Problem: 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:

cba927b2484fad94fb5ff7473e9aadef.png

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.

Examples

Input

4 3
0 1 W
1 2 W
5 3 B
5 4 B


Output

4


Input

2 1000
0 0 B
0 1 W


Output

2


Input

6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W


Output

4

Solution (in JAVA):

Solution:
// practice with kaiboy
import java.io.*;
import java.util.*;

public class Main extends PrintWriter {
	Main() { super(System.out, true); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		Main o = new Main(); o.main(); o.flush();
	}

	void main() {
		int n = sc.nextInt();
		int k = sc.nextInt(), k2 = k * 2, k4 = k * 4;
		int[][] bb = new int[k4][k4];
		int[][] ww = new int[k4][k4];
		while (n-- > 0) {
			int i = sc.nextInt() % k2;
			int j = sc.nextInt() % k2;
			char c = sc.next().charAt(0);
			if (c == 'B') {
				bb[i][j]++;
				bb[k2 + i][j]++;
				bb[i][k2 + j]++;
				bb[k2 + i][k2 + j]++;
			} else {
				ww[i][j]++;
				ww[k2 + i][j]++;
				ww[i][k2 + j]++;
				ww[k2 + i][k2 + j]++;
			}
		}
		for (int i = 0; i < k4; i++)
			for (int j = 1; j < k4; j++) {
				bb[i][j] += bb[i][j - 1];
				ww[i][j] += ww[i][j - 1];
			}
		for (int i = 1; i < k4; i++)
			for (int j = 0; j < k4; j++) {
				bb[i][j] += bb[i - 1][j];
				ww[i][j] += ww[i - 1][j];
			}
		int ans = 0;
		for (int i_ = 0; i_ < k2; i_++)
			for (int j_ = 0; j_ < k2; j_++) {
				int i, j, cnt = 0;
				i = i_; j = j_;
				cnt += bb[i + k][j + k] - bb[i][j + k] - bb[i + k][j] + bb[i][j];
				i = i_ + k; j = j_ + k;
				cnt += bb[i + k][j + k] - bb[i][j + k] - bb[i + k][j] + bb[i][j];
				i = i_ + k; j = j_;
				cnt += ww[i + k][j + k] - ww[i][j + k] - ww[i + k][j] + ww[i][j];
				i = i_; j = j_ + k;
				cnt += ww[i + k][j + k] - ww[i][j + k] - ww[i + k][j] + ww[i][j];
				ans = Math.max(ans, cnt);
			}
		println(ans);
	}
}