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;

namespace Beg086C
{
    class Program
    {
        static void Main(string[] args)
        {
            var yes = "Yes";
            var no = "No";
            var N = int.Parse(Console.ReadLine());
            var ts = new int[N+1];
            var xs = new int[N+1];
            var ys = new int[N+1];
            ts[0] = 0;
            xs[0] = 0;
            ys[0] = 0;
            var tooFar = false;
            var nonParity = false;
            for (int i =1;i<N + 1;i++)
            {
                var s = Console.ReadLine().Split(' ').Select(s0 => int.Parse(s0)).ToArray();
                ts[i] = s[0];
                xs[i] = s[1];
                ys[i] = s[2];
                tooFar = ts[i] - ts[i - 1] < Math.Abs(xs[i] - xs[i - 1]) + Math.Abs(ys[i] - ys[i - 1]);
                nonParity = (ts[i] - ts[i - 1]) % 2 == 0 ? (xs[i] + ys[i] + xs[i - 1] + ys[i - 1]) % 2 != 0 :
                                                           (xs[i] + ys[i] + xs[i - 1] + ys[i - 1]) % 2 != 1;
                if (tooFar||nonParity)
                {
                    Console.WriteLine(no);
                    break;
                }
            }
            if (!(tooFar || nonParity))
                Console.WriteLine(yes);


        }
    }
}