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 (7.3.0) (judge verdict: Wrong Answer)

#!/usr/bin/env python3
def main():
    N, K = map(int, input().split())
    black = [[0]*(2*K+1) for _ in range(2*K+1)]
    white = [[0]*(2*K+1) for _ in range(2*K+1)]
    for i in range(N):
        x, y, c = input().split()
        x, y = int(x), int(y)
        if c == "B":
            black[1+x % (2*K)][1+y % (2*K)] += 1
        else:
            white[1+x % (2*K)][1+y % (2*K)] += 1
    for i in range(2*K+1):
        for j in range(1, 2*K+1):
            black[i][j] += black[i][j-1]
            white[i][j] += white[i][j-1]
    for i in range(1, 2*K+1):
        for j in range(2*K+1):
            black[i][j] += black[i-1][j]
            white[i][j] += white[i-1][j]
    # print(*black, sep="\n")
    # print(*white, sep="\n")
    M = 2*K
    mtot = 0
    for offx in range(K):
        for offy in range(K):
            tot = 0
            tot += 2*black[offx][offy]
            tot -= 2*black[offx+K][offy]
            tot -= 2*black[offx][offy+K]
            tot += black[-1][offy]
            tot += black[offx][-1]
            tot += black[-1][-1]

            # 領域6
            tot += 2*white[offx+K][offy]
            tot += 2*white[offx][offy+K]
            tot -= 2*white[offx][offy]
            tot -= 2*white[offx+K][offy+K]
            tot -= white[-1][offy]
            tot += white[-1][offy+K]
            tot -= white[offx][-1]
            tot += white[offx+K][-1]

            mtot = max(mtot, tot)
    print(mtot)
    return


if __name__ == '__main__':
    main()