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.Scanner;

public class Main{
	static Scanner s = new Scanner(System.in);			//文字の入力

	static int N = s.nextInt();



	static boolean flag = true;

	static int sum =0;

	public static void main(String[] args){
		solve();
	}

	static void solve() {
		int t[] = new int [N];
		int x[] = new int [N];
		int y[] = new int [N];
		int z[] = new int [N];


		for(int i= 0;i<N;i++){
			t[i]=s.nextInt();
			x[i]=s.nextInt();
			y[i]=s.nextInt();			//入力
			z[i] = x[i]+ y[i];
			
		}
		boolean check1=false;
		boolean check2= false;
		if(N == 1){
			if(t[0] < (z[0]) || (t[0]%2+(z[0+1]-z[0])%2==1)){
				flag = false;
			}
		}else{
			for(int i= 0;i<N-1;i++){
				if(i == 0){
					if(t[i] < (z[i]) || (t[i]%2+(z[i+1]-z[i])%2==1)){
						flag = false;
					}

				}else if((t[i+1] - t[i]) < (z[i+1]-z[i])|| (t[i]%2+(z[i+1]-z[i])%2==1)){
					flag = false;
				}
			}
		}

		if(flag == true){
			System.out.println("Yes");
		}else{
			System.out.println("No");
		}
	}



}