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 Paiza
{
    class Program
    {
        public static void Main(string[] args)
        {


                if (true)
                {
                    arc089_a();
                }
                else
                {

                    abc085_c();
                    abc083_b();
                    abc087_b();
                    ABC081A();
                    ABC086A();
                    ABC081B();
                }
            
        }

        private static void arc089_a()
        {
            var N = int.Parse(Console.ReadLine());
            var t = Enumerable.Range(0, N).Select(x => Console.ReadLine().Split(' ').Select(y => int.Parse(y)).ToArray()).ToArray();

            int[] prev = new int[] { 0, 0, 0 };
            foreach (var item in t)
            {
                var dt = item[0] - prev[0];
                var dist = Math.Abs(item[1] - prev[1]) + Math.Abs(item[2] - prev[2]);
                var parity = item[0] % 2 == 0;
                if (dist > Math.Abs(item[0] - prev[0])) 
                {
                    Console.WriteLine("No");
                    return;
                }

                if (dist % 2 != dt % 2) 
                {
                    Console.WriteLine("No");
                    return;
                }

                prev = item;
            }

            Console.WriteLine("Yes");

        }

        private static void abc085_c()
        {
            var NY = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var N = NY[0];
            var Y = NY[1];
            // 10000 5000 1000
            for (int i = 0; i <= N; i++)
            {
                for (int j = 0; j <= N - j; j++)
                {
                    var k = N - i - j;
                    if (k >= 0)
                    {
                        if (i * 10000 + j * 5000 + k * 1000 == Y)
                        {
                            Console.WriteLine($"{i} {j} {k}");
                            return;
                        }
                    }
                }
            }

            Console.WriteLine("-1 -1 -1");
        }

        private static void abc083_b()
        {
            var NAB= Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList();
            var N = NAB[0];
            var A = NAB[1];
            var B = NAB[2];
            int sums = 0;

            for (int i = 1; i <= N; i++)
            {
                var sum = i.ToString()
                           .Select(x => x.ToString())
                           .Select(x => int.Parse(x))
                           .Sum(x => x);

                if (A<= sum && sum<=B )
                {
                    sums += i;
                }
            }
            Console.WriteLine(sums);
        }

        private static void abc087_b()
        {

            var ABCX = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            var A = ABCX[0];
            var B = ABCX[1];
            var C = ABCX[2];
            var X = ABCX[3];
            var count = 0;
            for (int i = 0; i <= A; i++)
            {
                for (int j = 0; j <= B; j++)
                {
                    for (int k = 0; k <= C; k++)
                    {
                        if (i*500 + j * 100 + k * 50 == X)
                        {
                            count++;
                        }
                    }
                }
            }

            Console.WriteLine(count);

        }

        private static void ABC081B()
        {
            var n = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            int c = 0;
            while (a.All(x => x % 2 == 0))
            {
                a = a.Select(x => x / 2).ToArray();
                c++;
            }

            Console.WriteLine(c);
        }

        private static void ABC081A()
        {
            Console.WriteLine(Console.ReadLine().Count(x => x.ToString() == "1"));
        }

        private static void ABC086A()
        {
            var a = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList();

            Console.WriteLine((a[1] * a[0]) % 2 == 0 ? "Even" : "Odd");
        }
    }
}