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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC086_C
{
    class Program
    {
        static void Main(string[] args)
        {
            int limit = int.Parse(Console.ReadLine());

            int now_x = 0;
            int now_y = 0;

            int[] time = new int[limit];
            int[] target_x = new int[limit];
            int[] target_y = new int[limit];
            string[] datas = new string[3];

            int interval = 0;
            bool can = true;

            for (int i = 0; i < limit; i++)
            {
                string input = Console.ReadLine();
                datas = input.Split(' ');
                time[i] = int.Parse(datas[0]);
                target_x[i] = int.Parse(datas[1]);
                target_y[i] = int.Parse(datas[2]);
            }

            for (int i = 0; i < limit; i++)
            {

                if (i != 0)
                {
                    interval = time[i] - time[i - 1];
                }
                else
                {
                    interval = time[0];
                }

                can = Search(interval, target_x[i], target_y[i], now_x, now_y);

                if (!can)
                {
                    Console.WriteLine("No");
                    return;
                }
                now_x = target_x[i];
                now_y = target_y[i];
            }
            Console.WriteLine("Yes");
        }

        public static bool Search(int time, int target_x, int target_y, int now_x, int now_y)  //timeには現在の時間と次回のゴールまでの時間の差を入力すること
        {
            int dis = Math.Abs(target_x - now_x) + Math.Abs(target_y - now_y);

            if (dis > time || dis % 2 != time % 2)
            {
                return false;
            }

            return true;
        }
    }
}