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: Accepted)

/// Thank you tanakh!!!
/// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

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

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

use std::cmp;

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

    let mut black = vec![vec![0; k * 2]; k * 2];
    let mut white = vec![vec![0; k * 2]; k * 2];
    for &(x, y, ref c) in xyc.iter() {
        let x = x % (k * 2);
        let y = y % (k * 2);
        if c == "B" {
            black[x][y] += 1;
        } else {
            white[x][y] += 1;
        }
    }

    let l = k * 2;

    let black = CumulativeSum::new(&black);
    let white = CumulativeSum::new(&white);

    let all_black = black.get_sum(0, 0, l - 1, l - 1);
    let all_white = white.get_sum(0, 0, l - 1, l - 1);
    assert_eq!(all_black + all_white, n);

    let mut ans = 0;

    for i in 0..k {
        for j in 0..k {
            let x = i + k;
            let y = j + k;

            //e b
            // a
            //c d

            let mut included_black = 0;
            let mut excluded_white = 0;
            // a
            included_black += black.get_sum(i, j, x - 1, y - 1);
            excluded_white += white.get_sum(i, j, x - 1, y - 1);

            // b
            included_black += black.get_sum(x, y, l - 1, l - 1);
            excluded_white += white.get_sum(x, y, l - 1, l - 1);

            // c
            if i > 0 && j > 0 {
                included_black += black.get_sum(0, 0, i - 1, j - 1);
                excluded_white += white.get_sum(0, 0, i - 1, j - 1);
            }

            // d
            if j > 0 {
                included_black += black.get_sum(x, 0, l - 1, j - 1);
                excluded_white += white.get_sum(x, 0, l - 1, j - 1);
            }

            // e
            if i > 0 {
                included_black += black.get_sum(0, y, i - 1, l - 1);
                excluded_white += white.get_sum(0, y, i - 1, l - 1);
            }

            let ans1 = included_black + all_white - excluded_white;
            let ans2 = excluded_white + all_black - included_black;

            ans = cmp::max(ans, cmp::max(ans1, ans2));
        }
    }
    println!("{}", ans);
}

pub struct CumulativeSum {
    ny: usize,
    nx: usize,
    sum: Vec<Vec<usize>>,
}

impl CumulativeSum {
    pub fn new(a: &Vec<Vec<usize>>) -> CumulativeSum {
        let ny = a.len();
        let nx = a[0].len();
        let mut sum = vec![vec![0; nx + 1]; ny + 1];
        for i in 0..ny {
            for j in 0..nx {
                sum[i + 1][j + 1] = a[i][j] + sum[i][j + 1] + sum[i + 1][j] - sum[i][j];
            }
        }
        CumulativeSum {
            ny: ny,
            nx: nx,
            sum: sum,
        }
    }

    pub fn get_sum(&self, y1: usize, x1: usize, y2: usize, x2: usize) -> usize {
        if y1 > y2 || x1 > x2 {
            return 0;
        }
        let y2 = cmp::min(y2, self.ny - 1);
        let x2 = cmp::min(x2, self.nx - 1);
        return self.sum[y2 + 1][x2 + 1] + self.sum[y1][x1]
            - self.sum[y1][x2 + 1]
            - self.sum[y2 + 1][x1];
    }
}