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: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.Reader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        int k;

        public void solve(int testNumber, MyInput in, PrintWriter out) {
            int n = in.nextInt();
            k = in.nextInt();
            int[][] mapB = new int[2 * k + 1][2 * k + 1];
            int[][] mapW = new int[2 * k + 1][2 * k + 1];
            for (int i = 0; i < n; i++) {
                int x = in.nextInt();
                int y = in.nextInt();
                if (in.nextChar() == 'B') {
                    mapB[y % (2 * k) + 1][x % (2 * k) + 1] = 1;
                } else {
                    mapW[y % (2 * k) + 1][x % (2 * k) + 1] = 1;
                }
            }
            for (int y = 0; y <= 2 * k; y++) {
                for (int x = 0; x < 2 * k; x++) {
                    mapB[y][x + 1] += mapB[y][x];
                    mapW[y][x + 1] += mapW[y][x];
                }
            }
            for (int x = 0; x <= 2 * k; x++) {
                for (int y = 0; y < 2 * k; y++) {
                    mapB[y + 1][x] += mapB[y][x];
                    mapW[y + 1][x] += mapW[y][x];
                }
            }
            int ans = 0;
            for (int y = 0; y < 2 * k; y++) {
                for (int x = 0; x < 2 * k; x++) {
                    ans = Math.max(ans,
                            count(mapB, x, y, x + k - 1, y + k - 1) +
                                    count(mapB, x + k, y + k, x + 2 * k - 1, y + 2 * k - 1) +
                                    count(mapW, x + k, y, x + 2 * k - 1, y + k - 1) +
                                    count(mapW, x, y + k, x + k - 1, y + 2 * k - 1));
                }
            }
            out.println(ans);
        }

        int count(int[][] xs, int x0, int y0, int x1, int y1) {
            if (x0 >= 2 * k) {
                x0 -= 2 * k;
                x1 -= 2 * k;
            }
            if (y0 >= 2 * k) {
                y0 -= 2 * k;
                y1 -= 2 * k;
            }
            if (x1 >= 2 * k) {
                return count(xs, x0, y0, 2 * k - 1, y1) + count(xs, 0, y0, x1 - 2 * k, y1);
            }
            if (y1 >= 2 * k) {
                return count(xs, x0, y0, x1, 2 * k - 1) + count(xs, x0, 0, x1, y1 - 2 * k);
            }
            return xs[y1 + 1][x1 + 1] - xs[y0][x1 + 1] - xs[y1 + 1][x0] + xs[y0][x0];
        }

    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}