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, y, c = [None] * N, [None] * N, [None] * N
KK = 2 * K
table = [[0] * (KK+1) for i in range(KK+1)]

for i in range(N):
    x[i], y[i], c[i] = input().split()
    x[i], y[i] = int(x[i]), int(y[i])
    if c[i] == 'W':
        x[i] += K
        c[i] = 'B'
    x[i] %= KK
    y[i] %= KK
    table[y[i]+1][x[i]+1] += 1

for i in range(KK+1):
    for j in range(KK):
        table[i][j+1] += table[i][j]
for i in range(KK):
    for j in range(KK+1):
        table[i+1][j] += table[i][j]

def s(x1, x2, y1, y2):
    global table, KK
    MOD = KK + 1
    x1 = x1 % MOD + x1 // MOD
    y1 = y1 % MOD + y1 // MOD
    x2 = x2 % MOD + x2 // MOD
    y2 = y2 % MOD + y2 // MOD
    x11 = x1
    x21 = 0
    y11 = y1
    y21 = 0
    if x1 < x2:
        x12 = x2
        x22 = 0
    else:
        x12 = KK
        x22 = x2
    if y1 < y2:
        y12 = y2
        y22 = 0
    else:
        y12 = KK
        y22 = y2
    f = lambda _x1, _x2, _y1, _y2: \
            table[_y2][_x2] - table[_y2][_x1] \
            - table[_y1][_x2] + table[_y1][_x1]
    # print('x11: %d, x12: %d, y11: %d, y12: %d' % (x11, x12, y11, y12))
    # a1 = f(x11, x12, y11, y12)
    # print('x21: %d, x22: %d, y11: %d, y12: %d' % (x21, x22, y11, y12))
    # a2 = f(x21, x22, y11, y12)
    # print('x11: %d, x12: %d, y21: %d, y22: %d' % (x11, x12, y21, y22))
    # a3 = f(x11, x12, y21, y22)
    # print('x21: %d, x22: %d, y21: %d, y22: %d' % (x21, x22, y21, y22))
    # a4 = f(x21, x22, y21, y22)
    # print(a1, a2, a3, a4)
    return f(x11, x12, y11, y12) + f(x21, x22, y11, y12) \
            + f(x11, x12, y21, y22) + f(x21, x22, y21, y22)

ans = 0
for i in range(KK):
    for j in range(K):
        tmp = s(i, i+K, j, j+K)
        ni, nj = i + K, j + K
        tmp += s(ni, ni+K, nj, nj+K)
        # print('tmp: %d' % tmp)
        ans = max((ans, tmp))
print(ans)