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)

use std::io::*;
use std::cmp;

fn read<T: std::str::FromStr>() -> T {
    let stdin = stdin();
    let mut buf = String::new();
	stdin.lock().read_line(&mut buf);
	buf.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
	read::<String>().trim().split_whitespace()
        .map(|w| w.parse().ok().unwrap()).collect()
}

fn read_mat<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn main() {
    let v = read_vec::<usize>();
    let (n,k) = (v[0],v[1]);
    let mut map: Vec<Vec<i64>> = vec![vec![0;2*k];k];
    for i in 0..n {
        let s = read::<String>();
        let w: Vec<&str> = s.trim().split_whitespace().collect();
        let x: usize = w[0].parse().ok().unwrap();
        let y: usize = w[1].parse().ok().unwrap();
        let xi = x % (2*k);
        let mut yi = y % (2*k);
        if w[2] == "W" {
            yi = (yi + k) % (2 * k);
        }
        if xi >= k {
            map[xi-k][(yi+k)%(2*k)] += 1;
        } else {
            map[xi][yi] += 1;
        }
    }

    for i in 1..k {
        map[i][0] += map[i-1][0];
    }
    for i in 1..2*k {
        map[0][i] += map[0][i-1];
    }
    for i in 1..k {
        for j in 1..2*k {
            map[i][j] += map[i-1][j] + map[i][j-1] - map[i-1][j-1];
        }
    }

    let mut max = map[k-1][k-1];
    for i in 1..k {
        let sum = map[k-1][k-1] + map[i-1][2*k-1] - 2*map[i-1][k-1];
        max = cmp::max(max,cmp::max(sum,n as i64 - sum));
    }
    for i in 0..k {
        let sum = map[k-1][i+k] - map[k-1][i];
        max = cmp::max(max,cmp::max(sum,n as i64 - sum));
        for j in 1..k {
            let sum = map[k-1][i+k] - map[k-1][i] + map[j-1][2*k-1] + 2*map[j-1][i] - 2*map[j-1][i+k];
            max = cmp::max(max,cmp::max(sum,n as i64 - sum));
        }
    }
    println!("{}",max);
}