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.Generic;

namespace Atcoder0121_4
{
    class Program
    {
        static void Main(string[] args)
        {
            int hope = 0;
            int hopeMax = 0;

            List<int> x = new List<int>();
            List<int> y = new List<int>();
            List<string> c = new List<string>();

            string[] input = Console.ReadLine().Split(' ');
            int n = int.Parse(input[0]);
            int k = int.Parse(input[1]);

            for (int i = 0; i < n; i++)
            {
                string[] input2 = Console.ReadLine().Split(' ');
                x.Add(int.Parse(input2[0]));
                y.Add(int.Parse(input2[1]));
                c.Add(input2[2]);
            }

            // (0,0) white
            for (int i = 0; i < k; i++)
            {
                for (int l = 0; l < k; l++)
                {
                    for (int m = 0; m < n; m++)
                    {
                        if (((x[m] + i) / k) % 2 == 0 && ((y[m] + l) / k) % 2 == 0 && c[m] == "W")
                        {
                            hope++;
                        }
                        else if (((x[m] + i) / k) % 2 == 1 && ((y[m] + l) / k) % 2 == 1 && c[m] == "B")
                        {
                            hope++;
                        }
                    }

                    if (hopeMax < hope)
                    {
                        hopeMax = hope;
                    }
                    hope = 0;
                }
            }

            //(0,0)block
            for (int i = 0; i < k; i++)
            {
                for (int l = 0; l < k; l++)
                {
                    for (int m = 0; m < n; m++)
                    {
                        if (((x[m] + i) / k) % 2 == 0 && ((y[m] + l) / k) % 2 == 0 && c[m] == "B")
                        {
                            hope++;
                        }
                        else if (((x[m] + i) / k) % 2 == 1 && ((y[m] + l) / k) % 2 == 1 && c[m] == "W")
                        {
                            hope++;
                        }
                    }

                    if (hopeMax < hope)
                    {
                        hopeMax = hope;
                    }
                    hope = 0;
                }
            }

            Console.WriteLine(hopeMax);
        }
    }
}