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: Accepted)

import scala.math.abs

object Main {
  def main(args: Array[String]): Unit = {
    solve
  }


  //  val sc = new java.util.Scanner(System.in)
  //  val n = sc.nextInt
  //  val list: Array[Array[Int]] = Array.fill[Int](n, 3)(sc.nextInt)
  //  //  val b = Breaks
  //
  //  var before = Array[Int](0, 0, 0)
  //  val canTravel = list.forall {
  //    target =>
  //      val step = target(0) - before(0)
  //      val distance = abs(target(1) - before(1)) + abs(target(2) - before(2))
  //      before = target
  //      if (step < distance || step % 2 != distance % 2) {
  //        false
  //      } else {
  //        true
  //      }
  //  }


  //  b.breakable {
  //    for (i <- 1 until list.length) {
  //      val step = list(i)(0) - list(i - 1)(0)
  //      val distance = abs(list(i)(1) - list(i - 1)(1)) + abs(list(i)(2) - list(i - 1)(2))
  //
  //      if (step < distance || step % 2 != distance % 2) {
  //        canTravel = false
  //        b.break
  //      }
  //    }
  //  }

  //  println(if (canTravel) "Yes" else "No")

  def solve(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt

    var (bt, bx, by) = (0, 0, 0)
    var canTravel = true
    for (i <- 1 to n) {
      if (canTravel) {
        val t, x, y = sc.nextInt
        val step = t - bt
        val distance = abs(x - bx) + abs(y - by)
        if (step < distance || step % 2 != distance % 2) {
          canTravel = false
        }
        bt = t
        bx = x
        by = y
      }
    }
    println(if (canTravel) "Yes" else "No")
  }
}