0]);
  var ans = 0;
  var set = new Set();
  var N2=N;
  function isPrime(n) {
    if (isNaN(n) || !isFinite(n) || n%1 || n<2) return false; 
    var m=Math.sqrt(n);
    for (var i=2;i<=m;i++) if (n%i==0) return false;
    return true;
  }
  for(var i=2;i<Math.sqrt(N);i++){
    if(!set.has(i)&&isPrime(i)){
      var x =i;
      for(var j=1;x<N;j++){
        if(N2%Math.pow(i,j)==0){
          ans++;
          N2=N2/Math.pow(i,j);
        }else{
          break;
        }
        set.add(Math.pow(i,j));
        x=Math.pow(i,j+1);
      }
    }
  }
  if(N!=1){
    ans++;
  }
  



  console.log('%s', ans);
  return ans;
}

function debug(n){
  var input = document.getElementById("input"+n).value;
  var ans=Main(input);
  var result="WA";
  if(ans==document.getElementById("output"+n).value.split("\n")[0]){
    result="AC";
  }
  document.getElementById("result"+n).innerHTML=result;
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));