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 System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using static System.Int32;
using static System.Math;
 
class Program
{
    class Bngm : IComparable<Bngm>
    {
        public int Start;
        public int End;
        public int Channel;

        public int CompareTo(Bngm other)
        {
            if (Start != other.Start) return Start - other.Start;
            if (End != other.End) return End - other.End;
            return Channel - other.Channel;
        }
    }

    static void Main(string[] args)
    {
        label:
        var sp = ReadLine().Split();
        int n = Parse(sp[0]);
        var set = new SortedSet<Bngm>();
        var endChDic = new Dictionary<KeyValuePair<int, int>, Bngm>();
        for(int i = 0; i < n; ++i)
        {
            sp = ReadLine().Split();
            var bngm = new Bngm();
            bngm.Start = Parse(sp[0]);
            bngm.End = Parse(sp[1]);
            bngm.Channel = Parse(sp[2]);
            var pair = new KeyValuePair<int, int>(bngm.Start, bngm.Channel);
            if (endChDic.ContainsKey(pair))
            {
                var prev = endChDic[pair];
                prev.End = bngm.End;
                endChDic.Remove(pair);
                endChDic[new KeyValuePair<int, int>(prev.End, prev.Channel)] = prev;
            }
            else
            {
                set.Add(bngm);
                endChDic[new KeyValuePair<int, int>(bngm.End, bngm.Channel)] = bngm;
            }
        }
        var list = new List<Bngm>();
        foreach(var bngm in set)
        {
            int i = 0;
            for (; i < list.Count; ++i)
            {
                var last = list[i];
                if (last.End < bngm.Start)
                {
                    list[i] = bngm;
                    break;
                }
                else if (last.End == bngm.Start && last.Channel == bngm.Channel)
                {
                    list[i] = bngm;
                    break;
                }
            }
            if (i == list.Count) list.Add(bngm);
            //WriteLine($"{bngm.Start} {bngm.End} {bngm.Channel}");
        }
        WriteLine(list.Count);
    }
}