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 ConsoleApp93 {
    class Program {
        static void Main(string[] args) {
            int N = int.Parse(Console.ReadLine());

            var t = new int[N];
            var x = new int[N];
            var y = new int[N];

            for (int i = 0; i < N; i++) {
                var st = Console.ReadLine().Split().Select(int.Parse).ToArray();
                t[i] = st[0];
                x[i] = st[1];
                y[i] = st[2];
            }

            bool flg = true;

            for (int i = 0; i < N; i++) {
                if (i == 0) {
                    if ((x[0] + y[0]) <= t[0] && ((x[0] + y[0]) - t[0]) % 2 == 0) {

                    } else {
                        flg = false;
                        break;
                    }
                    continue;
                }

                if ((Math.Abs(x[i] - x[i - 1]) + Math.Abs(y[i] - y[i - 1])) <= t[i] - t[i - 1] && (Math.Abs(x[i] - x[i - 1]) + Math.Abs(y[i] - y[i - 1]) - (t[i] - t[i - 1])) % 2 == 0) {

                } else {
                    flg = false;
                    break;
                }

            }

            Console.WriteLine(flg? "Yes" : "No");

        }
    }
}