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

X = []
for i in range(N):
    h, w, c = input().split()
    h, w = int(h) - 1, int(w) - 1
    if c == "W":
        h += K
    X.append((h % (2 * K), w % (2 * K)))


class Ruisekiwa2D:
    def __init__(self, h, w):
        self.H = h
        self.W = w
        self.G = [[0] * w for _ in range(h)]

    def load(self, points):
        # 問題によってイメージしやすいよう書き換えてください
        for x, y in points:
            self.G[x][y] += 1

    def load_imos(self, points):
        # pointsは[[左上h, 左上w, 右下h, 右下w], ...]であること
        for i1, j1, i2, j2 in points:
            self.G[i1][j1] += 1  # 左上
            if j2 + 1 < self.W:  # 右上
                self.G[i1][j2+1] -= 1
            if i2 + 1 < self.H:
                self.G[i2+1][j1] -= 1  # 左下
            if j2 + 1 < self.W and i2 + 1 < self.H:  # 右下
                self.G[i2+1][j2+1] += 1

    def calc(self):
        for y in range(self.W):
            for x in range(1, self.H):
                self.G[x][y] += self.G[x-1][y]

        for y in range(1, self.W):
            for x in range(self.H):
                self.G[x][y] += self.G[x][y-1]

    def get(self, i1, j1, i2, j2):
        if i1 > i2 or j1 > j2 or i1 < 0 or j1 < 0 or i2 < 0 or j2 < 0:
            return 0
        elif i1 > 0 and j1 > 0:
            return self.G[i2][j2] - self.G[i1-1][j2] - self.G[i2][j1-1] + self.G[i1-1][j1-1]
        elif i1 <= 0 < j1:
            return self.G[i2][j2] - self.G[i2][j1-1]
        elif j1 <= 0 < i1:
            return self.G[i2][j2] - self.G[i1 - 1][j2]
        else:
            return self.G[i2][j2]


R2D = Ruisekiwa2D(2 * K, 2 * K)
R2D.load(X)
R2D.calc()

ans = 0
for h in range(K):
    for w in range(K):
        tmp = 0
        tmp += R2D.get(h, w, h + K - 1, w + K - 1)  # 真ん中
        tmp += R2D.get(0, 0, h - 1, w - 1)  # 左上
        tmp += R2D.get(0, w + K, h - 1, 2 * K - 1)  # 右上
        tmp += R2D.get(h + K, 0, 2 * K - 1, w - 1)  # 左下
        tmp += R2D.get(h + K, w + K, 2 * K - 1, 2 * K - 1)  # 右下
        ans = max(ans, tmp, N - tmp)

print(ans)