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: Runtime Error)

import java.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int t[] = new int [10000];
		int x[] = new int [10000];
		int y[] = new int [10000];
		for(int i = 0; i < n; i++) {
			 t[i] = sc.nextInt();
			 x[i] = sc.nextInt();
			 y[i] = sc.nextInt();
		}
		if(t[0] % 2 == 1 && x[0] + y[0] == 0) {
			System.out.println("No");
    		return;
		}else if(t[0] < Math.abs(x[0]) + Math.abs(y[0]) 
		   || t[0] % 2 == 1 && (Math.abs(x[0]) + Math.abs(y[0])) % 2 == 0 
		   || t[0] % 2 == 0 && (Math.abs(x[0]) + Math.abs(y[0])) % 2 == 1) {
				System.out.println("No");
        		return;
		}
		for(int i = 1; i < n; i++) {
			if((t[i] - t[i - 1]) % 2 == 1 && (x[i] - x[i - 1]) + (y[i] - y[i - 1]) == 0) {
				System.out.println("No");
        		return;
			}
			else if(t[i] - t[i - 1] < Math.abs(x[i] - x[i - 1]) + Math.abs(y[i] - y[i - 1])
				   ||(t[i] - t[i - 1]) % 2 == 1 && (Math.abs(x[i] - x[i - 1]) + Math.abs(y[i] - y[i - 1])) % 2 == 0
			       ||(t[i] - t[i - 1]) % 2 == 0 && (Math.abs(x[i] - x[i - 1]) + Math.abs(y[i] - y[i - 1])) % 2 == 1) {
					System.out.println("No");
		            return;
				}
		}
		System.out.println("Yes");
	}
}