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)

# coding: utf-8
import sys
import numpy as np

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

# 縦K、横2*Kの長方形に全ての希望をWとして入れる
# numpyの累積和、最後にmaxをとる
N, K = lr()
table = [[0] * 2*K for _ in range(K)]
for _ in range(N):
    x, y, c = sr().split()
    x = int(x); y = int(y)
    if c == 'B':
        y -= K  # ここで全てWとして扱える
    x %= 2 * K; y %= 2 * K
    if x >= K and y >= K:
        x -= K; y -= K
    elif y >= K:
        x += K; y -= K
    # 長方形に入った
    table[y][x] += 1

table = np.array(table, dtype=np.int32)
table_cum = table.cumsum(axis=1).cumsum(axis=0)
table_cum[:, K:] -= table_cum[:, :-K]
answer = table_cum.max()
print(answer)