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.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Main {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int[] t = new int[N+1];
        int[] x = new int[N+1];
        int[] y = new int[N+1];
        int[] dist = new int[N];
        int[] t_diff = new int[N];
        t[0] = 0; x[0] = 0; y[0] = 0;
        for(int i = 1; i < N+1; i++){
            t[i] = in.nextInt();
            x[i] = in.nextInt();
            y[i] = in.nextInt();
        }
        String ret = "Yes";
        for(int i = 0; i < N; i++){
            dist[i] = Math.abs(x[i] - x[i+1]) + Math.abs(y[i] - y[i+1]);
            t_diff[i] = t[i+1] - t[i];
            if(dist[i] > t_diff[i] || (t_diff[i] - dist[i])%2==1 ){
                ret = "No";
                break;    
            }
        }
        System.out.println(ret);
        in.close();
    }
}