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: Accepted)

#include <stdio.h>

int main(){
	int N;
	scanf("%d",&N);
	int X[100001];
	int Y[100001];
	int T[100001];
	X[0]=0;
	Y[0]=0;
	T[0]=0;
	int i;
	for(i=1;i<=N;i++){
		scanf("%d",&T[i]);
		scanf("%d",&X[i]);
		scanf("%d",&Y[i]);
	}
	int c;
	c=0;
	int d;
	int t;
	for(i=1;i<=N;i++){
		d=(X[i]-X[i-1])+(Y[i]-Y[i-1]);
		t=T[i]-T[i-1];
		if(d>t){
			c=1;
			break;
		}
		if((t-d)%2!=0){
			c=1;
			break;
		}
	}
	if(c==0){
		printf("Yes");
	}else{
		printf("No");
	}
}