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 sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] t = new int[N+1];
        int[] x = new int[N+1];
        int[] y = new int[N+1];
        t[0] = 0;
        x[0] = 0;
        y[0] = 0;

        for (int i = 1; i <= N; i++) {
            t[i] = sc.nextInt();
            x[i] = sc.nextInt();
            y[i] = sc.nextInt();
        }

        boolean go = false;
        for (int i = 1; i <= N; i++) {
            int load = Math.abs(x[i]-x[i-1]) + Math.abs(y[i]-y[i-1]);
            int time = t[i] - t[i - 1];
            if (time >= load && (load) % 2 == (time) % 2) {
                go = true;
            } else {
                go = false;
                break;
            }
        }
        if (go) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }

        sc.close();
    }
}