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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			Question.Exec();
		}
	}

	public class Plane
	{
		public long Time;
		public long X;
		public long Y;
	}

	public static class Question
	{
		public static void Exec()
		{
			long n = int.Parse(Console.ReadLine());
			List<Plane> list = new List<Plane>();
			var p = new Plane();
			p.Time = 0;
			p.X = 0;
			p.Y = 0;
			list.Add(p);

			for (var j = 0; j < n; ++j) {
				var array = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();
				var plane = new Plane();
				plane.Time = array[0];
				plane.X = array[1];
				plane.Y = array[2];
				list.Add(plane);
			}

			string answer = "Yes";
			for (var j = 1; j <= n; ++j) {
				long time = list[j].Time - list[j - 1].Time;
				long x = Math.Abs(list[j].X - list[j - 1].X);
				long y = Math.Abs(list[j].Y - list[j - 1].Y);
				if (x + y > time) {
					answer = "No";
					break;
				}

				if ((x + y) % 2 != time % 2) {
					answer = "No";
					break;
				}
			}

			Console.WriteLine($"{answer}");

			Console.ReadKey();
		}
	}
}