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,time[100001],x[100001],y[100001],i,j=0,spot[2]={0,0};
  scanf("%d",&n);
  
  for(i=0;i<n;i++)
    {
      scanf("%d %d %d",&time[i],&x[i],&y[i]);
    }

  for(i=1;i<=time[n-1];i++)
    {
      if(spot[0] < x[j])
	{
	  spot[0]++;
	}
      else if(spot[0] > x[j])
	{
	  spot[0]--;
	}
      else if(spot[1] < y[j])
	{
	  spot[1]++;
	}
      else if(spot[1] > y[j])
	{
	  spot[1]--;
	}
      else
	{
	  spot[0]++;
	}
      //debug
      //printf("%d %d %d %d %d\n",i,spot[0],spot[1],x[j],y[j]);
      if(i == time[j])
	{
	  if(spot[0] != x[j] || spot[1] != y[j]) //不一致なのでNG
	    {
	      printf("No\n");
	      return 0;
	    }
	  j++;
	}
    }
  printf("Yes\n");
  return 0;
}