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.ArrayList;
import java.util.List;
import java.util.Scanner;

/**
 * https://qiita.com/drken/items/fd4e5e3630d0f5859067
 *
 * @author YukihiroLocal
 *
 */
public class Main {
  public static void main(String[] args) {


    Scanner sc = new Scanner(System.in);
    // get a integer

    int N = sc.nextInt();
    // System.out.println(" integer is " + N);

    List<Coordinate> coordinateList = new ArrayList<>();
    coordinateList.add(new Coordinate(0, 0, 0));
    for (int i = 0; i < N; i++) {
      int t = sc.nextInt();
      int x = sc.nextInt();
      int y = sc.nextInt();

      coordinateList.add(new Coordinate(t, x, y));
    } ;
    boolean continueFlag = true;
//    //N=1
//    int diffT =Math.abs( coordinateList.get(0).getT());
//    int diffX =Math.abs( coordinateList.get(0).getX());
//    int diffY =Math.abs( coordinateList.get(0).getY());
//    if(diffT >= diffX + diffY && (diffT - diffX - diffY ) % 2 == 0){
//      continueFlag = true;
//    }else {
//      continueFlag = false;
//    }

    //N>1
    for(int i = 0 ; i < N ; i++){
      int diffT =Math.abs( coordinateList.get(i).getT() - coordinateList.get(i+1).getT());
      int diffX =Math.abs( coordinateList.get(i).getX() - coordinateList.get(i+1).getX());
      int diffY =Math.abs( coordinateList.get(i).getY() - coordinateList.get(i+1).getY());
      if(diffT >= diffX + diffY && (diffT - diffX - diffY ) % 2 == 0){
        continueFlag = true;
      }else {
        continueFlag = false;
        break;
      }
    }
    if(continueFlag){
      System.out.println("Yes");
    }else{
      System.out.println("No");
    }

  };
}


class Coordinate {
  int t, x, y;

  Coordinate(int t, int x, int y) {
    this.t = t;
    this.x = x;
    this.y = y;
  }

  int getX() {
    return this.x;
  };

  int getT() {
    return this.t;
  };

  int getY() {
    return this.y;
  };
}