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 (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var (
	sc = bufio.NewReader(os.Stdin)
)

type pos struct {
	t, x, y int
}

func (p *pos) arrive(p2 *pos) bool {
	t := p.t - p2.t
	x := p.x - p2.x
	y := p.y - p2.y
	if x+y == t {
		return true
	}
	if x+y < t && (t-(x+y))%2 == 1 {
		return false
	}
	if x+y == 1 && t%2 == 0 {
		return false
	}
	if x+y > t {
		return false
	}
	return true
}

func main() {
	N := scanInt()
	c := &pos{t: 0, x: 0, y: 0}
	for i := 0; i < N; i++ {
		n := &pos{t: scanInt(), x: scanInt(), y: scanInt()}
		if !n.arrive(c) {
			fmt.Println("No")
			return
		}
		if !rec(c, n) {
			fmt.Println("No")
			return
		}
		c = n
	}
	fmt.Println("Yes")
}

func rec(c, n *pos) bool {
	if !n.arrive(c) {
		return false
	}
	if c.t == n.t {
		if c.x == n.x && c.y == n.y {
			return true
		} else {
			return false
		}
	}
	// x+1, y
	if rec(&pos{t: c.t + 1, x: c.x + 1, y: c.y}, n) {
		return true
	}
	// x-1, y
	if rec(&pos{t: c.t + 1, x: c.x - 1, y: c.y}, n) {
		return true
	}
	// x, y+1
	if rec(&pos{t: c.t + 1, x: c.x, y: c.y + 1}, n) {
		return true
	}
	// x, y-1
	if rec(&pos{t: c.t + 1, x: c.x, y: c.y - 1}, n) {
		return true
	}

	return false
}

func scan(a ...interface{}) { _, err := fmt.Fscan(sc, a...); pnc(err) }
func scanStr() (s string)   { scan(&s); return }
func scanInt() int          { i, err := strconv.Atoi(scanStr()); pnc(err); return i }
func scanFloat() float64    { f, err := strconv.ParseFloat(scanStr(), 64); pnc(err); return f }
func pnc(err error) {
	if err != nil {
		panic(err)
	}
}