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 (7.3.0) (judge verdict: Accepted)

n, k = map(int, input().split())

C = [[0]*(2*k) for _ in range(2*k)]

for i in range(n):
    x, y, c = map(str, input().split())
    x, y = int(x), int(y)
    if c == 'W':
        y += k
    C[y%(2*k)][x%(2*k)] += 1

#print(C)
s = [[0]*(2*k+1) for _ in range(2*k+1)]
for i in range(2*k):
    for j in range(2*k):
        s[i+1][j+1] = s[i+1][j] + s[i][j+1] - s[i][j] + C[i][j]

#print(s)

def count(x1, x2, y1, y2):
    return s[y2][x2]-s[y1][x2]-s[y2][x1]+s[y1][x1]

ans = 0
for i in range(k):
    for j in range(k):
        temp = 0
        temp += count(0, j, 0, i)
        temp += count(j, j+k, i, i+k)
        temp += count(0, j, i+k, 2*k)
        temp += count(j+k, 2*k, 0, i)
        temp += count(j+k, 2*k, i+k, 2*k)
        ans = max(ans, max(temp, n-temp))
print(ans)