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 = [], [], []
for _ in range(n):
  x, y, c = input().split()
  X.append(int(x)%(2*k))
  Y.append(int(y)%(2*k))
  C.append(c=="B")
G = [[0]*k for _ in range(k)]
cnt = 0
for x, y, c in zip(X, Y, C):
  if (x >= k and y < k) or (x < k and y >= k):
    x += k
    c ^= 1
  x %= k
  y %= k
  G[x][y] += (-1)**c
  cnt += c
for i in range(k):
  for j in range(k-1):
    G[i][j+1] += G[i][j]
for j in range(k):
  for i in range(k-1):
    G[i+1][j] += G[i][j]
ans = 0
for i in range(k):
  for j in range(k):
    temp = G[k-1][k-1] - G[i][k-1] - G[k-1][j] + G[i][j]*2 + cnt
    ans = max(ans, temp, n-temp)
print(ans)