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.IO;
using System.Collections.Generic;
using System.Text.RegularExpressions;
using System.Linq;

namespace atcoder_past_problem
{
    class Program
    {
        static void Main(string[] args)
        {
            new Program().Solve(new Input(Console.In));
        }

        public void Solve(Input input)
        {
            if (Solve2(input))
            {
                Console.WriteLine("Yes");
            }
            else
            {
                Console.WriteLine("No");
            }
        }

        public bool Solve2(Input input)
        {
            var n = input.ReadInt;
            var plan = new List<int[]>();
            for (var i = 0; i < n; i++)
            {
                plan.Add(input.ReadIntArray);
            }

            var axis = new int[] { 0, 0 };
            var time = 0;

            foreach (var p in plan)
            {
                var limit = p[0] - time;
                time = p[0];

                var distance = Math.Abs(axis[0] - p[1]) + Math.Abs(axis[1] - p[2]);
                if (limit < distance) return false;

                if (Math.Abs(limit - distance) % 2 != 0) return false;
                axis = new int[] {p[1], p[2]};
            }
            return true;
        }
    }

    public class Input
    {
        private TextReader Stream { get; }
        private char Separator { get; }
        private Queue<string> InputStream { get; }

        public Input(TextReader stream, char separator = ' ')
        {
            Stream = stream;
            Separator = separator;
            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 => Stream.ReadLine();
        public int ReadInt => int.Parse(Read);
        public long ReadLong => long.Parse(Read);
        public double ReadDouble => double.Parse(Read);
        public int[] ReadIntArray => Stream.ReadLine().Split(Separator).Select(i => int.Parse(i)).ToArray();
        public long[] ReadLongArray => Stream.ReadLine().Split(Separator).Select(l => long.Parse(l)).ToArray();
    }
}