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.Linq;
using System.Collections.Generic;


class Program
{
    static void Main(string[] args)
    {
        int N = int.Parse(Console.ReadLine());
        string[] inputStr = new string[3];
        int[,] input = new int[N+1,3];
        input[0,0] = 0; input[0,1] = 0; input[0,2] = 0;
        for(int i=1; i<=N; i++){
            inputStr = Console.ReadLine().Split(' ');
            for(int j=0; j<3; j++){
                input[i,j] = int.Parse(inputStr[j]);
            }
        }

        int distance; int time;
        string can = "Yes";

        for(int i=0; i<N; i++){
            distance = Math.Abs(input[i,1]-input[i+1,1]) + Math.Abs(input[i,2]-input[i+1,2]);
            time = input[i+1,0] - input[i,0];

            if(distance > time || distance%2 != time%2){
                can = "No";
                break;
            }
        }

        Console.WriteLine(can);
    }
}