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

namespace atCocderCs
{
    class Program
    {

        static void Main(string[] args)
        {
            string[] bufs = Console.ReadLine().Split(' ');
            int N = Convert.ToInt32(bufs[0]);
            int K = Convert.ToInt32(bufs[1]);

            var xs = new int[N];
            var ys = new int[N];
            var cs = new char[N];
            for (int i = 0; i < N; i++)
            {
                bufs = Console.ReadLine().Split(' ');
                xs[i] = Convert.ToInt32(Convert.ToInt64(bufs[0]) % (2 * K));
                ys[i] = Convert.ToInt32(Convert.ToInt64(bufs[1]) % (2 * K));
                cs[i] = bufs[2][0];
            }

            int mcnt = 0;
            for (int ix = 0; ix < K; ix++)
            {
                for (int iy = 0; iy < K; iy++)
                {
                    int cnt = 0;
                    for (int i = 0; i < N; i++)
                    {
                        var x = xs[i] - ix;
                        var y = ys[i] - iy;
                        var c = cs[i];

                        if ((x < 0 && (y < 0 || y >= K)) || (0 <= x && x < K && 0 <= y && y < K) ||( x >= K && (y < 0 || y >= K)))
                        {
                            if (c == 'W')
                                cnt++;
                        }
                        else
                        {
                            if (c == 'B')
                                cnt++;
                        }

                    }

                    if (cnt > mcnt)
                        mcnt = cnt;

                }
            }

            Console.WriteLine(mcnt);

        }

    }
}