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.Threading.Tasks;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {

            //var line1 = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
            //var N = line1[0];
            //var M = line1[1];
            //var a = new long[M];
            //var b = new long[M];

            //int bridge = 0;

            //int[,] dag = new int[N,N];

            //for (int i = 0; i < M; i++)
            //{
            //    var line2 = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
            //    a[i] = line2[0]-1;
            //    b[i] = line2[1]-1;
            //    dag[a[i], b[i]] = 1;
            //    dag[b[i], a[i]] = 1;
            //}

            //for (int i = 0; i < M; i++)
            //{
            //    bool[] visited = new bool[N];
            //    dag[a[i], b[i]] = 0;
            //    dag[b[i], a[i]] = 0;
            //    DFS(0,visited,dag);

            //    if (visited.Where(n => n == true).Count() != N)
            //    {
            //        bridge++;
            //    }

            //    dag[a[i], b[i]] = 1;
            //    dag[b[i], a[i]] = 1;
            //}
            //Console.WriteLine(bridge);
            //var line1 = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);

            //var A = line1[0];
            //var B = line1[1];
            //var C = line1[2];
            //var D = line1[3];
            //var E = line1[4];
            //var F = line1[5];

            //var N = int.Parse(Console.ReadLine());
            //char[] mozi = new char[N];
            //long[] MARCH = new long[5];
            //long cnt = 0;


            //for (int i = 0; i < N; i++)
            //{
            //    mozi[i] = Console.ReadLine().ToCharArray()[0];
            //}

            //MARCH[0] = mozi.Where(n => n == 'M').Count();
            //MARCH[1] = mozi.Where(n => n == 'A').Count();
            //MARCH[2] = mozi.Where(n => n == 'R').Count();
            //MARCH[3] = mozi.Where(n => n == 'C').Count();
            //MARCH[4] = mozi.Where(n => n == 'H').Count();

            //for (int i = 0; i < 3; i++)
            //{
            //    for (int j = i + 1; j < 4; j++)
            //    {
            //        for (int k = j + 1; k < 5; k++)
            //        {
            //            cnt += MARCH[i] * MARCH[j] * MARCH[k];
            //        }
            //    }
            //}

            //Console.WriteLine(cnt);

            //var N = int.Parse(Console.ReadLine());

            //var line1 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            //var line2 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            //int candy = 0;
            //int MAX = 0;

            //for (int i = 0; i < N; i++)
            //{
            //    for (int k = 0; k <= i; k++)
            //    {
            //        candy += line1[k];
            //    }

            //    for (int j = N - 1; j >= i; j--)
            //    {
            //        candy += line2[j];
            //    }

            //    MAX = Math.Max(candy,MAX);
            //    candy = 0;
            //}

            //Console.WriteLine(MAX);

            var N = int.Parse(Console.ReadLine());
            List<int[]> list = new List<int[]>();
            int t = 0;
            int x = 0;
            int y = 0;

            for (int i = 0; i < N; i++)
            {
                var txy = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
                list.Add(txy);
            }

            foreach (var item in list)
            {
                if (item[0] - t <= item[1] + item[2] || item[0]  + t >= item[1] + item[2])
                {

                    if (((item[0] - t) % 2 == 1 && Math.Abs(x + y - item[1] - item[2]) % 2 == 1) ||
                        ((item[0] - t) % 2 == 0 && Math.Abs(x + y - item[1] - item[2]) % 2 == 0))
                    {
                        t = item[0];
                        x = item[1];
                        y = item[2];
                    }
                    else
                    {
                        Console.WriteLine("No");
                        return;
                    }
                }
                else
                {
                    Console.WriteLine("No");
                    return;
                }
            }

            Console.WriteLine("Yes");

        }

        public static void DFS(int v,bool[] visited,int[,] dag)
        {
            visited[v] = true;

            for (int i = 0; i < visited.Length; i++)
            {
                if (dag[v, i] == 0) continue;
                if (visited[i]) continue;
                DFS(i,visited,dag);
            }

        }

        public static long LowerBound<T>(T[] arr, long start, long end, T value, IComparer<T> comparer)
        {
            long low = start;
            long high = end;
            long mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) < 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        //引数省略のオーバーロード
        public static long LowerBound<T>(T[] arr, T value) where T : IComparable
        {
            return LowerBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }

        public static long UpperBound<T>(T[] arr, long start, long end, T value, IComparer<T> comparer)
        {
            long low = start;
            long high = end;
            long mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) <= 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        //引数省略のオーバーロード
        public static long UpperBound<T>(T[] arr, T value)
        {
            return UpperBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }
    }

}