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(void)
{int N,X,Y,n,i,k,j,l,flag,m,di,tim;
scanf("%d",&N);
n=N+1;
flag=0;
int x[100001];
int t[100001];
int y[100001];
int dis[100001];
int time[100001];
x[0]=0;y[0]=0;t[0]=0;
for(i=1;i<=n-1;i++){
	scanf("%d%d%d",&t[i],&x[i],&y[i]);}
	for(k=0;k<=n-2;k++){
		if(x[k+1]>=x[k]){
			X=x[k+1]-x[k];}
			else{
				X=x[k]-x[k+1];}
				if(y[k+1]>=y[k]){
			Y=y[k+1]-y[k];}
			else{
				Y=y[k]-y[k+1];}
		dis[k]=X+Y;
		time[k]=t[k+1]-t[k];
		di=dis[k]%2;
		tim=time[k]%2;
		if(di!=tim || dis[k]>time[k]){
			printf("No");
			flag=1;
			break;}}
	if(flag==0){
		printf("Yes");}
			

	
	return 0;
}