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;

namespace cswork
{

    class Program
    {
        public Program() { }

        Scanner cin;

        void Omame()
        {
            cin = new Scanner();
            int n = cin.nextInt();
            int x0 = 0;
            int y0 = 0;
            int t0 = 0;
            for (int i = 0; i < n; i++)
            {
                int t = cin.nextInt();
                int x = cin.nextInt();
                int y = cin.nextInt();

                int l = Math.Abs(x - x0) + Math.Abs(y - y0);

                if (t - t0 >= l)
                {
                    if ((t - t0 - l) % 2 == 0)
                    {
                        x0 = x;
                        y0 = y;
                        t0 = t;
                        continue;
                    }
                }

                Console.WriteLine("NO");
                return;
            }

            Console.WriteLine("YES");
        }

        static void Main(string[] args)
        {
            new Program().Omame();
        }
    }

    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);
            i = 0;
            return next();
        }

        public int nextInt()
        {
            return int.Parse(next());
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }
    }
}