{"raw_statement":[{"iden":"problem statement","content":"Joisino is planning to record $N$ TV programs with recorders.\nThe TV can receive $C$ channels numbered $1$ through $C$.\nThe $i$\\-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 $c_i$.\nHere, there will never be more than one program that are broadcast on the same channel at the same time.\nWhen 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 $T$).\nFind the minimum number of recorders required to record the channels so that all the $N$ programs are completely recorded."},{"iden":"constraints","content":"*   $1≤N≤10^5$\n*   $1≤C≤30$\n*   $1≤s_i<t_i≤10^5$\n*   $1≤c_i≤C$\n*   If $c_i=c_j$ and $i≠j$, either $t_i≤s_j$ or $s_i≥t_j$.\n*   All input values are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $C$\n$s_1$ $t_1$ $c_1$\n$:$\n$s_N$ $t_N$ $c_N$"},{"iden":"sample input 1","content":"3 2\n1 7 2\n7 8 1\n8 12 1"},{"iden":"sample output 1","content":"2\n\nTwo recorders can record all the programs, for example, as follows:\n\n*   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 $7$.\n*   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 $12$."},{"iden":"sample input 2","content":"3 4\n1 3 2\n3 4 4\n1 4 3"},{"iden":"sample output 2","content":"3\n\nThere may be a channel where there is no program to record."},{"iden":"sample input 3","content":"9 4\n56 60 4\n33 37 2\n89 90 3\n32 43 1\n67 68 3\n49 51 3\n31 32 3\n70 71 1\n11 12 3"},{"iden":"sample output 3","content":"2"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}