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)

use std::io::prelude::*;

fn input<T>() -> T
where
    T: std::str::FromStr,
{
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn main() {
    let n: usize = input();
    let k: usize = input();
    let xyc: Vec<(usize, usize, String)> = (0..n)
        .map(|_| {
            let x = input();
            let y = input();
            let c: String = input();
            (x, y, c)
        })
        .collect();

    let kk = 2 * k;
    let mut p = vec![vec![0; kk + 1]; kk + 1];
    for (x, y, c) in xyc {
        if c == "W" {
            p[x % kk][(y + k) % kk] += 1;
        } else {
            p[x % kk][y % kk] += 1;
        }
    }

    let mut sum = vec![vec![0; kk + 1]; kk + 1];
    for i in 1..kk + 1 {
        for j in 1..kk + 1 {
            sum[i][j] = sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1] + p[i - 1][j - 1];
        }
    }

    let mut ans = 0;
    for i in 1..k + 1 {
        for j in 1..k + 1 {
            let mut temp = 0;
            temp += sum[i - 1][j - 1];
            temp += sum[i - 1][kk] - sum[i - 1][j - 1 + k];
            temp += sum[i - 1 + k][j - 1 + k] - sum[i - 1][j - 1 + k] - sum[i - 1 + k][j - 1]
                + sum[i - 1][j - 1];
            temp += sum[kk][j - 1] - sum[i - 1 + k][j - 1];
            temp +=
                sum[kk][kk] - sum[i - 1 + k][kk] - sum[kk][j - 1 + k] + sum[i - 1 + k][j - 1 + k];
            ans = std::cmp::max(ans, temp);
        }
    }

    println!("{}", ans);
}