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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;

namespace Competitive
{

    internal class Solution
    {
        public int N;
        public int[] T, X, Y;

        public void Run()
        {
            N = Input.ReadInt();
            T = new int[N];
            X = new int[N];
            Y = new int[N];

            for (int i = 0; i < N; i++)
            {
                var line = Input.ReadIntArray();
                T[i] = line[0];
                X[i] = line[1];
                Y[i] = line[2];
            }

            for (int i = 0; i < N; i++)
            {
                int x1 = i == 0 ? 0 : X[i - 1];
                int y1 = i == 0 ? 0 : Y[i - 1];
                int t1 = i == 0 ? 0 : T[i - 1];
                int x2 = X[i];
                int y2 = Y[i];
                int t2 = T[i];
                if (!check(x2 - x1, y2 - y1, t2 - t1))
                {
                    Console.WriteLine("NO");
                    return;
                }
            }

            Console.WriteLine("YES");
        }

        public bool check(int x, int y, int t)
        {
            int z = t - Math.Abs(x) + Math.Abs(y);
            return z >= 0 && z % 2 == 0;
        }
    }

    internal static class Input
    {
        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }

    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}