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: Time Limit Exceeded)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] t = new int[n];
        int[] x = new int[n];
        int[] y = new int[n];
        for(int i = 0; i < n; i++) {
            t[i] = sc.nextInt();
            x[i] = sc.nextInt();
            y[i] = sc.nextInt();
        }
        int currentX = 0;
        int currentY = 0;
        int currentTime = 0;
        for(int i = 0; i < n; i++) {
            if(!canGo(currentX, currentY, currentTime, x[i], y[i], t[i])) {
                System.out.println("No");
                return;
            }
            currentX = x[i];
            currentY = y[i];
            currentTime = t[i];
        }
        System.out.println("Yes");
    }
    private static boolean canGo(int currentX, int currentY, int currentTime, int destX, int destY, int destTime) {
        if(currentX == destX && currentY == destY &&  (destTime - currentTime) % 2 == 0) return true;
        if(currentX == destX && currentY == destY &&  (destTime - currentTime) % 2 != 0) return false;
        if(currentTime >= destTime) return false;
        return canGo(currentX+1, currentY, currentTime+1, destX, destY, destTime)||
                canGo(currentX, currentY+1, currentTime+1, destX, destY, destTime)||
                canGo(currentX-1, currentY, currentTime+1, destX, destY, destTime)||
                canGo(currentX, currentY-1, currentTime+1, destX, destY, destTime);
    }
}