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
input = sys.stdin.readline

N, K = map(int, input().split())
white = [[0]*(K+1) for _ in range(2*K+1)]
black = [[0]*(K+1) for _ in range(2*K+1)]
for _ in range(N):
    str_h, str_w, c = map(str, input().rstrip().split())
    h = int(str_h)%(2*K)
    w = int(str_w)%(2*K)
    if c == "W":
        if w >= K:
            if h >= K:
                white[h-K+1][w-K+1] += 1
            else:
                white[h+K+1][w-K+1] += 1
        else:
            white[h+1][w+1] += 1
    else:
        if w >= K:
            if h >= K:
                black[h-K+1][w-K+1] += 1
            else:
                black[h+K+1][w-K+1] += 1
        else:
            black[h+1][w+1] += 1

for h in range(1, 2*K+1):
    for w in range(1, K+1):
        white[h][w] += white[h][w-1] + white[h-1][w] - white[h-1][w-1]
        black[h][w] += black[h][w-1] + black[h-1][w] - black[h-1][w-1]

ans = 0
for h in range(K+1):
    for w in range(K+1):
        b1 = black[h][w]
        b2 = black[h+K][K] - black[h+K][w] - black[h][K] + black[h][w]
        b3 = black[2*K][w] - black[h+K][w]
        w1 = white[h][K] - white[h][w]
        w2 = white[h+K][w] - white[h][w]
        w3 = white[2*K][K] - white[2*K][w] - white[h+K][K] + white[h+K][w]
        ans = max(ans, b1+b2+b3+w1+w2+w3)

        b1 = white[h][w]
        b2 = white[h+K][K] - white[h+K][w] - white[h][K] + white[h][w]
        b3 = white[2*K][w] - white[h+K][w]
        w1 = black[h][K] - black[h][w]
        w2 = black[h+K][w] - black[h][w]
        w3 = black[2*K][K] - black[2*K][w] - black[h+K][K] + black[h+K][w]
        ans = max(ans, b1+b2+b3+w1+w2+w3)

print(ans)