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<iostream>
#include<bits/stdc++.h>
#include<climits>
#include<math.h>

#define forn(x,n,s) for(int i = x; i < n; i += s )
#define forr(x,n,s) for(int i = x; i>=n; i -= s)
#define PI 3.14159265358979323846264338327950L

using namespace std;

void go(){
  ios_base::sync_with_stdio(0);
  cin.tie(0);

  #ifndef ONLINE_JUDGE
       freopen("input.txt","r",stdin);
       freopen("output.txt","w",stdout);
  #endif
} 
long long int mod = 1e9+7;
int helper(int n){
    int cnt = 0,round = 1;
    while(n>0){
        if(n-round>=0) cnt++;
        n -= round;
        round++;
    }
    return cnt;
}

int main(){
    go(); 

    // code here
    long long int n;cin>>n;
    unordered_map<int,int> mp;
    long long int temp = n;
    int ans = 0;
    for(int i = 2;(long long int)i*i<=temp;i++){
        int cnt = 0;
        while(n>1 and n%i==0){
            cnt++;
            n = n/i;
        }
        ans += helper(cnt); 
    }
    if(n>1) ans++;
    cout<<ans;
}