Problem:
Score : 400 points

Problem Statement

Joisino is planning to record N TV programs with recorders.

The TV can receive C channels numbered 1 through C.

The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.

Here, there will never be more than one program that are broadcast on the same channel at the same time.

When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).

Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.

Constraints

1≤N≤10^5

1≤C≤30

1≤s_i<t_i≤10^5

1≤c_i≤C

If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.

All input values are integers.

Input

Input is given from Standard Input in the following format:

N C
s_1 t_1 c_1
:
s_N t_N c_N

Output

When the minimum required number of recorders is x, print the value of x.

Sample Input 1

3 2
1 7 2
7 8 1
8 12 1

Sample Output 1

2

Two recorders can record all the programs, for example, as follows:

With the first recorder, record Channel 2 from time 1 to time 7. The first program will be recorded. Note that this recorder will be unable to record other channels from time 0.5 to time 7.

With the second recorder, record Channel 1 from time 7 to time 12. The second and third programs will be recorded. Note that this recorder will be unable to record other channels from time 6.5 to time 12.

Sample Input 2

3 4
1 3 2
3 4 4
1 4 3

Sample Output 2

3

There may be a channel where there is no program to record.

Sample Input 3

9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3

Sample Output 3

2

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using Yorukatsu056.Questions;
using Yorukatsu056.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Yorukatsu056.Questions
{
    /// <summary>
    /// https://atcoder.jp/contests/abc080/tasks/abc080_d
    /// </summary>
    public class QuestionE : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nc = inputStream.ReadIntArray();
            var programCount = nc[0];
            var channels = nc[1];

            var programs = Enumerable.Repeat(0, channels).Select(_ => new List<TVProgram>()).ToArray();

            for (int i = 0; i < programCount; i++)
            {
                var stc = inputStream.ReadIntArray();
                var program = new TVProgram(stc[0], stc[1]);
                var channel = stc[2] - 1;
                programs[channel].Add(program);
            }

            var usedDecks = new int[100001];

            for (int channel = 0; channel < programs.Length; channel++)
            {
                var channelPrograms = programs[channel];
                channelPrograms.Sort();
                for (int prog = 0; prog < channelPrograms.Count; prog++)
                {
                    var hasPrevious = prog > 0 && channelPrograms[prog - 1].EndTime == channelPrograms[prog].StartTime;
                    if (hasPrevious)
                    {
                        usedDecks[channelPrograms[prog].StartTime]++;
                    }
                    else
                    {
                        usedDecks[channelPrograms[prog].StartTime - 1]++;
                    }

                    usedDecks[channelPrograms[prog].EndTime]--;
                }
            }

            for (int time = 0; time + 1 < usedDecks.Length; time++)
            {
                usedDecks[time + 1] += usedDecks[time];
            }

            yield return usedDecks.Max();
        }

        struct TVProgram : IComparable<TVProgram>
        {
            public int StartTime { get; }
            public int EndTime { get; }

            public TVProgram(int startTime, int endTime)
            {
                StartTime = startTime;
                EndTime = endTime;
            }

            public int CompareTo(TVProgram other) => StartTime.CompareTo(other.StartTime);
        }
    }
}


namespace Yorukatsu056
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionE();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Yorukatsu056.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Yorukatsu056.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion