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.ArrayList;
import java.util.Scanner;
public class Main {
	public static void main(String args[]) {
		Scanner scanner = new Scanner(System.in);
		int N = scanner.nextInt();
		int K = scanner.nextInt();
		ArrayList<String> c = new ArrayList<>();
		ArrayList<Integer> a = new ArrayList<>();
		ArrayList<Integer> b = new ArrayList<>();
		ArrayList<Boolean> booleans = new ArrayList<>();
		int max = 0;
		for(int i=0;i<N;i++){
			a.add(scanner.nextInt());
			b.add(scanner.nextInt());
			c.add(scanner.next());
			booleans.add(true);
		}
		for(int i=0;i<N;i++){
			if(!booleans.get(i)){
				continue;
			}
			for(int j=i+1;j<N;j++){
				if(((a.get(j))%K==(a.get(i))%K)&((b.get(j))%K==(b.get(i))%K)){
					booleans.set(j,false);
				}
			}
		}
		for(int i=0;i<N;i++){
			if(!booleans.get(i)){
				continue;
			}
			for(int w=0;w<K;w++){
				for(int h=0;h<K;h++){
					int pos = 0;
					for(int j=0;j<N;j++){
						if(c.get(i).equals(c.get(j))){
							if(((((((a.get(j)+w)/K)%2)+((b.get(j)+h)/K)%2)))%2==0){
								pos++;
							}
						}
						else{
							if(((((((a.get(j)+w)/K)%2)+((b.get(j)+h)/K)%2)))%2!=0){
								pos++;
							}
						}
					}
					if(max<pos){
						max = pos;
					}
					if(max==N){
						break;
					}
				}
			}
			if(max==N){
				break;
			}
		}
		System.out.println(max);
	}
}