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())
G = [[[0, 0] for j in range(2 * K + 1)] for i in range(2 * K + 1)]
W = 0
for i in range(N):
  x, y, c = input().split()
  G[int(x) % (2 * K)][int(y) % (2 * K)][0 if c == 'W' else 1] += 1
  W += 1 if c == 'W' else 0
for i in range(1, 2 * K + 1):
  for j in range(1, 2 * K + 1):
    G[i][j][0] = G[i][j - 1][0]
    G[i][j][1] = G[i][j - 1][1]
for i in range(1, 2 * K + 1):
  for j in range(1, 2 * K + 1):
    G[i][j][0] += G[i - 1][j][0]
    G[i][j][1] += G[i - 1][j][1]
cnt = 0
for i in range(1, K + 1):
  for j in range(1, K + 1):
    w = G[i - 1][j - 1][0] + G[i + K - 1][j + K - 1][0] - G[i - 1][j + K - 1][0] - G[i + K - 1][j - 1][0]
    b = G[i - 1][j - 1][1] + G[i + K - 1][j + K - 1][1] - G[i - 1][j + K - 1][1] - G[i + K - 1][j - 1][1]
    cnt = max([w + (N - W - b), W - w + b, cnt])
print(cnt)