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;

namespace ABC86
{
    class Program
    {
        static void Main(string[] args)
        {
            var solver = new Solver();
            solver.Solve3();
        }
    }

    public class Solver
    {

        public void Solve1()
        {
            var ab = Console.ReadLine().Split().Select(int.Parse).ToArray();
            Console.WriteLine(ab[0] * ab[1] % 2 == 0 ? "Even" : "Odd");

        }

        public void Solve2()
        {
            var ab = int.Parse(Console.ReadLine().Replace(" ", ""));

            Console.WriteLine(Math.Sqrt(ab) - (int)Math.Sqrt(ab) == 0 ? "Yes" : "No");

        }

        struct Txy
        {
            public long T;
            public long X;
            public long Y;
        }
        public void Solve3()
        {
            var n = int.Parse(Console.ReadLine());

            var txys = new List<Txy> { new Txy { T = 0, X = 0, Y = 0 } };
            for (int i = 0; i < n; i++)
            {
                var txy = Console.ReadLine().Split().Select(long.Parse).ToArray();
                txys.Add(new Txy { T = txy[0], X = txy[1], Y = txy[2] });
            }

            for (int i = 0; i < n; i++)
            {
                var judge = txys.ElementAt(i + 1).T - txys.ElementAt(i).T - (Math.Abs(txys.ElementAt(i + 1).X - txys.ElementAt(i).X) + Math.Abs(txys.ElementAt(i + 1).Y - txys.ElementAt(i).Y));


                if (judge >= 0 && judge % 2 == 0)
                {
 
                }
                else
                {
                    Console.WriteLine("No");
                    return;
                }
            }
            Console.WriteLine("Yes");

        }
    }
}