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.IO;
using System.Text.RegularExpressions;
using System.Text;
using System.Diagnostics;
using static System.Math;
using static System.Array;

//var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
namespace AtCoderSolve
{

    class Solve
    {
        const int mod = 1000000007;
        const int INF = 2147483647;
        const long SINF = 9223372036854775807;

        static int N;
        static int[] t, x, y;

        public static void Input()
        {
            var cin = new Scanner();
            N = int.Parse(Console.ReadLine());
            t = new int[N + 1];
            x = new int[N + 1];
            y = new int[N + 1];
            for(var i = 0; i <= N; i++)
            {
                if (i == 0)
                {
                    t[i] = 0;
                    x[i] = 0;
                    y[i] = 0;
                }
                else
                {
                    var input = cin.SplitReader();
                    t[i] = input[0];
                    x[i] = input[1];
                    y[i] = input[2];
                }
            }
          
        }

        static void Main(string[] args)
        {
            Input();

            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);

            bool ok = true;
            for(var i = 0; i < N; i++)
            {
                int dx = Abs(x[i + 1] - x[i]);
                int dy = Abs(y[i + 1] - y[i]);
                int dt = t[i + 1] - t[i];

                if (dx + dy > dt || (dx + dy) % 2 != dt % 2)
                {
                    ok = false;
                    break;
                }
            }

            Console.WriteLine(ok ? "Yes" : "No");

            //Console.Out.Flush();

        }

       
    }

    public class Scanner
    {
        public int[] SplitReader()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReaderL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }

    }

    public class Graph
    {
        
    }
}