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.RegularExpressions;
using Console = System.Console;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var points = int.Parse(Console.ReadLine());
            bool flg = true;
            int fromX = 0;
            int fromY = 0;
            int startTime = 0;
            for (int i = 0; i < points; i++)
            {
                var r = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                flg = CanArrive(fromX, fromY, r[1], r[2], startTime, r[0]);
                fromX = r[1];
                fromY = r[2];
                startTime = r[0];


                if (!flg)
                {
                    Console.WriteLine("No");
                    return;
                }
            }
            Console.WriteLine("Yes");
        }

        private static bool CanArrive(int fromX,int fromY,int toX,int toY,int startTime,int endTime)
        {
            var difTime = endTime - startTime;
            var difX = Math.Abs(toX - fromX);
            var difY = Math.Abs(toY - fromY);
            if (difTime < difX + difY)
            {
                return false;
            }

            if (difTime == difX + difY)
            {
                return true;
            }

            if (difTime % 2 == 1 && (difX + difY) % 2 == 1 ||
                difTime % 2 == 0 && (difX + difY) % 2 == 0)
            {
                return true;
            }

            return false;
        }
    }
}