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 QuestionC
    {
        public struct C
        {
            public int t;
            public int x;
            public int y;
        }

        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

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

            var c = new C[n];

            for (int i = 0; i < n; i++) {
                // 整数配列の入力
                var a = Console.ReadLine().Split(' ').Select(q => int.Parse(q)).ToArray();
                c[i] = new C { t = a[0], x = a[1], y = a[2] };
            }

            var nowT = 0;
            var nowX = 0;
            var nowY = 0;

            for(int i = 0; i < n; i++) {
                var diffT = c[i].t - nowT;
                var diffXY = Math.Abs(c[i].x - nowX) + Math.Abs(c[i].y - nowY);

                if (diffXY > diffT || diffXY % 2 != diffT % 2) {
                    Console.WriteLine("No");
                    Console.Out.Flush();
                    return;
                }

                nowT = c[i].t;
                nowX = c[i].x;
                nowY = c[i].y;
            }

            Console.WriteLine("Yes");

            Console.Out.Flush();
        }
    }
}