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;
    using System.Collections.Generic;
    using System.Text.RegularExpressions;
    using System.Text;
    using System.Net;

     
    public class Program
    {

        public void Proc() {
            int pointCount = int.Parse(Reader.ReadLine());

            int posX = 0;
            int posY = 0;
            int tm = 0;
            for(int i=0; i<pointCount;i++) {
                int[] inpt = Reader.ReadLine().Split(' ').Select(a=>int.Parse(a)).ToArray();
                int diff = inpt[0]-tm;
                int mnh = Math.Abs(posX-inpt[1])+Math.Abs(posY+inpt[2]);
                if(diff<mnh) {
                    Console.WriteLine("No");
                    return;
                }
                if((diff-mnh)%2!=0) {
                    Console.WriteLine("No");
                    return;
                }
                posX = inpt[1];
                posY = inpt[2];
                tm = inpt[0];
            }
            Console.WriteLine("Yes");

        }



        public class Reader {
            public static bool IsDebug = false;
            private static System.IO.StringReader SReader;
            private static string InitText = @"



2
3 1 2
6 1 1





";
            public static string ReadLine() {
                if(IsDebug) {
                    if(SReader == null) {
                        SReader = new System.IO.StringReader(InitText.Trim());
                    }
                    return SReader.ReadLine();
                } else {
                    return Console.ReadLine();
                }
            }
        }
        public static void Main(string[] args)
        {
            #if DEBUG
            Reader.IsDebug = true;
            #endif
            Program prg = new Program();
            prg.Proc();
        }
    }