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: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
const int maxn=1000;
int main()
{ 
	long long i,j;
	long long n;
	cin>>n;
	bool a[n+1];
	memset(a,true,sizeof(a));
	for(i=2;i*i<=n;++i)
		if(a[i]==1)
			for(j=i+i;j<=n;j+=i)
				a[j]=0;
	long long s[maxn+1],curr=0;
	s[0]=0;
	for(i=1;i<=maxn;++i)
	{
		curr+=i;
		s[i]=curr;
	}
	long long x=0,ans=0;
	for(i=2;i*i<=n,n>1;++i)
		if(a[i]==1)
		{
			while(n%i==0)
			{
				n/=i;
				x++;	
			}
			long long pos=upper_bound(s+1,s+maxn+1,x)-s;
			ans+=pos-1;
			x=0;
		}
	cout<<ans<<endl;
	return 0;
}