{"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 that each connected component of each color is a $K$ $×$ $K$ square. Below is an example of a checked pattern of side $3$:\n\n![image](https://img.atcoder.jp/arc089/cba927b2484fad94fb5ff7473e9aadef.png)\n\nAtCoDeer 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?\n\n## Constraints\n\n*   $1$ $≤$ $N$ $≤$ $10^5$\n*   $1$ $≤$ $K$ $≤$ $1000$\n*   $0$ $≤$ $x_i$ $≤$ $10^9$\n*   $0$ $≤$ $y_i$ $≤$ $10^9$\n*   If $i$ $≠$ $j$, then $(x_i,y_i)$ $≠$ $(x_j,y_j)$.\n*   $c_i$ is `B` or `W`.\n*   $N$, $K$, $x_i$ and $y_i$ are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$x_1$ $y_1$ $c_1$\n$x_2$ $y_2$ $c_2$\n$:$\n$x_N$ $y_N$ $c_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc089_b","tags":[],"sample_group":[["4 3\n0 1 W\n1 2 W\n5 3 B\n5 4 B","4\n\nHe can satisfy all his desires by painting as shown in the example above."],["2 1000\n0 0 B\n0 1 W","2"],["6 2\n1 2 B\n2 1 W\n2 2 B\n1 0 B\n0 6 W\n4 5 W","4"]],"created_at":"2026-03-03 11:01:13"}}