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: Wrong Answer)

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 int[] c;

	private int[,] csum;

	public Solver()
	{
		N = GetInt();
		K = GetInt();
		x = new int[N];
		y = new int[N];
		c = new int[N];
		for(int i = 0; i < N; i++)
		{
			x[i] = GetInt();
			y[i] = GetInt();
			c[i] = (GetString()[0] == 'B') ? 1 : 0;
		}
	}

	public void Solve()
	{
		int KK = 2 * K;
		int[] u = new int[N];
		int[] v = new int[N];
		for(int i = 0; i < N; i++)
		{
			u[i] = (x[i] % KK) + 1;
			v[i] = (c[i] == 1) ? (y[i] % KK) + 1 : ((y[i] + K) % KK) + 1;
		}

		csum = new int[KK + 1, KK + 1];
		for(int i = 0; i < N; i++)
			csum[u[i], v[i]]++;

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

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

		int ans = 0;
		for(int lowX = 1; lowX <= K + 1; lowX++)
		{
			int highX = lowX + K - 1;
			for(int lowY = 1; lowY <= K + 1; lowY++)
			{
				int highY = lowY + K - 1;
				int tmp = sum(lowX, lowY, highX, highY);

				if(lowX > 1 && lowY > 1)
					tmp += sum(1, 1, lowX - 1, lowY - 1);

				if(lowX > 1 && highY < KK)
					tmp += sum(1, highY + 1, lowX - 1, KK);

				if(highX < KK && lowY > 1)
					tmp += sum(highX + 1, 1, KK, lowY - 1);

				if(highX < KK && highY < KK)
					tmp += sum(highX + 1, highY + 1, KK, KK);

				ans = Math.Max(ans, tmp);
			}
		}

		Console.WriteLine(ans);
	}

	private int 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(); }
}