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 sys

sys.setrecursionlimit(10000)
INF = float('inf')

N, K = map(int, next(sys.stdin).split())

MOD = K * 2
grid = [[0 for _ in range(MOD)] for _ in range(MOD)]


def draw(sx, sy, ex, ey):
    sx %= MOD
    sy %= MOD
    ex = (ex - 1) % MOD + 1
    ey = (ey - 1) % MOD + 1

    if sx < ex and sy < ey:
        grid[sx][sy] += 1
        if ex < MOD:
            grid[ex][sy] -= 1
        if ey < MOD:
            grid[sx][ey] -= 1
        if ex < MOD and ey < MOD:
            grid[ex][ey] += 1

    elif ex <= sx:
        if ey <= sy:
            draw(0, 0, ex, ey)
            draw(0, sy, ex, MOD)
            draw(sx, 0, MOD, ey)
            draw(sx, sy, MOD, MOD)
        else:
            draw(0, sy, ex, ey)
            draw(sx, sy, MOD, ey)
    else:
        draw(sx, 0, ex, ey)
        draw(sx, sy, ex, MOD)


for _ in range(N):
    x, y, c = next(sys.stdin).split()
    x = int(x)
    y = int(y)
    if c == 'W':
        x += K

    # 黒マスをどこに置けばこの条件を満たすか
    # 累積和とったときに条件を満たす範囲だけ +1 されるように調整
    draw(x, y, x + K, y + K)
    draw(x + K, y + K, x + K * 2, y + K * 2)

for i in range(MOD - 1):
    for j in range(MOD):
        grid[i + 1][j] += grid[i][j]
for i in range(MOD - 1):
    for j in range(MOD):
        grid[j][i + 1] += grid[j][i]
ans = 0
for i in range(MOD):
    ans = max(ans, *grid[i])
print(ans)