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:
def main():
  n, k = map(int, input().split())
  mp1 = [[0] * k for _ in range(k)]
  mp2 = [[0] * k for _ in range(k)]
  for _ in range(n):
    x, y, c = input().split()
    t = int(x) // k + int(y) // k
    x = int(x) % k
    y = int(y) % k
    if c == "B":
      t += 1
    if t % 2:
      mp1[y][x] += 1
    else:
      mp2[y][x] += 1
  
  mp10 = mp1[0]
  mp20 = mp2[0]
  for x in range(1, k):
    mp10[x] += mp10[x - 1]
    mp20[x] += mp20[x - 1]
  
  for y in range(1, k):
    acc1 = 0
    acc2 = 0
    mp1y = mp1[y]
    mp2y = mp2[y]
    mp1y1 = mp1[y - 1]
    mp2y1 = mp2[y - 1]
    for x in range(k):
      acc1 += mp1y[x]
      mp1y[x] = acc1 + mp1y1[x]
      acc2 += mp2y[x]
      mp2y[x] = acc2 + mp2y1[x]
  
  ans = 0
  sum1 = mp1[k - 1][k - 1]
  sum2 = mp2[k - 1][k - 1]
  mp1k = mp1[k - 1]
  mp2k = mp2[k - 1]
  for y in range(k):
    mp1y = mp1[y]
    mp1yk = mp1y[k - 1]
    mp2y = mp2[y]
    mp2yk = mp2y[k - 1]
    for x in range(k):
      mp1yx = mp1y[x]
      mp2yx = mp2y[x]
      mp1kx = mp1k[x]
      mp2kx = mp2k[x]
  
      a1 = 2 * mp1yx + sum1 - mp1yk - mp1kx + mp2kx + mp2yk - 2 * mp2yx
      a2 = 2 * mp2yx + sum2 - mp2yk - mp2kx + mp1kx + mp1yk - 2 * mp1yx
  
      if ans < a1:
        ans = a1
      if ans < a2:
        ans = a2
  
  
  print(ans)

main()