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[] t = new int[n];
    int[] x = new int[n];
    int[] y = new int[n];
    for (int i = 0; i < n; i++) {
      t[i] = scanner.nextInt();
      x[i] = scanner.nextInt();
      y[i] = scanner.nextInt();
    }

    new Main().execute(n, t, x, y);
  }

  public void execute(int n, int[] t, int[] x, int[] y) {
    int startX = 0;
    int startY = 0;
    int step = 0;
    for (int i = 0; i < n; i++) {
      step = t[i] - step;

      if (!canWalk(step, startX, startY, x[i], y[i])) {
        System.out.println("No");
        return;
      }

      startX = x[i];
      startY = y[i];
    }

    System.out.println("Yes");
  }

  /**
   * Can we walk from (startX, startY) to (endX, endY) in `stepCount` steps
   */
  private boolean canWalk(int stepCount, int startX, int startY, int endX, int endY) {
    int minStep = Math.abs(endX - startX) + Math.abs(endY - startY);
    return (stepCount >= minStep) &&
        (stepCount % 2 == minStep % 2);
  }
}