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 static System.Console;
using System.Linq;

namespace AC
{
   public class shiokara
   {
      static void Main(string[] args)
      {
         int N = int.Parse(ReadLine());
         int curX = 0, curY = 0, nextX = 0, nextY = 0;
         int curT = 0, nextT = 0;
         int move = 0, time = 0;
         for(int i = 0; i < N; i++){
            int[] tmp = ReadLine().Split(' ').Select(int.Parse).ToArray();
            nextT = tmp[0]; nextX = tmp[1]; nextY = tmp[2];
            move = abs(curX, nextX) + abs(curY, nextY);
            time = abs(curT, nextT);
            if(time % move != 0 || move - time > 0){
               WriteLine("No");
               return;
            }
            curX = nextX; curY = nextY; curT = nextT;
         }
         WriteLine("Yes");
      }

      static int abs(int a, int b){
         if(a > b) return a - b;
         else return b - a;
      }
   }
}