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 (Clang 10.0.0) (judge verdict: Runtime Error)

#include <stdio.h>

int findprime(long int n){
  int i;
  for(i=2;i<=n;i++){
    if(n%i==0){
      break;
    }
  }
  return i;
}

int primeindex(long int n,int p){
  int i;
  for(i=1;;i++){
    if(n%p!=0){
      break;
    }
    n=n/p;
  }
  return i-1;
}

int numofdiv(int e){
  int i,s=0;
  for(i=1;;i++){
    s=s+i;
    if(e<s){
      break;
    }
  }
  return i-1;
}

long int expo(int p, int e){
  int i,y=1;
  for(i=0;i<e;i++){
    y=y*p;
  }
  return y;
}

int main(){
  long int n;
  scanf("%ld",&n);
  
  int i,s=0,p,e,k[48],j;
  if(n>1){
    for(i=0;n>1;i++){
      p=findprime(n);
      e=primeindex(n,p);
      k[i]=numofdiv(e);
      n=n/expo(p,e);
    }
    for(j=0;j<=i;j++){
      s=s+k[j];
    }
  }

  printf("%d\n",s);
  return 0;
}