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) throws Exception {
        Scanner sc = new Scanner(System.in);
        int itarateNum = sc.nextInt();
        
        String msg = "";
        
        for(int i=1; i<=itarateNum; i++){
            int n = sc.nextInt();
            int x = sc.nextInt();
            int y = sc.nextInt();
            
            int dummyX = 0;
            int dummyY = 0;
            
            for(int ii=1; ii<=n; ii++){
                boolean edited = false;
                
                if(dummyX<x){
                    dummyX++;
                    edited = true;
                }else if(dummyY<y){
                    dummyY++;
                    edited = true;
                }
                
                if(!edited){
                    if(dummyX>x){
                        dummyX--;
                        edited = true;
                    }else if(dummyY>y){
                        dummyY--;
                        edited = true;
                    }
                }
                
                if(!edited && dummyX == x){
                    dummyX++;
                }else if(!edited && dummyY == y){
                    dummyY++;
                }
            }
            
            if(dummyX == x && dummyY == y){
                msg = "Yes";
            }else{
                msg = "No";
                break;
            }
            
        }
        
        System.out.println(msg);

    }
}