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 scanner = new Scanner(System.in);
    int N = scanner.nextInt();
    int[] time = new int[N + 10];
    int[] x = new int[N + 10];
    int[] y = new int[N + 10];
    time[0] = 0;
    x[0] = 0;
    y[0] = 0;
    boolean isOK = false;

    for (int i = 1; i <= N; i++){
      time[i] = scanner.nextInt();
      x[i] = scanner.nextInt();
      y[i] = scanner.nextInt();
    }
    for (int i = 0; i < N; i++){
      if ((x[i + 1] + y[i + 1] - x[i] - y[i]) <= (time[i + 1] - time[i]) &&
      (x[i + 1] + y[i + 1] - x[i] - y[i]) % 2 == (time[i + 1]-time[i]) % 2){
        isOK = true;
        break;
      } else {
        isOK = false;
        break;}
    }
    if (isOK == true){
      System.out.println("Yes");
    } else {System.out.println("No");}
  }
}