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;
import java.util.List;
import java.util.ArrayList;
public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        List<Integer> t = new ArrayList<>();
        List<Integer> x = new ArrayList<>();
        List<Integer> y = new ArrayList<>();
        t.add(0);
        x.add(0);
        y.add(0);
        int[] xt = {-1,0,1,0};
        int[] yt = {0,1,0,-1};
        for(int i = 0;i < n;i++){
            t.add(sc.nextInt());
            x.add(sc.nextInt());
            y.add(sc.nextInt());
        }
        for(int i = 1;i < n;i++){
            int dt = t.get(i) - t.get(i-1);
            int dist = Math.abs(x.get(i)-x.get(i-1)) + Math.abs(y.get(i)-y.get(i-1));
            if(dist <= dt && (dist % 2) == (dt % 2)){
                System.out.println("Yes");
                return;
            }
        }
        System.out.println("No");
    }
}