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())+1;
        int[] t=new int[N];
        int[] x=new int[N];
        int[] y=new int[N];
        for(int i=1;i<N;i++) {
            int[] input2=Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
            t[i]=input2[0];
            x[i]=input2[1];
            y[i]=input2[2];
        }
        t[0]=x[0]=y[0]=0;
        
        
        if(AbsCheck(N,t,x,y)=="Yes" && ParityCheck(N,t,x,y)=="Yes") {
            Console.WriteLine("Yes");
        } else {
            Console.WriteLine("No");
        }
    }
    
    
    public static string AbsCheck(int N, int[] t, int[] x, int[] y) {    
        string flag="Yes";
        for(int i=1;i<N;i++) {
            int dt=t[i]-t[i-1];
            int dist=Math.Abs(x[i]-x[i-1])+Math.Abs(y[i]-y[i-1]);
            if(dt<dist) {
                flag="No";
                break;
            }
        }
        return flag;
    }
    
    public static string ParityCheck(int N, int[] t, int[] x, int[] y) {
        string flag="Yes";
        for(int i=1;i<N;i++) {
            int dt=t[i]-t[i-1];
            int dist=Math.Abs(x[i]-x[i-1])+Math.Abs(y[i]-y[i-1]);
            if(dt%2!=dist%2) {
                flag="No";
                break;
            }
        }
        return flag;
    }
}