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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
class TEST
{
    static List<int[]> testlist;
    public static void Main()
    {
        (int x, int y) nowPosition = (0, 0);

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

        testlist = new List<int[]>();
        for (int i = 0; i < N; i++)
        {
            string[] values = Console.ReadLine().Split(new string[] { " " }, StringSplitOptions.RemoveEmptyEntries);
            testlist.Add(GetStringtoInt(values));

        }

        for (int i = 0; i < testlist.Count; i++)
        {
            int needTimeToMove = 0;
            while (true)
            {
                if (nowPosition.x == testlist[i][1] && nowPosition.y == testlist[i][2])
                {
                    int value = GetNum(i);


                    if (value >= needTimeToMove && value % 2 == 0 && needTimeToMove % 2 == 0)
                        break;
                    else if (value >= needTimeToMove && value % 2 == 1 && needTimeToMove % 2 == 1)
                        break;
                    else
                    {
                        Console.WriteLine("No");
                        return;
                    }
                }
                else
                {
                    int sa = testlist[i][1] - nowPosition.x;
                    nowPosition.x += sa;
                    needTimeToMove += Math.Abs(sa);

                    sa = testlist[i][2] - nowPosition.y;
                    nowPosition.y += sa;
                    needTimeToMove += Math.Abs(sa);
                }
            }
        }
        Console.WriteLine("Yes");
    }

    static private int[] GetStringtoInt(string[] values)
    {
        int[] values_i = new int[values.Length];

        for (int i = 0; i < values.Length; i++)
        {
            values_i[i] = int.Parse(values[i]);
        }

        return values_i;
    }
    static private int GetNum(int index)
    {
        if (index == 0)
            return testlist[index][0];
        return testlist[index][0] - testlist[index - 1][0];
    }

}