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.*;
import static java.lang.Math.*;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);

		// 入力
		int n = sc.nextInt();// 中間ポイントの数

		int[] p = new int[n * 3];
		for(int i = 0; i < n * 3; i++){
			p[i] = sc.nextInt();
		}

		//
		String result = "Yes";
		for(int i = 0; i < n; i++){

			int t = 0;
			int x = 0;
			int y = 0;

			if(i == 0){
				t = p[i * 3];
				x = p[i * 3 + 1];
				y = p[i * 3 + 2];
			}else{
				t = p[i * 3] - p[(i - 1) * 3];
				x = p[i * 3 + 1] - p[(i - 1) * 3 + 1];
				y = p[i * 3 + 2] - p[(i - 1) * 3 + 2];
			}
			
			if(!canGo(t, x, y)){
				result = "No";
				break;
			}
		}

		// 出力
		System.out.println(result);
	}

	// 移動可能か
	static boolean canGo(int t, int x, int y){
		//System.out.print("t:" + t + " x:" + x + " y:" + y);

		// 制約条件
		if(t < abs(x) + abs(y)){
			// System.out.println(" No(条件１)");
			return false;
		}
		if(t%2 != abs(x + y)%2){
			// System.out.println(" No(条件２)");
			return false;
		}

		// System.out.println(" Yes");
		return true;
	}
}