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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

    fun main(args: Array<String>) {
        val input = read()
        println(traveling(input))
    }

    data class Inputs(val t: Int, val x: Int, val y: Int) {
        operator fun minus(other: Inputs): Inputs {
            return Inputs(this.t - other.t, this.x - other.x, this.y - other.y)
        }
    }

    fun read(): List<Inputs> {
        val n = Integer.parseInt(readLine()!!)
        val inputs = mutableListOf<Inputs>()
        for (i in 1..n) {
            val input = readLine()!!.split(' ').map { Integer.parseInt(it) }
            inputs.add(Inputs(input[0], input[1], input[2]))
        }
        return inputs
    }

    fun traveling(inputs: List<Inputs>): String {
        tailrec fun judge(prev: Inputs, list: List<Inputs>): Boolean {
            if (list.isEmpty()) return true
            val dist = list.first() - prev
            val absDist = Math.abs(dist.x) + Math.abs(dist.y)
            if (dist.t < absDist || (dist.t % 2) != (absDist % 2)) return false
            return judge(list.first(), list.drop(1))
        }
        return if (judge(Inputs(0, 0, 0), inputs)) "Yes" else "No"
    }