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)

import scala.util.control.Breaks._
import scala.math.abs

object Main {
  def main(args:Array[String]) = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt
    val txys = List(0, 0, 0) :: List.fill(n, 3)(sc.nextInt)

    var possible = true
    breakable { for (i <- 0 until n) {
      val List(t0, x0, y0) = txys(i)
      val List(t1, x1, y1) = txys(i + 1)
      val res = t1 - t0 - (abs(x1 - x0) + abs(y1 - y0))
      if (res < 0 || res%2 != 0) {
        possible = false
        break
      }
    } }
    println(if (possible) "Yes" else "No")
  }
}