Problem: 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:

cba927b2484fad94fb5ff7473e9aadef.png

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.

Examples

Input

4 3
0 1 W
1 2 W
5 3 B
5 4 B


Output

4


Input

2 1000
0 0 B
0 1 W


Output

2


Input

6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W


Output

4

Solution (in PYTHON3):

Solution:
def cumsum(T, K):
    R = [[0] * K for _ in range(K)]
    for i in range(K):
        t = 0
        for j in range(K):
            t += T[i][j]
            R[i][j] = t
    for i in range(K):
        t = 0
        for j in range(K):
            t += R[j][i]
            R[j][i] = t
    return R

def fm(B, W, K):
    m = 0
    for i in range(K):
        for j in range(K):
            t = B[i][j]
            if i == K - 1 or j == K - 1:
                t += W[K - 1][K - 1] - W[i][j]
            else:
                t += B[K - 1][K - 1] - B[K - 1][j] - B[i][K - 1] + B[i][j]
                t += W[K - 1][j] + W[i][K - 1] - 2 * W[i][j]
            m = max(m, t)
    return m

def main():
    N, K = map(int, input().split())
    K2 = 2 * K
    B = [[0] * K for _ in range(K)]
    W = [[0] * K for _ in range(K)]
    for _ in range(N):
        x1, y1, c = input().split()
        x, y = int(x1) % K2, int(y1) % K2
        if c == 'B':
            x = (x - K) % K2
        if x >= K and y >= K:
            x, y = x - K, y - K
        if x < K and y < K:
            B[x][y] += 1
        else:
            x, y = (x - K, y) if y < K else (x, y - K)
            W[x][y] += 1
    B = cumsum(B, K)
    W = cumsum(W, K)
    return max(fm(B, W, K), fm(W, B, K))

print(main())