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::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn main(){
    let line = read_as_vec::<usize>();

    let (n, k) = (line[0], line[1]);
    let mut hopes: Vec<(usize, usize)> = vec![];
    for _ in 0..n{
        let mut line = read_as_string();
        let color = line.pop().unwrap();
        let line = line.trim().split_whitespace().map(|c| usize::from_str(c).unwrap())
            .collect::<Vec<usize>>();
        let (x, mut y) = (line[0], line[1]);

        if color == 'W'{
            y += k;
        }

        hopes.push(((x%(2*k))+k+1, (y%(2*k))+k+1));
    }

    let mut acc_map = vec![vec![0;4*k+1];4*k+1];

    for &hope in &hopes{
        acc_map[hope.1][hope.0] += 1;
    }

    //accumulate
    for i in k+1..4*k+1{
        for j in k+1..4*k+1{
            acc_map[i][j] += acc_map[i-1][j] + acc_map[i][j-1] - acc_map[i-1][j-1];
        }
    }

    /*
    for row in acc_map.iter().rev(){
        println!("{:?}", row);
    }
    */
    let mut ans = 0;

    for i in k+1..2*k+1{
        for j in k+1..2*k+1{
            let mut cur_ans = 0;
            //println!("i = {}, j = {}", i, j);
            let ru_list = vec![
                (j+k-1,   i+k-1),
                (j+2*k-1, i-1),
                (j+2*k-1, i+2*k-1),
                (j-1,     i+2*k-1),
                (j-1,     i-1)
            ];
            //println!("{:?}", ru_list);
            for ru in ru_list{
                cur_ans += acc_map[ru.0][ru.1] + acc_map[ru.0-k][ru.1-k] - acc_map[ru.0-k][ru.1] - acc_map[ru.0][ru.1-k]
            }
            //println!("n = {}, cur_ans = {}, ans = {}", n, cur_ans, ans);
            ans = cmp::max(cmp::max(n- cur_ans, cur_ans), ans);
            //println!("n = {}, cur_ans = {}, ans = {} DONE", n, cur_ans, ans);
            /*
            if cur_ans > ans{
                ans = cur_ans;
            }
            */
        }
    }

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