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: Wrong Answer)

package main

import "fmt"

var N, K int
var x, y []int
var c []string

func main() {
	fmt.Scanf("%d %d", &N, &K)

	x := make([]int, N)
	y := make([]int, N)
	c := make([]string, N)

	K2 := K * 2

	for i := 0; i < N; i++ {
		fmt.Scanf("%d %d %s", &x[i], &y[i], &c[i])

		if c[i] == "W" {
			y[i] += K
		}

		x[i] %= K2
		y[i] %= K2
	}

	m := MakeMatrix(K2+1, K2+1)

	for i := 0; i < N; i++ {
		m[y[i]+1][x[i]+1]++
	}

	for y := 1; y < K2+1; y++ {
		for x := 1; x < K2+1; x++ {
			m[y][x] += m[y][x-1] + m[y-1][x] - m[y-1][x-1]
		}
	}

	max := 0
	for y := 0; y < K+1; y++ {
		for x := 0; x < K+1; x++ {
			tmp := m[y][x] - m[0][x] - m[y][0] + m[0][0]
			tmp += m[y][K2] - m[y][x+K] - m[0][K2] + m[0][x+K]
			tmp += m[y+K][x+K] - m[y+K][x] - m[y][x+K] + m[y][x]
			tmp += m[K2][x] - m[y+K][x] - m[K2][0] + m[y+K][0]
			tmp += m[K2][K2] - m[y+K][K2] - m[K2][x+K] + m[y+K][x+K]

			max = Max(max, tmp)
		}
	}

	fmt.Println(max)
}

func MakeMatrix(w, h int) [][]int {
	m := make([][]int, w)
	for x := 0; x < w; x++ {
		m[x] = make([]int, h)
	}

	return m
}

func Max(x, y int) int {
	if x > y {
		return x
	}
	return y
}