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.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.PrintWriter;
import java.io.IOException;

public class Main {

    public static void main(String[] args) throws IOException{
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(System.out);
        
        int N = Integer.parseInt(reader.readLine()),
            time = 0, //経過時間
            nowx = 0,
            nowy = 0;
        
        String ans = "Yes";
        
        for(int i = 0; i < N; i++){
            String[] line = reader.readLine().split(" ");
            int t = Integer.parseInt(line[0]),
                x = Integer.parseInt(line[1]),
                y = Integer.parseInt(line[2]);
            
            if(Math.abs(x-nowx) + Math.abs(y-nowy) > t - time){
                ans = "No";
                break;
            }else if (Math.abs(x-nowx) + Math.abs(y-nowy) < t - time){
                int distance = (t - time) - (Math.abs(x-nowx) + Math.abs(y-nowy));
                
                if(distance != 0 && distance % 2 == 1 ){
                    ans = "No";
                    break;
                }
            }
            
            time = t;
            nowx = x;
            nowy = y;
            
        }
    
    writer.println(ans);
        
    reader.close();
    writer.close();
    }
}