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.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+1];
      int[] x = new int[n+1];
      int[] y = new int[n+1];
      for(int i = 1;i <= n;i++){
      	t[i]=sc.nextInt();
        x[i]=sc.nextInt();
        y[i]=sc.nextInt();
      }
      for(int i = 0;i <= n-1;i++){
      	int k = Math.abs(x[i+1]-x[i])+Math.abs(y[i+1]-y[i]);
        if(t[i+1]-t[i]<k||(t[i+1]-t[i])%2!=k%2){
        	System.out.println("No");
            return;
        }
      }
      System.out.println("Yes");
    }
    public static int lcm(int x, int y){
      return x*y/gcd(x,y);
    }
    public static int gcd(int x, int y){
      if(x < y)return gcd(y,x);
      if(y==0)return x;
      return gcd(y,x%y);
    }
}