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: Runtime Error)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int t = 0;
		int x = 0;
		int y = 0;
		
		while (sc.hasNextInt()) {
			int next_t = sc.nextInt();
			int next_x = sc.nextInt();
			int next_y = sc.nextInt();
			
			int jikan = next_t - t;
			int dest = Math.abs(next_x - x) + Math.abs(next_y - y);

			if (jikan / 2 == 0) {
				if (dest / 2 == 1)  {
					System.out.println("No");
					return;
				}
			} else {
				if (dest / 2 == 0) {
					System.out.println("No");
					return;
				}
			}
			
			if (dest > jikan) {
				System.out.println("No");
				return;
			}
			
			t = next_t;
			x = next_x;
			y = next_y;
			
		}
		
		System.out.println("Yes");
	}
}