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)

/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		int min=0;
		int time=0;
		int row=0;
		int col=0;
		int count=0;
		int a[][]=new int[n][3];
		for(int i=0;i<n;i++)
		for(int j=0;j<3;j++)
		a[i][j]=in.nextInt();
		for(int k=0,s=1;s<n;s++,k++){
		time=a[s][0]-a[k][0];
		row=a[s][1]-a[k][1];
		col=a[s][2]-a[k][2];
		if(row<0)
		row=-row;
		if(col<0)
		col=-col;
		min=row+col;
		if(min<=time){
		if (row==0 || col==0)
		count ++;
		else if((time-min)%4==0)
		count ++;
		}
		
		}
		if(n!=1){if(count==(n-1))
		System.out.println("Yes");
		else System.out.println("No");}
		if(n==0 && time==0){
			System.out.println("Yes");
		}
}}