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 <bits/stdc++.h>


using namespace std;
#define ll long long

vector<int> primes;
vector<int> facs;

ll N;

int main()
{
	cin>>N;
	int sqt = sqrt(N);
	for(int i = 2; i <= sqt; ++i)
	{
		if(N % i == 0)
		{
			primes.push_back(i);
			int cnt = 0;
			while(N % i == 0)
			{
				++cnt;
				N /= i;
			}
			facs.push_back(cnt);
		}
	}
	if( N != 1)
	{
		primes.push_back(N);
		facs.push_back(1);
	}
	int ans = 0;
	for(int fac: facs)
	{
		int k = 1;
		while(fac >= k)
		{
			++ans;
			fac -= k;
			++k;
		}
	}
	cout<<ans<<endl;
	
}