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 gc
n, k = map(int, input().split())
k2 = k * 2
b = [[0] * (k * 3) for _ in range(k * 3)]
for i in range(n):
    x, y, c = input().split()
    x = int(x) % k2
    y = int(y) % k2
    if c == 'W':
        x = (x + k) % k2

    b[x][y] += 1
    if x < k:
        b[x + k2][y] += 1
    if y < k:
        b[x][y + k2] += 1
    if x < k and y < k:
        b[x + k2][y + k2] += 1

b_cs = [[0] * (k * 3 + 1) for _ in range(k * 3 + 1)]
for i in range(k * 3):
    for j in range(k * 3):
        b_cs[i + 1][j +
                    1] = b_cs[i + 1][j] + b_cs[i][j + 1] - b_cs[i][j] + b[i][j]


def func_b(x, y):
    return b_cs[x + k][y + k] - b_cs[x + k][y] - b_cs[x][y + k] + b_cs[x][y]


# print('black')
# print(*b, sep='\n')
# print(*b_cs, sep='\n')

ans = 0
for i in range(k):
    for j in range(k):
        cand = 0
        cand += func_b(i, j)
        cand += func_b(i + k, j + k)
        # print(i, j, cand)
        ans = max(ans, cand)

        cand = 0
        cand += func_b(i + k, j)
        cand += func_b(i, j + k)
        # print(i, j, cand)
        ans = max(ans, cand)

print(ans)