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.Scanner;
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] all = new int[3*N];
		int[] t = new int[N];
		int[] x = new int[N];
		int[] y = new int[N];

		for(int i=0; i<3*N; i++) {
			all[i] = sc.nextInt();
		}for(int j=0; j<N; j++) {
			t[j] = all[j/3];
			x[j] = all[(j-1)/3];
			y[j] = all[(j-2)/3];
		}

		int judge = 0;

		if(x[0] + y[0] <= t[0] && (x[0]+y[0]-t[0])%2 == 0) {
			judge += 1;
		}else {
			judge += 0;
		}

		for(int k=1; k<N; k++) {
			if(Math.abs(x[k]-x[k-1]) + Math.abs(y[k]-y[k-1])
			<= t[k]-t[k-1]) {
				if(Math.abs(x[k]-x[k-1]) + Math.abs(y[k]-y[k-1])
			- (t[k]-t[k-1]) % 2 == 0) {
					judge += 1;
				}else {
					judge += 0;
				}
			}else {
				judge += 0;
			}
		}

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

	}

}