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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.*;
import java.math.* ;
public class Main {
InputStream is;
	PrintWriter out;
	String INPUT = ""; 
//class  Declaration

static class pair implements Comparable<pair>{
	int x;
	int y;

	
	pair (int i,int j)
	{ x=i; y=j;
	
		
	}
	public int compareTo(pair p){
		if(this.x!=p.x) { return this.x-p.x;}
		else { return this.y-p.y;}
	}
	public int hashCode() { return (x+" "+y).hashCode();}
	public String toString(){ return x+" "+y;} 
	public boolean equals(Object o){ 
		pair x = (pair) o ;
		return (x.x==this.x&&x.y==this.y);}
}



int inf = (int)1e9 + 5;
long mod = (long)1e9 + 7;
HashMap<Long,Long> fac = new HashMap<>();
void solve() throws Exception{
	//ArrayList<Integer> prime = sieve((int)1e6);

	long n=nl();
	factorize(n);
	long ans  =0;
	for(long p : fac.keySet()){
		long cnt = fac.get(p);
		long diff = 0;
		for(int i=1;i<=60;++i){
			if((i*(i+1)/2 )<= cnt){
				diff  = i;
			}
		}
		ans +=diff;

	}
	pn(ans);
	

	
}
//Taken from gfg 
void factorize(long n) { 
	int count = 0; 

	// count the number of times 2 divides  
	while (!(n % 2 > 0)) { 
		// equivalent to n=n/2;  
		n >>= 1; 

		count++; 
	} 

	// if 2 divides it  
	if (count > 0) { 
		//System.out.println("2" + " " + count); 
		fac.put(2L,(long)count);
	} 

	// check for all the possible  
	// numbers that can divide it  
	for (long i = 3; i <= (long) Math.sqrt(n); i += 2) { 
		count = 0; 
		while (n % i == 0) { 
			count++; 
			n = n / i; 
		} 
		if (count > 0) { 
			//System.out.println(i + " " + count); 
			fac.put(i,(long)count);
			
		} 
	} 

	// if n at the end is a prime number.  
	if (n > 2) { 
		//System.out.println(n + " " + "1"); 
		fac.put(n,1L);
	} 
} 

long pow(long a,long b){
	long result = 1;
	while(b>0){
	if(b%2==1) result = (result * a) % mod;
		b/=2;
		a=(a*a)%mod;
	}
	return result;
}


void print(Object o){
System.out.println(o);
System.out.flush();
}
ArrayList<Integer> sieve(int n){
    ArrayList<Integer> al=new ArrayList<>();
        boolean prime[] = new boolean[n+1];
        for(int i=0;i<n;i++)
            prime[i] = true;
    for(int p = 2; p*p <=n; p++)
      {
         if(prime[p])
          {
              for(int i = p*2; i <= n; i += p)
               prime[i] = false;
          }
       }
   for(int i = 2; i <= n; i++)
   {
      if(prime[i] == true) 
          al.add(i);
   }
     return al;
        
   }


long gcd(long a, long b) 
{ 
if (b == 0) 
return a; 
return gcd(b, a % b);  
}
void run() throws Exception{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
}
	
	
public static void main(String[] args) throws Exception { new Main().run(); }
	
//output methods
private void pn(Object o)
{
	out.println(o);
}
private void p(Object o)
{
	out.print(o);
}



//input methods
		private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	

	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	
	
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
		
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }
	void watch(Object ... a) throws Exception{
		int i=1;
		print("watch starts :");
		for(Object o : a ) {
			//print(o);
			boolean notfound = true;
			if(o.getClass().isArray()){
				
				String type = o.getClass().getName().toString();
				//print("type is "+type);
				switch (type) {
					case "[I":{
						int[] test = (int[])o ;
						print(i+" "+Arrays.toString(test));
						break;
					}
					case "[[I":{
						int[][] obj = (int[][])o;
						
						print(i+" "+Arrays.deepToString(obj));
						break;
					}
					case "[J" : {
						
						long[] obj  = (long[])o ;
						print(i+" "+Arrays.toString(obj));
						break;
					}
					case "[[J": {
						
						long[][] obj = (long[][])o;
						print(i+" "+Arrays.deepToString(obj));
						break;
					}
					case "[D" :{
						
						double[] obj= (double[])o;
						print(i+" "+Arrays.toString(obj));
						break;
					}
					case "[[D" :{
						
						double[][] obj = (double[][])o;
						print(i+" "+Arrays.deepToString(obj));
						break;
					}
					case "[Ljava.lang.String": {
						
						String[] obj = (String[])o ;
						print(i+" "+Arrays.toString(obj));
						break;
					}
					case "[[Ljava.lang.String": {
						
						String[][] obj = (String[][])o ;
						print(i+" "+Arrays.deepToString(obj));
						break ; 
					}
					case "[C" :{
						char[] obj = (char[])o ;
						print(i+" "+Arrays.toString(obj));
						break;
					}
					case "[[C" :{
						
						char[][] obj = (char[][])o;
						print(i+" "+Arrays.deepToString(obj));
						break;
					}

						
				
					default:{
						print(i+" type not identified");
						break;
					}
				}
				notfound = false;
				
			}
			if(o.getClass() == ArrayList.class){
				print(i+" al: "+o);
				notfound = false;
			}
			if(o.getClass() == HashSet.class){
				print(i+" hs: "+o);
				notfound = false;
			}
			if(o.getClass() == TreeSet.class){
				print(i+" ts: "+o);
				notfound = false;
			}
			if(o.getClass() == TreeMap.class){
				print(i+" tm: "+o);
				notfound = false;
			}
			if(o.getClass() == HashMap.class){
				print(i+" hm: "+o);
				notfound = false;
			}
			if(o.getClass() == LinkedList.class){
				print(i+" ll: "+o);
				notfound = false;
			}
			if(o.getClass() == PriorityQueue.class){
				print(i+" pq : "+o);
				notfound = false;
			}
			if(o.getClass() == pair.class){
				print(i+" pq : "+o);
				notfound = false;
			}
			
			if(notfound){
				print(i+" unknown: "+o);
			}
			i++;
		}
		print("watch ends ");
	}

}