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 <bits/stdc++.h>
#define rep(i,a,b)	for(int i=a;i<=b;i++)
using namespace std;
const int N=2e5+5,M=6008;
int n,k,x,y,m;
string c;
int f[M][M];
int calc(int x1,int y1)
{
	int x2=x1+k-1,y2=y1+k-1;
	x1=max(1,x1),y1=max(1,y1);
	x2=min(x2,m),y2=min(y2,m);
	if(x2<x1||y2<y1)
		return 0;
	return f[x2][y2]-f[x1-1][y2]-f[x2][y1-1]+f[x1-1][y1-1];
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin>>n>>k;	
	m=2*k;
	memset(f,0,sizeof(f));
	rep(i,1,n)
	{
		cin>>x>>y>>c;
		if(c=="W")
			y+=k;
		x%=m,y%=m;
		x++,y++;
		f[x][y]++;
	}
	for(int i=1;i<=2*m;i++)
		for(int j=1;j<=2*m;j++)
			f[i][j]=f[i][j]+f[i][j-1]+f[i-1][j]-f[i-1][j-1];
	int res=0;
	for(int i=1;i<=m;i++)
	{
		for(int j=1;j<=m;j++)
		{
			int cnt=calc(i,j);
			cnt+=calc(i-k,j-k)+calc(i-k,j+k)+calc(i+k,j-k)+calc(i+k,j+k);
			cnt+=calc(i-m,j)+calc(i+m,j)+calc(i,j-m)+calc(i,j+m);
			res=max(res,cnt);
		}
	}
	cout<<res<<endl;
	return 0;
}