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;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		long n = long.Parse(Console.ReadLine());//long.Parseはstringをlongに変換。
    long[,] vertexes = new long[n,3];//ここに受け取る
    bool answer = true;
    long distance = 0;
    long time = 0;
    for(long i = 0; i < n; i++)
    {
      long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);//１行ごとに受け取る
      vertexes[i,0] = nums[0];
      vertexes[i,1] = nums[1];
      vertexes[i,2] = nums[2];
    }

    for(int i = 0; i < n; i++)
    {
      if(i>=1)
      {
        distance = Math.Abs(vertexes[i,1]-vertexes[i-1,1])
          + Math.Abs(vertexes[i,2]-vertexes[i-1,2]);
        time = vertexes[i,0] - vertexes[i-1,0];
      }else
      {
        distance = Math.Abs(vertexes[i,1])
          + Math.Abs(vertexes[i,2]);
        time = vertexes[i,0];
      }
      
      if(time < distance) answer = false;
      if(time%2 != distance%2) answer = false;
    }
    
		Console.WriteLine((answer) ? "Yes" : "No");
	}
}