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 Ruby (2.3.3) (judge verdict: Wrong Answer)

def checkKaramatsu(x,y,k,a)
  blackbasecount = 0
  whitebasecount = 0
  a.each do |ai|
    xi = ( ai[0] + x ) % (2*k)
    yi = ( ai[1] + y ) % (2*k)
    colorflg = 0
    if xi > k and yi > k then
      colorflg = 1
    elsif xi <= k and yi <= k then
      colorflg = 1
    end
    if colorflg == 1 and ai[2] == 'B' then
      blackbasecount += 1
    elsif colorflg == 1 and ai[2] == 'W' then
      whitebasecount += 1
    elsif colorflg == 0 and ai[2] == 'W' then
      blackbasecount += 1
    elsif colorflg == 0 and ai[2] == 'B' then
      whitebasecount += 1
    end
  end
  if blackbasecount >= whitebasecount then
    return blackbasecount
  else
    return whitebasecount
  end
end

def checkKaramatsus(k,a)
  ans = 0
  for x in 1..k do
    for y in 1..k do
      tmpans = checkKaramatsu(x,y,k,a)
      ans = tmpans if tmpans > ans 
    end
  end
  return ans
end

# スペース区切りの整数の入力
n,k=gets.chomp.split(" ").map(&:to_i)
a = Array.new
for i in 1..n do
  xi,yi,ci=gets.chomp.split(" ").map(&:to_s)
  xi=xi.to_i
  yi=yi.to_i
  a.push([xi,yi,ci])
end

puts checkKaramatsus(k,a)