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 $x$.