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: Wrong Answer)

operator fun Pair<Int, Int>.minus(pair: Pair<Int, Int>) = Pair(first - pair.first, second - pair.second)
fun Pair<Int, Int>.manhattanTo(pair: Pair<Int, Int>) = (this - pair).manhattanLength()
fun Pair<Int, Int>.manhattanLength() = Math.abs(first) + Math.abs(second)

data class Destination(private val t: Int, private val coordinate: Pair<Int, Int>) {
    private fun timeTo(destination: Destination) = destination.t - t

    fun canThenReachTo(destination: Destination) =
            coordinate.manhattanTo(destination.coordinate) <= timeTo(destination) &&
            timeTo(destination) % 2 == (coordinate - destination.coordinate).manhattanLength() % 2
}

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val destinations = (0 until n).map {
        val (t, x, y) = readLine()!!.split(" ").map { it.toInt() }
        Destination(t, Pair(x, y))
    }

    val travellable = destinations.mapIndexedNotNull { index, destination ->
        when(index) {
            n - 1 -> null
            else -> Pair(destination, destinations[index + 1])
        }
    }.all { it.first.canThenReachTo(it.second) }

    println(if (travellable) "Yes" else "No")
}