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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	n,k,ans,now,i,j,x,y:Longint;
	c:Char;
	w:array[0..4000,0..4000]of Longint;
function f(u,v:Longint):Longint;
begin
	f:=w[u+k,v+k]-w[u,v+k]-w[u+k,v]+w[u,v];
end;
begin
	read(n,k);
	for i:=1 to n do begin
		read(x,y,c,c);
		if c='B' then inc(x,k);
		x:=x mod(2*k);
		y:=y mod(2*k);
		inc(w[x+1+k,y+1+k]);
	end;
	for i:=1 to 4*k do for j:=1 to 4*k do inc(w[i,j],w[i-1,j]+w[i,j-1]-w[i-1,j-1]);
	for i:=0 to k-1 do for j:=0 to k-1 do begin
		now:=f(i,j)+f(i+k,j+k)+f(i+2*k,j)+f(i,j+2*k)+f(i+2*k,j+2*k);
		if now>ans then ans:=now;
		now:=f(i+k,j)+f(i,j+k)+f(i+2*k,j+k)+f(i+k,j+2*k);
		if now>ans then ans:=now;
	end;
	writeln(ans);
end.