100803: [AtCoder]ABC080 D - Recording

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