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;
typedef long long ll;
typedef vector<int> vi;
typedef pair<int,int> pi;

#define INF 1000000000
#define loop(i,a,b) for(int i=a;i<b;i++)
int main()
{
    //freopen("contest.txt","r",stdin);
    //freopen("contest.txt","w",stdout);
    ios::sync_with_stdio(0);
    cin.tie(0);
    ll a,i,count_0=0;
    cin>>a;
    if(a==1)
        cout<<0<<endl;
    else
    {
        int flag=0;
        for(i=2;i<sqrt(a);i++)
        {
            if(a%i==0){
                flag=1;
                break;
            }
        }
        if(flag==0)count_0++;
        if(flag==1)
        for(i=2;i<=a;i++)
        {
            if(a%i==0){
                a=a/i;
                count_0++;
            }
        }
        cout<<count_0<<endl;
    }

    return 0;
}