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: Wrong Answer)

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

using System.Collections;

class Program
{
    static void Main()
    {
        int N = int.Parse(Console.ReadLine());

        var txyList = Enumerable.Range(0, N).Select(n => Console.ReadLine())
            .Select(s => s.Split(' '))
            .Select(arr => arr.Select(s => int.Parse(s)).ToArray())
            .Select(arr => new { t = arr[0], x = arr[1], y = arr[2] })
            .ToList();

        bool isOK = true;

        foreach(var itm in txyList.Zip(txyList.Skip(1), (elm1, elm2) => new { elm1, elm2 } ))
        {
            var current = itm.elm1;
            var next = itm.elm2;

            var time = next.t - current.t;
            var distance = Math.Abs(current.x - next.x) + Math.Abs(current.y - next.y);

            if(time < distance || (time - distance) % 2 != 0)
            {
                isOK = false;
                break;
            }
        }

        Console.WriteLine(isOK ? "Yes" : "No");
    }

    static long calcGCD(long num1, long num2)
    {
        if(num1 < num2)
        {
            var tmp = num1;
            num1 = num2;
            num2 = tmp;
        }

        while(true)
        {
            long res;
            long div = Math.DivRem(num1, num2, out res);

            if (res == 0)
            {
                return num2;
            }
            else
            {
                num1 = num2;
                num2 = res;
            }
        }
    }
}


static class MathUtil
{
    public static T Max<T>(params T[] datas)
    {
        return datas.Max();
    }

    public static T Min<T>(params T[] datas)
    {
        return datas.Min();
    }

    public static IEnumerable<IEnumerable<int>> GetPermutation(int n)
    {
        if (n == 0)
        {
            yield return Single(0);
            yield break;
        }

        for (int i = 0; i <= n; i++)
        {
            foreach (var x in GetPermutation(n - 1))
            {
                yield return Single(i).Concat(x.Select(itm => itm < i ? itm : itm + 1));
            }
        }
    }

    private static IEnumerable<int> Single(int x)
    {
        yield return x;
    }

    public static IEnumerable<int> EnumeratePrimeNumbers()
    {
        List<int> primes = new List<int>() { 2 };
        yield return 2;

        for (int i = 3; i < int.MaxValue; i++)
        {
            bool isPrime = true;
            int Sqrt = (int)Math.Sqrt(i) + 1;

            foreach (var prime in primes)
            {
                if (prime > Sqrt)
                {
                    break;
                }
                if (i % prime == 0)
                {
                    isPrime = false;
                    break;
                }
            }

            if (isPrime)
            {
                primes.Add(i);
                yield return i;
            }
        }
    }
}