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 <iostream>
#include <cstdio>
#include <cmath>

using namespace std;

int N,K;

int board[2005][2005];

int getBlackNum(int x1,int y1,int x2,int y2)
{
	return board[x2][y2] - board[x1][y2] - board[x2][y1] + board[x1][y1];
}

int main()
{
	scanf("%d %d",&N,&K);
	char ch;
	int x,y;
	for(int i=0 ; i<N ; i++)
	{
		scanf("%d %d %c",&x,&y,&ch);
		if(ch == 'W')x += K;
		x %= K*2;
		y %= K*2;
		board[x+1][y+1]++;
	}
	for(int i=1 ; i<=2*K ; i++)
	{
		for(int j=1 ; j<=2*K ; j++)
		{
			board[i][j] += board[i-1][j] + board[i][j-1] - board[i-1][j-1];
		}
	}
	int Max = 0;
	for(int i=1; i<=K ; i++)
	{
		for(int j=1 ; j<=K ; j++)
		{
			int mid = getBlackNum(0,0,i,j) + getBlackNum(0,j+K,i,2*K) 
					+ getBlackNum(i+K,0,2*K,j) + getBlackNum(i+K,j+K,2*K,2*K)
					+ getBlackNum(i,j,i+K,j+K);
			Max = max(Max,max(mid,N-mid));
		}
	}
	printf("%d\n",Max);
	return 0;
}