Checker

AtCoder

IDarc089_b

Time2000ms

Memory256MB

Difficulty—

AtCoDeer is thinking of painting an infinite two-dimensional grid in a _checked pattern of side $K$_. Here, a checked pattern of side $K$ is a pattern where each square is painted black or white so that each connected component of each color is a $K$ $×$ $K$ square. Below is an example of a checked pattern of side $3$: ![image](https://img.atcoder.jp/arc089/cba927b2484fad94fb5ff7473e9aadef.png) AtCoDeer has $N$ desires. The $i$\-th desire is represented by $x_i$, $y_i$ and $c_i$. If $c_i$ is `B`, it means that he wants to paint the square $(x_i,y_i)$ black; if $c_i$ is `W`, he wants to paint the square $(x_i,y_i)$ white. At most how many desires can he satisfy at the same time? ## Constraints * $1$ $≤$ $N$ $≤$ $10^5$ * $1$ $≤$ $K$ $≤$ $1000$ * $0$ $≤$ $x_i$ $≤$ $10^9$ * $0$ $≤$ $y_i$ $≤$ $10^9$ * If $i$ $≠$ $j$, then $(x_i,y_i)$ $≠$ $(x_j,y_j)$. * $c_i$ is `B` or `W`. * $N$, $K$, $x_i$ and $y_i$ are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $x_1$ $y_1$ $c_1$ $x_2$ $y_2$ $c_2$ $:$ $x_N$ $y_N$ $c_N$ [samples]

Samples

Input #1

Output #1

4

He can satisfy all his desires by painting as shown in the example above.

Input #2

2 1000
0 0 B
0 1 W

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Checker",
    "description": {
      "content": "AtCoDeer is thinking of painting an infinite two-dimensional grid in a _checked pattern of side $K$_. Here, a checked pattern of side $K$ is a pattern where each square is painted black or white so th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc089_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "AtCoDeer is thinking of painting an infinite two-dimensional grid in a _checked pattern of side $K$_. Here, a checked pattern of side $K$ is a pattern where each square is painted black or white so th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments