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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		// 要素の入力、格納
		int N = sc.nextInt();
		int t[] = new int[N + 1];
		int x[] = new int[N + 1];
		int y[] = new int[N + 1];
		t[0] = 0;
		x[0] = 0;
		y[0] = 0;
		for (int i = 1; i < N + 1; i++) {
			t[i] = sc.nextInt();
			x[i] = sc.nextInt();
			y[i] = sc.nextInt();
		}

		String ans = "Yes";
		int dt = 0;
		int dx = 0;
		int dy = 0;
		int chk = 0;

		for (int i = 0; i < N; i++) {
			dt = t[i + 1] - t[i];
			dx = x[i + 1] - x[i];
			dy = y[i + 1] - y[i];
			chk = dt - (dx + dy);

			if (!(chk >= 0 && chk % 2 == 0)) {
				ans = "No";
				break;
			}
		}

		// 出力
		System.out.println(ans);
	}
}