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.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {

	String fileName = "erase";

	public void solve() throws IOException {
		int n = 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] = nextInt();
			x[i] = nextInt();
			y[i] = nextInt();
		}
		boolean b = true;
		for (int i = 0; i < n; i++) {
			int time = t[i + 1] - t[i];
			int dx = Math.abs(x[i + 1] - x[i]);
			int dy = Math.abs(y[i + 1] - y[i]);
//			out.println(dx + " " + dy + " " + time);
			int d = dx + dy;
			if ((time - d < 0) || (time - d) % 2 == 1) {
				b = false;
			}
		}
		if (b)
			out.println("Yes");
		else
			out.println("No");
	}

	public void run() {
		try {
			InputStreamReader isr = new InputStreamReader(System.in);
			br = new BufferedReader(isr);
			out = new PrintWriter(System.out, true);
			// out = new PrintWriter(fileName + ".out");
			// br = new BufferedReader(new FileReader(fileName + ".in"));
			solve();
			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	BufferedReader br;
	StringTokenizer in;
	static PrintWriter out;

	public String nextToken() throws IOException {
		while (in == null || !in.hasMoreTokens()) {
			in = new StringTokenizer(br.readLine());
		}
		return in.nextToken();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}

	public long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

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

}