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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <cmath>
#include <cstdint>
#include <iostream>
#include <vector>

using namespace std;

int main() {
  int64_t N;
  cin >> N;
  int64_t res = 0;
  for (int64_t n = 2, end = sqrt(N); n <= end; ++n) {
    if (N < n) break;
    if (N % n) continue;
    int64_t d = 0;
    while (N % n == 0) {
      ++d;
      N /= n;
    }
    for (int64_t i = 1, end = d; i <= end; ++i) {
      if (d - i >= 0) {
        ++res;
        d -= i;
      } else {
        break;
      }
    }
  }
  if (N > 1) ++res;
  cout << res << endl;
  
  return 0;
}