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-csc 3.5.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using System.IO;
using static System.Console;

namespace atcorder2
{
    class Program
    {
        public static long Read()
        {
            return long.Parse(Console.ReadLine());
        }

        public static long[] Reads()
        {
            return Console.ReadLine().Split().Select(long.Parse).ToArray();
        }


        public static long gcd(long x, long y)
        {
            if (y < x) gcd(y, x);
            while (y != 0)
            {
                var z = x % y;
                x = y;
                y = z;
            }
            return x;
        }
        public static long keta(long x)
        {
            var z = 1;
            while (x > 0)
            {
                x /= 10;
                z++;
            }
            return z;
        }
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var  n = Read();
            long t = 0, x = 0, y = 0;
            long bt = 0, bx = 0, by = 0;
            bool ans = true;
            for (int i = 0; i < n; i++)
            {
                var txy = Reads();
                t = txy[0];
                x = txy[1];
                y = txy[2];
                bool f = Math.Abs(x - bx) + Math.Abs(y - by) <= t - bt && Math.Abs(x - bx) + Math.Abs(y - by) % 2 == (t - bt) % 2;
                if (!f) ans = false;
                bt = t;
                bx = x;
                by = y;
            }
            WriteLine(ans ? "Yes" : "No");
            

            Console.Out.Flush();
        }
    }
}