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)

n,k=gets.split.map &:to_i
m=(6*k).times.map{[0]*(6*k)}
n.times.each{
	x,y,c=gets.split.zip([:to_i,:to_i,:to_s]).map{|x,y|y.to_proc[x]}
	y+=k if c==?W
	x%=2*k
	y%=2*k
	4.times{|i|
		(i%2).step(3,2){|j|
			m[x+i*k][y+j*k]+=1
			m[x+i*k+k][y+j*k]-=1
			m[x+i*k][y+j*k+k]-=1
			m[x+i*k+k][y+j*k+k]+=1
		}
	}
}
(0...6*k).each{|i|(1...6*k).each{|j|m[i][j]+=m[i][j-1]}}
(1...6*k).each{|i|(0...6*k).each{|j|m[i][j]+=m[i-1][j]}}
p m.map(&:max).max