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;


namespace AtCoder
{
    class Program
    {
        public static void Main()
        {
            new Program().Solve();
        }

        void Solve()
        {

            int n = int.Parse(Console.ReadLine());
            int preTime = 0;
            int x = 0, y = 0;
            bool canTravel = true;

            for (int i = 0; i < n; i++)
            {
                var input = Console.ReadLine().Split().Select(tmp => int.Parse(tmp)).ToArray();
                int t = input[0];
                int xt = input[1];
                int yt = input[2];

                if (!CanTravel(x, y, xt, yt, t - preTime))
                {
                    canTravel = false;
                    break;
                }
                preTime = t;
                x = xt;
                y = yt;
            }
            Console.WriteLine(canTravel ? "Yes" : "No");
        }

        bool CanTravel(int currentX, int currentY, int nextX, int nextY, int deltaTime)
        {
            int dx = Math.Abs(nextX - currentX);
            int dy = Math.Abs(nextY - currentY);
            deltaTime -= (dx + dy);

            if (deltaTime >= 0 && deltaTime % 2 == 0)
            {
                return true;
            }
            else
            {
                return false;
            }

        }
    }
}