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: Time Limit Exceeded)

object Main extends App {
  val n = io.StdIn.readLine().toInt
  val list = collection.mutable.ListBuffer[Array[Int]](Array(0 ,0, 0))
  (1 to n).foreach { i =>
    list += io.StdIn.readLine().split(' ').map(_.toInt).toArray
  }
  val cache = collection.mutable.HashMap[(Int, Int, Int), Boolean]()
  def f(t: Int, x: Int, y: Int): Boolean = {
   val absX = Math.abs(x)
    val absY = Math.abs(y)
    if (t == 0) (x == 0 && y == 0)
    else if (absX > t || absY > t || absX + absY > t) false
    else (f(t - 1, x + 1, y) || f(t - 1, x - 1, y) || f(t - 1, x, y + 1) || f(t - 1, x, y - 1)) 
  }
  list.zip(list.tail)
  val list2 = list.zip(list.tail).map{case (x1, x2) => (x2(0) - x1(0), x2(1) - x1(1), x2(2) - x1(2))}
  print(if(list2.forall{case (t, x, y) => cache.getOrElseUpdate((t, x, y), f(t, x, y))}) "Yes" else "No")
}