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.Linq;

namespace A
{
    class Program
    {
        static void Main(string[] args)
        {
            //var N = int.Parse(Console.ReadLine());
            //var txylist = Enumerable.Range(0, N)
            //    .Select(_ => Console.ReadLine().Split(' ').Select(int.Parse).ToArray());

            var N = Io.Read<int>();
            var txylist = Enumerable.Range(0, N).Select(_ => Io.ReadSplit<int>());

            var currentT = 0;
            var currentX = 0;
            var currentY = 0;
            var can = true;
            foreach (var txy in txylist)
            {
                var t = txy[0];
                var x = txy[1];
                var y = txy[2];

                var dt = t - currentT;
                var dx = Math.Abs(x - currentX);
                var dy = Math.Abs(y - currentY);

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

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

    class Io
    {
        public static string Read()
        {
            return Console.ReadLine();
        }

        public static T Read<T>()
        {
            return (T)Convert.ChangeType(Read(), typeof(T));
        }

        public static string[] ReadSplit(char devide = ' ')
        {
            return Read().Split(devide);
        }

        public static T[] ReadSplit<T>(char devide = ' ')
        {
            return ReadSplit(devide)
                .Select(s => (T)Convert.ChangeType(s, typeof(T)))
                .ToArray();
        }
    }
}