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.Text;
using System.Diagnostics;
using System.IO;

namespace AtCoder
{
    struct Point
    {
        public readonly int t;
        public readonly int x;
        public readonly int y;
        public Point(int[] values)
        {
            t = values[0];
            x = values[1];
            y = values[2];
        }
    }

    class Program
    {
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        private static bool Solve(Point[] points)
        {
            int x = 0;
            int y = 0;
            int t = 0;
            foreach (var p in points)
            {
                int d = Math.Abs(p.x - x) + Math.Abs(p.y - y);
                if (d > (p.t - t) || (p.t - t - d) % 2 != 0) { return false; }
                x = p.x;
                y = p.y;
                t = p.t;
            }
            return true;
        }

        static void Main(string[] args)
        {
            int N = ReadInt();
            var points = new Point[N];
            for (int i = 0; i < N; ++i)
            {
                var values = ReadInts();
                points[i] = new Point(values);
            }
            Console.WriteLine(Solve(points) ? "Yes" : "No");
        }
    }
}