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())
B=[[0]*(2*K) for i in range(2*K)]
W=[[0]*(2*K) for i in range(2*K)]
w=0
for i in range(N):
    x,y,c=map(str,input().split())
    x=int(x)
    y=int(y)
    if c=="B":
        B[y%(2*K)][x%(2*K)]+=1
    else:
        w+=1
        W[y%(2*K)][x%(2*K)]+=1
sumb=[[0]*(2*K+1) for i in range(2*K+1)]
sumw=[[0]*(2*K+1) for i in range(2*K+1)]
for i in range(2*K):
    for j in range(2*K):
        sumb[i+1][j+1]=sumb[i][j+1]+sumb[i+1][j]-sumb[i][j]+B[i][j]
        sumw[i+1][j+1]=sumw[i][j+1]+sumw[i+1][j]-sumw[i][j]+W[i][j]


ans=0
for i in range(K):
    for j in range(K):
        for _ in range(2):
            s=0
            s+=sumb[i][j]-sumb[i][0]-sumb[0][j]+sumb[0][0]#
            s+=sumb[i+K][j+K]-sumb[i][j+K]-sumb[i+K][j]+sumb[i][j]
            s+=sumb[i][2*K]-sumb[0][2*K]-sumb[i][j+K]+sumb[0][j+K]#
            s+=sumb[2*K][j]-sumb[i+K][j]-sumb[2*K][0]+sumb[i+K][0]#
            s+=sumb[2*K][2*K]-sumb[i+K][2*K]-sumb[2*K][j+K]+sumb[i+K][j+K]#

            s+=sumw[i][j+K]-sumw[0][j+K]-sumw[i][j]+sumw[0][j]#
            s+=sumw[i+K][j]-sumw[i][j]-sumw[i+K][0]+sumw[i][0]#
            s+=sumw[2*K][j+K]-sumw[i+K][j+K]-sumw[2*K][j]+sumw[i+K][j]#
            s+=sumw[i+K][2*K]-sumw[i+K][j+K]-sumw[i][2*K]+sumw[i][j+K]#

            ans=max(ans,s)
            sumb,sumw=sumw,sumb

print(ans)