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: Time Limit Exceeded)

import copy
from datetime import datetime

#print(datetime.now())
n,k = map(int ,input().split())
p = [[0] * (2*k) for i in range(2*k)]
ans = 0
for i in range(n):
  x,y,c = input().split()
  x = int(x)
  y = int(y)
  if c == 'B':
    x += k
  p[x%(2*k)][y%(2*k)] += 1
#[print(p[i]) for i in range(2*k)]
#print()
#print(datetime.now())

csum1 = copy.deepcopy(p)
for i in range(2*k):
    for j in range(1, k):
        csum1[i][0] += p[i][j]
    for j in range(1, 2*k):
        csum1[i][j] = csum1[i][j-1] - p[i][j-1] + p[i][(j+k-1)%(2*k)]
#print(datetime.now())
#[print(csum1[i]) for i in range(2*k)]
#print()

csum2 = copy.deepcopy(csum1)
#print(datetime.now())
for j in range(2*k):
    for i in range(1, k):
        csum2[0][j] += csum1[i][j]
    for i in range(1, 2*k):
        csum2[i][j] = csum2[i-1][j] - csum1[i-1][j] + csum1[(i+k-1)%(2*k)][j]

#[print(csum2[i]) for i in range(2*k)]
#print(datetime.now())
for i in range(2*k):
    for j in range(2*k):
        ans = max(ans, csum2[i][j] + csum2[(i+k)%(2*k)][(j+k)%(2*k)])

print(ans)