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)

def get_while(n):
    ans = []
    for _ in range(n):
       ans += [input().split(" ")]
    return ans

def solve(n, k, inputs_):
    inputs = list(inputs_)
    inputs = [[int(i[0]) % (2 * k), int(i[1]) % (2 * k), i[2]] for i in inputs]
    points = [[i[0], i[1] + k if i[2] == 'W' else 0] for i in inputs]
    ans = 0
    for x in range(2 * k):
        for y in range(2 * k):
            interim_ans = 0
            for p in points:
                p = [(p[0] - x) % (2 * k), (p[1] - y) % (2 * k)]
                condition = (0 <= p[0] <= (k - 1) and 0 <= p[1] <= (k - 1)) or (k <=  p[0] <=  (2 * k - 1) and k <= p[1] <= (2 * k - 1))
                if condition:
                    interim_ans = interim_ans + 1
            if interim_ans > ans:
                ans = interim_ans
    return ans

if __name__ == '__main__':
    n, k = list(map(lambda x: int(x), input().split(" ")))
    inputs = get_while(n)
    print(solve(n, k, inputs))