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:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt(), k = in.nextInt();
            int[] x = new int[n];
            int[] y = new int[n];
            char[] c = new char[n];
            for (int i = 0; i < n; i++) {
                x[i] = in.nextInt();
                y[i] = in.nextInt();
                c[i] = in.next().toCharArray()[0];
            }

            long[][] bdp = new long[k][k];
            long[][] wdp = new long[k][k];

            for (int i = 0; i < n; i++) {
                int cx = x[i], cy = y[i];
                boolean isBlack = (c[i] == 'B');
                if (cx < 0) {
                    cx = cx + k * (Math.abs(cx) / k + 1);
                }
                if (cy < 0) {
                    cy = cy + k * (Math.abs(cy) / k + 1);
                }

                boolean changeColor = ((cx / k) + (cy / k)) % 2 == 1;

                int ccx = cx % k, ccy = cy % k;
                if (!changeColor) {
                    if (isBlack) bdp[ccx][ccy]++;
                    else wdp[ccx][ccy]++;
                } else {
                    if (isBlack) wdp[ccx][ccy]++;
                    else bdp[ccx][ccy]++;
                }
            }

            for (int i = 1; i < k; i++) {
                wdp[i][0] += wdp[i - 1][0];
                bdp[i][0] += bdp[i - 1][0];
            }
            for (int i = 1; i < k; i++) {
                wdp[0][i] += wdp[0][i - 1];
                bdp[0][i] += bdp[0][i - 1];
            }

            for (int i = 1; i < k; ++i) {
                for (int j = 1; j < k; ++j) {
                    bdp[i][j] += bdp[i - 1][j] + bdp[i][j - 1] - bdp[i - 1][j - 1];
                    wdp[i][j] += wdp[i - 1][j] + wdp[i][j - 1] - wdp[i - 1][j - 1];
                }
            }

            long res = 0;

            for (int i = 0; i < k; i++) {
                for (int j = 0; j < k; j++) {
                    long blacks = bdp[k - 1][k - 1] - (bdp[k - 1][j] + bdp[i][k - 1] - bdp[i][j]) + bdp[i][j];
                    long whites = wdp[k - 1][j] + wdp[i][k - 1] - 2 * wdp[i][j];
                    res = Math.max(res, blacks + whites);
                }
            }

            for (int i = 0; i < k; i++) {
                for (int j = 0; j < k; j++) {
                    long whites = wdp[k - 1][k - 1] - (wdp[k - 1][j] + wdp[i][k - 1] - wdp[i][j]) + wdp[i][j];
                    long blacks = bdp[k - 1][j] + bdp[i][k - 1] - 2 * bdp[i][j];
                    res = Math.max(res, blacks + whites);
                }
            }

            out.println(res);
        }

    }
}