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;

namespace ABC086_C_Traveling
{
	internal class Program
	{
		public static void Main(string[] args)
		{
			int n = int.Parse(Console.ReadLine());
			string[] input;
			List<int> tList = new List<int>{0};
			List<int> xList = new List<int>{0};
			List<int> yList = new List<int>{0};
			
			for (int i = 0; i < n; i++)
			{
				input = Console.ReadLine().Split(' ');
				tList.Add(int.Parse(input[0]));
				xList.Add(int.Parse(input[1]));
				yList.Add(int.Parse(input[2]));
			}

			bool isCanTraveled = true;
			for (int i = 1; i <= n; i++)
			{
				int time = tList[i] - tList[i - 1];
				int xMove = Math.Abs(xList[i] - xList[i - 1]);
				int yMove = Math.Abs(yList[i] - yList[i - 1]);

				if (xMove == 0 && yMove == 0)
				{
					//移動時間が偶数ではない場合元の点には戻れない
					if (time % 2 != 0)
					{
						//Console.WriteLine("Error: 1");
						isCanTraveled = false;
						break;
					}
				}else if (xMove == 0)
				{
					//移動し終わってからの残り時間が偶数でない場合戻れない
					if ((time - yMove) % 2 != 0)
					{
						//Console.WriteLine("Error: 2");
						isCanTraveled = false;
						break;
					}
				}else if (yMove == 0)
				{
					//同様
					if ((time - xMove) % 2 != 0)
					{
						//Console.WriteLine("Error: 3");
						isCanTraveled = false;
						break;
					}
				}
				else
				{
					time -= xMove + yMove;
					if (time < 0 || time % 2 != 0)
					{
						//Console.WriteLine("Error: 4");
						isCanTraveled = false;
						break;
					}
				}
			}

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