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 (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

func out(x ...interface{}) {
	fmt.Println(x...)
}

var sc = bufio.NewScanner(os.Stdin)

func getInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func getString() string {
	sc.Scan()
	return sc.Text()
}

// min, max, asub, absなど基本関数
func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func asub(a, b int) int {
	if a > b {
		return a - b
	}
	return b - a
}

func abs(a int) int {
	if a >= 0 {
		return a
	}
	return -a
}

func lowerBound(a []int, x int) int {
	idx := sort.Search(len(a), func(i int) bool {
		return a[i] >= x
	})
	return idx
}

func upperBound(a []int, x int) int {
	idx := sort.Search(len(a), func(i int) bool {
		return a[i] > x
	})
	return idx
}

func calc(x1, y1, x2, y2 int, a [][]int) int {
	ret := a[x2][y2] + a[x1][y1] - a[x1][y2] - a[x2][y1]
	// out(x1, y1, x2, y2, ret)
	return ret
}

func main() {
	sc.Split(bufio.ScanWords)
	N, K := getInt(), getInt()
	black := make([][]int, 2*K+1)
	white := make([][]int, 2*K+1)
	for i := 0; i <= 2*K; i++ {
		black[i] = make([]int, 2*K+1)
		white[i] = make([]int, 2*K+1)
	}
	for i := 0; i < N; i++ {
		x, y, c := getInt(), getInt(), getString()
		x %= 2 * K
		y %= 2 * K
		if c == "B" {
			black[x+1][y+1]++
		} else {
			white[x+1][y+1]++
		}
	}

	// out("Black")
	// for i := 0; i <= 2*K; i++ {
	// 	for j := 0; j <= 2*K; j++ {
	// 		fmt.Print(black[j][i], " ")
	// 	}
	// 	out()
	// }
	// out("white")
	// for i := 0; i <= 2*K; i++ {
	// 	for j := 0; j <= 2*K; j++ {
	// 		fmt.Print(white[j][i], " ")
	// 	}
	// 	out()
	// }
	for i := 0; i <= 2*K; i++ {
		for j := 1; j <= 2*K; j++ {
			black[i][j] += black[i][j-1]
			white[i][j] += white[i][j-1]
		}
	}
	for i := 0; i <= 2*K; i++ {
		for j := 1; j <= 2*K; j++ {
			black[j][i] += black[j-1][i]
			white[j][i] += white[j-1][i]
		}
	}

	ans := 0
	for i := 0; i < K; i++ {
		for j := 0; j < K; j++ {
			// out(i, j, "-------")
			b0 := 0
			b1 := 0
			w0 := 0
			w1 := 0
			// out("black")
			b0 += calc(0, 0, i, j, black)
			b1 += calc(i, 0, i+K, j, black)
			b0 += calc(i+K, 0, 2*K, j, black)

			b1 += calc(0, j, i, j+K, black)
			b0 += calc(i, j, i+K, j+K, black)
			b1 += calc(i+K, j, 2*K, j+K, black)

			b0 += calc(0, j+K, i, 2*K, black)
			b1 += calc(i, j+K, i+K, 2*K, black)
			b0 += calc(i+K, i+K, K*2, K*2, black)
			// out("white")
			w0 += calc(0, 0, i, j, white)
			w1 += calc(i, 0, i+K, j, white)
			w0 += calc(i+K, 0, 2*K, j, white)

			w1 += calc(0, j, i, j+K, white)
			w0 += calc(i, j, i+K, j+K, white)
			w1 += calc(i+K, j, 2*K, j+K, white)

			w0 += calc(0, j+K, i, 2*K, white)
			w1 += calc(i, j+K, i+K, 2*K, white)
			w0 += calc(i+K, i+K, K*2, K*2, white)
			ret := max(w0+b1, w1+b0)
			// out(ret)
			ans = max(ans, ret)
		}
	}
	out(ans)
}