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;
using System.Text;
using System.Threading.Tasks;


    class Program
    {


        static void Main(string[] args)
        {
            Solve();
        }

        static void Solve()
        {
        Scan sc = new Scan();
        write wr = new write();


        int[] a = sc.intarr;
        int n = a[0];
        int t = 0, x = 0, y = 0;
        bool ans = true;

        for(int i = 0; i < n; ++i)
        {
            int[] b = sc.intarr;
            int nt = b[0], nx = b[1], ny = b[2];

            if (Math.Abs(x - nx) + Math.Abs(y - ny) <= nt - t && (Math.Abs(x - nx) + Math.Abs(y - ny) )% 2 == (nt - t)%2)
            {
                x = nx;
                y = ny;
                t = nt;
                continue;
            }
            else
            {
                ans = false;
            }
        }
        if (ans) wr.wri("Yes");
        else wr.wri("No");
    }
}


    class Scan
    {
    public string str => Console.ReadLine();

    public string[] strarr => str.Split(' ');

    public long[] longarr => strarr.Select(long.Parse).ToArray();
    public int [] intarr => strarr.Select(int.Parse).ToArray();



}

class write
{
    public void wri<Type>(Type x)
    {
        Console.WriteLine(x);
    }
}