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 = [ int(it) for it in input().split() ]
K2 = 2*K
li = [ (lambda x,y,z:[int(x)%K2,int(y)%K2,0 if z=="W" else 1] )(*(input().split())) for i in range(N)]

bm = [[0]*(K2+1) for i in range(K2+1)]
wm = [[0]*(K2+1) for i in range(K2+1)]
for x,y,z in li:
  if (z==0):
    wm[x+1][y+1] += 1
  else:
    bm[x+1][y+1] += 1

for i in range(1,2*K+1):
  for j in range(1,2*K+1):
    bm[i][j]=bm[i-1][j]+bm[i][j-1]-bm[i-1][j-1]+bm[i][j]
    wm[i][j]=wm[i-1][j]+wm[i][j-1]-wm[i-1][j-1]+wm[i][j]

ma = 0
for i in range(K):
  for j in range(K):
    for _ in range(2):
      s = 0
      s += bm[i][j]-bm[i][0]-bm[0][j]+bm[0][0]
      s += wm[K+i][j]-wm[K+i][0]-wm[i][j]+wm[i][0]
      s += wm[i][K+j]-wm[i][j]-wm[0][K+j]+wm[0][j]
      s += bm[i+K][j+K]-bm[i+K][j]-bm[i][j+K]+bm[i][j]
      s += bm[i][2*K]-bm[0][2*K]-bm[i][j+K]+bm[0][j+K]
      s += bm[2*K][j]-bm[2*K][0]-bm[i+K][j]+bm[i+K][0]
      s += wm[2*K][j+K]-wm[2*K][j]-wm[K+i][j+K]+wm[K+i][j]
      s += wm[i+K][2*K]-wm[i][2*K]-wm[K+i][j+K]+wm[i][j+K]
      s += bm[2*K][2*K]-bm[2*K][j+K]-bm[i+K][2*K]+bm[i+K][j+K]
      ma = max(ma,s)
      bm,wm=wm,bm
print (ma)