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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.util.NoSuchElementException;

public class Main {
    private static final PrintStream ps     = System.out;
    private static final InputStream IS     = System.in;
    private static final byte[]      BUFFER = new byte[1024];
    private static int               ptr    = 0;
    private static int               buflen = 0;

    static final int                 A      = (int) 100;

    public static void main(String[] args) {
        int n = ni();
        int C = ni();
        int[] count = new int[A + 1];
        boolean[][] st = new boolean[C + 1][A + 1];

        for (int i = 0; i < n; i++) {
            int s = ni(), t = ni(), c = ni();
            if (st[c][s]) {
                s++;
            }
            if (st[c][t]) {
                t--;
            }
            st[c][s] = true;
            st[c][t] = true;

            for (int j = s - 1; j < t; j++) {
                count[j]++;
            }
        }
        int max = Integer.MIN_VALUE;
        for (int i = 0; i <= A; i++) {
            max = Math.max(max, count[i]);
        }

        ps.println(max);
    }
    
    private static boolean hasNextByte() {
        if (ptr < buflen)
            return true;
        else {
            ptr = 0;
            try {
                buflen = IS.read(BUFFER);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0)
                return false;
        }
        return true;
    }

    private static int readByte() {
        if (hasNextByte())
            return BUFFER[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public static boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(BUFFER[ptr]))
            ptr++;
        return hasNextByte();
    }

    public static String n() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public static long nl() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b)
            throw new NumberFormatException();
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b))
                return minus ? -n : n;
            else
                throw new NumberFormatException();
            b = readByte();
        }
    }

    public static int ni() {
        long nl = nl();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

    public static double nextDouble() {
        return Double.parseDouble(n());
    }

    private static int[] nia(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = ni();
        return a;
    }
}