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: Time Limit Exceeded)

n,k = list(map(int,input().split()))
k2 = 2*k
G = [None for i in range(n)]
max = 0
for i in range(n):
    x,y,c = list(input().split())
    x = int(x)
    y = int(y)
    G[i]=x,y,c

def dps():
    global max
    count = 0
    for a in range(k):
        for b in range(k):
            for i in range(n):
                x = (G[i][0]+a)%k2
                y = (G[i][1]+b)%k2
                c = G[i][2]
                if x < k and y < k:
                    if c == 'W':
                        count += 1
                if x < k and y >= k:
                    if c == 'B':
                        count += 1
                if x >= k and y < k:
                    if c == 'B':
                        count += 1
                if x >= k and y >= k:
                    if c == 'W':
                        count += 1
            if max < count:
                max = count
            if max < n-count:
                max = n-count
            count = 0

dps()
print(max)