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"
	"errors"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

/*
var rdr = bufio.NewReaderSize(os.Stdin, 1000000)
// readLine can read long line string (at least 10^5)
func readLine() string {
	buf := make([]byte, 0, 1000000)
	for {
		l, p, e := rdr.ReadLine()
		if e != nil {
			panic(e)
		}
		buf = append(buf, l...)
		if !p {
			break
		}
	}
	return string(buf)
}
// NextLine reads a line text from stdin, and then returns its string.
func NextLine() string {
	return readLine()
}
*/

var sc = bufio.NewScanner(os.Stdin)

// NextLine reads a line text from stdin, and then returns its string.
func NextLine() string {
	sc.Scan()
	return sc.Text()
}

// NextIntsLine reads a line text, that consists of **ONLY INTEGERS DELIMITED BY SPACES**, from stdin.
// And then returns intergers slice.
func NextIntsLine() []int {
	ints := []int{}
	intsStr := NextLine()
	tmp := strings.Split(intsStr, " ")
	for _, s := range tmp {
		integer, _ := strconv.Atoi(s)
		ints = append(ints, integer)
	}
	return ints
}

// NextStringsLine reads a line text, that consists of **STRINGS DELIMITED BY SPACES**, from stdin.
// And then returns strings slice.
func NextStringsLine() []string {
	str := NextLine()
	return strings.Split(str, " ")
}

// NextRunesLine reads a line text, that consists of **ONLY CHARACTERS ARRANGED CONTINUOUSLY**, from stdin.
// Ant then returns runes slice.
func NextRunesLine() []rune {
	return []rune(NextLine())
}

// Max returns the max integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Max(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m < integer {
			m = integer
		}
	}
	return m
}

// Min returns the min integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Min(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m > integer {
			m = integer
		}
	}
	return m
}

// PowInt is integer version of math.Pow
func PowInt(a, e int) int {
	if a < 0 || e < 0 {
		panic(errors.New("[argument error]: PowInt does not accept negative integers"))
	}
	fa := float64(a)
	fe := float64(e)
	fanswer := math.Pow(fa, fe)
	return int(fanswer)
}

// AbsInt is integer version of math.Abs
func AbsInt(a int) int {
	fa := float64(a)
	fanswer := math.Abs(fa)
	return int(fanswer)
}

// DeleteElement returns a *NEW* slice, that have the same and minimum length and capacity.
// DeleteElement makes a new slice by using easy slice literal.
func DeleteElement(s []int, i int) []int {
	if i < 0 || len(s) <= i {
		panic(errors.New("[index error]"))
	}
	// appendのみの実装
	n := make([]int, 0, len(s)-1)
	n = append(n, s[:i]...)
	n = append(n, s[i+1:]...)
	return n
}

// Concat returns a *NEW* slice, that have the same and minimum length and capacity.
func Concat(s, t []rune) []rune {
	n := make([]rune, 0, len(s)+len(t))
	n = append(n, s...)
	n = append(n, t...)
	return n
}

// UpperRune is rune version of `strings.ToUpper()`.
func UpperRune(r rune) rune {
	str := strings.ToUpper(string(r))
	return []rune(str)[0]
}

// LowerRune is rune version of `strings.ToLower()`.
func LowerRune(r rune) rune {
	str := strings.ToLower(string(r))
	return []rune(str)[0]
}

// ToggleRune returns a upper case if an input is a lower case, v.v.
func ToggleRune(r rune) rune {
	var str string
	if 'a' <= r && r <= 'z' {
		str = strings.ToUpper(string(r))
	} else if 'A' <= r && r <= 'Z' {
		str = strings.ToLower(string(r))
	} else {
		str = string(r)
	}
	return []rune(str)[0]
}

// ToggleString iteratively calls ToggleRune, and returns the toggled string.
func ToggleString(s string) string {
	inputRunes := []rune(s)
	outputRunes := make([]rune, 0, len(inputRunes))
	for _, r := range inputRunes {
		outputRunes = append(outputRunes, ToggleRune(r))
	}
	return string(outputRunes)
}

// Strtoi is a wrapper of `strconv.Atoi()`.
// If `strconv.Atoi()` returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

// sort package (snippets)
//sort.Sort(sort.IntSlice(s))
//sort.Sort(sort.Reverse(sort.IntSlice(s)))
//sort.Sort(sort.Float64Slice(s))
//sort.Sort(sort.StringSlice(s))

// copy function
//a = []int{0, 1, 2}
//b = make([]int, len(a))
//copy(b, a)

