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>
#include<cstring>
inline int geti()
{
	int x,f=1;char c;
	while((c=getchar())<'0'||c>'9') if(c=='-') f=-1;
	x=c-'0';
	while((c=getchar())>='0'&&c<='9') x=x*10+c-'0';
	return x*f;
}

const int NN=100000,NK=1000;
int x[NN+5],y[NN+5],y1[3*NK+5],n,k,cnt,Max;
bool c[NN+5];
char op;

int main()
{
	n=geti();k=geti();
	for(int i=1;i<=n;i++)
	{
		x[i]=geti()%(2*k);
		y[i]=geti()%(2*k);
		scanf("%c",&op);
		c[i]=(op=='W');
	}
	for(int i=0;i<=k;i++)
	{
		cnt=0;
		memset(y1,0,sizeof(y1));
		for(int j=1;j<=n;j++)
		{
			int q=(x[j]>=i&&x[j]<i+k),
			p=(y[j]>=0&&y[j]<k);
			if(q^p==c[j])
			{
				cnt++;
				y1[y[j]]++;
			}
			else
				y1[y[j]]--;
		}
		for(int j=0;j<=k;j++)
		{
			if(cnt>Max) Max=cnt;
			if(n-cnt>Max) Max=n-cnt;
			if(j!=k)
				cnt=cnt-y1[j]-y1[k+j];
		}
	}
	printf("%d\n",Max);
	return 0;
}