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)

function calc(T,x,y,K)
	g(a,b,c,d)=T[c+1,d+1]-T[c+1,b]-T[a,d+1]+T[a,b]
	if x<=K
		if y<=K
			g(x,y,x+K,y+K)+g(1,1,x-1,y-1)+g(x+K+1,1,2K,y-1)+g(1,y+K+1,x-1,2K)+g(x+K+1,y+K+1,2K,2K)
		else
			g(x,y,x+K,2K)+g(x,1,x+K,y-K-1)+g(1,y-K,x-1,y-1)+g(x+K+1,y-K,2K,y-1)
		end
	else
		if y<=K
			g(x,y,2K,y+K)+g(1,y,x-K-1,y+K)+g(x-K,1,x-1,y-1)+g(x-K,y+K+1,x-1,2K)
		else
			calc(T,x-K,y-K,K)
		end
	end
end
function main()
	lines=readlines()
	N,K=map(x->parse(Int,x),split(shift!(lines)))
	sum=zeros(Int,2K+1,2K+1)
	for s=lines
		x,y,c=split(s)
		x=parse(Int,x)
		y=parse(Int,y)
		if c=="B"
			y+=K
		end
		x=mod1(x,2K)
		y=mod1(y,2K)
		if x<=K
			if y<=K
				sum[x+1,y+1]+=1
				sum[x+1+K,y+1+K]+=1
				sum[x+1,y+1+K]-=1
				sum[x+1+K,y+1]-=1
			else
				sum[x+1,y+1]+=1
				sum[x+1+K,y+1]-=1
				sum[x+1,1]+=1
				sum[x+1+K,1]-=1
				sum[x+1,y-K+1]-=1
				sum[x+1+K,y-K+1]+=1
			end
		else
			if y<=K
				sum[x+1,y+1]+=1
				sum[x+1,y+1+K]-=1
				sum[1,y+1]+=1
				sum[1,y+1+K]-=1
				sum[x-K+1,y+1]-=1
				sum[x-K+1,y+1+K]+=1
			else
				sum[x+1,y+1]+=1
				sum[1,y+1]+=1
				sum[x-K+1,y+1]-=1
				sum[x+1,1]+=1
				sum[x+1,y-K+1]-=1
				sum[1,1]+=1
				sum[1,y-K+1]-=1
				sum[x-K+1,1]-=1
				sum[x-K+1,y-K+1]+=1
			end
		end
	end
	for i=1:2K+1,j=1:2K+1
		sum[i,j]+=(i>1?sum[i-1,j]:0)+(j>1?sum[i,j-1]:0)-(i>1&&j>1?sum[i-1,j-1]:0)
	end
	ans=0
	for i=1:2K,j=1:2K
		ans=max(ans,calc(sum,i,j,K))
	end
	println(ans)
end
main()