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 getColor(x, y ,k)
	return ((x/k).ceil % 2 == 1) == ((y/k).ceil % 2 == 1) ? "W" : "B"
end

def getCount(map, bx, by, k)
	cnt = 0
	map.each{|(x, y ,z)|
#		p "X=#{x} , Y= #{y}, Z=#{z} bx=#{bx} by=#{by} getCol:%s" % getColor(x + bx, y + by, k)
		cnt += 1 if getColor(x + bx, y + by, k) == z
	}
	return cnt
end

n,k =  gets.split.map(&:to_i)
map = []
n.times{
	x, y ,z = gets.split
	map.push([x.to_i, y.to_i, z])
}
tmp = 0
Array(1..k+k).product(Array(1..k+k)).each do |(x, y)|
  cnt = getCount(map, x, y, k)
  tmp = cnt if tmp < cnt
  break if map.count == tmp
end

p tmp