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:
class Acc2D:
    def __init__(self, a):
        h, w = len(a), len(a[0])
        self.acc2D = self._build(h, w, a)

    def _build(self, h, w, a):
        ret = [[0] * (w + 1) for _ in range(h + 1)]
        for r in range(h):
            for c in range(w):
                ret[r + 1][c + 1] = ret[r][c + 1] + ret[r + 1][c] - ret[r][c] + a[r][c]
                # 末項は必要に応じて改変すること
        return ret

    def get(self, r1, r2, c1, c2):
        # [r1,r2), [c1,c2) : 0-indexed
        acc2D = self.acc2D
        return acc2D[r2][c2] - acc2D[r1][c2] - acc2D[r2][c1] + acc2D[r1][c1]


def main():
    import sys

    input = sys.stdin.readline

    n, k = map(int, input().split())

    g = [[0] * (k * 2) for _ in range(k * 2)]
    for _ in range(n):
        x, y, c_ = input().split()
        x = int(x) % (k * 2)
        y = int(y) % (k * 2)
        if c_ == 'W':
            y = (y + k) % (k * 2)
            # すべて黒にする
        g[y][x] += 1  # WA頂点の存在の有無ではなく、頂点数を数えるので、=1ではなく、+=1

    acc2D = Acc2D(g)

    ret = 0
    # 中央にk*kの区画をとり、黒または白に塗る(条件を満たす個数:黒=s,白=n-s)
    # 4辺を伸ばして、2k*2kの区画を分割し、各区画を評価する
    for r in range(k):  # r+k < k*2
        for c in range(k):  # c+k < k*2
            s = (
                    acc2D.get(0, r, 0, c)
                    + acc2D.get(0, r, c + k, k * 2)
                    + acc2D.get(r, r + k, c, c + k)
                    + acc2D.get(r + k, k * 2, 0, c)
                    + acc2D.get(r + k, k * 2, c + k, k * 2)
            )
            ret = max(ret, s, n - s)

    print(ret)


if __name__ == '__main__':
    main()