Recording

AtCoder

IDabc080_d

Time2000ms

Memory256MB

Difficulty—

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: $N$ $C$ $s_1$ $t_1$ $c_1$ $:$ $s_N$ $t_N$ $c_N$ [samples]

Samples

Input #1

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 $12$.

Input #2

Output #2

3

There may be a channel where there is no program to record.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Recording",
    "description": {
      "content": "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 $s_i$ t",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc080_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "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 $s_i$ t...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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