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)

N,K=map(int,input().split())
XYC=[list(input().split()) for i in range(N)]

MAP=[[0 for i in range(K*2+1)] for j in range(K*2+1)]
mod=K*2
for x,y,c in XYC:
    x=int(x)
    y=int(y)
    if c=="W":
        x+=K

    MAP[x%mod+1][y%mod+1]+=1
    MAP[(x+K)%mod+1][(y+K)%mod+1]+=1




for i in range(K*2+1):
    for j in range(1,K*2+1):
        MAP[i][j]=MAP[i][j-1]+MAP[i][j]

for i in range(K*2+1):
    for j in range(1,K*2+1):
        MAP[j][i]=MAP[j-1][i]+MAP[j][i]

ANS=0
for i in range(K):
    for j in range(K):

        if ANS<MAP[i+K][j+K]-MAP[i][j+K]-MAP[i+K][j]+MAP[i][j]:
            ANS=MAP[i+K][j+K]-MAP[i][j+K]-MAP[i+K][j]+MAP[i][j]
        if ANS<N-(MAP[i+K][j+K]-MAP[i][j+K]-MAP[i+K][j]+MAP[i][j]):
            ANS=N-(MAP[i+K][j+K]-MAP[i][j+K]-MAP[i+K][j]+MAP[i][j])
print(ANS)