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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n,k=map(int,input().split())
b=[(2*k+1)*[0]for _ in range(2*k+1)]
def add(i,j):
  global b
  b[min(max(1,i+1),2*k)][min(max(1,j+1),2*k)]+=1
  b[min(max(1,i+1+k),2*k)][min(max(1,j+1+k),2*k)]+=1
  b[min(max(1,i+1+k),2*k)][min(max(1,j+1),2*k)]-=1
  b[min(max(1,i+1),2*k)][min(max(1,j+1+k),2*k)]-=1
for _ in range(n):
  x,y,c=input().split()
  x=int(x)
  y=int(y)
  if c=="B":y+=k
  x%=2*k
  y%=2*k
  add(x,y)
  add(x+k,y+k)
  add(x+k,y-k)
  add(x-k,y+k)
  add(x-k,y-k)
  add(x+2*k,y)
  add(x-2*k,y)
  add(x,y+2*k)
  add(x,y-2*k)
ans=0
for i in range(1,2*k+1):
  for j in range(1,2*k+1):
    b[i][j]+=b[i-1][j]+b[i][j-1]-b[i-1][j-1]
    ans=max(ans,b[i][j])
print(ans)