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>
#include<stdlib.h>
int main()
{
  int N;
  int t, x, y;
  int t_b, x_b, y_b;
  int t_d, x_d, y_d;
  int i;
  int able;
  
  scanf("%d", &N);
  
  t_b = 0;
  x_b = 0;
  y_b = 0;
  able = 1;
  for(i = 0; i < N; i++){
    scanf("%d %d %d",&t,&x,&y);
    t_d = t - t_b;
    x_d = x - x_b;
    y_d = y - y_b;
    if(t_d >= x_d + y_d && abs((x_d + y_d)) % 2 == t_d % 2){
      t_b = t;
      x_b = x;
      y_b = y;
    }else{
      able = 0;
    }
  }
  
  // 出力
  if(able == 1){
    printf("Yes\n");
  }else{
    printf("No\n");
  }

  return 0;
}