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;

namespace D {
    class questionD {
        static void Main(string[] args) {
            int[] NKinput = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();//2つ以上のスペース区切り入力の取得
            int N = NKinput[0];
            int K = NKinput[1];
            int[,] whites = new int[K, 2 * K];
            for (int i = 0; i < N; i++) {
                string[] input = Console.ReadLine().Split(' ').ToArray();
                int x = int.Parse(input[0]) % (2 * K);
                int y = int.Parse(input[1]) % (2 * K);
                string mark = input[2];
                if (mark == "W") {
                    if (x >= K) {
                        x = (x + K) % (2 * K);
                        y = (y + K) % (2 * K);
                    }
                } else {
                    x = (x + K) % (2 * K);
                    if (x >= K) {
                        x = (x + K) % (2 * K);
                        y = (y + K) % (2 * K);
                    }
                }
                whites[x, y]++;
            }
            int[,] Ysums = new int[K, 2 * K];
            for (int i = 0; i < K; i++) {
                int sum = 0;
                for (int j = 0; j < K; j++) {
                    sum += whites[i, j];
                }
                Ysums[i, 0] = sum;
                //Console.WriteLine(Ysums[i, 0]);
            }
            //Console.WriteLine("abcdef");
            for (int i = 0; i < K; i++) {
                for (int j = 1; j < 2 * K; j++) {
                    Ysums[i, j] = Ysums[i, j - 1] + whites[i, (j - 1 + K) % (2 * K)] - whites[i, j - 1];
                    //Console.WriteLine(Ysums[i, j]);
                }
            }
            int max = 0;
            for (int j = 0; j < K; j++) {
                int sum = 0;
                for (int k = 0; k < K; k++) {
                    sum += Ysums[k, j];
                }
                if (sum > max) {
                    max = sum;
                }
                //Console.WriteLine(sum);
                for (int i = 0; i < K; i++) {
                    sum += Ysums[i, j + K] - Ysums[i, j];
                    if (sum > max) {
                        max = sum;
                    }
                    //Console.WriteLine(sum);
                }
                for (int i = 0; i < K; i++) {
                    sum += Ysums[i, j] - Ysums[i, j + K];
                    if (sum > max) {
                        max = sum;
                    }
                    //Console.WriteLine(sum);
                }
            }
            // Console.Write("改行なし a = {0} b = {1} c = {2}", a, b, c)//改行なし出力
            // Console.WriteLine("改行あり a = {0} b = {1} c = {2}", a, b, c);//改行付き出力
            Console.WriteLine(max);
        }
    }
}