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 Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(x)=parse(Int, x)
parseMap(x::Array{SubString{String}, 1}) = map(parseInt, x)

function main()
	n,k = readline() |> split |> parseMap
	b = zeros(Int,k,k)
	w = zeros(Int,k,k)
	for i in 1:n
		x,y,c = readline() |> chomp |> split
		x = parseInt(x)
		y = parseInt(y)
		s = div(x,k)+div(y,k)
		if s%2==0
			if c[1]=='B'
				b[x%k+1,y%k+1]+=1
			else
				w[x%k+1,y%k+1]+=1
			end
		else
			if c[1]=='W'
				b[x%k+1,y%k+1]+=1
			else
				w[x%k+1,y%k+1]+=1
			end
		end
	end
	bb = zeros(Int,k+1,k+1)
	ww = zeros(Int,k+1,k+1)
	for i in 1:k
		for j in 1:k
			bb[i+1,j+1]=bb[i+1,j]+b[i,j]
			ww[i+1,j+1]=ww[i+1,j]+w[i,j]
		end
	end
	for i in 1:k
		for j in 1:k
			bb[i+1,j+1]+=bb[i,j+1]
			ww[i+1,j+1]+=ww[i,j+1]
		end
	end
	s = 0
	for i in 1:k
		for j in 1:k
			s = max(s,bb[k+1,k+1]-bb[i,k+1]-bb[k+1,j]+bb[i,j]+ww[i,k+1]+ww[k+1,j]-ww[i,j],ww[k+1,k+1]-ww[i,k+1]-ww[k+1,j]+ww[i,j]+bb[i,k+1]+bb[k+1,j]-bb[i,j])
		end
	end
	println(s)
end

main()