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: Wrong Answer)

import java.util.*;
 
public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
	List<Integer> listT = new ArrayList<Integer>();
	List<Integer> listX = new ArrayList<Integer>();
	List<Integer> listY = new ArrayList<Integer>();
	while(sc.hasNext()){
		listT.add(sc.nextInt());
		listX.add(sc.nextInt());
		listY.add(sc.nextInt());
	}
	//経過時間
	int dt = listT.get(0);
	//移動距離
	int dist = listX.get(0) + listY.get(0);
	
	if(dist > dt){System.out.println("No");}
	
	for(int i = 0; i <= n-2; i++){
		dt = listT.get(i+1) - listT.get(i);
		dist = listX.get(i+1) - listX.get(i) 
			+ listY.get(i+1) - listY.get(i);
		if((dt%2!=0 && dist%2==0) || (dt%2==0 && dist%2!=0)){
			System.out.println("No");
			break;
		}
		if(i==n-2 &&((dt%2==0 && dist%2==0) || (dt%2!=0 && dist%2!=0))){
			System.out.println("Yes");
		}
	}
  }
}