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;

namespace ABC086_C
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var T = new int[N][];
            for (int i = 0; i < N; i++)
            {
                T[i] = Console.ReadLine().Split().Select(int.Parse).ToArray();
            }

            var canGo = true;
            var x = 0;
            var y = 0;

            for (int i = 0; i < N; i++)
            {
                var nx = T[i][1];
                var ny = T[i][2];
                canGo = Math.Abs(nx - x) + Math.Abs(ny - y) <= T[i][0];
                if (!canGo) break;
                canGo = (Math.Abs(nx - x) + Math.Abs(ny - y)) % 2 == 0 && T[i][0] % 2 == 0
                    || (Math.Abs(nx - x) + Math.Abs(ny - y)) % 2 == 1 && T[i][0] % 2 == 1;
                if (!canGo) break;
            }

            Console.WriteLine(canGo ? "Yes" : "No");
        }
    }
}