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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;

namespace ProgrammingContestTemplateByDotNetCore
{
    #region "Input and Output Classes"

    class Scanner : IDisposable
    {
        private readonly Queue<string> _buffer;
        private readonly char[] _sep;
        private readonly TextReader _reader;

        public Scanner(TextReader reader = null, char[] sep = null)
        {
            _buffer = new Queue<string>();
            _sep = sep ?? new[] { ' ' };
            _reader = reader ?? Console.In;
        }

        public Scanner(string path, char[] sep = null)
            : this(new StreamReader(path), sep) { }

        private void CheckBuffer()
        {
            if (_buffer.Any() || _reader.Peek() == -1)
                return;

            string str = string.Empty;
            for (;
                string.IsNullOrWhiteSpace(str);
                str = _reader.ReadLine()) { }

            var values = str.Split(_sep)
                .Where(s => !string.IsNullOrWhiteSpace(s));
            foreach (var item in values)
            {
                _buffer.Enqueue(item);
            }
        }

        public string Next()
        {
            CheckBuffer();
            return _buffer.Dequeue();
        }
        public string[] GetStringArray(int count)
            => GetTArray(count, x => x.Next());

        public int NextInt() => int.Parse(Next());
        public int[] GetIntArray(int count)
            => GetTArray(count, x => x.NextInt());

        public long NextLong() => long.Parse(Next());
        public long[] GetLongArray(int count)
            => GetTArray(count, x => x.NextLong());

        public double NextDouble() => double.Parse(Next());
        public double[] GetDoubleArray(int count)
            => GetTArray(count, x => x.NextDouble());

        public decimal NextDecimal() => decimal.Parse(Next());
        public decimal[] GetDecimalArray(int count)
            => GetTArray(count, x => x.NextDecimal());

        public BigInteger NextBigInt() => BigInteger.Parse(Next());
        public BigInteger[] GetBigIntArray(int count)
            => GetTArray(count, x => x.NextBigInt());

        public T GetT<T>(Func<Scanner, T> func) => func(this);
        public T[] GetTArray<T>(int count, Func<Scanner, T> func)
            => Enumerable.Range(0, count)
                .Select(e => GetT(func))
                .ToArray();

        public bool IsEnd
        {
            get
            {
                CheckBuffer();
                return !_buffer.Any();
            }
        }

        public void Dispose()
        {
            if (!_reader.Equals(Console.In))
                _reader.Dispose();
        }
    }

    class Writer : IDisposable
    {
        private readonly TextWriter _writer;
        private readonly StringBuilder _cache;
        private readonly bool _isReactive;

        public Writer(TextWriter writer = null, bool isReactive = false)
        {
            _writer = writer ?? Console.Out;
            _isReactive = isReactive;
            if (!_isReactive)
                _cache = new StringBuilder();
        }

        public Writer(string path)
            : this(new StreamWriter(path)) { }

        public Writer(bool isReactive)
            : this(null, isReactive) { }

        public void Write(object value)
        {
            if (_isReactive)
            {
                _writer.Write(value);
                _writer.Flush();
            }
            else
            {
                _cache.Append(value);
            }
        }

        public void WriteFormat(string format, params object[] values)
        {
            var value = string.Format(format, values);
            Write(value);
        }

        public void WriteLine(object value = null)
        {
            Write($"{value}{Environment.NewLine}");
        }

        public void WriteLine(string format, params object[] values)
        {
            WriteFormat($"{format}{Environment.NewLine}", values);
        }

        public void Dispose()
        {
            if (!_isReactive)
            {
                _writer.Write(_cache);
                _writer.Flush();
            }
            if (!_writer.Equals(Console.Out))
            {
                _writer.Dispose();
            }
        }
    }

    public static class Extensions
    {
        public static void Set<TKey, TValue>(
            this IDictionary<TKey, TValue> source,
            TKey key, TValue value)
        {
            if (source.ContainsKey(key))
                source[key] = value;
            else
                source.Add(key, value);
        }

        public static void Update<TKey, TValue>(
            this IDictionary<TKey, TValue> source,
            TKey key, Func<TValue, TValue> update)
        {
            if (!source.ContainsKey(key))
                source.Add(key, default(TValue));
            source[key] = update(source[key]);
        }
    }

#endregion

    class MainClass : IDisposable
    {
#region "Template"

        /// <summary> 入力を受け取る </summary>
        private readonly Scanner sc;
        /// <summary> 出力を行う </summary>
        private readonly Writer wr;
        private const string _inputFile = "input.txt";
        private const string _outFile = "output.txt";

        static void Main(string[] args)
        {
            using (new MainClass()) { }
        }

        public MainClass()
        {
            wr = new Writer(_isReactive);
            // TODO: ファイルに出力したい場合はこっち → wr = new Writer(_outFile);

#if DEBUG
            // 手元では、ファイルから入力を受け取る
            sc = new Scanner(_inputFile);
#else

            // 提出時、標準入力から受け取る
            sc = new Scanner();
#endif

            Solve();
        }

        public void Dispose()
        {
            sc?.Dispose();
            wr?.Dispose();
        }

        #endregion

        IReadOnlyDictionary<long, int> Calc(long v)
        {
            var dic = new Dictionary<long, int>();
            for (int i = 2; i * i <= v; i++)
            {
                int cnt = 0;
                while (v % i == 0)
                {
                    cnt++;
                    v /= i;
                }
                if (cnt == 0) continue;
                dic.Add(i, cnt);
            }
            if (v != 1) dic.Add(v, 1);
            return dic;
        }

        void Solve()
        {
            var N = sc.NextLong();
            var d = Calc(N);

            int ans = 0;
            foreach (var item in d)
            {
                var cnt = item.Value;
                for (int i = 1; cnt > 0; i++)
                {
                    if (cnt < i) break;
                    cnt -= i;
                    ans++;
                }
            }

            wr.WriteLine(ans);
        }

        /// <summary>
        /// TODO: リアクティブ問題か否かを指定してね♪
        /// </summary>
        private const bool _isReactive = false;
    }
}