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: Runtime Error)

using System;
using System.Diagnostics.CodeAnalysis;
using System.Globalization;
using System.Text;

namespace ChokudaiScanner
{
    class MainClass
    {
        static void Main()
        {
            Scanner cin = new Scanner();

            int N = cin.NextInt() + 1;
            int[][] vs = new int[N][];
            vs[0] = new int[3];
            for (int i = 1; i < N; i++)
            {
                vs[i] = cin.ArrayInt(3);
            }
            string ans = "Yes";
            
            for(int i = 0; i < N; i++)
            { 
                int dt = vs[i + 1][0] - vs[i][0];
                int dist = Math.Abs(vs[i + 1][1] - vs[i][1]) + Math.Abs(vs[i + 1][2] - vs[i][2]);
                if (dt < dist)
                {
                    ans = "No";
                    break;
                }
                if (dt % 2 != dist % 2)
                {
                        ans = "No";
                        break;
                }
            }
            Console.WriteLine(ans);
        }
    }

    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string Next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return Next();
            i = 0;
            return s[i++];
        }

        public string[] ArrayNext(int N)
        {
            string[] Array = new string[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = Next();
            }
            return Array;
        }

        public int NextInt()
        {
            return int.Parse(Next());
        }
        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextInt() + add;
            }
            return Array;
        }

        public long NextLong()
        {
            return long.Parse(Next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextLong() + add;
            }
            return Array;
        }

        public double NextDouble()
        {
            return double.Parse(Next());
        }


        public double[] ArrayDouble(int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextDouble() + add;
            }
            return Array;
        }
    }
}