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(final String[] args) {
        final Scanner sc = new Scanner(System.in);
        final int N = sc.nextInt();
        
        for (int i=0; i<N; i++) {
            final int[] txy = {sc.nextInt(),sc.nextInt(),sc.nextInt()};
            if(judgeValidMove(txy) == false) {
                System.out.println("No");
                return;
            }
        }
        System.out.println("Yes");
        sc.close();
    }

    public static boolean judgeValidMove(int[] txy){
        final int minDist = txy[1] + txy[2];
        final int difDist = txy[0] - minDist;
        // 到達可能な距離か
        if(txy[0] < minDist){
            return false;
        }
        // 最短でたどり着いた時間と予定時間の差が偶数なら到達可能
        if(difDist % 2 == 0){
            return true;
        } else {
            return false;
        }
    }
}