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.Linq;
using System.Collections.Generic;
class Program
{
    static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var plans = new List<List<int>>();
        for (int i = 0; i < n; i++)
        {
            plans.Add(Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList());
        }

        var ACD = new AtCoDeer();
        var times = 0;
        foreach (var plan in plans)
        {
            var time = ACD.MoveToPlace(plan[1], plan[2]);
            var bufTime = times + time;
            if (bufTime == plan[0])
            {
                times += plan[0];
            }
            else if (time < plan[0] && Math.Abs(Math.Max(bufTime, plan[0]) - Math.Min(bufTime, plan[0])) % 2 == 0)
            {
                times += plan[0];
            }
            else
            {
                Console.WriteLine("No");
                return;
            }
        }

        Console.WriteLine("Yes");
    }
}

internal class AtCoDeer
{
    public int x;
    public int y;

    public AtCoDeer()
    {
        x = 0;
        y = 0;
    }

    private void MoveUp()
    {
        x++;
    }

    private void MoveDown()
    {
        x--;
    }

    private void MoveRight()
    {
        y++;
    }

    private void MoveLeft()
    {
        y--;
    }

    public int MoveToPlace(int placeX, int placeY)
    {
        var count = 0;

        while (x != placeX || y != placeY)
        {
            if (x > placeX)
            {
                MoveDown();
            }
            else if (x < placeX)
            {
                MoveUp();
            }
            else if (y > placeY)
            {
                MoveLeft();
            }
            else if (y < placeY)
            {
                MoveRight();
            }

            count++;
        }

        return count;
    }
}