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)

import java.io.BufferedReader
import java.io.InputStreamReader

fun main(args: Array<String>) {
    val br = BufferedReader(InputStreamReader(System.`in`))
    val n = br.readLine().toInt()
    val node = mutableListOf<Triple<Int, Int, Int>>()
    node.add(Triple(0, 0, 0))
    for (i in 1..n) {
        val d = br.readLine().split(' ')
                .map { it.toInt() }
        node.add(Triple(d[0], d[1], d[2]))
    }
    println(if (judge(node, 1, node.size - 1)) "Yes" else "No"
    )
}

fun judge(node: List<Triple<Int, Int, Int>>, index: Int, limit: Int): Boolean {
    val current = node[index]
    val pre = node[index - 1]
    val step = current.first - pre.first
    val x = current.second - pre.second
    val y = current.third - pre.third
    val move = Math.abs(x) + Math.abs(y)
    if (move > step) {
        return false
    }
    return (move - step) % 2 == 0 && if (index < limit) judge(node, index + 1, limit) else true
}

fun err(print: Any) {
    System.err.println(print)
}