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.Linq;

namespace C
{
	internal class Program
	{
		public static void Main(string[] args)
		{
			var n = int.Parse(Console.ReadLine());
			var tn = new int[n];
			var xn = new int[n];
			var yn = new int[n];
			for (var i = 0; i < n; i++)
			{
				var line = Console.ReadLine().Split().Select(int.Parse).ToArray();
				tn[i] = line[0];
				xn[i] = line[1];
				yn[i] = line[2];
			}

			var dtn = new int[n];
			var dxn = new int[n];
			var dyn = new int[n];
			dtn[0] = tn[0];
			dxn[0] = xn[0];
			dyn[0] = yn[0];
			for (var i = 1; i < n; i++)
			{
				dtn[i] = tn[i] - tn[i - 1];
				dxn[i] = Math.Abs(xn[i] - xn[i - 1]);
				dyn[i] = Math.Abs(yn[i] - yn[i - 1]);
			}

			for (var i = 0; i < n; i++)
			{
				var tmp = dtn[i] - dxn[i] - dyn[i];
				if (tmp < 0 || tmp % 2 == 1)
				{
					Console.WriteLine("No");
					return;
				}
			}

			Console.WriteLine("Yes");
		}
	}
}