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){
		Main m = new Main();
		m.run();
	}
	
	Scanner sc = new Scanner(System.in);
	
	void run(){
		int N = sc.nextInt();
		
		int prevT = 0;
		int prevX = 0;
		int prevY = 0;
		boolean mutFlag = true;
		for (int i = 0; i < N ; i++){
			int t = sc.nextInt();
			int x = sc.nextInt();
			int y = sc.nextInt();
			
			mutFlag = check(t,x,y,prevT,prevX,prevY);
			if(!mutFlag){
				break;
			}
			prevT = t;
			prevX = x;
			prevY = y;
		}
		System.out.println(mutFlag ?"Yes" :"No");
		
		
	}
	
	boolean check(int t1,int x1,int y1, int t0,int x0,int y0){
		int time = t1 - t0;
		
		int distance = Math.abs(x1 - x0) + Math.abs(y1 - y0);
		if((distance + time) % 2 == 1){
			return false;
		}
		return distance <= time;
	}
}