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.Linq;

namespace ABC086
{
    class C
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            int[] t = new int[N + 1];
            int[] x = new int[N + 1];
            int[] y = new int[N + 1];

            x[0] = 0;
            y[0] = 0;
            t[0] = 0;

            for (int i = 1; i <= N; i++)
            {
                string[] input = Console.ReadLine().Split(' ');
                t[i] = int.Parse(input[0]);
                x[i] = int.Parse(input[1]);
                y[i] = int.Parse(input[2]);
            }

            int t2 = 0;
            int x2 = 0;
            int y2 = 0;
            for (int i = 0; i < N; i++)
            {
                x2 = x[i + 1] - x[i];
                y2 = y[i + 1] - y[i];
                t2 = t[i + 1] - t[i];

                if (t2 < (x2 + y2))
                {
                    Console.WriteLine("No");
                    return;
                }

                if ((t2 - (x2 + y2)) % 2 != 0)
                {
                    Console.WriteLine("No");
                    return;
                }
            }

            Console.WriteLine("Yes");

        }
    }
}