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;

class Program
{
    static void Main(string[] args)
    {
        int       i, j, k;
        int       n;
        int       dt, dstnc;
        int       flg;
        int[,]    txy;
        string[]  str;

        n   = int.Parse(Console.ReadLine());    /* 標準入力                          */
        txy = new int[n + 1, 3];
        txy[0, 0] = 0;
        txy[0, 1] = 0;
        txy[0, 2] = 0;

        for(i = 1; i <= n; i++){
            str = Console.ReadLine().Split(' ');    /* 2つ以上のスペース区切り入力の取得 */
            for(j = 0; j < 3; j++){
                txy[i, j] = int.Parse(str[j]);
            }
        }

        for(k = 0; k < n; k++){
            flg   = 0;
            dt    = txy[k + 1, 0] - txy[k, 0];
            dstnc = Math.Abs(txy[k + 1, 1] - txy[k, 1]) + Math.Abs(txy[k + 1, 2] - txy[k, 2]);

            if(dstnc > dt){
                break;
            }

            if((dstnc % 2 == 0) && (dt % 2 == 0)){
                flg = 1;
            }
            else if((dstnc % 2 == 1) && (dt % 2 == 1)){
                flg = 1;
            }

            if(flg == 0){
                break;
            }
        }

        if(k == n){
            Console.WriteLine("Yes");     /* 改行付き出力 */
        }
        else{
            Console.WriteLine("No");     /* 改行付き出力 */
        }
    }
}