/*******************************************************************/

var n, k int
var X, Y []int
var C []rune

var dots [][]int
var cumsum [][]int

func main() {
	tmp := NextIntsLine()
	n, k = tmp[0], tmp[1]
	for i := 0; i < n; i++ {
		strs := NextStringsLine()
		x, _ := strconv.Atoi(strs[0])
		y, _ := strconv.Atoi(strs[1])
		c := rune(strs[2][0])

		if c == 'W' {
			c = 'B'
			y += k
		}
		x %= 2 * k
		y %= 2 * k
		X = append(X, x)
		Y = append(Y, y)
		C = append(C, c)
	}

	for i := 0; i < 2*k; i++ {
		row := make([]int, 2*k)
		dots = append(dots, row)
	}
	for i := 0; i < n; i++ {
		y, x := Y[i], X[i]
		dots[y][x] = 1
	}

	initialize()
	//	fmt.Println(X, Y)
	//	fmt.Println(cumsum)
	//	for i := 2*k - 1; i >= 0; i-- {
	//		fmt.Println(cumsum[i])
	//	}

	/* bottom, left, top, right
	1. y-2*k, x-2*k, y-k-1, x-k-1
	2. y-2*k, x, y-k-1, x+k-1
	3. y-k, x-k, y-1, x-1
	4. y-k, x+k, y-1, x+2*k-1
	5. y, x-2*k, y+k-1, x-k-1
	6. y, x, y+k-1, x+k-1
	7. y+k, x-k, y+2*k-1, x-1
	8. y+k, x+k, y+2*k-1, x+2*k-1
	*/
	ans := -1
	for y := 0; y <= 2*k-1; y++ {
		for x := 0; x <= 2*k-1; x++ {
			//			tmpans := getSum(y, x, y+(k-1), x+(k-1))
			//			tmpans += getSum(0, 0, y-1, x-1)
			//			tmpans += getSum(0, x+(k-1)+1, y-1, 2*k-1)
			//			tmpans += getSum(y+(k-1)+1, 0, 2*k-1, x-1)
			//			tmpans += getSum(y+(k-1)+1, x+(k-1)+1, 2*k-1, 2*k-1)
			tmpans := 0
			tmpans += getSum(y-2*k, x-2*k, y-k-1, x-k-1)
			tmpans += getSum(y-2*k, x, y-k-1, x+k-1)
			tmpans += getSum(y-k, x-k, y-1, x-1)
			tmpans += getSum(y-k, x+k, y-1, x+2*k-1)
			tmpans += getSum(y, x-2*k, y+k-1, x-k-1)
			tmpans += getSum(y, x, y+k-1, x+k-1)
			tmpans += getSum(y+k, x-k, y+2*k-1, x-1)
			tmpans += getSum(y+k, x+k, y+2*k-1, x+2*k-1)
			ans = Max(ans, tmpans)
		}
	}
	fmt.Println(ans)
}

func initialize() {
	for i := 0; i < 2*k; i++ {
		tmp := make([]int, 2*k)
		cumsum = append(cumsum, tmp)
	}

	for y := 0; y < 2*k; y++ {
		for x := 0; x < 2*k; x++ {
			cumsum[y][x] = dots[y][x]
			if y > 0 {
				cumsum[y][x] += cumsum[y-1][x]
			}
			if x > 0 {
				cumsum[y][x] += cumsum[y][x-1]
			}
			if y > 0 && x > 0 {
				cumsum[y][x] -= cumsum[y-1][x-1]
			}
		}
	}
}

/*
top < 0 || right < 0 -> return 0
bottom >= 2*k || left >= 2*k -> return 0

左下:
x < 0 -> x = 0
y < 0 -> y = 0
右上:
x >= 2*k -> x = 2*k-1
y >= 2*k -> y = 2*k-1
*/
func getSum(bottom, left, top, right int) int {
	//	tmp := []int{bottom, left, top, right}
	//	for _, t := range tmp {
	//		if t < 0 || 2*k <= t {
	//			return 0
	//		}
	//	}
	if top < 0 || right < 0 || bottom >= 2*k || left >= 2*k {
		return 0
	}

	if left < 0 {
		left = 0
	}
	if bottom < 0 {
		bottom = 0
	}
	if right >= 2*k {
		right = 2*k - 1
	}
	if top >= 2*k {
		top = 2*k - 1
	}

	res := cumsum[top][right]
	if bottom > 0 {
		res -= cumsum[bottom-1][right]
	}
	if left > 0 {
		res -= cumsum[top][left-1]
	}
	if bottom > 0 && left > 0 {
		res += cumsum[bottom-1][left-1]
	}
	return res
}