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: Time Limit Exceeded)

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));

        }

        public void Solve(ConsoleInput cin)
        {
            var N = cin.ReadInt;
            List<int[]> txy = new List<int[]>();
            int[] tmp = { 0, 0, 0 };
            txy.Add(tmp);
            for (int i = 0; i < N; i++)
            {
                txy.Add(cin.ReadIntArray(3));
            }

            bool fin = false;
            for(int i = 1; i <= N; i++)
            {
                if ((txy[i][0] - txy[0][0]) % 2 == 0)//偶数の位置
                {
                    if ((((Math.Abs(txy[i][1] - txy[0][1]) % 2) + (Math.Abs(txy[i][2] - txy[0][2]) % 2)) % 2 != 0)) fin = true;
                }
                else
                {
                    if ((((Math.Abs(txy[i][1] - txy[0][1]) % 2) + (Math.Abs(txy[i][2] - txy[0][2]) % 2)) % 2 != 1)) fin = true;
                }
            }

            if(!fin)Solve2(txy, 0);
            else Console.WriteLine("No");
        }

        public void Solve2(List<int[]> txy, int count)
        {
            bool isOk = false;
            if((txy[count + 1][0] - txy[count][0]) % 2 == 0)//偶数の位置
            {
                if ((((Math.Abs(txy[count + 1][1] - txy[count][1]) % 2) + (Math.Abs(txy[count + 1][2] - txy[count][2]) % 2))%2 != 0)) goto ok;
            }
            else
            {
                if ((((Math.Abs(txy[count + 1][1] - txy[count][1]) % 2) + (Math.Abs(txy[count + 1][2] - txy[count][2]) % 2)) % 2 != 1)) goto ok;
            }
            if ((Math.Pow(txy[count + 1][0] - txy[count][0],2) >= (Math.Pow(txy[count + 1][1] - txy[count][1],2)) + Math.Pow(txy[count + 1][2] - txy[count][2],2)))
            {
                for (int ix = 0; ix <= txy[count + 1][0] - txy[count][0]; ix++)
                {
                    int ky = (txy[count + 1][0] - txy[count][0]) - ix;

                    if ((txy[count][1] + ix < 0 && txy[count + 1][1] > 0) || (txy[count][1] - ix > 0 && txy[count + 1][1] < 0)) continue;
                    if ((txy[count][2] + ky < 0 && txy[count + 1][2] > 0) || (txy[count][2] - ky > 0 && txy[count + 1][2] < 0))
                    {
                        continue;
                    }

                    for (int i = 0; i <= ix; i++)
                    {
                        int _toX = 1 * i - 1 * (ix - i);

                        for (int k = 0; k <= ky; k++)
                        {
                            int _toY = 1 * k - 1 * (ky - k);


                            if (txy[count][1] + _toX == txy[count + 1][1] && txy[count][2] + _toY == txy[count + 1][2])
                            {
                                isOk = true;
                                goto ok;
                            }
                        }

                    }

                }
            }

            ok:
            if (isOk)
            {
                if (count + 1 < txy.Count-1)
                {
                    count += 1;
                    Solve2(txy, count);
                }
                else
                {
                    Console.WriteLine("Yes");
                }
            }
            else
            {
                Console.WriteLine("No");
            }
        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }
}