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 CPP):

Solution:
#include<cstdio>
int max(int a, int b, int c) {
	if (a < b)return b < c ? c : b;
	else return a < c ? c : a;
}
int sum[2000][2000];
int main() {
	int n, k, i, j, x, y, tmp, m=0;
	char c;
	scanf("%d%d", &n, &k);
	for (i = 0; i < 2*k; i++) {
		for (j = 0; j < 2*k; j++) {
			sum[i][j] = 0;
		}
	}
	for (i = 0; i < n; i++) {
		scanf("%d %d %c", &x, &y, &c);
		if (c == 'B')x += k;
		x = x % (2 * k);
		y = y % (2 * k);
		sum[x][y]++;
	}
	for (i = 2 * k - 2; i >= 0; i--) {
		sum[2 * k - 1][i] += sum[2 * k - 1][i + 1];
		sum[i][2 * k - 1] += sum[i + 1][2 * k - 1];
	}
	for (i = 2 * k - 2; i >= 0; i--) {
		for (j = 2 * k - 2; j >= 0; j--) {
			sum[i][j] += sum[i + 1][j] + sum[i][j + 1] - sum[i + 1][j + 1];
		}
	}
	for (i = 0; i < k; i++) {
		for (j = 0; j < k; j++) {
			tmp = sum[i][j] - sum[i + k][j] - sum[i][k + j] + sum[i + k][j + k];
			tmp = sum[i][0] + sum[0][j] - sum[i + k][0] - sum[0][j + k] - 2*tmp;
			m = max(tmp, n-tmp, m);
		}
	}
	printf("%d", m);
	return 0;
}