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;
public class Hello{
    public static void Main(){
        int N = int.Parse(Console.ReadLine());
        int curT = 0;
        int curX = 0;
        int curY = 0;
        
        for(int i = 0;i < N;i++){
            string[] input = Console.ReadLine().Split(' ');
            int nexT = int.Parse(input[0]);
            int nexX = int.Parse(input[1]);
            int nexY = int.Parse(input[2]);
            
            int t = nexT - curT;
            int x = Math.Abs(nexX - curX);
            int y = Math.Abs(nexY - curY);
            int d = x + y;
            if(t >= d && (t % 2 == d % 2)){
                
            }else{
                Console.WriteLine("No");
                return;
            }
            curT = nexT;
            curX = nexX;
            curY = nexY;
        }
        Console.WriteLine("Yes");
    }
}