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:
import sys
input = sys.stdin.readline

N,K = list(map(int,input().split()))
data = [list(map(str, input().split())) for _ in range(N)]
base = 10**6

BW_data = [[0 for i in range(2*K)] for i in range(2*K)]

for x,y,c in data:
  x,y = int(x)%(2*K),int(y)%(2*K)
  if c == "B":
    BW_data[y][x] += 1
  else:
    BW_data[y][x] += base

def ACC2(l):
  H = len(l)
  W = len(l[0])
  ret = [[0]*(W+1) for i in range(H+1)]
  for i in range(H):
    for j in range(W):
      ret[i+1][j+1] = ret[i+1][j] + ret[i][j+1] - ret[i][j] + l[i][j]
  return ret

def RANGE_SUM_in_ACC(l,h1,h2,w1,w2):
  return l[h2][w2]-l[h2][w1]-l[h1][w2]+l[h1][w1]

BW_ACC = ACC2(BW_data)

BW_res = [[0 for i in range(2*K)] for i in range(K)]

for j in range(K):
  for i in range(2*K):
    if i<K:
      BW_res[j][i] += RANGE_SUM_in_ACC(BW_ACC,j,j+K,i,i+K)
      BW_res[j][i] += RANGE_SUM_in_ACC(BW_ACC,0,max(0,j),0,max(0,i))
      BW_res[j][i] += RANGE_SUM_in_ACC(BW_ACC,0,max(0,j),min(2*K,i+K),2*K)
      BW_res[j][i] += RANGE_SUM_in_ACC(BW_ACC,min(2*K,j+K),2*K,0,max(0,i))
      BW_res[j][i] += RANGE_SUM_in_ACC(BW_ACC,min(2*K,j+K),2*K,min(2*K,i+K),2*K)
    else:
      BW_res[j][i] = BW_ACC[-1][-1]-BW_res[j][i-K]
      
ans = 0
for j in range(K):
  for i in range(2*K):
    ans = max(ans,BW_res[j][i]%base+BW_res[j][(i+K)%(2*K)]//base)
print(ans)