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: Time Limit Exceeded)

extern crate core;

use std::io::{self, Read};

#[derive(Debug, Clone, PartialEq)]
enum Color {
    W,
    B,
}

#[derive(Debug, Clone, PartialEq)]
struct Data {
    x: i64,
    y: i64,
    c: Color,
}

fn main() {
    let mut input = String::new();
    io::stdin().read_to_string(&mut input).unwrap();
    let output = run(input.trim().to_string());
    println!("{}", output);
}

fn run(input: String) -> String {
    let k = input
        .split_whitespace()
        .nth(1)
        .unwrap()
        .parse::<i64>()
        .unwrap();
    let list = input
        .split("\n")
        .skip(1)
        .map(|x| {
            let l = x.split_whitespace().collect::<Vec<_>>();
            Data {
                x: l[0].parse::<i64>().unwrap(),
                y: l[1].parse::<i64>().unwrap(),
                c: if l[2] == "W" { Color::W } else { Color::B },
            }
        })
        .collect::<Vec<_>>();

    let mut max = 0;
    //x,yをずらす
    for (true_color, false_color) in vec![(Color::B, Color::W), (Color::W, Color::B)] {
        for dx in 0..k {
            for dy in 0..k {
                let count = list.iter()
                    .filter(|&d| {
                        let xm = (d.x + dx) % (k * 2) >= k;
                        let ym = (d.y + dy) % (k * 2) >= k;
                        //色
                        let m = xm == ym;
                        d.c == if m {
                            true_color.clone()
                        } else {
                            false_color.clone()
                        }
                    })
                    .count();

                if max < count {
                    max = count;
                }
            }
        }
    }

    max.to_string()
}

#[test]
fn test() {
    let tests = vec![
        ("4 3\n0 1 W\n1 2 W\n5 3 B\n5 4 B", "4"),
        ("2 1000\n0 0 B\n0 1 W", "2"),
        ("6 2\n1 2 B\n2 1 W\n2 2 B\n1 0 B\n0 6 W\n4 5 W", "4"),
    ];
    for (i, (input, output)) in tests.into_iter().enumerate() {
        println!("test:{}", i);
        assert_eq!(run(input.to_string()), output.to_string());
    }
}