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 Scala (2.11.7) (judge verdict: Wrong Answer)

import java.util.Scanner

import scala.annotation.tailrec

object Main extends App {
  val sc = new Scanner(System.in)
  val N = sc.nextInt
  val es = Element(0, Position(0, 0)) +: Seq.fill(N)(Element(sc.nextInt, Position(sc.nextInt, sc.nextInt)))

  println(if (solve(es)) "Yes" else "No")

  @tailrec
  private[this] def solve(es: Seq[Element]): Boolean = es match {
    case h +: n +: rest =>
      h.validNext(n) && solve(n +: rest)
    case _ => true
  }
}

case class Element(t: Int, p: Position) {
  def validNext(destination: Element): Boolean = {
    val distance = p.distance(destination.p)
    val dt = destination.t - t
    if (distance > dt) false
    else if (dt - distance % 2 == 0) true
    else false
  }
}

case class Position(x: Int, y: Int) {
  def distance(that: Position): Int =
    Math.abs(that.x - x) + Math.abs(that.y - y)
}