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: Accepted)

N, K = map(int, input().split())
T = [[0] * (2 * K + 5) for i in range(2 * K + 5)]
for i in range(N):
    x, y, c = input().split()
    x, y = int(x), int(y)
    if c == 'W':
        y += K
    T[x % (2 * K) + 1][y % (2 * K) + 1] += 1

for i in range(1, 2 * K + 1):
    for j in range(1, 2 * K + 1):
        T[i][j] += T[i][j - 1]


for j in range(1, 2 * K + 1):
    for i in range(1, 2 * K + 1):
        T[i][j] += T[i - 1][j]


num = 0
for i in range(K + 1):
    for j in range(K + 1):
        d = T[i][j]
        d += T[i + K][j + K] - T[i][j + K] - T[i + K][j] + T[i][j]
        d += T[2 * K][j] - T[i + K][j]
        d += T[i][2 * K] - T[i][j + K]
        d += T[2 * K][2 * K] - T[2 * K][j + K] - T[i + K][2 * K] + T[i + K][j + K]
        num = max(num, d)
        num = max(num, N - d)

print(num)