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: Accepted)

//catoonさんを参考に実装

function main(input) {
  const n = parseInt(input[0]);

  //素因数分解してmapにぶち込む
  const map = {};
  let k = n;
  for(let i = 2; i*i <= k; i++){
    if(k % i === 0){
      map[i] = 0;
      while(k % i === 0){
        map[i]++;
        k /= i;
      }
    }
  }

  //N自体が素数の場合は上で引っかからないのでここで処理
  if(k > 1){
    map[k] = 1;
  }

  //素数の値ではなく数のみを配列に入れる
  const primeCnt = [];
  for(let i in map){
    primeCnt.push(map[i])
  };

  //同じ素数でも複数に分けれる場合がある
  let cnt = 0;
  for(let i = 0; i < primeCnt.length; i++){
    for(let j = 1; j <= primeCnt[i]; j++){
      cnt++;
      primeCnt[i] -= j;
    }
  }
  console.log(cnt);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8').trim().split("\n"));