Problem:
Score : 300 points

Problem Statement

AtCoDeer the deer is going on a trip in a two-dimensional plane.
In his plan, he will depart from point (0, 0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i,y_i) at time t_i.

If AtCoDeer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1,y), (x-1,y), (x,y+1) and (x,y-1).
Note that he cannot stay at his place.
Determine whether he can carry out his plan.

Constraints

1 ≤ N ≤ 10^5

0 ≤ x_i ≤ 10^5

0 ≤ y_i ≤ 10^5

1 ≤ t_i ≤ 10^5

t_i < t_{i+1} (1 ≤ i ≤ N-1)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
t_1 x_1 y_1
t_2 x_2 y_2
:
t_N x_N y_N

Output

If AtCoDeer can carry out his plan, print Yes; if he cannot, print No.

Sample Input 1

2
3 1 2
6 1 1

Sample Output 1

Yes

For example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).

Sample Input 2

1
2 100 100

Sample Output 2

No

It is impossible to be at (100,100) two seconds after being at (0,0).

Sample Input 3

2
5 1 1
100 1 1

Sample Output 3

No

Solution in Go (1.6) (judge verdict: Runtime Error)

package main

import (
	"bufio"
	"fmt"
	"log"
	"math/rand"
	"os"
	"strconv"
	"time"
)

// const abcd = "abcdefghijklmnopqrstuvwxyz"
// const ABCD = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
// var dx = [...]int{0, 1, 0, -1, 1, -1, -1, 1}
// var dy = [...]int{1, 0, -1, 0, 1, 1, -1, -1}
// var inf int = 1e13

// var mod = 1000000007
var next = newScanner()

// ---------------------------------------------------------

func main() {
	log.SetFlags(log.Lshortfile)
	N, K := next.Int(), next.Int()
	x := make([]int, N)
	y := make([]int, N)
	c := make([]string, N)
	for i := 0; i < N; i++ {
		x[i] = next.Int()
		y[i] = next.Int()
		c[i] = next.String()
	}
	ans := 0

	// xor = SplitMix64{}
	// xor.Init(11)
	// for a := 0; a <= 2*K; a++ {
	// for b := 0; b <= 2*K; b++ {

	timeout := time.After(1950 * time.Millisecond)
	for {
		a := rand.Intn(2 * K)
		b := rand.Intn(2 * K)
		cnt := 0
		for i := 0; i < N; i++ {
			if ((x[i]+a)/K)%2 == ((y[i]+b)/K)%2 {
				if c[i] == "B" {
					cnt++
				}
			} else {
				if c[i] == "W" {
					cnt++
				}
			}
		}
		ans = max(ans, cnt)
		select {
		case <-timeout:
			goto ANS
		default:
			break
		}
	}
	// }
	// }
ANS:
	fmt.Println(ans)
	// K = 5
	// a := 4
	// b := 4
	// for i := 0; i < 20; i++ {
	// 	for j := 0; j < 20; j++ {
	// 		if (i+a)/K%2 == (j+b)/K%2 {
	// 			fmt.Print("■")
	// 		} else {
	// 			fmt.Print(".")
	// 		}
	// 	}
	//
	// 	fmt.Println("")
	// }
}

// ------------- xorshift ------------------------

// SplitMix64 is fast rand
type SplitMix64 struct {
	s uint64 // The state can be seeded with any value
}

// Next returns the next pseudo random number generated,
// before start you must provvide one 64 unsigned bit seed.
func (x *SplitMix64) Next() uint64 {
	x.s = x.s + uint64(0x9E3779B97F4A7C15)
	z := x.s
	z = (z ^ (z >> 30)) * uint64(0xBF58476D1CE4E5B9)
	z = (z ^ (z >> 27)) * uint64(0x94D049BB133111EB)
	return z ^ (z >> 31)

}

// Init returns a new SplitMix64 source seeded with the given value.
func (x *SplitMix64) Init(seed uint64) {
	x.s = seed
}

// ---------------------------------------------------------

// Pair is...
type Pair struct {
	a, b int
}

// Pairs is sorted by []Pair struct
type Pairs []Pair

func (p Pairs) Len() int {
	return len(p)
}
func (p Pairs) Swap(i, j int) {
	p[i], p[j] = p[j], p[i]
}

func (p Pairs) Less(i, j int) bool {
	return p[i].b < p[i].b
}

// func (p Pairs) Less(i, j int) bool {
// 	if p[i].a < p[j].a {
// 		return true
// 	} else if p[i].a == p[j].a {
// 		return p[i].b < p[j].b
// 	}
// 	return false
// }

// ------int method-------------------------
func in(c, a, z int) bool {
	return c >= a && c < z
}
func out(c, a, z int) bool {
	return !in(c, a, z)
}
func btoi(b bool) int {
	if b {
		return 1
	}
	return 0
}
func itob(a int) bool {
	if a == 0 {
		return false
	}
	return true
}
func max(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
		}
	}
	return r
}
func min(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
		}
	}
	return r
}
func sum(a []int) int {
	r := 0
	for i := 0; i < len(a); i++ {
		r += a[i]
	}
	return r
}
func pro(a []int) int {
	r := 1
	for i := 0; i < len(a); i++ {
		r *= a[i]
	}
	return r
}
func fill(a []int, n int) []int {
	for i := 0; i < len(a); i++ {
		a[i] = n
	}
	return a
}
func minmax(a, b int) (int, int) {
	if a > b {
		return b, a
	}
	return a, b
}
func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}
func ceil(a, b int) int {
	if a%b != 0 {
		return 1
	}
	return 0
}

// ---------- buffered scanner -----------------------------------------
type scanner struct {
	r   *bufio.Reader
	buf []byte
	p   int
}

func newScanner() *scanner {
	rdr := bufio.NewReaderSize(os.Stdin, 10000)
	return &scanner{r: rdr}
}
func (s *scanner) next() string {
	s.pre()
	start := s.p
	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			break
		}
	}
	result := string(s.buf[start:s.p])
	s.p++
	return result
}
func (s *scanner) Line() string {
	s.pre()
	start := s.p
	s.p = len(s.buf)
	return string(s.buf[start:])
}
func (s *scanner) String() string {
	return s.next()
}
func (s *scanner) Int() int {
	v, err := strconv.Atoi(s.next())
	if err != nil {
		log.Fatal(err)
	}
	return v
}
func (s *scanner) Ints(n int) []int {
	r := make([]int, n)
	for i := 0; i < n; i++ {
		r[i] = s.Int()
	}
	return r
}
func (s *scanner) Int64() int64 {
	v, err := strconv.ParseInt(s.next(), 10, 64)
	if err != nil {
		log.Fatal(err)
	}
	return v
}
func (s *scanner) Uint64() uint64 {
	v, err := strconv.ParseUint(s.next(), 10, 64)
	if err != nil {
		log.Fatal(err)
	}
	return v
}
func (s *scanner) Float64() float64 {
	v, err := strconv.ParseFloat(s.next(), 64)
	if err != nil {
		log.Fatal(err)
	}
	return v
}
func (s *scanner) pre() {
	if s.p >= len(s.buf) {
		s.readLine()
		s.p = 0
	}
}
func (s *scanner) readLine() {
	s.buf = make([]byte, 0)
	for {
		l, p, err := s.r.ReadLine()
		if err != nil {
			log.Fatal(err)
		}
		s.buf = append(s.buf, l...)
		if !p {
			break
		}
	}
}