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 Go (1.6) (judge verdict: Time Limit Exceeded)

///
// File:  d.go
// Author: ymiyamoto
//
// Created on Sun Jan 21 21:38:08 2018
//
package main

import "fmt"

type pos_t struct {
	x int
	y int
	c string
}

func main() {
	var N, K int
	fmt.Scan(&N, &K)

	poss := make([]pos_t, N)
	for i := 0; i < N; i++ {
		var x, y int
		var c string
		fmt.Scan(&x, &y, &c)
		poss[i].x = x % (2 * K)
		poss[i].y = y % (2 * K)
		poss[i].c = c
	}

	max := 0
	for i := 0; i < K; i++ {
		for j := 0; j < K; j++ {
			count1 := 0
			count2 := 0
			for k := 0; k < N; k++ {
				x := poss[k].x
				y := poss[k].y
				c := poss[k].c
				if (x < i && y < j) || (i <= x && x < i+K && j <= y && y < j+K) || (i+K <= x && y < j) ||
					(x < i && j+K <= y) || (i+K <= x && K+j <= y) {
					if c == "W" {
						count1++
					}
					if c == "B" {
						count2++
					}
				} else {
					if c == "B" {
						count1++
					}
					if c == "W" {
						count2++
					}
				}
				if max < count1 {
					max = count1
				}
				if max < count2 {
					max = count2
				}
			}
		}
	}

	fmt.Println(max)
}