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 Java8 (OpenJDK 1.8.0) (judge verdict: Memory Limit Exceeded)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static int INF = 1 << 30;
	static int MOD = 1000000007;
	static int[] mh4 = { 0, -1, 1, 0 };
	static int[] mw4 = { -1, 0, 0, 1 };
	static int[] mh8 = { -1, -1, -1, 0, 0, 1, 1, 1 };
	static int[] mw8 = { -1, 0, 1, -1, 1, -1, 0, 1 };

	static class TaskX {

		long[][] sum;
		public void solve(int testNumber, InputReader in, PrintWriter out) {

			int n = in.nextInt(), k = in.nextInt();
			long[][] tmp = new long[2*k][2*k];
			for (int i = 0; i < n; i++) {
				int x = in.nextInt();
				int y = in.nextInt();
				char c = in.nextString().charAt(0);
				if (c == 'B') {
					x += k;
				}
				tmp[x%(2*k)][y%(2*k)]++;
			}

			long[][] mat = new long[4*k+1][4*k+1];
			for (int i = 0; i < 4*k; i++) {
				for (int j = 0; j < 4*k; j++) {
					mat[i][j] = tmp[i%(2*k)][j%(2*k)];
				}
			}

			sum = new long[4*k+1][4*k+1];

			for (int i = 0; i <= 4*k; i++) {
				for (int j = 0; j <= 4*k; j++) {
					sum[i][j] = mat[i][j];
					if (j-1 >= 0) sum[i][j] += sum[i][j-1];
					if (i-1 >= 0) sum[i][j] += sum[i-1][j];
					if (i-1 >= 0 && j-1 >= 0) sum[i][j] -= sum[i-1][j-1];
				}
			}

			long ans = 0;
			for (int i = 0; i < 2*k; i++) {
				for (int j = 0; j < 2*k; j++) {
					ans = Math.max(ans, calcSum(i, j, i+k-1, j+k-1) + calcSum(i+k, j+k, i+2*k-1, j+2*k-1));
				}
			}

			out.println(ans);
		}

		long calcSum(int x1, int y1, int x2, int y2) {
			long res = sum[x2][y2];
			if (x1 > 0) res -= sum[x1-1][y2];
			if (y1 > 0) res -= sum[x2][y1-1];
			if (x1 > 0 && y1 > 0) res += sum[x1-1][y1-1];
			return res;
		}
	}

	static class InputReader {
		BufferedReader in;
		StringTokenizer tok;

		public String nextString() {
			while (!tok.hasMoreTokens()) {
				try {
					tok = new StringTokenizer(in.readLine(), " ");
				} catch (IOException e) {
					throw new InputMismatchException();
				}
			}
			return tok.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextString());
		}

		public long nextLong() {
			return Long.parseLong(nextString());
		}

		public double nextDouble() {
			return Double.parseDouble(nextString());
		}

		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public long[] nextLongArray(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public InputReader(InputStream inputStream) {
			in = new BufferedReader(new InputStreamReader(inputStream));
			tok = new StringTokenizer("");
		}
	}

}