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

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner scanner = new Scanner(System.in);
        Integer inputNum = Integer.parseInt(scanner.nextLine());
        String output = "Yes";

        List<TimeAndXY> list = new ArrayList<>();
        list.add(new TimeAndXY(0,0,0));

        for(int i=0; i<inputNum; i++){
            final TimeAndXY nextState = new TimeAndXY(scanner.nextLine());
            list.add(nextState);

        }
        scanner.close();
        for(int i=0; i<inputNum; i++){
            TimeAndXY lastState = list.get(i);
            TimeAndXY nextState = list.get(i=1);
            if( nextState.canMoveFrom(lastState) ){
                lastState = nextState;
            }
            else{
                output = "No";
                break;
            }
        }
        System.out.println(output);
    }

    public static class TimeAndXY {
        private final int time;
        private final int x;
        private final int y;
        public TimeAndXY(String input){
            String[] inputs = input.split(" ");
            this.time = Integer.parseInt(inputs[0]);
            this.x = Integer.parseInt(inputs[1]);
            this.y = Integer.parseInt(inputs[2]);
        }
        @Override
        public String toString(){
            return "t="+time+", x="+x+", y="+y;
        }


        public TimeAndXY(int time, int x, int y){
            this.time = time;
            this.x = x;
            this.y = y;
        }
        public boolean canMoveFrom(TimeAndXY moveFrom){
            int xmove = this.x - moveFrom.x;
            int ymove = this.y - moveFrom.y;
            int duration = this.time - moveFrom.time;
            int xymove = Math.abs(xmove) + Math.abs(ymove);
            if( xymove<=duration ){
                if(xymove%2==duration%2){
                    return true;
                }
            }
            return false;
        }
    }
}