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: Wrong Answer)

using System;
using System.Linq;
public class Hello{
    public static void Main(){
        int f=1;
        int n=int.Parse(System.Console.ReadLine());
        int[] hoge={0,0};
        int[] t={0,0,0};
        int s=0;
        for(int i=0;i<n;i++){
            t=System.Console.ReadLine().Trim().Split(' ').Select(x=>int.Parse(x)).ToArray();
            f=_func(hoge[0],hoge[1],t[0]-s,t[1],t[2])*1;
            hoge[0]=t[1];
            hoge[1]=t[2];
            s=t[0];
        }
        if(f==1)
        System.Console.WriteLine("Yes");
        else
        System.Console.WriteLine("No");
    }
    public static int _func(int n1,int n2,int t,int x,int y){
        if(t!=0){
        if((t-(y-n2))>=(x-n1) && x-n1!=0 && y-n2!=0 && (t-(y-n2))%(x-n1)==0) return 1;
        else if((t-(x-n1))>=(y-n2) && x-n1!=0 && y-n2!=0 && (t-(x-n1))%(y-n2)==0) return 1;
        else if(x-n1==0 && y-n2==0 && t%2==0) return 1;
        else if(x-n1==0 && y-n2==0 && t%2==1) return 0;
        else if(x-n1==0 && t%(y-n2)==0) return 1;
        else if(y-n2==0 && t%(x-n1)==0) return 1;
        else return 0;
        }
        else{
            if(x==n1&&y==n2) return 1;
            else return 0;
        }
    }
}