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: Time Limit Exceeded)

def s()
  gets()
end
def i()
  gets.to_i
end
def li()
  gets.split.map(&:to_i)
end
def ili()
  n = gets.to_i
  as = gets.split.map(&:to_i)
  [n, as]
end

n, k = li()
ps = []
cs = []
n.times{
  temp = s().split
  ps << temp[0..1].map(&:to_i)
  cs << temp[2]
}
max = 0
k.times{|i|
  k.times{|j|
    count_w = 0
    count_b = 0
    offset = [i,j]
    n.times{|i|
      if (((ps[i][0]+offset[0])/k)%2 == 0 && ((ps[i][1]+offset[1])/k)%2 == 0) || (((ps[i][0]+offset[0])/k)%2 == 1 && ((ps[i][1]+offset[1])/k)%2 == 1)
        if cs[i] == "W"
          count_w += 1
        else
          count_b += 1
        end
      else
        if cs[i] == "B"
          count_w += 1
        else
          count_b += 1
        end
      end
    }
    max = [max, count_w, count_b].max
  }
}
puts max