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)

import re
import numpy as np
temp=input().split(" ")
n=int(temp[0])
k=int(temp[1])
k2=2*k
tileb=[[0 for i in range(k2)] for j in range(k2)]
tileb=np.array(tileb)
for i in range(n):
    temp=input().split(" ")
    x=int(temp[0])
    y=int(temp[1])
    c=temp[2]
    if c=='B':  
        tileb[y%(k2)][x%(k2)]+=1
    elif c=='W':  
        tileb[(y+k)%k2][x%k2]+=1
#ruisekiwa=[[0 for i in range(k2)] for j in range(k2)]
# for x in range(0,k2):
#     ruisekiwa[0][x]=tileb[0][x]

ans=0
for y in range(1,k2):
    for x in range(1,k2):
        tileb[y][x]+=tileb[y][x-1]
for x in range(1,k2):
    for y in range(1,k2):
        tileb[y][x]+=tileb[y-1][x]

#print(tileb)

tileb=np.concatenate([tileb,tileb],axis=0)
# print(tileb)

tileb=np.concatenate([tileb,tileb],axis=1)
#print(tileb)


def nijiruisekiwa(x,y,k): #左下(x,y) 長さkの正方形領域の和
    global tileb     
    return tileb[y+k-1][x+k-1]-tileb[y+k-1][x-1]-tileb[y-1][x+k-1]+tileb[y-1][x-1]
for x in range(1,k2):
    for y in range(1,k2):
        temp=0
        a=nijiruisekiwa(x,y,k)
        b=nijiruisekiwa(x+k,y+k,k)

        temp=a+b
        if temp>ans:
            # print(a)
            # print(b)
            # print("x={0}  y={1}  ".format(x,y))
            # print(temp)
            ans=temp
print(ans)