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.Text;
using System.Collections.Generic;
using System.Linq;
using E = System.Linq.Enumerable;
 
class Program
 {
  static int[] A;
        static void Main(string[] args)
        {
          //入力を受け取る
          var N = long.Parse(Console.ReadLine());
          var txy = new int[N+1][];
          
          txy[0] = new int[3]; 
          for(int i = 1;i <= N; i++){
            txy[i] = new int[3];
            txy[i] = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
          }
          
          var ans = true;
          
          for(int i = 1;i <= N; i++){
            var time = txy[i][0]-txy[i-1][0];
            var dis  = Math.Abs(txy[i][1]-txy[i-1][1])+Math.Abs(txy[i][2]-txy[i-1][2]);
            var rest = time - dis;
            if(rest < 0 || rest%2 == 1){
              ans = false;
              break;
            }
          }
          if(ans){
            Console.WriteLine("Yes");
          }else{
            Console.WriteLine("No");
          }
          
        }
  
}