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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

class Program
{
    static void Main(string[] args)
    {
        int n = Input.nextInt();
        int nowx = 0;
        int nowy = 0;
        int nowt = 0;
        int tmpx;
        int tmpy;
        int tmpt;
        for (int i = 0; i < n; i++)
        {
            tmpt = Input.nextInt();
            tmpx = Input.nextInt();
            tmpy = Input.nextInt();
            
            if (tmpt - nowt < Math.Abs(tmpx - nowx) + Math.Abs(tmpy - nowy) || ((tmpt - nowt) - (Math.Abs(tmpx - nowx) + Math.Abs(tmpy - nowy))) % 2 != 0)
            {
                Console.WriteLine("No");
                return;
            }
            nowx = tmpx;
            nowy = tmpy;
            nowt = tmpt;
        }
        Console.WriteLine("Yes");


    }

}


class Input
{
    static string[] line = { };
    static int index = 0;
    static void readLine()
    {
        line = Console.ReadLine().Split(' ');
        index = 0;
    }
    public static int nextInt()
    {
        if (index == line.Length)
        {

            readLine();
        }
        index++;
        return int.Parse(line[index - 1]);
    }
    public static long nextLong()
    {
        if (index == line.Length)
        {

            readLine();
        }
        index++;
        return long.Parse(line[index - 1]);
    }
    public static string next()
    {
        if (index == line.Length)
        {

            readLine();
        }
        index++;
        return line[index - 1];
    }
}