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: Wrong Answer)

def main():
    from itertools import accumulate as ac
    n,k=map(int,input().split())
    kk=2*k
    xyc=[input().split() for _ in [0]*n]
    b=[[0]*(k+1) for _ in [0]*(kk+1)]
    w=[[0]*(k+1) for _ in [0]*(kk+1)]
    for x,y,c in xyc:
        if c=="B":b[int(x)%kk+1][int(y)%k+1]+=1
        else:w[int(x)%kk+1][int(y)%k+1]+=1
    b=[list(ac(i)) for i in b]
    w=[list(ac(i)) for i in w]
    for i in range(1,kk+1):
        for j in range(k+1):
            b[i][j]+=b[i-1][j]
    for i in range(1,kk+1):
        for j in range(k+1):
            w[i][j]+=w[i-1][j]
    ans=0
    for i in range(kk):
        for j in range(k):
            a_t=((0,max(i-k,0),-2),(max(i-k,0),i,-1),(i,min(i+k,kk),0),(min(i+k,kk),kk,1))
            b_t=((max(j-k,0),j,-1),(j,min(j+k,k),0))
            a_t=[(i,j,l) for i,j,l in a_t if i!=j]
            b_t=[(i,j,l) for i,j,l in b_t if i!=j]
            black=[]
            white=[]
            for i,j,l in a_t:
                for x,y,z in b_t:
                    if (l+z)%2==0:
                        black.append((i,x,j,y))
                    else:
                        white.append((i,x,j,y))
            ret=0
            for tx1,ty1,tx2,ty2 in black:
                ret+=b[tx1][ty1]+b[tx2][ty2]-b[tx1][ty2]-b[tx2][ty1]
            for tx1,ty1,tx2,ty2 in white:
                ret+=w[tx1][ty1]+w[tx2][ty2]-w[tx1][ty2]-w[tx2][ty1]
            ans=max(ans,ret)
    print(ans)
main()