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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.IO;

namespace Contest
{
    class Scanner
    {
        private string[] line = new string[0];
        private int index = 0;
        public string Next()
        {
            if (line.Length <= index)
            {
                line = Console.ReadLine().Split(' ');
                index = 0;
            }
            var res = line[index];
            index++;
            return res;
        }
        public int NextInt()
        {
            return int.Parse(Next());
        }
        public long NextLong()
        {
            return long.Parse(Next());
        }
        public string[] Array()
        {
            line = Console.ReadLine().Split(' ');
            index = line.Length;
            return line;
        }
        public int[] IntArray()
        {
            return Array().Select(int.Parse).ToArray();
        }
        public long[] LongArray()
        {
            return Array().Select(long.Parse).ToArray();
        }
    }

    class Program
    {
        private int N, K;
        private int[] X, Y;
        private void Scan()
        {
            var sc = new Scanner();
            N = sc.NextInt();
            K = sc.NextInt();
            X = new int[N];
            Y = new int[N];
            for (int i = 0; i < N; i++)
            {
                int x = sc.NextInt();
                int y = sc.NextInt();
                string c = sc.Next();
                if (c == "W")
                {
                    x += K;
                }
                x %= 2 * K;
                y %= 2 * K;
                X[i] = x;
                Y[i] = y;
            }
        }

        public void Solve()
        {
            Scan();
            var imos = new int[3 * K + 1, 3 * K + 1];
            for (int i = 0; i < N; i++)
            {
                imos[2 * K - X[i], 2 * K - Y[i]]++;
                imos[2 * K - X[i], 3 * K - Y[i]]--;
                imos[3 * K - X[i], 2 * K - Y[i]]--;
                imos[3 * K - X[i], 3 * K - Y[i]]++;
            }

            for (int i = 0; i <= 3 * K; i++)
            {
                for (int j = 1; j <= 3 * K; j++)
                {
                    imos[i, j] += imos[i, j - 1];
                }
            }
            for (int i = 1; i <= 3 * K; i++)
            {
                for (int j = 0; j <= 3 * K; j++)
                {
                    imos[i, j] += imos[i - 1, j];
                }
            }

            var ans = new int[2 * K, 2 * K];
            for (int i = 0; i < 3 * K; i++)
            {
                for (int j = 0; j < 3 * K; j++)
                {
                    ans[i % (2 * K), j % (2 * K)] += imos[i, j];
                }
            }

            int max = 0;
            for (int i = 0; i < K; i++)
            {
                for (int j = 0; j < 2 * K; j++)
                {
                    int p = 0;
                    p += ans[i, j];
                    p += ans[i + K, (j + K) % (2 * K)];
                    max = Math.Max(p, max);
                }
            }
            Console.WriteLine(max);
        }

        static void Main(string[] args)
        {
            new Program().Solve();
        }
    }
}