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;

namespace ABC086C
{
    class Program
    {
        static void Main(string[] args)
        {
            int count = int.Parse(Console.ReadLine());

            var points = new List<Point>();
            points.Add(new Point(0, 0, 0));
            for(int i = 0; i < count; i++)
            {
                var input = Console.ReadLine().Split().Select(s => int.Parse(s)).ToArray();
                points.Add(new Point(input[0], input[1], input[2]));
            }

            bool result = true;
            for(int i = 1; i < points.Count(); i++)
            {
                if (!points[i].IsMovable(points[i - 1]))
                {
                    result = false;
                    break;
                }
            }

            Console.WriteLine(result ? "Yes": "No");
        }
    }

    class Point
    {
        public Point(int time, int x, int y)
        {
            Time = time;
            X = x;
            Y = y;
        }

        public int Time { get; }
        public int X { get; }
        public int Y { get; }

        public bool IsMovable(Point previous)
        {
            int dt = this.Time - previous.Time;
            int movingX = this.X - previous.X;
            int movingY = this.Y - previous.Y;

            int moving = movingX + movingY;

            if(dt < moving)
            {
                return false;
            }

            if (dt == moving)
            {
                return true;
            }

            if(dt > moving)
            {
                if ((dt - moving) % 2 == 0)
                {
                    return true;
                }
            }
            

            return false;
        }
    }
}