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)

const fs = require('fs')
const n = parseInt(fs.readFileSync('/dev/stdin', 'utf8').trim())

function primeFactorize(n) {
  const primes = []
  for (let p = 2; p * p <= n; p += 1) {
    if (n % p != 0) continue

    let e = 0
    while (n % p == 0) {
      n /= p
      e += 1
    }
    primes.push({ p, e })
  }

  if (n != 1) primes.push({ p: n, e: 1 })
  return primes
}

let count = 0
const primes = primeFactorize(n)
primes.forEach(prime => {
  let e = prime.e
  for (let i = 1; i <= e; i += 1) {
    e -= i;
    count += 1;
  }
})

console.log(count)