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())
K2 = 2*K

A = [[ 0 for _ in range(K2) ] for _ in range(K2)]
for _ in range(N):
  x,y,c = input().split()
  x,y = int(x) % (K2), int(y) % (K2)
  if c == 'W':
    y = (y+K) % (K2)
  #if y >= K:
  #  x,y = (x+K) %K2, y-K
  A[x][y] += 1

for i in range(K2):
  A[i] = A[i]  + A[i][:K-1]
  
for i in range(K-1):
  A.append(A[i])
  
#for a in A:
#  print(a)


B = [[ 0 for _ in range(K2+K) ] for _ in range(K2+K)]
for i in range(K2+K-1):
  for j in range(K2+K-1):
    B[i+1][j+1] = B[i+1][j] + B[i][j+1] - B[i][j] + A[i][j]
    
ans = 0
for i in range(K):
  for j in range(K):
    # (i,j)(i+K-1)(j+K-1) , (i+K,j+K), (i+2k-1)(j+2k-1)
    wk = 0
    wk += B[i+K][j+K] - B[i][j+K] - B[i+K][j] + B[i][j]
    wk += B[i+K2][j+K2] - B[i+K][j+K2] - B[i+K2][j+K] + B[i+K][j+K]
    #print(i,i+K,i+K2)
    ans = max(wk,N-wk,ans) #N-wkは白黒反転させたとき
#for b in B:
#  print(b)
  
print(ans)