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 Python (3.4.3) (judge verdict: Wrong Answer)

N,K = map(int,input().split()) 
KK = 2*K
whites = [[0 for i in range(KK)] for j in range(K)]
total = [[0 for i in range(KK)] for j in range(K)]

for i in range(N):
	x,y,c = input().split()
	x,y = int(x), int(y)
	if c == 'B':
		if y >= K:
			y -= K
		else:
			y += K
	xx = x % K
	yy = y % KK
	whites[xx][yy] += 1

for x in range(K):
	for y in range(KK):
		tmp = whites[x][y]
		if x > 0:
			tmp += total[x-1][y]
		if y > 0:
			tmp += total[x][y-1]
			if x > 0:
				tmp -= total[x-1][y-1]
		total[x][y] = tmp
ans = 0
for y in range(K):
	tmp = total[K-1][y+K-1]
	if y > 0:
		tmp -= total[K-1][y-1]
	ans = max(ans, tmp)
print(ans)