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;

class Program
{
  public static void Main(string[] args)
  {
    int n = int.Parse(Console.ReadLine());
    int[,] s = new int[n+1, 3];
    s[0,0] = 0;
    s[0,1] = 0;
    s[0,2] = 0;
    for (int i = 1; i <= n; i ++) {
      int[] t = Console.ReadLine().Split().Select(int.Parse).ToArray();
      s[i,0] = t[0];
      s[i,1] = t[1];
      s[i,2] = t[2];
      int time = s[i,0] - s[i-1,0];
      int x = Math.Max(s[i,1], s[i-1,1]) - Math.Min(s[i,1], s[i-1,1]);
      int y = Math.Max(s[i,2], s[i-1,2]) - Math.Min(s[i,2], s[i-1,2]);
      int length = x + y;
      if (time < length) {
        Console.WriteLine("No");
        break;
      }
      else {
        while(true) {
          if (time == length) break;
          time -= 2;
          if (time < length) {
            Console.WriteLine("No");
            goto end;
          }
        }
      }
      if (i == n) Console.WriteLine("Yes");
    }
    end:;
  }
}