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;
 
namespace Application
{
	class Solution
	{
		static void Main(string[] args)
		{ 
			var currentTime = 0;
			var currentX = 0;
			var currentY = 0;
 
			var stepCount = int.Parse(Console.ReadLine());
 
			var result = "Yes";
 
			for (var i = 0; i < stepCount; i++)
			{
				var inputWords = Console.ReadLine().Split(' ');
				var nextTime = int.Parse(inputWords[0]);
				var nextX = int.Parse(inputWords[1]);
				var nextY = int.Parse(inputWords[2]);
 
				var diffTime = nextTime - currentTime;
				var diffX = Math.Abs(nextX - currentX);
				var diffY = Math.Abs(nextY - currentY);
 
				var move = diffTime - (diffX + diffY);
 
				// 到達可能
				if (move >= 0
					&& move % 2 == 0)
				{
					currentTime = nextTime;
					currentX = nextX;
					currentY = nextY;
				}
				else
				{
					result = "No";
					break;
				}
			}
 
			Console.WriteLine(result);
		}
	}
}