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;

namespace Practice
{
    class Program
    {
        static void Main(string[] args)
        {
            SolveA();
            //SolveB();
            //SolveC();
            //SolveD();
        }
        private const long MOD = 1000000007;
       
        static void SolveA()
        {
            int n = ReadAndParseInt();
            var t = new int[n];
            var x = new int[n];
            var y = new int[n];
            for(int i=0;i<n;++i)
            {
                var tmp = ReadAndParseIntArr();
                t[i] = tmp[0];
                x[i] = tmp[1];
                y[i] = tmp[2];
            }

            bool success = true;
            int prev_t = 0;
            int prev_x = 0;
            int prev_y = 0;
            for(int i=0;i<n;++i)
            {
                int dt = t[i] - prev_t;
                int dx = x[i] - prev_x;
                int dy = y[i] - prev_y;

                int dist = Math.Abs(dx) + Math.Abs(dy);
                if( dist > dt) { success = false; break; }
                if( (dist % 2) != (dt % 2)) { success = false; break; }

                prev_t = t[i];
                prev_x = x[i];
                prev_y = y[i];
            }
            string ans = success ? "Yes" : "No";
            Console.WriteLine(ans);
        }
        
        
        #region よく使う便利関数
        private static bool isPrime(long x)
        {
            if( x == 2) { return true; }
            if( x < 2 || x % 2 == 0) { return false; }
            long i = 3;
            while( i * i <= x)
            {
                if( x % i == 0) { return false; }
                i = i + 2;
            }
            return true;
        }
        private static long lcm(long x, long y)
        {
            return x / gcd(x, y) * y;
        }
        private static long gcd(long x, long y)
        {
            return y > 0 ? gcd(y, x % y) : x;
        }

        private static int ReadAndParseInt()
        {
            return int.Parse(Console.ReadLine());
        }
        private static int[] ReadAndParseIntArr()
        {
            return Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        }
        private static long ReadAndParseLong()
        {
            return long.Parse(Console.ReadLine());
        }
        private static long[] ReadAndParseLongArr()
        {
            return Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
        }
        #endregion
    }
}