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:
import sys
input = sys.stdin.readline

def main():
    N, K = map(int, input().split())
    L = 2*K
    state = [[[0, 0] for _ in range(L+1)] for _ in range(K+1)]

    for _ in range(N):
        x, y, c = map(str, input().split())
        a, b = int(x)%L, int(y)%L
        k = 0 if c == 'W' else 1
        if a >= K:
            if b >= K:
                a -= K
                b -= K
            else:
                a -= K
                b += K
        state[a+1][b+1][k] += 1


    for i in range(K):
        for j in range(L):
            for k in [0, 1]:
                state[i+1][j+1][k] += state[i+1][j][k] + state[i][j+1][k] - state[i][j][k]

    ans = 0
    for x in range(K):
        for y in range(K):
            for k in [0, 1]:
                count = 0
                count += state[x][y][k]
                count += state[x][L][k] - state[x][y+K][k]
                count += state[K][y+K][k] - state[x][y+K][k] - state[K][y][k] + state[x][y][k]

                l = k ^ 1
                count += state[K][y][l] - state[x][y][l]
                count += state[x][y+K][l] - state[x][y][l]
                count += state[K][L][l] - state[K][y+K][l] - state[x][L][l] + state[x][y+K][l]

                ans = max(ans, count)
    print(ans)

if __name__ == "__main__":
    main()