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())
white = [[0 for _ in range(k+1)] for _ in range(2*k+1)]

for _ in range(n):
	x, y, c = input().split()
	x, y = (int(x) - 1) % (2*k), (int(y) - 1) % k
	if c == "B":
		x = (x-k) % (2*k)

	if x < k:
		white[0][0] += 1
		white[x][0] += -1
		white[x+k][0] += -1
		white[2*k][0] += 1
		white[0][y] += -1
		white[x][y] += 2
		white[x+k][y] += -2
		white[2*k][y] += 1
		white[x][k] += -1
		white[x+k][k] += 1

	else:
		white[x-k][0] += 1
		white[x][0] += -1
		white[0][y] += 1
		white[x-k][y] += -2
		white[x][y] += 2
		white[2*k][y] += -1
		white[0][k] += -1
		white[x-k][k] += 1
		white[x][k] += -1
		white[2*k][k] += 1

#print(white)

for i in range(2*k+1):
	for j in range(k):
		white[i][j+1] += white[i][j]

for j in range(k+1):
	for i in range(2*k):
		white[i+1][j] += white[i][j]

#print(white)

ans = 0
for i in range(2*k):
	for j in range(k):
		ans = max(ans, white[i][j])

print(ans)