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;

namespace _089c
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            int[,] txy = new int[N+1,3];
            txy[0,0] = 0;
            txy[0,1] = 0;
            txy[0,2] = 0;
            for(int i = 1; i <= N; i++){
                var read = Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
                txy[i,0] = read[0];
                txy[i,1] = read[1];
                txy[i,2] = read[2];
            } 
            bool res = false;
            for(int i = 0; i < N ; i++){
                int t1 = txy[i,0];
                int x1 = txy[i,1];
                int y1 = txy[i,2];  
                int t2 = txy[i+1,0];
                int x2 = txy[i+1,1];
                int y2 = txy[i+1,2];
                int sa_x_y = Math.Abs(x2-x1)+Math.Abs(y2-y1);
                if(t2-t1>=sa_x_y){
                    if(t2-t1 ==sa_x_y){
                        res = true;
                    }else if(((t2-t1)-sa_x_y)%2==0){
                        res = true;
                    }else{
                        res = false;
                        break;
                    }
                }else{
                    res = false;
                    break;
                }  
            }
            Console.WriteLine(res?"Yes":"No");
        }
    }
}