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;

public class Hello{
    public static void Main(){
        // Your code here!
      
        int[] t = new int[100010];
        int[] x = new int[100010];
        int[] y = new int[100010];
        t[0] = 0;
        x[0] = 0;
        y[0] = 0;
        int N = int.Parse(Console.ReadLine());
        for(int i = 0; i < N; i++)
        {
            int[] s = Console.ReadLine().Split(' ').Select(v => int.Parse(v)).ToArray();
            t[i + 1] = s[0];
            x[i + 1] = s[1];
            y[i + 1] = s[2];
        }
        
        bool can = true;
        for(int i = 0; i < N; i++)
        {
            int dt = t[i + 1] - t[i];
            int dist = Math.Abs(x[i + 1] - x[i]) + Math.Abs(y[i + 1] - y[i]);
            if(dt < dist)
            {
                can = false;
                //Console.WriteLine("i = " + i);
                //Console.WriteLine("hoge");
            }
            else
            {
                if(dt % 2 != dist % 2)
                {
                    
                    can = false;
                    //Console.WriteLine("huga");
                } 
            }
        }
        
        if(can == true) Console.WriteLine("Yes");
        else Console.WriteLine("No");
    }
}