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: Wrong Answer)

#include<bits/stdc++.h>


using namespace std;

int main(){
  


  
  long long n;
  cin >> n;
  int ans = 0;
  
  for(int i = 2; i <=n; i++){
   
    int count = 0;
    while(n%i==0){
      n /= i;
      count++;
    }
    
    if(count==0) break;
    else if(count <=1) ans = ans +1;
    else if(count <=3) ans = ans +2;
    else if(count <=6) ans = ans +3;
    else if(count <=10) ans = ans +4;
    else if(count <=16) ans = ans +5;
    else if(count <=21) ans = ans +6;
    else if(count <=28) ans = ans +7;
    else if(count <=36) ans = ans +8;
    
    
  }
  
 
   


  cout << ans << endl;
}