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: Wrong Answer)

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

class Program
{
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());

		var ok = true;
		var x = 0;
		var y = 0;
		for (var i = 0; i < n; ++i) {
			var t = Array.ConvertAll(Console.ReadLine().Split(new[] { ' ' }), number => int.Parse(number));
			var def = Math.Abs(t[1] - x) + Math.Abs(t[2] - y);
			if (def > t[0]) {
				ok = false;
			} else if (def < t[0]) {
				if ((t[0] - def) % 2 == 1) {
					ok = false;
				}
			}

			x = t[1];
			y = t[2];
		}

		if (ok) {
			Console.WriteLine("Yes");
		} else {
			Console.WriteLine("No");
		}

		//デバッグ実行での確認用。そのまま提出しても問題なし
		Console.ReadKey();
	}
}