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.*;
import java.util.stream.*;

public class Main{
	public static void main(String... args){ new Main().solve(); }

	public void solve(){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int pt = 0;
		int px = 0;
		int py = 0;
		int ct = 0;
		int cx = 0;
		int cy = 0;
		int condition[][] = new int[n][2];
		for(int i=0; i<n; i++){
			ct = sc.nextInt();
			cx = sc.nextInt();
			cy = sc.nextInt();
			condition[i][0] = ct - pt;
			condition[i][1] = Math.abs(cx - px) + Math.abs(cy - py);
			pt = ct;
			px = cx;
			py = cy;
		}
		long cnt = Arrays.asList(condition).stream()
			.filter(a -> {
				if((a[0] % 2) == (a[1] % 2) && a[0] >= a[1]) return true;
				return false;
			})
			.count();
		if(cnt == n) System.out.println("Yes");
		else System.out.println("No");
	}
}