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 Python (3.8.2) (judge verdict: Wrong Answer)

import itertools
import numpy as np
N, K, *XYC = open(0).read().split()
N = int(N)
K = int(K)
board = np.zeros((4 * K + 1, 4 * K + 1), dtype=np.uint16)
for x, y, c in zip(XYC[::3], XYC[1::3], XYC[2::3]):
    x = int(x)
    y = int(y)
    if c == 'W':
        x += K
    x = x % (2 * K)
    y = y % (2 * K)
    board[x, y] += 1
    board[(x + K) % (2 * K), (y + K) % (2 * K)] += 1
board[1 + 2 * K:, 1 + 2 * K:] = board[:2 * K, :2 * K]
board[1:1 + 2 * K, 1 + 2 * K:] = board[1 + 2 * K:, 1 + 2 * K:]
board[1 + 2 * K:, 1:1 + 2 * K] = board[1 + 2 * K:, 1 + 2 * K:]
board[0, :] = 0
board[:, 0] = 0
board = np.cumsum(np.cumsum(board, axis=0), axis=1)
ans = np.max(board[K:3 * K, K:3 * K] + board[:2 * K, :2 * K] -
             board[:2 * K, K:3 * K] - board[K:3 * K, :2 * K])
print(ans)