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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;
using System.Security.Cryptography;

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const char White = '.';
    const char Black = '#';
    const long Mod = 1000000007;

    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        checked {
            object ret = process(new StreamReader(Console.OpenStandardInput()));
            Console.WriteLine(ret);
        }
#endif
    }

    static object process(TextReader input) {
        var n = long.Parse(input.ReadLine());

        counts = new DefaultDectionary<long, long>(0);

        var nums = PrimeFact(n);

        long sum = 0;
        foreach(var x in nums) {
            var c = counts[x];
            long i = 1;
            while (true) {
                c = c-i;
                if(c < 0) break;
                i++;
                sum++;
            }
        }

        return sum;
    }

    static DefaultDectionary<long, long> counts;

    static List<long> PrimeFact(long n) {
        var list = new List<long>();

        for (long i = 2; i <= Math.Sqrt(n); i++) {
            if (n % i == 0) {
                list.Add(i);
                while (n % i == 0) {
                    n /= i;
                    counts[i]++;
                }
            }
        }
        if (n > 1) {
            list.Add(n);
            counts[n]++;
        }
        return list;
    }

    class DefaultDectionary<Tkey, TValue> : Dictionary<Tkey, TValue>
    {
        TValue DefaultValue;
        public DefaultDectionary(TValue defaultvalue) {
            this.DefaultValue = defaultvalue;
        }
        public new TValue this[Tkey key] {
            get {
                if (this.ContainsKey(key)) return base[key];
                else return DefaultValue;
            }
            set {
                base[key] = value;
            }
        }
    }

    static long[] ToIntArray(string strs, int n) {
        var ret = new long[n];
        var spl = strs.Split(' ');
        for (int i = 0; i < n; i++)
            ret[i] = long.Parse(spl[i]);
        return ret;
    }
}