Problem:
Score : 500 points

Problem Statement

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:

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

Output

Print the maximum number of desires that can be satisfied at the same time.

Sample Input 1

4 3
0 1 W
1 2 W
5 3 B
5 4 B

Sample Output 1

4

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

Sample Input 2

2 1000
0 0 B
0 1 W

Sample Output 2

2

Sample Input 3

6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W

Sample Output 3

4

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};
 
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
 
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
 
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

fn main() {
    input!{
      n: usize,
      k: usize,
      xycs: [(usize, usize, String); n]
    }

    let mut w_wish_table = vec![vec![0i64; 2 * k]; 2 * k];
    let mut b_wish_table = vec![vec![0i64; 2 * k]; 2 * k];

    for (x, y, c) in xycs {
        if c == "W" {
            w_wish_table[x % (2 * k)][y % (2 * k)] += 1;
        } else {
            b_wish_table[x % (2 * k)][y % (2 * k)] += 1;
        }
    }
    // println!("a");

    let mut scores = vec![vec![0i64; 2 * k]; 2 * k];

    for i in 0..k {
        for j in 0..k {
            scores[0][0] += w_wish_table[i][j];
        }
    }
    for i in 0..k {
        for j in k..k * 2 {
            scores[0][0] += b_wish_table[i][j];
        }
    }
    for i in k..k * 2 {
        for j in k..k * 2 {
            scores[0][0] += w_wish_table[i][j];
        }
    }
    for i in k..k * 2 {
        for j in 0..k {
            scores[0][0] += b_wish_table[i][j];
        }
    }
    // println!("score0 {:?}", scores[0][0]);

    for i in 1..k * 2 {
        scores[i][0] = scores[i - 1][0];
        // TODO decrement
        let mut w_to_b_idx = (i - 1 + 2 * k) % (2 * k);
        let mut b_to_w_idx = (i - 1 + k) % (2 * k);
        for j in 0..k {
            scores[i][0] += b_wish_table[w_to_b_idx][j];
            scores[i][0] += w_wish_table[b_to_w_idx][j];
            scores[i][0] -= w_wish_table[w_to_b_idx][j];
            scores[i][0] -= b_wish_table[b_to_w_idx][j];
        }
        std::mem::swap(&mut w_to_b_idx, &mut b_to_w_idx);
        for j in k..k * 2 {
            scores[i][0] += b_wish_table[w_to_b_idx][j];
            scores[i][0] += w_wish_table[b_to_w_idx][j];
            scores[i][0] -= w_wish_table[w_to_b_idx][j];
            scores[i][0] -= b_wish_table[b_to_w_idx][j];
        }
    }
    // println!("score1 {:?}", scores);
    // println!("b");

    for i in 0..k * 2 {
        for j in 1..k * 2 {
            scores[i][j] = scores[i][j - 1];
            let w_to_b_idx = (j - 1 + 2 * k) % (2 * k);
            let b_to_w_idx = (j - 1 + k) % (2 * k);
            scores[i][j] += b_wish_table[i][w_to_b_idx];
            scores[i][j] += w_wish_table[i][b_to_w_idx];
            scores[i][j] -= w_wish_table[i][w_to_b_idx];
            scores[i][j] -= b_wish_table[i][b_to_w_idx];
        }
    }
    // println!("score1 {:?}", scores);
    println!(
        "{}",
        scores
            .iter()
            .map(|v| v.iter().max().unwrap())
            .max()
            .unwrap()
    );
}