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);

		int n = sc.nextInt();
		int[][] way= new int[n][3];

		for(int i =0;i<3*n;i++){
			int b=i%3;
			int a=(i-b)/3;
			int m = sc.nextInt();
			way[a][b]= m;
		}

		boolean koike = true;
		for(int i = 0;i<n-1;i++){
			koike &= judge(way[i][0],way[i][1],way[i][2],way[i+1][0],way[i+1][1],way[i+1][2]);
		}
		koike &= judge(0,0,0,way[0][0],way[0][1],way[0][2]);
		if(koike){
			System.out.println("Yes");
		}else{
			System.out.println("No");
		}
	}
	private static boolean judge(int a,int b, int c, int d, int e, int f){
		int t = d-a;
		int distance = Math.abs(e-b)+Math.abs(f-c);
		return t>=distance && (t-distance)%2==0;
	}
}