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.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ARC089.D();
        }
        class ARC089
        {
            public static void C()
            {
                var N = Read.Int();
                var TXY = new List<Tuple<int, int, int>>();
                TXY.Add(new Tuple<int, int, int>(0, 0, 0));
                for (int i = 0; i < N; ++i)
                {
                    var X = Read.IntN();
                    TXY.Add(new Tuple<int, int, int>(X[0], X[1], X[2]));
                }
                for (int i = 1; i <= N; ++i)
                {
                    var diffT = TXY[i].Item1 - TXY[i - 1].Item1;
                    var diffX = TXY[i].Item2 - TXY[i - 1].Item2;
                    var diffY = TXY[i].Item3 - TXY[i - 1].Item3;
                    var diffM = Math.Abs(diffX) + Math.Abs(diffY);
                    if (diffT < diffM || (diffT - diffM) % 2 > 0)
                    {
                        Console.WriteLine("No");
                        return;
                    }
                }
                Console.WriteLine("Yes");
            }
            public static void D()
            {
                var N = Read.Int();
                var K = Read.Int();
                var board = new int[K * 3, K * 3];
                for(int i = 0; i < N; ++i)
                {
                    var xyc = Read.StrN();
                    var X = (Convert.ToInt32(xyc[0]) + (xyc[2] == "B" ? K : 0)) % (K * 2);
                    var Y = Convert.ToInt32(xyc[1]) % (K * 2);
                    board[X, Y]++;
                    if (X < K)
                    {
                        board[X + K * 2, Y]++;
                    }
                    if (Y < K)
                    {
                        board[X, Y + K * 2]++;
                    }
                    if (X < K && Y < K)
                    {
                        board[X + K * 2, Y + K * 2]++;
                    }
                }
                var boardSum = new int[K * 3 + 1, K * 3 + 1];
                for(int i = 0; i < K * 3; ++i)
                {
                    for(int j = 0; j < K * 3; ++j)
                    {
                        boardSum[i + 1, j + 1] = board[i, j] + boardSum[i + 1, j] + boardSum[i, j + 1] - boardSum[i, j];
                    }
                }
                int max = 0;
                for(int i = 0; i < K; ++i)
                {
                    for(int j = 0; j < K; ++j)
                    {
                        var count = boardSum[i + K, j + K] - boardSum[i, j + K] - boardSum[i + K, j] + boardSum[i, j]
                            + boardSum[i + K * 2, j + K * 2] - boardSum[i + K, j + K * 2] - boardSum[i + K * 2, j + K] + boardSum[i + K, j + K];
                        max = Math.Max(max, count);
                    }
                }
                Console.WriteLine(max);
            }
        }

        class Util
        {
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN(); dict[ab[0]].Add(ab[1]);
                    if (!isDirectional) { dict[ab[1]].Add(ab[0]); }
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}