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 PyPy2 (5.6.0) (judge verdict: Wrong Answer)

N,K=map(int,raw_input().split())

a=[]
for i in range(N):
	x,y,c=raw_input().split()
	x=int(x)
	y=int(y)
	if c=="W": a.append( ( (x+K)%(2*K) , y%(2*K) ) )
	else: a.append( (x%(2*K) ,y%(2*K)) )


s=[ [ 0 for i in range(4*K) ] for j in range(4*K) ]
w=[ [ None for i in range(4*K) ] for j in range(4*K) ]


for x,y in a:
	s[x][y]+=1



for y in range(4*K):
	for x in range(4*K):
		if x==0: w[x][y]=s[x][y]
		else:
			w[x][y]=w[x-1][y]+s[x][y]

for x in range(4*K):
	for y in range(4*K-1,-1,-1):
		if y==4*K-1: w[x][y]=w[x][y]
		else: w[x][y]=w[x][y+1]+w[x][y]



def calc(x,y):
	if x<0 or y<0:
		return 0
	if y+K>4*K-1:
		return w[x][y]-w[x-K][y]
	elif x-K<0:
		return w[x][y]-w[x][y+K]		
	else:
		return w[x][y]-w[x-K][y]-w[x][y+K]+w[x-K][y+K]

ans=0
for x in range(K*2):
	for y in range(K*2):
		tmp=calc(x,y)+calc(x+2*K,y)+calc(x+K,y+K)+calc(x,y+2*K)+calc(x+2*K,y+2*K)+calc(x-2*K,y)+calc(x-K,y-K)+calc(x,y-2*K)+calc(x-2*K,y-2*K)
		ans=max(ans,tmp)

print ans