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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

   	public static void main(String[] args) {
   		Scanner sc = new Scanner(System.in);
   		int n = Integer.parseInt(sc.next());
   		int[][] plan = new int [n][3];
   		int[] planlog = new int [3];

   		for(int i=0;i<n;i++) {
   			plan[i][0] = Integer.parseInt(sc.next());
   			plan[i][1]=Integer.parseInt(sc.next());
   			plan[i][2]=Integer.parseInt(sc.next());
   		}
   		sc.close();
    
   		for(int i=0;i<n;i++) {
   			//time,X,Y差分
   			int absT = plan[i][0] - planlog[0];
   			int absX = Math.abs(plan[i][1] - planlog[1]);
   			int absY = Math.abs(plan[i][2] - planlog[2]);
   			//時間内に移動できるか && とどまることができるか
   			if(absT>=absX+absY&&absT%2==(absX+absY)%2) {
   				//System.out.println(absT+" "+absX+" "+absY);
   				planlog[0]=absT;
   				planlog[1]=absX;
   				planlog[2]=absY;
   			}else{
   				System.out.println("No");
   				return;
   			}
   		}
   		System.out.println("Yes");
   	}
    
}