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 = list(map(int, input().split()))
x = []
y = []
c = []
for i in range(N):
    temp = list(input().split())
    x.append(int(temp[0]))
    y.append(int(temp[1]))
    c.append(temp[2])

xt = []
yt = []
score = []
for n in range(N):
    flag = True
    xp = x[n] % (2 * K)
    yp = y[n] % (2 * K)
    for i in range(len(xt)):
        if xt[i] == xp and yt[i] == yp:
            flag = False
            idx = i
            break
    if flag:
        xt.append(xp)
        yt.append(yp)
        score.append(1)
    else:
        score[idx] += 1
x = xt
y = yt

result = 0
flag = True
for i in range(K):
    if flag:
        for j in range(K):
            if flag:
                val = [int((x[n] + i) % (2 * K) / K) + int((
                    y[n] + j) % (2 * K) / K) for n in range(len(x))]
                for k in [['B', 'W'], ['W', 'B']]:
                    count = 0
                    for n in range(len(x)):
                        if val[n] in [0, 2] and c[n] == k[0]:
                            count += score[n]
                        elif val[n] == 1 and c[n] == k[1]:
                            count += score[n]
                    if result < count:
                        result = count
                    if result == N:
                        flag = False
                        break

print(result)