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 Python (3.4.3) (judge verdict: Wrong Answer)

ri = lambda: int(input())
rl = lambda: list(map(int,input().split()))
rr = lambda N: [ri() for _ in range(N)]
YN = lambda b: print('YES') if b else print('NO')
INF = 10**18

N,K=rl()
X = [0]*N
Y = [0]*N
C = [0]*N
W = [[0 for _ in range(2*K+1)] for _ in range(2*K+1)]
B = [[0 for _ in range(2*K+1)] for _ in range(2*K+1)]
for i in range(N):
    x,y,c=input().split()
    x = int(x)%(2*K)
    y = int(y)%(2*K)
    X[i] = x
    Y[i] = y
    if c == 'W':
        W[x][y] += 1
        C[i] = 0
    else:
        B[x][y] += 1
        C[i] = 1

for xy in range(1,2*K):
    W[xy][0] += W[xy-1][0]
    W[0][xy] += W[0][xy-1]
    B[xy][0] += B[xy-1][0]
    B[0][xy] += B[0][xy-1]
for x in range(1,2*K):
    for y in range(1,2*K):
        W[x][y] += W[x-1][y] + W[x][y-1] - W[x-1][y-1]
        B[x][y] += B[x-1][y] + B[x][y-1] - B[x-1][y-1]

ans = 0
for x in range(K+1):
    for y in range(K+1):
        res = (W[x-1][y-1] +
        B[x+K-1][y-1] - B[x-1][y-1] +
        W[2*K-1][y-1] - W[x+K-1][y-1] + 
        B[x-1][y+K-1] - B[x-1][y-1] +
        W[x+K-1][y+K-1] - W[x-1][y+K-1] - W[x+K-1][y-1] + W[x-1][y-1] +
        B[2*K-1][y+K-1] - B[x+K-1][y+K-1] - B[2*K-1][y-1] + B[x+K-1][y-1] +
        W[x-1][2*K-1] - W[x-1][y+K-1] +
        B[x+K-1][2*K-1] - B[x-1][2*K-1] - B[x+K-1][y+K-1] + B[x-1][y+K-1] + 
        W[2*K-1][2*K-1] - W[x+K-1][2*K-1] - W[2*K-1][y+K-1] + W[x+K-1][y+K-1])

        ans = max(ans,res)

print(ans)