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 Program
{
 static void Main(string[] args) 
 {
   int cnt = 0;
   int operationNum = 0;
   int step = 0;
   int x = 0;
   int y = 0;
   int stamina = 0;
   int needStep = 0;
   int buff = 0;
   bool result = true;
   String[] operationStr = new String[3];
   
   operationNum = int.Parse(Console.ReadLine());

   int[,] operation = new int[operationNum,3];
   
   for( cnt = 0; cnt < operationNum; cnt++ )
   {
     operationStr = Console.ReadLine().Split(' ');
     operation[cnt,0] = int.Parse(operationStr[0]);
     operation[cnt,1] = int.Parse(operationStr[1]);
     operation[cnt,2] = int.Parse(operationStr[2]);
   }
   
   for( cnt = 0; cnt < operationNum; cnt++ )
   {
     stamina = operation[cnt,0] - step;
     needStep = Math.Abs( (operation[cnt,1] - x) ) + Math.Abs( (operation[cnt,2] - y) );
     
     if( needStep <= stamina )
     {
       buff = stamina - needStep;
       
       if( buff > 0 )
       {
         if( ( buff % 2 ) != 0 ) 
         {
           result = false;
           break;
         }
       }
       
       step = operation[cnt,0];
       x = operation[cnt,1];
       y = operation[cnt,2];
     }
     else
     {
       result = false;
       break;
     }
   }
   
   Console.WriteLine("{0}",(result?"Yes":"No"));
 }
}