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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*; 

class Main{
public static void main(String[] args){
	Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int ans=0;
  		int keit=0;
		int keix=0;
  		int keiy=0;
  
		for(int c=0;c<n;c++){
    		 int t=sc.nextInt();
          	 int x=sc.nextInt();
          	 int y=sc.nextInt();
          if(t%2==1&&(x+y)%2==0){
          ans++;
          break;
          }else if(t%2==0&&(x+y)%2==1){
          ans++;
          break;
          }else if((Math.abs(x-keix)+Math.abs(y-keiy))>t-keit){
          ans++;
           break;
          }
          keix=x;
          keiy=y;
          keit=t;
    	}
    
 	if(ans==0){
    		System.out.println("Yes");
    	}else{
     		System.out.println("No");
   	 }

    }
}