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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.Array.IO
import Control.Applicative
import Data.List
import Control.Monad

main = do
    [n,k] <- map read.words <$> getLine
    xs <- map (format.words) <$> getLineN n :: IO [[Int]]
    let xs' = map (convert k) xs
    putStrLn.show.maximum $ map (count k xs') [(x,y) | x <- [0..2*k-1], y <- [0..2*k-1]] where
        format [x,y,c] = if c == "W" then [read x, read y,0] else [read x,read y,1]

convert :: Int -> [Int] -> (Int,Int)
convert k [x,y,0] = (x `mod` (2*k),y `mod` (2*k))
convert k [x,y,1] = ((x+k) `mod` (2*k),y `mod` (2*k))

count k xs (bx,by) = length $ filter ((==True).g) xs where
    g (px,py) = (abs (px-bx) < k || abs (px-bx) > k+bx) && (abs (py-by) < k || abs (py-by) > k+by)

getLineN :: Int -> IO [String]
getLineN n = replicateM n getLine