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)

data class Point(val t: Int, val x: Int, val y: Int)

fun main(args: Array<String>) {
    val n = readLine()?.toInt() ?: return
    val points = Array(n + 1) {
        if (it == 0) {
            Point(0, 0, 0)
        } else {
            val (t, x, y) = readLine()?.split(" ")?.map { n -> n.toInt() } ?: return
            Point(t, x, y)
        }
    }

    for (t in 0 until n) {
        val dt = points[t + 1].t - points[t].t
        val dist = Math.abs(points[t + 1].x - points[t].x) +
                Math.abs(points[t + 1].y - points[t].y)
        if (dt < dist || dt % 2 != dist % 2) {
            println("NO")
            return
        }
    }
    println("YES")
}