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.io.*;
import java.util.*;

class Main {
	static final String YES = "Yes";
	static final String NO = "No";

	public static void main(String[] args) throws Exception {
		final Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[][] txy = new int[N][3];
		for (int i = 0; i < N; i++) {
			txy[i][0] = sc.nextInt();
			txy[i][1] = sc.nextInt();
			txy[i][2] = sc.nextInt();
		}
		Arrays.sort(txy, (a, b) -> Long.compare(a[0], b[0]));
		int a = 0, b = 0;
		for (int i = 0; i < N; i++) {
			int move = txy[i][0] - (i == 0 ? 0 : txy[i - 1][0]);
			int dist = d(txy[i][1], txy[i][2], a, b);
			if (move < dist || (move - dist) % 2 == 1) {
				System.out.println(NO);
				return;
			}

			a = txy[i][1];
			b = txy[i][2];
		}

		System.out.println(YES);
	}

	private static int d(int x, int y, int x2, int y2) {
		return Math.abs(x - x2) + Math.abs(y - y2);
	}
}