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: Accepted)

fun main(args: Array<String>) {
    val N = nextInt()
    var t = 0; var x = 0; var y = 0
    repeat(N) {
        val (T, X, Y) = listOfInt()
        val ts = T - t
        val ds = Math.abs(X - x) + Math.abs(Y - y)
        if (ds <= 0 || ts % ds != 0) {
            println("No")
            return
        }
        t = T; x = X; y = Y
    }
    println("Yes")
}

fun next() = readLine()!!
fun nextInt() = Integer.parseInt(next())
fun nextInt(offset: Int = 0) = nextInt() + offset
fun nextLong() = java.lang.Long.parseLong(next())
fun nextLong(offset: Long = 0L) = nextLong() + offset
fun nextDouble() = next().toDouble()
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map { Integer.parseInt(it) }