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;
class Program
{
    static void Main(string[] args)
    {
        // 整数の入力

        //// スペース区切りの整数の入力
        int N = int.Parse(Console.ReadLine());
        int[] t = new int[N + 1];
        int[] x = new int[N + 1];
        int[] y = new int[N + 1];

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

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

        //出力
        Console.WriteLine(hantei(N, t, x, y));
    }

    private static string hantei(int N, int[] t, int[] x, int[] y)
    {
        for (int j = 1; j < N + 1; j++)
        {
            int distance = Math.Abs(x[j] - x[j - 1]) + Math.Abs(y[j] - y[j - 1]);
            int time = t[j] - t[j - 1];
            if (distance < time
                && time - distance % 2 == 1
                )
            {
                continue;
            }
            else
            {
                return "No";
            }
        }
        return "Yes";
    }

}