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.Collections.Generic;
using System.IO;
using System.Linq;
using System.Net;
using static System.Console;
using static System.Math;
using System.Numerics;
using System.Security.Cryptography.X509Certificates;
using static CS_Contest.Utils;
using static Nakov.IO.Cin;

//using static CS_Contest.Library;

namespace CS_Contest {
	using Li = List<int>;
	using LLi = List<List<int>>;
	using Ll = List<long>;
	using ti3=Tuple<int,int,int>;
	internal class Program {
		private static void Main(string[] args) {
			var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
			SetOut(sw);
			new Calc().Solve();
			Out.Flush();
		}

		public class Calc {
			public class XY
			{
				public int X { get; set; }
				public int Y { get; set; }

				public XY(int x, int y) {
					X = x;
					Y = y;
				}

				public override bool Equals(object obj) {
					var item = obj as XY;
					return item.X == X && item.Y == Y;
				}
			}
			public void Solve() {
				int N = NextInt();

				var dic = new Dictionary<int,XY>();

				REP(N, _ =>
				{
					dic.Add(NextInt(),new XY(NextInt(),NextInt()));
				});

				var dx = new int[] { 0,1,0,-1 };
				var dy = new int[] {1, 0, -1, 0};


				Func<XY,XY, int, bool> dfs = null;
				dfs = (crr, goal, step) =>
				{
					if (step == 0) {
						return crr.Equals(goal);
					}

					var flag = false;
					REP(4, i =>
					{
						var X = dx[i] + crr.X;
						var Y = dy[i] + crr.Y;
						flag |= dfs(new XY(X, Y), goal, step - 1);
					});
					return flag;
				};

				var bf=new XY(0,0);
				if (dic.Any(item => !dfs(bf, item.Value, item.Key))) {
					"No".WL();
					return;
				}
				"Yes".WL();

				return;
			}
		}
	}

	public static class Utils {

	
		public static void WL(this object obj) => WriteLine(obj);

		public static void WL(this string obj) => WriteLine(obj);

		public static void WL<T>(this IEnumerable<T> list) => list.ToList().ForEach(x => x.WL());

		public static Li ReadInts() => ReadLine().Split().Select(int.Parse).ToList();

		public static string StringJoin<T>(this IEnumerable<T> l, string separator = "") => string.Join(separator, l);

		public static void REP(int n, Action<int> act) {
			for (var i = 0; i < n; i++) {
				act(i);
			}
		}


		public static int ManhattanDistance(int x1, int y1, int x2, int y2) => Abs(x2 - x1) + Abs(y2 - y1);

		public struct IndexT<T> {
			public T Value { get; set; }
			public int Index { get; set; }

			public IndexT(T v, int i) {
				Value = v; Index = i;
			}
			public override string ToString() {
				return Value + " " + Index;
			}
		}

		public static IEnumerable<IndexT<T>> ToIndexEnumerable<T>(this IEnumerable<T> list) => list.Select((x, i) => new IndexT<T>(x, i));

		public static Queue<T> ToQueue<T>(this IEnumerable<T> iEnumerable) {
			var rt = new Queue<T>();
			foreach (var item in iEnumerable) {
				rt.Enqueue(item);
			}
			return rt;
		}

		public static IndexT<T> IndexOf<T>(this IEnumerable<T> ie, Func<IndexT<T>, IndexT<T>, IndexT<T>> func) =>
			ie.ToIndexEnumerable().Aggregate(func);

		public static void Swap<T>(ref T x,ref T y) {
			var tmp = x;
			x = y;
			y = tmp;
		}
		public static Dictionary<TKey,int> CountUp<TKey>(this IEnumerable<TKey> l) {
			var dic = new Dictionary<TKey, int>();
			foreach (var item in l) {
				if (dic.ContainsKey(item)) dic[item]++;
				else dic.Add(item, 1);
			}
			return dic;
		}
		public static int Count<T>(this IEnumerable<T> l, T target) => l.Count(x => x.Equals(target));
	}

}
namespace Nakov.IO {
	using System;
	using System.Text;
	using System.Globalization;

	public static class Cin {
		public static string NextToken() {
			StringBuilder tokenChars = new StringBuilder();
			bool tokenFinished = false;
			bool skipWhiteSpaceMode = true;
			while (!tokenFinished) {
				int nextChar = Console.Read();
				if (nextChar == -1) {
					tokenFinished = true;
				} else {
					char ch = (char)nextChar;
					if (char.IsWhiteSpace(ch)) {
						if (!skipWhiteSpaceMode) {
							tokenFinished = true;
							if (ch == '\r' && (Environment.NewLine == "\r\n")) {
								Console.Read();
							}
						}
					} else {
						skipWhiteSpaceMode = false;
						tokenChars.Append(ch);
					}
				}
			}

			string token = tokenChars.ToString();
			return token;
		}

		public static int NextInt() {
			string token = Cin.NextToken();
			return int.Parse(token);
		}
		public static long NextLong() {
			string token = Cin.NextToken();
			return long.Parse(token);
		}
		public static double NextDouble(bool acceptAnyDecimalSeparator = true) {
			string token = Cin.NextToken();
			if (acceptAnyDecimalSeparator) {
				token = token.Replace(',', '.');
				double result = double.Parse(token, CultureInfo.InvariantCulture);
				return result;
			} else {
				double result = double.Parse(token);
				return result;
			}
		}
		public static decimal NextDecimal(bool acceptAnyDecimalSeparator = true) {
			string token = Cin.NextToken();
			if (acceptAnyDecimalSeparator) {
				token = token.Replace(',', '.');
				decimal result = decimal.Parse(token, CultureInfo.InvariantCulture);
				return result;
			} else {
				decimal result = decimal.Parse(token);
				return result;
			}
		}

	}
}