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 scan = new Scanner(System.in);

	int N = scan.nextInt();  //点の個数
	int now_t = 0;
	int now_x = 0;
	int now_y = 0;
	
	int[] t_ = new int[N];
	int[] x_ = new int[N];
	int[] y_ = new int[N];

	for(int i = 0; i < N; i++){
	    t_[i] = scan.nextInt();
	    x_[i] = scan.nextInt();
	    y_[i] = scan.nextInt();
	}

	int flag = 1;
	for(int i = 0; i < N; i++){
	    int len_t = t_[i]-now_t;
	    int len_x = Math.abs(now_x-x_[i]);
	    int len_y = Math.abs(now_y-y_[i]);
	    if(len_t >= len_x+len_y &&
	       (len_t-len_x-len_y) % 2 == 0){
		//移動できる
		now_t = t_[i];
		now_x = x_[i];
		now_y = y_[i];
	    }else{
		flag = -1;
		break;
	    }
	}

	if(flag == 1){
	    System.out.println("Yes");
	}else{
	    System.out.println("No");
	}
    }
}