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)

N, K = map(int, input().split())

cntH = [[0] * K for _ in range(K)]
cntW = [[0] * K for _ in range(K)]
for _ in range(N):
    x, y, c = map(str, input().split())
    x = int(x); y = int(y)
    
    if c == "W":
        cntW[y % K][x % K] += 1
    else:
        cntH[y % K][x % K] += 1

# 二次元累積和
for i in range(1, K):
    cntH[0][i] += cntH[0][i - 1]
    cntW[0][i] += cntW[0][i - 1]
    cntH[i][0] += cntH[i - 1][0]
    cntW[i][0] += cntW[i - 1][0]
for i in range(1, K):
    for j in range(1, K):
        cntH[i][j] += cntH[i - 1][j] + cntH[i][j - 1]
        cntW[i][j] += cntW[i - 1][j] + cntW[i][j - 1]

ans = 0
for i in range(K):
    for j in range(K):
        cnt1 = 0
        cnt2 = 0

        # 左上
        if i != 0 and j != 0:
            cnt1 += cntW[i - 1][j - 1]
            cnt2 += cntH[i - 1][j - 1]
        # 左下(白)
        if i != K - 1 and j != 0:
            cnt1 += cntH[K - 1][j - 1]
            cnt2 += cntW[K - 1][j - 1]
            if i != 0:
                cnt1 -= cntH[i - 1][j - 1]
                cnt2 -= cntW[i - 1][j - 1]
        # 右下(黒)
        if i != K - 1 and j != K - 1:
            cnt1 += cntW[K - 1][K - 1]
            cnt2 += cntH[K - 1][K - 1]
            if i != 0:
                cnt1 -= cntW[i - 1][K - 1]
                cnt2 -= cntH[i - 1][K - 1]
            if j != 0:
                cnt1 -= cntW[K - 1][j - 1]
                cnt2 -= cntH[K - 1][j - 1]
            if i != 0 and j != 0:
                cnt1 += cntW[i - 1][j - 1]
                cnt2 += cntH[i - 1][j - 1]
        # 右上(白)
        if i != 0 and j != K - 1:
            cnt1 += cntH[i - 1][K - 1]
            cnt2 += cntW[i - 1][K - 1]
            if j != 0:
                cnt1 -= cntH[i - 1][j - 1]
                cnt2 -= cntW[i - 1][j - 1]
        
        ans = max(ans, cnt1, cnt2)

print(ans)