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;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author rn-sshawish
 */
public class Main{

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        int t = 0, x = 0, y = 0;
        boolean state = true;
        for (int i = 0; i < n; i++) {
            int t1 = input.nextInt();
            int x1 = input.nextInt();
            int y1 = input.nextInt();
            int distanceDiff;

                int fiffY = Math.abs(x - x1);
//                if (fiffY != 0 && x != 0&& x1 != 0) {
//                    fiffY ++;
//                }
                int fiffX = Math.abs(y - y1);
//                if (fiffX != 0 && y != 0&& y1 != 0) {
//                    fiffX ++;
//                }
                distanceDiff = fiffX + fiffY;
            
            int timeDiff = t1 - t;
            if (distanceDiff <= timeDiff) {
                t = t1;
                x = x1;
                y = y1;
            } else {
                state = false;
                break;
            }
        }
        if (state) {
            System.out.println("Yes");
        } else {
            System.out.println("No");
        }

    }
}