Problem:
Score : 500 points

Problem 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:

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.

Sample Input 1

4 3
0 1 W
1 2 W
5 3 B
5 4 B

Sample Output 1

4

He can satisfy all his desires by painting as shown in the example above.

Sample Input 2

2 1000
0 0 B
0 1 W

Sample Output 2

2

Sample Input 3

6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W

Sample Output 3

4

Solution in Scala (2.11.7) (judge verdict: Time Limit Exceeded)

object Main extends App {
  val Array(n, k) = io.StdIn.readLine().split(' ').map(_.toInt)
  val k2 = k * 2
  type Record = (Int, Int)
  val list = collection.mutable.ListBuffer[Record]()
  (1 to n).foreach { i =>
    val temp = io.StdIn.readLine().split(' ')
    list += (
      if (temp(2) == "W")
        (temp(0).toInt % k2, temp(1).toInt % k2)
      else
        (temp(0).toInt % k2, (temp(1).toInt + k) % k2)
    )
  }
  def shift(x: Int): Int = if(x == k2 - 1) 0 else x + 1
  def shiftX(p: Record): Record = (shift(p._1), p._2)
  def shiftY(p: Record): Record = (p._1, shift(p._2))
  def count(ps: Seq[Record]): Int = ps.count {
    case (x, y) => ( (x < k && y < k) || (x >= k && y >= k))
  }

  var max = 0
  var shiftList = list

  (1 to k2).foreach { i =>
    (1 to k2).foreach { j => 
      val cnt = count(shiftList)
      max = Math.max(Math.max(cnt, n - cnt), max)
      shiftList =  shiftList.map(shiftX)
    }
    shiftList = shiftList.map(shiftY)
  }
  print(max)
}