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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp1
{
    static class CTraveling
    {
        public class Point{
            public int T;
            public int X;
            public int Y;            
            public Point(int t, int x, int y)
            {
                this.T = t;
                this.X = x;
                this.Y = y;
            }
        }

        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var plans = new List<Point>();

            plans.Add(new Point(0, 0, 0));
            for (int i = 0; i < n; i++)
            {
                var s = Console.ReadLine().Split(' ');
                plans.Add(new Point(int.Parse(s[0]), int.Parse(s[1]), int.Parse(s[2])));
            }            

            for (int i = 0; i < n; i++)
            {
                int timeDiff = plans[i + 1].T - plans[i].T;
                int distDiff = Math.Abs(plans[i + 1].X - plans[i].X) + Math.Abs(plans[i + 1].Y - plans[i].Y);

                if (timeDiff < distDiff)
                {
                    // 経過秒数より遠い地点には行けない
                    Console.WriteLine("NO");
                    Console.ReadLine();
                    return;
                }
                if (plans[i].T % 2 != (plans[i].X + plans[i].Y) % 2)
                {
                    Console.WriteLine("NO");
                    Console.ReadLine();
                    return;
                }
            }

            Console.WriteLine("YES");
            Console.ReadLine();
        }
    }
}