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.ComponentModel;

namespace atcoder_practice1
{
    class _086D0
    {


        static int[,] memo;
        static void Main()
        {
            string[] string_array;
            int N, K;
            string_array = Console.ReadLine().Split(' ');
            N = int.Parse(string_array[0]);
            K = int.Parse(string_array[1]);

            memo = new int[2*K + 1, 2*K + 1];

            for (int i=0;i < N; i++)
            {
                int x, y, x_, y_;
                string c;
                string_array = Console.ReadLine().Split(' ');
                x = int.Parse(string_array[0]);
                y = int.Parse(string_array[1]);
                c = string_array[2];

                if(c == "W")
                {
                    x += K;
                }

                x %= 2 * K;
                y %= 2 * K;

                x_ = x % K;
                y_ = y % K;

                if((x<K && y<K) || (x>=K && y >= K))
                {
                    imos(0, 0, x_ + 1, y_ + 1);
                    imos(x_ + K + 1, 0, 2 * K, y_ + 1);

                    imos(0, y_ + K + 1, x_ + 1, 2 * K);
                    imos(x_ + K + 1, y_ + K + 1, 2 * K, 2 * K);

                    imos(x_ + 1, y_ + 1, x_ + K + 1, y_ + K + 1);
                }
                else
                {
                    imos(x_ + 1, 0, x_ + K + 1, y_ + 1);
                    imos(x_ + 1, y_ + K + 1, x_ + K + 1, 2 * K);

                    imos(0, y_ + 1, x_ + 1, y_ + K + 1);
                    imos(x_ + K + 1, y_ + 1, 2 * K, y_ + K + 1);
                }
            }

            for (int i = 0; i < 2*K + 1; i++)
            {
                for (int j = 1; j < 2 * K + 1; j++)
                {
                    memo[i,j] += memo[i,j - 1];
                }
            }

            for (int i = 1; i < 2*K + 1; i++)
            {
                for (int j = 0; j < 2 * K + 1; j++)
                {
                    memo[i,j] += memo[i - 1,j];
                }
            }

            int m = 0;
            for (int i = 0; i < 2 * K; i++)
            {
                for (int j = 0; j < 2 * K; j++)
                {
                    m = Math.Max(m, memo[i,j]);
                }
            }

            Console.WriteLine(m);
        }

        static void imos(int x, int y, int x2, int y2 )
        {
            memo[x, y]++;
            memo[x, y2]--;
            memo[x2, y]--;
            memo[x2, y2]++;
        }

    }
}