Problem:
Score : 500 points

Problem Statement

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:

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.

Sample Input 1

4 3
0 1 W
1 2 W
5 3 B
5 4 B

Sample Output 1

4

He can satisfy all his desires by painting as shown in the example above.

Sample Input 2

2 1000
0 0 B
0 1 W

Sample Output 2

2

Sample Input 3

6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W

Sample Output 3

4

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

w[4444][4444];
n,k;i,j,x,y,c;ans;now;f;
g(u,v){return w[u+k][v+k]-w[u][v+k]-w[u+k][v]+w[u][v];}
main(){
	scanf("%d%d",&n,&k);
	for(i=0;i<n;i++){
		scanf("%d%d %c",&x,&y,&c);
		if(c=='B')x+=k;
		x%=2*k,y%=2*k;
		w[x+1+k][y+1+k]++;
	}
	for(i=1;i<=4*k;i++)for(j=1;j<=4*k;j++)w[i][j]+=w[i-1][j]+w[i][j-1]-w[i-1][j-1];
	for(i=0;i<k;i++)for(j=0;j<k;j++){
		now=g(i+k,j+2*k)+g(i+2*k,j+k)+g(i,j+k)+g(i+k,j);
		if(ans<now)ans=now;
		now=g(i+2*k,j+2*k)+g(i,j+2*k)+g(i+k,j+k)+g(i+2*k,j)+g(i,j);
		if(ans<now)ans=now;
	}
	printf("%d\n",ans);
}