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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

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

    let mut xy = vec![vec![0;k*2];k*2];
    for (x,y,c) in xycs {
        if c[0]=='W' { xy[x % (k*2)][y % (k*2)] += 1; } 
        else { xy[(x+k) % (k*2)][y % (k*2)] += 1; }
    }
    for x in 0..2*k { for y in 1..2*k { xy[x][y] += xy[x][y-1]; } }
    for y in 0..2*k { for x in 1..2*k { xy[x][y] += xy[x-1][y]; } }

    let mut ans=0;
    for x in 0..k { for y in 0..k {
        let ck = checker(&xy, x, y, k);
        ans = std::cmp::max(ans, ck);
        ans = std::cmp::max(ans, n - ck);
    }};
    println!("{}", ans);
}

fn checker(xy: &Vec<Vec<usize>>, x: usize, y: usize, k: usize) -> usize {
    let kk = k*2-1;
    let r1 = xy[kk][kk];
    let r2 = xy[x+k-1][kk];
    let r3 = xy[kk][y+k-1];
    let r4 = if x>0 { xy[x-1][kk] } else { 0 };
    let r5 = if y>0 { xy[kk][y-1] } else { 0 };
    let r6 = xy[x+k-1][y+k-1];
    let r7 = if x>0 { xy[x-1][y+k-1] } else { 0 };
    let r8 = if y>0 { xy[x+k-1][y-1] } else { 0 };
    let r9 = if x>0 && y>0 { xy[x-1][y-1] } else { 0 };

    r1 + r4 + r5 + 2*r6 + 2*r9 - r2 - r3 - 2*r7 - 2*r8 
}