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>
#define pf printf
#define sc(x) scanf("%d",&x);
#define scs(x) scanf("%s",x);
#define scl(x) scanf("%lld",&x);
#define rep(i,s,e) for(int i=s; i<=e; ++i)
#define dep(i,s,e) for(int i=s; i>=e; --i)
typedef long long ll;
using namespace std;
const ll mod=1e9+7;
const int Max=2e5+5;
int main()
{
	ll n,u=0;
	scl(n);
	for(ll i=2;i*i<=n;i++){
		if(n%i==0){
			ll	num=1,cou=0;
			while(n%i==0){
				n/=i;cou++;
				if(cou==num){u++;cou=0;num++;}
			}	
		}
	}pf("%lld\n",u+(n==1?0:1));
}