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: Wrong Answer)

import java.util.*;


class Main {
	
	public static int startX = 0;
	public static int startY = 0;


	public static void main(String args[]) {
		
		Main main = new Main();

		main.mainmain();

	}

	public void mainmain() {
		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();

		int time = 0;
		int x = 0;
		int y = 0;

		boolean result = true;

		List<inner> inners = new ArrayList<>();

		for ( int i = 0; i < N; i++ ) {

			time = sc.nextInt();
			x = sc.nextInt();
			y = sc.nextInt();

			inners.add(new inner(time, x, y));

		}

		Collections.sort(inners, new innerComparator());

		time  = 0;
		for ( inner in : inners ) {
			time = in.time - time;
			x = in.x;
			y = in.y;

			if (result) {
				
				result = check(time, x, y);
				startX = x;
				startY = y;

			}
		}


		System.out.println( (result) ? "Yes" : "No" );
	}

	public boolean check(int time, int x, int y) {
		int ckX = startX;
		int ckY = startY;
		for ( int i = 0; i < time; i++ ) {
			if ( ckX != x ) {
				ckX = ( ckX < x ) ? ckX + 1 : ckX - 1;
			} else {
				ckY = ( ckY < y ) ? ckY + 1 : ckY - 1;
			}
		}

		return ( ckX == x && ckY == y );
	}

	class inner {

		public int time;
		public int x;
		public int y;

		public inner(int time, int x, int y) {
			this.time = time;
			this.x = x;
			this.y = y;
		}

	}

	class innerComparator implements Comparator<inner> {
		public int compare(inner a, inner b) {
			int no1 = a.time;
			int no2 = b.time;

			if (no1 == no2) {
				return 0;
			} else if (no1 > no2) {
				return 1;
			} else {
				return -1;
			}
		}
	}

}