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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

class Main{
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		int num = sc.nextInt();
		int k = sc.nextInt();

		int x[] = new int[num];
		int y[] = new int[num];
		int c[] = new int[num];

		for(int n=0;n<num;n++){
			x[n] = sc.nextInt();
			y[n] = sc.nextInt();

			String s = sc.next();
			if(s.equals("B")) c[n] = 1;
			else c[n] = 0;
		}

		
		int maxsat = 0;
		for(int l=0;l<k;l++){
			for(int m=0;m<k;m++){
				
				int sat = 0;

				for(int n=0;n<num;n++){
					if((((x[n]/(k+l))%2 + (y[n]/(k+m))%2))%2 == c[n]) sat++;
				}

				if(sat < num-sat) sat = num-sat; 
				if(sat > maxsat) maxsat = sat;
			}
		}

		System.out.println(maxsat);
	}
}