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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Traveling
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            String input;
            String[] splitted;
            List<Plan> plans = new List<Plan>();
            plans.Add(new Plan("0", "0", "0"));
            for(int i = 0; i < N; i++)
            {
                input = Console.ReadLine();
                splitted = input.Split(' ');
                plans.Add(new Plan(splitted[0], splitted[1], splitted[2]));
            }
            bool flag = true;

            for(int i = 0; i < N; i++)
            {
                if (!plans[i].CanGo(plans[i + 1]))
                {
                    flag = false;
                    break;
                }
            }
            if (flag)
            {
                Console.WriteLine("Yes");
            }
            else
            {
                Console.WriteLine("No");
            }
        }
    }
    class Plan
    {
        public int t;
        public int x;
        public int y;
        public Plan(String T,String X,String Y)
        {
            t = int.Parse(T);
            x = int.Parse(X);
            y = int.Parse(Y);
        }
        public bool CanGo(Plan p)
        {
            int time = Math.Abs(t - p.t);
            int xMove = Math.Abs(x - p.x);
            int yMove = Math.Abs(y - p.y);
            if (xMove + yMove > time)
            {
                return false;
            }
            else if ((time - xMove - yMove) % 2 != 0)
            {
                return false;
            }
            else
            {
                return true;
            }
        }
    }
}