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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class D
{
	public static void Main() => (new Solver()).Solve();
}

public class Solver
{
	private int N;
	private int K;
	private int[] x;
	private int[] y;
	private char[] c;

	private long[,] csum;

	public Solver()
	{
		N = GetInt();
		K = GetInt();
		x = new int[N];
		y = new int[N];
		c = new char[N];
		for(int i = 0; i < N; i++)
		{
			x[i] = GetInt();
			y[i] = GetInt();
			c[i] = GetString()[0];
		}
	}

	public void Solve()
	{
		for(int i = 0; i < N; i++)
		{
			if(c[i] == 'W')
				y[i] += K;
			
			x[i] = (x[i] % (2 * K)) + 1;
			y[i] = (y[i] % (2 * K)) + 1;
		}

		csum = new long[4 * K + 1, 4 * K + 1];

		for(int i = 0; i < N; i++)
			for(int j = 0; j < 2; j++)
				for(int k = 0; k < 2; k++)
					csum[x[i] + 2 * K * j, y[i] + 2 * K * k]++;

		for(int i = 0; i <= 4 * K; i++)
			for(int j = 0; j < 4 * K; j++)
				csum[i, j + 1] += csum[i, j];

		for(int i = 0; i < 4 * K; i++)
			for(int j = 0; j <= 4 * K; j++)
				csum[i + 1, j] += csum[i, j];

		long ans = 0;
		for(int i = 1; i <= 2 * K; i++)
		{
			for(int j = 1; j <= 2 * K; j++)
			{
				long tmp = sum(i, j, i + K - 1, j + K - 1) + 
				           sum(i + K, j + K, i + 2 * K - 1, j + 2 * K - 1);
				ans = Math.Max(ans, tmp);
			}
		}

		Console.WriteLine(ans);
	}

	private long sum(int lowX, int lowY, int highX, int highY)
	{
		return csum[highX, highY] + 
		       csum[lowX - 1, lowY - 1] -
		       csum[highX, lowY - 1] - 
			   csum[lowX - 1, highY];
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}