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)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let 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)*}
    };
}
#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, mut $var:ident $($r:tt)*) => {
        let mut $var = $iter.next().unwrap().parse::<usize>().unwrap();
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, $var:ident $($r:tt)*) => {
        let $var = $iter.next().unwrap().parse::<usize>().unwrap();
        input_inner!{$iter $($r)*}
    };
}
#[allow(unused_macros)]
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>().unwrap()
    };
}
#[allow(unused_macros)]
macro_rules! outbuf {
    ($var:ident) => {
        use std::io::{stdout, BufWriter, Write};
        let stdout = stdout();
        let mut $var = BufWriter::new(stdout.lock());
    };
}

use std::cmp::max;
fn main() {
    input! {n, k, xyc: [(usize, usize, String); n]};
    // outbuf! {out};
    let mut ans = 0;
    let k2 = k * 2;
    let mut b = vec![vec![0; k2 + 1]; k2 + 1];
    let mut ba = vec![vec![0; k2 + 1]; k2 + 1];
    let mut bs = 0;
    for (mut x, y, c) in xyc {
        if c == "W" {
            x += k;
        }
        b[x % k2][y % k2] += 1;
        bs += 1;
    }
    for i in 0..k2 {
        for j in 0..k2 {
            ba[i + 1][j + 1] = ba[i + 1][j] + ba[i][j + 1] - ba[i][j] + b[i][j]
        }
    }
    let get2a = |x1: usize, x2: usize, y1: usize, y2: usize| {
        ba[x2][y2] - ba[x1][y2] - ba[x2][y1] + ba[x1][y1]
    };
    for i in 0..k {
        for j in 0..k {
            let x = get2a(i, i + k, 0, k2) + get2a(0, k2, j, j + k) - 2 * get2a(i, i + k, j, j + k);
            ans = max(ans, x);
            ans = max(ans, bs - x);
        }
    }
    println!("{}", ans);
}