output_description: Print the maximum number of desires that can be satisfied at the same time.
  
  * * *
input_description: 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
attempt: from subprocess import *
  
  call(
      (
          "julia",
          "-e",
          """
  const lines=readlines()
  input()=shift!(lines)
  int(s)=parse(Int16,s)
  intLine()=map(int,split(input()))
  function nextLine(k)
      x,y,c=split(input())
      int(x)%2k+1,(int(y)+(c=="W")k)%2k+1
  end
  function solve(k,g)
      m=0
      for i=1:2k,j=1:2k
          a=0
          for x=-1:2,y=-1:2
              (x+y)%2!=0&&continue
              v,w=i+x*k,j+y*k
              v>0<w&&(a+=g[min(2k,v)][min(2k,w)])
              v>k&&w>0&&(a-=g[min(2k,v-k)][min(2k,w)])
              w>k&&v>0&&(a-=g[min(2k,v)][min(2k,w-k)])
              v>k<w&&(a+=g[min(2k,v-k)][min(2k,w-k)])
          end
          m=max(m,a)
      end
      m
  end
  function main()
      n,k=intLine()
      g=Array{Int16,1}[[0for j=1:2k]for i=1:2k]
      for i=1:n
          x,y=nextLine(k)
          g[x][y]+=1
      end
      println(solve(k,cumsum(map(cumsum,g))))
  end
  main()
  """,
      )
  )
  
problem_description: Statement
  
  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](https://img.atcoder.jp/arc089/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?
samples: [{"input": "4 3\n    0 1 W\n    1 2 W\n    5 3 B\n    5 4 B", "output": "4\n    \n\nHe can satisfy all his desires by painting as shown in the example above.\n\n* * *"}, {"input": "2 1000\n    0 0 B\n    0 1 W", "output": "2\n    \n\n* * *"}, {"input": "6 2\n    1 2 B\n    2 1 W\n    2 2 B\n    1 0 B\n    0 6 W\n    4 5 W", "output": "4"}]