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;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class Abc_086_C
    {
        // https://atcoder.jp/contests/abc086/tasks/arc089_a
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            // 整数の入力
            int N = int.Parse(Console.ReadLine());

            int[] t = new int[N + 1];
            int[] x = new int[N + 1];
            int[] y = new int[N + 1];
            y[0] = x[0] = y[0] = 0;

            for (int i = 1; i <= N; ++i)
            {
                int[] inputIntArray = Console.ReadLine().Split(' ').Select(j => int.Parse(j)).ToArray();
                t[i] = inputIntArray[0];
                x[i] = inputIntArray[1];
                y[i] = inputIntArray[2];
            }

            var flag = true;
            for (int i = 0; i < N; ++i)
            {
                var time = t[i + 1] - t[i];
                var dist = Math.Abs(x[i + 1] - x[i]) + Math.Abs(y[i + 1] - y[i]);
                if (time < dist) flag = false;
                if (Math.Abs(time - dist) % 2 != 0) flag = false;
            }

            if (flag) Console.WriteLine("Yes");
            else Console.WriteLine("No");

            Console.Out.Flush();
        }
    }
}