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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
int main()
{
	int a,b,c,n,i=0,t[100005],x[100005],y[100005],x1=0,y1=0,flag=1;
	scanf("%d",&n);
	while(i<n){
		scanf("%d %d %d",&t[i],&x[i],&y[i]);
		i++;
	}
	i=0;
	for(a=0;a<n;a++){
		if(a==0){
			c=1;
		}else{
			c=t[a-1]+1;
		}
		for(b=c;b<=t[a];b++){
			if(x[a]>x1){
				x1++;
			}else if(x[a]<x1){
				x1--;
			}else if(x[a]==x1 && y[a]>y1){
				y1++;
			}else if(x[a]==x1 && y[a]<y1){
				y1--;
			}else if(x[a]==x1 && y[a]==y1 && (t[a]-b)>=1){
				y1--;
			}else{
				flag=0;
				break;
			}
	    }
	    if(x1!=x[a] && y1!=y[a]){
	    	flag=0;
	    	break;
		}
	}
	if(flag==1){
		printf("Yes");
	}else{
		printf("No");
	}	
}