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: Accepted)

import java.io.*;
import java.util.*;
 
 
public class Main implements Runnable {
 
  public void run() {
    BetterScanner scanner = new BetterScanner(System.in);
    int n = scanner.nextInt();
    int k = scanner.nextInt();
    int[] xx = new int[n];
    int[] yy = new int[n];
    for (int i = 0 ; i < n ; i ++) {
      int x = scanner.nextInt();
      int y = scanner.nextInt();
      String c = scanner.next();
      if (c.equals("B")) {
        x += k;
      }
      x %= 2 * k;
      y %= 2 * k;
      if (x >= k && y >= k) {
        x -= k;
        y -= k;
      } else if (y >= k) {
        x += k;
        y -= k;
      }
      xx[i] = x;
      yy[i] = y;
    }

    int[][] score = new int[3 * k][2 * k];
    for (int i = 0 ; i < n ; i ++) {
      int x = xx[i];
      int y = yy[i];
      score[x][y] ++;
      score[x + k][y] --;
      score[x][y + k] --;
      score[x + k][y + k] ++;
    }


    for (int x = 0 ; x < 3 * k ; x ++) {
      int acc = 0;
      for (int y = 0 ; y < 2 * k ; y ++) {
        acc += score[x][y];
        score[x][y] = acc;
      }
    }
    for (int y = 0 ; y < 2 * k ; y ++) {
      int acc = 0;
      for (int x = 0 ; x < 3 * k ; x ++) {
        acc += score[x][y];
        score[x][y] = acc;
      }
    }

    int max = 0;
    for (int x = 0 ; x < 2 * k ; x ++) {
      for (int y = 0 ; y < k ; y ++) {
        int current = score[x][y];
        if (x < k) {
          current += score[x + 2 * k][y];
          current += score[x + k][y + k];
        } else {
          current += score[x - k][y + k];
          current += score[x + k][y + k];
        }
        if (current > max) {
          max = current;
        }
      }
    }
    System.out.println(max);
  }
 
  public static void main(String[] args) {
    Main main = new Main();
    main.run();
  }
 
  // scanner slightly faster than usual ones
  public static class BetterScanner {
 
    private InputStream stream;
    private byte[] buffer = new byte[1024];
    private int pointer = 0;
    private int bufferLength = 0;
 
    public BetterScanner(InputStream stream) {
      this.stream = stream;
    }
 
    private boolean updateBuffer() {
      if (pointer >= bufferLength) {
        pointer = 0;
        try {
          bufferLength = stream.read(buffer);
        } catch (IOException exception) {
          exception.printStackTrace();
        }
        return bufferLength > 0;
      } else {
        return true;
      }
    }
 
    private int read() {
      if (updateBuffer()) {
        return buffer[pointer ++];
      } else {
        return -1;
      }
    }
 
    public boolean hasNext() {
      skipUnprintable();
      return updateBuffer();
    }
 
    private void skipUnprintable() { 
      while (updateBuffer() && !isPrintableChar(buffer[pointer])) {
        pointer ++;
      }
    }
 
    public String next() {
      if (hasNext()) {
        StringBuilder builder = new StringBuilder();
        int codePoint = read();
        while (isPrintableChar(codePoint)) {
          builder.appendCodePoint(codePoint);
          codePoint = read();
        }
        return builder.toString();
      } else {
        throw new NoSuchElementException();
      }
    }
 
    public long nextLong() {
      if (hasNext()) {
        long number = 0;
        boolean minus = false;
        int codePoint = read();
        if (codePoint == '-') {
          minus = true;
          codePoint = read();
        }
        if (codePoint >= '0' && codePoint <= '9') {
          while (true) {
            if (codePoint >= '0' && codePoint <= '9') {
              number *= 10;
              number += codePoint - '0';
            } else if (codePoint < 0 || !isPrintableChar(codePoint)) {
              return (minus) ? -number : number;
            } else {
              throw new NumberFormatException();
            }
            codePoint = read();
          }
        } else {
          throw new NumberFormatException();
        }
      } else {
        throw new NoSuchElementException();
      }
    }
 
    public int nextInt() {
      long number = nextLong();
      if (number >= Integer.MIN_VALUE && number <= Integer.MAX_VALUE) {
        return (int)number;
      } else {
        throw new NumberFormatException();
      }
    }
 
    private boolean isPrintableChar(int codePoint) {
      return codePoint >= 33 && codePoint <= 126;
    }
 
  }
 
}