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 PyPy3 (2.4.0) (judge verdict: Accepted)

def get(i1, j1, i2, j2):
  if i1 > i2 or j1 > j2 or i1 < 0 or j1 < 0 or i2 < 0 or j2 < 0:
    return 0
  elif i1 > 0 and j1 > 0:
    return l[i2][j2] - l[i1-1][j2] - l[i2][j1-1] + l[i1-1][j1-1]
  elif i1 <= 0 < j1:
    return l[i2][j2] - l[i2][j1-1]
  elif j1 <= 0 < i1:
    return l[i2][j2] - l[i1 - 1][j2]
  else:
    return l[i2][j2]

N, K = map(int, input().split())
K2 = 2*K
R = []
l=[[0] * K2 for _ in range(K2)]

for i in range(N):
  xi, yi, ci = input().split()
  if ci == "W":
    yi = int(yi) + K
  xi, yi = int(xi), int(yi)
  l[xi%K2][yi%K2]+=1

for y in range(K2):
  for x in range(1,K2):
    l[x][y] += l[x-1][y]
for y in range(1,K2):
  for x in range(K2):
    l[x][y] += l[x][y-1]

ans = 0
for i in range(K):
  for j in range(K):
    tmp = 0
    tmp += get(0, 0, i-1, j-1)
    tmp += get(0, j+K, i-1, K2-1)
    tmp += get(i+K, j+K, K2-1, K2-1)
    tmp += get(i+K, 0, K2-1, j-1)
    tmp += get(i, j, i+K-1, j+K-1)

    ans = max(ans, tmp, N-tmp)
print(ans)