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 (2.13.1) (judge verdict: Accepted)

object Main extends App {
  def isReachable(from: (Int, Int, Int), to: (Int, Int, Int)): Boolean = {
    val ((t1, x1, y1), (t2, x2, y2)) = (from, to)
    val (t, x, y) = (t2 - t1, math.abs(x1 - x2), math.abs(y1 - y2))
    x + y <= t && (t - x) % 2 == y % 2
  }

  val sc = new java.util.Scanner(System.in)
  val N = sc.nextInt()
  val (isReachableAll, _) =
    1.to(N).foldLeft(true -> (0: Int, 0: Int, 0: Int)) {
      case ((acc, from), _) =>
        val to = (sc.nextInt(), sc.nextInt, sc.nextInt)
        (acc && isReachable(from, to)) -> to
    }
  println(if (isReachableAll) "Yes" else "No")
}