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: Wrong Answer)

var n,tmp3,x1,y1,x2,y2,k,ans,tmp5:int64;
i,j:longint;
    x,y:array[1..200000]of int64;
    c,c2:array[-10..4000,-10..4000]of int64;
    tmp,tmp2:char;
begin
  readln(n,k);
  for i:=1 to n do
  begin
    readln(x[i],y[i],tmp,tmp2);
    x[i]:=x[i] mod (k*2);
    y[i]:=y[i] mod (k);
    if tmp2='W' then
    begin
      if x[i]>=k then x[i]:=x[i]-k
      else x[i]:=x[i]+k;
    end;
    inc(c[x[i],y[i]]);
  end;
  for i:=0 to k*2-1 do
    for j:=0 to k*2-1 do
    c2[i,j]:=c2[i-1,j]+c2[i,j-1]+c[i,j]-c2[i-1,j-1];
  for i:=0 to k do
    for j:=0 to k do
    begin
      x1:=i-1;
      y1:=j-1;
      x2:=i+k-1;
      y2:=j+k-1;
      tmp5:=c2[x2,y2]-c2[x1,y2]-c2[x2,y1]+c2[x1,y1];
      if (i<>0) and (j<>0) then
      begin
      x1:=-1;
      x2:=i-1;
      y1:=-1;
      y2:=j-1;
      tmp5:=tmp5+c2[x2,y2]-c2[x1,y2]-c2[x2,y1]+c2[x1,y1]; end;
      if (i<>0) and (j<>k) then
      begin
      x1:=-1;
      x2:=i-1;
      y1:=j+k-1;
      y2:=k*2-1;
      tmp5:=tmp5+c2[x2,y2]-c2[x1,y2]-c2[x2,y1]+c2[x1,y1]; end;
      if (i<>k) and (j<>0) then
      begin
      x1:=i+k-1;
      x2:=k*2-1;
      y1:=-1;
      y2:=j-1;
      tmp5:=tmp5+c2[x2,y2]-c2[x1,y2]-c2[x2,y1]+c2[x1,y1]; end;
      if (i<>k) and (j<>k) then
      begin
      x1:=i+k-1;
      x2:=k*2-1;
      y1:=j+k-1;
      y2:=k*2-1;
      tmp5:=tmp5+c2[x2,y2]-c2[x1,y2]-c2[x2,y1]+c2[x1,y1]; end;
      if tmp5>ans then ans:=tmp5;
    end;
    if ans<0 then writeln(0) else if ans>n then writeln(n) else
    writeln(ans);
end.