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.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, ' '));
            Console.ReadLine();
        }

        public void Solve(ConsoleInput cin)
        {
            int N = cin.ReadInt;
            int[] t = new int[110000], x = new int[110000], y = new int[110000];

            t[0] = x[0] = y[0] = 0;
            for(int i = 0; i < N; i++)
            {
                string s = cin.ReadLine;
                t[i+1] = int.Parse(s.Split(' ')[0]);
                x[i+1] = int.Parse(s.Split(' ')[1]);
                y[i+1] = int.Parse(s.Split(' ')[2]);
            }

            bool can = true;
            for(int i = 0; i < N; i++)
            {
                int dt = t[i + 1] - t[i];
                int dist = Abs(x[i + 1] - x[i]) + Abs(y[i + 1] - y[i]);

                if (dt < dist) can = false;
                if (dt % 2 != dist % 2) can = false;
                if (can == false) break;
            }
            Console.WriteLine(can ? "Yes" : "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 num) { var ret = new string[num]; for (long i = 0; i < num; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long num) { var ret = new int[num]; for (long i = 0; i < num; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long num) { var ret = new long[num]; for (long i = 0; i < num; ++i) ret[i] = ReadLong; return ret; }
    }
}