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())

# あとで開区間な累積和を取るので、K+1。
want_white = [[0] * (K+1) for _ in range(K+1)]
want_black = [[0] * (K+1) for _ in range(K+1)]

for _ in range(N):
    x_str, y_str, c_str = input().split()
    x = int(x_str)
    y = int(y_str)
    c = 1 if c_str == 'B' else 0

    x %= 2 * K
    y %= 2 * K
    if x >= K:
        x -= K
        c ^= 1
    if y >= K:
        y -= K
        c ^= 1

    if c:
        want_black[x+1][y+1] += 1
    else:
        want_white[x+1][y+1] += 1

# 累積和
for i in range(K+1):
    for j in range(K):
        want_black[i][j+1] += want_black[i][j]
        want_white[i][j+1] += want_white[i][j]

for i in range(K):
    for j in range(K+1):
        want_black[i+1][j] += want_black[i][j]
        want_white[i+1][j] += want_white[i][j]

# (h, w)が黒の左下になるとして、全探索。
ans = 0
for h in range(K+1):
    for w in range(K+1):
        count = want_black[-1][-1] - want_black[h][-1] - want_black[-1][w] + 2 * want_black[h][w]
        count += want_white[h][-1] + want_white[-1][w] - 2 * want_white[h][w]
        ans = max(ans, count, N - count)

print(ans)