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;

namespace atcoder_practice1
{
    class _086D0
    {
        static void Main()
        {
            NewMethod();
        }

        private static void NewMethod()
        {
            int N, t_2, x_2, y_2, dt, dx, dy;
            int t_1 = 0;
            int x_1 = 0;
            int y_1 = 0;
            string str;
            string[] str_array;
            int count = 0;
            N = int.Parse(Console.ReadLine());


            while (N != count)
            {
                str = Console.ReadLine();
                str_array = str.Split(' ');
                t_2 = int.Parse(str_array[0]);
                x_2 = int.Parse(str_array[1]);
                y_2 = int.Parse(str_array[2]);

                dt = t_2 - t_1;
                dx = Math.Abs(x_2 - x_1);
                dy = Math.Abs(y_2 - y_1);

                if (((dx + dy) % 2 != dt % 2) || (dt < dx + dy))
                {
                    Console.Write("No");
                    return;
                }

                t_1 = t_2;
                x_1 = x_2;
                y_1 = y_2;

                count++;

            }
            Console.WriteLine("Yes");
            return;
        }
    }
}