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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.nextLine());

        int nowX = 0;
        int nowY = 0;
        int nowT = 0;

        boolean isCan = false;

        for (int i = 0; i < N; i++) {
            String[] line = sc.nextLine().split(" ");
            int t = Integer.parseInt(line[0]);
            int x = Integer.parseInt(line[1]);
            int y = Integer.parseInt(line[2]);

            int dt = t - nowT;
            int dxy = Math.abs(x - nowX) + Math.abs(y - nowY);
            if (dt >= dxy && ((dt - dxy) % 2 == 0 || dt - dxy == 0)) {
                isCan = true;
                nowT = t;
                nowX = x;
                nowY = y;
            } else {
                isCan = false;
                break;
            }
        }

        if (isCan) {
            System.out.println("Yes");
        } else {
            System.out.println("No");
        }
    }
}