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;

class AtCoder
{
  	static int abs(int x)
    {
      if( x >= 0 ) return x;
      else return -x;
    }
  
    static void Main(string[] args)
    {
      Console.ReadLine();
        string s;
      	var cx = 0;
      	var cy = 0;
      	var ct = 0;
      	while((s=Console.ReadLine()) != null ){
        	var n = s.Split(' ');     
          	var t = int.Parse(n[0]);
          var t2 = t-ct;
          	var x = int.Parse(n[1]);
          	var y = int.Parse(n[2]);
          
           var m = abs(cx-x) + abs(cy-y);
          	if( t2 < m ) {
              Console.Write("No");
              return ;
            }
            if( m != t2 ){
              if( ((t2-m) & 0x00000001) == 1 ){
              Console.Write("No");
              return ;                
              }
            }
          
          cx = x;
          cy = y;
          ct = t;
      	}      	
      
                    Console.Write("Yes");
    }
}