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.*;

public class Main {

	public static void main(String[] args) {
		new Main().execute();
	}

	public void execute() {
		Scanner sc = new Scanner(System.in);
		final int N = sc.nextInt();

		int x = 0;
		int y = 0;
		int t = 0;
		for (int i = 0; i < N; i++) {
			int ti = sc.nextInt();
			int xi = sc.nextInt();
			int yi = sc.nextInt();
			int dt = ti - t;
			int d = manhattan(x, y, xi, yi);
			if (dt < d) {
				System.out.println("No");
				return;
			} else if ((dt - d) % 2 == 1) {
				System.out.println("No");
				return;
			} else {
				x = xi;
				y = yi;
				t = ti;
			}
		}
		System.out.println("Yes");
		sc.close();
	}

	private int manhattan(int x0, int y0, int x1, int y1) {
		return Math.abs(x0 - x1) + Math.abs(y0 - y1);
	}

}