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{
  def main(args: Array[String]) {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt
    val list = List.fill(n, 3)(sc.nextInt)

    val time: Seq[Int] = 0 +: list.map{ l => l(0) }.toSeq
    val dist: Seq[Int] = 0 +: list.map{ l => l(1) + l(2) }.toSeq

    var flag = true
    (0 until n).foreach{ i =>
      val time_diff = time(i + 1) - time(i)
      val dist_diff = Math.abs(dist(i + 1) - dist(i))
      if (time_diff < dist_diff || time_diff % 2 != dist_diff % 2)
        flag = false
    }
    if (flag)
      println("Yes")
    else
      println("No")
  }
}