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: Runtime Error)

def printarray(a)
  a.length.times do |i|
    a[0].length.times do |j|
       print "#{a[i][j]} "
    end
    puts ""
  end
  puts""
  puts"-----------------"
  puts""
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
k2 = 2 * k

# 市松マップ
m = Array.new((k2)+(k-1)){Array.new((k2)+(k-1),0)}

mm = Array.new(k){Array.new(k,0)}

n.times do |i|
  xi,yi,ci=gets.chomp.split(" ").map(&:to_s)
  xi=xi.to_i % k2
  yi=yi.to_i % k2
    
  #mapに埋めてく B基準
  if ci == 'B' then
#  puts "#{xi} #{yi} : #{xi + k2} #{yi + k2}"
#    puts ""

    m[xi][yi] += 1
#printarray m
    m[xi + k2][yi] += 1 if xi < k-1
#    puts "#{xi} #{yi + k2}"
    m[xi][yi + k2] += 1 if yi < k-1
    m[xi + k2][yi + k2] += 1 if xi < k-1 and yi < k-1
    
  else # WもBに合うようにずらす
    yi = yi + k
#  puts "#{xi} #{yi} : #{xi + k2} #{yi + k2}"
#  puts ""
    m[xi][yi] += 1
    m[xi + k2][yi] += 1 if xi < k-1
    m[xi][yi - k2] += 1 if yi >= k2
    m[xi+k2][yi - k2] += 1 if xi < k-1 and yi >= k2
  end
#printarray m
end
max = 0
(0..k-1).each do |mmi|
  (0..k-1).each do |mmj|
    sum = 0
    [0,k].each do |zeroork|
      (0..k-1).each do |mi|
        (0..k-1).each do |mj|
          sum += m[mi][mj]
        end
      end
    end
    max = sum if sum > max
  end
end
puts max