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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = Integer.parseInt(scanner.nextLine());

		List<List<Integer>> points = new ArrayList<>();
		List<Integer> start = new ArrayList<>();
		start.add(0);
		start.add(0);
		start.add(0);
		points.add(start);
		for (int i = 0; i < n; i++) {
			List<Integer> point = new ArrayList<>();
			String[] txy = scanner.nextLine().split(" ");
			point.add(Integer.parseInt(txy[0]));
			point.add(Integer.parseInt(txy[1]));
			point.add(Integer.parseInt(txy[2]));
			points.add(point);
		}

		for (int i = 1; i < n + 1; i++) {
			List<Integer> current = points.get(i - 1);
			List<Integer> target = points.get(i);
			int manhattan = manhattanDist(current.get(1), current.get(2), target.get(1), target.get(2));
			int seconds = target.get(0) - current.get(0);

			if (manhattan > seconds) {
				System.out.println("No");
				System.exit(0);
			}
			if ((seconds - manhattan) % 2 == 1) {
				System.out.println("No");
				System.exit(0);
			}
		}
		System.out.println("Yes");
	}

	public static int manhattanDist(int currentX, int currentY, int targetX, int targetY) {
		return Math.abs(targetX - currentX) + Math.abs(targetY - currentY);
	}
}