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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn main() {
    input! {
        n: usize,
        k: usize,
        xyc: [(usize,usize,char); n],
    }

    let mut p = vec![vec![0; 2*k]; k];
    for (mut x, mut y, c) in xyc {
        if c == 'B' {
            y += k;
        }
        y %= 2*k;
        if y >= k {
            y-=k;
            x+=k;
        }
        x %= 2*k;
        p[y][x] += 1;
    }
    
    let mut s = vec![vec![0; 2*k+1]; k+1];
    for i in 0..k {
        for j in 0..2*k {
            s[i+1][j+1] = s[i+1][j]+s[i][j+1]-s[i][j]+p[i][j];
        }
    }

    let f = |a:(usize,usize), b:(usize,usize)| s[a.0][a.1] + s[b.0][b.1] - s[a.0][b.1] - s[b.0][a.1];
    let mut res = 0;
    for i in 0..k {
        for j in 0..2*k {
            let mut x = 0;
            let j2 = j%k;
            x += f((i,j2), (0,0));
            x += f((k,j2+k), (i,j2));
            x += f((i, 2*k), (0,j2+k));
            if k <= j {
                x = n-x;
            }
            res = std::cmp::max(res, x);
        }
    }

    // for p in p {
    //     println!("{:?}", p);
    // }
    // for s in s {
    //     println!("{:?}", s);
    // }

    println!("{}", res);
}
*/

fn main() {
    let exe = "/tmp/bin1778006E";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";