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 (3.4.3) (judge verdict: Wrong Answer)

n, k = map(int, input().split())
b_x_list = []
b_y_list = []
w_x_list = []
w_y_list = []
order = []
for i in range(n):
    x_in, y_in, c_in = map(str, input().split())
    if c_in == "B":
        b_x_list.append(int(x_in))
        b_y_list.append(int(y_in))
    else:
        w_x_list.append(int(x_in))
        w_y_list.append(int(y_in))
    order.append([int(x_in), int(y_in), c_in])
"""
print(b_x_list)
print(b_y_list)
print(w_x_list)
print(w_y_list)
b_x = set(b_x_list)
b_y = set(b_y_list)
w_x = set(w_x_list)
w_y = set(w_y_list)
"""
num = 0
for i in range(k*2):
    for j in range(k*2):
        tmp_num = 0
        for l in range(len(w_x_list)):
            if i <= w_x_list[l] <= i+k and j <= w_y_list[l] <= j+k:
                tmp_num += 1
        if num < tmp_num + len(b_x_list):
            for l in range(len(b_x_list)):
                if (b_x_list[l] < i or i+k < b_x_list[l]) or (b_y_list[l] < j or j+k < b_y_list[l]):
                    tmp_num += 1
        num = max(num, tmp_num)
        if num == n:
            break

print(num)