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)

#縦k、横kのマスに移動させて考える
n, k = map(int, input().split())
x = []
y = []
mx = []
my = []
for _ in range(n):
    xx, yy, c = input().split()
    xx = int(xx)
    yy = int(yy)
    if c == 'W':
        xx += k
    xx %= 2 * k
    yy %= 2 * k
    if xx >= k:
        if yy >= k:
            x.append(xx - k)
            y.append(yy - k)
        else:
            mx.append(xx - k)
            my.append(yy)
    else:
        if yy >= k:
            mx.append(xx)
            my.append(yy - k)
        else:
            x.append(xx)
            y.append(yy)

graph = [[0 for _ in range(k)] for __ in range(k)]

#累積和
#lx + lmx = n
lx = len(x)
for i in range(lx):
    for j in range(x[i], k):
        graph[j][y[i]] += 1
    for j in range(x[i]):
        graph[j][0] += 1
        graph[j][y[i]] -= 1

lmx = len(mx)
for i in range(lmx):
    for j in range(mx[i], k):
        graph[j][my[i]] -= 1
    for j in range(mx[i]):
        graph[j][0] -= 1
        graph[j][my[i]] += 1

for i in range(k):
    for j in range(k-1):
        graph[i][j+1] += graph[i][j]

#最大値、最小値を取得
big = max([max(i) for i in graph]) + lmx
small = min([min(i) for i in graph]) - lx

if big + small >= 0:
    print(big)
else:
    print(-small)