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())
info = [list(input().split()) for i in range(n)]

cnt_b = [[0]*k for i in range(k)]
cnt_w = [[0]*k for i in range(k)]

for i in range(n):
    x, y, c = info[i]
    x, y = int(x), int(y)
    move_cnt = (x//k) + (y//k)
    if move_cnt % 2 == 0:
        if c == "B":
            cnt_b[x % k][y % k] += 1
        if c == "W":
            cnt_w[x % k][y % k] += 1
    else:
        if c == "B":
            cnt_w[x % k][y % k] += 1
        if c == "W":
            cnt_b[x % k][y % k] += 1

ruiseki_b = [[0]*(k+1) for i in range(k+1)]
ruiseki_w = [[0]*(k+1) for i in range(k+1)]
for i in range(k):
    for j in range(k):
        ruiseki_b[i+1][j+1] = ruiseki_b[i+1][j] + cnt_b[i][j]
        ruiseki_w[i+1][j+1] = ruiseki_w[i+1][j] + cnt_w[i][j]
for j in range(k):
    for i in range(k):
        ruiseki_b[i+1][j+1] += ruiseki_b[i][j+1]
        ruiseki_w[i+1][j+1] += ruiseki_w[i][j+1]
ans = 0
for i in range(k+1):
    for j in range(k+1):
        ans_b = ruiseki_b[k][k] - ruiseki_b[i][k] - ruiseki_b[k][j] + 2*ruiseki_b[i][j]
        ans_w = ruiseki_w[i][k] + ruiseki_w[k][j] - 2*ruiseki_w[i][j]
        ans = max(ans_w + ans_b, ans)
        ans_w = ruiseki_w[k][k] - ruiseki_w[i][k] - ruiseki_w[k][j] + 2*ruiseki_w[i][j]
        ans_b = ruiseki_b[i][k] + ruiseki_b[k][j] - 2*ruiseki_b[i][j]
        ans = max(ans_w + ans_b, ans)
print(ans)